nanomechanical actuation using molecular forces … · nanomechanical actuation using molecular...

NANOMECHANICAL ACTUATION USING MOLECULAR FORCES

OF AMINO AZO BENZENE DYE

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MECHANICAL

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

A. Joseph Rastegar

March 2014

This dissertation is online at: http://purl.stanford.edu/pb694jt6024

© 2014 by Ali Joseph Rastegar. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

ii

http://purl.stanford.edu/pb694jt6024

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Beth Pruitt, Primary Adviser


Nicholas Melosh, Co-Adviser


Roger Howe

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Abstract

The emerging fields of nanomotors and optomechanics are based on the harnessing of

light to generate force. However, our ability to detect the changes in material properties

as a result of these forces (such as small surface stresses) is limited by temperature

drift, environmental noise, and low-frequency flicker electronic noise. To addresses these

limitations, we functionalized microfabricated silicon cantilevers with an azo dye, silane-

based self-assembled monolayer. We developed a fast, one pot, simple, room-temperature

linkage chemistry to connect methyl red (the actuator) to 3-aminopropyltriethoxysilane (a

silicon attachment) to form (E)-2-((4-(dimethylamino)phenyl)diazenyl) -N- (3(triethoxysi-

lyl)propyl)benzamide (MR-APTES). These molecules change their shape when exposed to

light at specific wavelengths, enabling modulation of surface stress by light.

Atomic force microscopy, contact angle analysis, ellipsometry, and X-ray photoelectron

spectroscopy verified successful assembly of molecules on the cantilever. Ultraviolet and

visible spectra demonstrated optical switching of the synthesized molecule in solution.

MR-APTES was then used to form a self assembled monolayer (1 nm thick) on surface

of a silicon cantilever of 500 µm long 100 µm wide and 1 µm thick. The optical-mechanical

actuation of cantilever surface stress was observed by exciting the MR-APTES with a

405 nm laser and optically monitoring tip deflection, allowing us to measure forces of

approximately 0.3 pN per molecule. Cantilever tip deflection (3 nm) was measured with

a Witec alpha atomic force microscope. By turning the laser on and off at a specific rate

(1 Hz), we measured cantilever tip deflection via Fourier techniques, thus separating the

signal of interest from the noise. This technique, which is similar to electronic lock-in

techniques empowers the design of highly sensitive chemical sensors and forms the basis

of a new class of nanomechanical actuators.

iv

Acknowledgments

I am grateful to Professor Pruitt, and all members of the Stanford Microsystems Lab.

Special thanks to Dr. Ramesh Kassar, since without his help the chemistry would have

been an impossible task. The protocol for monolayer preparation and the initial recipe

were provided by Michael Vosgueritchian; most of the AFM pictures and contact angles

were taken with his help. Thanks to Dr. Doll for in depth discussion, assistance with the

calibration of cantilevers, and assistance with publication of our Langmuir paper. Thanks

to Dr. Park and Dr. Barlian for in depth testing of the circuit. Thanks to Mr. Mallon and

Dr. Ribeiro for fruitful discussions. I also would like to thank my reading committee for

great direction and advice.

On a personal note, I have been very fortunate to be in such great a environment among

so many talented and dedicated people at Stanford. I have worked on a topic far from my

expertise and comfort zone. So many people have contributed to my work, for which I am

deeply grateful. I would like to thank all my friends and family for their support.

I would also like to thank Mrs. Stanford for building such an incredible institution,

where one can learn the widest spectrum of knowledge from molecules to divinity. My

journey was magnificently fruitful, since beside learning a new technology, I learned the

teachings of Buddha at Stanford.

v

Contents

Abstract iv

Acknowledgments v

1 Introduction 11.1 Surface stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Components of surface stress . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Measurement of surface stress . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 State-of-the-art-solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.6 Detection modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.7 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Photochemistry 162.1 Absorbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Peptide linkage chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Self Assembled Monolayer - SAM 373.1 11-bromoundcyltrimethoxysilane . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 SAM process recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Transduction 514.1 Piezoresistive cantilevers . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

vi

4.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.3 Electrical noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.1 Thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4 Flicker noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4.1 Circuit for measuring resistor flicker noise . . . . . . . . . . . . . . 64

4.5 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 Measurements 715.1 Cantilever functionalization . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.2 Mounting of the cantilevers . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.3 Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.4 Analysis of tip motion due to heat . . . . . . . . . . . . . . . . . . . . . . 81

6 Discussion and conclusion 846.1 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.2 Experimental setup for two tone test . . . . . . . . . . . . . . . . . . . . . 89

6.3 Results of two tone test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.4 Summary of two tone test . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

A UV LED and laser driver 96

B X-ray photoelectron spectrometry 99

C Liquid chromatography-mass spectrometry 101

D Matlab signal processing code 104

Bibliography 110

vii

List of Tables

1.1 Tip deflection versus surface stress . . . . . . . . . . . . . . . . . . . . . . 10

3.1 SAM process optimized condition for various silane . . . . . . . . . . . . . 45

4.1 Selected process variables and performance characteristics for various

cantilevers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.2 Process parameters, α , and noise for four different devices . . . . . . . . . 56

4.3 Distributed load cantilever versus tip loaded cantilever . . . . . . . . . . . 60

C.1 Common mass of adducts found in electrospray current . . . . . . . . . . . 103

viii

List of Figures

1.1 Functionalized cantilever arrays can perform chemical detection . . . . . . 2

1.2 Optimal sensor system operating characteristic . . . . . . . . . . . . . . . 3

1.3 Depiction of mechanically based chemical senor . . . . . . . . . . . . . . . 4

1.4 Depiction of surface bonds . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Surface stress versus alkanethiol chain length . . . . . . . . . . . . . . . . 6

1.6 Major components of surface stress . . . . . . . . . . . . . . . . . . . . . 8

1.7 State of the art cantilever design for chemical sensing . . . . . . . . . . . . 10

1.8 Proposed system architecture . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.9 Overview of work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1 Retinal molecule. The molecule changes its shape due to absorption of light. 16

2.2 Various molecules that can change their shape with absorption of photon. . 17

2.3 Azobenzene molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Dodecylazophenol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Absorbance of dodecylazophenol . . . . . . . . . . . . . . . . . . . . . . . 20

2.6 AZO and MR-APTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.7 AZO-APTES and MR-APTES absorbance . . . . . . . . . . . . . . . . . . 23

2.8 Variety of thiol anchored azobenzene molecules . . . . . . . . . . . . . . . 25

2.9 Layer by layer synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.10 Williamson ether synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.11 Total ion current for the Williamson ether synthesis . . . . . . . . . . . . . 29

2.12 The ion mass found at different column times . . . . . . . . . . . . . . . . 30

2.13 Bromine signature in mass spectrometry . . . . . . . . . . . . . . . . . . . 31

2.14 4-(phenyldiazneyl)benzoic acid reaction . . . . . . . . . . . . . . . . . . . 34

ix

2.15 Simulated 1H NMR of 3-aminopropyltrimethoxysilane . . . . . . . . . . . 35

2.16 1H NMR of 3-aminopropyltrimethoxysilane . . . . . . . . . . . . . . . . . 36

3.1 View of forces in a SAM . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 Polymerized silane on silicon . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3 Polymerized silane on silicon cantilever . . . . . . . . . . . . . . . . . . . 39

3.4 2, 5-dimethyl-4-(phenyldiazenyl)phenol . . . . . . . . . . . . . . . . . . . 40

3.5 11-bromoundecyltrimethoxysilane . . . . . . . . . . . . . . . . . . . . . . 40

3.6 Three dimensional model of 11-bromoundecyltrimethoxysilane . . . . . . . 42

3.7 AFM and Contact angle of the 11-bromoundecyltrimethoxysilane SAM . . 43

3.8 AFM image of silicon surface functionalized with APTES . . . . . . . . . 46

3.9 APTES hydrolysis and condensation . . . . . . . . . . . . . . . . . . . . . 47

3.10 Summary of different adsorption mechanisms of APTES on SiO2 surface . 48

3.11 SAM process overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.12 XPS of piranha clean silicon . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.13 Effect of sonication on contact angle . . . . . . . . . . . . . . . . . . . . . 50

4.1 Placement of piezoresistor on the cantilever . . . . . . . . . . . . . . . . . 53

4.2 Electrical schematic of the piezoresistor cantilever. . . . . . . . . . . . . . 53

4.3 Hooge coefficient (α) vs. diffusion length . . . . . . . . . . . . . . . . . . 55

4.4 System noise floor and amplitude noise spectra for four piezoresistors . . . 57

4.5 Cantilever model for derivation of the equation . . . . . . . . . . . . . . . 59

4.6 Noise model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.7 1/f resistor noise measuring block diagram . . . . . . . . . . . . . . . . . . 64

4.8 1/f resistor noise measuring circuit . . . . . . . . . . . . . . . . . . . . . . 65

4.9 Cantilever tip deflection due to thermo-mechanical noise . . . . . . . . . . 69

5.1 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2 MR-APTES functionalization of cantilever . . . . . . . . . . . . . . . . . 73

5.3 Cantilever attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.4 The signal from a bare silicon cantilever . . . . . . . . . . . . . . . . . . . 75

5.5 The signal from MR-APTES coated cantilever . . . . . . . . . . . . . . . . 76

x

5.6 MR-APTES cantilever tip deflection spectrum. . . . . . . . . . . . . . . . 77

5.7 Finite impluse response of band pass filter . . . . . . . . . . . . . . . . . . 78

5.8 Band pass filter input and output for the MR-APTES cantilever . . . . . . . 79

5.9 Deflection spectrum of cantilever . . . . . . . . . . . . . . . . . . . . . . . 80

5.10 Cycle averaging of deflection . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.11 MR-APTES cantilever motion due to heat . . . . . . . . . . . . . . . . . . 81

5.12 Motion due to heat for 11-Bromoundcyltrimetoxysilane . . . . . . . . . . . 82

5.13 Gold coated cantilever motion due to heat . . . . . . . . . . . . . . . . . . 83

6.1 Block diagram of Stoney’s equation . . . . . . . . . . . . . . . . . . . . . 85

6.2 Non-linear system used for simulation of the two tone effect . . . . . . . . 86

6.3 Simulation of linear and non-linear system . . . . . . . . . . . . . . . . . . 87

6.4 Two tone simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.5 Two tone setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.6 Cantilever thermal frequency response . . . . . . . . . . . . . . . . . . . . 91

6.7 Two tone measurement at 100 nm above the slide . . . . . . . . . . . . . . 92

6.8 Amplitude of tone versus distance . . . . . . . . . . . . . . . . . . . . . . 93

A.1 Block diagram of the LED and laser driver circuit . . . . . . . . . . . . . . 97

A.2 Detailed schematic of UV-LED and laser Driver circuit . . . . . . . . . . . 98

B.1 XPS fundamentals of operation . . . . . . . . . . . . . . . . . . . . . . . . 100

C.1 Electrospray Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . 102

xi

Chapter 1

Introduction

Silicon micro-machined cantilevers are used in atomic force microscopy (AFM) [1], and in

recent years, silicon cantilevers have also been used as chemical sensors [2]. Cantilevers

are a potential tool for chemical analysis. Cantilevers can be functionalized to act as

highly specific chemical sensors and can easily be made into arrays; each cantilever in

an array can be functionalized with a specific selective coating. In developing a new

successful chemical analytical method, new sensors integrated into multiplex arrays need

to be invented, developed, and tested in various applications. Bringing together sensor

technology, a sensor array, and an analytical method constitutes a challenging and complex

system problem that is best addressed from three perspectives, each of which constitute a

separate project [3]. [4], as shown in Figure 1.1.

While current cross-reactive chemical sensor arrays promise to detect multiple analytes,

most are limited by non-selective receptors such as polymers, suffer confounding signals

from non-specific binding, and have poor reversibility and repeatability, especially in

water [5, 6]. In addition to cantilever sensitivity limitations, background noise presents

challenges for specific, selective detection of multiple analyte components in complex

samples. State-of-the-art approaches read out cantilever bending or resonance shifts and

use cross correlation between multiple cantilevers during transient response in a flow

through system to minimize the effect of background noise. Selectivity is improved

through a principal component analysis that considers the temporal responses of multiple

1

CHAPTER 1. INTRODUCTION 2

a)

b)

Figure 1.1: Functionalized cantilever arrays can perform chemical detection a) Cantileverscan easily be made into arrays with repeatable and matched performance. There are twomain detection methods of cantilever tip defelection: optical and piezoresistive. Reprintedfrom [4] with permission from Elsevier. b) A Cantisens gold deposited commerciallyavailable cantilever array. Image courtesy of Concentris GmbH.

cantilevers, but intensive system training and computation are required. Chemical reagents

can transduce signals in several ways. Optical properties of some molecules change

upon binding to others and thus binding events can be detected by changes in optical

activity of the reagents. Yet the big limitation of correlating changing optical properties to

detecting chemical species is that background chemicals in the sample significantly affect

the absorption profile of the sensing reagents and thus increase the false-positive detection

rates [7, 8](Fig. 1.2). It is not always clear how the absorption of a band in a spectra

increases or decreases based on presence of a analyte of interest because of interactions of


Se

nsi

tiv

ity

False Positives (%) (1-selectivity)

1 ppt

1 ppb

1 ppm

1 10 100

Excellent

Good

Mediu

m

Poor

current

receptor-based

lever-bending detectiongoal

Figure 1.2: Optimal sensor system operating characteristic. By functionalizing eachcantilever with a different selective coating and implementing intelligent algorithms, a highsensitivity versus low positive rate can be achieved. (ppm - part per million)

other components in the sample with the sensor.

Cantilevers form chemically specific sensors when molecular recognition agents are

coupled to the cantilever surface [9]. Cantilever-based sensing involves the transduction

of molecular interactions to an observable mechanical change, such as addition of mass

[10, 11], heat transfer [12–16], surface stress [17, 18], observation of resonance frequency

change, and tip deflection. Cantilevers functionalized with chemical reagents are more

sensitive than a bulk reaction because the sensing reagents have the opportunity to undergo

many weak interactions with the sample thus decreasing nonspecific binding events and

amplifying signal. In nature, biological molecules do not form strong bonds; rather,

they undergo weak interactions in many different sites of a molecule resulting in superb

specificity, as observed in enzyme interactions. Weak interactions at many sites also yields

strong bonding between molecules to provide a very selective reaction.

Upon binding of the analyte to the surface receptor, surface stress is induced [19] due

to various factors, such as conformational changes caused by analyte-receptor binding,

surface polarity, and surface interactions with the solvent (Fig. 1.3). Importantly, only

one surface of the cantilever must be functionalized [20] because functionalization of both

surfaces would result in equal stresses on both sides, and no tip deflection would occur. To


Figure 1.3: Depiction of mechanically based chemical senor. Upon binding of analyte tothe cantilever selective coating a surface stress is produced that causes the cantilever tobend. Figure courtesy of Dr. Beth Pruitt.

construct a differential surface, gold is usually deposited on one side of the cantilever and

thiol chemistry is used to attach the desired layer [21]. However, the large coefficient of

thermal expansion mismatch between gold and silicon renders the cantilever very sensitive

to temperature variations [22], reducing long-term measurement resolution. Other sources

of low frequency noise include environmental noise, such as humidity fluctuations, and

1/f noise in the signal conditioning electronics. Despite more than 15 years of research

and several start-up companies (Cantisense, Concentris), cantilever-based sensors have not

been widely commercialized due to the problems plaguing them. For cantilever sensors to

become a viable technology, a better understanding of surface stress signals, the system,

and components are needed. [17, 23].

1.1 Surface stress

The surface atoms of a solid surface differ from atoms in the bulk of the solid because the

surface atoms have fewer neighboring atoms to bond [24]. When a new surface is created,

electrons must redistribute themselves in response to the lack of atoms above the surface

(Fig. 1.4). The charge distribution near the surface is therefore different than that in the

bulk of the material; if the same charge density existed at the surface and in the bulk, there


Figure 1.4: Surface atoms with dangling bond for Si (100). a) High energy surface. Thesurface reconstructs to form b) a more favorable (lower) energetic surface that causes tensilestress. Reprinted from [24] with permission from Elsevier.

would be no surface stress [20]. In the case of a gold surface, there is an inherent tensile

surface stress [25].

From the chemical point of view, surface stress is the reversible work per unit area

required to elastically deform (strain) the surface by changing the surface area. Surface

stress can be expressed by the Shuttleworth equation (Eq. 1.1), where G is the surface

energy and ε is the surface strain. The quantity dGdε

represents the amount of energy needed

to move an atom from the bulk to the surface. For liquids, this term is zero, molecules are

free to move from the bulk to the surface. For micro-cantilevers with thin film adsorbate

coatings the change in surface energy can be directly equated to the change in surface stress

(Eq. 1.2). The variation in the generated surface stress can be viewed as the variation in

the surface energy [26].

σs = G+dGdε

(1.1)

∆σs = ∆G (1.2)


1.2 Components of surface stress

Based on non repeatability of our preliminary data, we hypothesized that the surface stress

resulting from adsorbate analyte binding must be very small; this hypothesis was recently

verified by the seminal work of Godin et al. where he elucidated the components of surface

stress [17]. Godin showed that for thiol-based anchored chemistry in which one side of the

cantilever is coated with gold the surface stress due to the vertical interaction between the

adsorbed molecule on the surface cannot be measured. Godin et al. also demonstrated that

surface stress is independent of the chain length (vertical interaction) of the alkane (number

of carbon atoms) within the measurement accuracy (Fig. 1.5).

There are three major components of surface stress. The first component of surface

stress is due to intermolecular interactions, which can be attractive (Van der Waals

interactions) or repulsive (Pauli exclusion). Intermolecular interactions result in surface

stresses on the order of 1-10 mN/m which can be either compressive or tensile as depicted

Figure 1.5: Surface stress versus alkanethiol chain length. The mean steady-statesurface stress resulting from hexanethiol (C6), octanethiol(c8), and decanethiol(c10) selfassembled mono layer. The steady surface stress is -6.3± 0.2 N/m. From [17], reproducedby permission of IOP Publishing. All rights reserved.


in Figure 1.6a. The intermolecular interaction is the main surface stress for biomolecular

sensing application. Unfortunately, it results in the lowest magnitude of surface stress,

therefore cantilevers capturing this type of interactions are operated at their lowest levels

of signal to noise ratio.

The second major component of surface stress is electrostatic interaction. Gold and

sulfur form a covalent bond. However, sulfur (S) is more electronegative (2.58). Therefore

sulfur has a higher tendency to keep electrons, gold has lower electronegativity (2.54)

therefore Au+− S− bond is polarized with slightly negative charge on the sulfur and a

slightly positive charge on the gold as depicted in Figure 1.6b. The same polarity charges

repel each other causing the surface to expand. From the point view of the film, it exhibits a

concave shape or a compressive film stress. The magnitude of the electrostatic components

of surface stress is approximately 0.01-0.1 N/m which depends on packing density.

The third major component of surface stress is surface charge transfer and redistri-

bution, which provides the largest magnitude of surface stress. When a bond is cleaved

at a gold surface, the bulk atoms experience different charge density than the surface

atoms, the surface atoms redistribute their charge (Fig. 1.6c). The loss of the bonds at

the newly formed surface triggers a charge redistribution that results in increased charge

density between the top surface atoms. In case of the gold, the tensile surface stress is

large enough to initiate surface reconstruction [20]. The magnitude of surface stress due to

surface charge transfer and redistribution is on the order of 1-10 N/m.


Figure 1.6: Major components of surface stress are demonstrated with alkanethiols on goldsurfaces. a) Intermolecular interactions are the main source of biomolecular surface stress(1 mN/m). The molecule tilts to reduce the inter-chain distance. b) Electrostatic componentof surface stress. The electrostatic repulsion from polarized Au+ − S− bond causes acompressive film stress on the order of 0.2 N/m. c) Charge transfer and redistribution ofgold due to sulfur bond cause very large surface stress on the order of 10 N/m. From [17],reproduced by permission of IOP Publishing. All rights reserved.


1.3 Measurement of surface stress

In 1909 Stoney published his seminal paper reporting that a metal film deposited on one

side of a thick substrate was in a state of tension or compression without any external load,

and that it consequently bent the substrate. He deposited 5.6 µm nickel to a 0.31 mm thick,

102 mm long x 12 mm wide ruler [27]. He correctly predicted the radius of curvature of

the rectangular plate with Equation 1.3, with the assumption that the film is much thinner

than the substrate. The modified Stoney’s equation for a rectangular cantilever beam given

by Equation 1.4 uses the biaxial Young’s modulus [28].

σ f ∗ t f =Es ∗ t2

s6∗R

(1.3)

∆y = 3σ f

E∗(lsts)2 (1.4)

Here σ f is the film or surface stress, R is the radius of curvature of the substrate, t f is

the thickness of the film, ls, ts are the length, and thickness of the cantilever, ∆y is the tip

deflection of the cantilever, Es,E∗ are the substrate uniaxial and biaxial Young’s moduli

respectively.

1.4 State-of-the-art-solution

The state of the art solution for measurement of surface stress due to analyte binding uses

two cantilevers. One cantilever is used as a reference and is not functionalized, while the

other, is functionalized with the adsorbate molecule (Fig. 1.7). Only one side of each

cantilever is coated with gold; thiol chemistry is mainly used to attach the adsorbate to

the sensing cantilever [19, 29, 30]. The magnitude of the surface stress for biomolecular

interactions are in the order of 1 mN/m while the charge transfer of sulfur gold bond

generates surface stress in the order of 10 N/m. Therefore a common mode signal which

is 10,000 times larger than the signal (80 dB) needs to be rejected. Since the signals are

subtracted electronically, any time delay or noise that is not common to both cantilevers at


Position sensitive

photodetector

Light

Source

Ref

Sens

Figure 1.7: State of the art cantilever design for chemical sensing. Two cantilevers areused, one as a reference and the other as sensing cantilever with different functionalization.The outputs are subtracted to measure the change in deflection due to analyte adsorbatebinding by the sensing cantilever [19].

the same exact time will be interpreted as signal.

In addition to the huge common mode issue, the temperature coefficient of expansion of

gold and silicon is a major issue. The thermal coefficients of expansion for gold and silicon

are 14 ppm/C and 2.6 ppm/C , respectively. Therefore, a small change in temperature

will cause large tip deflections for both the sensing and reference cantilevers (Table 1.1).

Temperature-based signal is reduced according to the degree to which the cantilevers are

matched. However, temperature signal will be misinterpreted as sensing signal in the

presence of cantilever mismatch or a small time lag between the cantilevers. Whenever

a system relies on the subtraction of two large numbers, the fluctuation of large numbers

Surface stress Tip deflection ∆C0.001 N/m 3.38 nm 0.03 C0.1 N/m 334 nm 2.76 C10 N/m 33.4 µm 276 C

Table 1.1: Tip deflection versus surface stress. ∆C indicates temperature change from 25C that will generate the same surface stress or tip deflection as the signal of interest for acantilever that is 100 µm wide, 500 µm long, and 1 µm thick, and has 25 nm thick goldcoating (Chapter 4.1).


critically impacts the reliability of the method.

To gain a better understanding of the magnitude of tip deflection involved we will

use equation 1.4. As a model structure we will use a 500 µm long 100 µm wide and 1

µm thick cantilever with 25 nm of gold deposited on the top surface. These cantilevers

are commercially available from Nanoworld USA. However, their thickness should be

measured, since it varies±50%. For all our experiments the cantilever calibration constants

were obtained from thermo-mechanical noise as outlined in Chapter 5 [31]. Table 1.1

shows the magnitude of tip deflection for the three ranges of surface stress. The thermal

expansion rate of gold is higher than silicon, hence it expands at a faster rate than silicon

and bends the cantilever tip down. From Table 1.1 we see for about 0.03C temperature

change the tip deflects 3.3 nm, which corresponds to a surface stress of 1 mN/m. For most

biomolecular application 1 mN/m is the maximum signal resulting from adsorbate analyte

binding. Based on Table 1.1 to measure biomolecular interaction with one percent accuracy

the system must maintain temperature stability of 0.0003 C. Such temperature stability is

not practical, and an alternative solution is needed.

1.5 Innovation

Reproducibility and signal to noise are two major issues that need to be addressed in

performing high sensitivity surface stress measurement. The most important issue effecting

reproducibility is gold. We propose removal of gold. The second major issue is the ability

to measure small surface stress signals on the order of 100 µN/m. We propose taking

advantage of narrow sub Hertz bandwidth of the chemical signal and moving it away from

the low frequency drift. Also combining the reference and sensing cantilever into one

gives the added benefit of common mode noise rejection. By eliminating gold we improve

reproducibility and repeatability. Gold grain structure and morphology has significant

impact in reproducibility of the result. Godin [17] shows surface stress is independent of

Alakanethiol chain length while Berger [18] shows that surface stress is Alkanethiol chain

length dependent. The discrepancy stems from the gold grain size, sulfur absorbtion and

heavily pitted gold surface. [32] We also propose combining the reference and the signal

cantilever into one. Taking advantage of the inherent natural subtraction of top surface


Σ

XBinding to

selective

coating

Tip

Deflection

Time

V

Voltage

Surface

Charge

Innovation

Liquid

Noise

Surface

Stress

Temperature

Cantilever AFM

Light on/off at F0

Rate

Figure 1.8: Architecture of the proposed single-cantilever system. The architectureresembles a lock-in amplifier, where the desired surface stress is modulated at a specificfrequency in order to distinguish it from background noise.

stress from the bottom surface stress which results in tip deflection. Subtraction of the

reference cantilever from the signal cantilever is done mechanically. Time lags do not

play important role since there is only one cantilever. The draw back to this technique is

the added complexity of different top and bottom cantilever surface functionalization. A

fundamental solution shown in Figure 1.8 is to make the desired surface stress time varying

at a specific frequency above the drift, and to observe the output at that specific frequency.

Then the other undesired effects such as temperature or the 1/f noise would not matter since

they would fall outside the band of the detection. A molecule that changes its shape due to

light is needed. By shining light on and off at a specific rate we can modulate the surface


stress at a specific frequency.

We propose modulating the cantilever surface stress signal over time using an azo dye in

order to spectrally separate the sensor signal from the background noise as shown in Figure

1.8. The physical behaviors of azo dyes are based on the isomerization of constituent

molecules, which undergo a large conformational change from one state to another in

response to the absorption of light at distinct wavelengths. The light-induced transition

of azobenzene derivatives (C6H5N=NC6H5) between the extended (trans) and compact

(cis) configuration gives rise to changes in molecular polarity, dipole moment, and shape.

Most azobenzene-based thin films are fabricated into materials such as polymers, liquid

crystals, Langmuir-Blodgett films, [33] and physically or chemically adsorbed monolayers

on gold surfaces [34–37]. In practice, photoswitches have been influenced by the density

and orientation of azobenzene-based self-assembled monolayers (SAMs). For example,

an azobenzene-contained alkanethiol self-assembled onto gold substrates exhibited no

response upon UV irradiation due to steric hindrance [38, 39]. The minimum area for

isomerization of azobenzene has been estimated to be 0.4 nm2 [40]. In contrast with

thiol-based SAMs, specific silane-based SAMs provide sufficient room between molecules

to prevent steric hindrance and have been shown as alignment layer for liquid crystal

networks. [41]

1.6 Detection modes

There are two major modes of detection of cantilever surface stress, optical or piezoresis-

tive. Following the development of the scanning tunneling microscope, the atomic force

microscope, and the use of small piezoresistive cantilevers for atomic force microscopy,

there has been increasing interest in the use of MEMS piezoresistors as a read out for

measuring chemical and biosensing variables. [42] Piezoresistive sensors are especially

well suited to this task, because they are small, low power, have a relatively stable DC

response, especially if temperature compensated, and can readily integrated into arrays to

provide a means of separating chemical species based on differential binding affinity for

varying coatings. [43] A silicon piezoresistive sensing element is formed on the surface of

small MEMS silicon cantilevers. A chemically sorptive layer is deposited on the silicon


surface. The layer expands or shrinks upon binding and causes the silicon cantilever to

bend causing a change in resistance of the silicon piezoresistor. Stoney’s equation relates

the bending radius of the micro cantilever caused by the stressed layer to the stress in the

piezoresistor.

1.7 Outline

As we move toward Nano Electro Mechanical systems (NEMS), the fields of mechanics

and chemistry merge. In this work we designed a mechanical actuator at molecular

(nano) scale. We then assembled the actuator molecules in a single structured layer

on a pure silicon cantilever. The actuator molecule absorbs a photon of 405 nm and

changes it shape. The change of molecular actuator shape result in expansion of actuator

assembled layer and causes the cantilever to bend. From the tip deflection of the

cantilever and careful measurements that exclude the effects of heating we were able

estimate on average force per molecule of 0.3 pN. The synthesized molecule was (E)-2-

((4-(dimethylamino)phenyl)diazenyl)-N-(3-(triethoxysilyl)propyl)benzamide, and self as-

sembled on hydroxylated silicon surface. [44]

Figure 1.9 gives the overall understanding of this work. It only represents the

experiments that worked. Yet most of the learning process was based on experiments that

did not work, which we have briefly included, and hope to serve as the basis of which path

not to follow.

Being aware that the chemistry is rather involved, we have published the recipe and

given the synthesis recipe to a commercial manufacturer that can provide the actuation

molecule for further investigation by interested researchers (www.medchemsource.com).

In Chapter 2 we search for a molecule that changes it shape with light. We also confront

the challenges of making the molecule. We found azobenzene, as the molecule of choice.

However practical issues of using the molecule prohibited its use. For example an optical

lens that could work at 320 nm was exceedingly expensive and a laser at 320 nm was not

available to us. Therefore, we choose a derivative (Methyl Red) that allowed shape change

at 405 nm. Chapter 2 also covers the synthesis of the azobenzene derivatives that can be


Figure 1.9: Overview of the work. A pure silicon bulk micromachined cantilever wascoated with an actuator molecule that caused tip motion, when excited by 405nm laser.Reprinted with permission from [44]. Copyright 2013 American Chemical Society.

attached to cantilever.

In Chapter 3 we discuss the self assembly and the techniques used to deposit and

characterize a monolayer. The issue of polymerization and surface preparation are

discussed in depth.

In Chapter 4 we explore different modes of transduction. By transduction we mean

conversion of the surface stress to an electrical response. We look at piezoresistive sensors

and explore how to lower their flicker noise. We also explore the design issues and the

differences between force loaded cantilevers and surface stress optimized cantilevers. In

Chapter 4 we also discuss calibration and the pertinent equations.

In Chapter 5 we discuss key aspects of measurements. We look at different noise

sources and provide a path to their minimization. The signal processing needed to pull

the signal from the noise is also discussed in depth.

In Chapter 6 we outline a new technique we refer to as a two tone test. The two tone test

provides a basis for measuring the curvature of a cantilever and has the potential to elucidate

direct intermolecular interactions. This method of measurement with further investigation

has the potential to unravel the components of surface stress.

Chapter 2

Photochemistry

We first set out to find a molecule that changes its shape due to light. We looked at nature

to see where it uses a molecule with large conformational change. Interestingly, our vision

is based on large conformational changes of retinal molecules. This molecule commonly

known as vitamin A is shown in Figure 2.1. The cis-Retinal molecule fits in a tight pocket

of a protein called opsin. Upon absorbing a visible photon cis-Retinal changes its shape

to trans-Retinal, so that it no longer fits in the pocket [45]. The shape change in the opsin

protein eventually leads into an electrical action potential impulse which we perceive as

vision [46].

The choices of available compounds are shown in Figure 2.2. Our first choice was

retinal, however due the difficulty of handling and isomerization we chose a different

molecule. Azobenzene was chosen due to its availability, wide industrial use, clean

O

O

Retinal isomerase

Visible photon

cis-Retinal trans-Retinal

Figure 2.1: Retinal molecule. The molecule changes its shape due to absorption of light.

16

CHAPTER 2. PHOTOCHEMISTRY 17

Figure 2.2: Various molecules that can change their shape with absorption of photon.

photochemistry, and reversibility. Azobenzene does not degrade and can be isomerized

frequently. Additionally, azobenzene has been widely studied and a plethora of literature

was available [47].

Azobenzene shown in Figure 2.3 is a common dye used for colors, and is the most

common dye used in the textile industry [46]. Amine substituted azobenzene degrades into

carcinoginc benzenamines easily over time, therefore their use is diminishing. Azobenzene

has the interesting property that it changes its shape due to absorbtion of light, [40].

The substituent of the benzene rings have profound influence on the wavelength of photo

absorption and isomerization. If the substituted molecules are bulky, they may not allow

the molecule to change shape. ”Photochromism” is the property of a substance to change

its color due to absorption of different wavelengths of light, and is used to describe

azobenzene. ”Photo” is from Latin for light and ”Chromo” from Greek meaning color. [48]

The molecule (E)-4-((4-dodecylphenyl)diazenyl)phenol in Figure 2.4 was purchased

from Ryan Scientific. We will call it dodecylazophenol for short. The hydroxyl (OH) of

the phenol was used in our first attempt to attach the molecule to the substrate. Dodecyl

means 12 hence a twelve carbon chain, such a long alkyl chain provides stability to the


NN

Azo Function

Benzene

NN

UV 365 nm Light

Heat, blue light 475 nm

Trans configuration Cis configuration

Figure 2.3: Azobenzene molecule is photochromatic, and changes its shape due toabsorption of light at different wavelengths.

molecule configuration. The benzene with the OH attached to it is called phenol and is a

carcinogen by itself. Our attempt was to use the Williamson ether synthesis [46, pg. 349]

for attachment of this molecule to the substrate. The substrate was first coated with 11-

bromoundecyltrimethoxy silane. We expected the OH of the phenol would displace the

bromine with a SN2 reaction mechanism and attach, however the oxygen in such a highly

conjugated system is not a good nucleophile and after many attempts we abandoned this

approach [49].

2.1 Absorbance

The major goals of synthesis were to make a molecule that allowed the attachment of the

azobenzene to the substrate, and that the attachment molecule would not hinder the activity

of azobenzene molecule. Azobenzene by itself did not attach to silicon or gold substrate, it

only physisorbed. Absorbance of derivative azobenzene molecule in liquid was the first step

in qualification of successful synthesis. Our first strategy was to attach a well characterized

optically inactive base layer to silicon and use a derivative azobenzene molecule to attach

to the base layer. The absorbance spectra of the dodecylazophenol molecule is shown in

Figure 2.5. The UV exposure was taken with a 4 Watt ultra violet lamp (UV) and the


OH

NN

OH

NN

(E)-4-((4-dodecylphenyl)diazenyl)phenolChemical Formula: C48H68N4O2

Exact Mass: 732.5Molecular Weight: 733.1

m/z: 732.5 (100.0%), 733.5 (54.3%), 734.5 (14.8%), 735.5 (2.7%)Elemental Analysis: C, 78.64; H, 9.35; N, 7.64; O, 4.36

Figure 2.4: We call this molecule dodecylazophenol for short. The long alkyl (12 carbon)chain provides stability for the switching of molecule.

primary purpose was to see the trends rather than actual quantitative measurement, such as

rate constant, etc. As expected when the molecule is exposed to UV (340 nm) it switches

its configuration from trans to cis, hence there are lower numbers of molecule in trans state

that can absorb the UV light hence lower absorbance in the UV region. When the molecule

is exposed to blue light or just left alone for few days in the dark at room temperature the

cis molecules revert back to trans and the absorbance equals the original absorbance, this

reversibility is the hallmark of photo switching. There are other molecules that upon UV

radiation change their absorbance; however they are not reversible, which usually means

disintegration, also the main reason that colors fade under sunlight.

The vertical axis of the graph is absorbance, according to Beer-Lambert Law the

absorption is A = ε ∗ l ∗ c , where ε is the extinction coefficient, l is the path length

in centimeters and is normally 1 cm for most cuvettes, and c is the concentration. By

measuring the absorbance, the concentration can be determined. It is important to note this

law is valid over several decades of concentrations, however at high concentration it tends

to break down due to aggregation of molecules. The absorbance can also be written as

log(I/I0), where I is the measured intensity from the solution and I0 is intensity measured

from the reference solvent. Absorption measure of 1 means the measured light is 10 times


lower intensity than the reference and absorption of 2 means the light is 100 times lower

intensity. Absorbance is usually positive since the intensity of the light through the solution

is lower than the solvent, the negative sign in front of the equation above makes log(x)

positive where x is less than 1.

The absorption in the UV region of the spectrum for an organic molecule is due to

excitation of an electron from π orbital to π∗ orbital. In order for a molecule to absorb UV

the π electron in the highest occupied molecular orbital (HOMO) needs to jump to π∗ which

is the lowest un-occupied molecular orbital (LUMO). For example hexane does not have

any double bonds so it will not absorb a photon in UV region, but acetone has an oxygen

double bonded to carbon so it will have a absorption in UV [50]. For a molecule to absorb

light an electron has to be excited; according to the Stark-Einstein law a molecule only

absorbs light to bring about a single transition, and the energy of the photon must match

between the ground state and some excited state [51]. The η to π∗ transition state is of

lower energy hence longer wavelength. The η - π∗ is due to nitrogen lone pair being excited

to the higher energy π∗ state. The cis-azobenzene molecule upon absorption of photon of

η - π∗ energy will change its shape to trans-azobenzene. Hence upon UV radiation the

300 320 340 360 380 400 420 440 460 480 5000

0.5

1

1.5

2

Wavelength in nm

Abs

orba

nce

1 minute UV exposure

η − π *

π−π* 3 minute UV Exposure

no UV exposure

Figure 2.5: Absorbance of dodecylazophenol. The strong absorption in the UV region isdue to molecules in trans configuration. When the molecules were placed in dark theyreverted to their original absorbance (not shown for clarity).


population of the the trans-azobenzene molecules diminishes and population of the cis-

azobenzene molecules increases [52].

To completely understand the details of electronic orbitals we need to solve the quantum

mechanical (Schrodinger) equation; however instead orbital molecular theory helps to gain

an intuitive understanding of the molecular system. The energy of light in electron volts is

given by E(ev) = 1240ev−nmλ (nm) . Hence a photon at 365 nm wavelength has an energy of 3.6

ev. The π −π∗ strong absorption of azobenze is due to its high quantum efficiency [53],

in fact the molecular absorption coefficient of Methyl red, an azobenzene, derivative is

ε = 27,660 dm3/(mol ∗ cm) [54]. The substituent on the benzene ring of azobenzene has

pronounced effect on the absorption spectra.

The wide variety of azobenzene chromophores display a wide range of properties

depending on the ring substituent. Two of the molecules that we synthesized are shown

in Figure 2.6. Azobenzenes are characterized into three types based on the ordering of

their η ,π∗ and π,π∗ energy states. They are called azobenzene, aminoazobenzene and

pseudo stilbene [55]. Absorbance of (E)-4-(phenyldiazenyl) -N- (3-(triethoxysilyl)propyl)

benzamide or AZO-APTES for short is shown in Figure 2.7a. The absorbance of (E) - 2-((

4- (dimethylamino) phenyl) diazenyl) -N- (3-(triethoxysilyl) propyl) benzamide or MR-

APTES is shown in Figure 2.7b.

Note the position of the amide bond is on the para location of the bottom benzene ring

and lack of substituent on the top benzene ring of AZO-APTES. There are no electron

donating groups for AZO-APTES. Azobenzene type molecules display a low intensity η−π∗ band in the visible region and a high intensity π−π∗ in the UV. The η−π∗ region is at

450 nm and the π−π∗ region is at 320 nm. Ortho or para substitution with an amino group

leads to the aminoazobenzene type where the η −π∗ and π −π∗ bands are very close or

overlapped in the violet or near-visible UV. Figure 2.7b shows this shift in the MR-APTES

absorbance. Note the position of the electron donating amine group at the para position

of the top benzene ring of MR-APTES in Figure 2.6. The photon absorption energy is the

difference between π and π∗. Due to an energy increase in the π orbital, and a decrease in

the π∗ orbital the π−π∗ band is shifted into the violet for MR-APTES.

The spectral shift of the π − π∗ is enhanced with the 4 and 4’ position substitution


NN

O NH

SiO

O

O

NN

O NH

SiO

O

O

N

(E)-4-(phenyldiazenyl)-N-(3-(triethoxysilyl)propyl)benzamideChemical Formula: C22H31N3O4Si

Exact Mass: 429.2

(E)-2-((4-(dimethylamino)phenyl)diazenyl)-N-(3-(triethoxysilyl)propyl)benzamide

Chemical Formula: C24H36N4O4SiExact Mass: 472.3

AZO-APTES MR-APTES

Figure 2.6: AZO-APTES and MR-APTES molecule for short.

of benzene rings with electron-donor and electron-acceptor (push/pull) substituent in the

pseudo-stilbene class of compounds. The π−π∗ band is shifted to the red, past that of the

η −π∗ to assume a reverse order. Cis to trans thermal isomerization can range from the

order of hours and days for azobenzenes to seconds and milliseconds for pseudo-stilbenes

[56]. The ability to change the absorbance spectra of azobenzene is of significant practical

importance. For example in our case due to lack of availability of 320 nm laser we could

not continue the experiments; however by using the MR-APTES the spectrum shifted to

where an available 405 nm could be employed.


a)

b)

Figure 2.7: AZO-APTES and MR-APTES absorbance. a) AZO-APTES absorbance greenand orange traces are absorbance after exposure to UV light. b)MR-APTES absorbance,orange and green traces are absorbance after 5, and 10 second exposure to 405 nm laser.Both materials were dissolved in anhydrous toluene.


2.2 Synthesis

The goals of synthesis were to make a molecule that 1) allows the attachment of the

azobenzene to the substrate, 2) allows enough space for the molecule to isomerize once

bound to substrate, and 3) allows for formation of the self assembled mono layer [37]. The

choice of substrate was very important since it dictated how the synthesis should proceed.

We had three choice of substrate: gold, silicon, and native silicon dioxide. Substrate for

us meant silicon cantilevers which we fabricated or purchased. First we started with gold

deposited on silicon cantilevers, hence a gold substrate and thiol chemistry [57]. Sulfur and

gold form excellent mono layer due to electron transfer from gold to sulfur [34]. The sulfur

gold bond is commonly used to form self-assembled monolayer (SAM) [36]. However,

photoswitchs have been influenced by the density and orientation of such azobenzene-

based SAM [35], [58]. If the free area of azobenzene photoswitch is less than 0.41 nm2

isomerization does not take place. Figure 2.8 shows different schemes used to make thiol

anchored azobenzene molecules to ensure free volume for isomerization once bound to

gold substrate [40]. We also found gold on silicon cantilevers is not a good choice due to

thermal issues detailed in Chapter 4.

The road to synthesis was rather difficult, many times we had to go back and try new

material. Also access to proper equipment and availability was a major issue. So we opted

for the most simple and reliable synthesis within our capability. All of the synthesis was

done under the fume hood. In retrospect the major lessons learned were:

• start with low cost starting material

• do not allow any material with greater than health hazard 2

• keep the reaction conditions mild and limited to room temperature.

Our second choice of pure silicon substrate was not practical in our setting. Silicon

forms a native oxide under room temperature. In order to remove this native oxide the

cantilevers must be etched with either ammonium fluoride or hydrofluoric acid [59]. These

acids can not be stored in glass, and a possible mix up in waste disposal may have disastrous


Figure 2.8: Thiol anchored azobenzene molecules with enough space for isomerization.Reprinted from Ref. [40] with permission from Paragon Publishing Group.

consequences. The oxide etching also adds an additional step of rinsing which causes a

yield loss with the fragile cantilevers.

Our first failed attempt of synthesis was to use solid state synthesis. That is to attach

a silane with a functional group to silicon and then to do the reaction with the functional

group of the attached silane. We started with 3-bromopropyltrimethoxysilane and (E)-2, 5-

dimethyl-4-(phenyldiazenyl)phenol. We hoped for Williamson ether synthesis [60]. Ethers

are prepared by SN2 reaction. The mechanism is that the negative charge on the oxygen

displaces the good leaving group such as bromine. [46, Pg.349] The proposed scheme

is shown in 2.9. Unfortunately after great effort layer by layer synthesis technique did

not result in product. In retrospect we hypothesized the key issues to be due the fact that

azobenzene is a highly conjugated molecule, and steric hinderance inhibits the SN2 reaction

when one of the reactant is bound to solid. Azobenzene has two aromatic rings. The charge


SiHO O O

Br

SiO

OH

Br

NN

HO

KIK2CO380C

Acetone

SiHO O O

Br

SiO

O

OH

B NN

6hrs

+ HBr

Figure 2.9: Layer by Layer synthesis. Unfortunately this scheme was not successful due topoor yield.

on the attacking oxygen is highly delocalized, and can not be compared to primary alcohol

in which Williamson ether synthesis is successful. Also steric hinderance can play a big

role in reaction kinetics. Hence the reaction did not go to completion, and we observed

many brominated groups left on the surface.

The second practical major issue was the fragile cantilevers did not survive boiling

acetone. It should however be noted that the 3-bromopropyltrimethoxysilane did provide a

good and repeatable monolayer. In order to eliminate boiling acetone we tried acetonitrile

as solvent and used cesium carbonate Cs2CO3 as our base at 40 C however the result were

not improved. Before abandoning the layer by layer synthesis we also tried a completely

different chemistry. We used 3-aminopropyltriethoxysilane (APTES) and a carbaxylic acid

terminated azobenzene and used a peptide linkage chemistry. Unfortunately APTES did not

provide a monolayer, as explained in section 3.2, however the peptide chemistry worked.

We abandoned the layer by layer synthesis and tried the Williamson ether synthesis

in solution. Figure 2.10 shows all the compounds, their structure, and atomic weight

that were used in the reaction. Potassium iodide was used as a catalyst. The reactant


concentrations were at 0.25M, and the catalyst potassium iodide at 0.01M. Figure 2.11

shows the the total positive electrospray current coming off of the liquid chromatograph

column. The chromatograph separates the compounds in time. The mass spec then provides

the mass of each time separated compound. The detail of liquid chromatography and mass

spectrometry (LC/MS) are given in appendix C.

Figure 2.12 shows the mass of separated component of column in each time portion.

Since the mass of the particles must be charged (ions) the atomic weight of each ion for

positive electrospray has a additional mass of (1) for hydrogen or additional mass +23 for

sodium (Na). The horizontal axis is the atomic mass and the vertical axis the ion current.

Note the appearance of partially hydrolyzed product in the middle graph. The mass of the

hydrolyzed and ionized product found in the middle graph is 375.2 amu.

In mass spectrometry brominated compounds have a distinct signature which is rather

easy to identify. Bromine has a molecular weight of 79 atomic mass unit (amu) and

its isotope a mass of 81 amu with the same abundance, hence a ratio of 1:1 is always

found. A brominated compound will show as two peaks of identical amplitude that are

2 atomic mass unit apart. As an example top graph of Figure 2.12 shows this signature.

The zoomed view of the this graph is shown in Figure 2.13 which we hypothesize to

be partially polymerized 3-bromopropyltrimethoxysilane. We had similar result with

dodecylazophenol shown in Figure 2.4. Unfortunately the starting material for the synthesis

were extremely expensive. The (E)-2, 5-dimethyl-4-(phenyldiazenyl)phenol was about

8000 USD/g from sigma aldrich, and dodecyl azo phenol was 160 USD/10 mg or 16,000

USD/g from Ryan scientific, Mt Pleasent, SC. Since we needed to purify the product,

optimize the reaction, and had issues with polymerization of product, we decided not to

pursue this reaction after the sixth try.


K+ I-

potassium iodideChemical Formula: IK


m/z: 165.9 (100.0%), 167.9 (7.2%)Elemental Analysis: I, 76.45; K, 23.55

NN

HO

(E)-2,5-dimethyl-4-(phenyldiazenyl)phenolChemical Formula: C14H14N2O

Exact Mass: 226.1

Si

NN

O

Si

O

OBr

(3-bromopropyl)trimethoxysilaneChemical Formula: C6H15BrO3Si


Cs+Cs+-O

O

O-

cesium carbonateChemical Formula: CCs2O3

Exact Mass: 325.8

N

Chemical Formula: C2H3NExact Mass: 41.0

O

O

(E)-1-(2,5-dimethyl-4-(3-(trimethoxysilyl)propoxy)phenyl)-2-phenyldiazeneChemical Formula: C20H28N2O4Si


m/z: 388.2 (100.0%), 389.2 (27.9%), 390.2 (7.8%), 391.2 (1.3%)

O

Si

NN

OO

O

(E)-(3-(2,5-dimethyl-4-(phenyldiazenyl)phenoxy)propyl)dimethoxysilanolChemical Formula: C19H26N2O4Si


m/z: 374.2 (100.0%), 375.2 (26.8%), 376.2 (7.5%), 377.2 (1.2%)

Cs2Co3KIACN24hr 40C

+

Acetonitrile

OH

O

Figure 2.10: Williamson ether synthesis. All components of the reaction with theiratomic weight, which were monitored in mass spectrometry. The product and a partiallyhydrolyzed product are also shown.


Figure 2.11: Total positive electrospray ion current (TIC) from the crude product of theWilliamson ether synthesis. The horizontal axis is time in minutes, and the vertical axistotal positive ion current. The crude product solution is separated in time in the liquidcolumn chromatograph.


Figure 2.12: The ion mass found at different column time: Top, ion mass at 19.8 minutes,middle ion mass at 17.8 minute which contains partially hydrolyzed product, and bottomion mass at 15.2 minute.


Figure 2.13: The expanded view of top graph of Figure 2.12 showing the bromine signatureof 2 amu apart.


2.3 Peptide linkage chemistry

In order to achieve a chemistry that was practical we looked at the most commercially

available and cost sensitive chemistry, peptide linkage chemistry. The reactants work at

room temperature, are commercially available and convert the reaction to completion with

high yield.

Peptide linkage is chemistry of attachment of the a carboxylic acid of one amino acid to

the amine group of the other, the amide linkage joining the amino acids is called the peptide

bond. Carboxylic acid is a stable molecule due its resonance structure and will not react

with and amine directly. There are several method for activation of the carboxylic acid,

however, each method presents challenges in purification, hydrolysis, and stability. [61]

The goal is to attach the azobenzene molecule to the surface of silicon. The attachment

to silicon is done through silane chemistry and is covered in the Chapter 3. Here the

attachment of azobenzene to silane is described.

Our first several attempts was the reaction of 4-(phenyl diazneyl) benzoic acid and 3-

aminopropyltrimethoxysilane as shown in Figure 2.14. The reaction steps are also provided

in the same figure. The 4-(phenyl diazneyl) benzoic acid was purchased from sigma aldrich

at cost of 25 USD/g and used as received. The 3-aminopropyltrimethoxysilane was also

purchased from sigma aldrich at cost of 85 USD/100 ml. Even thought the synthesis was

successful and product was obtained, the product was not stable, it would precipitate out of

the eluted solvent in matter of minutes to hours depending on the day.

To solve the mystery of the product disappearance we re-traced every step since

at the time we did not know if the issue was due to the synthesis condition, re-

actants, or some other unknown variable such as air moisture. We used Nuclear

magnetic resonance to investigate the reaction and the reactants, and as in any puz-

zle once solved it became obvious. Scott et al. [62] investigated the influence of

bath chemistry on 3-mercaptoporpytrimethoxysilane. Figure 2.15a shows a simulated

NMR of 3-aminopropylmethoxysilane and Figure 2.15b the analogous system of 3-

mercaptoporpytrimethoxysilane from Scott et al. Peak a, b, c can be used as internal

reference and are not affected by hydrolysis. Note that peak d does not appear in the

simulated NMR since hydrolysis was not simulated. Peak d was due to hydrolysis. From


the ratio of peak area d to e, the amount of hydrolysis was determined. Unfortunately the

3-aminopropyltrimethoxysilane was very sensitive to moisture, and the pH of the reaction.

Typical NMR of the 3-aminopropyltrimethoxysilane is shown in figure 2.16, the strong

methanol peak d (3.4ppm) is indicative of hydrolysis. After many tries and different batches

of the 3-aminopropyltrimethoxysilane we decided to use a different silane, one with more

stability, and purity. Hence we choose 3-aminopropyltriethoxysilane.


NH2Si

OO

O

3-(trimethoxysilyl)propan-1-amineExact Mass: 179.1

O

OH

NN

(E)-4-(phenyldiazenyl)benzoic acidExact Mass: 226.1

NSi

O

NN

H

(E)-4-(phenyldiazenyl)-N-(3-(trimethoxysilyl)propyl)benzamideExact Mass: 387.2

N

NO+

NN

N

N P-

F

FF

F

FF

2-(3H-[1,2,3]triazolo[4,5-b]pyridin-3-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate(V)

Exact Mass: 380.1

N

acetonitrileExact Mass: 41.0

1. Dissolve 226mg of azenyl Benzoic Acid in 3ml of Acetonitrile and 90ul of triethyl amine (1.2eq)(density .722) 2. add 456mg of HATU to solution (1.2eq).

4. ADD 215ul (1.2eq) of 3-aminoTrimethoxy silane

5.Stirr for 1 hour.

6. Evaporate the ACN

7.Purify using silica gel 50% Hexane to ethylacetate

O

O

NN

1,1,3,3-tetramethylureaExact Mass: 116.1

OO

OH

Exact Mass: 32.0

NN

N

N

HAOtExact Mass: 136.0

N

Exact Mass: 101.1

PRODUCT

OH

TriethylAmineDensity .72

P-

F

FF

F

FF

hexafluorophosphate(V)Exact Mass: 145.0

HATU

+

HATUACN

Figure 2.14: 4-(phenyldiazneyl)benzoic acid reaction with 3-aminopropyltrimethoxysilane.


a

5.11

3.55

3.55

3.55 0.58

1.6

2.65

NH2Si

OO

O

Estimation quality is indicated by color: good, medium, rough

e

ca

b

abc

e

b

Figure 2.15: a)Simulated 1H NMR of 3-aminopropyltrimethoxysilane b)1H NMR of 3-mercaptopropyltrimethoxysilane analogous system showing the effect of hydrolysis (peakd). Reprinted from [62] with permission from Elsevier.


Figure 2.16: Hydrolysis indication of 3-aminopropyltrimethoxysilane. 1H NMR of 3-aminopropyltrimethoxysilane in deuterated methanol showing hydrolysis.

Chapter 3

Self Assembled Monolayer - SAM

Self-assembled monolayers are molecular assemblies that are formed spontaneously by

exposure of an appropriate substrate to a solution of an active surfactant in an organic

solvent. Figure 3.1 shows the forces for self assembly. The chemisorption to the surface

brings molecules close together, which allows the short range forces (i.e. Van der Waals

forces) to become important. [37] One of the major challenges for our monolayer was

devising the right spacing needed for the azobenzene molecule to switch.

On page 24 the overall approach to synthesis was discussed, and silane chemistry was

chosen. Silicon is under carbon in the periodic table and has similar properties, with one

Figure 3.1: A schematic view of forces in a Self Assembled Monolayer. [63, Pg.238] Withpermission from Academic press.

37

CHAPTER 3. SELF ASSEMBLED MONOLAYER - SAM 38

a)

b)

Figure 3.2: Silane based SAM polymerized due to water on silicon surface. a, b) Visiblewhite layers are polymer islands due to self polymerization.

key distinction that silicon can not form a double bond with oxygen. The lack of double

bond is mainly due to the non overlapping of the orbital. Organic chemistry is mainly based

on the chemistry of carbon. Silicon differs from carbon in the area of inorganic reactivity. A

key point is when inorganic reactive groups such as chlorine, amine, ethoxy, methoxy, are

directly attached to silane they will hydrolyze in presence of water. Then they self condense

to form a stable siloxane structure. However, the goal is to obtain a monolayer by bonding

to the hydroxyl group of the surface. Mono layers can not be seen with a microscope or

naked eye, a layer thickness of typically 20A usually does not cause interference pattern

in visible range. Figure 3.2 shows the typical result of many experiments untill the recipe


a)

b)

Figure 3.3: Silane based SAM polymerized due to water on cantilever. a, b) Cantileversshowed the same polymerization as silicon pieces.

was developed. Figure 3.3 shows the same type of polymerization on cantilevers. When a

silane contains at least one carbon silicon bond it is called an organosilane. The chemical

reactivity of direct silicon-carbon bond is not high if a methyl or higher alkyl is used. The

bond disassociation energy of silicon with methyl group is about 90kcal/mol [64].

Our first approach to making the azobenzene SAM was a two step approach. The idea

follows the Merrifield solid phase synthesis [65]. The simple concept is to bind the silane

molecule with a functional group to silicon substrate first and then run the subsequent

reactions, since the molecule is bound to the substrate the subsequent reactions can be

done several time to achieve high yields. Also attaching the silane to silicon substrate as


NN

OH

(E)-2,5-dimethyl-4-(phenyldiazenyl)phenolChemical Formula: C14H14N2O

Exact Mass: 226.1

Figure 3.4: 2, 5-dimethyl-4-(phenyldiazenyl)phenol

Si

O

OO

Br

(11-bromoundecyl)trimethoxysilaneChemical Formula: C14H31BrO3Si


m/z: 356.1 (100.0%), 354.1 (96.9%), 357.1 (20.2%), 355.1 (20.1%), 358.1 (5.6%)Elemental Analysis: C, 47.32; H, 8.79; Br, 22.48; O, 13.51; Si, 7.90

Figure 3.5: 11-bromoundecyltrimethoxysilane

the first step was very attractive since the synthesis of the azobenzene would not cause self

polymerization. Unfortunately in practice the yield loss of fragile cantilevers was severe,

as can be seen from the broken cantilevers of Fig. 3.3b.

3.1 11-bromoundcyltrimethoxysilane

The first film that we deposited was 11-bromoundecyltrimethoxysilane. Our intent was to

do solid state Williamson ether synthesis with azobenzene derivative shown in fig 3.4.

To elaborate on the name, 11 stands for the location of the bromine on the carbon chain

(carbon 11). The bromo stands for bromine. Undecyl latin for eleven, and methoxy the

name for one carbon connected to oxygen. Here we have three methoxy group connected


to the silicon hence trimethoxysilane. Figure 3.5 shows the molecule.

We found the 11-bromoundecyltrimethoxysilane molecule to be stable in air and it

did not readily polymerize in toluene solution. The physical rendition of this molecule

is shown in Figure 3.6a. In a film that is dense and packed it is suggested by Ulman

that the molecule will be in this full stretched configuration. The height of the 11-

bromo undecyltrimethoxysilane molecule measured from this model is 15.6 A . The

height is measured from bromine atom to the silicon atom. The next molecule shown

in 3.6b is the octyltrimethoxysilane and the distance of silicon to last carbon is 10.2 A.

Octyltrimethoxysilane does not have any functional group after attachment to a silicon

substrate. The octyltrimethoxysilane molecule served two critical purposes, it was used as

a reference and in a mixed SAM was hypothesized to control molecular spacing.

SAM have better packing density due to Van der Waals forces as the number of carbon

atoms in the alkyl chain increases [66]. We used 3-propyltrimethoxysilane later to decrease

the density of the SAM and allow photo isomerization of the azobenzene derivative. The

AFM and contact angle image of the 11-bromoundecyltrimethoxysilane SAM is shown in

Figure 3.7.

The repeatability of the contact angle over several samples is an important indication

of the surface cleanliness. We measured a contact angle of 80 ±3 consistently over

all samples. A clean surface is essential for repeatable data. The large surface peaks of

Figure 3.7a are mostly due to cleaving process of silicon, in later samples we consistently

measured less than 0.3 nm roughness which theoretically does not give rise to hysteresis.

The measured contact angles were similar to the literature value of 83. [21]


a) b)

Figure 3.6: Three dimensional model of a) 11-bromoundecyltrimethoxysilane and b)Octyltrimethoxysilane.


a)

b)

Figure 3.7: a) AFM image and b) Contact angle of the 11-bromoundecyltrimethoxysilaneSAM. The molecule forms a smooth surface. The SAM resulting from this molecule onsilicon substrate were repeatable and consistent.


3.2 SAM process recipe

The successful and repeatable recipe that was developed for the SAM process is as follows.

The following recipe was used with minor modification for all of our silanes.

1. Cleave silicon samples of 1x1 cm, rinse with DI water, sonicate 1 minute in ethanol

and 1 minute in methanol. Rinse with DI water.

2. Place cleaved pieces of silicon in mixture of freshly made 4:1 H2SO4 12N to 30%

H2O2 (piranha) for five minutes.

3. Rinse with deionized water three times.

4. Sonicate for 30 seconds in DI water and then rinse with DI water.

5. Dry under N2 gas in hood for 10 minutes.

6. Dissolve the silane as given in Table 3.1.

7. Place pieces in 10 ml bottle for specified soak time as in Table 3.1 at room. (closed

container practically full, otherwise need inert gas)

8. Rinse with ethnol and then methanol.

9. Sonicate 30 second in toluene, and rinse with toluene.

We also tried the manufacturer recipe which required ethnol as a solvent. However

11-bromoundecyltrimethoxysilane formed a multi-layer film and polymerized. It is rather

important to minimize the exposure of the piranha cleaned silicon to air, and the following

rinsing and drying steps needed to be done quickly. The contact angle of a freshly prepared

silicon sample was zero and a day old sample was about 24. Table 3.1 shows the molecules

and the conditions where we were able to obtain repeatable monolayer with the above

process. Achieving high quality and repeatable mono layer with 3-aminopropyltrimethoxy

and 3-aminopropyltriethoxysilane in our environment and the above recipe did not work.

The aforementioned silanes usually formed multilayer films and polymerized with a haze

on a surface of the silicon. We hypothesize the formation of haze due to lack of argon


atmosphere, lack of high grade pure solvents, and clean and dry glassware [67]. Kim et al.

reports the same issue with APTES, in fact they report a surface roughness of the 3.0 nm -

4.0 nm for a 5 µm2 area. [68].

The silanization begins with the hydrolysis of ethoxy groups in APTES, a process

catalyzed by water, leading to the formation of silanols as in Figure 3.9. APTES silanols

then condense with each other or the surface silanols forming a monolayer of APTES with

the amine group away from the surface. A typical AFM of the silicon surface functionalized

with APTES is shown in Figure 3.8. Ulman hypothesis that the silanols form a trimer

before condensing on the surface. [63, Pg.257]. However based on our experience and

reported literature [68–71] the reality is far more complex. A better model and closer to our

observation summarized by Kristensen et al. is given in Figure 3.10. The amine group of

the APTES causes most of the issues. Since amine can become positively charged it sticks

to the surface hence disrupting the monolayer. We also found the repeatability of surfaces

prepared with 3-aminopropyltrimethoxysilane to be worse than APTES. We hypothesized

the higher reactivity due to lower steric hinderance of methoxy group, which allows for

faster hydrolysis by water.

The overall process is shown pictorially in Figure 3.11. The first step in the preparation

of silane mono layer on silicon is to hydroxylate the surface. Hydroxylation is achieved by

two main method, dry or wet. The dry method uses O2 plasma to break the silicon oxide

Silane molecule Soak time Concentration Quality of film11-bromoundecyltrimethoxy 24 h 1% by volume excellent and repeatable.3-bromopropyltrimethoxy 24 h 1% by volume excellent and repeatable.Octyltrimethoxy 24 h 1 % by volume excellent and repeatable.Azo-APTES 4 h 20 mM excellent and repeatable.MR-APTES 4 h 20 mM excellent and repeatable.3-aminopropyltriethoxy 2 h 10 mM Not repeatable.3-aminopropylmethoxy 1 h 1 mM Not repeatable.

Table 3.1: SAM process optimized condition for various silane


Figure 3.8: AFM image of silicon surface functionalized with APTES. APTES SAM werenon repeatable, and inconsistent in surface roughness and contact angle. APTES wassensitive to air and moisture.

bond and adds a hydroxyl bond to the surface (hydroxylation).

The wet method is to use piranha. We abandoned the O2 plasma, due to lack of a proven

recipe and clean equipment availability. The initial experiment with plasma hydroxylation

actually showed an oxide growth of 6 nm, and poor repeatability. We also observed oxide

growth of approximately 1 nm to 2 nm if the samples remained in the piranha solution for

more than 10 minutes, and exhibited poor repeatability. The optimized and most repeatable

contact angle was for 5 minutes of exposure to freshly made piranha. It should be noted the

rinsing and cleaning process after piranha is also very important. The residual water and


SiO

O

O

NH2

OH H

SiO O

H

O

NH2

SiO O

O

NH2

H2O

-EtOHSi

OO

NH2

- EtOHSi

O

O

O

NH2

Figure 3.9: APTES hydrolysis and condensation.

sulfuric acid catalyzes the reaction of silane with surface.

Figure 3.12 shows the Xray Photoelectron Spectrum (XPS) of a piranha cleaned

reference sample, the carbon on the surface is due to the long storage time of the sample in

air. However other elements besides silicon and oxygen are not present, we were especially

looking for sulfur residue due to sulfuric acid.

Sonication also plays an important role to remove the physically adsorbed monomers

and leave those covalently attached to the surface. Figure 3.13 shows the difference in

contact angle due to physically adsorbed monomers for Octyltrimethoxysilane. The sample

was sonicated for 60 second in toluene. A 36 change in contact angle was observed, we

hypothesized the contact angle change was due to physically adsorbed monomers. [72] The

contact angle change after sonication was not as dramatic when sufficient time was allowed

for complete formation of surface monolayer. Due to inconsistencies of determination

of optimum soak time to form a complete monolayer we discovered the significance of

sonication.


Figure 3.10: Summary of different adsorption mechanisms of APTES on SiO2 surface fromKristensen et al. a) Expected formation, free amine and covalently bonded to the surface.b) Protonated amine group and inversely bonded to the surface. c) Strong interaction dueto hydrogen bond of the amine and the surface silanol. d) Intermolecular hydrogen bondof the amine and silanol. e) Interaction of the amine and silicon. Reprinted from [70] withpermission from Elsevier.

NN

ON

Si

OO

HN

O

H2SO4/H2O2

Silicon <100>

Native Oxide

OH OHOH OH OH

Si

O

O

R

Si

O

O

R

Si

O

O

R

Si

O

O

R

Si

O

O

R

Si

O

OH

R

Native Oxide

OHOH OHOHOH

Si

O

O

R

Si

O

O

R

Si

O

O

R

Si

O

O

R

Si

O

O

R

Si

O

OH

R

Figure 3.11: SAM process overview


Figure 3.12: XPS of piranha clean silicon. Top, survey technique. Bottom, Si− Si, andSi−O2 region showing chemical shift of the binding energy due to Si−O2 bond.


a)

b)

Figure 3.13: Contact angle of a) Octyltrimethoxysilane before sonication and b) after 30secsonication. Soak time was 1h see Table 3.1.

Chapter 4

Transduction

4.1 Piezoresistive cantilevers

Microelectromechanical systems based on piezoresistive sensing (resistance change with

stress) are especially interesting for displacement sensing and excel at dynamic measure-

ments. They are portable, low power, and disposable. Chemical and biosensing applica-

tions based on displacement transduction require static and low frequency measurement

stability over time periods of tens of seconds to many hours. Hence, the 1/f noise of the

piezoresistors becomes one of the limiting factors for their use as chemical sensors. The

work presented in this section is some of the basis for [73].

Typically, 1/f noise levels for piezoresistive, silicon microcantilevers are reported as

100-500 nV/ Hz at 1 Hz with corner frequencies ranging from 45 Hz to 10 kHz [74–77].

Many existing designs are intended for operation at frequencies where 1/f noise does not

limit resolution. We tailored fabrication process parameters to achieve the lowest 1/f noise

amplitude spectral density of which we are aware for piezoresistive cantilevers. These

results are part of an effort to study the noise and sensitivity of piezoresistive cantilevers

as a function of various processing parameters, including type of anneal (steam vs. inert),

anneal temperature and time, type of passivation oxide, chemical vapor-deposited, low

temperature oxide or thermally grown oxide, and implant dose and energy [78]. We found

that highly boron doped piezoresistors in the range of 1020 cm−3 exhibited the lowest 1/f

noise and the best signal to noise ratio.

51

CHAPTER 4. TRANSDUCTION 52

The cantilevers were fabricated from silicon-on-insulator, single-crystal silicon wafers,

and released by deep reactive ion etching. Piezoresistors were ion implanted with 50 keV

boron. Additional fabrication details are reported elsewhere [76, 79]. The piezoresistors

were placed close to the integral edge restraint, but 130 µm from the fixed end to avoid

the otherwise subtractive, transverse, tensile stress region near the fixed boundary. We used

four piezoresistors in a full-bridge for thermal stability. The full active bridge provides four

times the sensitivity and twice the noise of the typical single piezoresistor, increasing the

signal-to-noise ratio by 6 dB.

Figure 4.1A shows the placement of the resistors. The stress simulation and the

measured resonance frequency are shown in Figures 4.1B, and 4.1C, respectively. The

electrical schematic of the resistors appears in Figure 4.2. Notice that for a given stress,

the resistance of a resistor (p-type) that is parallel to the stress (longitudinal) increases

and the resistance of a resistor that is perpendicular (transverse) to the stress decreases.

This important layout scheme allows for first order common mode rejection of unwanted

effect such as temperature, package stress, and surface induced noise [80]. This layout

takes advantage of the fact that longitudinal piezoresistive coefficient of a p-type resistor

in < 110 > direction made in n-type < 100 > substrate is positive σl ∼ +π44/2, and the

transverse piezoresistive coefficient is negative σl ∼−π44/2. E110 =168 GPa, and π44 for

p-type piezoresistor in < 110 > is 138 x 10−11Pa−1 [81, 82].


Figure 4.1: Placement of piezoresistor on the cantilever. A) Piezoresistor on the cantilever.B) Simulation of stress at the base of cantilever. C) Measured resonance frequency.Reprinted with permission from [73]. Copyright 2008, AIP Publishing LLC

Figure 4.2: Electrical schematic of the piezoresistor cantilever.


Full 1/4-active Tortonese Pruitt Chui Harley Yu YuDose (cm−2), boron 5×1016 1×1014 5×1014 1×1015 5×1014 na 5×1014 5 × 1015

Peak concentration (cm−3) 2.7×1019 6.2×1017 9×1018 6×1018 5×1014 4×1018 na naAnneal temp (C) 1100 1000 1000 1000 1000 700 1050 950Anneal time (min) 50 52 10 40 10 180 30 10Spring constant (N/m) 1.5 17 5-100 1-85 1.6 0.01 na naSensitivity (V/N) 610 179 ˜2000 15 na 2×106 na naωn (kHz) 1.6 3.7 40-800 1-6 280 50 12 naResistance (kΩ) 1.8 16.8 2.5-7 5.8 5-30 ˜16 na 3Johnson noise (nV/

√Hz) 5 16 9 10 9-22 16 14 6

Corner freq. (Hz) 0.6 20 45-750 200 200 1500 800 10, 0001/f noise at:10 Hz nV/

√Hz 5* 22 18 35 130 160 150-700 170

10 Hz (nV/V)/√

Hz 0.4* 6 5 5 26 32 25-117 281 Hz (nV/V)/

√Hz 1.2* 20 15 11 na na na na

0.1 Hz (nV/V)/√

Hz 3.7 na na na na na na na

Table 4.1: Selected process variables and performance characteristics for variouscantilevers including a full and a quarter active bridge with different doping and annealconditions, as well as several devices from the literature. In comparing 1/f noise, wenormalized the data by dividing by Vbias to achieve units of nV/(V ×

√Hz) or Hz−0.5.

nV/V is unitless, as is nΩ/Ω, which is appropriate since 1/f noise is a measure ofconductivity variation. Due to the low 1/f noise in this work, the total noise at the indicatedfrequencies is dominated by thermal noise and is denoted by *.

Table 4.1 compares noise of the full-bridge and single-resistor cantilevers, and

cantilevers from Tortonese [83], Pruitt [76], Chui [74], Harley [75] , Yu [77] , Yu [84],

and tabulates selected process and performance parameters where available. Highly doped

p-type resistors in the range of 1020 cm−3 concentration exhibit the lowest 1/f noise and

the best signal to noise ratio.

While aspects of 1/f noise remain controversial despite eight decades of research, [85]

the cause of 1/f noise is generally accepted to be conductivity fluctuations. Current flow

is needed only to convert resistance change to voltage change. For zero bias, only thermal

noise is present. To model 1/f noise, we use Hooge’s equation [86]:

SV =αV 2

biasN∆ f (4.1)

where N is the number of carriers, Vbias is the bias voltage, and α is an empirical


Figure 4.3: Hooge coefficient (α) vs. diffusion length for this work and from the literature.Here we add our data for higher

√Dt, heavily doped piezoresistors to Harley’s plot [75] and

extend the trend line to show a lower minimum α value of 10−7 for single crystal silicon.

coefficient. N depends on piezoresistor volume and implant dose. α depends on crystal

lattice perfection [87]. Longer time and higher temperature anneals lowers α [88].√

Dt

(diffusion length), where D is the dopant diffusion coefficient and t is the anneal time, is a

measure of anneal effectiveness.

In Figure 4.3 we extend Harley’s [75] plot of α vs.√

DT with data from the current

study. The p-type silicon piezoresistor α value is significantly lower than metals α value

[89]. Gold, bismuth, copper, and aluminum, which have α values of approximately 10−3,

achieve low noise by high N. Here we report only selected devices with a 1/f exponent of

approximately 1, which as Fleetwood, [90] hypothesized, represents a minimum achievable


Geometry Dose (cm−2) Anneal Time T (C) N R (Ω) α NoiseA 1/4 active bridge test die 1 × 1014 162 min steam 1000 1.4 × 109 28, 200 4.1 × 10−7 75B 1/4 active bridge test die 5 × 1015 20 min steam, 5 min N2 1000 1.8 × 1011 1100 3.3 × 10−7 6C 1/4 active bridge cantilever 5 × 1016 45 min steam,5 min N2 1100 7. 0 × 1011 470 1.4 × 10−7 1.2D Full-active bridge cantilever 5 × 1016 45 min steam,5 min N2 1100 1.8 × 1011 1800 1.4 × 10−7 3.7

Table 4.2: Process parameters, α , and noise for four different devices. Noise was measuredat 0.1 Hz with units of (nV/V)/

√Hz.

1/f noise level.

We also observed devices with similar process conditions but higher 1/f noise, often

were characterized by a higher 1/f exponent with presumably different underlying noise

generating mechanisms such as current constriction, as suggested by [91]. The longer

diffusion length and higher dose correspond to a deeper junction, which lowers device

sensitivity, but which Harley [75] advises is negligible for junctions less than 1/3 of

the cantilever thickness. A full-active bridge with its four-fold sensitivity increase more

than compensates for the deeper junction and lower piezoresistance coefficients at higher

doping.

An HP3562A spectrum analyzer and a modulated, low noise amplifier were used to

measure resistor thermal and 1/f noise over the range of 0.01-100 Hz. Due to low device

noise levels, we used a custom electronic circuit to measure the low frequency noise

of the piezoresistors. A TI INA103 amplifier with low noise (1 nV/√

Hz at 500 Hz)

at intermediate frequencies was used in a modulation/demodulation circuit, exciting the

bridge with a 5 Vrms sinusoidal wave. Since the output of the piezoresistive bridge is

proportional to applied voltage multiplied by the conductivity variation, (source of 1/f

noise) the bridge can be considered to be a natural modulator. The modulated output is

amplified (gain of 1000), and then bandpass filtered (center frequency 500 Hz, bandwidth of

approximately 200 Hz) to reduce the effect of noise folding. The signal is then demodulated

with an AD630 multiplier and low-pass, three-pole filtered (100 Hz). As shown in Figure

4.4, this system achieves noise floor of less than 3nv/√

Hz from 0. 01 Hz to 10 Hz.

Table 4.2 compares four devices with three different implant doses and anneals. Device

C, a 1/4 active cantilever with a high dose (5×1016/cm2) implant, and a larger piezoresistor

volume than the full bridge, has the lowest 1/f noise. Cantilevers C & D have a high√

Dt


Figure 4.4: System noise floor and amplitude noise spectra for four piezoresistors. Thehigher doped devices with longer and higher temperature anneals display less noise. Thesystem noise floor down to 0.01 Hz was verified to be lower than 3 nV/

√Hz by measuring

the Johnson-dominated noise of a 680 ohm metal wire wound resistor bridge with 18 mVrmsexcitation.

anneal and consequently a low α . For the full-active bridge at a full-scale output of 200

mV at 5 Vbias, in the band 0.01-10 Hz, the dynamic range was >140 dB.

We determined cantilever sensitivity using a previously reported Laser Doppler Vi-

brometer technique [76,79] our result was confirmed by thermomechanical excitation (Fig.

4.1C). The force sensitivity of the full-active bridge was 10 pN/√

Hz at 1 Hz with amplitude

resolution of 6 pm/√

Hz. The force resolution was 100 pN for the frequency band of 0.1-

100 Hz. These low noise results are promising for the design of piezoresistive devices for

low frequency measurements, a key prerequisite for the chemical sensing applications.


4.2 Design

The optimization of the design of tip loaded piezoresistive cantilevers is different from

design of piezoresistive cantilevers optimized for surface stress. [92]. Here we derive the

tip deflection for a distributed surface stress loaded cantilever and highlight the fundamental

differences between tip loaded and distributed loaded cantilevers. The optimization of tip

loaded cantilever was reported by Park, Rastegar et al. [93].

d2ydx2∼=

1R=

ME∗I

y(0) = 0dydx

(0) = 0 (4.2)

E∗ =E

1−ν(4.3)

M = σwt/2 I = wt3/12 (4.4)

y =Mx2

2E∗I(4.5)

κ =1R=

6σ

E∗t2 (4.6)

R∼ l2

2∆y(4.7)

∆y = 3σ

E∗(lt)2 (4.8)

Equation 4.8 is the tip deflection of a cantilever based on surface stress. Note the

unit of surface stress is N/m, and that of surface energy J/m2 [94]. The key assumptions

here are thin film and small curvature. The thin film assumes that the position of neutral

axis remains the same. In a beam, the neutral axis does not change its length when the

beam is bent (dashed lines in Fig. 4.5A, B). The approximation of Equation 4.7 assumes

small curvature. In Figure 4.5, the cantilever is under uniformly loaded surface stress

σ . This surface stress effect is modeled as a concentrated moment M applied at the

cantilever beam’s free end. I is the moment of inertia given by Equation 4.4 for a beam

with rectangular cross section. l, w, and t are the length, width, and thickness of the beam,

respectively. E is the Young’s modulus and E∗ is the biaxial modulus. When the beam

is horizontally stretched its thickness reduces, which is given by Poisson’s ratio ν . The


X

Y

σ

A

B C

l

w

Figure 4.5: A) Cantilever model and coordinate system. B) Compressive surface stress. C)Tensile surface stress. A mnemonic tip to remember the convention is to look at the bottomsurface of the film, and remembering tensile stress has a positive sign.

governing differential equation for an elastic beam is given by Equation 4.2, where R is the

radius of curvature.

Note that Equation 4.4 gives the moment in terms of surface stress, width, and thick-

ness; however, the radius of curvature is only proportional to surface stress and the square

of the thickness (Equation 4.6). Equations 4.4 and 4.6 reveal the fundamental difference

between distributed loaded cantilevers and tip loaded cantilevers. In a piezoresistive tip

loaded cantilever, the moment at the base is simply the force at the tip multiplied by the

length of cantilever. The piezoresistors are placed at the base of the cantilever near the

top surface, since maximum stress occurs at the surfaces near the base. However, for

a distributed loaded cantilever that is not the case. Table 4.3 summarizes the important

differences between surface stress cantilevers and tip loaded cantilevers. For surface stress


Surface stress Tip loadedTip deflection ∆y = 3σ f

E∗ ∗ (l/t)2 ∆y = 4FE∗w ∗ (l/t)3

Change in resistance ∆ρ

ρ= πlσl +πtσt

∆ρ

ρ= πlσl +πtσt

Output voltage Vout ≈ 3σ fts∗ π44

2 ∗Vin Vout ≈ 6Flwt2

s∗ π44

2 ∗Vin

Table 4.3: Distributed load cantilever versus tip loaded cantilever. Full bridge configurationof the piezoresistor is assumed. Vin is the bridge voltage.

based cantilevers it is important to note that reducing the thickness and increasing the length

of the cantilever will maximize tip deflection. However, for piezoresistive surface stress

cantilevers only reducing the thickness maximizes the output voltage [95].

4.3 Electrical noise

Noise is any unwanted signal. Electrical noise is the random variation of potential between

the ends of a conductor. The electrical noise in a piezoresistor sets the fundamental lower

limit of piezoresistive transducer resolution. In this section, we focus our discussion on the

dominant random electrical noise sources in piezoresistors: Johnson or thermal noise and

1/f or flicker noise. Note that current noise or shot noise due to the direct current through a

resistor at low current values (approximately 1 mA) is not significant. Other noise sources

such as inductive or capacitive line pickup also exist, but they are not random in nature and

are not discussed [96]. For many applications, the accuracy of piezoresistive transducers

is limited by temperature effects or thermo-mechanical hysteresis, e.g., in commercial

piezoresistive devices such as piezoresistive pressure sensors. Integrated shield layers have

been shown to reduce noise effects, including temperature sensitivity [97].

4.3.1 Thermal noise

Thermal noise, also known as Johnson or Johnson-Nyquist noise, is universal to all

resistors. It was first observed by Johnson and theoretically explained by Nyquist [98] in

1928. Johnson attributed ”the statistical fluctuation of electric charge in the conductor”

as the source of noise and measured the effect of these fluctuations via vacuum-tube


resistance.

VJ =√

4kbT R (4.9)

Thermal noise is related to the absolute temperature T (K) of the resistor, resistance

value R(Ω), and Boltzmann’s constant kb(J/K). The root mean squared value of voltage

across a resistor in 1 Hz bandwidth is shown by Equation 4.9. Thermal noise in any resistor

is fundamental, cannot be eliminated, and is independent of the material that the resistor is

made of. Since Equation 4.9 only depends on temperature and resistance, it can be used as

an absolute calibration method for systems if the temperature and the resistance are known.

4.4 Flicker noise

Flicker or 1/f noise, as its name implies, has a power spectrum that is inversely proportional

to frequency. The origins of 1/f noise are still not fully understood and remains an active

topic of research [86], [99]. In particular, 1/f noise in piezoresistors is dependent on

fabrication process parameters, such as implant parameters (dose and energy) and type

of anneal [100]. 1/fn noise is also a good measure of the quality of resistors [101]; noise

in excess of the normal value, or a non-unity slope n > 1 are indicative of poor fabrication

process quality [102]. Researchers have optimized piezoresistive device performance while

taking into consideration 1/f noise [75, 77]. Despite many decades of research, the source

of 1/f noise is still debated [103]. McWhorter and Hooge proposed two opposing theories

on the source of 1/f noise. These views are currently the leading explanations for the origin

of 1/f noise.

Figure 4.6 shows these models graphically. The McWhorter model attributes the 1/f

noise to surface defects, while the Hooge model implicates bulk defect [105]. Experimental

results show that 1/f noise is due to fluctuation in the conductivity of the carriers [88].

Hooges shows that 1/f low frequency noise modulated the thermal noise when no current

was passed through the resistor [85]. This experiment demonstrates that 1/f noise is not

current-generated. In a typical measurement, current is only needed to transform the


Figure 4.6: Conductivity fluctuations based on a) Hooge model (bulk effect) b) McWhortermodel (surface effect). Reprinted from [104] with permission from IEEE publishing group.

existing conductivity fluctuations into measurable voltage fluctuations. Thermal and 1/f

noise are fundamentally different. Thermal noise is a voltage noise; therefore it does

not depend on the amount current passed through the resistor. In contrast, 1/f noise is a

conductivity noise; therefore the voltage noise given by equation 4.10 is proportional to

the amount of current passed though the resistor (proportional to bias voltage, Vb).

Hooge’s empirical 1/f noise model, fit to observed data, predicts that noise power

density increases with decreasing carrier concentration according to equation 4.11.

V1/ f =Vb

√α

N f(4.10)

S1/ f =V 2

b α

N f(4.11)


where S1/ f ,V1/ f , f ,N,Vb, are the Hooge noise power density, Hooge noise, frequency,

total number of carriers in the resistor volume, and bias voltage across the resistor,

respectively. A non-dimensional fitting parameter, α , is ascribed to the ”quality of the

lattice” and typically ranges from 10−3 to 10−7.

Attempts to observe the lower limit of 1/f, below which the spectrum flattens, have not

been successful because of the more dominant Johnson noise [85]. Measurements down

to 3µ Hz showed that the noise spectrum is still 1/f [106]. Harley showed that resistors

with the same surface to volume ratio have different 1/f noise characteristics and 1/f noise

scales with the volume of the resistors, consistent to Hooge empirical equation [75]. Hooge

defines 1/f noise as only those spectra with a frequency exponent of 0.9-1.1 [99], [107].

Noise with different spectral density and other frequency exponents, sometimes referred to

as 1/f-like noise, is not predicted by the Hooge equation and is often confused with the 1/f

noise [85], [105].

According to Hooge, noise with higher exponent of 1.5 or 2, is an indication of noise

mechanisms other than lattice fluctuations and should not be treated as 1/f noise. These

mechanisms could give insights into reliability and failure analysis of piezoresistors. For

example, Neri found that the exponent in 1/f is closer to 2 in metal traces that exhibit

electromigration [107] .

Vandamme also showed excess 1/f noise in semiconductors can be attributed to small

constriction and current crowding [91]. The third harmonic appears when a low frequency

(less than 1 MHz) sine wave is applied to piezoresistors with current flow paths that

contained constrictions. Applied power heats small constrictions in the resistor and

changes the resistor value proportional to the temperature coefficient of the piezoresistor.

Therefore, the input excitation exhibits a cubic nonlinearity. Current crowding theory

also explains why polysilicon has higher 1/f noise than crystalline silicon [99]. At grain

boundaries, small constrictions are present, thus reducing the total number of carriers (N)

and effectively increasing the 1/f noise. Basically 1/f voltage noise does increase linearly

with the applied excitation. If the noise spectrum trends otherwise, then other mechanisms,

such as current crowding, could be present. The noise floor of the experimental setup may

be verified by reducing the applied excitation and observing only the thermal noise of the

piezoresistor.


Figure 4.7: 1/f resistor noise measuring block diagram.

4.4.1 Circuit for measuring resistor flicker noise

We did not have access to commercially available instruments that directly measure resistor

noise such as Stanford research SRS830 lock-in amplifier and Keithley model 6220/2182A

current generator. Also, we did not find any amplifier that had less than 4 nV/√

Hz at

0.01 Hz. Hence, an alternative electronic circuit was devised in order to measure the low

frequency noise of our piezoresistive cantilevers.

An HP3562A spectrum analyzer in conjunction with a modulated low noise amplifier

was used to measure the resistor thermal and 1/f noise in the range of 0.01 Hz - 1000 Hz.

The initial circuit used a INA103 instrumentation amplifier, which has 1 nV/√

Hz, at a

spot frequency of 1 kHz. However, the instrumentation amplifier input referred voltage,

and input current noise at low frequency were 40 nV/√

Hz and 30 pA/√

Hz, respectively,

at a spot frequency of 1 Hz. This high flicker noise became a limiting factor.

However, by use of modulation we were able to reject the amplifier flicker noise. Note

that INA103 has high input bias current, bridge resistances of greater than 5 kΩ are not

recommended for use with the INA103 front end. Since the amplifier has lower noise at

higher frequencies, for example, 1 nV/√

Hz at 500 Hz, INA103 can provide the basis for a

low flicker noise design if the circuit is operated at 500 Hz.

The output of the bridge is proportional to the applied voltage times the conductivity

variation, the bridge is a natural modulator; the output voltage of the bridge is a


multiplication of the change in resistivity ∆R and the bridge voltage Vb. Exciting the bridge

with an AC signal and then amplifying the modulated signal will prevents operation a the

region of high flicker noise. Demodulating the signal back to low frequency provides the

solution. This technique was commonly used in the early days of radios and is the basis for

lock-in amplifier design.

Figure 4.7 illustrates the block diagram of the circuit. The sensor conductivity

fluctuation is modulated at the desired frequency, and amplified by a gain of 1000 using

INA103. The signal then passes through a passive band pass filter with a bandwidth of

approximately 200 Hz and center frequency of 500 Hz to reduce noise folding into the

baseband after demodulation. The signal then is demodulated using the AD630 with a gain

of 4/π .

After demodulation, the signal passes through a third-order passive filter. An external

low phase noise oscillator is paramount, since the phase noise of the oscillator will directly

contribute to the flicker noise. The 500 Hz modulation frequency was chosen primarily

due to limitations of the AD630. The actual circuit implementation of the 1/f resistor noise

Figure 4.8: 1/f resistor noise measuring circuit implementation.


block diagram appears in Figure 4.8.

4.5 Calibration

Several methods to calibrate cantilever sensitivity have been previously discussed [108].

However, the simplest and quickest method is the thermo-mechanical noise calibration. As

discussed on page 61, noise can also be used to calibrate a system.

Since the detector output of the AFM only provides a voltage, a constant is needed to

convert the voltage into the actual tip displacement. Ref. [109] refers to the calibration

constant as inverse optical lever sensitivity (InvOLS).

The tip deflection was calibrated by measuring the thermo-mechanical noise of the

cantilevers, using equations in this section to calibrate the cantilever tip deflection and

ultimately surface stress.

Equation 4.12 equates the thermal noise energy to the energy of the cantilever where

k is the spring constant of the cantilever and z is the tip deflection. This equation is valid

for cantilevers of any shape or material. Equation 4.13 is the total amount energy at room

temperature (27C). kb is the Boltzman constant and T is the temperature in units of Kelivn.

kbT can be thought of as 4.1 *10−21 J or 4.1 nm-pN (nanometer*pico Newton) or 0.026

electron volt (eV).

Equation 4.14 is the force constant of the cantilever from the mechanical dimensions; l

is length, w is width, and t is thickness, and E is Young’s modulus. k is dependent on the

shape and the material that the cantilever is made of. We used a rectangular cantilever.

In order to maximize the tip deflection of the cantilever for a surface stress caused by

chemical binding, from Equation 4.26 it is apparent that the cantilever should be as long

and as thin as possible to maximize the (l/t)2.


1/2kbT = 1/2kz2 (4.12)

kbT = 4.1∗10−21Joules (4.13)

k =Ewt3

4l3 (4.14)

f0vac =

√k

Me(4.15)

Me = 0.2427∗M (4.16)

The vacuum resonance frequency f0vac of a rectangular cantilever is given by Equation

4.15, where Me is the normalized effective mass, which is equal to 0.2427 of beam mass

(M) for rectangular beams of l/w > 5 [110]. For our chemical sensing cantilevers l is 500

µm w = 100 µm and t = 1 µm. Our cantilevers were purchased from Nanoworld and were

made of pure silicon in the < 110 > direction. Silicon has Young’s modules of Exy=169

GPa in the < 110 > direction and a Poisson ratio of νxy= 0.06 [81].

There were significant differences in cantilever thickness from device to device. The

manufacturer specifies a thickness range of 0.5 µm - 2.5 µm with a typical thickness of

1 µm, which is understandable due to etching tolerances. Length varied ±1% and width

by ±5% which are within the lithographic tolerances of ± 5 µm. Since measurement of

thickness is rather difficult and destructive, each cantilever must be calibrated using the

thermo-mechanical noise before use.

Our strategy for cantilever calibration was:

• Fit the noise from the cantilever’s fundamental resonance mode to a simple harmonic

oscillator;

• From the value of resonance frequency, solve for cantilever thickness;

• From the thickness, find the spring constant k;

• Integrate the resonance voltage noise over the bandwidth and equate it to the energy

to solve for tip displacement and InvOLS;

• From tip displacement and Stoney’s equation, solve for surface stress.


The power response of a simple harmonic oscillator is given by Equation 4.17, where

α is the normalization factor, and Q is the ratio of energy stored to energy lost, which is

given by Equation 4.18 where ∆ f is the 3 dB bandwidth. A key simplification equates the

vacuum resonance frequency to the measured resonance frequency. Equation 4.19 relates

the vacuum resonance frequency to the damped resonance frequency. If Q > 10, then the

error is less than 1%.

G( f ) =α

(1− ( f 2

f 20)2 + ( f/ f0)2

Q2

(4.17)

Q =f0

∆ f(4.18)

fd = f0

√1− 1

2Q(4.19)

t = 2π f0l2

√.968ρ

E(4.20)

Equations 4.15 and 4.14 are solved to yield the thickness in Equation 4.20, where l is

the length of rectangular cantilever (500 µm) E = E110 (169 GPa), and ρ is the density of

silicon (2330 kg/m3).

Figure 4.9 shows the voltage noise spectral density from AFM. The Q of the cantilever

acts as a mechanical gain source that amplifies the random collision of air molecules

(thermo-mechanical noise) with the cantilever surface. Therefore, the peak voltage is the

thermo-mechanical noise amplified by Q.

The total noise power is given by Equation 4.21, where G( f ) is the transfer function of a

simple harmonic oscillator and P( f ) is the thermo-mechanical noise power spectrum. The

equation simplifies to noise bandwidth times the amplified noise power (Eq. 4.23) [111].

Note that f0/Q is bandwidth ∆ f , and π

2 ∆ f is the equivalent noise bandwidth. Pdc can be

determined from the resonance noise voltage of Figure 4.9 divided by Q. The cantilever tip

movement due to thermo-mechanical noise is given by Equation 4.24, hence the sensitivity

(InvOLS) is given by Equation 4.25 which is the ratio of equation 4.24 and 4.21.


Figure 4.9: Cantilever tip deflection voltage noise spectral density (orange circles), and fitto a simple harmonic oscillator noise transfer function (black line) taking into account 1/fand white noise .


∆V 2 =∫

G( f )2P( f )d f =π

2f0QPdc (4.21)

Pdc = (Resonance−noise− voltage

Q)2 (4.22)

∆V 2 = (Resonance−noise− voltage)2 ∗ π

2∆ f (4.23)

∆y2 =KbT

k(4.24)

InvOLS = Sensitivity =

√KbT

k2

πQ f0Pdc(m/V ) (4.25)

The last task is to relate cantilever tip deflection to surface stress. Equation 4.26 can be

solved for surface stress (Eq. 4.27). Surface stress per volt is given by Equation 4.28.

∆y = 3σ

E∗(lt)2 (4.26)

σ = (tl)2 E∗∆y

3(N/m) (4.27)

Ss = (tl)2 E∗

3

√KbT

k2

πQ f0Pdc(N/m/V ) (4.28)

Chapter 5

Measurements

In this section we discuss functionalization, mounting, measurements, and experiments

which validated tip deflection of cantilever was due to MR-APTES mono layer.

Optomechanical modulation of the cantilever was measured by the optical beam bounce

method using Witec-Alpha AFM. Figure 5.1 shows the setup. Extreme care was taken to

isolate the cantilever from any mechanical coupling. A 405 nm solid-state laser was placed

beneath the cantilever, and the illumination intensity was set by a custom-made laser driver.

The on-off time of the laser was set by a waveform generator. The cantilever was placed

on a glass slide (Corning 2947) in air. When the MR-APTES was exposed to the 405 nm

laser, the molecule isomerized from trans to cis; when the laser was turned off, the molecule

reverted back to the more energetically favorable trans configuration. The cis configuration

occupied more space than the trans configuration, and hence, the cantilever accommodated

this change in volume by bending. Reprinted with permission from [44]. Copyright 2013

American Chemical Society.

71

CHAPTER 5. MEASUREMENTS 72

Position

Sensor

Position

LASER

Coated

Cantilever

Collimating Lens

405nm

LASER

Actuator

Figure 5.1: Representation of measurement setup (not drawn to scale).


NN

ON

Si

OO

HN

O

H2SO4/H2O2

Silicon <100>

Native Oxide

OH OHOH OH OH

Native Oxide

OHOH OHOHOH

Si

O

O Si

O

Si

O

OH

NN

O

N

HN

NN

O

N

HN

NN

O

N

HN

OOH

Si

O

O Si

O

Si

O

OH

NN

O

N

HN

NN

O

N

HN

NN

O

N

HN

OOH

Figure 5.2: MR-APTES functionalization of cantilever.

5.1 Cantilever functionalization

To prepare the monolayer, we made a 20 mM solution of MR-APTES in anhydrous

toluene. We ensured the use of dry glassware and dry solvent since water catalyzes

the polymerization of APTES. Our protocol achieved acceptable yield with azobenzoic

and benzoic acid, whereas the molecules polymerized in solution when coupled to 3-

aminopropyltrimethoxy silane, which is more reactive with water. [62] Single crystal

silicon microcantilevers were purchased from Nanoworld and were 1 µm thick, 100 µm

wide, and 500 µm long. Cantilevers were placed in room-temperature piranha solution

(4:1 H2SO4 : 30%H2O2) for 5 min (Figure 5.2). The cantilevers were then thoroughly

rinsed with deionized water, sonicated for 30 s in deionized water, and rinsed again with

high-purity deionized water (18 MOhm; Millipore). The water contact angle is practically

zero at this step if the surface is properly hydroxylated. [112] The cantilevers were then

dried for 10 min and placed in a glass vial of 20 mM MR-APTES in anhydrous toluene.

The vial was purged with nitrogen and the lid was closed for 2 h at room temperature.

Care was taken to keep water out of the reaction because water catalyzes the attachment

of ethoxy silane to the hydroxylated silicon dioxide surface; excess water thus causes the

silane to polymerize on the surface. After 2 h, the cantilevers were removed, rinsed with

pure toluene, and sonicated for 10 s in ethanol.


Figure 5.3: A cantilever attached to a magnetic washer. The thermal mismatch ofexpansions was a major source of error. For all data presented, the cantilevers were placedon a low absorbance glass slide (Corning 2947).

5.2 Mounting of the cantilevers

Initially, the cantilevers were mounted in the system based on the recommendations of the

manufacturer of the AFM. The cantilever was fastened to a magnetic washer using epoxy

(Fig. 5.3). However, we measured consistently excessive high signal levels. We detected

motion even on the reference cantilever, which fortunately had different characteristics than

the functionalized cantilever. We hypothesized existence of the photon momentum transfer

however, the photon forces are in the order of pN for a 10 mW laser light, which could

not explain the observed massive deflections [113]. After a great deal of investigation,

we identified a mismatch between the thermal expansion coefficient of the metal washer,

the epoxy, and the silicon that caused the observed excessive cantilever tip deflection.

Hence the cantilevers were placed on low absorbance glass slides (Corning 2947) to prevent

thermal mismatches and convection heating of the air surrounding the cantilever.

Substantial noise and drift were detected in the reference bare cantilever and the MR-

APTES coated cantilever raw deflection as shown in Figure 5.4. The cantilever beams


Figure 5.4: The signal from a bare silicon cantilever. The horizontal axis is time in secondsand the vertical axis is the output voltage of the top-bottom detector of the AFM. Thisvoltage is proportional to the tip deflection of the cantilever. For each cantilever, theproportionality constant was calibrated based on the equations developed in section 4.5.The sensitivity for this cantilever was 46 nm/V.

were soft in order to maximize the effect of surface stress, which made them more

susceptible to environmental noise. The spring constant of cantilevers were approximately

30 mN/m. Figure 5.5 shows the signal from the MR-APTES coated cantilever. The power

of modulation becomes intuitively apparent, as we can detect the periodic signal in the

noisy waveform of Figure 5.5. Since the frequency of excitation is precisely known, with

processing we can filter around the known excitation frequency and reject broadband noise.

The repetitive nature of the input signal also allowed for averaging and improved signal to

noise ratio by orders of magnitude. Random white noise is not repetitive, and it has zero

average. Hence, by simply cycle averaging the signal and noise the repeatable portion of

the signal appears.


0 20 40 60 80 100 120−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0MR Canti2−Right.mat

50 50.5 51 51.5 52 52.5 53 53.5

−0.24

−0.22

−0.2

−0.18

−0.16

−0.14

−0.12

−0.1

−0.08

MR Canti2−Right.mat

Figure 5.5: The signal from the MR-APTES coated cantilever. Top, the entire signal (120s). Bottom expanded view of several cycles.


Figure 5.6: MR-APTES cantilever tip deflection spectrum.

5.3 Signal processing

Initially, we used a HP3564 spectrum analyzer for data acquisition. However, using Matlab

and a National instrument data acquisition card was more versatile. We used the spectrum

analyzer to validate our measurement setup and found better than 0.1% agreement between

the instruments. The absolute voltage measurement accuracies were important, since they

directly relate to tip deflection measurement errors. We used a 100 Hz anti-aliasing filter

to collect data. The raw AFM voltage spectrum of tip deflection of the MR-APTES coated

signal is shown in Figure 5.6.

A finite impulse response filter with 16384 tap was designed to filter the main harmonic.

The filter had a center frequency of 1 Hz and bandwidth of 0.1 Hz. The frequency response


Figure 5.7: Finite impluse response of band pass filter used to filter the data.

and phase of the filter are shown in Figure 5.7.

The input signal and the output signal of the filter appear in Figure 5.8. Note the absence

of the drift and the delay in the output signal. Since the filter is bandpass, the low frequency

components are taken out. The delay is due to the inherent nature of limited bandwidth.

The time constant for 0.1 Hz bandwidth is 10 s. There were 16384 taps with the sample

frequency of 1 kHz which will result in 16.384 seconds delay for the filter, with a linear

phase. The output signal in time domain mainly resembles a sine wave. Such filtering lends

well for design of lock-in instrumentation amplifiers, which identifies whether a signal is

present among large noise. However important aspect of the signal, such as rise and fall

times, are lost. Upon verification of the signal, we used spectral analysis and averaging to


Figure 5.8: The band pass filter input (top) and output (bottom) for the MR-APTEScantilever. Note the delay and lack of drift.

gain insight into cantilever motion.

The deflection spectra of an uncoated reference cantilever and an MR-APTES coated

cantilever are presented in Figure 5.9; deflection of the coated cantilever is one order of

magnitude greater than the reference cantilever at the laser modulation frequency (1 Hz)

and exhibits large, even harmonics.

Another powerful technique that can elucidate the tip motion is cycle-averaging the

signal (Fig. 5.10). Since the signal repeats on a cycle-by-cycle basis, noise is minimized

by averaging the cantilever motion on a cycle-by-cycle basis. Appendix D contains the

code.


Figure 5.9: MR-APTES enables optomechanical actuation of microcantilevers. When abare silicon reference cantilever (left) is excited with a 405-nm laser at 1 Hz, a small peakappears at the modulation frequency and even harmonics are not visible. The deflectionamplitude of a cantilever functionalized with MR-APTES (right) increases 10-fold at themodulation frequency and even harmonics are visible in the spectrum due to the differencein the on- and off-rates of actuation.

Figure 5.10: Optomechanical motion of the cantilever. Left, raw output of the AFM tipdeflection for an MR-APTES-coated cantilever. Right, mean corrected cycle average of119 pulses of the MR-APTES (orange) and the reference cantilever (blue). The uncoatedreference cantilever does not show motion, while the MR-APTES coated cantilever does.One hundred nineteen pulses were averaged to improve the signal to noise ratio. The turn-on time is substantially faster than the turn-off time due to the finite rate of cis-trans thermalisomerization.


5.4 Analysis of tip motion due to heat

Heating and cooling can also cause tip deflection. By measuring tip deflection at different

wavelengths that can cause the same amount of heat, we can rule out the effect of heat.

We used a laser with a wavelength at which MR-APTES does not isomerize (635 nm;

Fig. 5.11). At both wavelengths, most of the heat generated was due to the absorption

of photons by the silicon cantilever rather than by the monolayer. Yi et al. [114] reported

an absorbance of 8 ∗ 10−3 for two MR-APTES monolayer (both side of glass slide) at a

maximum absorbance wavelength of 435 nm. Therefore, most of the light is transmitted

through the MR-APTES into the silicon. The absorption coefficient of silicon is 1.0 x

107/m and 3.5 x 105/m at 405 nm and 635 nm, respectively; therefore, the incident light is

efficiently absorbed by the 1000 nm thick cantilever beam in both cases. When we varied

the laser power at 405 nm from 1 mW to 8 mW, we observed a linear increase in the

amplitude of deflection and did not observe any discernible response at 635 nm when the

power was varied.

By observing tip deflection in the frequency domain, it is possible to gain more

insight about the signal. For example, in the cycle average of the reference cantilever,

Figure 5.11: An MR-APTES-coated cantilever exhibits actuation when excited with 405nm laser, and no actuation when excited with a 635 nm laser. The laser power wasapproximately 2 mW for both wavelengths. The wavelength specificity is consistent withan optomechanical rather than thermal actuation mechanism.


Figure 5.12: Cantilevers coated with a non-photoswitchable (11-bromoundecyltrimethoxysilane) SAM do not exhibit actuation. The laser powerused here was the same as that used with MR-APTES-coated cantilevers (2 mW).

the tip deflection at 1 Hz was obscured by noise, but we detect a small peak in the

frequency domain with the functionalized cantilever. A perfectly symmetrical square

wave in which the on and off times are identical shows only odd harmonics, which

can be mathematically shown by Fourier analysis. For the gold-coated and reference

cantilevers, we only observe odd harmonics that are related to the equal on and off times.

As expected, the heating (light on) and cooling (light off) mechanisms are symmetric. In

the case of MR-APTES, the photostationary states are reached faster during illumination

than when the molecule is allowed to reach a stationary state in the dark. Therefore,

the on and off times are asymmetric even though the input is symmetric, an effect that

appears as even harmonics in the Fourier spectrum. In summary, the presence of even

harmonics suggests asymmetry between the on and off times of the cantilever: thermal

actuation is symmetric, while optomechanical actuation is not. This difference is due

to the MR-APTES SAM. To investigate the effects of cantilever heating, we used gold

and 11-Bromouncyltrimethoxysilane coated (Fig. 5.12) cantilevers. Figure 5.13 shows tip

deflection of a gold-coated cantilever excited with less than 100 µW laser power. The 1 µm

thick silicon layer of the gold-coated cantilever absorbs the transmitted light and converts it

to heat. The thermal coefficient of expansion of silicon is 2.6 ppm/K and the coefficient for

gold is 14 ppm/K. Because the metal is only deposited on the top of the cantilever, the heat


Figure 5.13: Time (left) and frequency domain (right) of the tip deflection of a gold-coatedcantilever. The silicon-gold bimorph structure deflects due to the temperature increaseinduced by the incident optical power (< 100 µW). Even harmonics are not present in thesignal because the heating and cooling rates are the same. One hundred nineteen pulseswere averaged.

expands the metal and the cantilever bends downward to accommodate this expansion.

Chapter 6

Discussion and conclusion

We have shown by modulation techniques that small surface stresses can repeatedly and

reliably be measured. Due to the success of our approach, a fundamental follow up question

that arose was “how do surface stresses of various component interact ”. In this Chapter

we present an approach and preliminary data for the aforementioned question.

According to Stoney’s equations the tip deflection of a cantilever is a linear function

of surface stress, and all components of the thin film surface stress are additive ( Eq. 6.1).

The tip displacement is a constant or a linear gain factor as shown in Equation 6.2. The tip

deflection depends only on cantilever geometry and its material property (Eq. 6.4). Figure

6.1 is a graphical presentation of Equation 6.1.

∆y = 3(σ f1 +σ f2 +σ f3)

E∗(lsts)2 (6.1)

∆y =Constant ∗ (σ f1 +σ f2 +σ f3) (6.2)∆y∆σ

=Constant (6.3)

Constant =3

E∗(lsts)2 (6.4)

Our first question involves the extent of linearity of the relationship between tip

deflection and surface stress. To achieve such measurements we need to be able to change

84

CHAPTER 6. DISCUSSION AND CONCLUSION 85

ΣTip

Deflection

Film 2 Surface

Stress

Film1 Surface

stress

Surface

Stress

Film 3 Surface

stress

Constant

Figure 6.1: Block diagram of Stoney’s equation. Tip deflection is a linear superposition ofsurface stresses (Eq. 6.1).

the input (surface stress) and observe the output (tip deflection). We employed gold plated

cantilevers and used temperature to induce a surface stress due to the thermal mismatch of

gold and silicon. We used an AFM system to measure cantilever tip deflection.

Rather than just simply slow sweeping the surface stress, which did not produce any

repeatable measurement we extended the idea of modulation. Instead of applying heat at

a single frequency of operation, we used two heat sources and operated them at different

rates. Our heat sources were two light emitting diodes (LEDs) that could be turned off

and on at different rates. If the system is truly linear, then the surface stress at different

frequencies should not mix.

To better elucidate this concept, it is important to note that nonlinearity can be modeled

as Equation 6.5 or as a power series such as Taylor expansion(Eq. 6.6). Also, nonlinearity

will cause multiplication of the input signals due to squaring of inputs (Eq. 6.9) . Hence, if

two time varying inputs are applied, their multiplication is expected. When two sine waves

of different frequencies are multiplied, there will be sum and difference frequencies present

(Euler identity Eq. 6.13). The sum and difference frequencies are hallmark of non-linear

systems.


ΣOut

Input 2

Input 1

InNon linear

Figure 6.2: Non-linear system used for simulation of the two tone effect. In any non-linearsystem, the inputs will interact (Eq. 6.6).

out put = inputexponent (6.5)

out put ∼ input +a12!∗ input2/2!+a2∗ input3/3!+ ... (6.6)

input = input1 + input2 + ... (6.7)

out put ∼ a1∗ (input1 + input2)2 + ... (6.8)

out put ∼ input21 +2∗ input1 ∗ input2 + input2

2 + ... (6.9)

input1 = sin( f1t) (6.10)

input2 = sin( f2t) (6.11)

out put ∼ [sin( f1t)+ sin( f2t)]2 + ... (6.12)

out put ∼ c1sin( f1t)+ c2sin( f2t)+ (6.13)

c3cos( f1t− f2t)+ c4cos( f1t + f2t)+ ...

σ f = σ1sin( f1t)+σ2sin( f2t) (6.14)

∆y = σexponetf ∗Constant (6.15)

We simulate an ideal non-linear system (Fig. 6.2) and provide the preliminary result of

the two tone experiment. Figure 6.3a contains the input output characteristics of a perfectly

linear system, and Figure 6.3b depicts the percentage error, which is zero. Figure 6.4a

shows the two tone input at 20 Hz and 30 Hz frequency applied to the system. Since

the system is linear, the intermodulation products are not present. Unfortunately, the time


a b

c d

Figure 6.3: Simulation of linear and non-linear systema) Input versus output of a linearsystem. b) Percentage error from the ideal linear system. c) Input versus output of non-linear system d) Percentage error from the ideal linear system. The input and output canbe any variables. For this work the input will be surface stress and the output will be tipdeflection of a gold coated rectangular cantilever.

domain information is not as clear as the frequency domain, leading to a high degree of

abstractness.

Figure 6.3c depicts a non-linear system, and Figure 6.3d shows the error. The

intermodulation harmonics are apparent at the sum and the difference frequency (Fig.

6.4d). As the non linearity increases, so does the magnitude of the intermodulation

harmonics. For a system with high nonlinearity the intermodulation products are no longer

bound to the sum and difference frequencies, since those frequencies will be mixed with

the input and generate new sum and difference frequencies.


a b

a b

Figure 6.4: Two tone simulation. a) Two tone input versus time b) Two tone spectrum c)Two tone output of a non linear system c) Two tone spectrum of the output. Note the sumand difference frequencies are present in the output of the non-linear system.

6.1 Hypothesis

Two tone test provides an easy and quantitative means of measuring non linearity. Inducing

a curvature into a cantilever beam to test the hypothesis was rather challenging, which

motivated us to take a qualitative approach. Our hypothesis was due to simplification of

the beam equation for soft cantilevers. Tip deflection was no longer a linear function of

surface stress and effect of non linearity were significant and depend on the curvature of

the cantilever. For the same magnitude of surface stress, a curved cantilever would show

higher non linearity than one without curvature.


6.2 Experimental setup for two tone test

In order to induce curvature into the cantilever beam, we brought the cantilever tip close

to a microscope slide without actually touching the slide (Fig. 6.5). At close distances

between the microscope slide and cantilever the short range molecular forces act on the

soft cantilever tip and cause bending of cantilever without actually touching the glass.

We measured non-linearity vs AFM Z position of the cantilever above the slide. The

cantilever was first brought to contact and then pulled back, so that it was not in contact

(determined from vibration of tip motion). The cantilever was purchased from nano world.

The dimension of the cantilever as stated by the manufacturer were 500 µm length, 100

µm width, and 1 µm thick. There was 25 nm of gold on the top surface of the cantilever.

A custom LED were built with two distinct wavelengths. One LED operated at 420 nm

and the other at 320 nm. The LEDs were used to heat the cantilever, and each of individual

LED power could be adjusted. Due to the thermal mismatch of gold and silicon the tip

vibrated at the on off rate of each LED. Note that each LED could be turned on and off at

any rate.

6.3 Results of two tone test

Due to its small dimensions, cantilever cooling and heating was rather fast. The measured

frequency response of the cantilever vs temperature appears in Figure 6.6. We used two

frequencies 70 Hz and 150 Hz. Expecting a difference frequency of 80 Hz and a sum

frequency of 220 Hz. When the AFM Z position was pulled away only by 100 nm, as

expected we observed low amount of non linearity (Fig. 6.7). Since the AFM Z position

pulled the root of the cantilever further away from the slide surface more curvature was

experienced by the cantilever and more non linearity resulted, until the tip completely

snapped off. Figure 6.8 displays the percentage amplitude change of the tone referenced to

the input tones.


Position

Sensor

Position

LASER

Gold Coated

Cantilever

Custom LED Package

Two LED in the package

Transparent

Slide

Figure 6.5: Two tone setup to detect tip deflection due to heating by two LEDs.


Figure 6.6: Cantilever thermal frequency response. The peak at 4.6 kHz is due to theresonance frequency of the cantilever. The operating frequencies are in the flat band of theresponse.


Figure 6.7: Two tone measurement at an AFM Z height 100 nm above the slide. Note thedifference and sum frequency at 80 Hz and 220 Hz.


Figure 6.8: Percent amplitude of the tones to main excitation vs. distance of the AFM Zheight. As the Z height increases, the tip attempts to move further away from the surface,but is held in place due to surface forces and experiences higher curvature. As hypothesizedhigher non linearity occurred until the tip snapped off.


6.4 Summary of two tone test

In conclusion, these experiments demonstrate the potential of using two tone tests to

measure nonlinearities. We hypothesized the non linearities were due to curvature of

the beam. For cantilever with small tip deflection, the output is expected to be a linear

function of surface stress. However, for even small tip deflection (less than one thousandth

of the cantilever length) nonlinearities occur. These non linearities are hypothesized to

be proportional to the initial curvature of the cantilever. This technique can be used for

chemical sensing and bio-sensing using multiple films. Also cantilever curvature can be

estimated using measurements from a single point at the tip. More importantly two tone

testing reveals the interaction between films. For example, if the cantilever is coated with a

film that has a different behavior due to heat than light then the effect of light and heat can

be separated by analyzing the intermodulation products.


6.5 Conclusion

As micro mechanical systems reduce their size the new field of nano mechanics emerges.

Physical and practical issues such as lithography limit how small devices can be made.

The search for analogous functions such as actuators, sensors continues. To reduce the

device dimensions to molecular size, mechanics and chemistry must merge. We have

demonstrated that a monolayer of the aminoazobenzene MR-APTES physically exerts a

surface stress due to absorbance of a 405 nm photon, resulting in the deflection of the

tip of a micro-machined cantilever, corresponding to an average force on the order of

0.3 pN per molecule. The induced surface stress is hypothesized to be due to the trans-

cis isomerization of MR-APTES. Since this isomerization can be repeatedly induced,

averaging and Fourier techniques can be used for signal processing. The optomechanical

modulation of surface stress should enable the spectral separation of the signal of interest

from background noise sources in chemical sensors, enabling a new generation of surface

stress-based chemical sensors with improved signal to noise ratio.

Appendix A

UV LED and laser driver

For the initial testing of the azobenzene dye, a custom light emitting diode (LED) was

purchased from ST-Electronics. Two LED diodes at 432nm and 320 nm 100 µW were

custom packaged in the same enclosure with a semi hemispherical lens. The 405 nm, and

632 nm laser were purchased from Thor labs. The 405 nm Laser LP-405-SF10 came with

pig tail fiber. Since the beam at the output of the fiber behaves as point source a 405 nm

collimator was used to collimate the beam. A 632 nm collimator was also used for the

for the LP-632-SF10. The same electronics with a slight modification that was designed

to drive the LED was used to drive the laser. The block diagram of the circuit is shown

in Figure A.1a. A precision variable current source with an NMOS electrically controlled

switch was designed to turn on and off the laser or LED with an external signal generator.

A 1 Ω resistor was used to monitor the current, which represent the laser or LED light

power output. The laser light output power after the critical threshold current is directly

proportional to the current as shown from manufacturer data in Figure A.1b. For the 405

nm laser the threshold current as specified by manufacturer was 34.3 mA. We operated

the laser above 37.5 mA to ensure minimal power fluctuation. A detailed schematic of the

circuit appears in Figure A.2. The current source had better than 60 dB supply rejection and

maintained the current to better than 0.01% accuracy. The laser output power was verified

with PM-10 sensor with a Fieldmate power meter and matched the power from current

power curve of Figure A.1b within the accuracy of the meter.

96

APPENDIX A. UV LED AND LASER DRIVER 97

a

Precision Current

source

Light emitting diode

Or LASER

1 Ohm current

sense resistor

NMOS

switch

b

Figure A.1: a) Block diagram of the LED and laser driver circuit. A 20 turn potentiometerwas used to vary the current source. The 1 Ω resistor converts the current to a voltagewithout loss of headroom. The voltage across the resistor was monitored during operation.b) Manufacturer light power output of the laser measured at the fiber output. The lightoutput power of the laser is directly proportional to the current through the laser. The laseroutput power measured with PM-10 sensor and a fieldmate meter matched the power vs.current curve within the accuracy of the meter.

APPENDIX A. UV LED AND LASER DRIVER 98

Figure A.2: Detailed schematic of UV-LED and laser driver circuit. Resistor R3 waschanged to 10 Ω for laser drive application.

Appendix B

X-ray photoelectron spectrometry

X-ray Photoelectron Spectroscopy (XPS) provides surface chemical characterization capa-

bilities, probing the surface top 10 A. High surface sensitivity makes the technique ideal

for studying deposited films and verifying their composition. XPS is based on irradiation

of the sample with monochromatic xrays. The high energy photons cause ionization of

the material by direct electron emission (photoelectron) as well as secondary electron

emission (Auger)as shown in Figure B.1. Since both photoelectrons and Auger electrons

are ejected during x-ray bombardment, both are observed in XPS spectra. From the energy

of photoelectron the chemical nature of surface can be determined, also called as Electron

Spectroscopy for Chemical Analysis (ESCA).

Photoelectrons are usually scattered through a variety of inelastic processes, but some

escape the sample surface unscattered. These electrons are collected by the instrument

electron lens, analyzed according to their kinetic energy, and counted. The kinetic energy

(KE) of each photoelectron is directly proportional to the energy of the ionizing photon

and the binding energy (BE) of the corresponding atomic orbital from which the electron

was emitted, through the following relationship: KE = hv−BE. Hence each element has

a specific signature spectrum. XPS was performed on an SSI S-Probe monochromatized

x-ray photoelectron spectrometer system, with an Al (Kα) x-ray source (1486.6 eV) in an

ultra high vacuum system with a base pressure in the 10−9 Torr range. The survey scans

were collected by using a hemispherical electron energy analyzer at a pass energy of 156.5

99

APPENDIX B. X-RAY PHOTOELECTRON SPECTROMETRY 100

Figure B.1: XPS fundamentals of operation courtesy of Dr. Hitzman.

eV with 1-eV resolution. The XPS data were processed by Shirley background correction

followed by fitting to Voigt profiles. A bulk C(1s) peak at 284.6 eV was used to adjust all

of the peaks in order to correct the binding energies for the charge shift.

Appendix C

Liquid chromatography-massspectrometry

A chromatography medium consists of two components of different phases, a mobile phase

and a stationary phase. A liquid mobile phase moving over a solid stationary phase. The

stationary phase consists of an adsorbing material, such as fine grain silicon dioxide, with

diameter of less than 1 µm. The mixture is dispersed into the mobile phase, which moves

along the stationary phase. Compounds in the mixture adsorb on the stationary phase from

time to time, and then come off again. The components must be soluble in the mobile

phase, which means they have affinity for the solvent. The stationary phase is usually fairly

polar. The higher the polarity differences between the components, and the longer the

path, the more separation will occur. The acronym HPLC originally indicated the fact that

high pressure was used to generate the flow required for liquid chromatography in packed

columns.

The output of the column then is then fed to an electrospray, a device that uses high

electric field to disperse the fine aerosol as shown in Figure C.1A. The Ions are then fed

to a quadruple mass spectrometer. We found by setting the ionization voltage to 25 V in

the Waters mass spectrometer far less fragmentation occurred than at the standard setting.

We used the C18-01-LowV setting of the Waters instrument shown in Figure C.1B for all

the data presented in this report. We kept the concentration of the sample between 20-50

101

APPENDIX C. LIQUID CHROMATOGRAPHY-MASS SPECTROMETRY 102

A

B

Figure C.1: A) Electrospray block diagram. B) Photo of the Waters mass spectrometerinstrument. We used a low voltage setting to reduce fragmentation. Figure courtesy of Dr.Allis Chein.

µM, and used the least amount of organic solvent to prevent breakthrough the column. It

is also important to note that in the negative (ESI−) or positive electrospray current (ESI+)

common masses of adduct are found (Table C.1).

APPENDIX C. LIQUID CHROMATOGRAPHY-MASS SPECTROMETRY 103

ESI+ ESI−

M+H+ M−H−

M+Na+ M+Cl−

M+NH+4 M−H + f ormic acid−

2M+H+n 2M−H−

M+nHn+ M+nHn−

Table C.1: Common mass of adducts found in electrospray current. For example, in theESI− mass, of the compound (M) plus the mass of chlorine (Cl) is commonly found.

Appendix D

Matlab signal processing code

Two signal processing codes were used to filter the data. The first code called ”Post.m”

achieves the filtering described on page 77. The second code ”CycleAvg.m” uses one cycle

of the data as a matched filter.

In the post processing code Post.m note the filtering and point selection.

c l o s e a l lc l e a r a l l

%W r i t t e n by A . Joseph R a s t e g a r da ta p o s t p r o c e s s i n g

%−−−Uncomment t h e da ta f i l e −−−−−

%t h e n run t h e s c r i p t ( p r e s s F5 )

%f i l e n a m e 1 = ’ Trace ’

%f i l e n a m e 1= ’MR Cant i2−R i g h t . mat ’

%f i l e n a m e 1 = ’MR Cant i2−R i g h t . mat ’

f i l e n a m e 1 = ’ Ref c a n t i on G l a s s Try 2 . mat ’

load ( f i l e n a m e 1 )

Bandpass = . 1 ;% i n H e r t z

C e n t e r =1; % Chop Frequency

Freqend = 5 %end f r e q o f a l l t h e s p e c t r a l p l o t

l p c o r n e r = 10 %c o r n e r o f t h e low pass f i l t e r

104

APPENDIX D. MATLAB SIGNAL PROCESSING CODE 105

f i g u r ex=Vtb ;

p l o t ( t , x ) ;

t i t l e ( f i l e n a m e 1 )

%−− i n p u t p l o t i s x

f i g u r eh = s p e c t r u m . pe r iodog ram ;

psd ( h , x , ’ Fs ’ , Fs ) ;

TITLE ( f i l e n a m e 1 )

a x i s ( [ 0 Freqend −80 0 ] ) ;

%−−FFT

f i g u r em = l e n g t h ( Vtb ) ; % Window l e n g t h

NFFT = pow2 ( nextpow2 (m) ) ; % Trans form l e n g t h

fx = f f t ( x , NFFT ) /m; % DFT

f = Fs / 2 * l i n s p a c e ( 0 , 1 , NFFT / 2 + 1 ) ; % Frequency range

p l o t ( f , 1 . 4 * abs ( fx ( 1 : NFFT / 2 + 1 ) ) , ’ b ’ )

x l a b e l ( ’ F requency ( Hz ) ’ )

y l a b e l ( ’Vrms ’ )

%t i t l e ( ’\ b f Spec trum o f Vtb ’ )


a x i s ( [ . 1 Freqend 0 . 0 3 ] ) ;

f i g u r eLowpassco rne r = l p c o r n e r / Fs / 2 ;

low= ( C e n t e r / ( Fs / 2 ) ) − ( Bandpass / ( Fs / 2 ) ) ;

h igh =( C e n t e r / ( Fs / 2 ) ) + ( Bandpass / ( Fs / 2 ) ) ;

b= f i r 1 ( 2 ˆ 1 4 , [ low h igh ] ) ; %band pass f i l t e r

%b= f i r 1 ( 2 ˆ 8 , [ Lowpasscorner ] ) ; %low pass f i l t e r


f r e q z ( b , 1 , 2 ˆ 1 6 , Fs )

a x i s ( [ 0 3 −80 5 ] ) ;

s u b p l o t ( 2 , 1 , 2 ) ;

a x i s ( [ 0 3 −2000 7 0 0 ] ) ;

y= f f t f i l t ( b , x ) ;

%−−o u t p u t p l o t i s y

f i g u r eS u b p l o t ( 2 , 1 , 1 ) ;

p l o t ( t , x ) ;

a x i s ( [ 0 120 −.5 . 2 ] ) ;

TITLE ( ’ F i l t e r i n p u t ’ )

v1= a x i s ;

xx=x−mean ( x ) ;

xrms= s q r t ( mean ( xx . * xx ) ) ;

t e x t ( 1 0 , v1 (4 ) − . 1 , [ ’RMS−mean i n mV= ’ num2str ( xrms * 1 0 0 0 ) ] ) ;

S u b p l o t ( 2 , 1 , 2 ) ;

p l o t ( t , y )

a x i s ( [ 0 120 −.3 . 3 ] ) ;

t i t l e ( ’ F i l t e r o u t p u t ’ ) ;

tmin =min ( t ) ;

ymax=max ( y ) ;

ymean=mean ( y ) ;

yy=y−ymean ;

yrms= s q r t ( mean ( yy . * yy ) ) ;

v= a x i s ;

t e x t ( 1 0 , v (4 ) − . 1 , [ ’RMS−mean i n mV = ’ num2str ( yrms * 1 0 0 0 ) ] ) ;

%msspec trum ( h , y , ’ Fs ’ , Fs , ’ NFFT ’ , 2 ˆ 1 4 )

s c r s z = g e t ( 0 , ’ S c r e e n S i z e ’ ) ;

%f i g u r e


%( ’ P o s i t i o n ’ , [ 2 0 s c r s z (4) /2−50 s c r s z ( 3 ) / 2 s c r s z ( 4 ) / 2 −5 0 ] ) ;

h = s p e c t r u m . pe r iodog ram ;

% Cr ea te a per iodogram s p e c t r a l e s t i m a t o r .

psd ( h , y , ’ Fs ’ , Fs ) ;

% C a l c u l a t e s and p l o t s t h e two−s i d e d PSD .

a x i s ( [ 0 Freqend −80 0 ] ) ;


f i g u r e ( 3 )

The filter code CycleAvg.m

c l e a r a l lc l o s e a l lc l cc o n s t a n t s ( ) ;

f i l e n a m e 1 = ’ Ref c a n t i on G l a s s Try 2 . mat ’

f i l e n a m e 2 = ’MR Cant i2−r i g h t . mat ’

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−load ( f i l e n a m e 1 )

Fmod =1;

hold a l lP e r i o d = Fs / Fmod ;

t 1 = ( 1 : P e r i o d + 1 ) * 1 / Fs ;

maxCycle= l e n g t h ( t ) / Pe r iod −1;

[ a , b ]=max ( d i f f ( Vled ( 1 : P e r i o d + 1 ) ) ) ;

%The r i s i n g edge t r i g g e r from t h e l a s e r on P u l s e

S=b ;

Vseg1 =0;


mean1 =0;

c y c l e =maxCycle

f o r n = 1 : c y c l e

Vseg1=Vtb ( S+( n−1)* P e r i o d : S+n* P e r i o d )+ Vseg1 ;

endm=mean ( Vseg1 ) ;

p l o t ( t1 , ( Vseg1−m) / max ( n ) , ’ . ’ )

load ( f i l e n a m e 2 )

[ a , b ]=max ( d i f f ( Vled ( 1 : P e r i o d ) ) ) ;

S=b ;

Vseg =0;

f o r n = 1 : c y c l e

Vseg=Vtb ( S+( n−1)* P e r i o d : S+n* P e r i o d )+ Vseg ;

endm=mean ( Vseg ) ;

p l o t ( t1 , ( Vseg−m) / max ( n ) , ’ . ’ )

box o f f

x l im ([− . 1 1 . 1 ] ) ;

x l a b e l ( ’ Time i n second ’ )

y l a b e l ( ’ Vo l t ’ )

p r i n t P l o t ( ’ Cycle Avg Of MR C a n t i and r e f ’ )

f i g u r ehold a l lp l o t ( 0 , 0 )

p l o t ( t ( 1 : 2 0 0 0 0 ) , Vtb ( 1 : 2 0 0 0 0 ) )

box o f f


x l a b e l ( ’ Time i n second ’ )

y l a b e l ( ’ Vo l t ’ )

x l im ( [ 0 3 5 ] )

y l im ([− . 27 0 ] )

p r i n t P l o t ( ’Raw o u t p u t ’ )

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