Conference Proceedings of the Society for Experimental Mechanics Series
Series EditorTom ProulxSociety for Experimental Mechanics, Inc.,Bethel, CT, USA
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Gordon A. Shaw • Bart Prorok • LaVern A. Starman
Editors
MEMS and Nanotechnology, Volume 6
Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics
EditorsGordon A. ShawNIST, GaithersburgMD, USA
Bart ProrokAuburn UniversityAL, USA
LaVern A. StarmanAir Force Institute of TechnologyWright Patterson Air Force BaseOH, USA
ISSN 2191-5644 ISSN 2191-5652 (electronic)ISBN 978-1-4614-4435-0 ISBN 978-1-4614-4436-7 (eBook)DOI 10.1007/978-1-4614-4436-7Springer New York Heidelberg Dordrecht London
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Preface
MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimental and AppliedMechanics represents one of seven volumes of technical papers presented at the Society for Experimental Mechanics’
(SEM) 12th International Congress and Exposition on Experimental and Applied Mechanics, held at Costa Mesa, California,
June 11–14, 2012. The full set of proceedings also includes volumes on Dynamic Behavior of Materials, Challenges in
Mechanics of Time-Dependent Materials, and Processes in Conventional and Multifunctional Materials, Imaging Methods
for Novel Materials and Challenging Applications, Experimental and Applied Mechanics, Mechanics of Biological Systems
and Materials, and Composite Materials and Joining Technologies for Composites.
Each collection presents early findings from experimental and computational investigations on an important area
within Experimental Mechanics. The 13th International Symposium on MEMS and Nanotechnology conference track
was organized byGordonA. Shaw, National Institute of Standards and Technology; Barton Prorok, AuburnUniversity; LaVern
A. Starman, Air Force Institute of Technology; and sponsored by the SEM MEMS and Nanotechnology Technical Division.
Microelectromechanical systems (MEMS) and nanotechnology are revolutionary enabling technologies (ETs). These
technologies merge the functions of sensing, actuation, and controls with computation and communication to affect the way
people and machines interact with the physical world. This is done by integrating advances in various multidisciplinary
fields to produce very small devices that use very low power and operate in many different environments. Today,
developments in MEMS and nanotechnology are being made at an unprecedented rate, driven by both technology and
user requirements. These developments depend on micromechanical and nanomechanical analyses, and characterization of
structures comprising nanophase materials.
To provide a forum for an up-to-date account of the advances in the field of MEMS and nanotechnology and to promote
an alliance of governmental, industrial, and academic practitioners of ET, SEM initiated a Symposium Series on MEMS andNanotechnology.
The 2012 Symposium is the 13th in the series and addresses pertinent issues relating to design, analysis, fabrication,
testing, optimization, and applications of MEMS and nanotechnology, especially as these issues relate to experimental
mechanics of microscale and nanoscale structures. Topics included in this volume are:
Devices and Fabrication
Measurement Challenges in Single Molecule/Single Atom Mechanical Testing
Nanoindentation
Size Effects in Metals
Optical Methods
Reliability, Residual Stress and Tribology
It is with deep gratitude that we thank the organizing committee, session chairs, authors and keynote speakers,
participants, and SEM staff for making the 12th-ISMAN a valuable and unforgettable experience.
The opinions expressed herein are those of the individual authors and not necessarily those of the Society for Experi-
mental Mechanics, Inc.
Gaithersburg, MD, USA Gordon A. Shaw
Auburn, AL, USA Bart Prorok
Wright Patterson Air Force Base, OH, USA LaVern A. Starman
v
Contents
1 Silicon Carbide High Temperature MEMS Capacitive Strain Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
R.P. Weisenberger, R.A. Coutu Jr., and LaVern A. Starman
2 Characterizing External Resistive, Inductive and Capacitive Loads for Micro-Switches . . . . . . . . . . . . . . 11
Benjamin Toler and Ronald Coutu Jr.
3 Principles Involved in Interpreting Single-Molecule Force Measurement of Biomolecules . . . . . . . . . . . . 19
Sithara S. Wijeratne, Nolan C. Harris, and Ching-Hwa Kiang
4 Measurement of the Gold-Gold Bond Rupture Force at 4 K in a Single-Atom Chain
Using Photon-Momentum-Based Force Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Douglas T. Smith and J.R. Pratt
5 A Precision Force Microscope for Biophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Gavin M. King, Allison B. Churnside, and Thomas T. Perkins
6 Hydrodynamic Force Compensation for Single-Molecule Mechanical Testing
Using Colloidal Probe Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Gordon A. Shaw
7 New Insight into Pile-Up in Thin Film Indentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Kevin Schwieker, James Frye, and Barton C. Prorok
8 Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Jennifer Hay, Verena Maier, Karsten Durst, and Mathias G€oken
9 Frequency Multiplication and Demultiplication in MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
David B. Blocher, Alan T. Zehnder, and Richard H. Rand
10 Characterizing Metal Insulator Transition (MIT) Materials for Use as Micro-Switch Elements . . . . . . . . 59
Brent L. Danner and Ronald A. Coutu Jr.
11 Stiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts . . . . . . . . . . . . . . . . . . . . . . . . 67
Ling Wu, Jean-Claude Golinval, and Ludovic Noels
12 Simultaneous Measurement of Force and Conductance Across Single Molecule Junctions . . . . . . . . . . . . 75
Sriharsha V. Aradhya, Michael Frei, Mark S. Hybertsen, and Latha Venkataraman
13 High Speed Magnetic Tweezers at 10,000fps with Reflected Hg-Lamp Illumination . . . . . . . . . . . . . . . . . 85
Bob M. Lansdorp and Omar A. Saleh
14 Etching Silicon Dioxide for CNT Field Emission Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Nathan E. Glauvitz, Ronald A. Coutu Jr., Peter J. Collins, and LaVern A. Starman
15 Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Benjamin Klusemann, Alain Franz Knorr, Horst Vehoff, and Bob Svendsen
vii
16 Evaluation of Mechanical Properties of Nano-structured Al6061 Synthesized Using Machining . . . . . . . . 111
Paresh S. Ghangrekar, H. Murthy, and Balkrishna C. Rao
17 Hardening Behaviour of Thin Wires Under Loading with Strain Gradients . . . . . . . . . . . . . . . . . . . . . . . 119
Ying Chen, Mario Walter, and Oliver Kraft
18 Mapping the Histology of the Human Tympanic Membrane by Spatial Domain Optical
Coherence Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Corey Rutledge, Michael Thyden, Cosme Furlong, John J. Rosowski, and Jeffery Tao Cheng
19 Opto-Mechanical Characterization of a MEMS Sensor for Real-Time Infrared Imaging . . . . . . . . . . . . . 131
Everett Tripp, Frank Pantuso, Lei Zhang, Ellery Harrington, and Cosme Furlong
20 Global Digital Image Correlation for Pressure Deflected Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Jan Neggers, Johan Hoefnagels, Francois Hild, Stephane Roux, and Marc Geers
21 Design and Development of Internal Friction and Energy Loss Measurement
on Nanocrystalline Aluminum Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
T.-C. Hu, F.-C. Hsu, M.-T. Lin, C.-J. Tong, and Y.-T. Wang
22 Detection of Damage of Epoxy Composites Using Carbon Nanotube Network . . . . . . . . . . . . . . . . . . . . . 149
S. Cardoso, C. Mooney, R. Pivonka, V.B. Chalivendra, A. Shukla, and S.Z. Yang
viii Contents
Chapter 1
Silicon Carbide High Temperature MEMS Capacitive Strain Sensor
R.P. Weisenberger, R.A. Coutu Jr., and LaVern A. Starman
Abstract Strain sensing at high temperatures, greater than 700�F, is often difficult. Traditional strain sensing uses the
piezoresistive effect, which is temperature dependent. To reduce the temperature dependence of the strain sensor one could
be built from a robust material such as silicon carbide, SiC. Making measurements using capacitive effects eliminates the
effects of temperature within the sensing element. Using the more traditional MEMS material silicon is only an option at
lower temperatures. Silicon has good reliability as a mechanical structure to around 900�F, and good electrical properties to300�F. Having good properties above 700�F, silicon carbide is a robust material that has the ability to be used in high
temperature MEMS applications. Using the capacitive effect for measuring strain was the original way to perform this task
until the piezoresistive effect was harnessed. MEMS based capacitive strain sensors that have been built previously are
known as resonant strain sensors, or the double ended tuning fork resonator. One step further from the double ended tuning
fork is a novel capacitive strain sensor device. An examination of the novel approach to measure strain is performed.
Modeling and simulation is presented using L-Edit and Coventorware. This asserts the device’s characteristics and gives the
novel design merit to be used as a strain sensor.
Nomenclature
MEMS Microelectromechanical systems
1.1 Introduction
Experimental analysis of materials based properties use Hooke’s Law of the relationship between material stress and
deformation of that material [1]. Deformation of material occurs throughout, including at its surface. Measuring deformation
at the surface is typically done using a strain sensor. In hypersonic vehicle applications, there is a need to measure this
deformation at high temperatures, often exceeding 700�C [2]. Other applications for high temperature strain measurements,
exceeding 700�C, include oil and gas equipment, nuclear and power station equipment [3].
Hypersonic vehicles experience temperatures in excess of 500�C on inlet ramp surfaces at Mach 5 [2]. On that same
surface, temperatures exceed 700�C at Mach 6. Another point on the hypersonic engine is the stagnation wall of leading
edge, which experiences temperatures exceeding 700�C at Mach 5 [2]. Many points on the hypersonic vehicle could use a
high temperate strain sensor to measure the effects of load introduced to them. During the design and verification process,
conditions must be duplicated at which the intended material would be subjected to in actual flight conditions.
R.P. Weisenberger
Air Force Research Laboratory, 2790 D Street, Wright Patterson Air Force Base, OH 45433, USA
e-mail: [email protected]
R.A. Coutu Jr. (*) • LaVern A. Starman
Air Force Institute of Technology, 2950 Hobson Way, Wright Patterson Air Force Base, OH 45433, USA
e-mail: [email protected]; [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_1, # The Society for Experimental Mechanics, Inc. 2013
1
1.2 Problem Statement and Research Objectives
Measuring strain is difficult in high temperature environments, over 700�F. The objective of this research is to design, model
and simulate a novel strain sensor which operates at this high temperature. Within this document stress, strain, stress strain
relationship is given as a background. An alternative design for measuring strain using a double ended tuning fork is
discussed. Modeling and simulation of a new high temperature capacitive strain sensor made with silicon carbide is tested
with a finite element simulator known as Coventorware#.
1.3 Stress and Strain
When a material, such as a metal, is subjected to a load, stress is present. Stress is the measure of forces internal to a body and
strain is the measure of deformation of the displacement between particles [4]. Uniformly distributed stress occurs when a
system of forces acting on an area gets distributed uniformly over the area. Each element of the described area is subjected to
an equal loading value. Stress at each element will be at the same magnitude which is defined as the average stress value [5].
This is determined by dividing the total force by the total area. Uniformly distributed stress is defined by (1.1). The
assumption is that stress is uniformly distributed within a body.
StresssAverage ¼ TotalForce
TotalArea¼ P
A(1.1)
Where stress exists in a material there is some type of deformation of that material. This is known as strain and represented
by e. Like stress, there are two types of strain, linear strain and shear strain. Linear strain can obtain two notable states, in
tension or compression. Linear strain will be in tension, tensile strain, or increasing (positive) strain, if the material lengthens
in a straight line. Linear strain will be in compression, compressive strain, or decreasing (negative) strain, if the material
shortens in a straight line [5]. Assume a bar of some length L is loaded longitudinally, and assume that bar elongates
uniformly, and the cross sectional area keeps its shape as a plane and perpendicular to the loading axis throughout the
elongation process. This bar is represented in Fig. 1.1. Unit strain of elongated bar is given by (1.2), which represents
average strain. L is the original length of the bar, and d is the total elongation of the bar [5]. Equation 1.2 cannot be used if thebar’s cross sectional area is not constant or of the load is not uniformly distributed. Then strain per unit, or unit strain, is
determined by differential elongation at a point on the bar or dd of a cross sectional length dL, as expressed in (1.3) [5].
Strain ¼ e ¼ dL
(1.2)
e ¼ dddL
(1.3)
Stress and strain are depended upon each other, and related through material properties. Robert Hooke stated this
relationship is accomplished by a constant of proportionality known as the modulus of elasticity, E (need reference). For
the bar subjected to elongation is shown as (1.4). sL is known as the longitudinal stress, elongation direction. eL is the
longitudinal strain.
sL ¼ EeL (1.4)
Strain is measured using a strain sensor [5], a device which is mounted or manufactured on the straining surface that
translates strain into an electrical signal. Conventional strain transducer, known as a strain gauge, uses an insulating flexible
backing that supports a metallic foil element. The flexible backing is adhered to the straining surface, such as a metallic beam
put under stress. The object becomes deformed when the backing flexes and the foil becomes deformed, and changes its
electrical resistance. The foil can be modeled as a strained conductor. Let’s assume a conductor is unrestrained laterally and
is strained in its axial direction, its length will change and its cross section will also change, this effect is known as the
Poisson Effect (reference needed), this is shown in Fig. 1.2. If the strain increases the length of the conductor its cross
sectional area will decrease, and vice versa if strain decreases the length its cross sectional area will increase. Also resistivity
2 R.P. Weisenberger et al.
of the conductor material will change because of the arrangement of the atoms inside, but the volume does not change.
Strain can be found using the ratio of the change in resistance over its original resistance over the gauge factor, defined in
(1.5). The gauge factor related to how the gauge is manufactured and what material the foil element is made from.
DR ¼ Change in resistance due to strain, RG ¼ undeformed resistance, GF ¼ gauge factor defined by the manufacturer,
and e is strain. Which strain is simply defined, in (1.6), as a change in bar length (Dl) over the original length (L).
GF ¼DRRG
� �e
(1.5)
e ¼ DlL
(1.6)
Most commercially available strain transducers can withstand relatively benign temperature environments, or less than
700�F [6]. The insulating flexible backing typically cannot withstand the extreme environments and the metallic foil’s
resistivity changes as a function of temperature. Thus, strain gauges that utilize piezoresistive elements are not desirable at
high temperature [1].
1.4 Silicon Carbide as a Mechanical Material
To make a high temperature strain sensor it needs to be made of material which could withstand that high temperature
environment. One such material is silicon carbide, or SiC. SiC is a one-dimensional polymorphism called polytypism and
exists in more than 250 structural polytypes [7]. There are only three crystalline structures; cubic, hexagonal, and
rhombohedral. All of the polytypes have identical planar arrangement of silicon and carbon atoms. The differences in the
polytypes are in the way the planar arrangements are stacked. The order of stacking determines the types of close packed
structures and their properties. When the layers are stacked a certain way they are depicted with the conventional
nomenclature with a number of SiC double layers with the appending letter, C for cubic, H for hexagonal, R, for
rhombohedral. For example 3C-SiC has cubic lattice with three layers. Each polytype exhibits different properties,
for example 3C-SiC, three cubic layers of SiC, has a bandgap of 2.2 eV and 4H-SiC, four hexagonal layers, has a bandgap
of 3.4 eV [7]. A summary of selected polytypes is given in Table 1.1.
Silicon carbide as a crystalline material for making MEMS devices allows high temperature devices with excellent
mechanical and electrical properties. A more conventional MEMS material with well known properties and manufacturing
abilities is silicon, although silicon based devices are not suited for high temperatures. Silicon material properties degrade
at temperatures greater than 500�C [8]. Electrical properties of silicon cannot operate extendedly above 150�C [9].
Fig. 1.1 Bar subjected
to load and elongation
Fig. 1.2 Conductor
subject to strain
1 Silicon Carbide High Temperature MEMS Capacitive Strain Sensor 3
Using silicon Carbide to produce a MEMS based strain device is a possible option. Silicon carbide allows for many
advantages to include: increased temperature operation, high radiation exposure, corrosive media, and large impact
survivability [8].
1.5 Double Ended Tuning Fork
To make a strain sensor that alleviates high temperature effects on strain measurements one could made from the double
ended tuning fork device. Double ended tuning fork resonant sensors are already in use for high precision strain
measurements [10]. The double ended tuning fork is modeled as a spring mass damping resonator system. The concept is
drawn in Fig. 1.3. A shuttle mass is suspended over a substrate, and is attached at each end to anchors. The anchors are
attached to the substrate. Attached to the shuttle mass are interdigitated fingers. Built next to the interdigitated fingers
are other interlaced interdigitated fingers which are attached to the substrate via anchors [10]. The shuttle mass is allowed to
move toward, and subsequently away from, the interlaced interdigitated fingers [10]. The anchors are mechanically attached
to the substrate. The entire body of the movable double ended tuning fork, shuttle mass, spring supports, interdigitated
fingers, and anchor are all a part of the shuttle assembly. The anchor and interdigitated fingers on each side of the shuttle
mass are to separate fixed components. The shuttle mass assembly can move axially, to and away from the interdigitated
anchor fingers. This structure is fabricated on top of a flexible backing of a minimum thickness, so strain is transmitted
through to the sensor. The flexible backing is allowed to strain as the straining substrate. This is the same technique
conventional strain sensors use in operation.
The double ended tuning fork strain sensor works when stress occurs from within the substrate, directly below the double
ended tuning fork MEMS structure. When the substrate is strained, the distance between the interdigitated fingers and the
spring support anchor gets larger, as shown in Fig. 1.4, this gives you increasing strain. The reverse happens the distance
between the interdigitated fingers gets closer to the anchor, as shown in Fig. 1.5, which gives you decreasing strain.
The interdigitated finger set can be modeled as a parallel plate capacitor modeled as (1.7). The area is dependent on the
shape of the interdigitated fingers and d is the distance between the interdigitated fingers and the anchor. Because strain is
the change in length, DL, over the original length, L, (1.6), the change in distance between the anchor and the interdigitatedfingers, change in d, as reference to the original distance, original d, the change in gap depicts strain. This allows for a strain
sensing effect.
C ¼ eAd
(1.7)
To operate the sensor, the sensor is driven by a frequency modulated voltage that puts the spring mass damper shuttle
mass system into oscillation. That frequency is dependent on capacitance, and is found by varying the frequency until
oscillation. When strain is applied to the substrate, the interdigitated fingers separate and the oscillation frequency changes
[10]. The frequency is adjusted again until oscillation is again achieved. Capacitance is backed out and strain can be
determined.
Table 1.1 Selected properties
of silicon carbideProperty (unit) Unit 3C-SiC 6H-SiC
Yield strength (109 Nm�2)
Knoop hardness kgmm�2 3,300 2,917
Young’s modulus Gpa 448 448
Density gcm�3 3.21 3.21
Lattice constant A 4.359 a0: 3.08
c0: 15.12
Thermal expansion coefficient 10�6 K�1 2.9 4.2
Thermal conductivity Wcm�1 K�1 4.9 4.9
Sublimes at �C T > 3,100 T > 3,100
Energy gap eV 2.2 2.99
Dielectric constant 9.7 10
Electron mobility cm2V�1 s�1 1,000 400
Hole mobility cm2V�1 s�1 40 50
4 R.P. Weisenberger et al.
Fig. 1.3 Double ended
tuning fork
Fig. 1.4 Increasing strain
Fig. 1.5 Decreasing strain
1 Silicon Carbide High Temperature MEMS Capacitive Strain Sensor 5
1.6 Capicitive Strains Sensor Design
Double ended tuning fork strain sensors have the ability to measure strain greater than 0.11 mm [8], but lack the ability to
measure larger surface areas, allowing them to be used on large scale testing apparatuses and making it not usable for
hypersonic vehicle testing which require large surface area strain measurements. A new sensor design which can allow an
increase in surface area and subsequentlymeasured capacitance across the device is designed. This device can also be scalable
to allow larger measuring areas depending on stresses expected in the measured material. The design takes the good things
about the double ended tuning forkmodifies to eliminate the need to frequency tune. The design eliminates the moving shuttle
and increases the number of interdigitated fingers. The device’s requirement to tune to the proper frequency would be
eliminated, allowing for a passive measuring of capacitance. Figure 1.6 shows the modified version of the strain sensor.
This new sensor allows for growth by increasing the quantity of interdigitated fingers. This can be done by increasing the
number of interdigitated finger sets, shown in Fig. 1.6, or by increasing the number of axial finger sets. Each axial finger set
is connected to subsequent axial finger sets. Each interdigitated finger sets is fixed to the surface of the substrate, which could
still be a flexible backing material or a stiff substrate of the measured material. There are no “floating” pieces. Everything is
anchored. The interdigitated fingers are however cantilever beams, i.e. only anchored at the root of the beam.
A simple capacitance equation is developed based on the concept that the interdigitated fingers are treated as a parallel
plate capacitor, shown in (1.8). This simple model does not include effects from the surface of the substrate. Cross finger
effects, or effects from fingers located two or more positions away only the interdigitated finger sets. It also does not include
fringe effects. Figure 1.7 depicts variables used to create the equation. NIDFS and NAFS are dependent on the interdigitated
finger sets and the number of axial finger sets respectively, which are dependent on the size of strain sensor required and are
not determined at this time. LO is original distance between the axial finger sets, depicted as LS in Fig. 1.7 which equals the
original length LO minus the change in length DL.
Csensor ¼ NAFS� NIDF
� e½LT � ðLO � DLÞ��ðTÞLG
þ eðWTÞ�ðTÞðLO � DLÞ
� �þ eðWTÞ�ðTÞðLO � DLÞ
� �(1.8)
As shown, the capacitance is dependent on DL, or change in length, which comes from strain, e. Using (1.6) strain can bedetermined; L is the overall sensing length, or length between each anchor, which does not including anchors and non
sensing features, original strain sensor length can be found by adding the number of axial finger sets over the length of the
sensor, as shown in (1.8).
Fig. 1.6 New sensor design
6 R.P. Weisenberger et al.
A simple axial finger set design is modeled and simulated in Coventorware#. Coventorware# is a custom built MEMS
software written by Coventor# for multiphysics finite element modeling and simulation. Figure 1.8 depicts the simple axial
finger set. One end of the substrate is fixed, the load reaction end, and the other end a load is introduced into it, introduced
load end. An electric potential, creating electric flux, is applied between the positive and negative fingers. To determine if
capacitance increases as strain is applied three forces are simulated 0, 531, and 1,062 mN/mm2. As stated before when the
interdigitated finger set model is subjected to load, stress and strain exist within the material causing the fingers to separate,
giving an increase or decrease of capacitance.
1.6.1 Sensor Fabrication
The overall process of making the sensor begins with a handle silicon wafer. An oxide is grown, with a poly-SiC “flexible
backing” layer grown on top. This makes a SiCOI or silicon carbide on insulator wafer. A nitride passivation layer is added
for signal isolation. N-type doped poly-SiC traces are formed, for signal egress. A second sacrificial oxide layer is grown
within the poly-SiC, and it is patterned to form the anchors. The poly-SiC mechanical layer is added and patterned to form
the interdigitated finger pattern. After the device is created, the mechanical layer is released along with the sacrificial oxide
between the carrier wafer and the “flexible backing” poly-SiC, and is complete. The completed process is depicted in profile
in Fig. 1.9, and subsequent released device is depicted in profile in Fig. 1.10.
Fig. 1.7 Variables used in the new strain sensor
Fig. 1.8 Interdigitated finger set in Coventorware#
1 Silicon Carbide High Temperature MEMS Capacitive Strain Sensor 7
1.7 Results
The results of change of capacitance from Coventorware# are shown in Figs. 1.11 and 1.12. Figure 1.11 shows
displacement in meters and force in micronewtons per square meter. It also shows that as force increases strain increases.
Figure 1.12 shows capacitance in farads and force in micronewtons per square meter. It also shows that as force increases
capacitance also increases.
The results show that the interdigitated finger set is a good parallel plate capacitor design for measuring strain using the
capacitive effect, even though the magnitudes are fairly small, on the order of 5.62e–16F, If the quantity of interdigitated
finger sets in increased, thus increasing the amount of capacitance that is produced. It also increases the area that is available
to measure strain on the surface.
Mechanical LayerSacrificial Oxide 2
Sacrificial Oxide 1
Si Carrier Wafer
Signal LayerNitride Passivation Layer
Device Substrate
Fig. 1.9 Unreleased strain
sensor process
Mechanical LayerSignal LayerNitride Passivation Layer
Device Substrate
Fig. 1.10 Released strain
sensor process
Force vs. displacement7
x 10-7
6
5
4
3
2
1
00 500 1000 1500 2000 2500
disp
lace
men
t
Fig. 1.11 Force versus
displacement
8 R.P. Weisenberger et al.
1.8 Conclusions
The objective of this research; to design, model and simulate a novel high temperature strain sensor, was met. First stress,
strain, and the stress strain relationship were discussed. The double ended tuning fork resonant strain sensor was discussed.
Silicon carbide as MEMS materials was discusses. The high temperature strain sensor was discussed, designed, modeled and
simulated to determine if the interdigitated finger set was able to be used as a capacitive strain sensor. This design can be
increased on the mass scale to satisfy the design requirements. This design is a viable solution testing of strain measurements
on high temperature hypersonic components, for which the Air Force Research Lab’s Air Vehicles Directorate has research
programs.
References
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3. Hezarjaribi Y, Hamidon MN, Keshmiri SH, Bahadorimehr AR (2008) Capacitive pressure sensors based on MEMS, operating in harsh
environments. In: 2008 IEEE international conference on semiconductor electronics (ICSE 2008), Johor Bahru, Johor, Malaysia, 25–27 Nov
2008, pp 184–187
4. Murray WM, Miller WR (1992) Fundamental concepts for strain gages, ch. 1. In: The bonded electrical resistance strain gage. Oxford
University Press, New York, pp 3–41
5. MurrayWM,Miller WR (1992) Stress–strain analysis and stress–strain relations, ch. 2. In: The bonded electrical resistance strain gage. Oxford
University Press, New York, pp 42–89
6. Hezarjaribi Y (2009) Capacitive pressure sensors based on MEMS, operating in harsh environments. In: ICSE, Johor Bahru, Johor, Malaysia,
pp 184–187
7. Cheung R (2006) Introduction to silicon carbide (SiC) microelectromechanical systems (MEMS). In: Silicon carbide microelectromechanical
systems for harsh environments. Imperial College Press, London, pp 3–4, and p 181
8. Azevedo RG (2007) A SiC MEMS resonant strain sensor for harsh environment applications. IEEE Sens J 7(4):568–576
9. Azevedo RG, Jones DG, Jog AV, Jamshidi B, Myers DR, Chen Li, Fu Xiao-an, Mehregany M, Wijesundara MBJ, Pisano AP (2007) A SiC
MEMS resonant strain sensor for harsh environment applications. IEEE Sens J 7(4):568–576
10. Wojciechowski KE, Boser BE, Pisano AP (2004) A MEMS resonant strain sensor operated in air. In: 17th IEEE international conference on
micro electro mechanical systems 2004 (MEMS), Netherland, pp 841–845
Farads vs. Load
Far
ads
x 10-16
5.62
5.61
5.6
5.59
5.58
5.57
5.56
5.55
0 500 1000 1500 2000 25005.54
Fig. 1.12 Force versus load
1 Silicon Carbide High Temperature MEMS Capacitive Strain Sensor 9
Chapter 2
Characterizing External Resistive, Inductive and Capacitive Loads
for Micro-Switches
Benjamin Toler and Ronald Coutu Jr.
Abstract Microelectromechanical systems (MEMS) switches offer much lower power consumption, much better isolation,
and lower insertion loss compared to conventional field-effect transistors and PIN diodes however, the MEMS switch
reliability is a major obstacle for large-volume commercial applications [1]. To enhance reliability, circuit designers
need simple and accurate behavioral models of embedded switches in CAD tools to enable system-level simulations [2].
Where Macro-switch researchers assess electric contact performance based on the type of load that is being switched, in
MEMS literature, micro-switch performance and reliability is characterized by testing the devices under “hot-switched” or
“cold-switched” load conditions; simple models are developed from the “hot” and “cold” characterizations. By applying
macro-switch performance characterization techniques, i.e. examining reliability based on the type of load that is being
switched, clear characterizations of “hot” switching and “cold” switching external resistive, capacitive, and inductive loads
are produced. External resistive loads were found to act as current limiters and should be suitable under certain criteria for
reducing current density through the contact area and thus limiting device failure to mechanical failure modes. Alternatively,
external capacitive loads increased current density under “hot” switching conditions at the moment the micro-switch closes;
which increases the risk for material transfer and device failure. Under DC conditions, the inductive loads had little effect in
either “hot” or “cold” switching environments.
Keywords Micro-switch reliability • Capacitive loads • Resistive loads • Inductive loads • Contact resistance
2.1 Introduction
This paper presents a study of external resistive, inductive, and capacitive loads under “hot” and “cold” switching conditions
and characterizes the effects on micro-switch reliability. Micro-switches consume no DC power and can be manufactured on
low-cost silicon or glass substrates [3]. An example of a micro-switch is shown in Fig. 2.1. Micro-switches with metallic
contacts have low insertion loss and wide operation frequency band from DC to tens of GHz [3]. The combination of
broadband frequency operation and low-cost manufacturability makes them appealing for use in modern telecommunica-
tion, automotive, and defense applications [3]. Despite the advantages of micro-switches, reliability is still a major concern
for many micro-switch applications.
In the literature, there is little detail describing the effects of “hot” switching and “cold” switching external loads on
micro-switch reliability. Because of size and geometry, micro-switches are more sensitive to variations in temperature and
current density than their macro-switch counterparts. Both current density and temperature at the contact area are influenced
by “hot” switching or “cold” switching external loads. Different configurations of external resistive, capacitive, and
inductive loads were examined for their impact to micro-switch reliability in both series and parallel configurations.
Previous work by Yang et al. studied contact degradation in “hot” and “cold” operations of direct contact gold micro-
switches [4]. Their results showed that for both high and low-electric field “hot” switching, material transfer took place due to
transient heat [4]. Also, their study revealed that mechanical wear became the primary effect to contact resistance under “cold”
switching conditions [4]. Characterizations of the external load models were consistent with the results of their experiment.
B. Toler • R. Coutu Jr. (*)
Air Force Institute of Technology, 2950 Hobson Way, WPAFB, OH 45433, USA
e-mail: [email protected]; [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_2, # The Society for Experimental Mechanics, Inc. 2013
11
2.2 Micro-Switch Resistance Modeling
Under plastic deformation, permanent surface change occurs by the displacement of atoms in asperity peaks whereas
neighboring atoms are retained under elastic deformation [5]. For DC micro-switches, asperity peaks, or “a-spots”, are
conducting contact areas [6] which are “small cold welds providing the only conducting paths for the transfer of electrical
current” [7]. To account for the asperity contact area and force under plastic deformation, the well known model from Abbot
and Firestone that assumes sufficiently large contact pressure and no material creep is used [8]. Single asperity contact area
and force are defined using (2.1) and (2.2) [9]:
A ¼ 2pRa (2.1)
FcP ¼ HA (2.2)
where H is the Meyer hardness of the softer material [9], A is contact area, R is asperity peak radius of curvature, and a is
asperity vertical deformation [9]. This study considers contact resistance based on plastic deformation and diffusive electron
transport and is represented using (2.2) as:
RcDP ¼ r2
ffiffiffiffiffiffiffiHpFcP
r(2.3)
The MEMS literature indicates that varying the type of load during testing reveals the physical limitation for
micro-switches [10]. Rebeiz states that a good assumption for failure of the micro-switch is assumed to be when the contact
resistance becomes greater than 5O, which results in an insertion loss of�0.5 dB [3]. According to Rebeiz, the primary cause
of micro-switch failure is due to plastic deformation in the contact interface such as “damage, pitting, and hardening of the
metal contact area [which] is a result of the impact forces between the top and bottom metal contacts” [3]. The description
relates closely to “cold” switching mechanical failure. In “hot” switching, contributors to early micro-switch failure include
“arcing, material transfer, high current density in the contact region, and localized high-temperature spots” [3].
2.3 Cold Switching
“Cold” switching is generally known to be actuating the switch repeatedly without applying RF or DC power during
actuations, limiting the switch lifetime to mechanical failures such as structural fatigue, memory effect, stiction of the
actuators, etc. [10]. Simply put, “cold” switching is powering the circuit off, then actuating the switch off then on, then
Fig. 2.1 Micro-switch
example
12 B. Toler and R. Coutu Jr.
powering the circuit back on. To model “cold” switching, the circuit elements would not contain stored energy at the time the
switch closes and all energy would dissipate between actuations. This limits the types of failures of micro-switches to purely
mechanical failure modes and extends the reliability of the micro-switch. Zavracky et al. reported over 2 � 109 cycles as thelifetime for Au sputtered contacts that were packaged in nitrogen [11]; a considerable difference compared to the 5 � 108cycles Zavracky reported for “hot-switched” contacts. Majumder et al. reports greater than 107 “hot-switched” cycles and
approximately 1011 “cold-switched” cycles for micro-switches with a “platinum group” contact metal [12].
Fretting is a form of structural fatigue which is defined as accelerated surface damage occurring at the interface of
contacting materials subjected to small oscillatory movements [7]. Braunovic states that the lack of published information of
failures due to fretting is because fretting is a “time-related process causing an appreciable effect only after a long period of
time as a result of the accumulation of wear debris and oxides in the contact zone” [7]. However, contact force has significant
influence on the contact resistance in fretting conditions [7]. As the force applied on the contact is increased, the contact
resistance declines until there is a significant amount of wear debris and oxide to form an insulating layer [7]. As the
insulating layer develops, the resistance increases despite larger applications of force. Fretting is a rate dependent
phenomenon and the frequency of oscillations will affect the contact resistance [7].
Another “cold” switch mechanical failure cause is pitting. Pitting and hardening occur when two metals make contact
repeatedly at the same location [3]. The repeated actuations create cavities at the surface and are confined to a point or small
area [7]. The areas are described as being irregularly shaped and are filled with corrosion products over time [7]. The build-
up of corrosion products in conjunction with pitting reduces the area available for current flow and will induce high
temperatures at those areas while the switch is closed. The result will be a localized high temperature failure mode as seen in
“hot” switching conditions.
2.4 Hot Switching
According to Kim, the lifetime of a switch is more restricted by “hot”-switching than by “cold”-switching because most of
the signals that are transmitted through the switch have high power loads in real cases [10]. Electrical failure mechanisms,
like temperature, current density, and material transfer are all factors in reliability under “hot” switching [3]. A major
consideration in “hot” switching is a large temperature rise which occurs in the contact region due to the small contact area
on the a-spots [3]. With a small contact region comes a large contact resistance, which in the case of “hot”-switching will
result in large heat dissipation in that area at the time the switch closes. Increased temperature at these localized points may
soften the contact metal and lead to bridge transfer. A problem with bridge transfer is that the internal stresses cause the
contact metal to shrink and crack [7]. Oxidation then leads to a reduced number of electrical conducting paths thereby
leading to overheating and ultimately mechanical failure [7].
An increase in current density raises the temperature for the contact areas on the cathode and anode. Concerning the
topology of the contact surface, which has asperities, a higher current density will cause high temperature spots at asperities.
The relationship between the temperature in the contact and voltage drop across the contact is described by Pitney as:
V2c ¼ 4LðT2
c � T2oÞ (2.4)
where Vc is the voltage drop across the contact, L is the Lorenz constant, Tc is the temperature in the contact, and To is thebulk temperature [5]. Examining (2.4), an increase in current would result in an increase in temperature due to “I2 R” heating[5]. The resistance is expected to increase because of the metal’s positive temperature coefficient of resistance, a [5].
The equation for resistance Rct, at the new temperature Tc is then:
Rct ¼ Rco 1þ 2
3a Tc � Toð Þ
� �(2.5)
but (2.5) only holds true until a temperature is reached that softening of the metal begins to occur [5]. When the contact
metals are softening, the asperities collapse, increasing their areas to facilitate cooling [5]. The collapsing of asperities
increases the effective contact area and results in a decrease of the contact resistance. This is seen by rearranging (2.2) and
(2.3), which gives contact resistance as a function of area:
Rc ¼ r2
ffiffiffiffiffiffiffiffi1
2Ra
r(2.6)
2 Characterizing External Resistive, Inductive and Capacitive Loads for Micro-Switches 13
and R is asperity peak radius of curvature and a is asperity vertical deformation [9]. As area increases, Rc decreases. High
temperature for the small volumes ofmaterial changes the softness of the contact material and promotes bridge transfer [5]. Likearcing, bridge transfer is a form of material transfer which reduces the effective area of the asperities and increases the contact
resistance [5]. Also, increased temperature decreases the mobility of electrons in a metal, resulting in increased resistivity.
Another “hot” switching characteristic is the potential for arcing between the cathode and anode. As stated by Rebeiz,
when the contact metals first separate, they are very close to each other and very sharp (due to asperities), which result in a
direct field emission [3]. The cause of the arc is explained further, “these electrons flow from cathode to anode, where they
form a tiny spot of great temperature due to the energy dissipation and the high electric field generated form a space charge
of ions . . . the metal vapor arc material transfer always occur[s] from anode to cathode” [3]. Due to arcing, the material
transfer causes the switch to wear out faster when using DC current in a uniform direction.
Considering DC, electro-migration is another form of material transfer which causes micro-switch failure [7]. Electro-
migration is defined as “the forced motion of metal ions under the influence of an electric field” [7]. Atomic flux (J) is given by:
J ¼ D
kTJreZ� (2.7)
D ¼ Doe�Q
kT (2.8)
where D is the diffusion coefficient, J is the current density, r is the electrical resistivity and eZ* is the effective charge, k isthe Boltzmann constant, T is the absolute temperature, Do and Q are the diffusivity constant and activation energy for
diffusion, respectively [7]. As shown by (2.7), atomic flux is directly proportional to current density. Voids form as a result
of electro-migration and ultimately cause device failure [7]. Braunovic states that an increase in current density in the a-spots
can be substantial and create the right conditions for electro-migration to occur [7].
2.5 Circuit Analysis
There are three states to examine in circuit analysis, initial, steady state, and transient. The initial state is for considering that
there is energy stored in the circuit elements; which could be very descriptive for switchingwithout turning off the circuit signal
(“hot-switch”). The transient state is when the switch is first closed and the elements in the circuit are ‘powering’ up.When the
switch has been closed for a relatively long time and the transients have settled, the circuit is now in steady state. Recall that
inductors become a short circuit to DC and a capacitor becomes an open circuit to DC under steady state conditions. Under AC
conditions, the capacitor becomes a short and the inductor becomes open. Based on a given configuration of circuit elements,
themeasured contact resistance can change based on the driven load. Figure 2.2 shows a representation of themeasured contact
resistance versus applied actuation voltage for a switch with a drive electrode 150 mm-wide [13].
As can be seen in Fig. 2.2, the greater actuation voltage produces a lower contact resistance by enhancing the effective
contact area [13]. Scaling down to micro-switches, contact forces are on the order of mN, which is much smaller than their
macro counterparts [4]. With such low contact force, surface contamination and the topology of the contact area become
important considerations for determining resistance [4]. Loading affects the surface conditions by determining the amount of
current flowing through the contact as well as the potential for arcing and material transfer. Both series and parallel
configurations for resistive, capacitive, and inductive loads and combinations of resistive, capacitive, and inductive loads
were examined however, only a model from each resistive, capacitive, and inductive load configuration is shown here.
2.6 Analysis of Resistive Loads
For a resistive load in series, the relationship of current and voltage is linear and will scale for various values of purely
resistive loads until a change in the contact interface occurs. As shown by Fig. 2.3, a resistive load is placed in series with the
contact resistance.
I ¼ V
RL þ Rcð Þ (2.9)
14 B. Toler and R. Coutu Jr.
Shown by Fig. 2.4 and (2.9), the current scales as 1
RLþRcfor the configuration in Fig. 2.3; where Rc is the resistance of the
contact under plastic deformation and diffusive electron transport and RL is the resistive load.
Under “cold” switching conditions, the resistance of the contact will change due to material transfer and a change in the
effective contact area [6]. Also, over time, when the device is affected by the failure mechanisms of pitting or fretting,
the contact resistance will dominate the expression and reduce the current until device failure, at which time there is no
current flow. Under “hot” switch conditions the material transfer to be worse due to arcing [3]. Material transfer would be
caused by repetitive actuation with DC currents in a uniform direction [4]. With material transfer comes a lesser effective
area, which increases the contact resistance. While the failure modes may differ between “cold” switching and “hot”
switching, the current limiting effects of resistive loads are the same for both “hot” and “cold” switching conditions.
The effect of a resistive load is different when placed in series or parallel. For series external loads, the addition of a
resistive load causes a current limiting effect. A potential method to increase the reliability of a micro-switch is to
purposefully match the external resistive load with the contact resistance. For equal values of RL and Rc, the current is
effectively halved. Similarly, as the contact resistance decreases, the resistive load limits the amount of current able to flow
through the contact. Limiting current also affects the I2 R losses and therefore restricts temperature; effectively reducing the
probability of failure due to temperature. Also, since the effect of a resistive load equivalent to contact resistance in series
halves the current, using a lower-performance-higher-resistance contact metal could extend the life of the micro-switch
further than using a low resistance high performance contact metal; assuming the higher resistance is due a material property
which affects durability such as hardness.
A resistor in parallel configuration will decrease the current through the contact with a decrease in resistive load. Increasing
the resistive load would increase the current up to the maximum supplied and therefore would increase current density
through the contact; which ultimately would lead to early device failure.With higher than the contact resistance value external
resistive loads, both a “cold” and “hot” switched parallel external resistive load would induce temperature increases leading to
reduced reliability. Lower than the contact resistance values, external resistive loads would enhance reliability by reducing
the current flow through the contact but may defeat any purpose of having a switch since it would act effectively as a short.
Fritting of contaminant films -Quasi-metallic contact
Increased metal-to-metal contact
Maximum contact force(minimum resistance)
Actuation Voltage (V)C
lose
dSw
itch
Res
ista
nce
(Ω)
Vpi Vepi
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
15 20 25 30 35 40 45 50 55 60 65
Fig. 2.2 Representative plot
of measured switch versus
applied actuation voltage [13]
Rc
DC
RL
I
Fig. 2.3 Resistive load in
series with contact resistance
2 Characterizing External Resistive, Inductive and Capacitive Loads for Micro-Switches 15
2.7 Analysis of Capacitive Loads
Capacitive loads in series under DC conditions become open circuits in steady state. In Fig. 2.5, an external capacitive load is
in parallel with a micro-switch. In this configuration, the capacitor charges when the switch is open. When the switch
is closed, the capacitor discharges through the switch and effectively increases current density as shown in Fig. 2.6.
Equation 2.10 represents the current through the contact over time as the capacitor discharges upon switch closure.
An increase in current density promotes contact interface deformation via temperature effects, material transfer, and
electro-migration and reduces reliability.
I tð Þ ¼ V
ðRL þ RcÞ 1þ e
�t
CRL�Rc
RLþRc
� �� �! ð2:10Þ
Under “cold” switch conditions, the capacitor would discharge during the time when the signal is stopped until the switch
opens. While the switch is closed and signal is transmitted, the capacitor would charge and then become open. For
configurations where capacitors ‘open’ the circuit, there is no current flow which implies infinite resistance. “Cold”
switching conditions may induce “hot” switching type failure modes such as electro-migration and material transfer since
there is still current flow at the moment the switch closes before the signal is transmitted and before the switch opens after the
signal transmitted is turned off. Likewise, “hot” switching conditions increase the opportunity for material transfer and
interface deformation by increased current density when the capacitor is discharging between actuations. Overall, the
addition of an external capacitive load in parallel is deleterious to reliability.
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Cur
rent
(m
A)
Resistance (Ohms)
Fig. 2.4 Relationship
of current and resistance
Rc
DC
CL
I2
I1Fig. 2.5 Capacitive load
in parallel with contact
resistance
16 B. Toler and R. Coutu Jr.
In macro-switches, for contacts with sufficient voltage and current, an arc ignites in the gap created by the actuation [6].
The concept is explained by Holm that during a decreasing load, the contact area diminishes and the contact resistance
increases; the resulting power dissipation occurs at high temperature for a small volume of metal causing it to evaporate
explosively [6]. A plasma develops and an arc is formed immediately on opening the contact [6]. In the case of micro-
switches, field emission produces arc-like effects of material transfer [3].
2.8 Analysis of Inductive Loads
Concerning inductive loads under DC conditions, the inductors become short circuits over time making the effective
resistance limited to the contact resistance. The inductors ‘shorting’ will provide current flow equal to the max possible
current through the contact with the applied voltage; increasing the opportunity for “hot” switching failure modes like
material transfer and electro-migration. When “cold” switched, the natural response for the inductive loads is high resistance
until steady state, when the inductor is ‘energized’. For a micro-switch with an external inductive load in series, the inductor
would initially act as a current buffer until energized by limiting the effective current upon closing the switch. This behavior
reduces the intensity of failure mechanisms at moments when the connection is being made. Compared to “cold” switch
conditions, the inductors would still have some of their energy between actuations during “hot” switching and would have
minimal impact to the resistance of the contact.
Consider the inductive load configuration of Fig. 2.7 in the case of “hot” switching, the inductor would be energized and
discharge current between actuations. In the “cold” switching condition, the inductor affects the time it takes to reach steady
state since it resists change in current during the transient phase. The inductor would act as a current limiter until steady state;
it would gradually increase the amount of current flow based on its value of inductance. For the switch, having an inductor in
series will limit the initial flow of current through the contact area on initial contact. With reduced current at the moment of
initial contact, the switch will be more susceptible to failure caused by plastic deformation over repeated actuations than by
arcing and other electrical failure modes.
0
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10
Cur
rent
(m
A)
Time
Fig. 2.6 Current through the
contact for a charging external
parallel capacitive load at the
time the switch closes
Rc
DC
LL
I1
Fig. 2.7 Inductive load in
series with contact resistance
2 Characterizing External Resistive, Inductive and Capacitive Loads for Micro-Switches 17
2.9 Conclusions
The purpose of this work was to characterize external resistive, capacitive, and inductive loads and their effects on micro-
switch reliability under “hot” and “cold” switch conditions to better define “hot” and “cold” switch condition effects on
reliability. “Cold” switching failure mechanisms included fretting and pitting through repeated actuations. The reliability of
the micro-switch under “cold” switching conditions is limited to the material properties of the contact metals. “Hot”
switching failure mechanisms included material transfer, increased current density, electro-migration, and temperature.
Certain configurations were determined to enhance micro-switch reliability. Specifically, that an external resistive load in
series acts as a current limiter for both “hot” and “cold” switching conditions and reduces the probability of an electrical
failure mode thereby enhancing the reliability of the micro-switch. In addition, there is a possibility of increasing the
reliability of the switch by using a higher resistance contact metals with a matching external resistive load; the current
limiting effect restrict temperature in conjunction with the increased hardness of the higher resistance contact metal would
most likely extend the reliability of the micro-switch further than a low resistance contact metal. Alternatively, it was found
that certain configurations of resistive, inductive, and capacitive loads promote early failure via increased arcing, material
transfer, and current density. An external capacitive load in parallel was determined to be detrimental to micro-switch
reliability under “hot” switching conditions since it compounded the current during discharge and raised the probability for
increased current density, temperature, and material transfer. For “cold” switching conditions, the discharge of the capacitor
essentially continues to provide current through the contact after the signal has stopped transmitting and before the switch
opens; effectively turning a “cold” switching condition into a “hot” switching condition and reducing reliability with the
increased probability of electrical failure. Lastly, the external inductive load for DC conditions reduced susceptibility of
failure via increased current density and temperature by limiting the current at the moment of initial contact in “hot”
switching conditions. “Cold” switching conditions for external inductive loads have negligible effect to contact resistance
and micro-switch reliability.
Acknowledgements The authors would like to thank Lt Col LaVern A. Starman for his support and assistance with theory and analysis. The
authors would also like to extend gratitude to AFIT technicians, Mr. Rich Johnston and Mr. Tom Stephenson for their work.
Disclaimer The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air
Force, Department of Defense, or the U. S. Government.
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18 B. Toler and R. Coutu Jr.
Chapter 3
Principles Involved in Interpreting Single-Molecule Force
Measurement of Biomolecules
Sithara S. Wijeratne, Nolan C. Harris, and Ching-Hwa Kiang
Abstract Single-molecule manipulation techniques provide a unique tool for a close-up investigation of the complex
biological properties and interactions. During the force measurement, a single molecule is pulled while its force response is
monitored. However, quantifying these non-equilibrium data and using them to understand the structure-function relation-
ship of biological systems have been challenging. We describe the mechanics of nanoscale biomolecules and the use of these
force measurements for the free energy reconstruction using the recently derived non-equilibrium work theorem, i.e.,
Jarzynski’s equality. We also compare the results with those from other phenomenological approaches. Finally, mechanical
characterization of systems such as overstretching transitions of DNA are presented, and the implications and challenges of
these single-molecule force studies are discussed.
3.1 Introduction
Nanoscale manipulation of individual biomolecules, using techniques such as the atomic force microscope (AFM) and laser
optical tweezers (LOT), has increased the scope and depth in studying important biological interactions, e.g., protein folding,
receptor-ligand binding, and double-stranded DNA melting. In recent years, single-molecule manipulation via AFM has
been used to characterize the mechanical properties of various nucleic acids and proteins [1–5]. However, since single-
molecule manipulation experiments are typically performed under non-equilibrium conditions, extracting thermodynamic
properties from these measurements has been difficult. The recently derived Jarzynski’s equality, which relates non-
equilibrium work fluctuations to equilibrium free energy differences, provides the possibility for extracting equilibrium
information from these non-equilibrium single-molecule manipulation data. Here, we describe two examples for analyzing
single-molecule force data. Thermodynamic property of unfolding a muscle protein is analyzed using Jarzynski’s equality,
which is used to reconstruct the free energy landscape associated with this process. The mechanical properties of melting and
overstretching transitions of DNA are revealed using one-dimensional polymer physics models.
3.2 Single-Molecule Manipulation Experiments
In the mid 1990s, researchers developed new techniques to study the intra- and intermolecular forces characterizing specific
interactions between individual molecules. Examples of such interactions include receptor-ligand binding, antibody-antigen
binding, and binding between complementary strands of DNA. Techniques such as AFM [6–8], LOT [9, 10], and magnetic
tweezers [11], biomembrane force probe (BFP) [12], and surface force apparatus experiments [13] had the sensitivity to
measure forces in picoNewton (pN) and distance in subnanometer (nm) resolutions, thus making them suitable for
measuring molecular interaction forces.
In single-molecule manipulation, the coordinate measured is the change in vertical distance between the AFM tip and
sample surface. The biological sample is typically absorbed onto a substrate surface mounted on the AFM piezoelectric
S.S. Wijeratne • N.C. Harris • C.-H. Kiang (*)
Department of Physics and Astronomy, Rice University Houston, Houston, TX 77005, USA
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_3, # The Society for Experimental Mechanics, Inc. 2013
19
actuator, which is controlled by an ultrafast feedback loop, moves the stage vertically to change the tip-sample distance.
Once the probe contacts the sample surface, molecules may adsorb to the AFM tip via either a specific interaction, as is the
case with functionalized AFM probes, or nonspecific interaction, as is the case with DNA and large protein molecules. The
probe is then retracted, extending the attached molecule. The molecule, attached at one end to the substrate and at the other
to the probe, is pulled by the cantilever, causing the cantilever to bend (see Fig. 3.1). The bending of the cantilever is
monitored using an optical lever system and converted to molecular force based on the spring constant of the cantilever and
Hooke’s Law,
F ¼ ksDz; (3.1)
where F is the force (pN), ks is the spring constant of the cantilever (pN/nm), Dz is the cantilever displacement (nm). Dz isdetermined by Dz ¼ VD, where V is the voltage (V) and D is the deflection sensitivity (nm/V). The ability to precisely and
accurately control the tip-sample distance, to move the piezo actuator at a desired speed or maintain a constant force, is
required for single-molecule manipulation experiments. For this reason, modern single-molecule AFMs are equipped with
an independent capacitive sensor that monitors actual stage displacement within an ultrafast feedback loop. Piezo position,
l, is related to molecular end-to-end extension, z, by
z ¼ l� Dz: (3.2)
Therefore, the data are usually presented as force-extension curves.
3.3 Elasticity Models of Biomolecules
In single-molecule manipulation, an external force is applied to an individual molecule attached between a substrate surface
and a flexible AFM cantilever. The mechanics of the molecular response can be described using one-dimensional polymer
elasticity models, of which the two most commonly used are the freely jointed chain (FJC) and the wormlike chain (WLC)
models. The FJC model assumes a polymer chain consisting of n inextensible Kuhn segments of characteristic length lkconnected via freely rotating joints (see Fig. 3.2a). The Kuhn segments are assumed to be orientationally independent, with
no interaction between segments, resulting in an elastic response to the applied force [14],
zðFÞ ¼ lc cothFlkkBT
� �� kBT
Flk
� �; (3.3)
where lc ¼ nlk is the contour length of the polymer, kB is the Boltzmann constant, and T is the absolute temperature. The FJC
model only takes into account the entropic contribution of the polymer chain up to the contour length lc. However, at highforces, it was observed that the enthalpic contribution of individual Kuhn segments resulted in a deviation from the
z
λ
Δz
Cantilever
Stage
Fig. 3.1 AFM single-
molecule manipulation
experiment. One end of the
molecule is attached to the
cantilever tip and the other
end to a gold substrate. The
cantilever spring obeys
Hooke’s law, whereas the
DNA molecule follows the
wormlike chain (WLC)
model (see text)
20 S.S. Wijeratne et al.
non-extensible model [15]. The extensible FJC model (eFJC) [15, 16] accounts for the finite stretch modulus of Kuhn
segments by modeling each segment as a spring with elasticity kseg (see Fig. 3.2b),
zðFÞ ¼ lc cothFlkkBT
� �� kBT
Flk
� �1þ F
kseglk
� �: (3.4)
The WLC model treats a polymer molecule as a homogenous elastic rod, or a wormlike chain, characterized by its
contour length, lc, and persistence length, lp (see Fig. 3.2c). The persistence length, lp, characterizes the bending stiffness ofthe WLC, which assumes for lengths longer than lp, the correlation between tangents to the polymer is lost. The WLC model
is used to fit the force-extension data (Fig. 3.3) to determine the parameters that represent the bending characteristics of the
molecule [17, 18, 19, 20],
FðzÞ ¼ kBT
lp
1
4ð1� zlcÞ2 �
1
4þ z
lc
" #: (3.5)
lk
kseg
lk
lp
a b c d
FJC eFJC WLC eWLC
lp
Fig. 3.2 Polymer elasticity models commonly used to interpret in single-molecule manipulation data. (a) The FJC consists of orientationally
independent, inextensible Kuhn segments of length lk connected via freely rotating joints. (b) The eFJC model accounts for the enthalpic stretching
of Kuhn segments by modeling each segment as a spring with elasticity kseg. (c) The WLC models a polymer molecule as a flexible rod with
stiffness characterized by the persistence length, lp. (d) The extensible WLC (eWLC) model considers the flexible rod in WLC stretchable
0 100 200 300
Separation (nm)
0
200
400
600
For
ce (
pN)
Fig. 3.3 Force-extension curve of titin (I27)8 with WLC model (dashed lines) fit to each individual domain stretching event
3 Principles Involved in Interpreting Single-Molecule Force Measurement of Biomolecules 21
The mechanical extensibility of double-stranded DNA (dsDNA) (Fig. 3.4) is best described by the extensible WLC
model (eWLC),
zðFÞ ¼ lp 1� 1ffiffiffiffiffiffiffiffiffiffiffiffi4blpF
p þ F
K
!; (3.6)
where b ¼ ð1=kBTÞ and K is the elastic stretch modulus for dsDNA.
3.4 Thermodynamic Property from Analysis of Single-Molecule Manipulation Data
3.4.1 Bell’s Model
One commonly used method to obtain thermodynamic data from single-molecule manipulation experiments using an
extension of Bell’s model, was originally used to quantify the effect of applied force in the context of cell-cell adhesion.
According to Bell’s model [21], the lifetime, t, of a bond being stretched by external force is given by,
t ¼ t0 exp½bðE0 � gFÞ�; (3.7)
where 1/t0 is the natural frequency of the atoms in the solid, E0 is the bond energy and g is a parameter dependent on the
structure of the solid. While Bell’s model has been shown to fit data from single-molecule experiments in some cases, it
sometimes fails over broader ranges of pulling velocity and when trying to fit full unfolding force probability distributions.
Other approaches, which assume a particular nonlinear free energy potential with Kramers theory, have been argued to be
able to more accurately reproduce unfolding force distributions from single-molecule experiments [22, 23]. These are
phenomenological approaches, and the results depend largely on parameter fitting.
3.5 Nonequilibrium Work Theorem
In 1997, Christopher Jarzynski derived the nonequilibrium work theorem [24], relating the work performed during
a nonequilibrium process to the corresponding equilibrium free energy difference. Jarzynski’s equality is suitable
for analyzing single-molecule manipulation data, where the measured work value is on the order of thermal fluctuations.
To elucidate how Jarzynski’s equality can be used here, let’s consider the equality using the treatment laid
0 500 1000 1500
Extension (nm)
0
100
200
300
400
For
ce (
pN)
Experimental Data
eFJC
FJC
WLC
eWLC
Fig. 3.4 Experimental
force-extension data for the
stretching of l-dsDNAfitted with different
one-dimensional
polymer models
22 S.S. Wijeratne et al.
out in Ref. [25], for the context of a single-molecule manipulation pulling experiment (Fig. 3.1). For this process,
Jarzynski’s equality states [24, 25],
he�bWi ¼ðdWrðWÞe�bW ¼ e�bDG: (3.8)
The brackets represent an average over infinite realizations of the process. This method allows us to obtain the entire free
energy curve; however, the results are dependent on high quality data and therefore, time consuming.
3.6 Conclusions
Single-molecule manipulation is an emerging technique with the capability to unravel a wealth of information that was
previously outside the realm of real experiments. The possibilities of the biological phenomenon that can be studied are
seemingly endless. We can use single-molecule manipulation to quantify the mechanics and energetics that underly protein
folding and DNA melting. Equilibrium thermodynamics of protein folding can be obtained. We are now moving forward to
apply these techniques to complex biomolecular systems and molecular-cellular, where information about the interactions
and mechanics are of interest. The analysis techniques are easily ported to apply to any force-extension data, and promise to
yield an abundance of information in the years to come.
Acknowledgments We thank NSF DMR-0907676 and Welch Foundation No. C-1632 for support.
References
1. Rief M, Gautel M, Oesterhelt F, Fernandez JM, Gaub HE (1997) Reversible unfolding of individual titin immunoglobulin domains by AFM.
Science 276:1109–1112
2. Harris NC, Song Y, Kiang C-H (2007) Experimental free energy surface reconstruction from single-molecule force spectroscopy using
Jarzynski’s equality. Phys Rev Lett 99:068101
3. Botello E, Harris NC, Sargent J, Chen W-H, Lin K-J, Kiang C-H (2009) Temperature and chemical denaturant dependence of forced unfolding
of titin I27. J Phys Chem B 113:10845–10848
4. Calderon CP, Harris NC, Kiang C-H, Cox DD (2009) Analyzing single-molecule manipulation experiments. J Mol Recognit 22:356
5. Chen W-S, Chen W-H, Chen Z, Gooding AA, Lin K-J, Kiang C-H (2010) Direct observation of multiple pathways of single-stranded DNA
stretching. Phys Rev Lett 105:218104
6. Florin E-L, Moy VT, Gaub HE (1994) Adhesion forces between individual ligand-receptor pairs. Science 264:415–417
7. Lee GU, Kidwell DA, Colton RJ (1994) Sensing discrete streptavidin-biotin interactions with atomic force microscopy. Langmuir 10:354–357
8. Lee GU, Chrisey LA, Colton RJ (1994) Direct measurement of the forces between complementary strands of DNA. Science 266:771–773
9. Ashkin A, Dziedzic JM, Yamane T (1997) Optical trapping and manipulation of single cells using infared laser beams. Nature 330:769–771
10. Kuo SC, Sheetz MP (1993) Force of single kinesin molecules measured with optical tweezers. Science 260:232–234
11. Wang N, Butler JP, Ingber DE (1993) Mechanotransduction across the cell surface and through the cytoskeleton. Science 260:1124–1127
12. Evans E (1991) Entropy-driven tension in vesicle membranes and unbinding of adherent vesicles. Langmuir 7:1900–1908
13. Helm CA, Knoll W, Israelachvili JN (1991) Measurement of ligand-receptor interactions. Proc Natl Acad Sci USA 88:8169–8173
14. Flory PJ (1969) Statistical mechanics of chain molecules. Interscience Publishers, New York
15. Smith SB, Cui YJ, Bustamante C (1996) Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA
molecules. Science 271:795–799
16. Smith SB, Finzi L, Bustamante C (1992) Direct mechanical measurements of the elasticity of the single DNA molecules by using magnetic
beads. Science 258:1122–1125
17. Bustamante C, Marko JF, Siggia ED, Smith S (1994) Entropic elasticity of lambda-phage DNA. Science 265:1599–1600
18. Marko JF, Siggia ED (1995) Stretching DNA. Macromolecules 28:8759–8770
19. Calderon CP, Chen W-H, Lin K-J, Harris NC, Kiang C-H (2009) Quantifying DNA melting transitions using single-molecule force
spectroscopy. J Phys Condens Matter 21:034114
20. Calderon CP, Harris NC, Kiang C-H, Cox DD (2009) Quantifying multiscale noise sources in single-molecule time series. J Phys Chem B
113:138–148
21. Bell GI (1978) Models for the specific adhesion of cells to cells. Science 200:618–627
22. Dudko OK, Hummer G, Szabo A (2006) Intrinsic rates and activation free energies from single-molecule pulling experiments. Phys Rev Lett
96:108101
23. Dudko OK, Mathe J, Szabo A, Meller A, Hummer G (2007) Extracting kinetics from single-molecule force spectroscopy: Nanopore unzipping
of DNA hairpins. Biophys J 92:4188–4195
24. Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78:2690–2693
25. Jarzynski C (2006) Work fluctuation theorems and single-molecule biophysics. Prog Theor Phys Suppl 165:1–17
3 Principles Involved in Interpreting Single-Molecule Force Measurement of Biomolecules 23
Chapter 4
Measurement of the Gold-Gold Bond Rupture Force at 4 K
in a Single-Atom Chain Using Photon-Momentum-Based
Force Calibration
Douglas T. Smith and J.R. Pratt
Abstract We present instrumentation and methodology for simultaneously measuring force and displacement at the atomic
scale at 4 K. The technique, which uses a macroscopic cantilever as a force sensor and high-resolution, high-stability fiber-
optic interferometers for displacement measurement, is particularly well-suited to making accurate, traceable measurements
of force and displacement in nanometer- and atomic-scale mechanical deformation experiments. The technique emphasizes
accurate co-location of force and displacement measurement and measures cantilever stiffness at the contact point in situ at
4 K using photon momentum. We present preliminary results of measurements made of the force required to rupture a single
atomic bond in a gold single-atom chain formed between a gold flat and a gold tip. Finally, we discuss the possible use of the
gold-gold bond rupture force as an intrinsic force calibration value for forces near 1 nN.
4.1 Introduction
The study of nanoscale contacts and nanowires is of great interest in many areas of nanotechnology, because these structures
often exhibit electronic and mechanical properties that vary dramatically from macroscopic structures made from the same
materials. Most notable perhaps is the quantization of electric current through quasi-one-dimensional structures, a phenom-
enon first discussed by Landauer [1, 2] and the topic of many experimental, theoretical, and computational studies performed
since then. Often electrical conductivity, G, is observed to be quantized in units of G0 ¼ 2e2/h, where e is the charge on theelectron and h is Planck’s constant. For a comprehensive review of these studies, and the experimental techniques used to
perform them, see Agraıt et al. [3]. More recently, there have been both experimental and computation studies of stable non-
integer conduction states in nanowires and single-atom chains (an extended string of atoms that is only one atom in diameter)
[4]. In addition, nanowires and single-atom chains can display unusual and sometimes highly reproducible mechanical
behavior, and have been proposed as possible force calibration reference systems for forces at the nanonewton level and
below [5]. In this work, we report new experimental measurements of the force required to break the bond between two Au
atoms in a single-atom chain at 4 K, using the conductance of the chain as an indicator of the chain’s physical configuration.
4.2 Experimental Method
We performed electrical and mechanical studies of Au single-atom chains under vacuum at 4 K using an experimental
platform we refer to as a feedback-stabilized break junction (FSBJ) [6]. The instrument is shown schematically in Fig. 4.1.
The heart of the system is the point of contact between the tip of a Au wire and a Au flat, a detail of which is shown in the
upper right corner of the figure. The Au wire is mounted on a nanopositioning stage (“z-axis”) that allows the wire tip to
make and break contact with the Au flat, and the Au flat is positioned on a lateral positioning stage (“x-axis”) that allows the
D.T. Smith (*)
Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
e-mail: [email protected]
J.R. Pratt
Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_4, # The Society for Experimental Mechanics, Inc. 2013
25
Au tip to contact different locations on the Au flat. Parallel to the Au wire is a glass optical fiber the end of which has been
cleaved to form a smooth surface perpendicular to the fiber axis. This cleaved surface is aligned to be parallel to the Au flat,
and is positioned such that when the Au wire tip contacts the flat, the end of the fiber is approximately 100–200 mm away
from the flat. The fiber and the Au wire are mounted securely in a glass double-bore ferrule so that they move together. The
parallel glass and Au surfaces form a Fabry-Perot cavity that is part of a fiber interferometer system located outside of the
cryo-vacuum chamber.
Details of the design and performance of the interferometer are described elsewhere [7], but a key feature is that it
is optimized for long-term stability and is able to detect changes in the length of the Fabry-Perot cavity smaller than 5 pm.
The output of the interferometer system is used to create closed-loop control of the z-axis positioner, and hence the position
of the Au tip relative to the Au flat, with the same long-term stability and precision. Figure 4.2 shows the level of control over
Fig. 4.1 A schematic representation of the feedback-stabilized break junction apparatus. The inset in the upper right corner shows an enlargement
of the break junction region, with the Fabry-Perot cavity and Au probe tip. The break junction experiments are performed in vacuum at 4 K
Fig. 4.2 Observed changes in the length of a Fabry-Perot cavity, as measured by a fiber-optic interferometer system, as the setpoint of a feedback
control loop is varied step-wise by increments corresponding to 500, 100, 50, 10 and 5 pm. The inset is an enlargement of the data for time>200 s.
5 pm changes in cavity length can be clearly resolved
26 D.T. Smith and J.R. Pratt
the cavity length that we achieve; the setpoint of the control loop was changed by increments corresponding to step-wise
movements of the z-axis positioner of 500, 100, 50, 10 and 5 pm, and the data show the observed change in cavity length.
A change in position of 5 pm is clearly visible. This level of long-term stability allows us to draw out gold single-atom chains
and study their electronic and mechanical properties in detail. Individual chains are typically held for 1 or 2 min, but could
often be maintained for 10 min or more. Figure 4.3 presents typical conductance data for a gold nanocontact as the Au tip
position is varied, with movements both toward the Au flat and away from it; a constant 5 mV bias voltage is applied across
the contact, and current is measure with a conventional current preamplifier. (For 5 mV bias, the conductivity G0
corresponds to a current of approximately 390 nA). Stable conduction states are observed for both integer and non-
integer multiples of G0. Conductance drops to zero when the Au single-atom chain (present when G � 1 G0) breaks; a
measureable conductance returns when the Au tip advances and reforms a contact.
4.3 Break Junction Force Measurement
In order to measure the mechanical properties of gold nanowires and single-atom chains, and in particular the tensile force at
which a gold-gold bond in a single-atom chain ruptures and the chain breaks, the experimental arrangement in Fig. 4.1 was
modified to include a cantilever force sensor; the basic design is shown in Fig. 4.4. Here, the Au flat has been replaced by a
glass cantilever that has been gold-coated on both sides; it is shown in side view in the figure. The cantilever is
approximately 2 mm wide, 8 mm long and 100 mm thick, and is clamped at its base in an electrically insulating mount.
An electrical connection at its base allows for the application of a bias voltage across the junction and measurement of
current through the junction. On the front (left) side of the cantilever, the arrangement is identical to the previous instrument,
with an interferometer cavity beside the Au wire to measure and control the position of the Au tip relative to the front surface
of the cantilever. On the back side of the cantilever, a second optical fiber, which is securely mounted in a glass ferrule
attached to the same block as the cantilever base, forms a Fabry-Perot cavity for a second, independent interferometer
system that measures the deflection of the cantilever and hence the force between the Au tip and the flat Au surface on the
front of the cantilever once the stiffness of the cantilever at that location has been determined.
Accurate determination of the cantilever stiffness at the location where the Au tip contacts the Au-coated cantilever
surface is critical to making accurate measurements of the interaction force at the contact. Many mechanical aspects of the
break junction assembly can change when it is cooled from room temperature to 4 K, such as the dimensions of the cantilever,
the mechanical properties of the materials that comprise the cantilever, the clamping conditions at the base of the cantilever
and the positions of the probe tip and optical fibers relative to the base of the cantilever. As a result, making a measurement
of cantilever stiffness at room temperature and assuming that that value was correct at 4 K was not considered to be
sufficiently reliable. Instead, a method was devised to measure the cantilever stiffness at the point of contact in situ at 4 K.
0 500 1000 1500Time (s)
0
1
2
3
4
5
Con
duct
ance
Qua
nta
(2e2
/h)
Fig. 4.3 The conductivity of
an Au break junction, in units
of the conductance quantum
G0 ¼ 2e2/h (where e is thecharge on the electron and
h is Planck’s constant), as the
Au probe contacts the Au flat
and withdraws several times.
Stable conduction states are
observed for both integer
and non-integer values of G0
4 Measurement of the Gold-Gold Bond Rupture Force at 4 K in a Single-Atom. . . 27
With this method, the light source for the optical fiber at the back of the cantilever was temporarily changed outside
the cryo-vacuum chamber during an experiment from the very low-level (� 200 mW) precision infrared laser used in the
interferometer system to a much higher-power incoherent superluminescent diode (SLD) light source with center wave-
length 1,550 nm whose intensity was modulated sinusoidally between 2 and 12 mW at a frequency well below the resonant
frequency of the cantilever. This produced a sinusoidally varying photon momentum force on the cantilever, and the
mechanical response of the cantilever was monitored using the fiber interferometer on the opposite side of the cantilever.
Analysis of this response allowed a determination of the cantilever stiffness at the contact point of 43 N/m. Through careful
consideration of alignment issues and potential sources of error inherent in measuring the photon flux striking the cantilever
[8] and the reflectivity of the Au surface on the cantilever, we estimate the accuracy of the stiffness measurement to be
approximately�3 N/m. With knowledge of the cantilever stiffness, it is then possible to study various mechanical properties
of gold nanocontacts and single-atom chains, such as their stiffness and tensile strength. By measuring the abrupt change in
the cantilever position when a single-atom chain breaks, we have been able to make direct measurements of the Au-Au bond
breaking force, and find it to be consistent with values obtained by density functional theory (DFT) calculations [9] to within
experimental error.
Acknowledgments The authors gratefully acknowledge the many DFT calculations performed by Francesca Tavazza, Lyle Levine, and Anne
Chaka; those calculations were invaluable in the interpretation of the experimental results. This work was funded in part by the Innovations in
Measurement Science program at the National Institute of Standards and Technology.
References
1. Landauer R (1957) Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J Res Dev 1:223
2. B€uttiker M, Imry I, Landauer R, Pinhas S (1985) Generalized many-channel conductance formula with application to small rings. Phys Rev B
31:6207
3. Agraıt N, Yeyati AL, van Ruitenbeek JM (2003) Quantum properties of atomic-sized conductors. Phys Rep 377:81
4. Tavazza F, Smith DT, Levine LE, Pratt JR, Chaka AM (2011) Electron transport in gold nanowires: stable 1-, 2- and 3-dimensional atomic
structures and noninteger conduction states. Phys Rev Lett 107:126802
5. Pratt JR, Shaw GA, Smith DT (2010) Nanomechanical standards based on the intrinsic mechanics of molecules and atoms. In: Proceedings of
the SEM annual conference, Indianapolis, IN, USA, 7–10 June 2010
Fig. 4.4 A schematic representation of the feedback-stabilized break junction instrument after modification to incorporate a cantilever force
sensor (shown here in side view). The cantilever is 2 mm wide by 100 mm thick, and its free length is 8 mm. The optical fibers and Au probe are
located approximately 1 mm down from the free end of the cantilever, and positioned near its center axis; care was taken to assure that the Au
probe and both optical fibers were located the same distance from the base of the cantilever
28 D.T. Smith and J.R. Pratt
6. Smith DT, Pratt JR, Tavazza T, Levine LE, Chaka AM (2010) An ultra-stable platform for the study of single-atom chains. J Appl Phys
107:084307
7. Smith DT, Pratt JR, Howard LP (2009) A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement
measurement. Rev Sci Instrum 80:035105
8. Pratt JR, Wilkinson P, Shaw G (2011). In: Proceedings of the ASME 2011 international design engineering technical conferences (DETC2011-
47455), Washington, DC, USA, 29–31 Aug 2011
9. Tavazza F, Levine LE, Chaka AM (2009) Elongation and breaking mechanisms of gold nanowires under a wide range of tensile conditions.
J Appl Phys 106:043522
4 Measurement of the Gold-Gold Bond Rupture Force at 4 K in a Single-Atom. . . 29
Chapter 5
A Precision Force Microscope for Biophysics
Gavin M. King, Allison B. Churnside, and Thomas T. Perkins
Abstract Mechanical drift between an atomic force microscope (AFM) tip and sample is a longstanding problem that limits
tip-sample stability, registration, and the signal-to-noise ratio during imaging. We demonstrate a robust solution to drift that
enables novel precision measurements, especially of biological macromolecules in physiologically relevant conditions. Our
strategy – inspired by precision optical trapping microscopy – is to actively stabilize both the tip and the sample using locally
generated optical signals. In particular, we scatter a laser off the apex of commercial AFM tips and use the scattered light to
locally measure and thereby actively control the tip’s three-dimensional position above a sample surface with atomic
precision in ambient conditions. With this enhanced stability, we overcome the traditional need to scan rapidly while
imaging and achieve a fivefold increase in the image signal-to-noise ratio. Finally, we demonstrate atomic-scale (�100 pm)
tip-sample stability and registration over tens of minutes with a series of AFM images. The stabilization technique requires
low laser power (<1 mW), imparts a minimal perturbation upon the cantilever, and is independent of the tip-sample
interaction. This work extends atomic-scale tip-sample control, previously restricted to cryogenic temperatures and
ultrahigh vacuum, to a wide range of perturbative operating environments.
5.1 Introduction
Scanning probe microscopes (SPMs) are major enabling tools underlying scientific discovery and technological innovation
at nanometer length scales and are applied across diverse fields. This large family of instruments has captured the
imagination of scientists and the public alike in their ability to image and manipulate individual atoms and molecules.
Since their invention nearly three decades ago, SPMs have proven to be highly versatile tools because they are capable of
operating in a wide variety of conditions and on numerous types of samples. Along these lines, the SPM’s potential to study
the structure, structural energetics, and structural dynamics of individual biological macromolecules in biologically relevant
conditions (i.e., in fluid at room temperature) have made it an exciting addition to the biophysicist’s tool chest.
Despite its successes in biology, the pinnacle of precision and performance in scanning probe microscopy has only been
achieved in highly isolated non-biological environments. While such high precision SPM instruments have led to outstand-
ing research and iconic images in nanoscience [1] they are operated at cryogenic temperatures and are surrounded by nested
layers of vibration isolation in unoccupied, temperature regulated rooms. These heroic levels of largely passive isolation are
G.M. King (*)
Department of Physics and Joint with Biochemistry, University of Missouri, Columbia, MO 65211, USA
e-mail: [email protected]
A.B. Churnside
JILA, National Institute of Standard and Technology and University of Colorado, Boulder, CO 80309, USA
Department of Physics, University of Colorado, Boulder, CO 80309, USA
T.T. Perkins
JILA, National Institute of Standard and Technology and University of Colorado, Boulder, CO 80309, USA
Department of Molecular, Cellular and Developmental Biology, University of Colorado, Boulder, CO 80309, USA
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_5, # The Society for Experimental Mechanics, Inc. 2013
31
necessary to minimize a major noise source in SPM – unwanted mechanical drift between the scanning probe tip and the
sample. Drift occurs in all scanning probe instruments due to environmental perturbations. When operating such instruments
at liquid helium temperatures, the gold-standard conditions for high precision SPM work, tip-sample drift rates are reduced
to ~0.01 A/min. This extreme instrumental stability facilitates detailed dynamic studies and enables atomic-scale patterning
of matter. In recent work [2], we have shown that it is possible to approach similar levels of tip-sample stability in ambient
“real-world” operating conditions, where instrumental drift rates are typically 1,000-fold higher.
Mechanical drift between an SPM tip and sample limits many aspects of SPM instrument performance and deleteriously
affects diverse applications such as nanopore measurements [3], tip-based nanolithography [4], and high resolution studies
of protein structure [5]. In particular, an atomic force microscope (AFM), the most prominent member of the SPM family,
would benefit from the ability to (1) enhance image resolution by scanning slowly and averaging cantilever response; to (2)
return the tip to a precise feature in an image (e.g., a region of a protein); to (3) hover the tip over a feature for long time
periods to study local dynamics (e.g., conformational fluctuations); and to (4) precisely control the 3D position of the tip
when disengaged from the surface (e.g., force spectroscopy). Unfortunately, none of these important tasks can be achieved
with current AFMs in real-world conditions due to drift. Long-term atomic-scale stability between the tip and sample is
needed to fully exploit the advantages of AFM across a broad array of disciplines.
5.2 Instrumentation
The issue of tip-sample stability has been addressed sporadically in the SPM community, with most researchers focusing on
other means to improve microscope performance such as enhancing tip sharpness or improving the sensitivity of force
detection. In the literature there exists only a handful of drift-compensation methods. Tracking techniques [6–8] can provide
atomic precision in ultrahigh vacuum, but they forfeit scanning or assume unvarying drift rates. Imaging-based techniques
[9] can reduce drift rates to ~500 pm/min in ambient conditions [10], but require predictions of future drift or compensate for
drift only once per image. External optical techniques, applied in one [11, 12] or more dimensions [13–15], have not
achieved atomic-scale tip-sample stability or image registration (<10 nm overlay precision) [15] in ambient conditions.
To surmount the limitations imposed by drift, we developed a unique, ultra-stable AFM measurement platform. Our
approach, which was inspired by precision optical trapping techniques [16–18], establishes a local optical differential
reference frame to control the tip-sample displacement (Fig. 5.1). Briefly, focused lasers of different wavelength (red and
green) locally report tip and sample position by scattering off the apex of the tip itself and a fiducial mark (nanoscale silicon
disk) affixed to the sample plane. Backscattered light is separated by wavelength and collected to yield the 3D position of
each object with atomic precision. This data is used as feedback to piezo stages to actively stabilize the tip position with
Fig. 5.1 Schematic of the ultra-stable AFM technique. (a) Detailed view of the tip and sample shows focused lasers (red and green) scattering offan AFM tip and a nano-scale fiducial mark (silicon disk) engineered into the sample plane. Back-scattered signals were collected and used to
deduce the position of the tip and the sample relative to each laser beam. (b) Two stabilized diode lasers (SDL) at different wavelengths
[l ¼ 810 nm (green), l ¼ 845 nm (red)] were sent into the microscope and focused by a high numerical-aperture (NA ¼ 1.4) objective (Obj).Back-scattered light was efficiently separated from the incoming light by an optical isolator formed by a polarizing beam splitter (PBS) and a
quarter-wave plate (l/4). The signals, at different wavelengths, were separated by dichroic mirrors and detected by independent quadrant
photodiodes (QPD). A third laser [l ¼ 785 nm (blue)] was reflected off the backside of the cantilever for force control. Tip and sample control
were achieved via feedback loops to two piezoelectric (PZT) stages. Blue-shaded components are in optically conjugate planes (Figure reproduced
from Ref. [2] with permission)
32 G.M. King et al.
respect to the sample. The precision of the technique hinges on maintaining extreme 3D differential pointing stability
between the two laser focal volumes. The method requires low laser power (1 mW), is independent of the tip-sample
interaction, and imparts a negligible perturbation on the tip. A third laser (blue) is reflected off the backside of the cantileverto report tip-sample force in a standard optical lever arm arrangement.
5.3 Results
The nascent ultra-stable AFM instrument has achieved an unprecedented level of tip-sample control in ambient conditions.
For example, the instrument has the newfound ability to hover an AFM tip over specific regions of interest with single-
Angstrom stability for time periods on the order of tens of minutes. We demonstrated this ability by using the backscattered
optical signals to measure and actively control the 3D position of an AFM tip 300 nm above the sample surface (Fig. 5.2).
For this demonstration, both backscattered lasers (red and green) were focused onto a silicon tip. We employed the 810-nm
(green) signal for feedback and the 845-nm (red) signal as an independent “out-of-loop” monitor of instrument stability [18].
Stabilities, determined from this out-of-loop monitor, were 26, 39, and 25 pm in x, y, and z, respectively (r.m.s.,
Df ¼ 0.01–10 Hz). Thus, we demonstrated simultaneous lateral and vertical tip control at atomic length scales (Fig. 5.2b).
Histograms of this data provided a complementary analysis and were well fit by Gaussians, with standard deviations of 28 and
26 pm in x and z, respectively. These reported stabilities represent the ultimate positional control between tip and sample that
can be achieved with our current apparatus, and include the uncertainty due to 3D pointing noise between the detection lasers.
Moreover, this direct measurement of tip position is independent of the traditional observable in AFM, cantilever deflection
(Fig. 5.1, blue). Thus, BSD provides a complimentary, local measurement of tip position that is independent of the tip-sample
force.
In addition to the precise 3D tip control, we also achieved a fivefold enhancement of the signal-to-noise ratio (S/N) in
imaging via slow stabilized scanning (Fig. 5.3). For conventional high resolution AFM imaging, the unwanted presence of
lateral drift necessitates fast scanning rates, restricting the ability to average the cantilever response before moving the tip to
the next pixel in the image. Here we demonstrate the potential to improve AFM image quality in real time through stabilized
slow scanning and real-time signal averaging. Specifically, we acquired three 30 � 30 nm2 images of a single 5-nm Au
nanosphere at increasing averaging times per pixel (0.2, 2, and 20 ms for Fig. 5.4b–d, respectively) in contact mode
(F � 200 pN). Improvement in image quality is visually apparent. Quantitatively, line scans through the center of each
image (Fig. 5.3d) revealed a fivefold reduction in the r.m.s. surface roughness over the center of the nanosphere. We note that
for many applications, real-time averaging is superior to post processing of the images; it does not require assumptions of
sample periodicity, symmetry, or image-to-image registration.
Finally, we designed an experiment to directly demonstrate atomic-scale tip-sample stability and registration. It is this
registration and stability, not resolution, that is the unique feature of the instrument. Resolution – the ability to differentiate
two neighboring objects – has been reported at the atomic scale in ambient conditions [19]; such resolution, however, is not
Fig. 5.2 Ultra-stable “hovering” an AFM tip 300 nm above a sample surface in room temperature air. (a) Tip position records versus time were
low-pass filtered to 10 Hz and offset vertically for clarity [x (red), y (blue), z (green)]. To yield the most accurate measurement of stability,
positions were determined by an “out-of-loop” monitor laser while the tip was actively stabilized with the other laser. (b) A scatter plot of the tip
position in the x-z plane from the 100 s record in (a). Histograms of the data projected onto the x and z axes were well fit by Gaussians with standarddeviations of 28 and 26 pm, respectively (Figure reproduced from Ref. [2] with permission)
5 A Precision Force Microscope for Biophysics 33
required to demonstrate atomic-scale stability and registration. Rather, what is needed is excellent localization precision
(i.e., the ability to determine the center of a single object). Localization precision always exceeds resolution. Indeed,
localization precision of 1/10th of a pixel and 1/100th of the resolution limit is common in optical microscopy [20, 21]. AFM
images are a convolution of tip and sample geometry. Thus, to demonstrate tip-sample stability, we tracked the center of an
object through a series of successive images.
Such image-based verification of stability and registration requires a stationary, unchanging object that can withstand
over an hour of continuous imaging; apparent motion could arise from instability of the object relative to the cover slip [17]
and from tip or sample degradation. To satisfy these requirements, we used single 5-nm diameter Au nanospheres, which are
known to be robust and incompressible [22], and imaged with silicon nitride tips at modest forces (~200 pN). We acquired
seven sequential images over 82 min. Images at the beginning, middle, and end of the time course are displayed in
Fig. 5.4a–c.
To track the nanosphere’s location with subpixel precision, we determined its center point using a 2D cross-correlation.
Specifically, we used the first image (Fig. 5.4a) as the kernel to analyze the subsequent six images. We fit the central 5 nm of
the cross-correlation to a 2D Gaussian and localized the peak with excellent precision [<10 pm (1/50th pixel)] in each axis
due, in part, to the high S/N of the images. From this analysis, we deduced the nanosphere’s location [e.g., xp ¼ 25.199
� 0.004 nm (peak � sfit)].
This precise cross-correlation analysis tracked the nanosphere’s location during 82 min of continuous imaging (Fig. 5.4e).
The precision of this control (and analysis technique) is further verified by small average deviations – 23 and 40 pm in x andy, respectively – of the nanosphere’s location from the linear fits. The residual lateral drift rates were a mere 4 and 5 pm/min
Fig. 5.3 Real-time signal averaging coupled with stabilized scanning improves signal-to-noise ratio in AFM images. (a–c) Sequential images of a
5-nm gold nanosphere taken with increased averaging. Specifically, the averaging times per pixel were 0.2, 2, and 20 ms for panels (a–c),
respectively. (d) Line scans through the center region of images [b (light purple), c (orange), and d (dark purple)] (Figure reproduced from Ref. [2]
with permission)
Fig. 5.4 Ultra-stable AFM imaging and residual drift analysis. (a–c) Images of a 5-nm gold nanosphere taken at times T ¼ 0, 41, and 82 min,
respectively. (d) The 2D cross-correlation between the first and last images. (e) Relative lateral position of the nanosphere plotted versus time
as determined by cross-correlation analysis [x (red), y (blue)]. From linear fits to the data (lines), we deduced residual lateral drift rates of 4 and
5 pm/min in x and y, respectively (Figure reproduced from Ref. [2] with permission)
34 G.M. King et al.
in x and y, representing a 250-fold reduction of the inherent instrumental drift rate and a 100-fold improvement over current
state of the art [10]. Indeed, these residual rates, achieved in air at room temperature, are close to those found in cryogenic
conditions (~1 pm/min, 8 K) [23]. Further, these rates represent an upper bound for the actual drift since the analysis assumes
a stationary object and no degradation of the tip or sample.
5.4 Conclusions
Precision measurements in SPM are currently confined to highly isolated non-biological research environments where
external perturbations are minimized via mostly passive means. In this paper, we demonstrated a robust and active ultra-
stable measurement platform based on generating a local differential laser-based reference frame for tip and sample position
detection. With an ultra-stable AFM, images can be obtained at high resolution while maintaining atomic-scale registration
between the tip and the sample during and after the scan. Hence, regions of interest can be identified in a scan and later
interrogated in detail. In addition to imaging, our ultra-stable SPM measurement platform allows for precision 3D tip
control. Thus, even when the tip is disengaged from the sample surface and the traditional SPM feedback mechanisms
(i.e. force, current) vanish, we maintain the ability to monitor the position and maneuver the tip with a high degree of
precision.
On a conceptual level, what we have developed is a robust optical “tripod” for AFMmeasurements. Our work extends the
full utility and precision of this widely used tool to a wide variety of real-world operating conditions. For example, we have
recently extended our ultra-stable AFM’s capabilities into room temperature fluid to study proteins in biologically relevant
conditions. We anticipate that the newfound capabilities of ultra-stable AFM will find applications in a variety of fields
ranging from fundamental studies in single molecule biophysics to tip-based nanofabrication.
Acknowledgments This work was supported by a Burroughs Wellcome Fund Career Award at the Scientific Interface (GMK) and a Burroughs
Wellcome Fund Career Award in the Biomedical Sciences (TTP), a National Research Council Research Associateship Award (GMK), an NIH
Molecular Biophysics Training Scholarship (ABC, T32 GM-065103), a Butcher Grant, the NSF (grant #: 0923544) and NIST. Mention of
commercial products is for information only; it does not imply NIST’s recommendation or endorsement, nor does it imply that the products
mentioned are necessarily the best available for the purpose. TTP is a staff member of NIST’s Quantum Physics Division.
References
1. Eigler DM, Schwizer EK (1990) Positioning single atoms with a scanning tunneling microscope. Nature 344:524–526
2. King GM et al (2009) Ultrastable atomic force microscopy: atomic-scale stability and registration in ambient conditions. Nano Lett 9:1451
3. King GM, Golovchenko JA (2005) Probing nanotube-nanopore interactions. Phys Rev Lett 95:216103
4. Piner RD et al (1999) “Dip-Pen” nanolithography. Science 283:661–663
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Appl Phys Lett 90:203103
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Sci Eng 3:199–207
11. Proksch R, Dahlberg ED (1993) Optically stabilized, constant-height mode-operation of a magnetic force microscope. J Appl Phys
73:5808–5810
12. Sparks AW, Manalis SR (2004) Scanning probe microscopy with inherent disturbance suppression. Appl Phys Lett 85:3929–3931
13. Teague EC (1989) The National-Institute-of-Standards-and-Technology molecular measuring machine project – metrology and precision
engineering design. J Vac Sci Technol B 7:1898–1902
14. Moon EE, Smith HI (2006) Nanometer-precision pattern registration for scanning-probe lithographies using interferometric-spatial-phase
imaging. J Vac Sci Technol B 24:3083–3087
15. Moon EE et al (2007) Atomic-force lithography with interferometric tip-to-substrate position metrology. J Vac Sci Technol B 25:2284–2287
16. Nugent-Glandorf L, Perkins TT (2004) Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane
detection. Opt Lett 29:2611–2613
17. Carter AR et al (2007) Stabilization of an optical microscope to 0.1 nm in three dimensions. Appl Opt 46:421–427
18. Carter AR et al (2007) Back-scattered detection provides atomic-scale localization precision, stability, and registration in 3D. Opt Express
15:13434–13445
5 A Precision Force Microscope for Biophysics 35
19. Schimmel T et al (1999) True atomic resolution under ambient conditions obtained by atomic force microscopy in the contact mode. Appl Phys
A: Mater Sci Process 68:399–402
20. Gelles J et al (1988) Tracking kinesin-driven movements with nanometre-scale precision. Nature 331:450–453
21. Yildiz A et al (2003) Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization. Science 300:2061–2065
22. Vesenka J et al (1993) Colloidal gold particles as an incompressible atomic force microscope imaging standard for assessing the compress-
ibility of biomolecules. Biophys J 65:992–997
23. Stipe BC et al (1998) Single-molecule vibrational spectroscopy and microscopy. Science 280:1732–1735
36 G.M. King et al.
Chapter 6
Hydrodynamic Force Compensation for Single-Molecule Mechanical
Testing Using Colloidal Probe Atomic Force Microscopy
Gordon A. Shaw
Abstract The use of colloidal probes for mechanical testing of single molecules in an atomic force microscope (AFM)
provides an attractive alternative to conventional microfabricated AFM cantilever force sensors, in that they have a much
greater surface area available for specific binding to a target molecule. This is of particular importance for molecules have a
low binding probability or are sterically inhibited from binding in some way. There are, however, several features unique to
colloidal probe force measurements performed in a fluid environment, one of which is the presence of hydrodynamic forces
acting on the sphere at the tip of the cantilever as it moves through the fluid. This force must be subtracted from the total
measured force to isolate the molecular interaction of interest. Herein, a method is described to perform such a correction
based on Brenner’s equation, and the method is demonstrated on data from the mechanical testing of a single DNAmolecule.
6.1 Introduction
The atomic force microscope (AFM) allows force metrology to be performed in the force range from piconewtons to
micronewtons using a microfabricated cantilever spring as a force sensor. By measuring a displacement signal near the end
of the cantilever (most commonly from an optical lever system), and using Hooke’s law, the force applied at the end of the
cantilever can be determined for small displacements. The application of metrological principles to the accurate measure-
ment of force with the AFM has been ongoing [1, 2], with some emphasis being placed on the measurement of force using
colloidal probes [3]. These probes are a variant of the microfabricated AFM cantilever that have a micrometer-scale sphere
attached to the end, and are useful for probing a larger surface area than conventional AFM probes, the tips of which have
radii of curvature on the order of only 10 nm. Because of this larger surface area, viscous drag forces near the static fluid
layer at the interface between a fluid and solid surface are somewhat enhanced for colloidal probes relative to conventional
AFM probes. As a result, an effective strategy for subtracting the viscous drag force is required if the interaction between the
colloidal probe’s sphere and a surface is to be measured.
The viscous drag force on a colloidal probe as it approaches a surface can be modeled using Brenner’s equation for low
Reynold’s number fluids. At probe-surface separations that are small relative to the radius of the sphere [4],
FH ¼ 6p�b2U=a (6.1)
Where � is the viscosity of the medium, b is the radius of the sphere, U is the velocity at which the sphere moves relative to
the surface, and a is the separation between the sphere and surface at the closest point, as illustrated in Fig. 6.1. This
approximate solution has been used in two different methods as a way to calculate a force to calibrate the spring constant of
colloidal probe cantilevers, and shows reasonable agreement with other spring constant calibration methods [4]. Importantly,
the separation between the probe and surface must be large enough (approximately 150 nm for a gold-coated probe retracting
from a glass surface [5]) that forces associated with the electrochemical double layer are negligible for (6.1) to be useful.
G.A. Shaw (*)
Physical Measurement Laboratory, U.S. National Institute of Standards and Technology, Gaithersburg, MD, USA
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_6, # The Society for Experimental Mechanics, Inc. 2013
37
6.2 Application to DNA Intrinsic Force Reference Molecule
In the particular case of molecular force spectroscopy, a chemically functionalized colloidal probe can be used to bind
one end of a molecule to be stretched. In the current case, this molecule is a 2,820 base pair double-stranded DNA molecule.
The molecule has been designed to be used as a force reference, and the force necessary to complete the half of the
molecule’s overstretch transition [6] is being calibrated in a fashion traceable to the International System of Units (SI).
The DNA is synthesized using pBR 322 as a template, and is terminated at its 50 ends with an amine, and a biotin group. The
amine-terminated end of the molecule is covalently affixed to an aldehyde-functionalized glass surface, and the remainder of
the surface is passivated with amine-terminated polyethylene glycol. A streptavidin-coated colloidal probe is then used to
bind the other end of the DNA molecule to allow the mechanical testing of individual DNA molecules. The force versus
extension curve for one such molecule is shown in Fig. 6.2. The force curve was measured using an Asylum MFP 3D AFM1
in phosphate buffered saline (PBS) at 29�C. Force was determined by multiplying the optical lever signal by cantilever
spring constant, the inverse optical lever sensitivity, and a correction term for colloidal probe geometry [6]. The inverse
optical lever sensitivity was determined by pressing the probe into a rigid surface at high enough forces that the contact
compliance is constant while simultaneously measuring the change in the optical lever signal voltage. The cantilever spring
constant was measured with a laser Doppler vibrometer by applying the thermal calibration method [8, 9].
At distances greater than 150 nm from the surface, the hydrodynamic forces dominate the force at the end of the colloidal
probe until the DNA molecule is stretched into its enthalpic regime. In the region where hydrodynamic force prevail, the
force displacement curve measured by the colloidal probe as it is retracted from the surface can be fit to
Ff ¼ Aþ B=ðsþ CÞ (6.2)
Where A, B, and C are adjustable parameters, and s is the probe surface separation. An optimized fit of this function to the
force curve in Fig. 6.2 is shown as a dashed line. The stretching force from the tethered DNA molecule must also be small in
the fitting regime. The worm-like chain model can be used to calculate the restoring force applied by a double-stranded DNA
molecule stretched from its randomly coiled equilibrium condition [6, 10]. Assuming a persistence length of 47.4 nm [10],
and a contour length of 968 nm calculated assuming a length of 0.342 nm/base pair and adding the length of the primers
attached to the ends of the molecule, the length of the force reference DNA molecule at 1 pN of force is 825 nm. Fitting to
regions in which the DNA is stretched to less than this length effectively minimizes the contribution of the DNA stretching
Fig. 6.1 Illustration of hydrodynamic force acting on a colloidal probe used for single molecule mechanical testing. The velocity and force vectors
illustrated show the case where the colloidal probe is being retracted away from the sample. In this case the hydrodynamic force acts in a direction
opposite the pulling direction. The force a single long polymer molecule exerts on the probe is denoted Fm
1NIST Disclaimer: This article is authored by employees of the U.S. federal government, and is not subject to copyright. Commercial equipment
and materials are identified in order to adequately specify certain procedures. In no case does such identification imply recommendation or
endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the
best available for the purpose.
38 G.A. Shaw
force to the hydrodynamic fit. In addition, at larger separations, the biotin-streptavidin complex attaching the DNAmolecule
to the colloidal probe ruptures, as evidenced by a sharp decrease in force after the end of the overstretch plateau has been
reached. This region of the force curve is used to increase the quality of the fit as well. Subsequently, the hydrodynamic force
can be reconstructed from the coefficients in (6.2) and subtracted from the force data, leaving the molecular force curve.
An uncorrected force curve, hydrodynamic fit, and corrected curve are shown in Fig. 6.2 as are the regions of the curve
used for the hydrodynamic fit. The portions of the curve used for fitting are also indicated. The hydrodynamic force acting on
the colloidal probe at the center of the overstretch plateau is approximately 17 pN, as determined from the curve fit in
Fig. 6.2a. This would seriously affect a measurement of the overstretch force, approximately 70 pN as measured at the center
of the overstretch plateau in Fig. 6.2b. There is significant low frequency noise at small probe surface separations; the effect
is atypically large for in this curve for the purpose of illustration, however it is important to note this effect when calculating
uncertainty. In addition, the curve shown is significantly different from other DNA overstretch data in the literature in
another way. The overstretch appears at a much smaller probe surface separation than would be predicted from its 968 nm
contour length. This is due to the pulling geometry. The DNA molecule examined in this curve is not attached to the nadir of
the colloidal probe, but is rather attached some distance up the side of the sphere, as is schematically illustrated in Fig. 6.1.
In addition, it is being pulled at an angle relative to the surface normal. These effects have previously been noted [10, 11],
however their correction is beyond the scope of the current paper. For the purposes of the hydrodynamic force subtraction, it
is important to check after this geometric correction to ensure that the area used for the hydrodynamic fitting is dominated by
hydrodynamic force and the tensile force on the molecule is less than approximately 1 pN, as described above.
6.3 Conclusion
A procedure for fitting and subtracting hydrodynamic forces from colloidal probe AFM single molecule mechanical testing
experiments is described. If applied correctly, the hydrodynamic correction helps to ensure accurate measurement of
molecular forces in this type of testing. Pitfalls can arise due to low frequency noise, and selection of the data used to do
the curve fitting necessary for the correction. Options for minimizing the impact of these issues on the force data are
outlined, but their contribution must still be considered if an uncertainty analysis is carried out.
References
1. Shaw GA, Kramar JA, Pratt JR (2007) SI-traceable spring constant calibration of microfabricated cantilevers for small force measurement.
Exp Mech 47:143–151
2. Kim M-S, Pratt JR, Brand U, Jones CW (2012) Report on the first international comparison of small force facilities: a pilot study at the
micronewton level. Metrologia 49:70–81
Fig. 6.2 Smoothed AFM force curves before (a) and after (b) subtraction of hydrodynamic force. The experimental data is shown as normal force
measured from cantilever deflection versus the separation between the nadir of the colloidal probe and the functionalized glass surface calculated
by subtracting the cantilever deflection distance from the change in stage position as the DNA is pulled. The location of zero separation is
approximate in these curves. The dashed line in (a) is the fit to the hydrodynamic function, and the fit regions used are marked with horizontalarrows
6 Hydrodynamic Force Compensation for Single-Molecule Mechanical Testing. . . 39
3. Chung K-H, Shaw GA, Pratt JR (2009) Accurate noncontact calibration of colloidal probe sensitivities in atomic force microscopy. Rev Sci
Instrum 80:065107-065107-13
4. Craig VSJ, Neto C (2001) In situ calibration of colloid probe cantilevers in force microscopy: hydrodynamic drag on a sphere approaching a
wall. Langmuir 17:6018–6022
5. Sheth SR, Leckband D (1997) Measurements of attractive forces between proteins and end-grafted poly(ethylene glycol) chains. Proc Natl
Acad Sci USA 94:8399–8404
6. Smith SB, Cui Y, Bustamante C (1996) Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA
molecules. Science 271:795–799
7. Edwards SA, Ducker WA, Sader JE (2008) Influence of atomic force microscope cantilever tilt and induced torque on force measurements.
J Appl Phys 103:064513-064513-6
8. Butt H-J, Jasche M (1995) Calculation of thermal noise in atomic force microscopy. Nanotechnology 6:1–7
9. Gates RS, Pratt JR (2012) Accurate and precise calibration of AFM cantilver spring constants using laser Doppler vibrometry (submitted)
10. Wang MD, Yin H, Landick R, Gelles J, Block SM (1997) Stretching DNA with optical tweezers. Biophys J 72:1335–1346
11. Ke C, Jiang Y, Rivera M, Clark RL, Marszalek PE (2007) Pulling geometry-induced errors in single molecule force spectroscopy
measurements. Biophys J 92:L76–L78
40 G.A. Shaw
Chapter 7
New Insight into Pile-Up in Thin Film Indentation
Kevin Schwieker, James Frye, and Barton C. Prorok
Abstract This work builds involves leveraging our recent thin film mechanics model on the discontinuous transfer of strain
from the film to the substrate. In applying this model with well-defined film and substrate properties we were able to
decouple the effects of elastic modulus and Poisson’s ratio mismatch in the indentation process. In doing so we identified
new insight in the processes of pile-up and strong evidence suggested a dependence on film thickness and ratios of film/
substrate of elastic modulus and Poisson’s ratio. Atomic force microscopy was employed to characterize the degree of pile-
up and correlate it with the above dependencies. We believe these efforts will enable the prediction of the degree of pile-up
and subsequently the removal of its influence in measuring thin film behavior.
7.1 Introduction
Indentation of materials on a macro and micro scale has been a cornerstone of determining mechanical properties, such as
hardness, of materials for the last century. During indentation, a tip with known geometric size and mechanical properties is
pressed into a material. Once loading is complete, the hardness of the indented material is then calculated from the maximum
load applied and the measured contact area from the remaining indent. As the experimentation method has progressed, there
has been a desire to make smaller and less intrusive indents on smaller and smaller scales. Over the last few decades
instrumented indentation on the nano-scale, nanoindentation, has gained attention as a method to extract the hardness and
Young’s modulus of a samples that require higher precision and much lower loads that can be applied by direct human
interaction.
With nanoindentation came the possibility to indent on a sample that consists of a thin layer, or film, of one material on
the surface of a different bulk material, or substrate. The interest in thin films comes from their use in a wide range of
material applications such as optical coatings, very large-scale integrated circuits, anti-corrosion, anti-wear and fuel cells.
Even when the applications are not centered on the mechanical behavior of the thin films, increasing their ability to
withstand processing, and durability during their lifetime is still needed. One current shortcoming of nanoindenting thin
films being widely researched is that as the film’s thickness decreases, the substrate starts to play more of a role in the
properties determined through indentation, even at very low penetration depths of the film. Recent authors [1–7] have
developed theoretical models based on both experimental and finite element analysis that attempt to extract the mechanical
properties of the film, independent of the substrate. While all of these models have their strengths, they also tend to only
work for certain material combinations; such as compliant films on hard substrates, or hard films on compliant substrates.
The goal of this research is to thoroughly review one of the more recent models to of been developed that takes a new
approach in describing the film and substrates composite behavior. This model, developed by Zhou et al. [6, 7] takes into
account that the transfer of energy across the film-substrate interface is not linear, but actually discontinuous; allowing it to
better describe the film’s behavior for a broader range of material combinations. A group of materials were selected for their
similar Poisson’s ratio, but varying Young’s modulus, to have a single thin film layer sputtered on them which also has a
similar Poisson’s ratio to the substrates. The samples were then nanoindented, comparing the Young’s modulus verses
indention depth to the behavior expected through the evaluated model.
K. Schwieker • J. Frye • B.C. Prorok (*)
Department of Mechanical Engineering, Auburn University, Auburn, AL 36849, USA
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_7, # The Society for Experimental Mechanics, Inc. 2013
41
One substantial challenge to nanoindentation is the difficulty in accurately measuring the contact area during displace-
ment, due to how the material being indented can plastically deform around the indenter, causing a change in actual contact
area between the sample and tip, also known as erroneous contact area. If the material is soft it will tend to pile-up around the
indenter tip, causing an increase in contact area, leading to an overestimation of the material’s modulus, and hardness, as
there is more material providing elastic recovery. Harder materials have the tendency to translate their strain further away
from the tip, allowing for a greater volume of material to distribute the deformation, causing the area around the tip to sink-
in, reducing the contact area of the tip. The sink-in effect leads to an underestimation of the material’s modulus, and
hardness. A cross sectional schematic of both effects during indentation, and the resulting top-down view of the recovered
material after unload is shown in Fig. 7.1 [7].
The goal of this research is to thoroughly review one of the more recent models to of been developed that takes a new
approach in describing the film and substrates composite behavior. This model, developed by Zhou et al. [6, 7] takes into
account that the transfer of energy across the film-substrate interface is not linear, but actually discontinuous; allowing it to
better describe the film’s behavior for a broader range of material combinations. A group of materials were selected for their
similar Poisson’s ratio, but varying Young’s modulus, to have a single thin film layer sputtered on them which also has a
similar Poisson’s ratio to the substrates. The samples were then indented, comparing the Young’s modulus verses indention
depth to the behavior expected through the evaluated model. An interesting relationship was observed that may reveal new
information about Pile-up and sink-in and methods to mitigate their effects.
7.2 Experimental Procedure
For this work, a platinum film was simultaneously deposited on several substrates to investigate the influence of pile-up and
sink-in for different material combinations. Here the chosen materials all have identical Poisson’s ratio but different elastic
moduli. This enabled separation the Poisson’s ratio effect on pile-up and sink-in. Table 7.1 lists the materials and properties
employed.
The Pt film was simultaneously deposited onto the substrates by sputtering. A thin Ti film was first deposited to aid in
adhesion to the substrate. Table 7.2 lists the parameters employed.
The resulting platinum film was observed with SEM and found to have consistent coverage and excellent surface quality,
shown in Fig. 7.2. Table 7.3 shows that using the profilometer, the film thickness of each film-substrate combination was
measured in three locations and then averaged to determine the film thickness of 230 nm. As the platinum film had a good
surface quality with no disproportionally large protrusions over the film’s surface, this platinum film was determined to be
the best candidate for indentations.
Each Substrate was indented to assess their material properties before the Pt film was deposited. Twenty five indents were
made to determine an average value. The deposited PT film was than indented on each substrate using 25 indents per each
film/substrate combination.
Fig. 7.1 Schematics of the
pile-up and sink-in effect [7]
42 K. Schwieker et al.
7.3 Results and Discussions
The indentation results of the Pt film on the Cu substrate are given in Fig. 7.3 as an example. The solid circles are the average
experimental data while the solid squares are the elastic modulus of the film as extracted by the Zhou and Prorok model. This
was performed for each film-substrate combination with the results given in Table 7.4.
Table 7.1 Material selection
for the films and substratesFilms Substrates
Material E (GPa) n Material E (GPa) n
Al 70 0.35 In 11 0.44
Pt 168 0.36 Sn 50 0.36
Al (100) 63–70 0.35
Cu (100) 66–117 0.35
Ti 116 0.32
Pt 168 0.36
Si 178 0.28
Ta 186 0.34
Table 7.2 Sputtering
parameters of 230 nm Pt film
with Ti adhesion layer
Substrates Al, Si, Cu, In, Sn, Pt, Ti, Ta
Base pressure (Torr) 2.6 � 10�6
Magnetron type DC DC
Target material Pt Ti
Pre-sputtering power (W) 100 400
Pre-sputtering time (s) 15 25
Sputtering power (W) 100 400
Sputtering time (s) 800 25
Gas 1 (Ar) flow rate (sccm) 25 25
Gas 2 (O2/N2) flow rate (sccm) 0 0
Deposition pressure (mTorr) 4.7 4.7
Deposition temperature (�C) 23 23
Soak time (s) 0 0
Substrate holder rotation (%) 50 50
Ignition pressure (mTorr) 50 50
Expected film thickness (nm) 250 10
Actual film thickness (nm) 230 10
Fig. 7.2 Surface quality
of platinum film
7 New Insight into Pile-Up in Thin Film Indentation 43
The method indicates that the film properties can be extracted reliably. Probably the more interesting result is how the
pile-up and sink-in differed from substrate to substrate. Figure 7.4 gives scanning electron microscopy images of each indent
for the 230 nm thick Pt film at a maximum indent depth of 500 nm, or well past the film thickness.
Each substrate yielded a different degree of sink-in for the Pt film which can be isolated to the change in film/substrate
elastic modulus ratio. Furthermore in most cases, even though the indent depth was twice the film thickness the indent never
punched through the film (SI substrate the exception). Instead, the substrate was often the more compliant of the two in
yielded significantly causing s strong degree of sink-in. Case-in-point, it was noticed that the residual indention in the Pt-In
Table 7.3 Film thickness of sputtered platinum films
Substrate
Location 1
(nm)
Location 2
(nm)
Location 3
(nm)
Average
(nm)
SiO2 220 235 220 225
Si 235 236 231 234
Pt 210 235 214 220
Al 235 236 225 232
Ta 232 225 240 232
Ti 239 246 220 235
In 210 233 243 229
Sn 230 246 210 229
Cu 231 243 228 234
0
0.1
0.2
0.3
0.4
0.5
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Poisson's R
atioM
odul
us (
GPa)
Normalized Displacement (h/t)
230nm Pt on Cu ExperimentalZ-P ModelFilm EFilm Alpha
Fig. 7.3 Indentation results of a 230 nm Pt film on a Cu substrate
Table 7.4 Determination of film properties on the various substrates
Substrate E0substrate nsubstrate E0
film nfilmIn 12 0.44 ? ?
Sn 42 0.36 163 � 5 0.36
Al 60 0.35 157 � 7 0.35
Cu 100 0.35 158 � 7 0.35
Ti 116 0.32 162 � 2 0.35
Pt 168 0.36 167 � 4 0.35
Ta 153 0.34 171 � 7 0.36
Si 178 0.28 166 � 2 0.36
44 K. Schwieker et al.
surface was much smaller than that of the other materials, so another micrograph at 1,000 magnification was taken, Fig. 7.5.
In this micrograph there is a visible halo of deformation that spreads out wider than the readily identifiable indention shown
in Fig. 7.5a. It is believed that since the film is so much stiffer, that as the tip pushes down on the film, a larger area of the film
than that just below the tip begins to push down on the substrate; as demonstrated in Fig. 7.5b, c. Shortly after the tip contacts
the film’s surface, the film’s modulus as calculated through the Z–P model starts to rise toward its correct value, but once the
previously mechanism becomes dominate, there is more plastic deformation than expected, allowing for less elastic
recovery, so the film’s modulus starts to drop toward that of the substrate as the substrate becomes the driving force for
elastic recovery.
7.4 Conclusions
Instrumented indentation testing was used with the continuous stiffness method in order to evaluate nine different substrates,
with the same film. Once deposited, the platinum film was evaluated through SEM and was found that surface quality and
consistency were ideal for nanoindentation. The experimental data from indenting these samples was then compared to the
model, and the associated extracted film’s Young’s modulus and Poisson’s ratio to see to what degree they remain constant
through indentation. The Zhou–Prorok model is adept at predicting substrate effect behavior for plastically deforming
substrates, when sink-in is the dominating factor of erroneous contact area, not pile-up.
Fig. 7.4 Intents in the PT/substrate combinations for a 230 nm thick Pt film and a 500 nm maximum indent depth
7 New Insight into Pile-Up in Thin Film Indentation 45
References
1. Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation. J Mater Res 1:601–609
2. Hay J, Crawford B (2011) Measuring substrate-independent modulus of thin films. J Mater Res 26:727–738
3. King RB (1987) Elastic analysis of some punch problems for a layered medium. Int J Solids Struct 23:1657–1664
4. Pharr GM, Strader JH, Oliver WC (2009) Critical issues in making small-depth mechanical property measurements by nanoindentation with
continuous stiffness measurement. J Mater Res 24:653–666
5. Saha R, Nix WD (2002) Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater
50:23–38
6. Zhou B, Prorok BC (2009) A discontinuous elastic interface transfer model of thin film nanoindentation. Exp Mech 50:793–801
7. Zhou B, Prorok BC (2010) A new paradigm in thin film indentation. J Mater Res 25:1671–1678
8. McElhaney KW, Vlassak JJ, Nix WD (1998) Determination of indenter tip geometry and indentation contact area for depth-sensing indentation
experiments. J Mater Res 13:7
Fig. 7.5 Residual indents
in an Pt/In film/substrate
composite
46 K. Schwieker et al.
Chapter 8
Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation
Jennifer Hay, Verena Maier, Karsten Durst, and Mathias G€oken
Abstract For materials which exhibit a power-law relationship between stress and strain rate, it is theoretically possible to
evaluate the exponent (m) which governs the relationship by means of instrumented indentation. However, in practice, tests
at small strain rates take so long that the results can easily be dominated by thermal drift. A new test method is developed in
which several constant strain rates are examined within a single indentation test by switching strain rates as the indenter
continues to move into the material. Switching strain rates within a single test overcomes the problem of long testing times
by examining large strain rates first and transitioning to smaller strain rates as the test proceeds. The new method is used to
test a sample of fine-grained nickel sold by NIST as a standard reference material for Vickers hardness. The strain-rate
sensitivity of this sample is measured to be m ¼ 0.021. This value is in good agreement with values obtained by others on
fine-grained nickel using both instrumented indentation and uniaxial creep testing.
8.1 Introduction
In many materials, the plastic stress that can be sustained depends on strain rate through a power-law relationship: higher
stresses are sustained with higher strain rates and vice versa. In a uniaxial tensile configuration, this relationship between
plastic stress, s, and strain rate, _eu is expressed as
s ¼ B� _emu ; (8.1)
where B* is a constant and m is the strain-rate sensitivity (SRS), which is always greater than or equal to zero. For materials
which manifest negligible strain-rate sensitivity, m is near zero, making s a constant. (Sapphire is an example of such a
material.) Materials with greater strain-rate sensitivity have greater values of m.Provided that hardness (H) is directly related to plastic stress, then hardness also manifests this same phenomenon, giving
the relation
H ¼ B_em: (8.2)
J. Hay (*)
Agilent Technologies, Inc., Nano-Measurements Operation, 105 Meco Ln., Suite 200, Oak Ridge, TN 37830, USA
e-mail: [email protected]
V. Maier • K. Durst • M. G€okenDepartment of Materials Science and Engineering Institute 1: General Materials Properties, University Erlangen-Nuremberg,
Martensstrasse 5, Erlangen D-91058, Germany
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_8, # The Society for Experimental Mechanics, Inc. 2013
47
In (8.2), B is a constant (though different in value from B* in (8.1)) and _e is the indentation strain rate, defined as the
loading rate divided by the load ( _P/P).1 The strain-rate sensitivity, m, has the same meaning and value in (8.2) as it does in
(8.1). Taking the logarithm of both sides of (8.2) and simplifying yields
lnðHÞ ¼ m � ln _eð Þ þ lnðBÞ: (8.3)
Thus, for many materials, there is a linear relationship between the logarithm of hardness and the logarithm of strain rate,
with the slope being the strain-rate sensitivity, m.Lucas and Oliver showed that the strain-rate sensitivity, m, could be evaluated by performing a series of indentations,
with each indentation performed using a different strain rate [1]. However, the approach of Lucas and Oliver is
problematic, because indentations at small strain rates take so long that the results can easily be dominated by thermal
drift. Recently, Maier et al. showed that all strain rates of interest may be executed within a single indentation test by
switching strain rates as the indenter continues to move into the material [2].
The protocol proposed by Maier et al. has a number of practical advantages. First, the testing time and thermal drift are
minimized by using fast strain rates when the applied force is small and slow strain rates when the applied force is large.
To understand this benefit, it is important to understand how a controlled-strain-rate experiment works. The force-
application rate required to maintain a given strain rate changes with applied force. For example, let us compare the
force-application rate required to achieve a strain rate of 0.01/s at 1 and 100 mN. Knowing the definition of strain rate
ð_e ¼ _P=PÞ, we calculate the necessary force-application rate for each situation ( _P) as the product of the desired strain rate
and the applied force. When the applied force is 1 mN, we have
_P ¼ 0:01=sec�1mN ¼ 0:01mN=sec:
When the applied force is 100 mN, we have
_P ¼ 0:01=sec�100mN ¼ 1mN=sec;
which is much faster. Though the same strain rate is achieved in both cases, the associated force rate is much higher in the
second case, because the applied force is much higher. Thus, it may take a prohibitively long time to examine a small strain
rate when the applied force is small, but that same small strain rate can be examined rather quickly when the applied force is
large. The protocol suggested by Maier et al. takes advantage of this reality by examining the largest strain rate at the
beginning of the test (when the applied force is small) and by examining progressively smaller strain rates as the applied
force increases. In this way, both testing time and thermal drift are minimized. The protocol of Maier et al. has been
implemented in a commercial test method; this article reports the results obtained with this new method on a nickel standard
reference material (SRM) produced by the U.S. National Institute of Standards and Technology (NIST).
The protocol of Maier et al. has a second important benefit: because all strain rates of interest are examined in every test, it
is possible to map out the spatial distribution of strain-rate sensitivity. Although this capacity was not exercised in this work,
Maier et al. measured local strain-rate sensitivity in and around a bond layer in roll-bonded aluminum.
8.2 Experimental Procedure
8.2.1 Sample
The sample tested in this work was a NIST standard reference material (SRM) for Vickers hardness. The sample consists of a
1.35 cm square test block of electrodeposited bright nickel, approximately 750 mm thick, on an AISI 1010 steel substrate,
mounted and highly polished in a thermosetting epoxy. A template certificate for this kind of sample can be found on the
1 Strictly, the term “indentation strain rate” refers to the displacement rate divided by the displacement ( _h/h). However, beginning with the
definition of hardness, it is easily shown that _h/h � 0.5( _P/P). Equation 8.2 holds true for either definition of strain rate, because the constant
difference between the two definitions (0.5) is simply absorbed into the constant B. Because the Agilent G200 NanoIndenter is a force-controlled
instrument, it is logistically easier to control _P/P than _h/h. Thus, in this work, the term “strain rate” refers to _P/P, unless specifically stated
otherwise.
48 J. Hay et al.
NIST website [3]. The qualities which make this sample ideal as a Vickers SRM also make it ideal for the present
demonstration. It has a smooth surface, is resistant to tarnish and corrosion, and has a small grain size. These qualities are
important, because ideally, changes in strain rate should be the only explanation for the observed changes in hardness.
Changes in hardness due to other factors such as surface layers, indentation size effect, and constraint influence can all
compromise the validity of the measured strain-rate sensitivity.
8.2.2 Equipment
An Agilent G200 NanoIndenter with a Berkovich indenter was used for all testing. The Continuous Stiffness Measurement
Option (CSM) was used in order to achieve hardness and elastic modulus as a continuous function of penetration depth [4].
8.2.3 Test Method
Twelve indentation tests were performed using the test method “G-Series XP CSM Strain-Rate Sensitivity.” This test
method allows the user to prescribe a penetration that must be achieved prior to strain-rate cycling. This initial penetration is
used to achieve a penetration depth that is large enough so that no further changes in hardness are expected due to indentation
size effect, surface inhomogeneities, tip anomalies, etc. Once this initial penetration has been achieved, the method
prescribes cycling between a test strain rate and a base strain rate. The test strain rate is executed in the first part of the
cycle, and the base strain rate is executed in the second part of the cycle. The return to the base strain rate after each test strain
rate provides a means for confirming that hardness is not changing with increasing penetration for any reason other than the
changing influence of strain rate. Figure 8.1 shows the strain-rate history for each indentation test on the Ni SRM.
8.3 Results and Discussion
The elastic modulus (E) of the Ni SRMwas measured to be 229 � 3 GPa, and the strain-rate sensitivity (m) was measured to
be 0.021 � 0.002. Table 8.1 is a survey of strain-rate-sensitivity values measured by others for fine-grained Ni.
Figure 8.2 shows the continuous elastic modulus during strain-rate cycling for one typical test. As expected, the modulus
did not change significantly during strain-rate cycling. Modulus is reported for each cycle by averaging the continuous
measurements which fall within 80–90% of the displacement range for the base-strain-rate segment of the cycle. In Fig. 8.2,
Fig. 8.1 Strain-rate cycling
imposed on the test sample.
The test strain rate is imposed
in the first part of the cycle.
The base strain rate is imposed
in the second part of the cycle
(For black-and-white copies,
the cycles are ordered from
left to right)
8 Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation 49
these measurements are plotted as green data points. The modulus value reported for each test is the average of the three
cycle-level results for that test. The average over all tests, 229 GPa, is 15% higher than the nominal value of 200 GPa for
pure nickel. One possible explanation for the discrepancy is that the Oliver-Pharr model for the contact area may
overestimate the true contact area. Because the calculation of elastic modulus by indentation goes as the inverse of the
square root of the contact area, an underestimation of the contact area leads to an overestimation of the modulus. Finite-
element simulations of indentations into a material with nickel-like properties could be used to further investigate this
explanation, because finite-element simulations allow a comparison between contact area determined by the Oliver-Pharr
model and contact are determined from the finite-element mesh.
Figure 8.3 shows the continuous hardness measured during strain-rate cycling for a typical test. (These data are from the
same test for which the modulus is plotted in Fig. 8.2.) The influence of changing strain rate is obvious. At each change, there
is a transient in the hardness response as the microstructure adjusts to the new rate. For each test strain rate, the hardness
values within 80–90% of the displacement range for the segment are averaged to report a single value of hardness; data
within this range for each cycle are plotted as black symbols in Fig. 8.3. Figure 8.4 shows Ln(H) vs. Ln(_e) for all 12 tests. Thelinearity of these results supports the hypothesis that this material is well described by (8.2). For each test, the strain-rate
sensitivity,m, is calculated as the slope of Ln(H) vs. Ln(_e). The value for strain-rate sensitivity obtained by averaging over all12 tests (m ¼ 0.021 � 0.002) is well within the range of SRS values that have been measured by others for fine-grained Ni
(Table 8.1).
A hardness value for each implementation of the base strain rate was also determined. For each base strain rate, the
hardness values within 80–90% of the displacement range for the segment are averaged to report a single value of hardness
for that segment; in Fig. 8.3, the included hardness values are plotted as green symbols. For all 12 tests, Fig. 8.5 shows
hardness associated with the base strain rate for each cycle. The lack of any trend in hardness with cycle number confirms
that hardness is not changing with depth when the same strain rate is applied.
Table 8.1 Survey of SRS (m) values measured by others on fine-grained Ni
Source Sample Method m
This work Ni Vickers SRM Indentation 0.021
Maier et al. [2] Nanocrystalline Ni Indentation 0.019
Maier et al. [2] Nanocrystalline Ni Uniaxial creep (compression) 0.016
Shen et al. [5] Nanocrystalline Ni Uniaxial creep (tension) 0.016–0.045
Dalla Torre et al. [6, 7] Nanocrystalline Ni Uniaxial creep (tension) 0.010–0.030
Wang et al. [8] Nanocrystalline Ni Uniaxial creep (tension) 0.019
Fig. 8.2 Modulus during
strain-rate cycling for one
typical test. Each vertical linemarks the beginning of a
different strain rate,
corresponding to those
identified in Fig. 8.1.
As expected, modulus is
not sensitive to strain rate
50 J. Hay et al.
8.4 Conclusions
An experimentally robust test method has been implemented for measuring strain-rate sensitivity by instrumented indenta-
tion. The method overcomes problems associated with long testing times by imposing small strain rates only when the
applied force is large. Using this method, the strain-rate sensitivity of a sample of nickel sold by NIST as a Vickers SRMwas
measured to be m ¼ 0.021. This value is in good agreement with values obtained by others on similar materials using both
instrumented indentation and uniaxial creep testing.
Fig. 8.3 Hardness during
strain-rate cycling. Sensitivity
to strain rate is evident. Blacksymbols denote data used to
calculate the hardness for each
test strain rate. Green symbolsdenote data used to calculate
the hardness for each base
strain rate
Fig. 8.4 Plot of ln(H) versusln(_e) for each of 12 tests.
Slope of ln(H) with respect
to ln(_e) for each test gives
the strain-rate sensitivity, m,for that test. Linearity of
these data demonstrates
that strain-rate sensitivity
for this material is well
modeled by (8.2)
8 Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation 51
References
1. Lucas BN, Oliver WC (1999) Indentation power-law creep of high-purity indium. Metall Mater Trans A Phys Metall Mater Sci 30(3):601–610
2. Maier V, Durst K, Mueller J, Backes B, Hoppel H, G€oken M (2011) Nanoindentation strain rate jump tests for determining the local strain rate
sensitivity in nanocrystalline Ni and ultrafine-grained Al. J Mater Res 26(11):1421–1430
3. NIST Certificate Standard Reference Material 1896a Vickers Microhardness of Nickel [cited 2011 October 10, 2011]. Available from: http://ts.
nist.gov/MeasurementServices/ReferenceMaterials/upload/1896a.pdf
4. Hay JL, Agee P, Herbert EG (2010) Continuous stiffness measurement during instrumented indentation testing. Exp Tech 34(3):86–94
5. Shen X, Lian JS, Jiang Z, Jiang Q (2008) High strength and high ductility of electrodeposited nanocrystalline Ni with broad grain size
distribution. Mater Sci Eng A487:410
6. Dalla Torre F, Van Swygenhoven H, Victoria M (2002) Nanocrystalline electrodeposited Ni: microstructure and tensile properties. Acta Mater
50:3957
7. Dalla Torre F, Sp€atig P, Sch€aublin R, Victoria M (2005) Deformation behavior and microstructure of nanocrystalline electrodeposited and high
pressure torsioned nickel. Acta Mater 53:2337
8. Wang YM, Hamza AV, Ma E (2006) Temperature-dependent strain-rate sensitivity and activation volume in nanocrystalline Ni. Acta Mater
54:2715
Fig. 8.5 Hardness measured
during the base-strain-rate
segment of each cycle. Lack
of any trend with cycle
number demonstrates that the
same hardness is measured
when the same strain rate
is applied, despite increasing
penetration
52 J. Hay et al.
Chapter 9
Frequency Multiplication and Demultiplication in MEMS
David B. Blocher, Alan T. Zehnder, and Richard H. Rand
Abstract In his 1927 paper in Nature, B. van der Pol described experiments in which an electrical circuit forming a
relaxation oscillator was externally forced with continuously varying frequency. The circuit’s response, he found, was
entrained to be only at whole submultiples of the forcing frequency, i.e. f/2, f/3, up to f/40. We describe similar results found
in an optically actuated MEMS limit cycle oscillator. Doubly supported beams are excited into self-oscillation in their first
mode of vibration by illuminating them within an interference field which couples absorption to displacement. While in limit
cycle oscillation, they are mechanically shaken out of plane with continuously varying frequency, and the limit cycle
response is seen to be entrained to multiples or submultiples of the forcing frequency f/3, f/2, f, 2f, up to 7f.
9.1 Introduction
Drawing on nano-fabrication technologies developed for microprocessors, in the last decades researchers have produced
micro-scale mechanical devices with applications such as switches [1], accelerometers, pressure sensors, projection displays
[2], temperature sensors [3], mass sensors [4–6], electrical filters [7, 8], and reference oscillators [9]. Such microelec-
tromechanical systems (MEMS) may be cheaply mass produced using techniques compatible with traditional electronics
fabrication, making them likely candidates for next generation sensors and actuators.
For some applications MEMS devices undergo quasi-static deflection, though many applications rely on the resonant
properties of the device. In order to achieve periodic motion, devices are typically driven electrostatically [9], piezoelectri-
cally [11] or thermo-optically [12] using an externally modulated drive. Self-sustained vibrations in the presence of
unmodulated drive have been reported in thermo-optical systems [13]. These self-oscillations, termed limit cycle (LC)
oscillations, are due to automodulation of thermal-stresses created by feedback between displacement and absorption. Self-
resonant systems may also use electrical feedback [14], and offer the promise of stand-alone cheap sensors since they do not
require expensive drive equipment to obtain periodic motion.
When an LC oscillator operating with frequency, fLCO, is externally driven at forcing frequency, fD, and forcing
amplitude, AD, the type of response depends on the strength of forcing and level of frequency detuning. For low drive
amplitudes with drive frequencies well separated from fLCO, the oscillator is unaffected by the drive. The frequency content
of the motion is mostly at fLCO with a small component at fD. For high drive amplitudes at frequencies close to fLCO the
frequency of the limit cycle is shifted to respond only at fD [15], and the limit cycle is said to be 1:1 entrained or locked.
Entrainment may also occur when the forcing frequency is near an integer multiple or demultiple of the limit cycle
frequency, i.e. n:1 subharmonic entrainment at fD ffi nfLCO or 1:n superharmonic entrainment at fD ffi (1/n)fLCO, where n
is an integer. In this case, the limit cycle frequency is shifted to the nearest multiple or submultiple of the drive frequency.
Observation of this phenomenon in an electrical circuit led Van der Pol to call the phenomenon frequency demultiplication
(or multiplication) [16]. A simplified model of subharmonic entrainment based on a one-dimensional flow with jumps
exhibited strong qualitative resemblance to Van der Pol’s original experiments [17]. Zalalutdinov et al. demonstrated 1:1
and 2:1 entrainment in a MEMS pillar [18], but to our knowledge superharmonic or higher order subharmonic entrainment
have not been demonstrated in a MEMS resonator.
D.B. Blocher (*) • A.T. Zehnder • R.H. Rand
Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_9, # The Society for Experimental Mechanics, Inc. 2013
53
In this work, we study entrainment of thermo-optically excited limit cycle oscillations in a doubly-supported MEMS
beam. Self-oscillating beams are driven at a variable frequency and amplitude, and the frequency of response characterized.
Entrainment is seen at fD:fLCO ratios as low as 1:7 and as high as 3:1. The presence of significant frequency noise reduces the
strength of locking, and asymmetry gives the region of locking considerable hysteresis.
In the following section we describe the fabrication of our devices, and the apparatus used to drive and detect their
motion. Next we outline the procedure used to obtain and entrain limit cycle motion. Finally we characterize frequency noise
and report entrainment results.
9.2 Experimental
Doubly supported beam resonators are fabricated out of single crystal silicon using an SOI process. It has been suggested
that large absorption contrast leads to strong coupling between displacement and heating and thus low critical power for self-
oscillation, Pcrit [19]. Thus, interference patterns are predicted using the code presented in Ref. [20] and wafer device
thickness and buried oxide thickness are selected to optimize absorption contrast in the final devices for low Pcrit. The wafer
is diced and fabrication proceeds on chips. Beams 2 mm wide and 7–40 mm long are patterned using photolithography and
defined with dry etching. Beams are released in a wet etch and critical point drying used to prevent stiction. Final device
thickness is measured to be 201 nm with 400 nm gap to substrate, and 1.6 mm undercutting (Fig. 9.1a). Data presented here
are for a 35 mm long beam. SEM and optical imaging indicates that it is post-buckled due to residual compressive stresses in
the device layer. The buckling amplitude is measured to be 286 nm using optical profilometry.
Devices are mounted on a piezoelectric disk, interferometrically driven under high vacuum (~10�7 mbar) and transduced
using a method described in Ref. [21]. An unmodulated HeNe laser is focused to a ~5 mm diameter spot at the center of the
beam. The beam-gap-substrate system forms a Fabry-Perot interferometer which couples laser absorption to out of plane
displacement. Motion of the beam through the interference field modulates the intensity of the reflected signal which is
measured in a high-speed photodiode and its frequency content determined on a spectrum analyzer (Fig. 9.1b). We can also
inertially drive the beam out of plane by applying a sinusoidal voltage across the piezo. At a threshold power of Pcrit ffi 225
mW, the beam is observed to spontaneously transition into limit cycle oscillation at its first mode frequency of 1.94 MHz.
Post-buckled beams are known to be amplitude-softening [22], i.e. their frequency of oscillation decreases with amplitude.
Increasing the laser power beyond Pcrit is seen to increase the amplitude of oscillation, decreasing the frequency down to
1.63 MHz at 3 mW laser power. Significant frequency instability is observed as sporadic motion of the resonant peak on the
spectrum analyzer, and 200 successive measurements of the frequency of undriven LC oscillation at 3 mW laser power give
a standard deviation in frequency of Df/f ~ 4 � 10�3.
In order to study entrainment, the laser power is increased beyond the threshold power for limit cycle oscillation, and
the self-oscillating devices are inertially driven. A function generator is used to create a swept sine wave which drives the
piezoelectric disk through a high frequency amplifier. The spectral content of the device motion may be observed on
the spectrum analyzer. A frequency counter is used to accurately track the forcing frequency. When entrained, a single stable
peak is seen at fD 6¼ fLCO.When not entrained, a noisy peak is seen at fLCO 6¼ fD and a second steady peak is usually seen at fD,
g 0
3.0
4.0
5.0
6.0
Gap
to S
ubst
rate
Absorption [%]
g 0+½λ
g 0 -
½λ
Image of device tested
a b
Top View yx
z
Diagram of experimental setup
z ySide View x
Gap toSubstrate
Thickness
SpectrumAnalyzer
Photo-Diode
Laser
Si
Si
SiO2
10 µm
Fig. 9.1 (a) Microscopic image of beam tested. (b) Absorption in a Fabry-Perot interferometer. Deflection of the beam from its initial gap to
substrate changes the amount of light absorbed. For high enough laser power, P > Pcrit, feedback leads to self-oscillation. Modulation of the
reflected signal is measured in a high speed photodiode and used to transduce motion
54 D.B. Blocher et al.
though it may disappear below the noise floor. The sweep rate is kept low enough (~0.2 %/s) that the drive frequency changes
roughly quasi-statically. The peak-to-peak voltage across the piezo is recorded and used as a measure of the drive amplitude,
AD. Note that due to the frequency dependent electrical andmechanical properties of the piezoelectric disk, this measure is not
directly related to the displacement amplitude. At high drive amplitudes and frequencies, distortion is seen and drive levels are
kept low enough at any given frequency so that the total harmonic distortion is less than 10%. The signal from the photodiode
is large enough to be picked up on an oscilloscope which may also be used to verify entrainment by triggering on the drive
signal and examining the photodiode (oscillator) signal.When the oscillator is phase locked to the drive, the photodiode signal
will appear as signal. When locking is lost, the oscillator phase will drift with respect to the drive, and the photodiode signal
will appear as high amplitude noise on the oscilloscope.
Due to the high level of frequency noise, the beam may jump in and/or out of entrainment for low forcing amplitudes,
causing entrainment to be an inherently statistical phenomenon. In order to study statistics for 1:1 entrainment, resonators
were also driven using the spectrum analyzer as the frequency source. In source mode, the spectrum analyzer band-pass
filters the response at the drive frequency, only displaying response at fD. When the limit cycle is entrained (fLCO ¼ fD), then
the return signal is not filtered out and a high response signal is measured. When entrainment is lost (fLCO 6¼ fD), then the
response signal is filtered out and the measured response is small. When using the spectrum analyzer as the source to study
1:1 entrainment, the measured response is a plateau whose end points show the frequency at which locking begins and is lost
(Fig. 9.2).
9.3 Results and Discussion
Using the spectrum analyzer as a frequency source, statistics of 1:1 entrainment are measured (Fig. 9.3). Due to high
frequency noise, for low drive amplitudes the limit cycle is only entrained part of the time even when fD � fLCO. Increasing
the drive amplitude increases the width of the entrainment region on any given sweep, sharpens the edges of the region of
entrainment and allows for strong locking – where the limit cycle is seen to be entrained at a given frequency on every
sweep. Note that the entrainment region depends on sweep direction due to asymmetry and hysteresis in the system. For
example, when sweeping up in frequency with AD ¼ 0.622 V, locking occurs when fD is 2 % below fLCO, but is maintained
up to 7 % above fLCO. Sweeping down, locking occurs when fD is 2 % above fLCO and is maintained down to 7 % below fLCO.
0.950.9 1 1.051.1
-30
-40
-50
-60
-70
-80
-90
-100
fD/fLCO
Ret
urn
Sig
nal [
dBm
]
ffree-downflock-down
ffree-up
flock-up
Fig. 9.2 Measured region of entrainment for AD ¼ 0.622 V drive amplitude. Upward sweep is in red and downward sweep in black. In source
mode, the spectrum analyzer filters for signal at fD only. When entrained, fLCO is locked to fD, leading to a large unfiltered return signal. When
entrainment is lost, the limit cycle returns to its unforced frequency, fLCO 6¼ fD, and the filtered return signal is small. Note the logarithmic scale –
due to nonlinearities in the transduction scheme, displacement is not linearly related to return signal, and calibrated displacement amplitude
measurements are impracticable
9 Frequency Multiplication and Demultiplication in MEMS 55
Using the function generator as a frequency source, and the spectrum analyzer to measure the response frequency, the
regions of superharmonic (Fig. 9.4), 1:1 and subharmonic (Fig. 9.5) entrainment are measured by tracking the resonant peak
of the response on the spectrum analyzer. Due to the time lag associated with the frequency measurement and finite sweep
speed, measured data points are slightly under-predicted. In addition, data is un-averaged leading to a jitter in the boundaries
of the entrainment region due to frequency noise.
Note that for the same forcing amplitude, AD, the width of the entrainment region is lower for higher order superharmonic
entrainment (Fig. 9.4). This is likely due to a combination of two factors. First of all, when superharmonically entrained at 1:n,
if the drive frequency, fD, increases by 1 Hz then the limit cycle frequency, fLCO, increases by n Hz. Thus a small width of
entrainment measured in terms of changes in fD is large when measured in terms of fLCO. In addition, the efficiency of energy
pumping decreases for increasing order of entrainment, transfer being most efficient when the frequency of response matches
the drive frequency. In the language of perturbation theory, 1:1 entrainment may be obtained with “soft” excitation where the
amplitude of excitation is the same order as the damping and nonlinear terms. However, sub- or superharmonic entrainment
require that the excitation be “hard,” i.e. scaled one or more orders higher than the damping and nonlinear terms [23].
0.90 0.95 1 1.05 1.100
10
20
30
40
50
60
70
80
90
100
0.90 0.95 1 1.05 1.100
10
20
30
40
50
60
70
80
90
100
a b
Per
cent
age
of T
ime
Ent
rain
ed
Sweep DownSweep Up
fD / fLCO fD / fLCO
0.622 V0.312 V0.156 V0.078 V
Fig. 9.3 Statistics for 1:1 entrainment at various drive amplitudes, AD. Asymmetry in the system causes results to differ when the drive frequency
is swept up (a) versus down (b)
0
2
4
6
8
10
12
14
16
1 2
1 3
1 4
1 5
1 6
1 7
V Pie
zo p
eak−
to−
peak
[V]
flock-up
ffree-up
flock-down
ffree-up
fD / fLCO
Fig. 9.4 Regions of superharmonic entrainment. The frequency dependent impedance of the piezo limits the achievable drive voltage at higher
frequencies due to distortion. Note that a logarithmic frequency scale is used so that for all superharmonics measured, the width of the entrainment
region is visible
56 D.B. Blocher et al.
Superharmonic entrainment of order 1:7 is only observed in our devices at the highest achievable drive amplitude, and 1:8
entrainment is not observed. See Fig. 9.6 for an oscilloscope trace of 1:4 superharmonic entrainment.
For subharmonic forcing, the width of entrainment at 3:1 appears to be slightly larger than for 2:1 at the same forcing
amplitude. This is likely due to the fact that for n:1 subharmonic entrainment, an increase in fD by 1 Hz leads to a (1/n) Hz
increase in fLCO, artificially increasing width of entrainment for subharmonic forcing when measured with respect to the
drive frequency. 4:1 and higher subharmonic entrainment is not observed. Measured by changes in fD or fLCO, the largest
region of entrainment is seen for 1:1 forcing. For 1:1, sub- and superharmonic entrainment, the width of the entrainment
region increases with AD as expected – stronger forcing can entrain the limit cycle at larger frequency detuning. Finally, we
note that the region of entrainment seems to decrease in frequency for higher amplitude of forcing, particularly for 1:1 and
subharmonic entrainment leading to a left-tilted V shape. It has been shown that an amplitude-hardening limit cycle
oscillator is constrained to the backbone curve when entrained, giving asymmetry in the region of entrainment with a
right-tilted V shape [18, 24]. In this work we see that the same is true for amplitude-softening LC oscillators, with the
direction of tilt switched – higher amplitudes of forcing may result in higher amplitude oscillations which push the oscillator
up the backbone curve, decreasing the frequency at which the oscillator entrains. However, a shift in the entrainment
frequencies for high amplitude forcing has also been demonstrated in models with no softening or hardening behavior [17].
Finally we note that 1:n superharmonic entrainment is seen to occur at frequencies slightly less than (1/n)fLCO. This may also
be related to the amplitude frequency relationship though more work is needed to determine the exact cause.
Fig. 9.5 Regions of 1:1 and subharmonic entrainment
1 5.00m 1.00V2 2 RUN
Drive2
1
Response
Vp-p(2) = 1.937 VVp-p(1) = 13.13 mVFreq (1) = 1.869MHz
v 600ns 500n
s
Fig. 9.6 Oscilloscope trace demonstrating 1:4 superharmonic entrainment. Note that during one forcing period, the resonator traverses four cycles
of motion. The small peak at the bottom of each response cycle is caused by nonlinearities in our detection method and does not represent changes
in the direction of motion of the device
9 Frequency Multiplication and Demultiplication in MEMS 57
9.4 Conclusion
In this paper we demonstrate subharmonic, superharmonic and 1:1 entrainment in an optically driven MEMS limit cycle
oscillation. The high level of frequency noise for the LC oscillator prevents strong locking for low forcing amplitudes,
though short term locking is observed. For higher forcing amplitudes, the limit cycle frequency is stabilized by strong
locking which can detune fLCO by up to 15 %. A shift towards lower frequency locking for higher forcing amplitudes is
observed which may be related to the amplitude-softening nonlinear stiffness of our device. Superharmonic entrainment at
1:7 is observed for the first time in a MEMS oscillator as well as 3:1 subharmonic entrainment. Sub- and superharmonic
entrainment may be of particular interest for applications as a replacement to distortion based frequency multipliers, or as
means to manipulate and control high frequency signals with lower frequency subharmonics.
Acknowledgements This work is supported under NSF grant 0600174 and was performed in part at the Cornell NanoScale Facility, a member of
the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765). This work
also made use of the Integrated Advanced Microscopy and Materials facilities of the Cornell Center for Materials Research (CCMR) with support
from the National Science Foundation Materials Research Science and Engineering Centers (MRSEC) program (DMR 1120296).
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18. Zalalutdinov M, Aubin K, Pandey M, Zehnder A, Rand R, Craighead H, Parpia J, Houston B (2003) Frequency entrainment for
micromechanical oscillator. Appl Phys Lett 83(16):3281
19. Zalalutdinov M, Parpia J, Aubin K, Craighead H, Alan T, Zehnder A, Rand R (2003) Hopf bifurcation in a disk-shaped NEMS. In: Proceedings
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24. Pandey M, Aubin K, Zalalutdinov M, Reichenbach R, Zehnder A, Rand R, Craighead H (2006) Analysis of frequency locking in optically
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58 D.B. Blocher et al.
Chapter 10
Characterizing Metal Insulator Transition (MIT) Materials
for Use as Micro-Switch Elements
Brent L. Danner and Ronald A. Coutu Jr.
Abstract Metal insulator transition (MIT) materials, or phase change materials (PCM) are material compounds that have
the ability to be either conductors or insulators. Vanadium dioxide (VO2) and germanium telluride (GeTe) exhibit such a
transition property. These materials have ferroelectric properties as well as a variable resistivity. The ability to vary the
resistance of a single material is useful when designing integrated circuits on the micro scale. By varying the temperature or
the electric field across these materials, we are able to change the resistivity within a portion of a line. This can in turn be
used to create a switch within a wire. In order to measure these changing properties, we developed novel surface
micromachined test structures capable of using a variety of MIT materials. By varying the electric field or the thermal
gradient across an area of the wire segment, we were able to adjust the resistivity of the material. Therefore, by tailoring the
properties of specific portions of a conductor, we were able to control current flow in a circuit without needing a
micro-mechanical or a microelectronic device.
10.1 Introduction
The ability to control the flow of current in a wire without using a mechanical component provides a possibility for more
robust switching capability. The research done involving metal insulator transition (MIT) materials has been focused on
using vanadium dioxide (VO2) and germanium telluride (GeTe) as the switching components. This is due to VO2 being an
insulator at room temperature with a monoclinic crystalline phase and a metal with a tetragonal crystalline phase when
thermally or electrically activated [1]. Bouyge et al. began using VO2 in reconfigurable microwave systems and was able to
create a variable resistivity of three to five orders of magnitude using an electric field across the VO2 wire segment [2]. Using
two metallic electrodes to create the electric field across the material, transition times from an insulator state to a metallic
state were achieved in a few hundred nano-seconds [3]. While this method of varying resistivity has a great potential in the
future capability of tuning RF devices, it isn’t always practical to insert multiple electrodes in compact micro devices. MIT
materials also have the ability to switch phases when a thermal gradient is placed across the material. This transition was
found to occur constantly at 340 K in VO2 [1, 3, 4]. The changing of the material is caused by a combination of electronic
and lattice degrees of freedom within the molecules of VO2 [5]. After reaching the transition temperature, VO2 can switch at
times less than 100 ns [6]. Germanium telluride (GeTe) has also been used as an MIT material. Using Joule heating, GeTe
can be transitioned from an amorphous to a crystalline phase [7]. Unlike the low temperature transition of VO2, GeTe has a
crystallization temperature of greater than 423 K [8]. Due to the stability of these states, this material can be used in phase-
change memory cells [7]. These chalcogenide materials can also shift phases using both thermal and electrical stimulation.
Phase change memory can be created and tuned using different doping levels of the chalcogenides and by altering the alloy
stoichiometry [9]. Much of the testing done on these phase change materials (PCM) has been done on sapphire substrates in
order to reduce the leakage current into the substrate [2, 3, 10]. Through this research, using PCMs as micro-switches on a
silicon substrate is investigated.
B.L. Danner • R.A. Coutu Jr. (*)
Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_10, # The Society for Experimental Mechanics, Inc. 2013
59
10.2 Design/Modeling
Varying the resistivity of a wire in a microstructure provides the ability to change the total length of a wire, and therefore its
inductance. Making this change in a fast, controlled manner can be extremely useful in the micro world. By running several
wire segments of MIT material as part of a single wire and adjusting the resistivity in select sections, it is possible to select
which wire segment the current flows through.
Two designs were used to vary the resistivity across the MIT materials. The first option used a single MIT wire segment
capable of being placed on a thermal electric stand. The second option incorporated a single MIT wire segment placed
between two metallic pads. With a biased applied to the pads, an electric field is created across the MIT material, changing
its resistivity.
The first design utilizes various lengths and widths of PCM wires in order to test a broad range of their capabilities.
Previous studies have tested VO2 with lengths between 150 and 1,000 mm [2]. Using this as a starting point, tests were done
on wire segments with lengths ranging from 200 to 2,000 mm. All segments were also created in widths of 20 and 40 mm.
These baseline dimensions were also used in testing GeTe wires. Figure 10.1 shows the layout of a micro structure used to
test each of the different PCMs.
The second design was used to test the varying resistivity in MIT materials when an electric field was placed across them.
In order to accurately compare the results from both the thermal and electrical tests, the same size wires were used in each
design. Electrical contact pads were placed above and below the MIT wire and connected to the two parallel plates, one on
each side of the wire. These plates ran nearly the entire length of the MIT material in order to fully transition as much of the
material as possible from an insulator to a conductor. In order to avoid creating large fringing fields from the parallel plates
to the test pads at the end of the wire, the plates were fabricated with a 10 mm gap between the pads. Other structures with
various spacing between the capacitor plates and the test pads where created to measure the effect of these fringe fields
generated in between the two.
An electric field was then generated across the MIT wire in order to change the resistivity of the material. Using various
voltages and different gaps between the capacitor plates, a variety of electrical field strengths were tested. The first order
magnitude of these fields was calculated using
E ¼ V
d; (10.1)
where V is the voltage applied across the parallel plates and d is the distance between the plates. Previous studies used
voltages between 10 and 20 V, but the distance between capacitor plates was not given [1, 3]. These designs were created
with distances of 80 and 100 mm. This gap, along with the ability to vary the voltage across the plates, allows for a broad
range of electrical fields to be tested.
Figure 10.2 is a model of the MIT wire between two parallel plates with 100 mm spacing between the plates and 10 mmspacing between the plates and the test pads. Similar to the thermal test structures, a volt meter was used to measure the
resistance across the MIT wire. The resistivity was measured using a four point probe. This value is then used to predict
the resistance of the wire segment using
R ¼ rLA
; (10.2)
where R is the resistance, L is the length of the MIT wire, A is the cross-sectional area of the wire, and r is the resistivity of
the material. By measuring the resistance while varying the voltage applied to the parallel plates, the transition of the MIT
Fig. 10.1 Layout of
thermally varied resistivity
60 B.L. Danner and R.A. Coutu Jr.
material was observed. While any electric field across any material will have some impact on the resistivity, the drastic
variance in the resistivity that MIT materials exhibit makes them unique.
Vanadium witness samples were oxidized in the O2 plasma asher in order to determine the appropriate length of time
required to fully oxidize the wires. In order to create the vanadium dioxide desired, the test samples were oxidized in the O2
plasma asher at 250 W for 45 min. One sample was not oxidized and used as the baseline resistivity of sample.
Witness samples of both VO2 and GeTe were used to model the resistance of the PCMwires at room temperature. Using a
four point probe, the sheet resistance of these materials was measured. Since all of our samples are much longer and wider
than they are thick, sheet resistance is an appropriate way of finding the resistivity of the thin film. A surface profilometer
was then used to measure the thickness of the deposited material. The VO2 wire segments had an average thickness of
199 nm and the GeTe segments had an average thickness of 202 nm. The resistivity of the material can be found using
r ¼ RSt; (10.3)
where r is the resistivity of the material, Rs is the measured sheet resistance, and t is the thickness of the thin film. The
average resistivity of the thin GeTe film was calculated to be 5.71 � 10�4 O-mm. The resistivity of VO2 ashed for 10 min in
the O2 plasma asher was calculated to be 1.67 � 10�6 O-mm. Figure 10.3 shows the resistivity of GeTe, VO2, and vanadium
on the witness samples at room temperature. Variances in the measured resistivity can be attributed to the localized heating
of the samples due to current flow in the four point probe. Using (10.2), the resistance of a MIT wire segment with a length of
200 mm and a width of 20 mm is 28.5 kO for GeTe and 83.5 O for VO2. This resistance at room temperature serves as a
baseline for the full range of switching capabilities of these materials.
The novel test structures designed here enable testing of various MIT materials while using the same design. Both designs
allow for the substitution of different MIT materials into the wire section and provide the ability to vary the temperature and
electric field enough to elicit the transition from an insulator to a conductor. Therefore, using only two masks, these designs
can be fabricated to test the varying resistance in any material.
Fig. 10.2 Layout
of electrically varied
resistivity
1.E−03
1.E−04
1.E−05
Log
10R
esistivi
ty (
Ω−μ
m)
1.E−06
Time (min)
GeTe
Vanadium
VO26 min O2plasma ashed
VO210 min O2plasma ashed
1 2 3 4 5 6 7
Fig. 10.3 Resistivity
measurements obtained
using a four point probe
10 Characterizing Metal Insulator Transition (MIT) Materials for Use as Micro-Switch Elements 61
10.3 Fabrication
The test structures were microfabricated on a 100 Silicon wafer. Testing the capabilities of these materials on a relatively
inexpensive and readily available substrate provides the eventual opportunity to use MIT switches on a large scale in
microelectromechanical systems (MEMS). Both the thermal and electrical test structures were designed using the electronic
design automation software tool L-Edit. Consideration in the design was taken to ensure that the structures were easily
testable and manufacturable in AFIT’s class 1000 cleanroom.
Using L-Edit to layout the design, a positive tone mask was fabricated using a Heidelberg mPG 101 Mask Maker. Several
samples were microfabricated using VO2. Using a 99.99 % pure vanadium (V) target, approximately 200 nm were sputter
deposited onto the wafer. Careful consideration was taken to ensure the vanadium layer was not too thick, preventing the
ability to do a liftoff. Using photolithography, the PCM wires were patterned onto two layers of photoresist on the Si
substrate as seen in Fig. 10.4b. Liftoff was used to form the MIT wire segments allowing for a uniform fabrication process
for all materials. The vanadium wires were then placed in an O2 plasma asher to create VO2.
Additional samples were fabricated using GeTe. Using RF sputtering deposition, a 200 nm film was deposited onto the Si
wafers. Using liftoff, various wire length segments were created with the GeTe. After the liftoff, small “wings” could be seen
on the top edges of the wire segments due to the conformance of the GeTe film prior to liftoff. The thin film of GeTe in
Fig. 10.5 shows the porous nature of the wire segment. The vacancies in the film can cause electron scattering when
measuring the resistance of the PCM wires.
After all of the MIT wire segments were plasma ashed to remove surface contaminants, test pads and parallel plate
capacitors were deposited on top of them. Using an EVG 620 mask aligner and a second positive tone mask, the samples
Fig. 10.4 (a) MIT material sputter deposited, (b) MIT wire patterned using photolithography and liftoff, (c) evaporation deposition of gold, and
(d) patterned gold contacts using photolithography and liftoff
Fig. 10.5 SEM photograph of GeTe thin film
62 B.L. Danner and R.A. Coutu Jr.
were exposed to UV light and developed. A 20 nm layer of titanium (Ti) was then evaporated onto all of the samples as an
adhesive layer for the gold. A 280 nm thick gold layer was then evaporated on top of the Ti, as seen in Fig. 10.4c. Gold was
chosen for the metal parts of the test structure because of its low resistivity. The gold was then patterned using liftoff, shown
in Fig. 10.4d. Figure 10.6 shows a SEM picture of the finished electrically variable resistivity test structure.
10.4 Testing
The first test was done by placing the vanadium, vanadium dioxide, and germanium telluride samples on a thermal electric
stand in order to create a thermal gradient across the material. Figure 10.7 shows the thermal test structure under the SEM.
The samples were then heated from 30�C up to 80�C (the max temperature of the thermal stand). Using a digital multimeter
connected to hair tip probes and then .1 mm tungsten probes, the resistance was measured over each of the wires. Using
(10.2), the resistivity of each of the samples was calculated. Figure 10.8 shows the resistivity of the control sample plotted as
a function of temperature.
Using the hair tip probes, the GeTe resistivity increased starting at 50�C. Over a 30�C range, the resistivity was increased
by an order of magnitude. The VO2 wire resistivity remained consistent across the entire range of the thermal gradient. This
is due to only the surface of the thin film being oxidized in the plasma asher and can be seen in the comparison of the
vanadium and VO2 resistivity’s as the temperature was increased. The resistivity of the wires at room temperature varies
from the model due to inconsistencies in the geometry of the wires. The “wings”, formed by using liftoff as a fabrication
technique, add additional area to the wire segments. The porous nature of the thin film also contributed to the resistivities
being different. The interface between the MIT wire and the gold test pads also add a measurement bias to the resistance.
The second test was conducted on each of the wires using a variable electric field. Figure 10.9 shows the resistivity
change as a higher voltage was applied to the parallel plates for GeTe. The resistivity of each of the wires increased three to
five orders of magnitude from 37 to 45 V. When the voltage applied to the parallel plates exceeded 50 V, clipping occurred
and the resistance could no longer be measured.
The VO2 wire segments were tested using voltages on the parallel plate capacitor from 0 to 200 V. The shorter wires saw
minimal changes in the resistivity across the wires. The baseline resistivity changes of the vanadium followed closely with
that of the VO2 wires. This is attributed to the thin film of the wire only being oxidized on the surface, causing only a fraction
of the material to transition from an insulator to a metal. The wires with a length of 10,000 mm saw an increase in resistivity
near an order of magnitude with a 20 V bias applied to the plates. Due to the large length of the wire, there was a greater
oxidized area of the material. This allowed for more of a transition to occur in the thin film and therefore an increase in the
resistivity of the wire segment. Figure 10.10 shows the resistivity of the wire segments as the voltage was increased across
the parallel plates for vanadium and VO2.
Using the electric field test structures, the AC response, at 1 kHz, of the 10,000 mm PCM wires was measured. For the
VO2 samples, with a zero volt bias across the parallel plates, the AC response mirrored that of the input. When the electric
field was charged with a 110 V bias, the amplitude of the output signal was decreased by 20 % and a 7 V DC offset was added
Fig. 10.6 SEM photograph
of electrical test structure
10 Characterizing Metal Insulator Transition (MIT) Materials for Use as Micro-Switch Elements 63
to the signal. In the vanadium wire segments, the amplitude of the AC signal when 0 V were applied to the parallel plates was
only 35 % of the input signal. However, when 5 V were applied to the plates, the amplitude of the output signal again
matched that of the input signal with an additional 600 mV DC offset. With 110 V across the plates, the vanadium wire
segments caused a slight decrease in the amplitude, while only incurring a DC offset equal to half that of the VO2 samples.
Figure 10.11a, b shows the AC response for the VO2 wire segments. Figure 10.11c–e shows the AC response for the
vanadium wire segments.
2.6E-06 1.E-02
1.E-03
1.E-04
1.E-05
1.E-0630 40 50 60 70 80
2.4E-062.2E-062.0E-061.8E-061.6E-061.4E-061.2E-061.0E-06
VO2 20W600L
VO2 40W600L
V 20W600L
V 40W600L
V 20W2000L
Temperature (�C) Temperature (�C)
VO2 20W2000L
Res
istiv
ity (
Ω-μ
m)
Log
10 o
f R
esistivi
ty(Ω
-μm
)
30 40 50 60 70 80
20W600Lhairtip probe
20W600Lhairtip probe
20W2000Lhairtip probe
20W2000Ltungsten tip
20W600Ltungsten tip
a b
Fig. 10.8 (a) Resistivity of vanadium and VO2 with varying temperatures, and (b) resistivity of GeTe with varying temperatures
1.E+00
Log
10 o
f R
esistivi
ty(Ω
−μm
) 1.E-02
1.E-04
1.E-06
0 5 10 15 20 25 30 35 40 45 50
Vo1tage Applied to Parallel Plates (V)
MIT Transition
20W200L20W200L40W200L20W200L40W2000L
Fig. 10.9 Varying resistivity of and GeTe using an electric field
Fig. 10.7 SEM photograph of thermal test structure
64 B.L. Danner and R.A. Coutu Jr.
10.5 Conclusions
The resistivity of the MIT material can be altered by applying a thermal gradient or an electric field across the wire segments.
The GeTe wires were changed from a conductor to an insulator by applying a bias across the parallel plate capacitor. The
resistivity increased over three orders of magnitude with the introduction of the electric field. The lattice structure of the
GeTe films becomes amorphous with the introduction of a 35 V bias across the parallel plates. Short thin film VO2 wires saw
minimal changes in resistivity due to only the surface of the wire segment being oxidized. The resistivity of long VO2 wires
increased an order of magnitude when a 25 V potential was placed across the parallel plate capacitor. These changes in the
PCM wires allow for the creation of micro switches without a mechanical component.
10.6 Recommendations
The adaptability of these test structure designs and fabrication processes allow for a variety of MIT materials to be tested.
Comparison of the switching capability of these different materials will provide the ability to fabricate high quality micro
switches without a mechanical component. Measuring the switching times of both testing methods using different MIT
1.E-04
5 10 15 20 25 30 50 60 70 80 100
150
175
20040
1.E-05
MIT Transition
Voltage (V)
V 20W 200L
Log 1
0Res
istiv
ity(Ω
-μm
)
VOZ 20W 200L
VOZ 20W 2000L
VOZ 20W 10000L
VOZ 20W 10000L
V 40W 200L
V 20W 2000L
1.E-06
Fig. 10.10 Varying resistivity of vanadium and vanadium dioxide with an increasing potential across the parallel plates
Fig. 10.11 AC response across 10,000 mm (a) and (b) vanadium wires and (c–e) VO2 wires
10 Characterizing Metal Insulator Transition (MIT) Materials for Use as Micro-Switch Elements 65
materials will be the focus of future investigations. When testing the capabilities of VO2, use reactive sputtering with
vanadium and oxygen in order to compare the resistivity differences between a pure VO2 wire and a vanadium wire with a
VO2 thin film on the surface. The variance in resistivity of MIT wires using localized heating should be explored. Test the
full range of RF capabilities of the MIT wires.
Acknowledgements The authors are thankful to the AFIT cleanroom technicians, Mr. Rich Johnston and Mr. Tom Stephenson, for their support
in the fabrication of these devices.
Disclaimer The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air
Force, Department of Defense, or the U.S. Government.
References
1. Givernaud J, Champeaux C, Catherinot A, Pothier A, Blondy P, Crunteanu A (2008) Tunable band stop filters based on metal-insulator
transition in vanadium dioxide thin films. Presented at 2008 IEEE MTT-S international microwave symposium digest, Atlanta
2. Bouyge D, Crunteanu A, Orlianges JC, Passerieux D, Champeaux C, Catherinot A, Velez A, Bonache J, Martin F, Blondy P (2009)
Reconfigurable bandpass filter based on split ring resonators and vanadium dioxide (VO2) microwave switches. Presented at Asia-Pacific
microwave conference 2009 (APMC 2009), Singapore
3. Crunteanu A, Dumas-Bouchiat F, Champeaux C, Catherinot A, Pofhier A, Blondy P (2007) Microwave switching functions using reversible
metal-insulator transition (MIT) in VO2 thin films. Presented at European microwave conference, 2007, Germany
4. Cavalleri A, Toth C, Siders CW, Squier JA, Raksi F, Forget P, Kieffer JC (2001) Femtosecond structural dynamics in VO2 during an ultrafast
solid-solid phase transition. Phys Rev Lett 87(23):237401
5. Schilbe P, Maurer D (2004) Lattice dynamics in VO2 near the metal-insulator transition. Mater Sci Eng A 370(1–2):449–452
6. Dumas-Bouchiat F, Champeaux C, Catherinot A, Crunteanu A, Blondy P (2007) Rf-microwave switches based on reversible semiconduc-
tor–metal transition of VO2 thin films synthesized by pulsed-laser deposition. Appl Phys Lett 91(22):223505
7. Di Ventra M, Pershin YV (2011) Memory materials: a unifying description. Mater Today 14(12):584–591
8. Chen M, Rubin KA, Barton RW (1986) Compound materials for reversible, phase-change optical data storage. Appl Phys Lett 49(9):502
9. Lelmini D, Lacaita AL (2011) Phase change materials in non-volatile storage. Mater Today 14(12):600–607
10. Stotz M, Fritze S, Downar H, Wenger J (1999) Thermally controlled coplanar microwave switches. Presented at 29th European microwave
conference, vol 2, Munich, 5–7 Oct 1999
66 B.L. Danner and R.A. Coutu Jr.
Chapter 11
Stiction Failure in Microswitches Due to Elasto-Plastic
Adhesive Contacts
Ling Wu, Jean-Claude Golinval, and Ludovic Noels
Abstract Undesirable stiction, which results from the contact between surfaces, is a major failure mode in micro-switches.
Indeed the adhesive forces can become so important that the two surfaces remain permanently glued, limiting the life-time of
the MEMS. This is especially true when the contact happens between surfaces where elasto-plastic asperities deform
permanently until the surfaces reach plastic accommodation, increasing the surface forces. To predict this behavior, a micro
adhesive-contact model is developed, which accounts for the surfaces topography evolutions during elasto-plastic contacts.
This model can be used at a higher scale to study the MEMS behavior, and thus its life-time. TheMEMS devices studied here
are assumed to work in a dry environment. In these operating conditions only the Van der Waals forces have to be considered
for adhesion. For illustration purpose, an electrostatic-structural analysis is performed on a micro-switch. To determine the
degree of plasticity involved, the impact energy of the movable electrode at pull-in is estimated. Thus the maximal adhesive
force is predicted using the developed model.
11.1 Introduction
The inherent characters of MEMS such as the large surface area-to-volume ratio, smooth surfaces, small interfacial gaps and
small restoring forces, make them particularly vulnerable to stiction which is one of the most common failure mechanism of
MEMS [1]. Stiction happens when two components entering into contact permanently adhere to each-other because the
restoring forces are smaller than the surface forces (capillary, van der Waals (VDW) or electrostatic). This can happen either
during the fabrication process at etching (release stiction) or during normal use (in-use stiction).
To improve the reliability ofMEMS, models are required in order to predict and avoid in-use stiction failure. Amulti-scale
model can predict at the lower scale the adhesive contact forces of two rough surfaces, and thus can integrate these curves on
the surface of the finite elements as a contact law at the higher scale [2, 3]. The authors recently proposed [4] a model
predicting the micro adhesive-contact curves, i.e. the adhesive-contact force vs. the surface separation distance, for two
interacting micro-surfaces. This analytical model, accounting for elastic deformations of the asperities, and for van derWaals
forces, is based on classical adhesion theories [5–10] and can be easily integrated in the multiscale framework [2, 3].
Although the two-scale framework [3] based on the elastic micro-model [4] has been shown to predict accurate results for
elastic materials in dry environment [3], in order to extend the applicability of the method to other environments, the micro-
model requires enhancements, and in particular its extension to the elasto-plastic behavior of the asperities. As a first step
toward this end, this paper presents an improved model for the single elastic–plastic asperity-plane interaction problem.
When elastic–plastic rough surfaces interact, each asperity will be affected differently due to the statistical nature of the
asperity distribution on the surfaces: higher asperities will experience plastic deformations first. Due to the plastic behavior,
L. Wu
Aerospace and Mechanical Engineering Department, University of Liege, Chemin des Chevreuils 1, B4000 Liege, Belgium
School of Aeronautics, Northwestern Polytechnical University, 710072 Xi’an, China
e-mail: [email protected]
J.-C. Golinval • L. Noels (*)
Aerospace and Mechanical Engineering Department, University of Liege, Chemin des Chevreuils 1, B4000 Liege, Belgium
e-mail: [email protected]; [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_11, # The Society for Experimental Mechanics, Inc. 2013
67
the contact force on deformed asperities is lower than in the elastic case for the same contact interference (distance between
undeformed profiles), while the adhesive force increases due to the change of the asperity profile. Because of the combination
of these two phenomena the pull-out force – maximum attractive forces or the minimum compressive forces between the two
interacting surfaces – is higher than that between two pure elastic contacting rough surfaces. Another qualitative difference
with elastic surfaces is the difference of behavior under cyclic loading: after repeated contacts, the distribution of asperities
heights and the tip radii of the higher asperities change [11], until plastic accommodation or shakedown [11]. This induces a
“contact hardening” [13] and the pull-out force increases until accommodation, unless in-use stiction happens first.
To account for the elasto-plastic behavior, the authors [14] have developed a micro-model able to predict stiction for
elastic–plastic rough surfaces by first considering the problem of a single elasto-plastic asperity interaction and thus the
generalization to the interaction of rough surfaces. The single asperity/plane contact problem is modeled using semi-
analytical models [15–17] which evaluate the deformed asperity profile during hysteretic loading/unloading without
considering the adhesion effect. Assuming adhesion will not affect the plastic deformations, which is not the case for
extremely soft materials as gold [18], we can consider the Maugis theory [7] completed by Kim expansion [8] to evaluate the
adhesion forces during the unloading phase [4] from the tip radius evolution during loading process. As amain difference with
previous models [15–17], adhesion forces are evaluated taking into account the effect of the non-constant asperity curvature
resulting from elasto-plastic deformations, which conducts to an accurate prediction of the pull-out forces [14]. In this model
only van der Waals forces are considered, which is a realistic assumption below 30% humidity [1]. The interaction of two
rough surfaces is achieved by considering a usual statistical distribution of asperities [5, 6], however, contrarily to the elastic
case, the distribution of asperities heights and the asperity profiles of the higher asperities change due to the plastic
deformations. These changes, and the resulting adhesive-contact forces, are evaluated using the single asperity model. As a
result, micro adhesive-contact curves of two interacting elasto-plastic rough surfaces can be predicted in an analytical way
during loading and unloading.
The purpose of this paper is to predict the reliability of a micro-switch by considering the effect of repeated interactions
between the movable/substrate electrodes. For illustration purpose a one-dimensional model is considered and contact
occurs between two Ruthenium (Ru) films. We also show that unloading curves change after repeated interactions until
reaching accommodation. Thus, the pull-out force can be predicted in terms of the pull-in force and of the cycles number,
opening the way to a stiction-free design.
The organization of the paper is as follows. In Sect. 11.2, the micro-model for elasto-plastic adhesive-contact is
summarized. First the single elasto-plastic asperity/plane interaction model with no adhesion effect is described. Then,
the adhesion forces are evaluated from the deformed asperity profile taking into account the effect of the non-constant
asperity curvature resulting from elasto-plastic deformations. Finally the micro adhesive-contact curves of two interacting
elasto-plastic rough surfaces are deduced. This model can then be used in Sect. 11.3 to study the micro-switch reliability. In
particular the effect of cyclic loading on the pull-out force, and thus on the stiction risk, is predicted.
11.2 Micro-model for Elasto-Plastic Adhesive-Contacts
In this section, the single elasto-plastic asperity/plane interaction model with no adhesion effect is first described before
evaluating the adhesion forces from the deformed asperity profile. Then, using a statistical distribution of asperities heights
accounting for the changes in asperity profiles and heights due to the plastic deformations, the micro adhesive-contact curves
of two interacting elasto-plastic rough surfaces can be predicted.
11.2.1 Single Asperity Elasto-Plastic Contacts
Let an asperity of tip radius R, Young modulus E, and yield stress SY, interacts with a rigid plane at an interference distance d,positive in case of contact and negative otherwise, see Figs. 11.1a, b, defined as the distance between the original profile of
the asperity tip and the plane. When the plane starts interacting with the asperity during loading, the critical yield
interference dCP is defined as the interference at which the asperity starts yielding and can be expressed as [15–17]
dCPR
¼ pCvSY2E
� �2(11.1)
68 L. Wu et al.
In this expression Cv is a coefficient that depends on the Poisson ratio v, and that can be evaluated from Cv ¼ 1.295e0.736v,
e.g. [16]. As, with our assumption, the asperity starts yielding at positive interference, there exists a corresponding critical
contact radius aCP, Fig. 11.1a, and a critical contact force FCP, respectively evaluated as
aCP ¼ffiffiffiffiffiffiffidCPR
r(11.2)
FCP
R¼ 2
3pCvSYdCP (11.3)
During the loading phase, assuming the interference goes beyond the critical interference dCP, the asperity is subject to
permanent plastic deformations that depend on dmax, the maximal interference reached. After unloading, the asperity
exhibits a permanent reduction of the asperity height dres, and a modified asperity tip radius Rres, see Fig. 11.1c, that were
curve-fitted from finite element numerical simulations [17]
dresdrmax
¼ 1� dCPdrmax
� �0:28" #1� dCP
drmax
� �0:69" #(11.4)
Rres
R¼ 1þ 1:275
SYE
� �0:216 dmax
dCP� 1
� �(11.5)
11.2.2 Single Asperity Elasto-Plastic Adhesive Contacts
In Maugis theory [7], the inter-atomic attraction effect is modeled using a Dugdale assumption: within a critical value of
separation z0, two surfaces are attracted with a constant force per unit area s0, while if the separation z exceeds z0, theadhesive traction vanishes. The associated adhesive energy readsϖ ¼ s0z0. Maugis theory for the interaction of two elastic
asperities characterized by two Young modulii E1 and E2, two Poisson ratios v1 and v2, and by two tip radii R1 and R2, is
based on the definition of a transition parameter
l ¼ 2s0ffiffiffiffiffiffiffiffiffip�oK2
R3
q whereK ¼ 4
3
1� v12
E1
þ 1� v22
E2
� ��1
andR ¼ R1R2
R1 þ R2
(11.6)
are respectively the equivalent modulus and initial tip radius of two interacting asperities, or the initial radius of an asperity
interacting with a plane. The transition parameter defines a solution ranging from JKR regime [5] – soft materials with a
large contact curvature surface and with a high surface energy – to the DMT regime [6] – hard materials with a reduced
contact curvature and with a low surface energy. This solution provides, for a given interaction d, the adhesive contact forceFn, the interacting contact radius a and the adhesive-contact radius c on which adhesive forces apply, see Fig. 11.1a. The
system of equations is written in terms of the non-dimensional values
A ¼ aK
p �oR2
� �1=3; �Fn ¼ Fn
p�oR; D ¼ d
K2
p2 �o2R
� �1=3and m ¼ c
a(11.7)
Fig. 11.1 Definition of single asperity interference [14]
11 Stiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts 69
and reads
1 ¼ lA2
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1
pþ m2 � 2� �
arctanffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1
ph iþ 4l2A
3
ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1
parctan
ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1
p� mþ 1
h i(11.8)
D ¼ A2 � 4lA3
ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1
p(11.9)
�Fn ¼ A3 � lA2ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1
pþ m2 arctan
ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1
ph i(11.10)
This set of equations is completed by the interference evaluation
d ¼ a2
R� 8s0
3K
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2 � a2
p(11.11)
Kim et al. [8] extended Maugis-Dugdale solution to the non-contact regime when a ¼ 0 and c 6¼ 0, see Fig. 11.1b, see [4]
for details. Practically, this expansion has to be considered when l <0.938.
Although this adhesive theory is based on Hertz contact model, and thus assumes an elastic behavior, we proposed [14] to
apply this theory on the permanently deformed asperity profile. As during the unloading the behavior remains elastic, at the
exception of extremely soft materials, Maugis theory completed by Kim extension constitutes a good approximation.
However, we proposed to account for a non-constant asperity radius in terms of the interference, see Fig. 11.1c, and to
perform the adhesive-contact theory on the assumed elastically deformed asperity, which has an effective tip radius Reff at a
contact interference d � dres. This is motivated by the fact that Maugis theory assumes a uniform asperity radius to apply
Hertz theory although this case is only met at the limit case d ¼ dres. The following expression has been proposed [14]
Reff
R¼ Rres
R� 1:275 1� c1ð Þ SY
E
� �0:216 dmax
dCP� 1
� �1� e
c2d�dres
dmax�dres
1� ec2
0@
1A (11.12)
In this expression, c1 and c2 are functions that have to be determined by inverse analysis from finite-element results.
Using the simulations performed for Ru [19], we proposed [14]
c1 ¼ 0:22þ 0:6242e�0:092
drmax
dCP and c2 ¼ 10
1þ drmax 10dCP=ð Þ2 � 5 (11.13)
Because of the elasto-plastic behavior happening during contacts, the theory developed here results in different adhesive-
contact forces during loading FnL(d) and unloading Fn
U(d). During the loading phase, once dCP is reached, the maximum
interference is identical to the current one (dmax ¼ d) and the deformed profile can be evaluated from (11.4) and (11.5).
Thus, the loading force FnL(d) is evaluated from Maugis solution by solving the system (11.8), (11.9), (11.10), and (11.11),
with as input for R the effective radius (11.12), and as input for d the effective value d � dres, where dres increases during thewhole loading process. During unloading however, the residual (dres) and maximal (dmax) interferences reached remain
constant. The adhesive-contact force during unloading FnU(d) is computed from the Kim extension [8] of Maugis theory [7],
with as input for R the effective radius (11.12), and as input for d the effective value d � dres. Contrarily to the loading
process, the effect of adhesion needs to be considered at the intermediate pull-out stage, which is achieved by using the Kim
extension [8].
The elastic–plastic adhesive contact of a micro sphere was studied for Ruthenium (Ru) in [19]. Ru has the advantage of
not exhibiting plastic deformations under adhesive effects only. Material properties and the initial asperity tip radius are
reported in Table 11.1. To demonstrate the accuracy of the proposed method, Fig. 11.2 compares the predicted adhesive-
contact forces to the FE results for the loading and unloading adhesive-contact forces at three maximum interferences dmax
successively equal to 17, 34 and 51 nm. It is seen that an excellent agreement is obtained for the three loading conditions.
70 L. Wu et al.
11.2.3 Rough Surfaces Interaction
Greenwood and Williamson ‘asperity-based model’ [9] is applied to simulate the rough surface/plane interaction. A rough
surface is described by a collection of spherical asperities with identical end radii R, whose heights h have a statistical
distribution
’ðhÞ ¼ 1
ssffiffiffiffiffiffi2p
p exp�h2
2s2s
� �(11.14)
where ss is the standard deviations in asperity heights. The contact of two rough surfaces can be represented by the contact
between an equivalent rough surface and a smooth plane [10]: if the two initial contacting rough surfaces have respectively
the asperities end radii of R1 and R2, the equivalent radius is defined by (11.6), and if the standard deviation in asperity
heights are ss1 and ss2, the equivalent rough surface is defined by the standard deviation in asperity heights ss ¼ (ss12 +
ss22)1/2. The interaction between two rough surfaces is also characterized by the distance d between the two rough surface
mean planes of asperity heights, and by N, the surface density of asperities. All these values can be identified from the study
of the surfaces topography, and, in particular, depend on the surface RMS roughness Rq, see [3] for details.
The surface loading and unloading forces, respectively FnTL and FnT
U can now be evaluated by integrating on the surface
the effect of each asperity, for which the interference reads d ¼ h � d, using the framework described in Sect. 11.2.2.
Toward this end, non-dimensional values are defined
�FnT ¼ FnT
p �oR; �d ¼ d
ffiffiffiffiffiffiffiffiffiffiffiffiffiK2
p2 �o2R
3
rand ss ¼ ss
ffiffiffiffiffiffiffiffiffiffiffiffiffiK2
p2 �o2R
3
rð11:15Þ
Table 11.1 Properties
of Ru filmsR [mm] 4
E [GPa] 410
v [�] 0.3
SY [GPa] 3.42
z0 [nm] 0.169
ϖ [J/m2] 1
ss [nm] 7.78
Rq [nm] 7.81
N [mm�2] 10
Fig. 11.2 Comparison of
the single asperity model
with finite element results
for Ru
11 Stiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts 71
which allows writing
�FnT ¼ N
�ssffiffiffiffiffiffi2p
pð�Fn Dð Þe�
Dþdð Þ22�ss2 dD (11.16)
It bears emphasize that as asperities enter into plasticity for different surface distances, the effective profile is different for
each asperity. Details on the integration (11.16) are provided in [14].
11.3 Cyclic Loading of a Micro-switch
A one-dimensional model of micro-switch is considered, see Fig. 11.3. In this model, a potential difference U is applied
between a movable electrode and a substrate electrode covered by a dielectric layer of thickness td and permittivity ed. Themovable electrode is attached to a spring of stiffness per unit area KS, and is initially at a distance d0 from the substrate.
The switch is supposed to work in vacuum, permittivity e0, so the damping effect of a squeeze film is neglected. Typical
values for SiN dielectric are reported in Table 11.2. Contact is assumed to occur between two Ru surfaces, for which typical
topography values are reported in Table 11.1. Ru films of thickness ts are deposited on the movable electrode, and also on a
part of the substrate.
From these data, the pull-in voltage and the impact energy can be computed in terms of the stiffness KS. This computation
has been performed in [14], and in this application we consider an impact energy of EI ¼ 0.5 J/m2. This impact energy per
unit surface of the contacting area affects the plastic deformations of the asperities and thus the adhesion-contact forces.
Indeed, once an impact occurs, the energy EI is converted into elastic and plastic deformations energies. The asperities
loading process finishes once all the energy has been converted. The energy for elastic wave propagation is neglected in this
work; however the elastic energy in the Ru film is accounted for. With these assumptions, the distance de between the two
rough surfaces mean planes of asperity heights reached at the end of the impact process is deduced from
EI ¼ð1
de
FnTLðdÞdd þ FnT
L deð Þ� �2ts
2E(11.17)
Once the distance de has been computed, the deformed profile of the asperities is known, and the unloading process can be
studied. In particular, the adhesive contact forces FnTU are evaluated from (11.16) in terms of the distance d > de.
Fig. 11.3 1D micro-switch
application
Table 11.2 Properties
of the micro-switchd0 [mm] 2
td [mm] 0.15
e0 [pF/m] 8.854
ed / e0 [�] 7.6
ts [nm] 180
72 L. Wu et al.
These two steps characterize one loading/unloading cycle. To study cyclic loading, the same analyses have to be
performed with updated asperities profiles. Indeed, after the first cycle, the profile of the surface is modified as only higher
asperities entered into contact and exhibited plastic deformations. History is tracked by keeping after each loading the
function dmax(h) of the maximal interference reached for an asperity of initial height h. From this function the profile change
of an asperity of initial height h can be known to evaluate its effect on the loading/unloading forces (11.16). Thus, the
reliability of the micro-switch can be studied by considering the effect of repeated interactions between the movable/
substrate electrodes. Indeed, the unloading curves change after repeated interactions until reaching accommodation, as
illustrated on Fig. 11.4, where the unloading curves after 1, 2, 3 and 10 cycles are reported. From this figure it appears that
the pull-out force after accommodation can be predicted, opening the way to stiction-free design. On this figure the elastic
solution is also reported, and is shown to underestimate the pull-out force. Also the loading curve is represented.
11.4 Conclusions
In order to predict stiction in MEMS structures, a possible approach is to consider a multi-scale framework. If at the higher
scale a finite element analysis can be considered, it requires an adhesive-contact law to be integrated on the interacting
surfaces.
The definition of this adhesive-contact law constitutes the micro-scale problem. In this paper, this adhesive contact-
distance curve of two interacting elasto-plastic rough surfaces was established using a semi-analytical analysis. First the
deformed profile of the asperity is evaluated from literaturemodels, which uncouple the plastic deformation from the adhesive
effect. This assumption usually holds except for materials suffering from jump-in induced plasticity, as for gold, for which
the sole adhesion effect can lead to plastic deformations. Then, we useMaugis-Kim adhesive theory to evaluate the adhesive-
contact forces. In order to account for the deformed shape of the asperity, assumed as spherical in the Hertz contact of the
Maugis theory, we propose to evaluate an effective asperity radius which depends on the interference. With this method, we
can predict the loading/unloading hysteresis curves of a single elastic–plastic asperity interacting with a rigid plane. Finally a
statistical model of asperity height is considered to study the interaction of two elasto-plastic rough surfaces.
The predictions of this model are illustrated by considering the cyclic loading of a 1D micro-switch application. It is
shown that the repeated loading of a MEMS switch changes the structure of the contacting surface due to the plastic
deformations. Thus, with time, the contact surfaces become smoother, increasing the adhesion effect. This effect should be
considered at the design stage to avoid in-use stiction.
Fig. 11.4 Cyclic loading of the 1D micro-switch
11 Stiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts 73
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74 L. Wu et al.
Chapter 12
Simultaneous Measurement of Force and Conductance Across
Single Molecule Junctions
Sriharsha V. Aradhya, Michael Frei, Mark S. Hybertsen, and Latha Venkataraman
Abstract Measurement of electronics and mechanics of single molecules provides a fundamental understanding of
conductance as well as bonding at the atomic scale. To study the mechanics at these length scales, we have built a
conducting atomic force microscope (AFM) optimized for high displacement and force resolution. Here, we simultaneously
measure conductance and force across single Au-molecule-Au junctions in order to obtain complementary information
about the electronics and structure in these systems. First we show that single-atom Au contacts, which have a conductance
of G0 (2e2/h), have a rupture force of about 1.4 nN, in excellent agreement with previous theoretical and experimental
studies. For a series of amine and pyridine linked molecules which are bound to Au electrodes through an Au-N donor-
acceptor bond, we observe that the rupture force depends on the backbone chemistry and can range from 0.5 to 0.8 nN. We
also study junctions formed with molecules that bind through P-Au and S-Au interactions. We find that both the conductance
signatures and junction evolution of covalent S-Au bond (thiolate) and a donor-acceptor S-Au bond (thiol) are dramatically
different. Finally, we perform density functional theory based adiabatic molecular junction elongation and rupture
calculations which give us an insight into the underlying mechanisms in these experiments.
12.1 Introduction
Understanding the physical properties of single molecule junctions is of fundamental importance to nanoscale electronics
[1–7]. While the electrical and thermal properties of a variety of organic molecules bound to metal electrodes have been
probed [6–14], measurements of rupture forces of single metal-molecule-metal junctions are new [15–19]. Mechanical
information at these length scales can help address a multitude of untested predictions regarding the interplay between
structure, mechanics and electronics of these junctions. In particular, probing the relation between mechanical and electronic
properties of single molecule circuits provides a deeper understanding of the structure-conductance relation in these systems.
The force signature for particular bond rupture events occurring during junction formation and evolution are probed in these
measurements, similar to the more established conductance signatures for a variety of known molecular backbones and
linker group combinations. However, conductance data alone is often insufficient to fully explain the complex, atomic
processes that control the evolution of the junction structure, in particular under stress. In this respect, force measurements
can potentially be used to determine bond rupture forces, junction stiffness, and their relation to the loading rate, that has
been demonstrated for biomolecular systems [20, 21].
Here, we use a modified atomic force microscope (AFM) to form single molecule junctions between an Au substrate and
an Au-coated cantilever (Fig. 12.1). The simultaneously measured conductance and force between the AFM tip and substrate
are analyzed to determine bond rupture forces [17, 18]. We analyze force data to obtain bond rupture forces from a large,
statistically significant set of individual measurements. We first show that the force required to break an Au-Au bond is
S.V. Aradhya • M. Frei • L. Venkataraman (*)
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
e-mail: [email protected]; [email protected]
M.S. Hybertsen
Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_12, # The Society for Experimental Mechanics, Inc. 2013
75
1.4 nN, based on over 31,000 individual measurements and in good agreement with previous published results [22–24].
We then show that for single molecule junctions, the N-Au bond-rupture force depends on the molecular backbone, and
varies from 0.8 nN for 4,40 bipyridine to 0.5 nN in 1,4 diaminobenzene [17]. We then compare the conductance and rupture
forces of single molecule junctions formed by alkane backbones terminated with four different linker groups: amine,
methylsulfide, diphenylphosphine and thiol [18]. For the first three, which bind to Au through a donor-acceptor bond, we see
clear conductance signatures, with junctions rupturing under 0.6–0.8 nN stress. In contrast, junctions with thiol linkers
undergo multiple plastic deformation events during elongation, indicative of structural rearrangements. However, we find
that these events have an average rupture force that is smaller than the 1.4 nN observed for the rupture force of a single Au
atom contact. These results show that the rupture of an Au-S covalently bonded junction, which would most likely occur at
an Au-Au bond, does not require a force of 1.4 nN contrary to what is commonly assumed. Finally, we perform density
functional theory (DFT) calculations for adiabatic junction elongation trajectories. Chemical trends in the maximum
sustained force determined from these calculations agree well with the experimental results for rupture forces.
12.2 Experimental Methods
A schematic representation of the AFM setup is shown in Fig. 12.2a. The conductive AFM consists of a modified AFM head
(Veeco Multimode), external adder and filter circuits (SRS), as well as a homebuilt cantilever holder. A constant bias is
applied between an Au coated cantilever (TAP300, BudgetSensors) and an Au substrate placed on top of a single-axis
piezoelectric positioner with a built-in position sensor (Mad City Labs). The resulting current is converted to a voltage with a
current amplifier (Keithley 428). Data collection and control of the piezoelectric positioner are done by means of a data
acquisition board (National Instruments, PXI-4461) driven by a customized program using Igor software (Wavemetrics
Inc.). The AFM cantilever coated with a 5 nm Chromium adhesion layer and 100 nm of Au (99.999% purity, Alfa Aesar)
served as one electrode. An Au substrate (mica with 100 nm Au layer, 99.999% purity, Alfa Aesar) served as the second
electrode. The cantilever and substrate were UV/ozone cleaned prior to use. Force was determined by measuring the
deflections of a laser spot focused on the back of the cantilever, collected on the detector. The detector signal was calibrated
to yield the force data, using the thermal power spectrum method [23, 25]. For the simultaneous conductance and force trace
measurements, the substrate approached the cantilever tip until a set conductance larger than 5 G0 was measured to ensure
that the Au-molecule-Au junction from the previous measurement was completely destroyed. The sample was withdrawn at
a rate of 18 nm/s and the current and force versus position data was recorded at a sampling frequency of 100 kHz. All
position determinations were based on measurements with the built-in position sensor within our custom piezoelectric
positioner. This position sensor was calibrated both by the manufacturer and by us using laser interference measurements.
We found the absolute values of the measured displacements to be accurate to within 5%.
We simultaneously measure the conductance and force of molecular junctions by repeatedly forming and rupturing Au
point contacts between the tip and substrate of the AFM (Fig. 12.2a). Simultaneous measurements of cantilever deflection
relate to the force applied across the junction. The AFM is operated in ambient conditions at room temperature. Conductance
is measured by applying a constant bias of 25 mV between the tip and substrate, and measuring the resulting current. For
each measurement, an Au point-contact is first formed between the substrate and cantilever. It is then pulled apart and
Fig. 12.1 Illustration of
stretching and breaking
of a single molecule junction
between the AFM cantilever
and the substrate. Chemical
structure of the linker groups
and molecular backbones
measured in this study are
shown along with arrowsof size proportional to their
respective measured rupture
forces
76 S.V. Aradhya et al.
broken, while conductance and force are recorded as a function of sample displacement. This process is repeated thousands
of times to obtain large data sets of conductance and simultaneously acquired force versus junction elongation. Before
adding any molecule to the substrate, at least 1,000 conductance and force traces were collected to ensure that no
contamination was present in the setup. Individual conductance traces for an Au point-contact show stepwise decrease in
conductance until a single atom contact is formed with a conductance of G0 ¼ 2e2/h, the quantum of conductance
(Fig. 12.2b). The simultaneously acquired force traces show a characteristic saw-tooth pattern (Fig. 12.2b) indicating two
distinct force regimes: gradual linear increases due to elastic (reversible) elongations and sharp drops due to permanent
deformations of the junction. Upon further stretching, the single atomic gold wire breaks and the conductance exhibits a
tunneling signature when no molecules are present, while the cantilever displacement changes abruptly. When
measurements are carried out in an environment of molecules, an additional conductance step is frequently observed at a
molecule-dependent conductance value below 1 G0 along with an additional abrupt change in the force trace. The full trace
of force versus elongation presents a rich dataset describing the mechanical evolution of these junctions under stress. In this
study, we focus on the force associated with the breaking of a single atomic Au contacts or an Au-molecule-Au junctions.
This can be determined by analyzing the change in the cantilever deflection at the location where the 1 G0 or the molecular
conductance step ends and the junction breaks.
To extract statistically significant characteristics from the evolution of junction conductance and force as a function of
sample displacement, we construct two-dimensional (2D) histograms from the conductance and force traces, setting the origin
of the displacement axis at the point where either the 1 G0 conductance step or the molecular conductance step breaks. This
well-defined position on the x-axis is determined individually for each trace, using an automated algorithm. A fraction of the
traces do not show a conductance plateau at G0 or a plateau corresponding to a molecular junction. It is likely that the absence
of the G0 or the molecular conductance plateau means that a single-atom point contact or a single molecule junction was not
formed during that particular measurement. Therefore, these traces were not used for further analysis, as they do not contain
the bond rupture event of interest. The statistical occurrence of the junction of interest varies with the case, but a statistically
significant and unbiased data set results in each case. Each data point on the digitized conductance (force) trace was thus
assigned a conductance (force) coordinate (along the y-axis) and a position coordinate (along the x-axis). Two-dimensional
conductance histograms were then generated without further analysis. For the two-dimensional force histogram, we also set
the force at the new zero-displacement position to zero force by subtracting an offset from the entire force trace. This
realigned all force traces to a common point such that each force and displacement value was now determined relative to the
value at the end of the conductance step in each trace. After this realignment, thousands of force traces were added to generate
a two-dimensional force histogram. A statistically averaged force profile is obtained from this histogram from the peak of a
Gaussian that is fit to vertical sections at every displacement bin.
Figure 12.3a, b shows two-dimensional conductance and force histograms, respectively, constructed from over 31,000
traces measured without any molecules present and using 20 different tip/sample pairs. Insets to Fig. 12.3a, b show a
sample conductance and simultaneously acquired force trace, respectively, to illustrate where the zero in displacement is set.
The conductance is plotted on a logarithmic axis, whereas the force and the position (x-) axes use linear bins in these plots.
Negative displacements are events that occur before the end of the 1 G0 plateau while positive corresponds to data beyond the
Fig. 12.2 (a) Schematic of the modified conductive atomic force microscope. An Au point contact is formed between a Cr/Au-coated cantilever
and an Au-coated substrate with the relative separation controlled by a piezo. The force acting on the junction is detected by optically measuring
the deflection of the cantilever. (b) Sample conductance (red) and force (blue) data showing the evolution and rupture of an Au point contact, at abias of 25 mV and a piezo displacement speed of 18 nm/s. Step-wise decreases in conductance are accompanied by sudden jumps in the force
12 Simultaneous Measurement of Force and Conductance Across Single Molecule Junctions 77
end of the plateau. These histograms are generated from traces where the G0 step can be identified with our automated
algorithm. Approximately 80% (31,033 out of 39,000) of the measured traces exhibit a clearly identifiable 1 G0 step and are
included. Figure 12.3a shows clear peaks at integer multiples of G0 occurring at negative displacements, and almost no counts
at positive displacements, since zero displacement is set at the point when the G0 contact breaks.
The 2D force histogram, created from the same set of traces, (Fig. 12.3b) shows a trend in the force that is increasing with
increasing displacement, just prior to the clear sharp drop at zero displacement. The force required to break the G0 contact can
be determined from the magnitude of this drop. The force profile is effectively an averaged force trace for the single atom
contact rupture event. It shows a clearly defined drop of 1.4 � 0.2 nN at zero displacement, as illustrated in Fig. 12.3b,
corresponding to the breaking force of a single Au-Au bond. This value is in good agreement with published experimental and
theoretical results [22–24], validating our 2D analysis method. We note here that this result is from a statistically significant
data set of about 31,000 traces, providing a robust and unbiased determination of the single Au-Au bond breaking force.
12.3 Single Molecule Measurements
We apply this same technique to compare the bond rupture force in single molecule junctions. We study seven molecules
chosen to represent (a) four different molecular backbones (butane, hexane, benzene and bipyridine), each with a nitrogen
termination, and (b) four linker groups (Amine [NH2], thiomethyl [SMe], thiol [SH] and diphenylphosphine [DPP]), each
attached to similar saturated backbones (of 4 or 5 carbon atoms). The chemical names (and abbreviations used in the
following discussion) for the molecules are: (a) 1,4 diaminobenzene (BDA), (b) 4,40 bipyridine (BP), (c) 1,6-hexanediamine
(C6A), (d) 1,4-butanediamine (C4A) (e) 1,4-bis(methylsulfide) butane (C4SMe), (f) 1,5 bis-(diphenyl-phosphino)pentane
(C5DPP), and (g) 1,4-butanedithiol (C4SH). Each compound is obtained from commercial sources, and used without further
purification. Conductance is determined by measuring current through the junction at a constant applied bias of 25 mV for all
molecules, except 75 mV for C6A and for BP. The molecules are deposited onto the Au substrate either by evaporation or by
addition of a dilute concentration of molecule in the solvent 1,2,4-tricholorobenzene (TCB). Both the conductance and force
results are independent of the deposition method. Over 10,000 individual conductance and simultaneously acquired force
traces are collected with multiple tip/sample pairs for each molecule and these are analyzed by generating 2D histograms, as
detailed above, to characterize the molecular breaking force.
Figure 12.4a shows a 2D conductance histogram for C4A where the origin in the displacement axis is set at the end of the
molecular conductance step. Logarithmic bins for the conductance (y-) axis and linear bins for the displacement (x-) axis are
chosen for image clarity. The measured traces that show a molecular conductance step were selected using an automated
algorithm for both conductance and force analysis. Insets of Fig. 12.4a, b show conductance and simultaneous force data for
one particular junction breaking event, out of the over 3,500 individual measurements used to construct the 2D histograms.
A clear feature is seen in the conductance histogram at 9 � 10�4 G0, which gives us the most probable conductance of an
Fig. 12.3 (a) Two-dimensional conductance histogram constructed from over 31,000 traces. All traces are aligned such that the end of the plateau at
1 G0 is at zero along the displacement axis. A large number of counts is visible at integer multiples of G0. Inset: Sample conductance trace aligned to
zero displacement at the end of the 1 G0 plateau. (b) Two-dimensional force histogram constructed from simultaneously acquired force traces.
The force profile (black curve) is overlaid and shows a clear jump at zero displacement. The rupture force of 1.4 nN for a single atomic contact is
determined by extrapolating the fit of the force profile (dotted line). Inset: Force trace acquired simultaneously with conductance trace shown in the
inset to panel (a), aligned at the 1 G0 break
78 S.V. Aradhya et al.
Au-C4A-Au junction. This peak extends over a displacement of about 0.15 nm, indicating that molecular junctions can be
elongated over this distance prior to the final rupture.
Every molecule, except C4SH, shows characteristic conductance features due to the selective binding of the N, SMe or
DPP linker to undercoordinated Au atoms [26, 27]. Particularly, BP shows two characteristic conductance peaks (a ‘high-G’
and a ‘low-G’ peak) that occur at distinct junction elongation distances [28–30]. In this work, we probe the rupture from the
low-G peak, which corresponds to a geometry where the molecule bridges the two Au electrodes vertically [30]. Except
C4SH, for which we do not find any well-defined conductance, we note that the conductance peak positions (corresponding
to the most frequently measured conductance, see Table 12.1) are in good agreement with previously published data
collected in solution using the scanning tunneling microscope-based break junction technique [27, 30]. This further validates
our measurement and molecule deposition techniques. Furthermore, the clear conductance signature seen for all these
molecules allows us to measure specific single Au-molecule-Au junction rupture events unambiguously. In each case, except
the thiolate (SH) linker, it is also known that the binding mechanism is the (N, P or S)-Au donor-acceptor interaction [26, 27,
30–33]. In Table 12.1, we show bond rupture forces determined from 2D force histograms for six molecules considered here,
except C4SH. We see that in all these cases, the Au-molecule-Au junction ruptures at a force smaller than that of an Au-Au
bond, indicating that rupture occurs at the respective donor-acceptor bonds consistent with earlier work [16, 27, 33].
Specifically in the amine linked molecules, by comparing the measured rupture forces for C4A and C6A we see first that for
these two alkanes with 4 and 6 carbons in the backbone, the rupture forces are very similar. Additionally, we see that the
force required to break the N-Au bond in the conjugated molecule, BDA, is considerably smaller than in C4A and C6A,
which are fully saturated.
For the thiol (SH) linker, there are multiple bonding scenarios for an Au-S covalent bond, many possible locations for the
adsorption of the H atom on the electrodes and also a possibility of forming an Au-SH donor-acceptor bond [34]. In our
conductance results of C4SH, we see a qualitatively different behavior from those of the other three linkers. We see a
multitude of conductance features over a wide range of conductance spanning from just below G0 to the experimental noise
floor. This fact reflects previous studies [35, 36] which have explained such observations based on the many possible binding
mechanisms and geometries accessible to thiol linkers. Figure 12.5a, c demonstrates the lack of any clear conductance feature
in individual measurements of C4SH, in comparison to measurements with C4SMe, in our experiments. This precludes the
unambiguous assignment of the displacement at which the junction ruptured in each trace, which is essential in constructing a
2D conductance or force histogram. We therefore focus the analysis on the force traces, and use an alternate approach, based
on identification of all sharp drops in individual force traces with an automated algorithm. Each force drop corresponds either
to a structural rearrangement in the junction or junction rupture. Each such event can be associated with the conductance of the
junction immediately prior to the abrupt jump in force. One key difference between the 2D force analysis technique used
above and this alternate force event identification method is that the former relies on the identification of events through
conductance and therefore does not bias the results towards larger force values that are more easily identified.
Fig. 12.4 (a) Two-dimensional conductance histogram of C4A constructed from over 3,500 traces with a molecular conductance step. Features
representing a sequence of Au contacts clearly appear at integer multiples of G0. A molecular signature can be clearly seen at 9 � 10�4 G0. Inset:
A sample conductance trace showing a G0 and molecular plateau with zero displacement set to the end of the molecular plateau. (b) The two-
dimensional force histogram for C4A is constructed from the simultaneously acquired force traces of the same set of traces used to construct the
conductance histogram. The average force profile (black curve) shows a clear drop at zero-displacement, which gives a statistically determined
breaking force for the N-Au bond of ~0.6 nN. Inset: The simultaneously acquired force trace aligned after the molecular step is shown
12 Simultaneous Measurement of Force and Conductance Across Single Molecule Junctions 79
Table 12.1 Comparison of most frequently measured conductance and rupture force for molecular junctions with a nitrogen termination having
different backbones (rows 1–4) and saturated backbones having different linker groups (rows 4–6)
No. Molecule Chemical structure
Conductance
(G0)
Bond rupture force (nN)
Expt. DFT
1 1,4 benzenediamine (BDA) 6 � 10�3 0.5 0.46
2 4,40 bipyridine (BP) 1 � 10�4 0.8 1.00
3 1,6 hexanediamine (C6A) 1 � 10�4 0.6 –
4 1,4 butanediamine (C4A) 9 � 10�4 0.6 0.84
5 1,4-bis(methylsulfide) butane (C4SMe) 1 � 10�3 0.7 0.84
6 1,5 bis-(diphenyl-phosphino)-pentane (C5DPP) 7 � 10�4 0.8a 1.4b
Rupture forces predicted by DFT adiabatic trajectory simulations of representative junctions are also listed for quantitative comparisonaExperiments with C5DPP showed evidence of significant fluctuations in force over the course of individual molecular conductance signaturesbDFT calculations for butane with dimethylphosphine links [33]
Fig. 12.5 Sample conductance (red) and force (blue) traces for C4SMe (a) and C4SH (c). The double headed arrows indicate a 0.2 nm
displacement. 2D histograms showing each identified force drop event and its corresponding conductance value for C4SMe (b – 51,000 events)
and C4SH (d – 121,000 events). The conductance bin size is 30 bins per decade, and the force bin size is 0.04 nN
80 S.V. Aradhya et al.
In Fig. 12.5b, d we show the two-dimensional histograms correlating the change in force for each force event against the
associated conductance immediately prior to the force event from all measured traces for C4SMe and C4SH. Each count in
this 2D histogram represents a force and conductance value of an individual trace, as determined by the automated
algorithm. We see first that both histograms show a large number of force events at a conductance value around 1 G0.
These force events correspond to rearrangement and the final breaking of a single-atom gold contact. Second, for C4SH
(Fig. 12.5d), we find numerous force events spread along the conductance axis from just below 1 G0 to the experimental
conductance noise floor of about 2 � 10�5 G0. For C4SH, we find that 75% of all measured traces exhibit force events with a
conductance below 1 G0. Furthermore, from this selected subset, we find that each trace has an average of 2.7 force events.
This is a direct indication that junctions formed with the S-Au bond undergo substantial rearrangements with varied atomic
structure that sustain a broad range of conductance values. In contrast, the C4SMe data (Fig. 12.5b) shows that almost all
force events below 1 G0 occur within a narrowly defined conductance range [33]. Of all the measured traces, 40% show force
events for a conductance below 1 G0, and of this subset, each trace has an average of 1.5 force events. Thus although some
structural rearrangement might occur in SMe terminated molecular junctions, they are not accompanied by large changes in
conductance. This agrees with previous DFT based junction elongation simulations that show shifts in attachment point for
the donor-acceptor bond with modest changes in junction conductance [33]. Finally, the C4SH data also shows a significant
number of force events with conductance values within our experimental noise; a large number of force events occur at a
conductance that is too low to measure in this set-up. This could be due to the formation of molecular dimers or due to
pulling out of chains of gold atoms, as has been seen in simulations [37–40].
12.4 Discussion
We have used DFT-based calculations to simulate the junction elongation [40, 41] process and to understand the trends in the
rupture forces for the molecules studied here. Representative junction structures are developed with similar orientation and
link bonding for comparisons. Each Au tip and surface were modeled with an Au pyramid (20 atoms each) with (111)
surfaces with the tip atom on the top pyramid moved to an adatom site on one facet resulting in a blunt, three atom tip [33].
Here we focused on the portion of the trajectory where the junction was elongated from a local energy minimum through the
inflection point and finally probed the dissociated structure after one bond ruptures. The back layer of Au atoms in each
pyramid was held fixed with a bulk lattice parameter of 4.08 A. All other degrees of freedom were relaxed until all forces
were less than 0.005–0.01 eV/A for each junction structure. The junction was elongated in steps of 0.05–0.1 A by increasing
the separation between the pyramids along the z direction and then fully optimizing the geometry. Density functional theory
total energy calculations and geometry optimization were performed with the VASP package [42], using the projector
augmented wave approach which naturally included scalar relativistic effects for Au [43, 44] and the generalized gradient
approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) [45] for the exchange-correlation density functional. The
model junction was placed in a hexagonal supercell (a ¼ 2.0 nm, c ¼ 3.5 nm) and the basis set for solution of the Kohn-
Sham equations was determined by a 400 eV cutoff.
The qualitative features of the calculated energy and force curves of an adiabatic junction trajectory are demonstrated in
Fig. 12.6a. In this case the calculations were performed by pulling on a C4SMe junction (Fig. 12.6b). Under the application
of increasing force due to junction elongation, the total energy increases from its local minimum value. Finally, a maximum
sustained force value (here ~0.8 nN) is reached. In these junction structures, the link bonds are not identical. One of the two
undergoes most of the elongation and after the maximum sustained force that link bond length rapidly increases,
corresponding to bond rupture. The calculated values listed for the maximum sustained force in Table 12.1 represent
model structures for each junction with similar backbone orientation, giving a good basis for assessing chemical trends.
They do generally represent a single adiabatic junction elongation trajectory. However, our previous studies [33] have
shown that small changes in junction structure (attachment point or molecule orientation) can lead to ~0.1–0.2 nN variations
in the maximum sustained force. More generally, we can also expect that diverse junction structures are sampled in the
experiments, including variations in Au-linker bond orientation in the junction and relative to the pulling direction
(Fig. 12.6c–f).
With due considerations for the variations in junction structures as well as the fluctuations due to temperature and
mechanical vibrations encountered in experiments, there is a good agreement between the DFT calculations of maximum
sustained force and experimental rupture forces. For the phosphine links (C5DPP in the experiments), calculations suggested
a substantially larger maximum sustained force. The typical maximum sustained force for the Au-P donor-acceptor bond
was around 1.4 nN for butane with the dimethylphosphine linker and there were clear indications that the stress is sufficient
to rearrange the local Au atomic arrangement near the link bond [27, 33]. However, the selectivity of the link bonding motif,
12 Simultaneous Measurement of Force and Conductance Across Single Molecule Junctions 81
to specific undercoordinated Au atomic sites, still results in the well-defined conductance plateaus. In phosphine linked
junctions, modest steps in conductance are often observed in individual experimental traces that may correspond to
rearrangement. Qualitatively, the DFT-based simulations are consistent with the measurements, but the relatively low
measured average rupture force has not been explained. One possibility is that constraints in full junction formation (bonds
to substrate and tip, accommodating the bulky tertiary phenyl groups) result in structures where the donor-acceptor bonds are
weaker than optimal. The rearrangement of the local Au atomic structure may also be significant.
For junctions with S-Au linkage, DFT based calculations have indicated that selected scenarios support a maximum
sustained Au-S bond force in excess of 1.5 nN [41, 46]. More strikingly, detailed molecular dynamics simulations of thiol
linked junction evolution show a rich series of rupture/rearrangement events with the molecule removing one or more Au
atoms in the final, ruptured state [37–40]. Also, the position and resulting effects of the hydrogen from the SH can lead to
drastic changes in force and conductance values [40, 41, 46, 47]. The experimental behavior of conductance and force
trajectories for C4SH junctions, summarized in Fig. 12.5c, d, are consistent with a sustained force that is sufficient to drive
substantial rearrangement of the local structure during elongation. However, most of these events occur with a change in
force that is substantially less than the average force required to rupture the Au point contact. This does not imply that they
do not break at the Au-Au bond. Molecular dynamics simulations illustrate that junctions formed with Au-S links can result
in contact structures that have varied geometries. In contrast to the idealized structure (Fig. 12.6c), the terminal Au atom
could be on the side of an electrode structure (Fig. 12.6d), the constraints on junction formation with two distinct link bonds,
one to each electrode, can result in an angle between the backbone and the pulling direction (Fig. 12.6e), and the
coordination of the Au atom to which the S is bonded can be altered (Fig. 12.6f). A key factor is the strength of the Au-S
bond relative to the softness of the Au resulting in local rearrangement under stress [37–40]. Our calculated adiabatic
trajectories for selected scenarios illustrate that the maximum sustained force can be both larger and smaller than the
nominal Au single point contact rupture force, depending on the structure. A broader-based survey of structure as well as
investigation of the role of thermal fluctuations and solvent interactions will be essential to fully understand the measured
rupture forces in cases like thiol bonded junctions with strong bonds to Au. The occurrence of these non-ideal evolution
scenarios is supported by our experimental results for conductance and force of C5DPP and C4SH single molecule junctions.
In summary, we demonstrated an experimental approach to simultaneously measure force and conductance data for
single molecular junctions, developing and establishing a new, two-dimensional histogram method to statistically evaluate
thousands of individual measurements. This method leads to an experimentally determined average breaking force of a
single Au-Au bond of 1.4 nN, based on over 31,000 individual measurements. Using a set of N terminated molecules, we
showed that the electronic structure of the molecular backbone alters N-Au bond strengths considerably, as can be seen both
in the calculations and measurements: 1,4-benzenediamine binds most weakly to Au atoms, while the pyridine-gold bond
exhibits the largest breaking force among the molecules considered here. We then presented measurements for four different
chemical linker groups connected to saturated backbones. Analyzing this data using the 2D conductance and force
Fig. 12.6 (a) Calculated total energy (top) and force (bottom) curves from an adiabatic trajectory calculation for C4SMe, shown as a function of
displacement. Bar shown at right indicates the asymptotic value. This calculation demonstrates the typical qualitative features of single-molecule
junctions with donor-acceptor interactions. (b) Snapshot of the C4SMe junction structure near the local energy minimum. (c–f) Illustrations of
possible contact structures in single-molecule junctions formed with C4SH. Scenarios include: (c) H atom remains on the S, (d) Au atom is not at
the apex of the electrode, (e) junction is formed at an angle, and (f) Au atom coordination is altered due to chain formation
82 S.V. Aradhya et al.
histograms, we have shown that amine, methylsulfide, and diphenylphosphine linkers break in a molecular junction with a
most probable breaking force of about 0.6, 0.7, and 0.8 nN respectively, indicating rupture at the donor-acceptor linkage. In
the case of thiol linkers, we compiled force and conductance data from individual traces, since we did not observe a well-
defined molecular conductance signature. Correlating the occurrence of force events with conductance, we find that C4SH
junctions on average have more force events per trace than C4SMe. This observation supports the notion that a strong
covalent sulfur-gold bond drives more significant rearrangement of these molecular junctions. By combining simultaneous
measurement of force and conductance with statistical analysis and DFT simulations we obtain a quantitative insight into the
electronics and mechanics of single-molecule junctions. In the future, these results can help us understand and engineer
molecular electronic devices with varied functionality.
Acknowledgements This work was supported by the National Science Foundation (Career Award CHE-07-44185) and by the Packard
Foundation. A portion of this work was performed using facilities in the Center for Functional Nanomaterials at Brookhaven National Laboratory
and supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886.
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(1):354–358
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84 S.V. Aradhya et al.
Chapter 13
High Speed Magnetic Tweezers at 10,000fps
with Reflected Hg-Lamp Illumination
Bob M. Lansdorp and Omar A. Saleh
Abstract The magnetic tweezer is a simple and stable single-molecule manipulation instrument. However, the standard
probe-tracking methods have typically failed to reach the high resolution (�0.3 nm) needed to measure motor protein
stepping. In this paper we present a novel illumination geometry, based on an inverted microscope with Hg lamp
illumination, that aims to push the resolution of magnetic tweezers to their ultimate thermal limits. Using a metal-coated
coverslip and motorized magnets, we convert a standard inverted microscope into a high-resolution magnetic tweezers
instrument. Our novel optical geometry reduces the restrictions on magnet design inherent to transmission-based illumina-
tion, and does not require fiber-optic coupling. We introduce a high-speed CMOS camera as the optical detector, and
demonstrate how an improvement in temporal resolution directly impacts the spatial resolution.
13.1 Introduction
Single molecule experiments measure the motion of a probe particle in order to deduce the properties of single molecules
such as DNA. In the case of optical and magnetic tweezers, the resolution of particle tracking is limited both by the
instrumental error and by the fundamental thermal limit caused by Brownian motion of the probe particle. For certain
applications, it is desirable to improve the instrumental resolution of particle tracking towards the thermal limit.
Following [1], we have identified the frame rate of the particle-imaging camera as a key factor limiting the instrumental
resolution. High-speed CMOS cameras can overcome the limitations of low frame-rate CCDs, but these cameras require
new illumination strategies to obtain sufficient light. We present a new illumination geometry that pushes magnetic tweezers
towards the thermal limit of maximum instrumental resolution.
13.2 A Novel Illumination Geometry
Although micron-sized beads scatter light in all directions, they scatter orders of magnitude more strongly in the forward
direction than back (see Fig. 13.1). Thus, it is desirable from an experimental point of view to utilize forward scattered light
to maximize the signal intensity.
To collect forward-scattered light from magnetic beads using a standard inverted microscope (Nikon Eclipse TE2000-U)
with epi-illumination, we employ a novel reflective geometry. On the return journey through the sample, forward-scattered
photons are collected by the objective (see Fig. 13.2b).
B.M. Lansdorp (*)
Graduate Student, Materials Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA
e-mail: [email protected]
O.A. Saleh
Professor, Materials Department and Biomolecular Science and Engineering Program, University of California Santa Barbara,
Santa Barbara, CA 93106, USA
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_13, # The Society for Experimental Mechanics, Inc. 2013
85
By placing a lens into the illumination optical path, we change the positions of the F-iris and A-iris conjugate planes.
We find that by tuning the focal length of the lens and the flowcell thickness, we can retain independent control over the
field-stop and collimation with the existing two irises.
Although a fiber-coupled Hg lamp has recently been used for high-speed particle tracking in 2D [1], a fiber might
interfere with our magnets. Our geometry collects the maximum amount of light while simultaneously providing added
flexibility to design magnets independently of optics.
Fig. 13.1 A polar plot of Mie scattering function (Taken from [2]). For 1mm sized beads, the forward-scatter intensity is three orders of magnitude
more intense than backscatter
Fig. 13.2 Novel illumination geometry inverts F and A irises. (a) Conventional RICM illumination. (b) Novel illumination geometry with added lens
86 B.M. Lansdorp and O.A. Saleh
The advantages of our design include: high intensity forward-scatter collection, minimization of backscatter on first pass
through sample by forming a conjugate image of an iris after reflection, and flexibility to design magnets independently of
optics.
13.3 Optics Design
We characterize our novel optical geometry, which is based on a single lens placed in a filter cube, in two steps. First, we
vary the lens focal length and measure the position of the resulting F-iris conjugate plane. Second, we vary the thickness of
the flowcell to find a configuration that brings the A-iris in focus.
In the first optimization, we place a range of Thorlabs lenses (f¼50mm, 75mm, 100mm, 125mm, 150mm, 200mm,
400mm) into the filter cube (see Fig. 13.3) and find that placing a 125mm lens into the filter cube results in no measurable in-
focus F-iris conjugate plane within the allowed travel range of the objective. We hereby deduce that f¼125mm results in a
nearly infinity-conjugate F-iris, and therefore nearly collimated light when the F-iris is closed down to a small hole.
In the second part of our optimization, we aim to find the location of the A-iris conjugate plane when a lens of f¼125mm
is inserted. To accomplish this goal, we construct a number of flowcells with various thicknesses and fill them with air (n¼1),
water (n¼1.33), and immersion oil (n¼1.515), and manually defocus the microscope to find the best-focus position of the
A-iris. Given the schematic representation of our experiment shown in Fig. 13.4, we can write the following two equations
which describe the position of the various focal planes:
h0 ¼ hA þ s1:515
n
� �(13.1)
and:
X ¼ hA þ 1:515
n
� �2tmeas � sð Þ (13.2)
To correct for the index of refraction mismatch,
tmeas ¼ ðh0 � hRÞ n
1:515
� �(13.3)
The results of this experiment are shown in Table 13.1. In the ideal experiment, s¼0 and the A-iris is in-focus after
passing through the sample. For each flowcell, given the actual A-iris position, we can make a prediction for the ideal
flowcell thickness such that s¼0 and the A-iris is in focus.
tideal ¼ tmeas þ ðhR � hAÞ n
1:515(13.4)
Fig. 13.3 A standard filter
cube that allows easy
placement of an
additional lens
13 High Speed Magnetic Tweezers at 10,000fps with Reflected Hg-Lamp Illumination 87
From Table 13.1 is it clear that a flowcell thickness of approximately 46mmwill result in an in-focus A-iris which can then
act as a field-stop. Effectively, by adding an f¼125mm lens and manufacturing a 46mm flowcell, we have reversed the A and
F irises. The A-iris is now a field-stop and the F-iris controls collimation.
X
h_0
100X objective
to tube lensand CCD
from A iris
h_A
St
Fig. 13.4 A schematic
illustrating the relative
positions of the A iris
conjugate plane and the
coverslips
Table 13.1 Experimental measurements of best-focus surfaces
Exp n h0 (mm)
hR for reflective
surface (mm)
hA for A-iris
(mm) tideal (mm)
1 1 202 107 165 51.0
2 1 192 121 172 44.9
3 1 186 131 180 43.1
4 1.33 200 156 206 44.0
5 1.33 201 138 187 43.1
6 1.33 201 141 194 46.6
7 1 200 121 175 47.5
8 1 201 125 179 47.5
9 1 205 125 180 48.4
10 1 206 128 181 46.6
11 1 203 112 167 48.4
12 1.33 202 138 190 45.8
13 1.33 208 141 193 45.8
14 1.33 206 144 196 45.8
15 1.33 205 154 204 44.0
16 1.515 202 161 210 43.1
17 1.515 208 164 214 44.0
18 1.515 210 156 204 42.2
19 1.515 208 151 201 44.0
20 1.33 209 100 156 49.3
Average – – – 46
88 B.M. Lansdorp and O.A. Saleh
13.4 Flowcell Manufacture
To manufacture a flowcell with the requirements mentioned above, we sandwiched steel shims of thickness 38mm (Small
Parts) between an Al-coated reflective coverslip (Deposition Research Lab, Inc) and a # 1 coverslip. We sealed the perimeter
of our flowcell using parafilm strips cut to approximately 1mm width using a razor blade, and left the sandwich on a hotplate
with a steel weight on top at 120∘C for 5min to seal the flowcell. Unfortunately, the result in Fig. 13.5b was measured to be
93mm instead of the nominal 46mm, which we attribute to burrs on our shims and insufficient time on the hotplate. We did
manufacture one flowcell with height of 46mm by placing it on a 145∘C hotplate for 15min, and found that the A-iris was
indeed in focus. By optimizing the manufacturing process, we expect to more reliably make accurate flowcells in the future.
13.5 Resolution Limits in Single Molecule Experiments
There are two main sources of noise in video-based particle tracking: Brownian motion of the probe particle during the
exposure time, and instrumental error in determining the probe particle position. The fundamental resolution of a thermally-
limited particle-tracking instrument [3] due to Brownian motion is:
s2SMMðtÞ ¼2kBTak2t
1þ 2akt
e�kta � a
2kte�2kta � 3a
2kt
� �(13.5)
where ktether is the tether stiffness, t is the averaging time, kBT is the thermal energy and a is the drag coefficient for the probe
particle. This thermal limitation affects both optical and magnetic tweezers, but magnetic tweezers may hold some
advantages over optical tweezers since the surface-bound tethers can be made very short and stiff, whereas dumb-bell
optical tweezers experience difficulty trapping beads that are closer together than the diffraction limit.
In the case of video-tracking, the instrument error can be reduced by using specialized reflective beads [4] or more simply
by using a high bandwidth camera and down-sampling. We have employed the latter approach, in combination with a high-
speed CMOS camera.
13.6 Particle Tracking Error
To determine the instrumental resolution of our system, we measured the position of 1.05mm superparamagnetic beads stuck
to a glass coverslip surface as a function of time at 10,000fps using a high-speed CMOS (Phantom v7.3). The z-position of
particles is determined by comparing particle images to a calibration image (shown in Fig. 13.6b). We measure a per-frame
z-axis resolution of 7nm per frame at 10,000fps (see Fig. 13.7).
We note that the higher-order fringes present in a previously conducted low-speed experiment Fig. 13.6a were not present
in the high-speed experiment because the imperfect flowcell thickness resulted in imperfect collimation and blurred the
higher order fringes. We expect to be able to improve the collimation and approach our previously attained per-frame
resolution of approximately 2nm.
Fig. 13.5 Schematic and experimental flowcell with well-defined thickness. (a) Schematic. (b) Inverted view of experimental flowcell
13 High Speed Magnetic Tweezers at 10,000fps with Reflected Hg-Lamp Illumination 89
We expect the total particle tracking error of our magnetic tweezer to be a combination of the thermal noise (Eq.13.5) and
the per-frame instrumental resolution:
s2total ¼ s2SMM þ s2instr (13.6)
We can predict the total noise in our instrument when a double-stranded DNA tether of length 50nm is pulled upwards with a
force of 0.56pN by a 530nm radius magnetic bead (resulting in a ¼ 1:4� 10�4pN s/nm after the Faxen’ correction [5], and
kz¼0.12pN/nm for a worm-like-chain [6]). The instrumental noise dominates for a low frame-rate CCD, but a high-speed
camera approaches the thermal limit (see Fig. 13.7).
13.7 Conclusion
Wehave demonstrated a novel illumination geometry that pushes the resolution of ourmagnetic tweezer to 0.35nm at 10Hz.We
expect to further improve our instrumental resolution by optimizing the flowcell manufacturing process and the resulting
calibration images of our beads.We expect that ourmagnetic tweezerswill soon reach the thermal limit for short and stiff tethers.
Fig. 13.6 A comparison of calibration images used to determine bead z position. A piezo objective is used to step in increments of 100nm per
pixel in the vertical direction. A calibration using a microfabricated reference yielded 163nm/pixel for the CCD and 148nm/pixel for the HS-
CMOS. (a) 1.05mm beads with 4f optics using 635nm LED illumination with CCD detection at 60fps and 163nm/pixel. (b) 1.05mm beads with
546nm Hg emission line and hs-CMOS detection at 10,000fps and 148nm/pixel. (c) Partially melted 2.5mm diameter Polystyrene reference bead
and 1.05mm diameter superparamagnetic microspheres
10
5
1
0.5
0.10.0001 0.001 0.01 0.1 1
Time [s]
Alla
n D
evia
tion
s [n
m]
Fig. 13.7 Allan deviation measured experimentally at 10,000fps (red dots) and 60Hz (green dots). The theoretical thermal noise (black line)results in predictions for the total noise at 10,000fps (red dashed line) and 60Hz (green dashed line)
90 B.M. Lansdorp and O.A. Saleh
Acknowledgements We gratefully acknowledge S. Pennathur and T. Wynne for lending us their hs-CMOS camera, A. Weinberg for
manufacturing parts, and F. Freitas for reviewing this manuscript. B.L. acknowledges support from an NSERC PGS-D fellowship.
References
1. Otto O, Czerwinski F, Gornall JL, Stober G, Oddershede LB, Seidel R, Keyser UF (2010) Real-time particle tracking at 10,000fps using optical
fiber illumination. Opt Express 18(22):22722–22733
2. Prahl S (2012) Mie scattering calculation. http://omlc.ogi.edu/calc/. Accessed 29 Feb 2012
3. Lansdorp BM, Saleh OA (2012) Power spectrum and allan variance methods for calibrating single-molecule video-tracking instruments. Rev
Sci Instrum 83(2):025115
4. Kim K, Saleh OA (2009) A high-resolution magnetic tweezer for single-molecule measurements. Nucleic Acids Res 37(20):e136
5. Sch€affer E, Nørrelykke SF, Howard J (2007) Surface forces and drag coefficients of microspheres near a plane surface measured with optical
tweezers. Langmuir 23(7):3654–3665
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13 High Speed Magnetic Tweezers at 10,000fps with Reflected Hg-Lamp Illumination 91
Chapter 14
Etching Silicon Dioxide for CNT Field Emission Device
Nathan E. Glauvitz, Ronald A. Coutu Jr., Peter J. Collins, and LaVern A. Starman
Abstract Carbon nanotube (CNT) based electron field emission devices may have an advantage over metal Spindt tip style
designs due to the ability to create a highly localized electric field at the extremely small diameter tip of the CNT. The primary
objective for this work is to create a robust micro structure to support low voltage field emission from the CNTs in a gated
device. This paper will discuss the micro fabrication techniques used to etch 2–4 mm thick thermal oxide layers on silicon
substrates. A chrome layer is deposited by electron beam evaporation to make the gate layer of the triode device and act as an
etch mask. The metal layer is then coated with photoresist, patterned with hole openings ranging from 8 to 12 mm in diameter
and wet etched in acid through to the SiO2 layer. Different dry etch chemistries combined with wet etching are used to study
the effect on the SiO2 sidewall. The shape and slope of the SiO2 sidewall and gate opening play a vital role in fabricating a
robust triode device that doesn’t easily short out when the CNTs are grown later in the process.
14.1 Introduction
There are many applications for CNTs to be used in electronic devices such as field emission (FE) tips in vacuum electronics,
field emission displays [1], or space charge neutralization for satellites [2, 3]. Under vacuum conditions and high local
electric fields, electrons can tunnel out of a solid high aspect ratio material into a vacuum as describe by Fowler-Nordheim
theory [4]. The physical and electrical properties of CNTs make them nearly ideal FE tips. For power limited applications,
low operating voltage and low leakage currents are highly desired device performance characteristics. In CNT vacuum
electronics, lower electron extraction potentials can be achieved via three general methods: reduce the anode and cathode
gap, optimize the CNT growth length and CNT spacing to reduce the screening effects, or use a triode type configuration
where a gate extraction electrode is positioned very close to the emitter tips. The latter method of creating a gate opening in
close proximity to the CNT tip will be the focus of this work; specifically the oxide layer sidewall geometry of the hole
openings to provide the robust structure to support a thin film metal gate. The close proximity of the gate allows lower
extraction potentials to cause electron tunneling from CNT tips into vacuum.
The most common techniques used to micromachine an oxide layer in a top-down device fabrication method to create
gated FE device are plasma etching, wet etching [5], or a combination of plasma and wet etching [6]. In this work, a radio
frequency (RF) parallel plate reactive ion etch (RIE) plasma system is used to initially dry etch the oxide layer followed by a
brief wet etch in a buffered oxide etch (BOE). Through the use of RIE, etch parameters can be modified to control the
undercut of the gate and the slope of the sidewall. Reduced undercut of the gate allows the use of thicker oxide layers and
tighter hole packing densities compared to a wet etch only method. Also, since CNTs can have a rapid growth rate in the
thermal chemical vapor deposition (T-CVD) system, a thicker oxide allows for some flexibility in the growth duration.
Once the substrate is exposed through the oxide, single mask or multiple mask step techniques can be used to pattern
the CNT catalyst material in the holes. In single mask techniques, the gate metal and oxide layer is etched, and the same
photoresist layer is then used for metal lift off after catalyst deposition. Single mask techniques have the advantage of
self-alignment where the catalyst is naturally centered in the emission hole site. Wong et al. used a single mask technique for
catalyst deposition along with a plasma pretreatment process on the catalyst layer which caused the CNTs to grow in a
N.E. Glauvitz • R.A. Coutu Jr. (*) • P.J. Collins • LaVern A. Starman
Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_14, # The Society for Experimental Mechanics, Inc. 2013
93
convex-shape [5]. The method pursued in this work is a top-down fabrication approach where an additional mask step is used
to center the catalyst metal in the emission hole site. Proper positioning of the catalyst metal is an essential step in the
fabrication of these gated FE devices since poor alignment can result in increased gate leakage current. Excessive CNT
growth length is another problem seen in gated FE devices. Longer than desired CNTs can create an electrical short from the
substrate to the gate and potentially cause the device to fail. In this work, the oxide sidewall geometry and undercut of the
gate metal was studied to mitigate those potential gate leakage problems in the triode design. The barrier layer, catalyst metal
thickness, catalyzation and growth times were then used to control the CNT diameter, spacing, and length to achieve uniform
growth [7–9].
14.2 Device Fabrication
Field emission devices fabricated here consist of three structural layers, a wafer substrate, an oxide insulator layer, and a
metal extraction gate. The fabrication steps numbered in Fig. 14.1 begin with highly doped n-type silicon (100) wafers
purchased from Ultrasil Corporation with thermally grown oxides. Wafers with 2, 3, and 4 mm oxide thicknesses were
selected in order to compare the field emission characteristics of the devices which will be presented in later work.
Figure 14.1 (1) shows a 220 nm chromium gate layer was deposited on the oxidized wafers in an electron beam evaporator.
The wafers were then cleaved into 12 mm � 12 mm squares so the samples could be loaded into the T-CVD system. Devices
were fabricated using standard photolithography techniques, four mask steps, and were thoroughly cleaned between each
photo masking step. The first mask step shown in Fig. 14.1 (2) defined the area of the chrome gate electrode. Similarly, the
second mask in Fig. 14.1 (3) was used to protect an area larger than the chrome gate and the SiO2 layer was etched in BOE
(7:1) to create a large oxide mesa and an outer surface contact area to the sample substrate. In Fig. 14.1 (4) samples were
coated again with resist and the third mask is used to pattern the hole openings in the gate metal which were etched with
chromium etchant. Circular hole patterns 8 mm in diameter were linearly packed with 18 mm array spacing, resulting in
127,008 emission sites covering an area of approximately 0.43 cm2. Coving the same area, hole sizes of 10 and 12 mmdiameter openings were also fabricated and consisted of 108,676 and 65,520 emission sites respectively. Kapton tape was
then used to cover the exposed outer edge of the oxide mesa and silicon substrate, protecting those areas during the following
RIE etch.
In Fig. 14.1 (5), the SiO2 etch parameter study was conducted with a Trion Phantom III RIE system. The RIE power, gas
etchants, flow rates, and process pressure were modified to achieve the desired etch depth and SiO2 sidewall profiles. Etch
study results are presented in the next section.
After the RIE process, the remaining thin oxide layer at the bottom of the hole openings was removed in a heated BOE
solution, shown in Fig. 14.1 (6). The complete removal of the oxide to the silicon surface in the hole openings across the
Si substrate
SiO2
Chrome
Ti + Fe layers
CNTs
Gate
After RIE
After BOE
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Si substrate
SiO2
Ti + Fe layers
CNTs
After RIE
After BOE
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Oxide Mesa
Gate metal hole
Fig. 14.1 Fabrication steps to form gated CNT field emission device began with (1) deposition of chrome gate metal, (2) defined gate area, (3)formed oxide mesa, (4) defined gate metal holes in chrome layer, (5) etched SiO2 in RIE, (6) etched in BOE to clear remaining oxide to substrate,
(7) deposited patterned Ti and Fe in holes, and (8) the final device after CNT growth in the T-CVD system
94 N.E. Glauvitz et al.
entire array was closely monitored to minimize undercut of the gate metal and to ensure a clean substrate surface area for
later CNT growth. An oxide free substrate surface for CNT growth is needed because it provides the electrical contact point
to the base of the CNTs. Also a clean uniform silicon surface should promote a more uniform CNT growth. Then a 220 A
titanium barrier layer was deposited by e-beam evaporation on the samples. A final photoresist pattern in Fig. 14.1 (7) was
then used to center the catalyst in the holes. A 75 A layer of iron was deposited via RF sputtering for the CNT catalyst
material. Samples were soaked in acetone and briefly placed in an ultrasonic bath to lift-off the unwanted iron and
photoresist. The lift-off procedure was a critical step in the fabrication process and this is where a limited undercut of the
gate metal was beneficial. In the ultrasonic bath, chrome at the edge of the hole openings would break off on the samples that
had too much undercut from the BOE step.
CNTs were grown on samples in the T-CVD system which consists of a one inch diameter quartz tube positioned
horizontally through a heater, a mechanical rough pump, mass flow controllers, flowmeter, and feedstock gasses. A complete
description of the T-CVD CNT growth process can be found in previous work [9]. Earlier work in Ref. [9] studied the effects
of barrier layer and catalyst layer thicknesses on the resulting CNT carpet growths. For gated devices fabricated here, the
growth time was reduced to 30–40 s in durations due to the close proximity of the gate metal on the oxide.
14.3 Silicon Dioxide Etch and Device Results
The objective of this etch study was to optimize the underlying oxide to form a robust support structure for the extraction
gate. Both dry plasma reactive ion etching and wet etching of the oxide layer were used to achieve a robust oxide support.
All samples etched in the RIE used a patterned chrome layer as the etch mask. Etch parameters in the Trion Phantom III
system were systematically modified and the resulting etches were studied to select the optimal conditions to be used on the
final devices. The Trion RIE system is configured with a 600 W maximum, 13.56 MHz solid state RF generator. Table 14.1
lists the RIE etch parameters used and the resulting SiO2 etch rates.
Effects of RIE power, chemical etchant, flow rates, and process pressure were studied in a scanning electron microscope
(SEM) to achieve the desired SiO2 sidewall profiles and etch depth. Relatively low RIE powers of 100–150 W with CF4etchant or CF4 with a small percentage of O2 were tested. Sample A, etched with the parameters listed in Table 14.1 was
accomplished as the baseline etch and utilized the suggested parameters in the Trion publication [10]. Shown in Fig. 14.2 are
SEM images of Sample A after the 2 mm oxide layer was partially etched through after 38.3 min in the RIE. An SEM image
of a single hole shown in Fig. 14.2a was taken at a 45� angle to highlight the bottom oxide surface roughness and a small
amount of oxide undercut of the chrome mask. A close-up view of the cleaved edge in Fig. 14.2b shows roughly a quarter
micron undercut of the chrome mask and provides another perspective of the surface roughness from the micro-mask formed
on the oxide layer. This initial etch yielded more undercut than desired and a relatively slow etch rate. The observed etch rate
of Sample A was over six times slower than the Trion reported etch rate [10]. The difference between the two rates is likely
Table 14.1 Reactive ion etch parameters tested and the resulting etch rates
Sample Power (W)
Pressure
(mTorr)
CF4 flow
(sccm)
O2 flow
(sccm)
Etch rate
(nm/min)
A 100 150 45 5 23.5
B 100 150 40 – 14.8
C 100 100 40 – 17.6
D 100 25 40 – 45.9
E 125 25 40 – 66.1
F 125 25 40 4 78.3
G 125 50 40 4 77.0
H 125 50 40 6 71.8
I 125 50 40 8 71.4
Ja 125 25 40 – 61.3
125 50 – 100
K 150 50 40 6 80.1
L 150 25 40 – 84.0
M 150 12 25 3 86.3aAccomplished 200 s CF4 followed by 90 s O2 plasma; series repeated ten times
14 Etching Silicon Dioxide for CNT Field Emission Device 95
due to several factors such as differences in the oxide material composition or RIE system configurations. Thermally grown
oxides have reported slower etch rates than phosphosilicate glass or CVD SiO2 when using CF4 based etch chemistry [11].
Another factor that could have contributed to the difference in etch rates was the amount of reactants flowed through the
chamber and the utilization factor. Samples etched here had very low utilization factors since the exposed oxide area was
small and the etch rate was so slow. The etch reaction in the holes was likely inhibited by excessive flow of the reactant
species and contributed to the observed slower etch rate.
The flow of CF4 was then reduced slightly to 40 sccm after the initial run and the effects of the process pressure were
studied using only CF4. Samples B, C, and D shown in Fig. 14.3 had a 2 mm thick oxide layer and were etched for 26.7 min
using 100 W of RIE power under different pressure conditions. The top images taken at a 45� angle in Fig. 14.3 show a
portion of a hole etch while the bottom images show the cross section edge of the oxide etch and chrome mask. Sample B and
C were etched with the pressure set at 150 and 100 mTorr respectively. The higher pressure etches with CF4 only resulted in
slower etch rates (14.8–17.6 nm/min) without the addition of oxygen, but the amount of undercut was reduced. Sample C
processed at 100 mTorr had close to vertical SiO2 sidewalls. While Sample D, the 25 mTorr etch shown in Fig. 14.3, etched
nearly three times faster and created a 68� sloped sidewall relative to the silicon surface. The sidewall appeared to be formed
from a combination of the oxide layer and redeposited material from the RIE process. This lower pressure etch of Sample D
clearly eliminated any undercut issues of the chrome mask but it did cause a small trench effect where the RIE etch occurred
more rapidly along the edge of the mask. The reduced process pressure delivered more ion energy to the surface which
increased the reaction rate of the oxide layer. To further increase the reaction rate, the power must be increased.
The RIE power was then adjusted to 125W on the next six samples to obtain a faster etch rate. Sample E in Fig. 14.4 is the
result of 125 W, 25 mTorr, 40 sccm of CF4, after 38 min in the RIE. The oxide sidewall angle on a cleaved sample measured
approximately 69� from the horizontal plane and was seen only on the top half of the oxide. This etch resulted in the clean
removal of the top half of the oxide thickness, while the lower half of the oxide contained spires of oxide below the micro-
mask layer. The micro-masking effect in the center of the hole opening is fairly dense when there is no oxygen present during
the etch. With the addition of 10%, 15%, or 20% oxygen to the etch chemistry and a slight increase in process pressure;
Samples G, H, and I in Fig. 14.4 had a reduction in the sidewall slope, a visual reduction of the micro-mask surface density,
and no undercut of the chrome gate metal. Sample H appeared to have the most vertical oxide sidewalls and virtually no edge
effect trenching. The last image in Fig. 14.4; Sample J was made in an effort to increase the oxide sidewall slope and reduce
the amount of micro-masking through a series of alternated etches. A 200 s pure CF4 etch followed by a 90 s O2 plasma clean
were performed and the sequence was repeated ten times. By cycling through the CF4 and O2 plasmas, the clear etch depth
increased only slightly and the sidewall slope improved by approximately 4� over Sample E.
The final three RIE etches were performed at 150 W on samples with 4 mm oxide layers. In Fig 14.5, the cleaved
edge of Sample K and Sample M show a portion of the hole etch after RIE. This view after the RIE etch is presented to
illustrate the increased clear etch depth above the micro-mask layer achieved on Sample M through the reduction of etchant
flow and lower process pressure. Additional RIE parameter modifications could be performed in an attempt to eliminate
the micro-mask layer but previously accomplished etches have produced the desired oxide sidewalls to move onto the
BOE step.
Based on the RIE etch results above, several samples were continued in the fabrication process and etched in heated BOE.
The heated BOE solution etched the oxide at approximately 200 nm/min and was used to clear the remaining oxide at the
Fig. 14.2 SEM image (a) of a single hole on Sample A was taken at a 45� view after RIE illustrates the oxide surface roughness and undercut on
the chrome mask. Image (b) is a view of the side of a hole opening on the cleaved edge shows nearly a quarter micron undercut of the chrome mask
and the small micro-mask layer on the surface of the partially etched oxide
96 N.E. Glauvitz et al.
bottom of the holes to the substrate surface. As the BOE step preformed an isotropic removal of the oxide from the hole
openings, samples with shorter durations in BOE consequently had better support structures for the gate metal. Figure 14.6a
shows Sample H after RIE. Sample H was then etched in heated BOE for 90 s. Figure 14.6b shows Sample H again after
successful metal lift-off of the iron catalyst and proved the oxide layer is very robust with only minor damage to the gate
metal. Sample E in Fig. 14.6c shows the partial etch of the oxide after 60 s in heated BOE. Sample E initially shown in
Fig. 14.4 after RIE, possessed a sloped sidewall from the low pressure CF4 only etch. After the short time in BOE, any
remnant of the sloped sidewall is gone leaving a near vertical oxide wall in the hole. The trench effect from the RIE is clearly
visible after BOE, as shown in Fig. 14.6c where the region near the mask edge has opened up to the substrate while the center
of the hole is yet covered with a thin oxide layer. The required wet etch time to clear away the remaining oxide layer in the
center of the hole caused more undercut of the gate oxide than desired and degraded the oxide support of gate metal.
Fig. 14.4 SEM images taken at a 45� angle illustrate the sidewall profile and micro-masking which occurred for some of the 125 W etched
samples. Sample E was etched with CF4 only, while Samples G, H, and I were etched at a higher pressure and had the addition of 10%, 15%, or
20% of O2 respectively. Sample J was made by alternating pure CF4 and O2 plasmas
Fig. 14.3 SEM images of Samples B, C and D show a portion of an etch hole at a 45� view (top), a cleaved edge view (bottom) which shows
examples of the measured etch depth on the samples and the oxide surface structure
14 Etching Silicon Dioxide for CNT Field Emission Device 97
The most robust samples fabricated were produced with the RIE configured at 125W, 50 mTorr pressure, 40 sccm of CF4,
6 sccm of O2 and required less than 2 min in heated BOE. Samples that were etched more than 2 min in the BOE solution had
portions of the chrome gate over the hole openings break off during the catalyst metal lift-off process. Sample I was etched
in BOE for 2 min after the RIE step. Shown in Fig. 14.7 is Sample I as a completed device after a 30 s CNT growth phase.
The CNTs in the emission hole sites grew very uniformly across the sample with a few exceptions. The measured gate
resistance to the substrate on the sample was in the kO range, not an open. The low gate resistance is likely due to
Fig. 14.5 SEM images of a hole etch on the cleaved edge of Sample K and M are shown to highlight the improved clear etch depth to the micro
mask layer achieved on Sample M by reducing the etchant flow and process pressure
Fig. 14.6 Sample H shown in image (a) after RIE produced nearly vertical sidewalls and a reduced amount of micro masking compared to the
other etches. In image (b) is Sample H after 90 s in heated BOE and iron catalyst deposition in the center of the hole, it held up very well to
the metal lift-off. While Sample E, shown in Fig. 14.4 after RIE, began with the sloped side walls and now shows almost vertical oxide walls in
(c) after 60 s in BOE
Fig. 14.7 Top view (left) of Sample I after 30 s CNT growth and close-up view (right) at a 45� angle show a near vertical oxide sidewall creating a
small overhang of the chrome gate
98 N.E. Glauvitz et al.
contamination found in a few hole combined with the occasional excessive CNT length found at sites. Other problem sites
were due to the photoresist patterning used for catalyst deposition and then metal lift-off. Improperly masked holes allowed
iron catalyst metal to be deposited at the base of the oxide layer and resulted in CNTs that grew tens of microns long.
14.4 Conclusions
In this effort, robust gate structures were fabricated for CNT field emission devices through the use of RIE and wet etching of
a thermal oxide layer. The patterned layer of evaporated chrome was used as the RIE etch mask and later as the gate
extraction electrode for the device. Through the series of RIE and wet etches, a favorable RIE configuration of 125 W,
50 mTorr pressure, 40 sccm of CF4, and 6 sccm of O2 was found. Further refinement of the RIE parameters and reduced flow
of the etch gasses would likely produce an improved oxide etch. It was important to minimize the undercut of the gate during
the buffered oxide etch and that was achieved by performing the initial RIE duration to reach just above the silicon surface.
By the addition of some oxygen to etch chemistry, a cleaner hole etch was achieved and was preferred over the CF4 only etch
which produced the increased oxide sidewall slope. Future work will include further design refinement of the triode
structures, field emission data collection, and analysis to maximize the emission current density of the devices.
Acknowledgements The authors would like to thank the Air Force Research Laboratory (AFRL) Propulsion Directorate for their assistance, use
of their resources and facilities, especially the sputtering and T-CVD systems. The authors also thank the technical support and dedicated work of
AFIT’s own cleanroom staff, Rich Johnston and Thomas Stephenson.
Disclaimer Theviews expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Air
Force, Department of Defense, or the U.S. Government.
References
1. Choi YC, Jeong KS, Han IT, Kim HJ, Jin YW, Kim JM, Lee BG, Park JH, Choe DH (2006) Double-gated field emitter array with carbon
nanotubes grown by chemical vapor deposition. Appl Phys Lett 88(26):263504
2. Velasquez-Garci LF, Akinwande AI (2007) A MEMS CNT-based neutralizer for micro-propulsion applications. Paper presented at the 30th
international electric propulsion conference, Florence, 17–20 Sep 2007
3. Aplin KL, Kent BJ, Song W, Castelli C (2009) Field emission performance of multiwalled carbon nanotubes for a low-power spacecraft
neutraliser. Acta Astronaut 64(9–10):875–881
4. Fursey G (2005) In: Brodi I, Schwoebel P (eds) Field emission in vacuum microelectronics. Kluwer Academic/Plenum Publishers, New York
5. Wong YM, Kang WP, Davidson JL, Choi BK, Hofmeister W, Huang JH (2006) Fabrication of aligned convex CNT field emission triode by
MPCVD. Diamond Relat Mater 15(2–3):334–340
6. Williams LT, Kumsomboone VS, Ready WJ, Walker MLR (2010) Lifetime and failure mechanisms of an arrayed carbon nanotube field
emission cathode. IEEE Trans Electron Dev 57(11):3163–3168
7. Srivastava SK, Vankar VD, Kumar V (2007) Effect of catalyst film thickness on the growth, microstructure and field emission characteristics
of carbon nanotubes. Paper presented at physics of semiconductor devices. IWPSD 2007. International workshop on 16–20 Dec 2007,
Bombay, India
8. Wang Y, Luo Z, Li B, Ho PS, Yao Z, Shi L, Bryan EN, Nemanich RJ (2007) Comparison study of catalyst nanoparticle formation and carbon
nanotube growth: support effect. J Appl Phys 101(12):124310–124310-8
9. Crossley BL, Glauvitz NE, Quinton BT, Coutu RAJ, Collins PJ (2011) Characterizing multi-walled carbon nanotube synthesis for field
emission applications. In: Marulanda JM (ed) Carbon nanotubes applications on electron devices. In Tech Education and Publishing, Croatia,
pp 105–126
10. Crockett A, Almoustafa M. Plasma delayering of integrated circuits. M. Trion Technology, Tempe, Arizona, and Vanderlinde, W. Laboratory
for Physical Sciences, College Park, MD, USA http://www.triontech.com/pdfs/Plasma%20Delayering%20of%20Integrated%20Circuits%
20V4%20080%E2%80%A6.pdf still available 7/25/2012
11. Madou M (2002) Fundamentals of microfabrication: the science of miniaturization, 2nd edn. CRC, Boca Raton. ISBN 0-8493-0826-7
14 Etching Silicon Dioxide for CNT Field Emission Device 99
Chapter 15
Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity
Benjamin Klusemann, Alain Franz Knorr, Horst Vehoff, and Bob Svendsen
Abstract In this contribution experimental and theoretical investigations of sheet metal mesocrystals with coarse texture
are performed. One focus of this work is on size effects due to a lack of statistical homogeneity. The overall mechanical
response is then strongly influenced by the orientation of the individual grains. For this purpose a crystal-plasticity-based
finite-element model is developed for each grain, the grain morphology, and the specimen as a whole. The crystal plasticity
model itself is rate-dependent and accounts for local dissipative hardening effects. This model is applied to simulate the
thin sheet metal specimens with coarse texture subjected to tensile loading at room temperature. Investigations are done
for body-centered-cubic Fe-3%Si and face-centered-cubic Ni samples. Comparison of simulation results to experiment
are given.
15.1 Introduction
The relation between microstructure, material properties and mechanical response is a basic issue of research in material
science and material mechanics. From the modeling point of view, a common concept used to account for the effect of the
microstructure on the material behavior is that of a representative volume element (RVE). This concept is based on
the assumption of scale separation between the microstructural and macrostructural lengthscale. If the characteristic size
of the system (e.g., sheet thickness) approaches that of the microstructure (e.g., grain size), however, such scale separation is
no longer given and one must resort to other means of representing the effect of microstructural heterogeneity on the system
behavior. As the macrostructural lengthscale approaches the microstructural one, the degree of material heterogeneity
increases, and the local microstructural behavior may deviate significantly from the average macrostructural behavior [e.g.,
10, 17]. In this case, the model has to account for the microstructural details such as orientation details of the grain structure
[e.g., 18] or phase distribution [e.g., 13, 23]. In the extreme case, the microstructural and macrostructural lengthscales are of
the same order of magnitude, and one must resort to numerical modeling of the microstructure with the help of, e.g., the
finite-element method [e.g., 4, 14, 19, 28]. In the case of polycrystalline materials, for example, such finite-element models
are often constructed with the help of, e.g., optical and/or EBSD data on the grain morphology. In specimens with more than
one grain over the thickness, the common method of projecting the two-dimensional EBSD information uniformly in the
third dimension will generally lead to incorrect results [e.g., 26]. If the specimen is one grain thick, however, such an
optical-/SEM-/EBSD-based approach should be reasonable. For such a specimen a number of size effects are expected
to influence its mechanical properties. These effects have been known for years and are still the subject of active research
[e.g., 5, 6, 9, 12].
The overall mechanical response is strongly influenced by the orientation of the individual grains if the number of grains
over the thickness is fairly small [5]. In the case of thin sheets the mechanical properties in a given cross section are
increasingly dominated by each individual grain as reported in [7]. Due to the different orientations of the grains located in
the sheet plane, the deformation is no longer uniform even under homogeneous loading conditions. This heterogeneity and
B. Klusemann (*) • B. Svendsen
Material Mechanics, RWTH Aachen University, Aachen, Germany
e-mail: [email protected]
A.F. Knorr • H. Vehoff
Chair of Material Science, University of Saarland, Saarbr€ucken, Germany
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_15, # The Society for Experimental Mechanics, Inc. 2013
101
the size-dependence of deformation give rise to size effects [e.g., 8]. To understand and predict the behavior of such
specimens correctly, simulation and experiment have to be compared locally, e.g., within individual grains in a polycrystal-
line specimen. For this purpose, detailed local experimental information is necessary [7].
The purpose of the current work is the investigation and modeling of so called oligocrystals which are specimens
consisting of one or more coarse-textured layers over their thickness. As example a body-centered cubic Fe-3%Si and a face-
centered cubic pure Ni sheet metal sample are investigated. The Fe-3%Si sample has been investigated experimentally by
Henning and Vehoff [7, 8]. These samples are grown in such a way that there is only one grain over the thickness, and grain
boundaries are perpendicular to the sample surface. The modeling is carried out with the help of crystal-plasticity and the
finite-element method [CPFEM: e.g., 5, 18, 19]. Related previous experimental and modeling work to oligocrystals includes
for example that of [21], who investigated grain interaction in an Al oligocrystal with columnar grains subject to plane strain
channel die extrusion. In addition, [28] examined plastic localization and surface roughening in an Al oligocrystal. Statistical
size effects also relevant to the current work have been investigated by F€ul€op et al. [5] in ultra-thin (0.1–0.5 mm) Al
oligocrystals. On the other hand, [24] investigated the behavior of a Cu oligocrystal characterized by multiple grains over the
thickness during plane strain compression. The discrepancy between experiment and simulation results noted by them was
attributed among other things to a lack of information about the grain morphology in the thickness direction.
The paper is structured in the following fashion. First the single-crystal model is given. After this experimental and
simulation results for an Fe-3%Si and an pure Ni oligocrystal are presented. The work ends with a summary.
15.2 Single-Crystal Model
Let sa; na, and ta: ¼ na � sa represent the glide direction, glide plane normal, and direction transverse to the glide direction
in the glide plane, of the ath glide system, respectively. As usual, (sa; ta; na) represent an orthonormal system assumed
constant with respect to the intermediate local configuration as determined by the inelastic local deformation FP. As usual,
the evolution of the intermediate local configuration and FP is modeled by the large-deformation form
_FP ¼ LPFP ¼X
a_ga sa � FT
Pna (15.1)
in the case of glide-based large-deformation crystal plasticity. Here, g1; g2; . . . represent the glide-system shears whose
evolution is modeled here via the power-law form
_ga ¼ _g0tatda
��������m0
dirðtaÞ (15.2)
in terms of the Schmid ta :¼ sa �Mna and Mandel M stresses. Here, dirðtaÞ ¼ ta=jtaj is the shear-rate direction, _g0represents a characteristic glide shear-rate, m0 is the strain-rate exponent, and tda is the dissipative slip resistance whose
evolution is modeled by the interaction form
_tda ¼X
bhdab j _gbj (15.3)
[e.g., 1]. Here, the saturation model
hdab ¼ qab h0 ð1� tdb=tds0 Þ
n0; a; b ¼ 1; 2; . . . ; (15.4)
[e.g., 2] is assumed for the components of the hardening matrix, with qab ¼ 1:0 ð1:4Þ for a ¼ b ða 6¼ bÞ the components of
the matrix of hardening-rate ratios [e.g., 1] for the bcc case, h0 the initial hardening rate, tds0 the saturation value of tdb, and n0the hardening rate exponent. For the fcc case the components of the matrix of hardening-rate ratios qab are given by qab ¼1:0 ð1:4Þ for a same glide plane as b (a other glide plane as bÞ. The current model is completed by the linear elastic
constitutive relation
SE ¼ CEEE (15.5)
102 B. Klusemann et al.
for the elastic second Piola-Kirchhoff stress SE determining the Mandel M � SE and Kirchhoff
K ¼ FESEFTE (15.6)
stresses, the former in the context of small elastic strain. Here, CE is the constant elasticity tensor, EE ¼ 12ðFT
EFE � IÞrepresents the elastic Green strain, and FE :¼ FF�1
P is the elastic local deformation as usual.
The algorithmic formulation of the model combines explicit update at the integration-point level combined with implicit
update at the finite-element/structural level for satisfaction of the boundary conditions. The resulting mixed algorithm has
been implemented into the commercial program ABAQUS via the user material (UMAT) and user element (UEL)
interfaces. The simulations to be discussed below were all carried out in ABAQUS/Standard. To ensure reliable and robust
numerical results, adaptive time-step-size control is employed for the explicit update of inelastic model quantities used at the
integration-point level. In particular, this latter is based on the magnitude of the inelastic velocity gradient jLPj related to thecorresponding approximation of the algorithmic flow rule for FP. The critical value of this parameter for stability is
determined empirically via one-element tests. For more details, the interested reader is referred to [11].
15.3 Results for Fe-3%Si
For theexperimental investigationof [7], a test sampleof approximately5 mmwidth and15 mmlengthwas laser-cut froma larger
Fe-3%Si sheet of thickness 1 mm consisting of a single layer of grains having amean diameter of about 2 mm. The specimenwas
subject to simple tension under quasi-static loading conditions (10� 3 s�1). During the test, sample geometry, grain morphology,
and the local lattice orientation were measured at selected total strain states (0%, 1.5%, 4%, 10%, 19.5%) in the tension direction.
The experimental results from [7]with respect to the orientation gradient and change in specimen shape and grainmorphology are
shown in Fig. 15.1. The orientation gradient [e.g., 8, 25] is ameasure of the local (maximum)mismatch between the orientation of
a given point and that of its neighbors. More precisely, this is a measure of the change in lattice orientation between two
neighboring (regularly-spaced) measurement points in the plane of the EBSD measurements. To calculate these, let Ri andRiþ1
represent the orientation of two adjacent points in either the i¼ x or i¼ y direction in the plane. Then
Dyi : ¼ minQ2Gc
arccos1
2ðRi �QRiþ1 � 1Þ
� ��������� (15.7)
represents the orientation gradient at i modulo crystal symmetry transformations, i.e., elements of the crystal symmetry
group Gc (here cubic). The values of Dyx and Dyy determine in turn the measure
Dy1 ¼ maxfDyx;Dyyg (15.8)
of maximal local orientation gradient and so the OG mapping. In the experimental case, Ri and Riþ1 are determined directly
from the EBSD data. In the model case, Ri and Riþ1 in (15.7) and so (15.8) are determined by the spatial distribution of the
elastic local rotation RE.
The 3D model specimen in Fig. 15.2 was obtained from the 2D experimental information of the undeformed sample via
direct extrusion of the specimen shape and grain morphology into the third dimension. This represents a possible source of
discrepancy between the experimental and simulation results to be discussed below. Transition regions on either end of the
actual specimen consisting of elastic isotropic material have been introduced in order to transmit the tension boundary
conditions more accurately to the more complex specimen boundary [29]. As input data for the simulation the measured
EBSD data is used as initial orientation. The orientation in every grain is assumed to be homogeneous.
Room-temperature values for the material parameter in the single-crystal model assumed for the simulations are shown in
Table 15.1 which are taken from [14]. Here it is assumed that slip in Fe-3%Si occurs in h111i direction on the f110g and
{112} planes. Further it is also assumed that the material parameters for {110} and {112} systems are equal and that these
systems do not interact. To model this, the corresponding coupling terms in the hardening matrix qab are set to zero.
In the following the deformation behavior and the evolution of the orientation gradient between experiment and simulation
are investigated. For sake of comparison and to understand the influence of the assumed hardening law better simulations have
been carried out neglecting all hardening. In the initial stages of loading where little or no hardening can have occurred, this is
not unreasonable and allows a check of the initial conditions of the model independent of the hardening modeling.
15 Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity 103
Fig. 15.2 FE-model of the Fe-3%Si tensile specimen. Individual grains are numbered for reference in the sequel
Fig. 15.1 Orientation gradient (OG) Dy1 during tensile loading of Fe-3%Si oligocrystal determined experimentally at (from top to bottom)1.5 %, 4 %, 10 %, and 19.5 %, total strain [7]. The OG results are superimposed on the current specimen geometry and grain morphology in
contour form (red line used as approximation of shape change). Points in the specimen where EBSD data was not obtained or too poor to determine
the OG distribution are shown in black
Table 15.1 Material parameter values assumed for bcc Fe-3%Si. In particular, the elastic constant values are from [20], and the other paramters
have been determined in [14]. Glide-system parameter values are assumed to be equal for both glide-system families {110} and {112} considered
in this work
cE11 [GPa] cE12 [GPa] cE44 [GPa] td0½MPa� _g0 [s�1] m0 h0 [MPa] tds0 ½MPa� n0
222 135 120 161 10�3 20 243.9 1,137 0.48
104 B. Klusemann et al.
First we turn to a comparison of experimental and simulation results for change in specimen shape and grain morphology
as shown in Fig. 15.3. As shown by the comparison of grain boundary motion for the results where hardening is neglected,
generally the simulation underestimates the amount of grain deformation in the grains to the left of grains 13 and 14, and
overestimates it in grains 13, 14 and 15. Discrepancies such as those seen in grains 13 and 14 are significantly enhanced by
incipient specimen-level deformation localization and shear-band formation, in particular in the case of ideal viscoplasticity.
It is interesting to note that grain 14 had already the highest Schmid factor at the start of the deformation [14]. Comparing the
simulation results including hardening to the results neglecting hardening suggests that, up to 4%, little or no deviation
between the simulation results is visible. These results agree as well with experiment up to this point. After this point,
however, the effect of including hardening becomes quite apparent. In particular, hardening results in a reduction in the
prediction of the amount of grain deformation, something particularly apparent in the grains to the left of grain 13, but also in
grains 13, 14 and 15. The grain boundary morphology is also well predicted, even at large deformation only a deviation in the
contraction of grain 15 and 16 is observed.
Next we turn to the investigation of the orientation gradient. The experimental results shown in Fig. 15.1 as well as the
simulation results in Fig. 15.4 are only depicting the orientation gradient inside each grain due to the fact that the initial
orientation gradient over the grain boundaries (misorientation) is much larger than the orientation gradient during loading.
Again the simulations are performed for neglecting and including hardening. Consider first the simulation results neglecting
hardening. As for the deformation results a localization of the gradient can be observed for grain 13, 14 and 15. It can be
seen from these results that the simulation neglecting hardening cannot predict the correct tendency for the OG in the
experiment. Again up to 4% deformation a similar orientation gradient can be observed for the simulations neglecting and
including hardening, however, afterwards no correlation is anymore visible. In contrast the simulation results including
hardening predicts for example the band-like distribution of high OG at the boundary between grains 1 and 4 (and perhaps
grain 5 as well where data is missing) as seen in the experiment. As well, the homogeneous lattice orientation, i.e., lack of
an OG, in the middle of grains 4 and 8 in the experiment is also seen in grains 4, 5 and 8 in the model. Further, the
development of higher OGs in grain 9 near its boundary with grain 13, as well as in grains 13 and 15 near their common
boundary, is present in the model results. On the other hand, the OG band in grain 15 parallel to its boundary with grain 16
is missing, as is the OG in grain 17 near its boundary with grain 15. In addition, the experimental and model OG
distributions in grain 16, especially near the boundary with grain 14, are different. Then again, the development of OG
bands in grain 11 near its boundaries with grains 8 and 12, although much more diffuse than in the experiment, is present.
In summary, the simulations including hardening of the bcc Fe-3%Si sample were able to predict the experimental results
with respect to the deformation behavior and the orientation gradient evolution quite good.
Fig. 15.3 Comparison of experimental (red thin line) and simulation (black thick line) results of Fe-3%Si oligocrystal for the specimen geometry
and grain morphology at (a) 1.5 %,(b) 4 %, (c) 10 %, (d) 19.5 %, total strain in the tension direction for simulations neglecting (left) and including(right) hardening
15 Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity 105
15.4 Results for Ni
An investigation of a face-centered cubic metal was done on an 99.99%-pure nickel sample. A test sample of approximately
18 mmwidth and 50 mm length was cut by spark erosion from a larger sheet of 2 mm thickness. After the annealing process
(first 24 h at 1,350∘C then further 24 h at 1,425∘C) the average specimen thickness is reduced to 0.5 mm and grains have a
mean diameter of about 1 mm, which implies the achieved single grain layer condition. Due to the annealing process also
width and length of the test sample have been reduced to 16.5 and 48.5 mm, the thickness varied linear from 0.3 to 0.6 mm
from left to right.
The specimen was subject to simple tension under quasi-static loading conditions (10� 3 s�1). During the test, the sample
geometry, grain morphology, and the local lattice orientation were measured at certain total strain states (0%, 1%, 2%, 4%,
6%) in the tension direction.
The 3D model specimen of the pure Ni sample in Fig. 15.5 was obtained via extrusion of the specimen shape and grain
morphology into the third dimension from the 2D experimental information of the undeformed Ni sample. Transition
regions on either end of the actual specimen consisting of elastic isotropic material have been introduced in order to transmit
the tension boundary conditions more accurately. As input data for the simulation the measured EBSD data is used as initial
orientation with the orientation in every grain assumed to be homogeneous.
In the case of face-centered cubic pure nickel it is known that the deformation occurs on 4 {111} planes in 3 < 110 >directions. The material parameter for these slip systems are identified on experimental data from [22] for [111] single
crystal tensile data for room-temperature and quasi-static loading conditions (_e0 ¼ 8:3 � 10�4 s�1). For the model identifica-
tion a single crystal in the simulation is rotated into the [111] direction and therefore the axes of the crystallographic system
have to be rotated by the euler angles ff1 ¼ cos 1ffiffi3
p ; F ¼ p4; f2 ¼ 0g. The tensile load is applied into x-direction which
results initially in six active slip systems. The identification is done using LS-OPT in conjunction with ABAQUS by fitting
the stress-strain curves. The optimization techniques rely on response surface methodology (RSM) [15], a mathematical
method for constructing smooth approximations of functions in a design space. The approximations are based on results
Fig. 15.4 Comparison of modeling results for the orientation gradient (OG) Dy1 of Fe-3%Si oligocrystal at total deformation states of (from topto bottom) 1.5%, 4%, 10%, and 19.5% in the tension direction for simulations neglecting (left) and including (right) hardening
106 B. Klusemann et al.
calculated at numerous points in the multi-dimensional design space. In this study, the material parameters are the design
variables, and the model together with the data determines the objective function of the corresponding optimization problem.
The shear-rate sensitivity, m0 is assumed to be 20 and reference shear rate _g0 to be 10� 3 s�1 for the current case of quasi-
static loading conditions which is in accordance to [27]. The identified parameters are shown in Table 15.2. Here it has to be
noted that the material parameters are only fitted for crystal orientation of [111]. However, it is known that Ni shows
significant different stress-strain curves for different orientations [e.g., 3, 15] depending on the fact whether the crystal is
showing single or double slip. Of course, this represents one possible source of discrepancy between the experimental and
simulation results.
During the experiment the applied displacement and corresponding reaction force were continuously recorded. The
results are shown in Fig. 15.6. The reference area used to calculate the first Piola-Kirchhoff stress is the initially smallest
cross-section of the specimen given by A0 ¼ 1.544mm. The simulation results were obtained in the same way. However, in
contrast to the experiment the specimen was continuously loaded in the simulation. It can be observed that the initial yield
point in the experiment is lower compared to the results in the simulation which might be related to the fact that the material
parameters used in the simulation are obtained from [111] single crystal data. After 4% total strain the simulation
underestimates the required force for the specified displacement. This might due to the evolution of geometrically necessary
Table 15.2 Identified hardening parameter values for pure nickel based on the experimental data from [22] for an [111] single crystal
cE11 [GPa] cE12 [GPa] cE44 [GPa] td0½MPa� _g0 [s�1] m0 h0 [MPa] tds0 ½MPa� n0
246 147.3 124.7 8.65 10� 3 20 427.9 900 14.77
experimentsimulation
2 4 6 800
50
150
100
200
strain[%]
firs
t Pio
la-K
irch
hoff
str
ess
[MPa]
Fig. 15.6 Comparison of experimental and simulation results for first Piola-Kirchhoff stress (P ¼ FA0
with A0 ¼ 1.544 mm) in loading direction
over strain ( Dll0 with l0 ¼ 49.5 mm) for pure Ni oligocrystal
Fig. 15.5 Model of the pure Ni tensile specimen
15 Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity 107
dislocations (GNDs) in the specimen which strengthen the material. The influence of including these GNDs in the simulation
for additional hardening is on-going research and will be studied with help of the experimental obtained orientation gradient.
Next we investigate the development of the specimen geometry and grain morphology. Exemplarily the results for 4%
total strain are compared between experiment and simulation in Fig. 15.7a. In general, it can be observed that the simulation
is able to predict the specimen geometry and grain morphology for 4% total strain quite well. However, from these results it
is very difficult to see where the main activity occurs. Therefore the total slip of the {111} glide system family is shown in
Fig. 15.7b. It can be observed that the main deformation occurred in grain D (for labeling see Fig. 15.5). Furthermore a
relative high activity can be seen in grain A, B and at the boundary of grain D to grain C. This is related to the fact that in this
region the specimen is slightly smaller in width and thickness compared to regions more on the right of the specimen. Figure
15.7c shows a micrograph from light microscopy after the shear band is visible which occurs at � 6% total strain (cp.
Fig. 15.6). Although in the simulation failure is not considered, the total slip indicates where the highest deformation is
present. This can be seen as an indicator where a shear band would be most likely start. From the simulation results it would
be most likely that a shear band could occur in the region of grain D, C and E. In the experiment the shear band was observed
in grain D and C which at least for grain D this could be anticipated by the simulation.
In summary, these first exemplary simulation results of the face-centered pure Ni sample show that the simulation was
able to predict the general behavior correctly, however, certain deviations occur which might be related to the fact that only
[111] single crystal data were considered for the material parameter identification. Further a failure model has to be included
to be able to predict the shear band.
Fig. 15.7 (a) Comparison of experimental (red line) and simulation (black line) results for the specimen geometry and grain morphology at 4 %
total strain in the tension direction. (b) Total slip for {111} glide system family at 6 % total strain projected on deformed geometry. (c) Micrograph
from light microscopy of the specimen after shear band occur at � 6 % total strain
108 B. Klusemann et al.
15.5 Summary and Outlook
The current work has focused on the modeling and simulation of the behavior of two thin metal sheets, one consisting of a
single layer of large grains of Fe-3%Si (bcc) and one consisting of a single layer of large grains of pure Ni (fcc). Since such
material are highly heterogeneous, they are modeled with the help of single-crystal plasticity for each grain in the specimen
and the finite-element method for the grain morphology and specimen as a whole. The single-crystal model is rate-dependent
and accounts for (local) dissipative hardening effects.
The predictions of the model are compared with experimental results of thin sheets of Fe-3%Si and pure Ni loaded
incrementally in tension. For the Fe-3%Si sample the specimen geometry and grain morphology and the development of the
orientation gradient were analyzed. Two modeling cases were examined and compared with each other. In the first case, all
hardening was neglected, resulting in ideal viscoplastic behavior of the grains. Initially, reasonable agreement is obtained;
but as one can imagine, further loading and increasing deformation leads to significant hardening. As such, neglecting all
hardening results in overestimate of the deformation in favorably oriented grains and to corresponding mismatch with
experiment. Including hardening leads to quite good agreement. For the pure Nickel sample the stress-strain curve were
compared between simulation and experiment which showed some deviations. Further, the specimen geometry and grain
morphology were exemplary investigated as well as the strain field. In general the simulation showed the same tendency as
obtained in the experiment. However, certain deviations occur which might be related to the fact that only [111] single
crystal data were considered for the material parameter identification.
Besides dissipative hardening, the effects of additional strengthening due to grain size and misorientation distributions, as
well as that of additional hardening due to GND development in the specimen, on the deformation behavior will be
investigated in the future. Further a failure model has to be included to be able to predict the occurrence of the shear band in
the experiment which will be on-going work.
Due to the fact that with Fe-3%Si and pure Nickel representatives of body-centered-cubic and face-centered-cubic
materials were investigated, the next step would be the investigation of the third important crystal system, the hexagonal
closed packed system.
Acknowledgements Financial support of this work from the German Research Foundation (DFG) under contracts Sv 8/8-2 and VE 132/24-2 is
gratefully acknowledged.
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110 B. Klusemann et al.
Chapter 16
Evaluation of Mechanical Properties of Nano-structured
Al6061 Synthesized Using Machining
Paresh S. Ghangrekar, H. Murthy, and Balkrishna C. Rao
Abstract This work focuses on the synthesis of nano-structured Al6061 using machining under plane strain and evaluation
of its mechanical properties. It discusses an unusual application of the machining process by using it as a severe plastic
deformation (SPD) process to develop nano-structured or ultra-fine grained materials. Chips obtained from this process show
higher hardness than the bulk material which is in agreement with results reported in existing literature. Chips with minimum
curvature have been obtained using restricted contact tool and extrusion-machining processes. Hardness of the straight chips
obtained by the stated methods, though higher than the bulk material, was less than the hardness of the curled chips obtained
from conventional orthogonal machining. Furthermore, hardness of the chips obtained using tool with restricted contact
length of 0.6mm showed lesser variation. Hence they were used to prepare samples for the tensile test. A novel method was
used to prepare small test specimens from chips to measure tensile strength. Specimens made from the chips had higher
ultimate tensile strength (53%) and yield strength (85%) than that of bulk material. Improvement in strength was
accompanied by a reduction in ductility (58%) for chips as compared to bulk material. It was observed that for both the
chip and the bulk material, the reduction in gauge length leads to lower values of Young s modulus showing size effect.
16.1 Introduction
Materials with ultra-fine grained microstructure have appealing properties when compared to those of conventional
materials [1, 2]. The role of large strain deformation in microstructure refinement has been reported in the past by Embury
and Fisher [3] and Langford and Cohen [4]. Equal channel angular pressing/extrusion (ECAP/E), high pressure torsional
straining (HPT) and accumulative roll bonding (ARB) are some of the traditional severe plastic deformation (SPD)
processes. Enhancement in mechanical properties of nano-structured materials obtained from ECAP and HPT processes
have been observed by many researchers. But these traditional SPD processes have disadvantages as follows. They require
multiple passes to get large strains and some high strength metals and alloys are difficult to deform in this manner due to
constraints imposed by the forming equipment, tools and dies [5, 6]. Further, application of traditional SPD processes for
these materials is also restricted by the production-cost being above $100 per pound [7].
Machining has been used in recent years as an SPD process. Figure 16.1 shows the schematic of a typical machining
process. A wedge shaped tool is fed orthogonally against a stationary workpiece at a low cutting speed (Vo). This ensures
both low-temperature condition at the tool-chip interface region and condition of plane-strain. Intense plastic deformation on
the shear plane oriented at an angle (b) with the surface of the workpiece results in a shaving (or chip) that possesses an ultra-fine grain structure. The rake angle (a) of the tool determines the direction of chip flow as it is formed and the clearance angle
provides a small clearance between tool flank and newly generated machined surface. During machining, the cutting edge
of the tool is positioned at a certain distance below the original work surface. This corresponds to the undeformed chip
thickness (to). As the chip is formed along the shear plane, its thickness increases to tc. The ratio of to to tc is called
chip thickness ratio (rc) and is usually less than 1. A state of plane strain (2-D) deformation prevails when the tool edge is
P.S. Ghangrekar • H. Murthy (*)
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
e-mail: [email protected]
B.C. Rao
Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600036, India
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_16, # The Society for Experimental Mechanics, Inc. 2013
111
perpendicular to the cutting velocity (Vo) and the undeformed chip width (aw) is large compared to the undeformed chip
thickness (to). As opposed to traditional SPD processes, it is possible to impose shear strains ranging between 1 and 10 in a
single pass of the tool during the machining process [5]. The unconstrained nature of the machining process also enables the
creation of nano-crystalline materials with enhanced hardness values from a wide range of metals and alloys [5]. Hence it is a
big source of shavings or chips that are nano-structured with enhanced properties. These chips can be up cycled as advanced
materials. Furthermore, machining is economical vis-a-vis traditional SPD processes.
Precipitation heat treatable aluminum alloys like Al6061-T6 are widely used in aerospace and automotive sectors because
of their high strength to weight ratio. It has been observed that the presence of the second phase particles (precipitates)
accelerates grain refinement during the plastic deformation process [8]. Shankar et al. [8] have utilized this grain refinement
with precipitation to obtain a nano-structured aluminum 6061-T6 alloy through the machining process. This paper discusses
the mechanical properties of straight chips obtained from machining under controlled conditions.
16.2 Machining as Severe Plastic Deformation Process
16.2.1 Experimental Setup and Preliminary Tests
Large-strain cutting operations under plane-strain conditions were performed on a Deckel CNC milling machine.
A schematic of this setup is presented in Fig. 16.2. To ensure orthogonal conditions while cutting the work-piece, a fixture
has been fabricated for aligning the cutting tool. Rectangular plates made of solution treated aluminum 6061-T6 alloy were
machined to create nano-structured chips. Each of these plates having dimensions of 100 � 50 � 3mm was solution treated
at 550 ∘C for 10 h prior to the machining operation. The cutting tool is made of High Speed Steel (HSS) with a rake angle of
5∘. Tests have been conducted with the 5∘ tool since this falls between the extremes of positive and negative rakes.
Orthogonal machining tests were carried out with 0.3 mm depth of cut at a low cutting speed of 517 mm/min.
Shavings or chips obtained had thicknesses in the range of 1.23–1.58 mm. To obtain scratch-free specimens for
measuring hardness, chips were polished successively with finer abrasive materials including the final 0.1mm microid
diamond compound with aerosol spray. The production of longer chips entailed use of longer rectangular plates (150 mm).
16.2.2 Methods to Produce Straight Chips
Attempts were made to procure chips with minimum curvature or straight chips so that they could be used to prepare samples
for measuring the tensile strength of the nano-crystalline Al6061-T6 alloy. To produce chips with minimum curvature, it is
necessary to understand the mechanism of chip curl. Available literature on the reasons for chip curl seem to indicate that the
chip curl mechanism is related to the two zones of deformation in orthogonal cutting. These are described as the primary
deformation zone in which the chip is formed and the secondary deformation zone in which there is severe deformation of
the chip material due to large frictional forces between the chip and the rake face of the tool. Furthermore, at the tool-chip
interface there exist two zones which exhibit different frictional characteristics: the sticking zone and sliding zones [9]. Sizes
of these zones and the contact tool could have a bearing on the curvature of the chips.
Cuttingtool
Workpiece
Chip
V0
t0
tc
Shear plane
β
α
aw
Fig. 16.1 Schematic of a
typical machining process. Vo
is the cutting velocity, aw is
the undeformed chip width, tois the undeformed chip
thickness, tc is the chipthickness, b is the shear
plane angle and a is the
rake angle [5]
112 P.S. Ghangrekar et al.
Jawahir [10] presented the impact of restricting tool contact on breaking chips effectively and found that there is a
possibility of obtaining straight chips during machining in some cases. For a range of materials machined orthogonally,
Worthington and Redford [9] have provided experimental evidence that chips are formed with minimum curvature when the
zone of sticking friction is equal in length to that of the restricted contact. Jawahir [10] also showed that within the range
investigated, sticking length varies linearly with chip thickness. Experiments have been conducted to produce straight chips
using restricted contact machining. Figure 16.3a shows the machining operation under restricted contact condition between
the tool and chip. Here, h is the restricted contact length; hn is the natural contact length; V0 is the cutting velocity and a is the
primary rake angle. Rectangular plates made of aluminum 6061-T6 having dimensions of 150 � 50 � 3 mm were solution
treated before machining. The 5∘ rake angle tools with restricted contact lengths of 0.6 and 0.8mm have been used for
cutting. It resulted in the production of chips with minimum curvature which were suitable for preparation of tensile test
specimens. The depth of cut and cutting speed are similar to those used for preliminary tests with the conventional tool.
Extrusion machining is also useful in obtaining straight cips. As shown in Fig. 16.3b, a fixture was made of High Speed
Steel (HSS) with a groove for guiding the chip generated from the machining process. The groove was designed to procure a
chip with thickness and width similar to that of the chip obtained by the unconstrained machining process. This arrangement
represents a combination of extrusion and machining processes. Extrusion-machining experiments have been carried out
with the 5∘ rake angle tool under machining conditions similar to the preliminary tests. In this case as well, the curvature was
reduced. Representative chips obtained from different machining tests are shown in Fig. 16.4. It clearly indicates the
production of straighter chips using restricted-contact tools and extrusion-machining. The thicknesses of chips with
minimum curvature are in the range of 1.05–1.1 mm whereas those from conventional orthogonal machining operation
are slightly higher, i.e. 1.23–1.5 mm.
The chips have been polished unto 0.1 mm for carrying out metallographic tests. Subsequently, they were etched with
Keller’s reagent [11] to reveal their microstructure.In all the cases shown in Fig. 16.5, the microstructure clearly reveals flow
lines which are characteristic of a continuous lamellar structure resulting from plastic shear.
Fixture fortool alignment
Workpiece
52mm
40mm
135mm
Fig. 16.2 Schematic of the
Deckel milling machine used
for machining
hn h
Restricted contactlength tool
Conventional tool
Workpiece
Chip
V0
Slot to insert toolGroove to guide a chip
a bFig. 16.3 (a) Schematic to
depict machining with
restricted contact tool. h is the
restricted contact length, hn isthe natural contact length and
Vo is the cutting velocity [10]
(b) Fixture for implementing
extrusion-machining
16 Evaluation of Mechanical Properties. . . 113
16.3 Mechanical Properties of Chips
16.3.1 Hardness Tests
The chips obtained were polished unto 0.1mmmicroid diamond compound with aerosol spray for performing micro-hardness
tests on the samples. The results of the hardness tests on two specimens obtained from different large strain machining
processes are presented in Table 16.1. The hardness values of the straighter chips are less than those of chips obtained by the
conventional orthogonal machining process. Moreover, the chips machined by using a tool of 0.6 mm restricted contact
show less variation in their hardness values when compared to those obtained using both the 0.8 mm restricted contact tool
and the extrusion-machining process. The deviation in hardness values of the chips obtained from extrusion-machining
might be because, the groove made in the fixture does not allow the chip to flow freely. Furthermore, the resisting force
offered by the groove might vary from one location to another during the flow of the chip. Thus, the chips obtained from
machining with a tool of 0.6 mm restricted contact has been used to study the mechanical properties. Specimens made out of
bulk material as well as chips were peak-aged at 175∘ for 8 h to study the effect of peak-aging on hardness and tensile
properties. Table 16.2 shows the effect of peak-aging heat treatment on hardness values of bulk and chip material. It has been
observed that peak-aging on bulk material improves it’s hardness by about 30% and peak aging of chip obtained from bulk
material shows negligible effect on hardness values.
16.3.2 Tensile Testing
16.3.2.1 Preparation of Small Tensile Test Specimens
The chips obtained using the tool with restricted contact length of 0.6mm were used in tensile tests since they show lesser
variation in hardness values as discussed in the previous section. A portion of the chip, which was nearly straight, was cut out
from the raw chip to prepare a given tensile test specimen. The raw chips have two surfaces, one of them being smoother
Fig. 16.4 Chips obtained from: (a) conventional orthogonal machining; (b) and (c) machining using tools with restricted contact lengths of 0.6
and 0.8 mm respectively; (d) extrusion-machining
Fig. 16.5 Microstructure of chips obtained from: (a) and (b) machining using tool with restricted contact lengths of 0.6 and 0.8 mm respectively;
(c) extrusion-machining
114 P.S. Ghangrekar et al.
when compared to the other. Both the surfaces should be smooth for tensile test specimens so that there is no crack initiation
due to surface defects. This can be achieved by polishing. Small size of the chip makes this polishing difficult. Special care
has been taken while polishing the raw chips having small curvature. This is shown in Fig. 16.6a where the middle portion on
the lower side of the chip requires more polishing compared to the extreme portion on lower side. Hence chips have been
polished up to 0.4 mm thickness with a tolerance of 0.01 mm such that the rough portion as seen in Fig. 16.6a is avoided.
Fabrication of the tensile test specimens from polished chips itself is quite challenging. The small size of the tensile
specimen limited the use of techniques such as electric discharge machining (EDM) for fabrication. Hence manual polishing
was employed to prepare test specimens. In this regard, steel templates have been prepared to match the dimensions of the
tensile test specimen shown in Fig. 16.7. The straight portion of the chip (polished up to 0.4 mm thickness) has been placed
between two properly aligned templates and clamped in machine vice (Fig. 16.6a). Then the specimen was prepared to the
required dimensions by filing and polishing it slowly with a tolerance limit of 0.01 mm throughout the gauge length. During
the preparation, dimensions of the specimen were checked frequently to keep variation of width within 0.01 mm throughout
the gauge length. A typical tensile test specimen is shown in Fig. 16.6b. For comparison, tensile test specimens have also
been prepared from solution treated Al6061 bulk material. Moreover, some specimens made from bulk solution treated
Al6061 and chips obtained from solution treated Al6061 have been peak-aged prior to tensile tests to study the effect of
peak-aging on tensile strength.
Table 16.1 Results of micro-hardness tests for chips obtained from different machining processes using
Vicker’s indenter at 50 gm load. Twenty indentations were taken for each sample. Hardness of the bulk
material was 85.4 � 2.8 Average values are reported along with standard deviation
Large-strain process
Hardness values
(HV or kg/mm2)
Sample 1 Sample 2
Conventional orthogonal machining 143.4 � 2.4 138.8 � 2.6
Machining with 0.8 mm restricted tool 128.7 � 7.9 136.9 � 5.1
Machining with 0.6 mm restricted tool 137.0 � 4.2 134.7 � 4.9
Extrusion-machining 121.2 � 7.7 124.9 � 9.2
Table 16.2 Results of micro-hardness tests for bulk material and chips obtained from 0.6mm restricted
contact machining process using Vicker’s indenter at 50 gm load. Twenty indentations were taken
for each sample. Both samples were tested before and after peak-aging to observe the effect of further
peak-aging on hardness. Average values are reported along with standard deviation
Specimen
Hardness values
(HV or kg/mm2)
Without peak-aging With peak-aging
Bulk 85.4 � 2.8 111.2 � 2.5
Chip 137.0 � 4.2 134.7 � 4.9 133.9 � 3.3 136.1 � 2.9
Chip Polished chip
1.1 mm
28 mm
0.4 mm
Template
Polished chip
a b c
Fig. 16.6 (a) Polishing chips with minimum curvature to obtain straight chips. (b) Arrangement of steel templates and polished aluminum chip for
specimen preparation. (c) Photograph of the small tensile test specimen
16 Evaluation of Mechanical Properties. . . 115
16.3.2.2 Tensile Stress-Strain Tests
An INSTRON tensile testing machine has been used to conduct the tests on small tensile test specimens, at a moderate
displacement rate of 0.96 mm/min. Typical tensile stress-strain curves for representative specimens made from bulk material
and chips are shown in Fig 16.8a. It can be seen that the chips have lower ductility when compared with that of the bulk
material by approximately 58%.Yield stress and ultimate tensile stress values for solution treated Al6061 bulk, peak-aged
Al6061 bulk, chips obtained from solution treated Al6061 andpeak-aged chips obtained from solution treated Al6061 are
presented inTable 16.3 and Fig. 16.8b. To ensure repeatability, five specimens were prepared for each of the four conditions
and subsequently tested. For each condition, Table 16.3 reports the average of five stress values along with the standard
deviation. Following observations could be made from these results:
• The ultimate tensile strength of the chips shows about 53% increase compared to that of the bulk material.
• The yield strength of the chips shows about 85% increase compared to that of bulk material.
• Peak-aging treatment on the bulk material improves its tensile strength by 30%. But, peak-aged chips have approximately
same tensile strength as that of chips without peak-aging.
5 5 58 5
3
R10.625
All dimensions are in mm
0.4
Fig. 16.7 Dimensions of a given tensile test specimen
0 0.02 0.04 0.06 0.080
100
200
300
400
500
Strain
Stre
ss (M
Pa)
bulkchip from bulkpeak−aged bulk peak−aged chip
Bulk Peak−aged bulk Chip Peak−aged chip0
100
200
300
400
500
Material (solution treated Al6061)
Stre
ss,
σ, (
in M
Pa)
σyield
σultimate
a b
Fig. 16.8 (a) Tensile stress-strain curves for smaller specimens made out of solution treated Al6061: comparison between bulk material and chip
with and without peak-aging; (b) Yield stress and ultimate tensile stress values from tensile tests on small specimens
116 P.S. Ghangrekar et al.
• Peak-aging of bulk material increases yield strength by about 51%. However, peak-aged chips show negligible
improvement in yield stress when compared to that of non-peak-aged chips.
Kim et al. [12] have investigated post-aging behavior of equal channel angular pressed Al6061 and found that post-aging
treatment on nano-structured material improves ultimate tensile strength only by about 10%. Similar slight improvement in
the tensile strength of peak-aged chips compared to the non-peak-aged type may not be visible here because of the 5% error
in area of gauge section and this possibility needs to be investigated further.
Young’s modulus values were calculated for all the specimens and were found to be in the range of 21–25 GPa which is
well below the values for larger samples of Al6061 material (i.e. 70 GPa). Sergueeva et al. [13] have studied the effect of
gauge length and sample size on measured properties during tensile testing. It has been proved experimentally that as gauge
length and sample size decrease, the Young’s modulus also decreases while the tensile strength remains constant. Similarly
in our studies, Young’s modulus measured for Al6061 sample with gauge length of 8mm is in the range of 21–25 GPa, which
is 64–70% below the Young’s modulus specified in literature. Therefore, to corroborate the effect of gauge length and
sample size, another specimen with larger dimensions (i.e. gauge length¼ 40 mm, gauge thickness¼ 3 mm and gauge width
¼ 2.5 mm) made out of the bulk material was tested. In this case, the tensile strength was observed to remain same for the
larger specimen with a Young’s modulus value of 70 GPa. Accordingly, this size effect needs further investigation.
16.4 Conclusion
Ultra-fine grained Al6061 alloy has been obtained using machining as a severe plastic deformation (SPD) process. The
hardness of the chip obtained exceeds that of the bulk material indicating the impact of a finer grain structure on yield
strength. This research has demonstrated the possibility of obtaining chips with minimum curvature using restricted contact
tool and the extrusion-machining processes. Flow lines typical of large strain deformation are seen in the continuous chips
obtained in all the machining processes. Hardness of the straight chips obtained by the stated methods, though higher than
that of the bulk material, is less than the hardness of curled chips obtained from conventional orthogonal machining.
Furthermore, hardness of chips obtained using a tool with restricted contact length of 0.6 mm shows lesser variation.
Therefore, a 0.6 mm restricted contact tool was used to create samples for the tensile tests. It was observed from the results of
the tensile test that the strength of Al6061 chips is higher than solution treated bulk Al6061 with a 53% increase in ultimate
tensile strength and 85% increase in the value of yield stress. The peak-aging heat treatment on bulk material resulted in a
30% increase in ultimate tensile strength and 51% increase in yield strength. In contrast, chips from solution treated Al6061
show negligible change in tensile strength and yield strength after the peak-aging heat treatment. This shows that if we use
machining as an SPD process, we get much better improvement in strength as compared to peak-aging. The improvement in
strength was accompanied by a reduction in ductility by 58% for chips obtained from solution treated bulk material vis-a-vis
bulk material. Moreover, this work has also reported the influence of specimen size on Young’s modulus. It has been shown
that Young’s moduli for smaller specimens is 60–70% lesser than those for larger specimens.
Acknowledgements Authors would like to thank the following laboratories at IIT Madras for providing facilities for the experimental work:
Manufacturing Engineering Section (Mechanical Engineering Dept.), Physical Metallurgy Laboratory (Metallurgy and Material Science Dept.)
and Structures Laboratory (Civil Engineering Dept.). Authors would also like to thank Frontier life line pvt. ltd., Chennai for permitting us to use
their INSTRON 3345 tensile testing machine.
Table 16.3 Yield stress and ultimate tensile stress values from tensile tests on small specimens. Bulk
material is solution treated Al6061. Five specimens were tested under each condition. Average values are
reported along with standard deviation
Specimen Yield stress (MPa) Ultimate stress (MPa)
Bulk material 223 � 45.0 284 � 43.5
Chip obtained from bulk material 413 � 43.6 435 � 41.1
Peak-aged bulk material 335 � 16.6 368 � 12.0
Peak-aged chips obtained from bulk material 418 � 13.8 430 � 17.2
16 Evaluation of Mechanical Properties. . . 117
References
1. Gleiter H (1989) Nanocrystalline materials. Prog Mater Sci 33:223–315
2. Siegel RW (1986) Creating nanophase materials. Sci Am 275:74–79
3. Embury JD, Fisher RM (1966) The structure and properties of drawn pearlite. Acta Metall 14(2):147–159
4. Langford G, Cohen M (1969) Strain hardening of iron by severe plastic deformation. Trans ASM 62:623–638
5. Swaminathan S, Shankar MR, Lee S, Hwang J, King AH, Kezara RF, Rao BC, Brown TL, Chandrasekar S, Compton WD, Trumble KP (2005)
Large strain deformation and ultrafine grained materials by machining. Mater Sci Eng A 410–411:358–363
6. Swaminathan S, Shankar MR, Rao BC, Compton WD, Chandrasekar S, King AH, Trumble KP (2007) Severe plastic deformation (spd) and
nanostructured materials by machining. J Mater Sci 42:1529–1541
7. Briesen H, Fuhrmann A, Pratsinis SE (1998) Electrically assisted aerosol reactors using ring electrodes. In: Duenwu H, Beaucage G, Burns G,
Mark JE (eds) Nanostructured powders and their industrial applications. Proceedings of materials research society symposium, San Francisco,
vol 520. pp 3–14, 1998
8. Shankar MR, Chandrasekar S, Compton WD, King AH (2005) Characteristics of aluminum 6061-t6 deformed to large plastic strains by
machining. Mater Sci Eng A 410–411:364–368, 2005
9. Worthington B, Redford AH (1973) Chip curl and the action of the groove type chip former. Int J Mach Tool Des Res 13:257–270
10. Jawahir IS (1988) The tool restricted contact effect as a major influencing factor in chip breaking: An experimental analysis. Ann CIRP Manuf
Technol 37(1):121–126
11. ASTM Standard (2007) Volume E407. ASTM International, West Conshohocken
12. Kim JK, Kim HK, Park JW, Kim WJ (2005) Large enhancement in mechanical properties of the 6061 al alloys after a single pressing by ecap.
Scr Mater 53:1207–1211
13. Sergueeva AV, Zhou J, Meacham BE, Branagan DJ (2009) Gage length and sample size effect on measured properties during tensile testing.
Mater Sci Eng A 526:79–83
118 P.S. Ghangrekar et al.
Chapter 17
Hardening Behaviour of Thin Wires Under Loading
with Strain Gradients
Ying Chen, Mario Walter, and Oliver Kraft
Abstract Based on the work of Fleck et al., the influence of strain gradients on the deformation behaviour of metals in small
dimensions has been studied intensively. However, since almost 20 years comparable torsion experiments have never been
repeated. In this work, the deformation behaviour of Au and Al (containing 1 wt.-% Si) wires with diameters ranging from 15
to 40 mm was investigated in both tension and torsion, using a self-developed test facility. Size effects were observed in the
torsion tests as in the classical experiments, performed by Fleck and co-workers. However, thermal treatments of the wires in
combination with grain structural analysis show clearly that the microstructure of the wires plays an important role when
comparing the as-received and the annealed state with fine and coarse grains, respectively. Moreover, a variation of the
deformation velocity within the tests on AlSi1 wires showed an additional influence on the strength level in tension and
the size effect in torsion.
17.1 Introduction
From many experiments like torsion tests on small wires [1], micro-beam bending test [2] or also indentation tests [3, 4] it is
known, that gradients in plastic strain, resulting from multi-axial loading conditions, show a significant influence on the
hardening behaviour of metallic materials. When strain gradients are present, it has been found that the hardening scales
inversely with a characteristic length in which plastic deformation occurs and thus, leading to increasing flow stresses with
decreasing component sizes. Accordingly, it can be argued that the impact of strain gradients on themechanical behaviour has
to be taken into account by a mathematical description of the deformation behaviour of metals in small dimensions [5–11].
However, the interplay between material parameters like grain size and the sample size with and without the occurrence of
strain gradients, as well as the influence of testing parameters like the strain rate on the deformation behaviour has to be
studied. In this context, carefully conducted tensile and torsion experiments on small-scaled Au and AlSi1 wires,
accompanied by a thorough characterization and control of the microstructure of the investigated specimens, were performed
in order to separate the impact of the strain gradient and the microstructure on the commonly observed size effects.
17.2 Experimental Issues
Both, the tensile tests and the torsion tests were performed using a self constructed high resolution micro testing facility
based on a small tabletop testing machine (Zwick Z2.5, Ulm, Germany). To measure the torsion moment during twisting a
specimen, a wire is clamped under a low axial pre-load between a load cell and a rotation table. At a defined height, a stiff
cross-beam is glued to the wire. At this beam, two load cells (high-resolution atomic force microscope tips, supplied by
Y. Chen (*) • M. Walter • O. Kraft
Karlsruher Institut f€ur Technologie – Institut f€ur Angewandte Materialien, Hermann-von-Helmholtz-Platz 1,
Eggenstein-Leopoldshafen 76344, Germany
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_17, # The Society for Experimental Mechanics, Inc. 2013
119
Kleindiek, Reutlingen, Germany) are positioned opposing each other with well defined equal distances to the specimen in a
symmetrical configuration. By using the rotation table, the specimen is twisted in the direction of the positioned load sensors.
Since the movement of the cross-beam is inhibited, as illustrated in Fig. 17.1, the torsion moment can be determined directly
as a function of the torque angle. As the inner moment is equal to the outer moment, the torsion momentMt is obtained from:
Mt ¼ Md left þMd right ¼ aFleft þ aFright (17.1)
where a is the distance between the centre of the wire and the load cell, Fleft and Fright are the measured forces, andMd left and
Md right the corresponding torsion moments.
This measuring principle allows applying and measuring torsion moments even in the nNm-range. A more detailed
description of the test set-up as well as the general capability of the measurement system is given in [12, 13].
To investigate the mechanical behaviour of metals in small dimensions under both uniaxial (without gradients) and multi-
axial (with gradients) load conditions, wires from pure Au (diameter D ¼ 15, 25 and 40 mm; purity >99.99%; supplied by
Haeraeus, Hanau Germany) were tested at room temperature RT in the ‘as received’ state as well as in a specified recrystallized
state in tension (initial gauge length l0 ¼ 30 mm; strain rate de/dt ¼ 3.34 � 10�5, 3.34 � 10�4, and 3.34 � 10�3 s�1) and
torsion (initial gauge length l0 ¼ 50 mm; rotation angle rate d’/dt ¼ 0.086, 0.172 and 0.345 rad/s). The heat treatments were
carried out using a high vacuum tube furnace and for the micro structural investigations, a dual beam workstation Focused Ion
Beam (FIB) and Scannin Electron Microscope (SEM) from FEI was used. Additionally, AlSi1 wires (Al 1 wt.-% Si, diameter
D ¼ 17.5 and 40 mm; supplied by Haeraeus) were investigated in the ‘as received’ state under equal test conditions.
17.3 Results
The microstructure of the Au wires in the ‘as received’ state is found to be fine grained (Fig. 17.2), with almost identical
average grain size d for all diameters, ranging from d ¼ 0.54 via 0.64–0.7 mm with increasing specimen diameter.
Due to the fabrication process by presumably cold drawing, a comparable high dislocation density may be assumed.
In combination with the comparable microstructure, the general deformation behaviour in tension of wires with different
diameters is also almost identical (Fig. 17.3 – right). However, it can be observed, that both the uniform elongation and the
elongation at fracture are increasing with increasing diameter. An influence of the deformation velocity on the strength of
Fig. 17.1 Schematically
illustration of the measuring
principle
120 Y. Chen et al.
the Au wires was not found, but on the uniform elongation and elongation at fracture – both values increase with increasing
de/dt as exemplified for the wires with D ¼ 15 mm (Fig. 17.3 – left).
In torsion, the twist rate in general shows no influence on the deformation behaviour of wires with equal diameters
(Fig. 17.4 – left). However, in contrast to tension, a significant size effect can be observed for 15 mm wires compared to 25
and 40 mm wires. The deformation behaviour of the thicker wires is almost identical as illustrated in Fig 17.4 – right.
To investigate the material behaviour concerning the influence of strain gradients for the full recrystallized state
(i.e. coarse grains, low dislocation density), the three different wires were annealed. Different conditions were chosen to
achieve similar deformation behaviour in tension, particularly at lower strains (e < 1%, compare Fig. 17.6 – left). The
resulting micro structures are shown in Fig. 17.5. One can see, that the wires reveal almost the same number of grains within
a cross section and thus, an increasing average grain size with increasing wire diameter. In this case, a size effect in torsion
can be observed as illustrated in Fig. 17.6 – right. Comparable to the ‘as received’ state, an impact of the deformation
velocity on the strength level in both tension and torsion was not observed.
Comparable to the Au wires, AlSi1 wires reveal also a fine grained micro structure in the ‘as received’ state. The average
grain size is slightly smaller with 0.33 mm for the wires with D ¼ 17.5 and 0.38 mm for the wires with D ¼ 40 mm,
respectively. However, in contrast to the investigations on the noble metal, a significant influence of the deformation rate on
the strength was found during the tests on AlSi1 wires – in tension (Fig. 17.7) as well as in torsion (Fig. 17.8 – right).
Furthermore, it was again observed in tension, that both the uniform elongation and the elongation at fracture is increasing
with increasing de/dt.
Fig. 17.2 FIB micrographs of Au wires in the ‘as received’ state
Fig. 17.3 Deformation behaviour of Au micro wires (‘as received’ state – related micrographs see Fig. 17.2) in tension. Left: results of
investigations to the strain rate dependency. Right: results of investigations to the size dependency
17 Hardening Behaviour of Thin Wires Under Loading with Strain Gradients 121
Fig. 17.4 Deformation behaviour of Au micro wires (‘as received’ state – related micrographs see Fig. 17.2) in torsion. Left: results of
investigations to the twist rate dependency. Right: results of investigations to the size dependency
Fig. 17.5 FIB micrographs of Au wires in the full recrystallized state
Fig. 17.6 Deformation behaviour of Au micro wires (full recrystallized state – related micrographs see Fig. 17.5). Left: almost identical
stress–strain progress for e < ca. 1%. Right: results of investigations to the size dependency in torsion
Although the 40 mm wire shows a higher strength in tension compared to the 17.5 mm wire (Fig. 17.8 – left), a size effect
is clearly observable in torsion – even when comparing the thicker wire tested with the highest twist rate and the smaller wire
tested with the lowest twist rate (Fig. 17.8 – right).
17.4 Discussion
The results presented here reveal that strain gradients obviously affect the strength of polycrystalline metals in small
dimensions. However, as mentioned above the microstructure of the investigated specimens, as well as the test conditions
have a strong impact on the observed size effect. When comparing the results of the investigations on the Au wires, one may
argue that in the fully recrystallized state the size effect in torsion may not be solely attributed to the strain gradients but is
Fig. 17.7 Deformation behaviour of AlSi1 micro wires (‘as received’ state) in tension. Left: results of investigations to the strain rate dependencyfor wires with D ¼ 17.5 mm. Right: results of investigations to the strain rate dependency for wires with D ¼ 40 mm
Fig. 17.8 Deformation behaviour of AlSi1 micro wires (‘as received’ state) in tension and torsion. Left: results of investigations to the size
dependency in tension. Right: results of investigations to the size dependency in torsion
17 Hardening Behaviour of Thin Wires Under Loading with Strain Gradients 123
also related to the grain size (Fig. 17.9 – right). Surprisingly, the influence of the grain size is not seen in tension. This is
shown in Fig. 17.9 – left, where the yield strength, determined as flow stress at 0.2% plastic strain, is plotted versus the
inverse square root of the grain size in the wires. For the tension tests, no influence of the grain is observed.
In contrast, in the ‘as received’ state for both Au and AlSi1, the strain gradients lead to a significant size effect.
In particular for wires smaller than 25 mm, the strength in torsion increases strongly. For these wires, the characteristic
length of the microstructure, with fine grains and high dislocation density, is much smaller than the wire diameter. Therefore,
it is quite surprising that the wire diameter seems to govern the strength and not the internal length. On the other hand, it is
feasible that the wires are quite inhomogeneously deformed during processing and that, as a result, the strength varies within
the wires leading to different observations in tension and torsion. As these findings are not conclusive, more wires with
different annealing conditions and diameters of less than 15 mm will be tested in the future.
References
1. Fleck NA, Muller GM, Ashby MF, Hutchinson JW (1994) Strain gradient plasticity: theory and experiment. Acta Metall Mater 42(2):475–487
2. St€olken JS, Evans AG (1998) A microbend test method for measuring the plasticity length scale. Acta Mater 46:5109–5115
3. McElhaney KW, Vlassak JJ, NixWD (1998) Determination of indenter tip geometry and indentation contact area for depth sensing indentation
experiments. J Mater Res 13:1300–1306
4. Ma Q, Clarke DR (1996) Size dependent hardness of silver single crystals. J Mater Res 10:853–863
5. Ashby MF (1970) The deformation of plastically non-homogeneous materials. Philos Mag 21:399
6. de Borst R, M€uhlhaus H-B (1992) Gradient dependent plasticity: formulation and algorithmic aspects. Int J Numer Methods Eng 35:521
7. Gao H, Huang Y, Nix WD, Hutchinson JW (1999) Mechanism-based strain gradient plasticity – I. Therory. J Mech Phys Solids 47:1239
8. Nix D, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46:411–425
9. Fleck NA, Hutchinson JW (1993) A phenomenological theory for strain gradient effects in plasticity. J Mech Phys Solids 41:1825–1857
10. Fleck NA, Hutchinson JW (1997) Strain gradient plasticity. Adv Appl Mech 33:295–361
11. Dunstan DJ, Ehrler B, Bossis R, Joly S, P’ng KMP, Bushby AJ (2009) Elastic limit and strain hardening of thin wires in torsion. Phys Rev Lett
103:155501
12. Walter M, Kraft O, Klotz M (2011) European patent no. 1903326
13. Walter M, Kraft O (2011) A new method to measure torsion moments on small scaled specimens. Rev Sci Instrum 82(3):035109
Fig. 17.9 Hall–Petch behaviour for the annealed Au wires in tension and torsion, plotting the flow stress at 0.2 % plastic strain versus the inverse
square root of the grain size
124 Y. Chen et al.
Chapter 18
Mapping the Histology of the Human Tympanic Membrane
by Spatial Domain Optical Coherence Tomography
Corey Rutledge, Michael Thyden, Cosme Furlong, John J. Rosowski, and Jeffery Tao Cheng
Abstract The tympanic membrane is one of the major structures of the ear that aids in the hearing process, giving humans
one of the five major senses. It is hypothesized that sound induced displacements of the membrane, which allow humans to
hear, are directly related to the membrane’s medial layer which is comprised of a network of collagen fibers. Limitations in
available medical imaging techniques have thus far inhibited the further study of these fibers. In this paper we detail an
imaging system that we developed with the capability to quantitatively and noninvasively image the internal structures of
biological tissues in vitro through spatial domain optical coherence tomography (OCT). By utilizing spatial OCT, we can
correlate the characteristics of internal collagen fibers to sound induced displacements in the tympanic membrane. This will
eventually lead to improved modeling of the middle-ear and a better understanding of hearing mechanics.
18.1 Background
The hearing process contains a complex network of physical structures acting with the nervous system to allow humans to
perceive sound in the environment. One of themajor structures in this process is the tympanic membrane (TM), which is a thin
film of tissue that converts pressure waves in the air into mechanical vibrations and transmits them to the middle-ear. The TM
is comprised of three layers with the outermost and innermost layers providing protection for the medial layer, also known as
the lamina propria. The lamina propria is composed of collagen fibers arranged in a pattern that resembles that of a spider web.
These collagen fibers are responsible for the major mechanical properties of the TM as a whole, and are essential in sound
transmission to the middle-ear. Figure 18.1 shows an image of the theoretical orientation of collagen fibers in the TM.
While the existence of these collagen fibers in the TM is known, current imaging techniques have not been able to
quantitatively detail their structure and orientation. This is mainly because of limitations in available optical systems
to image internal structures. Most optical techniques are only capable of surface measurements and fewer still can generate
three-dimensional representations of the shape data gathered. To overcome these limitations, we have developed a spatial
domain optical coherence tomography imaging system that is capable of imaging internal structures present in biological
tissues. By post-processing these images we can create three-dimensional representations of the internal collagen fiber
structures present in the lamina propria of the TM.
C. Rutledge (*) • M. Thyden
Mechanical Engineering Department, Center for Holographic Studies and Laser micro-Mechatronics, Worcester Polytechnic Institute,
100 Institute Road, Worcester, MA 01609, USA
e-mail: [email protected]; [email protected]
C. Furlong
Mechanical Engineering Department, Center for Holographic Studies and Laser micro-Mechatronics, Worcester Polytechnic Institute,
100 Institute Road, Worcester, MA 01609, USA
Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA
J.J. Rosowski • J.T. Cheng
Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_18, # The Society for Experimental Mechanics, Inc. 2013
125
18.2 Methodology
Optical coherence tomography (OCT) is a rapidly growing imaging technique that has been used to characterize biological
tissues and structures [2]. Spatial OCT follows the basic principles of white-light interferometry. In our experimental setup,
we selected a light source with a wavelength that can penetrate tissue at a sufficient depth to enable imaging of internal
structures of tissue. A 720 nm infrared light source was used. This light source was directed into a beam splitter, which split
light into object and reference beams. By use of mirrors, both of the beams were recombined resulting in either constructive
or deconstructive interference. This yielded fringe patterns when the optical path length difference between the object and
reference beams was less than the coherence length of the light source. Our light source is characterized by a coherence
length of 20 mm. Figure 18.2 is an image of the experimental setup that was developed.
To acquire 3D information on a sample, our system required the ability to scan a sample in the axial direction. To do this,
we used a piezo-electric positioner with 100 mm traveling distance and sub-nanometer resolution as well as a custom made
LabVIEW program to send a linear voltage ramp to our piezo. This allowed us to capture the intensity modulations resulting
from interference fringes over the full coherence length of our light source for each individual pixel in an image. A theoretical
intensity modulation through the depth of a tissue is shown in Fig. 18.3. As seen in this figure, intensity modulation increases
as the three principal layers of the tympanic membrane are scanned.
An experimentally acquired intensity modulation is shown in Fig. 18.4. The maximum of the intensity modulation was
isolated by applying a Hilbert transform to the intensity modulation to generate an envelope over the signal. This envelope
defines the peak of the intensity modulation and the vertical location of a geometrical feature within a sample. By gathering
the maxima of the intensity modulation for each pixel in the field-of-view of a set of stacked images, these locations can be
used to generate three-dimensional tomographic images of a tissue.
Acquiring intensity modulations required the use of several software packages. As stated earlier, LabVIEW was used to
send a linear voltage to our piezo-electric positioner. All image acquisition was synchronized in LaserVIEW, which is an in-
house developed software package designed specifically for interferometric holography measurements. The interferogram
allows for live viewing of the sample being imaged, and video files containing images in .llvid format can be recorded.
LaserVIEW also allows for specification of camera frame rate and exposure time, which was essential to determining
distance between images and total time for our voltage ramp. All image processing and data analysis was conducted in
MATLAB 2011b, including analysis of video files created in LaserVIEW to create three dimensional tomographic images.
Accuracy and resolution of our system were characterized by measurements of NIST traceable gauge blocks. By imaging
these blocks, we were able to successfully image step sizes on the order of 100 nm with a resolution of 5 nm at the maximum
field of view on the order of 1.37 � 1.72 mm.
18.3 Representative Measurements
For our experimental procedure, a chinchilla TM was first imaged. The membrane was partially dissected, with the
epidermal layer removed and the lamina propria exposed. This allowed sufficient access to the collagen fibers for imaging.
The field of view used for the chinchilla TM imaging was 0.87 � 0.65 mm. After successfully gathering data from the
Fig. 18.1 A depiction of the
fibers in the lamina propria
of the TM oriented around
the malleus and umbo [1]
126 C. Rutledge et al.
chinchilla TM, we next moved to a human TM. The human TM was that of the left ear of a 52 year old male. For this
experiment, a field of view of 0.75 � 0.75 mm was used. Images were gathered starting next to the umbo and in the radial
direction to acquire structural data as distance from the umbo increased. The goal was to determine information on the
collagen fiber size as well as to determine if the density of collagen fibers changed as distance from the umbo increased.
From analysis of acquired images of the chinchilla TM lamina propria, we were able to determine that the diameter of
collagen fibers was approximately 5 mm (see Fig. 18.5). Additionally, we found that a 135 � 135 mm location could contain
between 15 and 20 collagen fibers. It was also clear from our results that the fiber orientation changed. This led us to believe
that the density of collagen fibers changed as distance from the umbo increased. These measurements correlate with data
reported in the literature [3].
Fig. 18.2 Spatial OCT experimental setup
Fig. 18.3 Intensity modulations as different layers of the TM are scanned [1]
18 Mapping the Histology of the Human Tympanic Membrane by Spatial. . . 127
0
10
20
30
mic
rom
eter
s40
50
60-60 -40 -20 0
Amplitude
20 40 60
Fig. 18.4 Intensity modulation with generated envelope for an individual pixel in the axial direction. Measurements performed on a human TM
Fig. 18.5 Spatial OCT image of the lamina propria of a chinchilla and corresponding interferogram. The field of view is 0.87 � 0.65 mm
0-10-20-30-40-50
800 700 600 500 400
y axis (microns)
x axis (microns)
dept
h (m
icro
ns)
dept
h (m
icro
ns)
300 200 100 00
100
200300
400500
600
700
800
0-20-40
800700
600500
400300
200100 0 0
100 x axis (microns)
y axis (microns)
200
300
400
500
600
700
800
Fig. 18.6 Spatial OCT image for the human TM lamina propria. The field of view is 750 � 750 mm
Figure 18.6 shows spatial OCT images of the human TM lamina propria. The images were taken approximately half way
from the umbo to the outer edge of the TM. The donor was known to have mild tympanosclerosis, which could be an
indication as to why inconsistencies exist in the fiber size. By specifying 135 � 135 mm sections of the OCT images, fiber
sizes were identified as varying from 1 to 15 mm in diameter. Between 10 and 15 collagen fibers could be seen in
135 � 135 mm locations throughout the images in Fig. 18.6. Figure 18.7 shows a representation of the lamina propria for
a human TM generated through spatial OCT. Eight spatial OCT images were stitched together that were gathered
horizontally across the TM. The anatomical characteristics and fiber orientation of the TM can be clearly observed.
18.4 Conclusions
Spatial domain optical coherence tomography can be a very effective means to image the internal structure of the tympanic
membrane. Through analysis of OCT generated TM images, the collagen fiber size and density throughout the tympanic
membrane can be determined. Because of the difference in collagen fiber density throughout the TM, it is very likely that
TM displacements relate to the structure and orientation of the collagen fibers [4]. Future research will attempt to correlate
TM displacements at a location under a specific frequency to the anatomical characteristics of the TM generated through
spatial OCT.
References
1. Lim DJ (1995) Structure and function of the tympanic membrane: a review. Acta Oto-Rhino-Laryngol Belg 49:101–115
2. Chan A, Duker JS, Ko TH, Schuman JS, Fujimoto JG (2006) Ultrahigh resolution optical coherence tomography of retinal pigment epithelial
tear following blunt trauma. Arch Ophthalmol 124:281–283
3. Jackson RP, Chlebicki C, Krasieva TB, Puria S (2008) Multiphoton microscopy imaging of collagen fiber layers and orientation in the tympanic
membrane. Proc SPIE 2842:1–7
4. Cheng JT, Aarnisalo AA, Harrington E, del Socorro Hernandez-Montes M, Furlong C, Merchant SN, Rosowski JJ (2010) Motion of the surface
of the human tympanic membrane measured with stroboscopic holography. Hear Res 263(1–2):66–77
Fig. 18.7 Spatial OCT representation of a TM lamina propria cross-section. The field of view is 0.75 � 6 mm, which represents the stitching of
eight different measurements
18 Mapping the Histology of the Human Tympanic Membrane by Spatial. . . 129
Chapter 19
Opto-Mechanical Characterization of a MEMS Sensor
for Real-Time Infrared Imaging
Everett Tripp, Frank Pantuso, Lei Zhang, Ellery Harrington, and Cosme Furlong
Abstract MEMS technology has led to the development of new uncooled infrared imaging detectors. These MEMS
detectors consist of arrays of bi-metallic cantilevered beams that deflect linearly as a function of temperature associated
with infrared radiation from the scene. The main advantage of these detectors is the optical readout system that measures the
tilt of the beams based on the intensity reflected light. This removes the need for electronic readout at each of the sensing
elements and reduces the fabrication cost and complexity of sensor design, as well as eliminating the electronic noise at the
detector. The optical readout accuracy is sensitive to the uniformity of individual pixels on the array. The hypothesis of the
present research is that direct measurements of the change in deflection will reduce the need for high pixel uniformity.
Measurements of deflection change for a vacuum packaged detector with responsivity of 2.4 nm/K are made with a Linnik
interferometer employing the four phase step technique. The interferometer can measure real-time, full-field height
variations across the array. In double-exposure mode, the current height map is subtracted from a reference image so that
the change in deflection is measured. A software algorithm locates each mirror on the array, extracts the measured deflection
at the tip of a mirror, and uses that measurement to form a pixel of a thermogram in real-time. A blackbody target projector
with temperature controllable to 0.001 K is used to test the thermal resolution of the imaging system. The minimum
temperature resolution is below 250 mK.
19.1 Background
AMEMS uncooled infrared imaging detector consists of an array of bi-metallic cantilevered beams that deflect proportional
to infrared radiation from the scene. One material needs to be an efficient infrared absorber. The difference between
coefficients of thermal expansion between the two materials needs to be as large as possible to maximize the deflection of the
beam with respect to temperature at the scene. An electronic signal can be measured through a change in capacitance
between the tip of the cantilever and the substrate. The electronic readout is complicated and costly to manufacture.
Additionally, the electronic signal introduces additional noise from heat.
Optical readout systems provide an alternative. The second of the two metallic layers is an efficient reflector of visible
light. Light is reflected off of the array of cantilevers. The intensity of the reflected light detected by a camera corresponds to
the tilt of the mirror and thus to the temperature. Compensation arms of the sensing element deflect at a rate proportional
to the substrate temperature. This is situated so that the compensation arm opposes rotation of the sensor arm. Net deflection
is then only proportional to temperature changes at the scene. Noise can be controlled by adjustments to the optical system
and the design of the detector can be simplified. An image of an individual array element is shown in Fig. 19.1 [1].
E. Tripp (*) • E. Harrington • C. Furlong
Mechanical Engineering Department, Center for Holographic Studies and Laser micro-Mechatronics, Worcester Polytechnic Institute,
100 Institute Road, Worcester, MA 01609, USA
e-mail: [email protected]
F. Pantuso • L. Zhang
Agiltron Incorporated, 15 Presidential Way, Woburn, MA 01801, USA
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_19, # The Society for Experimental Mechanics, Inc. 2013
131
Manufacturing errors exist across the array. Ideally, every pixel will have the same tilt at the same temperature.
Nevertheless, the thin layers of the structure can become rotated or rounded. As a result of these distortions, the intensity
of reflected light with respect to temperature is not uniform across the array. This limits the potential temperature resolution
of the readout system.
19.2 Methodology
Holographic techniques can be used to compensate for the nonuniformity in the array. The use of interferometry to produce
full-field, non-contact, real-time holograms of a MEMS opto-mechanical array has been demonstrated [2]. This is done with
four-phase step interferometry to measure the optical phase of the array. In double exposure holography, a reference phase
map is measured in an unloaded state. Additional images are subtracted from the reference image so that only changes in
optical phase due to loading are measured. The measurements are real-time, full field, and non-contact.
The IR absorbing side of a MEMS opto-mechanical detector is mounted at the focal point of a long wave infrared imaging
lens. The reflective side of the array is focused on the object path of a Linnik interferometer with 4� magnification.
The MEMS detector is housed in a vacuum-sealed package. The array is viewed through an optical window. This introduces
an additional optical path length difference greater than the coherence length of the LED illumination source. Interference
between the two paths will not occur as a result. A compensation window of the same material and thickness as the optical
window is placed in the reference path to correct for the optical path length difference. A piezo-electric transducer moves the
reference mirror of the interferometer through the four phase step positions. Figure 19.2 is an image of the experimental
setup [3].
LaserView is in-house developed software designed specifically for interferometric holography measurements. The
software syncs the camera shutter signal with the signal to the positioner so that one interferogram is captured at each phase
position. The software calculates optical phase and modulation from the interferograms. A reference image can be captured
at any time to display the double exposed phase map. When a temperature load from the scene is applied, the mirrors of the
array tilt. The change in phase due to this tilt is visible in the double-exposed phase map.
Because the mirrors tilt, mirror response is at a maximum at one edge of each mirror. An algorithm is used to calculate a
value that represents the real-time height change associated with each mirror. Measurements are made with modulation only
on the surface of the mirrors. A threshold modulation value is set so that the image can be segmented into regions based on
mirror location. A median value is calculated at a location offset from the centroid of the mirror. These values are placed at
the respective centroids. All other pixels have no value. The total number of pixels is reduced to eliminate the gaps. The
result is a thermogram of the heat distributions as measured by the readout system on the detector. A differential blackbody
projector with temperature controllable to 0.001 K produces uniform scenes of known temperature. The blackbody target
is used to test the resolution of the readout system. The imaging system with the blackbody calibration setup is shown
in Fig. 19.3.
Fig. 19.1 Bimetallic MEMS cantilever layout [1]
132 E. Tripp et al.
19.3 Results
Real-time images are produced with the optical readout system. Because of the magnification of the interferometer, only
40 � 40 mirrors or approximately 2% of the entire array area is observed by the camera at once. Consequently, the spatial
resolution of the calculated thermograms is 40 � 40 pixels. Images appear pixelated. The frame rate of the readout system
nearly matches the frame rate of the camera itself. Figure 19.4 is a thermogram of the blackbody at 35�C. The blackbodyprojector produces uniform scenes of known temperature. A number of sequential images are captured of the uniform scene
so that spatial and temporal noise of the measurements can be calculated. The average responses of the array at two different
temperatures are used to calculate the pixel responsivity. Noise Equivalent Differential Temperature (NEDT) is the point at
which the measurement signal and the signal noise are equivalent. This provides an estimation of the temperature resolution.
NEDT is then the noise in nm divided by the response in nm/K. With real-time temporal averaging, the mean response of the
mirrors in the array is 1.5 nm/K with a noise of 0.33 nm for an NEDT of 220 mK. This is greater than the target value of
100 mK.
Fig. 19.2 Interferometric
readout system
Fig. 19.3 Imaging system
with blackbody calibration
setup
19 Opto-Mechanical Characterization of a MEMS Sensor for Real-Time Infrared Imaging 133
Figure 19.5a is a thermogram of three fingers as generated by the algorithm from the optical phase map and modulation
image. The temperature differential between the finger nails and the skin is noticeable. The temperature difference is
600 mK. Figure 19.5b is a thermogram of a portrait if a human face. Temperature differences between hair, clothing, and
eyes are noticeable. The temperature difference between the skin and the eyes is 800 mK.
19.4 Conclusions
Double exposure holography eliminated spatial noise in the measurements due to detector non-uniformity. The optical phase
measurements introduce noise from positioner non-linearity and camera noise. This noise is propagated by the median value
selection algorithm. The noise introduced by the holographic system is greater than the reduction in spatial noise from the
use of holography. Reduction in noise of the holographic measurements either through improvements to the existing system
or alternative holographic approaches will allow the system to achieve an NEDT lower than the target value of 100 mk.
References
1. Erdtman M, Simelgor G, Radhakrishan L, Zhang L, Liu Y, Emelie P, Salerno J (2010) Photomechanical imager FPA design for
manufacturability. In: Proceedings of the SPIE, Infrared technology and applications XXXVI, Orlando, FL USA 7660:766017–766017-8
2. Dobrev I, Balboa M, Fossett R, Furlong C, Harrington E (2011) MEMS for real-time infrared imaging. In: Proceedings of the SEM, MEMS
and nanotechnology, Uncasville, CT USA 4:119–125
3. Tripp E (2012) Interferometric optical readout system for a MEMS infrared imaging detector. MS thesis, Mechanical Engineering Department,
Worcester Polytechnic Institute
Fig. 19.4 Thermogram
of blackbody target at
temperature of 35�C
Fig. 19.5 Example
thermograms of (a) fingers
with temperature differential
of 600 mK between the nail
and skin and (b) a portrait with
temperature differential of
800 mK between the eyes and
the skin
134 E. Tripp et al.
Chapter 20
Global Digital Image Correlation for Pressure Deflected Membranes
Jan Neggers, Johan Hoefnagels, Francois Hild, Stephane Roux, and Marc Geers
Abstract Bulge testing is known for its ability to quantify the mechanical behavior of homogeneous thin membranes.
In this method the measured quantities are related to the averaged stress and strain using bulge equations that only exist for a
very limited set of membrane geometries. A novel 3D Digital Image Correlation (DIC) method is proposed to directly
measure the strain and curvature fields without using any closed form approximation of the deformation kinematics.
Importantly, for membranes under pressure, the stress is directly related to the curvature.
20.1 Introduction
Thin films, which often have one dimension smaller than the intrinsic micro-structural length scale of the material, are
regularly applied in micro-electronic devices or integrated systems [1]. Typically, these films exhibit a so-called size effect,
which means that the thin film material response is different from their bulk counterparts [2]. Therefore, experimental
methods that can characterize these thin films in the same form as they are produced and used are invaluable. An important
experiment in this class is the bulge test.In a bulge test a thin film or membrane is deflected using a pressurized medium. From the pressure and deflection at the
apex of the bulge, the stress-strain response is calculated by means of analytical descriptions of the membrane deformation,
called the bulge-equations [3]. There exist bulge-equations for circular, square, and, rectangular membranes, typically
derived from plate theory [4]. These bulge-equations work very well within the assumptions of the plate theory. However,
the limits are not always obviously fulfilled especially considering the membrane boundary [5]. Additionally, the results are
sensitive to experimental inaccuracies like sample variations, sample misalignment, temperature variations.
In this article a new bulge test method is proposed that does not use any a priori assumed description of the membrane
deformation, which relies on a single spot measurement. Instead, a full-field surface profile of the membrane at each
deformation increment is measured. From this profile, the full-field membrane strain is calculated using Digital Image
Correlation (DIC). Moreover, the full-field curvature is calculated from the profile, which is directly related to the membrane
stress. The proposed methodology results in a direct measurement of the stress and strain on the part of the membrane of
interest, i.e., the complex deformation at the boundary can be excluded from the measurement.
To prove this new method, it is benchmarked against a virtual experiment. This virtual experiment is a simulated
representation of a real experiment. In this synthetic environment, none of the experimental inaccuracies exist, and thus it
allows for a thorough evaluation of the methodology as if performed on a perfectly executed experiment. Moreover, also
virtual measurement noise can be injected in various ways to evaluate the robustness of the methodology to experimental
inaccuracies.
J. Neggers (*) • J. Hoefnagels • M. Geers
Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ, Eindhoven, Netherlands
e-mail: [email protected]
F. Hild • S. Roux
LMT Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud Paris, 61 avenue du President Wilson, 94235 Cachan Cedex, France
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_20, # The Society for Experimental Mechanics, Inc. 2013
135
20.2 Virtual Experiment
The reference experiment is the deflection of a 100 nm thick Silicon Nitride (Si3N4) membrane with “in-plane” dimensions
of 1�6 mm, which is also used as a reference configuration in [5, 6], and results in a plane-strain stress state in the center of
the membrane, and a membrane with dimensions of 1 � 1 mm, which results in a biaxial stress state in the center of the
membrane. In the experiment, a 3D pattern is applied to the membrane using 80–500 nm Ag particles, and the deflection of
the membrane is measured with an optical profilometer that has an “in-plane” pixel size of 380 nm [6]. The membrane is
deflected by pressurising a liquid “ethanol” on the back side of the membrane incrementally to a pressure of 1 bar.
The virtual experiment consists of a Finite Element Method (FEM) simulation using (50,000) 3D 4-node bilinear Mindlin
shell elements (Fig. 20.1). This large number of elements is used to improve the interpolation from the FEM discretization to
the pixel discretization that represents the optical profilometer data. In the simulation a pure elastic material model, with a
Young’s modulus of E ¼ 235 GPa and a Poisson’s ratio of n ¼ 0.27, is used in the large displacements formulation to
represent the material properties of Si3N4. The three displacement nodal Degrees Of Freedom (DOF) are used to artificially
deform a real picture of an undeformed membrane with a particle pattern (Fig. 20.2). The resulting data is similar to the data
normally obtained from a real experiment but with some differences: (1) there is no measurement noise in the data, only
interpolation errors, which are very similar to the pixel discretization of a optical profilometer camera, (2) the displacement-,
strain-, and stress-fields are known before analysing the data, and they can be used as a reference to quantify the accuracy of
the data-analysis.
20.3 Global DIC
To obtain the displacement field from the virtual experiment data a “global DIC” method is developed. The implementation
uses the same reasoning as previous “global DIC” implementations [7, 8]. In particular, the ability to resolve 3D displacement
fields, as a function of a 2D position vector, which is required for any profilimetric type measurement. The method is based on
Fig. 20.1 The deformed shape of the two virtual experiments, i.e., (a) the square membrane, (b) the rectangular membrane. Note that the out of
plane deformation is amplified by the micrometer scale of the z-axes, and that the visible grid does not represent the actual mesh grid, which would
be too fine to show in such an image
x [µm]
y [µ
m]
−100 −50 0 50 100
−50
0
50
z [µ
m]
1
2
3
4
−100 −50 0 50 100
−50
0
50 56
58
60
x [µm]
y [µ
m]
z [µ
m]
−100 −50 0 50 100
−50
0
5045
46
47
48
49
50
x [µm]
y [µ
m]
z [µ
m]
a b c
Fig. 20.2 A real picture of a pattern on top of a membrane is used as a reference image f(x) (a), which is deformed using the FEM displacement
field from the rectangular membrane (b) and the square membrane (c), thereby creating the deformed images g(x). Both combinations of f(x) andg(x) are then used in the correlation procedure
136 J. Neggers et al.
the conservation of the squared height difference of the topography between a deformed surface profile g(x) and a referencesurface profile f(x) integrated over the considered domain
�2 ¼ð½ f ðxÞ � gðxþ uxyðxÞÞ þ uzðxÞ�2dx ¼
ðrðxÞ2dx; (20.1)
where x is an in-plane coordinate vector, uxy the in-plane displacement, uz the out-of-plane displacement, r(x) the residualfield, and � the global residual that is minimized in the global DIC procedure. The displacement field is parametrized as a
sum of shape functions ’n(x) that act over the entire region of interest and are weighted with a discrete set of DOF un
uðxÞ ¼Xn
un’nðxÞei; (20.2)
where i ¼ { x, y, z} and the basis functions ’n(x) are polynomials dependent on the in-plane coordinate x ¼ xex þ yey
’n ¼ xaðnÞybðnÞ: (20.3)
Note that each basis function (of degree [a, b]) can be applied in three position directions, associated with three degrees of
freedom. The purpose of using this type of shape functions is because a C1 continuity on the displacement field is enforced,
which is important for the accuracy of the curvature calculation. The smoothness of the displacement fields may lead to an
incorrect conclusion that there was no error in the method. However, this particular global DIC implementation effectively
filters out any measurement noise in one step, leaving smooth displacement data and allows for the validation of the assumed
kinematic hypothesis.
The curvature tensor k is calculated as the gradient of the normal vector n
kðxÞ ¼ r � nðxÞ; (20.4)
which in turn is the gradient of the position field z (corrected for rotations)
nðxÞ ¼ rzðxÞjjrzðxÞjj : (20.5)
Since the curvature of a membrane is only defined in the tangential plane, components of the curvature are extracted using
two orthogonal membrane tangent vectors, i.e., tx and ty, where tx is the vector tangent to the membrane normal to the eydirection, and ty is the vector tangent to the membrane normal to the ex direction, resulting in the curvature fields
kxxðxÞ ¼ txðxÞ � kðxÞ � txðxÞ; (20.6)
kyyðxÞ ¼ tyðxÞ � kðxÞ � tyðxÞ; (20.7)
Similarly, the strain is calculated by using the Green-Lagrange strain tensor E ¼ 12ðruÞ þ ðruÞt þ ðruÞt � ðruÞ� �
, from
which two strain components are extracted
exxðxÞ ¼ txðxÞ � EðxÞ � txðxÞ; (20.8)
eyyðxÞ ¼ tyðxÞ � EðxÞ � tyðxÞ; (20.9)
For the rectangular membrane the plane-strain membrane stress in the center of the membrane can be related to the
curvature using the hoop equations [5]
sxx ¼ P
t kxx; (20.10)
20 Global Digital Image Correlation for Pressure Deflected Membranes 137
where P is the applied pressure to deflect the membrane and t the membrane thickness. For the square membrane the
deformation shape in the center of the membrane can be considered to be axisymmetric. Consequently, the principal stresses
are related to the principal curvatures, which are in this case aligned with the global ex and ey directions [9]
sxx ¼ P
2t kyy; (20.11)
syy ¼ P
t kyy1� kxx
2kyy
� �: (20.12)
Since these two curvatures are equal in the center of the membrane, the two corresponding stresses are also equal at that
location.
20.4 Results
Figures 20.3 and 20.4 show the measured displacement fields for the center area of both square and rectangular membranes.
For the rectangular membrane, six DOFs with corresponding shape functions are used,
’1 ¼ x0y0ez; ’2 ¼ x1y0ex;
’3 ¼ x0y1ey; ’4 ¼ x2y0ez;
’5 ¼ x3y0ex; ’6 ¼ x4y0ex;
−100 −50 0 50 100
−50
0
50
−1
−0.5
0
0.5
1
x [µm]
Ux
[µm
]
y [µ
m]
−100 −50 0 50 100
−50
0
50−2
−1
0
1
2
x 10−3
x [µm]
Uy
[µm
]
y [µ
m]
−100 −50 0 50 100
−50
0
50
54
55
56
57
x [µm]
Uz
[µm
]
y [µ
m]
−100 −50 0 50 100
−50
0
50
r [n
m]
−40
−20
0
20
40
x [µm]
y [µ
m]
a b
c d
Fig. 20.3 The components of the correlated displacement field (a–c) and the correlation residual field (d) for the center part of the rectangular
membrane
138 J. Neggers et al.
and for the square membrane, 14 DOFs are used,
’1 ¼ x0y0ez; ’2 ¼ x1y0ex; ’3 ¼ x0y1ey; ’4 ¼ x0y2ez;
’5 ¼ x2y0ez; ’6 ¼ x0y3ey; ’7 ¼ x1y2ex; ’8 ¼ x2y1ey;
’9 ¼ x3y0ex; ’10 ¼ x0y4ez; ’11 ¼ x2y2ez; ’12 ¼ x4y0ez;
’13 ¼ x0y5ey; ’14 ¼ x5y0ex:
This is a very limited set of degrees of freedom, which is useful to limit noise and interpolation errors. However, more can be
added to allow for unknown kinematics, e.g., rigid body translations, sample misalignment.
Each simulation consisted of many increments, however, only eight increments at regular pressure intervals are used for
the analysis. The image correlation method was robust enough to correlate the displacement field between the coarse
increment steps, without finding a false minimum. Figure 20.5 shows the stress-strain response in tx the direction for both therectangular and square membrane. Both membranes show an expected linear relationship between stress and strain, the
corresponding stiffnesses are related to the Young’s modulus and Poisson’s ratio
Eb ¼ E
1� n¼ 2G; (20.13)
Ep ¼ E
1� n2¼ 2G
1þ n: (20.14)
Note that for both virtual experiments the same solution strategy is applied, while the membrane deformation paths are
different. This provides means to extract not only the Young’s modulus but also the Poisson’s ratio, if a membrane is inflated
that is shaped such that it has both a locationwhich biaxially deforms and a locationwhich deforms in plane-strain. The simplest
example of such a sample would be a substrate with two membranes, close to each other such that they can be measured in
parallel. The two elastic properties can be extracted from the biaxial modulus Eb and the plane-strain modulus Ep using,
E ¼ 2Eb � E2b
Ep; (20.15)
−100 −50 0 50 100
−50
0
50−0.5
0
0.5
x [µm]
Ux
[µm
]
y [µ
m]
−100 −50 0 50 100
−50
0
50
−0.4
−0.2
0
0.2
0.4
x [µm]
Uy
[µm
]
y [µ
m]
−100 −50 0 50 100
−50
0
50
44
45
46
47
x [µm]U
z [µ
m]
y [µ
m]
−100 −50 0 50 100
−50
0
50
r [n
m]
−60
−40
−20
0
20
40
x [µm]
y [µ
m]
a b
c d
Fig. 20.4 The components of the correlated displacement field (a–c) and the correlation residual field (d) for the center part of the squaremembrane
20 Global Digital Image Correlation for Pressure Deflected Membranes 139
n ¼ Eb
Ep� 1: (20.16)
This has been done for the current virtual experiments and the corresponding elastic modulus of E¼ 236 GPa and Poisson’s
ratio of n ¼ 0.27 are in good agreement with the material properties which were used in the simulation.
20.5 Conclusion
A custom version of global Digital Image Correlation has been developed to cope with the 3D nature of the surface
profilometry data, where the gray-level is interpreted as a z-position. The newly-developed 3D global DIC method yields
full-field displacement maps of the bulging membrane and utilizes a long wavelength discretization basis to force a smooth
and continuously differentiable measured displacement field. This makes it possible to calculate the membrane curvature
field from the double derivative of the position field with high accuracy.
Both the displacement measurement and the curvature calculation procedure have been tested on simulated finite element
experiments. The results from these studies give confidence that the method can be used to capture the three-dimensional
displacement fields and curvature fields of bulge membranes without using any a priori knowledge of the kinematics,
relieving the need for the bulge equations with its associated assumptions. The method will be further developed to be able to
capture full-field stress and strain maps, the details of which are still under development.
References
1. Nix WD (1989) Mechanical properties of thin films. Metall Trans A 20A:2217–2245
2. Gruber PA, B€ohm J, Onuseit F, Wanner A, Spolenak R, Arzt E (2008) Size effects on yield strength and strain hardening for ultra-thin Cu films
with and without passivation: a study by synchrotron and bulge test techniques. Acta Mater 56:2318–2335
3. Xiang Y, Chen X, Vlassak JJ (2005) Plane-strain bulge test for thin films. J Mater Res 20(9):2360–2370
4. Vlassak JJ, NixWD (1992) A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J Mater Res 7
(12):3242–3249
5. Neggers J, Hoefnagels JPM, Geers MGD (2012) On the validity regime of the bulge equations. J Mater Res 27(9):1245–1250
6. Neggers J, Hoefnagels JPM, Hild F, Roux S, Geers MGD (2012) A global digital image correlation enhanced full-field bulge test method.
Procedia IUTAM Full-field measurements and identification in solid mechanics (submitted)
7. Besnard G, Hild F, Roux S (2006) Finite-element displacement fields analysis from digital images: application to Portevin-Le Chatelier bands.
Exp Mech 46:141–157
8. Hild F, Roux S, Guerrero N, Marante ME, Florez-Lopez J (2011) Calibration of constitutive models of steel beams subject to local buckling by
using digital image correlation. Eur J Mech A/Solids 30:1–10
9. Hsu FPK, Liu AMC, Downs J, Rigamonti D, Humphrey JD (1995) A triplane video-based experimental system for studying axisymmetrically
inflated biomembranes. IEEE Trans Biomed Eng 42:442–445
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
0.5
1
1.5
2
2.5
measured square membraneEb = 323.1 GPa
measured rectangular membraneEp = 254.5 GPa
estimated uniaxial responseE = 236.0 GPa,n = 0.27
Strain [%]St
ress
[G
Pa]
FEMGDIC
Fig. 20.5 The stress-strain
response for the center spot of
the square membrane and the
rectangular membrane, each
conforming to Hooke’s law
140 J. Neggers et al.
Chapter 21
Design and Development of Internal Friction and Energy Loss
Measurement on Nanocrystalline Aluminum Thin Films
T.-C. Hu, F.-C. Hsu, M.-T. Lin, C.-J. Tong, and Y.-T. Wang
Abstract A technique developed for studying the internal friction and energy loss of nano-scale thin metal films on
substrate is presented. The test microstructure was designed on the triangular cantilever beam and fabricated by the standard
C-MOS processes, which can improve stress distribution non-uniform problem of conventional cantilever beam. The
thickness of deposited film on its surface could reduce to several nanometers. Nanocrystalline Al thin film with thickness
of sub-micrometer and nanometer were performed to observe its internal friction and energy loss response under dynamic
frequency response of the cantilever beam structure generated by electrostatic force within vacuum pressure. The results
show the measurement system used here can accurately measures the energy loss of thin film. The internal friction
measurement results provided evidence for the grain boundary motion and dislocation motion in the nanoscale thin films.
Moreover, the length scale dependence on loss mechanism of tested films was observed.
21.1 Introduction
Metal films used in manufacturing or packaging technologies are deposited in sequence. Metal films applied in IC and micro
electro-mechanical system, MEMS, structures are stacked layer on layer, attached directly to each other. Each fabrication
step may involve a different temperature, so the entire structure is subjected to temperature changes throughout the complete
process. Whether the processing temperature is raised or dropped, the mechanical stresses due to the mismatch of thermal
expansion coefficients of different directly contacting materials can be easily produced. Sometimes these stresses will
become very large [1], and may result in mechanical failure in the device.
In MEMS applications, a moving part is always involved. Metal films deposited onto the moving part can be subjected to
dynamic loads. In the miniaturized structure the operating frequency may reach megahertz or gigahertz. Bulk machines were
never designed to operate at such high frequencies because of restriction within that dimension. Therefore, the dynamic
mechanical properties and responses of thin metal films are more critical, especially energy loss.
As mention above, it is important to understand the mechanical properties of small scale materials. There are many testing
methods for obtaining information about thin film mechanical properties, such as wafer curvature and nano-indentation
[2–5]. Most results only discuss quasistatic properties using those methods. Thus, measurement and analysis of the dynamic
properties of thin films must establish alternate measurement criteria. This study presents results using a resonant system for
determining the energy loss mechanism of thin Al films.
T.-C. Hu • F.-C. Hsu • M.-T. Lin (*) • C.-J. Tong • Y.-T. Wang
Graduate Institute of Precision Engineering, National Chung Hsing University, 250, Kuo-Kuang Rd.,
Taichung, Taiwan 40227, Republic of China
e-mail: [email protected]
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_21, # The Society for Experimental Mechanics, Inc. 2013
141
21.2 Experimental Detail
Paddle sample with uniform stress distribution cantilever beam has been used to carry very thin Al films because of metal
films can’t support itself in such small thickness. Sample dimensions have designed 20 � 20 mm of the frame, 5 � 5 mm of
the square, and 3 mm of tapered beam length which with vary width. There is a thin (40 mm) section (the uniform stress
beam) between the frame of the chip (250 mm thick, the thickness of the Si wafer from which it was fabricated) and the thick
paddle plate (also 250 mm). Because of their relative stiffness, all of the bending in the assembly occurs in the thin section.
All test samples were fabricated through the standard C-MOS processes which already proposed in previously research
[6, 7]. Traditional Si wafer that usually use to fabricate memory, CPU, GPU and so on, their requirement of the resistivity
about several tens Ohm-cm. But the paddle sample with such resistivity will not directly measure the energy loss and internal
friction information due to bare Si paddle sample use the existing measurement, therefore high doping Si wafers are use
to collocate paddle capacitance measurement which as well designed in previously research [8]. Polycrystalline Al films
with thickness ranges from 0.03 to 0.25 mmwere deposited from 5 N Al target onto the top surface of bare Si paddle samples.
The Al film deposited using pulse DC sputter system with 200 W deposit power at 5 � 10�3 torr deposit pressure which
balance by 10 sccm argon flow.
Test system in this work is designed to eliminate mechanical contact entirely, relying on electrostatic force instead.
Bending force has been designed generate by excitation which connects from waveform generator to drive electrode
underneath square plate. Excitation has two different kind exciting voltages, sweep frequency volts and constant frequency
volts. Sweep frequency excitation is used to finding out the resonance of paddle sample after complete fabrication in
resonance experiment. Constant frequency excitation is used to build stable amplitude before paddle sample free vibration
after suddenly turned off the excitation. Free decay is a common method that use to measure energy loss and internal friction
information. When the paddle samples have a bend due to the excitation work, displacement current will has the
corresponding change through the coupling capacitor. The changes in displacement current also immediately receive by
lock-in amplifier and recorder by Labview program. The lock-in amplifier output signal can be make a plot of output voltage
against experiment time then use Fast Fourier Transform, FFT, to analysis the frequency component in the response.
Environment pressure is the main factor in the decay rate experiment; therefore all capacitance measurement was located in
high vacuum chamber to reduce affect due to environment gas. When measure the decay rate due to bare Si paddle sample
with a thin Al film on the surface, the decay rate was indicated the total response not Al film alone. So, before measure the
Ai/Si component the decay rate of bare Si paddle sample is must be obtained firstly. Then, further compare and calculate
both results of bare Si sample without and with Al films, the internal friction in pure Al film can be extract from total
response by (21.1). Qf�1 is represents internal friction in thin metal film, QSi
�1 is the internal friction of Si alone, Qc�1 is the
internal friction in Al/Si component that is a weighted average of the internal friction in the substrate thickness, film
thickness, Qf�1 and QSi
�1 respectively. ESi and Ef are respectively representing the Young’s modulus of Si substrate and Al
film. Thickness of Si beam and Al film has been expressed in tSi and tf. All measurement was operating at the same pressure
in order to can get rid of the effect due to gas damping in follow calculation.
Q�1f ¼ tSi
3tf� ESi
EfQ�1
c �Q�1Si
� �(21.1)
21.3 Results
First, bare Si paddle samples were mounted into the capacitance measurement to find out the resonance of paddle sample.
An AC excitation applies on the drive electrode with various frequency excitation frequencies, the excitation sweep range
from 50 to 300 Hz. The lock-in amplifier output versus experiment time has plotted in Fig. 21.1, the FFT power spectrum
also translated and plotted in Fig. 21.2. Maximum peak in the FFT power spectrum is expressing the resonance of tested
paddle sample, in this result the resonance is indicated 233.37 Hz. According to the resonance of paddle sample (which
finding out in resonance experiment), the excitation on drive electrode was setting on a constant frequency that could help
paddle sample build stable amplitude before turned off the excitation. Once the AC excitation suddenly turned off, the stable
vibrate amplitude is starting decay (the free decay vibrate frequency also nearly the resonance). Continuously recorder the
lock-in amplifier output until the paddle sample stop vibration, then make a plot versus time as Fig. 21.3. Figure 21.3 is
the free decay result use one of bare Si paddle samples, and use exponential decay function to fitting the signal envelope, the
142 T.-C. Hu et al.
2.6
2.4
2.2
2
1.8
Lock
in o
utpu
t(V
)
1.6
1.4
1.2
1
0 500 1000 1500 2000
Time(sec)
2500 3000 3500 40000.8
Max Amplitude= 2.4647VTime=835.907sec
Fig. 21.1 The lock-in amplifier output versus experiment time use sweep frequency excitation in nitrogen at 6.8 � 10�5 torr. The scan range is
from 50 to 350 Hz
900
800
700
600
500
400
300
200
100
00 50 100 150 200 250
Frequency (Hz)
300 350 400 450 500
Pow
er
Frequency = 233.3726HzPower = 794.4649
Fig. 21.2 FFT power spectrum for bare Si paddle sample that translate from Fig. 21.1
21 Design and Development of Internal Friction and Energy Loss Measurement. . . 143
decay rate in Fig. 21.3 was indicated 0.00498 s�1. The decay rate of bare Si paddle sample that measured in nitrogen at
6.8 � 10�5 torr between 0.0044 and 0.0056 s�1. The corresponding logarithmic decrement has calculated in 1.8 � 10�5 to
2.2 � 10�5, those results indicated only have very slight different in each bare Si paddle sample.
The Al films follow deposited on the paddle sample full surface after finish the bare Si paddle sample measurement.
By various deposit time the Al film thickness have well control. All thickness of Al films will directly measured from focus
ionic beam, FIB, cross-section images. We make the 30, 60, 100, and 200 nm Al films respectively deposited on the bare Si
paddle sample those already measured in last procedure. All paddle samples with Al film also need re-finding out the new
resonance because of the Al film will change the beam stiffness and the square mass. The re-measure resonance results
indicated the depositing Al film onto bare Si paddle sample top surface will lead to the resonance has slight change
(increase), only 0.6 Hz delta frequency of paddle sample carry the thickest Al film. Figure 21.4 presents the delta frequency
of each bare Si paddle with different thickness Al film on the surface. It is clearly to see the delta frequency increasing with
Al film thickness.
According to the new resonance of Al/Si component, the excitation on the drive electrode need adjust to the same value
and re-build stable vibration amplitude. Waiting for a while until the response stable and suddenly turned off the excitation
again. Continuously record and plotted response then fitting signal envelope by exponential decay function (shows as
Fig. 21.5). Make a comparison between bare Si paddle sample with and without Al film, the decay rate due to paddle sample
with Al films significant larger than (increase from 0.00498 to 0.0224 s�1) paddle sample without film. The corresponding
logarithmic decrement also has calculated in 3.05 � 10�5. Summarize the logarithmic decrement due to bare Si sample and
after deposit Al films in one plot (show as Fig. 21.6). The black data points in Fig. 21.6 represent the logarithmic decrement
due to four different bare Si samples, the results also indicated the Si paddle sample almost have similar logarithmic
decrement at the same environment pressure. Gray data points express the logarithmic decrement use Si paddle sample has
Al film on the surface. The results clearly present the logarithmic decrement increase near linearly with Al film thickness in
addition very significant. Compare the delta resonance and delta logarithmic results, when the deposit film thickness has
been reduced lower than 200 nm, the change in resonance is difficult observe but easily observed from logarithmic
decrement change. Further extract the internal friction in pure Al film from total response by (21.1), the internal friction
around between 6.5 � 10�3 and 8.8 � 10�3. The relationship between internal friction in Al film and film deposited
thickness has been plotted in Fig. 21.7. Internal friction in Al films are inverse proportional to the film thickness except for
2.3
2.2
Decay function = 0.3279* e(-0.00498t)+ 1.79562.1
2
1.9
1.8
lock
in o
utpu
t(V
)
1.7
1.6
1.5
1.4
1.31400 1600 1800 2000 2200
t(sec)2400 2600 2800 3000 3200
Fig. 21.3 Free decay results of bare Si paddle sample, the excitation has suddenly turned off at 1,500 s, which measured in nitrogen at
6.8 � 10�5 torr
144 T.-C. Hu et al.
the thinnest one. The thinnest Al film only 30 nm thick and the micro structure image do not observed significant grain
structure. The result indicated the structure still have island structure and not yet link to a grain, so the internal friction would
slight smaller than the film with very small grain size. Once the films show the grain structure, the internal friction goes down
with grain size goes up.
Fig. 21.4 The relationship between delta frequency and deposited Al film thicknesses
2.3
2.2
2.1
2
1.9
1.8
lock
in o
utpu
t(V
)
1.7
1.6
1.5
1.4
1.3300 400
t(sec)500 600 700 800 900
Decay function =0.32026*e(-0.0224t)+1.7942
Fig. 21.5 Free decay result of Si paddle sample with Al metal film on the surface, excitation suddenly turned off at 400 s, which measured in
nitrogen at 6.8 � 10�5 torr
21 Design and Development of Internal Friction and Energy Loss Measurement. . . 145
21.4 Conclusions
In this paper, we proposed a uniform stress distribution test sample to correlate the high vacuum capacitance measurement.
We also successfully measured the energy loss and internal friction information in Al thin films that thickness has been
reduced less than 100 nm. We found the internal friction in Al films seem not depend much on the Al film thickness. Internal
friction in the thinnest Al film slight smaller than the maximum internal friction because of the film still stay island structure
not yet cluster to the grain structure. In the 60 nm Al film, very small grain structure has been observed that due to the
independent island already link each other. With the thickness growth, the grain size also become larger and larger that
induces the internal friction in Al film goes down. Therefore, fewer grain boundaries in the Al film will reduce the grain
boundary relaxation also can reduce the energy loss when the Al film under free vibration.
Fig. 21.6 Comparison of logarithmic decrement between bare Si paddle sample and deposited Al film on the paddle sample surface
Fig. 21.7 The internal friction in Al film versus deposited thicknesses
146 T.-C. Hu et al.
References
1. Nix WD (1989) Mechanical properties of thin films. Metall Mater Trans A 20:2217–2245
2. Flinn PA (1991) Measurement and interpretation of stress in copper films as a function of thermal history. J Mater Res 6:1548–1501
3. Vinci RP, Zielinski EM, Bravman JC (1995) Thermal strain and stress in copper thin films. Thin Solid Films 262:142–153
4. Keller RM, Baker SP, Arzt E (1998) Quantitative analysis of strengthening mechanisms in thin Cu films: effects of film thickness, grain size, and
passivation. J Mater Res 13:1307–1317
5. Suresh S, Nieh TG, Choi BW (1999) Nano-indentation of copper thin films on silicon substrates. Scr Mater 41:951–957
6. Tong CJ, Cheng YC, Lin MT, Chung KJ, Hsu JS, Wu CL (2010) Optical micro-paddle beam deflection measurement for electrostatic
mechanical testing of nano-scale thin film application to MEMS. Microsyst Technol 16:1131–1137
7. Cheng YC, Tong CJ, Lin MT (2011) Measurement of static and dynamic mechanical behavior of micro and nano-scale thin metal films: using
micro-cantilever beam deflection. Microsyst Technol 17:721–731
8. Tong CJ, Lin MT (2009) Design and development of a novel paddle test structure for the mechanical behavior measurement of thin films
application for MEMS. Microsyst Technol 15:1207–1216
21 Design and Development of Internal Friction and Energy Loss Measurement. . . 147
Chapter 22
Detection of Damage of Epoxy Composites Using Carbon
Nanotube Network
S. Cardoso, C. Mooney, R. Pivonka, V.B. Chalivendra, A. Shukla, and S.Z. Yang
Abstract A detailed experimental study is conducted to understand damage initiation and growth in epoxy particulate
composites using a multi-wall carbon nanotube (MWCNTs) conductive network under two different loading conditions:
(a) quasi-static shear and (b) fracture. Two different particulates (a) Cenospheres (aluminum silicate hollow spheres), and
(b) carboxyl-terminated butadiene acrylonitrile copolymer (CTBN) rubber of three different volume fractions (10%, 20%
and 30%) and mass fractions (10phr, 20phr and 30phr) respectively are used in thermoset epoxy resin composites. First,
MWCNTs are well dispersed in an epoxy matrix using ultrasonication, and later the above particulates are added and shear-
mixed into the solution to prepare composites. A v-notch rail shear specimen configuration for shear experiments, and single
edge notch tension (SENT) configuration for fracture are considered in this experimental study. A four-point probe
methodology along with high-resolution data acquisition is employed to capture electrical-resistance response of network
changes associated with non-linear deformation, damage initiation and growth within composites under said loading
conditions. It is identified from experiments that the electrical response associated with the above mechanisms is quite
different with the addition of particulates compared to that of epoxy with no particulate.
22.1 Introduction
Carbon nanotubes (CNTs) have been at the forefront of materials research since their conception from the buckminsterful-
lerene [1, 2]. With a vast wealth of studies performed to determine the mechanical, electrical and other properties of CNTs,
the potential for various applications have and are currently being explored [3–6]. To date, a wide range of different material
types with the inclusion of CNTs have been considered under various loading conditions such as tensile, compressive and
impact. Many of the noted studies are performed on polymer systems for their ease of manipulation and growing application
base. Qian et al. investigated the apparent changes in mechanical strength of polystyrene with carbon nanotube addition
when under tensile load [7]. Ultimately, it was determined that the nanotubes themselves are far stronger than the matrix in
which they resided, and were capable of yielding an increase in break stress of up to 25% with a CNT loading of 1% wt.
Similar studies have been performed under differing loading conditions.
Carbon nanotubes are also capable of acting as a sensory network when properly dispersed into a medium. Recently,
Heeder et al. investigated the use of CNTs as a sensory network in detecting damage within epoxy composites under static
and dynamic loading conditions [8, 9]. Employing a four circumferential ring measurement technique, samples were loaded
under quasi-static compression and Split-Hopkinson pressure bar (SHPB) impact. The samples also contained other
particulate additives, such that the damage associated with varying content fractions of additive could be monitored and
compared.
Though fracture studies pertaining to composites are readily available in literature today, there is little to the authors’
knowledge of fracture investigations using CNTs as a sensory network [10–12]. The same holds true for CNT embedded
composites under pure shear conditions [13–15]. The present study is concerned with the evolution of damage occurring
S. Cardoso • C. Mooney • R. Pivonka • V.B. Chalivendra (*)
University of Massachusetts Dartmouth, 285 Old Westport Rd., North Dartmouth, MA 02747, USA
e-mail: [email protected]
A. Shukla • S.Z. Yang
University of Rhode Island, 75 Lower College Road, Kingston, RI 02881, USA
G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,
DOI 10.1007/978-1-4614-4436-7_22, # The Society for Experimental Mechanics, Inc. 2013
149
within specimen under the foregoing conditions. The purpose is to use a CNT sensory network for the detection and analysis
of damage within the process zone of fracture specimen, and along the loading plane of pure shear specimen. In addition,
each of these cases is performed on nanocomposites containing particulate additives, in order to determine the effect of the
additive on the evolution of damage. Fracture testing is performed on samples of plain epoxy, and those with an addition of
carboxyl-terminated butadiene acrylonitrile copolymer (CTBN) rubber at a given weight fraction (10phr, 20phr and 30phr).
Similarly, the shear study is performed on similar sample types. Specimen containing cenospheres (aluminum silicate
hollow spheres) will also be considered in shear to compare the effects of rigid and elastomeric particulates. Similar to the
rubber case, three volume fractions of rigid particulates (10%, 20% and 30%) will be used.
22.2 Materials and Experimental Procedure
Epoxy and hardener were selected to facilitate easy fabrication. Bisphenol-A epoxy resin (Buehler Epothin 20-8140-128)
was chosen for its ease of casting. The resin is accompanied by a hardener counterpart (Buehler Epothin 20-8142-064).
CNTs were obtained from NanoLab Inc. They are 95% or higher purity, have an outer diameter of 30 � 15 nm, lengths of
5–20 microns with specific surface area of 200–400 m2/g. CVC Thermoset specialties HYPRO 1300X13 Polymer was
chosen as the CTBN rubber component. Cenospheres (hollow aluminum silicate spheres) with a diameter range of
10–300 mm and a wall thickness of one-tenth of the diameter were also used.
Only a general outline of the procedure is presented for completeness; however the readers can refer to reference [9] for
additional information and more specific details. Pre-determined amounts of resin and CNT are mechanically combined and
shear mixed. 0.3% wt. of CNTs is used for fracture while 0.2% wt. of CNTs is used for shear. The required amount of CNTs
was determined separately, in attempt to optimize the sensory network. Carbon nanotubes are dispersed using a combination
of ultrasonication and shear mixing techniques. A separate extensive study was conducted to identify the amount CNTs and
the duration of sonication that provides the best dispersion without damaging the CNTs or reducing the overall conductivity
of the fabricated material. For applicable cases, particulate additives are added to the mixture in pre-measured quantities, and
the solution is vacuumed to remove trapped gasses. Finally the hardener is added to complete the mixture, which is then
vacuumed briefly before being poured into pre-prepared rotating molds. Sheets are cast from the mixture and allowed to
cure, from which samples of a specific geometry are made. Figure 22.1 illustrated the nominal dimensions for (a) Fracture
and (b) shear specimen. Electrical leads are fixed to each sample with conductive silver epoxy, and the gripped ends are
insulated to ensure that current is not transferred from the sample to the machine. Resistance is monitored using a high-
resolution electrometer based four point/four circumferential ring probe system. Here, the resistance change is simply
calculated by dividing the difference in resistance with respect to the static resistance by the static difference. This quotient is
multiplied by a factor of 100 for a percentage scenario. SENT samples are gripped using standard tensile fixtures on a screw-
driven material testing machine, while shear samples are gripped using a v-notch rail shear fixture with the same machine.
The geometry and test configuration used for the shear investigation are outlined in by ASTM standards (ASTM 7078).
a b25.40 mm
101.60 mm
31.75 mm 15.88 mm
57.15 mm 3.18 mm
90°
0.30 mm
6.35 mm
3.00 mm
Fig. 22.1 Geometry for (a) fracture and (b) shear specimen
150 S. Cardoso et al.
22.3 Results and Discussion
22.3.1 Fracture Results
Carbon nanotube embedded SENT specimens of the following compositions were loaded under opening mode conditions:
epoxy without additive, 10phr, 20phr and 30phr CTBN rubber. To adequately determine the damage as it occurs within the
process zone the electrical leads were fixed in very close proximity to the machined crack tip in four point configuration,
wherein the resistance changes recorded reflects damage as it evolves within this small zone. The change in crack tip
opening displacement (CTOD) is used as a common reference for analysis of the electro-mechanical response of the system.
CTOD is measured directly by the Tracy method (1976) from images taken using a high resolution camera outfitted with
magnifying lenses. For consistency, data collection was performed only until the first sign of crack propagation for all cases.
In order to have complete confidence in the experimentally obtained results, several experiments were performed for each
material case. For the sake of brevity and convenience for making comparisons, only a single representative result from each
material group is presented. Figure 22.2 illustrates these representative results on a common set of axes. In the following
passages, each result is discussed in detail.
The electro-mechanical response of plain epoxy containing 0.3% wt. of CNTs is shown in Fig. 22.2. Initially, there is very
little change in the measured resistance, meaning that there is no significant damage mechanism occurring. After the initial
portion, a linear increase in resistance is found. Volume dilatation occurs within this stage of the specimen loading, pulling
apart carbon nanotubes in the loading direction. A change in the slope on the increasing resistance curve denotes another
change in the conductive network. As the specimen is continuously loaded, the matrix is manipulated, reducing overall
resistance within the process zone. All epoxy samples underwent fast fracture prior to large changes in CTOD.
Also presented in Fig. 22.2 is the electro-mechanical response of 0.3% wt. CNT embedded epoxy containing 10phr
rubber reinforcement. The specimen initially shows little response, explained by the same reasoning as for the epoxy case.
A second stage of damage is a linearly increasing resistance of constant slope. The same mechanisms occurring within plain
epoxy are also occurring here. A final stage of damage finds a slightly reduced slope in the increasing resistance trend.
Macro-scale changes in the matrix are driving the response. Given the relatively low content of rubber existing within the
sample, the material still fails under brittle fracture without any indication of crack propagation.
20phr composites experience minimal resistance change during the earliest stage of loading. This is shown in Fig. 22.2.
The same reasoning from previous discussions applies here. Another segment of the material deformation is characterized
by a linear increase in resistance of constant slope, again a result from the separation of CNTs. Following the second damage
stage, the material undergoes further deformation resulting in another resistance increase. Previous discussions concerning
the mechanisms behind the reduction in slope are still applicable for the 20phr case. The 20phr specimen still fails under a
brittle fracture with no crack propagation.
The response of epoxy composites containing 0.3% wt. CNTs and 30phr rubber is also shown on Fig. 22.2. 30phr also
exhibits a short stage of minimal recorded changes. Another damage stage is denoted by a fairly linear increase in resistance.
15
Epoxy
10phr
20phr
30phr
10
5
0
-5
-10
-15
Δ CTOD (mm)
Res
ista
nce
Cha
nge
(%)
0 0.05 0.1 0.15 0.2 0.25 0.3Fig. 22.2 Comparison
of electro-mechanical
response in fracture
22 Detection of Damage of Epoxy Composites Using Carbon Nanotube Network 151
The mechanisms explained previously remain unchanged for the 30phr case. With increasing CTOD, the third stage of
damage reflects a resistance drop at a constant rate. There are several contributors to this net effect. Large scale manipulation
of the matrix, and high concentrations of rubber enabling overall thinning are the reasons for such a drop. A final stage,
ending just prior to crack propagation, is characterized by another increase in resistance. With a drastic amount of damage
existing in the process zone, micro-cracks form rapidly yielding breakage in the sensory network. 30phr specimen did not
observe a brittle failure.
22.3.2 Shear Results
V-notch rail shear methodology is used to example the following composites under pure shear loading conditions: plain
epoxy without particulate inclusion, 10phr, 20phr and 30phr rubber, 10%, 20% and 30% cenospheres. The damage
mechanisms associated with pure shear loading will be obtained for each item in this broad spectrum of materials ranging
from high fractions of rigid particulates to high fractions of elastomeric particulates. At the present time, only the extremes
of the particulate cases (30phr rubber and 30% cenospheres) have been studied. Electrical leads are placed in a four
circumferential ring configuration such that the inner probes are separated by the plane on which shear is induced. The
measured voltage is therefore across the shear plane. For the case of rubber embedded samples, data collection is ended at
the first indication of sample failure. A representative result from each case in presented for discussion.
Figure 22.3 contains the electro-mechanical response of epoxy containing 0.2% wt. CNT and 30% volume of
rigid cenosphere particulate. Heavy rigid particle loading causes the resulting composite to be brittle in nature, as shown
by the linear stress–strain relationship. It appears that the 30% fraction of cenospheres reduces the overall potential for
damage detection of the sensory network. In all, very little resistance change is recorded throughout the specimen loading.
In this region, as the specimen undergoes shear deformation, the CNTs re-orient themselves in such a manner that no net
change is recorded. The slight inflection observed at the end of the resistance curve denotes the beginning of a second
damage. In this case, the bonds between particles and matrix are broken. This interfacial separation distorts the conductive
network.
A representative response of epoxy containing 30phr rubber reinforcement is presented in Fig. 22.4. Several damage
stages are present for the elastomeric composite case. First, a stage exhibiting minimal response is observed, again meaning
that the CNTs have been continuously re-oriented. A second stage of damage exhibits a dropping resistance trend as
the stress within the body is at its highest. The rubber particles are a blunting force for micro-crack formation and growth
within the matrix, allowing the network to be more conductive. Finally, the response shows an exponentially increasing
resistance until the first sign of failure is detected. Having sustained high stress, drastic amounts of damage are now
present in the measured region. This increasing amount of damage makes electron transfer far more difficult for the sensory
network.
30
25
20
15
10
5
0
Strain (%)
Res
ista
nce
Cha
nge
(%)
Str
ess
(MP
a)
0
1
-1
2
3
4
5
0 1 2 3 4 5 6 7
Fig. 22.3 Electro-mechanical
response of epoxy with 30%
cenospheres in shear
152 S. Cardoso et al.
22.4 Conclusion
Fracture testing was performed with emphasis on recording damage within the process zone for composites incorporating
10phr, 20phr and 30phr CTBN rubber. It was found that each material type saw a short region where little response was
recorded and no significant mechanism was acting within the measured zone. Epoxy, 10phr and 20phr samples all exhibited
the same general trend of increase due to volume dilatation and matrix changes. 30phr specimen saw several stages of
damage, each with its own explanation.
Shear testing was performed in a v-notch rail shear configuration on epoxy composites separately toughened with rubber
(10phr, 20phr and 30phr) and rigid particles (10%, 20% and 30% cenospheres). Only 30% cenosphere and 30phr rubber
results are presently available. Samples containing 30% rigid reinforcement had little response due to CNT re-orientation.
A slight increase in resistance is also recorded due to drastic damage. 30phr rubber toughened epoxy still endures a long
stage of damage where resistance is fairly static. A clear drop in resistance is also recorded, due to the prevention of micro-
cracks. Severe damage finally yields a large scale resistance increase.
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18
16
14
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10
8
6
4
2
0
0
-20
20
40
60
80
100
120
20 2510 150 5S
tres
s (M
Pa)
Strain (%)
Res
ista
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Cha
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(%)
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rubber in shear
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