modeling, design and realization of microfluidic components · the development of microfluidic...

MODELING, DESIGN AND REALIZATION

OF

MICROFLUIDIC COMPONENTS

Edwin Oosterbroek

The research described in this thesis was carried out at the Micromechanical TransducersGroup of the MESA Research Institute at the University of Twente, Enschede, TheNetherlands. The project was financially supported by the OSF funds “Micro total analysissystems (µTAS), societal impact and fundamental micromechanical, optical and chemicalaspects” of the University of Twente.

Promotiecommissie:

VoorzitterProf.dr. H. Wallinga Universiteit Twente

SecretarisProf.dr. H. Wallinga Universiteit Twente

PromotorenProf.dr.ir. A. van den Berg Universiteit TwenteProf.dr. M.C. Elwenspoek Universiteit Twente

LedenProf.dr.ir. J.A.M. Kuipers Universiteit TwenteProf.dr.ir. H. Tijdeman Universiteit TwenteProf.dr. P.J. French Technische Universiteit DelftProf. G. Stemme The Royal Institute of Technology, StockholmProf. R. Zengerle Albert-Ludwigs Universität, Freiburg

CIP-GEGEVENS KONINKLIJKE BIBLIOTHEEK, DEN HAAG

Oosterbroek, Rijk EdwinModeling, design and realization of microfluidic components / Rijk Edwin Oosterbroek[S.I. : s.n.]Ph.D. thesis University of Twente, Enschede, The NetherlandsISBN 90-36513464

Subject headings: µTAS / microsystem technology / flowsensors / microvalves / modeling

Copyright © 1999 by R.E. Oosterbroek, Enschede, The Netherlands

MODELING, DESIGN AND REALIZATION

OF

MICROFLUIDIC COMPONENTS

PROEFSCHRIFT

ter verkrijging van

de graad van doctor aan de Universiteit Twente,

op gezag van de rector magnificus,

prof.dr. F.A. van Vught,

volgens besluit van het College voor Promoties

in het openbaar te verdedigen

op vrijdag 12 november 1999 te 16.45 uur.

door

Rijk Edwin Oosterbroek

geboren op 28 januari 1970

te Borne

Dit proefschrift is goedgekeurd door de promotoren:Prof.dr.ir. A. van den BergProf.dr. M.C. Elwenspoek

CONTENTS

1 INTRODUCTION.................................................................................................................. 1

1.1 Title explanation............................................................................................................. 11.2 Microsystem research..................................................................................................... 21.3 Project description .......................................................................................................... 31.4 Outline ............................................................................................................................ 3

2 HISTORY AND LITERATURE SURVEY OF MST AND µTAS....................................... 7

2.1 Classification of microsystems technology .................................................................... 72.2 Microsystem technology history .................................................................................... 92.3 Classification of µTAS................................................................................................. 112.4 History of micro chemical analysis systems................................................................. 132.5 Designing and modeling of microsystems.................................................................... 142.6 Device and system simulation tools ............................................................................. 182.7 Trends and prospects of MST and µTAS ..................................................................... 21

3 MICRO FLUID DYNAMICS.............................................................................................. 31

3.1 Introduction .................................................................................................................. 313.2 Quantitative down-scaling effects ................................................................................ 323.3 Fluid dynamics ............................................................................................................. 363.4 Surface effects in micro-flows...................................................................................... 38

3.4.1 Introduction........................................................................................................... 383.4.2 Surface energy ...................................................................................................... 383.4.3 Double layers ........................................................................................................ 40

3.5 Hydraulic channel resistance in stationary flows ......................................................... 433.5.1 Introduction........................................................................................................... 433.5.2 Numerical solutions of the Laplace equation........................................................ 433.5.3 Exact analytical solutions ..................................................................................... 463.5.4 The virtual work principle .................................................................................... 473.5.5 Channel resistance ................................................................................................ 56

3.6 Conclusions: ................................................................................................................. 60

4 THE PRESSURE / FLOW SENSOR, A CASE STUDY .................................................... 65

4.1 Introduction .................................................................................................................. 654.2 The flow sensing principle ........................................................................................... 674.3 Fabrication.................................................................................................................... 684.4 Modeling of the stationary sensor behavior ................................................................. 72

4.4.1 Membrane deflection ............................................................................................ 724.4.2 Electric pressure-sensor capacitance..................................................................... 744.4.3 The hydraulic resistance ....................................................................................... 75

4.5 Modeling of the quasi-dynamic sensor behavior.......................................................... 784.6 Accuracy and stability .................................................................................................. 824.7 Viscosity versus inertance induced dissipation ............................................................ 844.8 Conclusions and discussion.......................................................................................... 85

5 MICROVALVES................................................................................................................. 89

5.1 Introduction .................................................................................................................. 895.2 Valve types ................................................................................................................... 91

5.2.1 Passive valves ....................................................................................................... 915.2.2 Active valves......................................................................................................... 92

5.3 The bossed valve .......................................................................................................... 945.3.1 Introduction........................................................................................................... 945.3.2 Surface micromachined bossed valves ................................................................. 945.3.3 Bulk micromachined bossed valves...................................................................... 975.3.4 Selective fusion bonding..................................................................................... 100

5.4 The membrane valve .................................................................................................. 1035.4.1 Introduction......................................................................................................... 1035.4.2 Membrane check / pressure actuated normally open valves............................... 1045.4.3 Pressure actuated normally closed valves........................................................... 105

5.5 The duckbill check valve............................................................................................ 1075.5.1 Principle .............................................................................................................. 1075.5.2 Design and fabrication of thin <111> oriented membranes................................ 1085.5.3 Membrane tapering ............................................................................................. 1115.5.4 Applications ........................................................................................................ 1135.5.5 Selective anodic bonding .................................................................................... 114

5.6 Micromachining possibilities in <111> oriented silicon ............................................ 1155.6.1 Introduction......................................................................................................... 1155.6.2 Crystallographic orientations in <111> wafers................................................... 1155.6.3 Pre-etching without wall coating ........................................................................ 1175.6.4 Pre-etching with wall coating ............................................................................. 118

5.7 Conclusions ................................................................................................................ 121

6 FLOW-STRUCTURE COUPLING................................................................................... 135

6.1 Introduction ................................................................................................................1356.2 Flow-structure interaction in check valves ................................................................. 1366.3 Numerical implementation ......................................................................................... 139

6.3.1 Introduction......................................................................................................... 1396.3.2 Bi-directional coupled solving............................................................................ 140

6.4 Domain de-coupling ................................................................................................... 1486.5 Stability....................................................................................................................... 1486.6 Conclusions ................................................................................................................ 152

7 VALVE CHARACTERIZATION..................................................................................... 155

7.1 Introduction ................................................................................................................1557.2 Characterization setup ................................................................................................ 1567.3 The bossed valve ........................................................................................................ 158

7.3.1 Structural mechanics........................................................................................... 1587.3.2 Flow-structure coupling...................................................................................... 166

7.4 The membrane valve .................................................................................................. 1717.4.1 Membrane check / pressure actuated normally open valve ................................ 1717.4.2 The pressure actuated normally closed valve ..................................................... 178

7.5 The duckbill valve ...................................................................................................... 1837.5.1 Membrane analysis ............................................................................................. 183

7.5.2 Flow-structure coupling...................................................................................... 1897.6 Conclusions ................................................................................................................ 193

8 CONCLUSIONS & OUTLOOK ....................................................................................... 197

8.1 Overview .................................................................................................................... 1978.2 Outlook....................................................................................................................... 199

A BOSSED VALVE FABRICATION PROCESS DESCRIPTION ..................................... 203

B DUCKBILL VALVE FABRICATION PROCESS DESCRIPTION ................................ 217

SUMMARY ............................................................................................................................ 227

SAMENVATTING ................................................................................................................. 229

BIBLIOGRAPHY ................................................................................................................... 231

DANKWOORD ...................................................................................................................... 235

BIOGRAPHY.......................................................................................................................... 238

LEVENSLOOP ....................................................................................................................... 239

1

11 IINNTTRROODDUUCCTTIIOONN

The first chapter gives an impression of the fascinatingworld of micromechanics and the relevance of theachievements of microsystem research for “daily life” andthe future. Specific attention is paid to position of the work,described in this thesis, in the framework of the researchdone within the MESA+ Research Institute and morespecific within the µTAS orientation. Thereafter, the aims ofthe project are discussed and a brief overview is given of thesubject-matter of the following chapters in this thesis.

1.1 Title explanation

The thesis title “Modeling, design and realization of microfluidics components” refers to thedescribed activities performed in the microfluidic research area. Microfluidics is a rathernew term for describing the world of controlling and using small fluid flows with use ofmicrosystem components. The word originates from the term “fluidics” used in the “macroworld”. It is a contraction of the words “fluid” and “logics” and used to indicate the researcharea that deals with fluid control to make logic Boolean switches [14,4,20]. With use of theCoanda effect valve-less bi- or mono-stable switches are made to construct for exampleAND and OR switches. Microfluidics however covers a broader area including all types ofpassive and active valves, micro flow and pressure sources as well as flow and pressuresensors [16,11,32,6] made with micromachining techniques.

In this thesis a few components within the microfluidics area will be scrutinized. Fromthese components the design trajectories will be followed, starting with the theoretical

2 Chapter 1

description followed by the modeling and fabrication stage and finishing with performingmeasurement results.

1.2 Microsystem research

The fascinating and fast growing world of microsystem technology plays more often animportant role in daily life. Simply said, microsystem technology covers the area of small,microns sized systems and devices. A more detailed discussion about the definition ofmicrosystem technology is found in chapter 2. Examples of microdevices that are verysuccessful nowadays are among others the inkjet nozzles [3], airbag (acceleration) sensors[22], pressure sensors [8,19] in for example car engines and magnetic recording heads forcomputer harddisks [15,30,18]. The research area started some 30 years ago, arisen from theelectronic semiconductor development. This history has influenced the development ofmicromechanics substantially. Microsystems allow for example high level integration withelectronic integrated circuitry and large reduction of costs by mass fabrication processing.Integration with electronic circuits allows for the extension of the nowadays highlydeveloped microprocessors with sensors and actuators [29]. In this way electronic circuitrywill get “sense-organs” and “hands”. On the other hand, dimension reduction not only allowsthe fabrication of smaller systems but also can improve signal quality as well as sensitivityand facilitates exploiting physical and chemical effects that become dominant and usablewhen downscaling occurs [12,13].

For chemical analysis systems this means that for classical analysis methods, theneeded time can be speeded-up, less sample material and reagents are needed and betterquality reaction products can be obtained [26]. In chapter 2 the benefits of downscaling willbe discussed in more detail as well as the fast growing area of µTAS which stands for MicroTotal Analysis Systems [26]. µTAS covers the research of miniaturized chemical analysissystems and the microfluidics components needed to complete such systems. The last yearsthe development of microfluidic components is strongly influenced by the successes of theµTAS analysis research and the fast growth of companies active in this business [24].Miniaturization has caused a revolution in information gathering in biochemistry. The lab-on-a-chip approach makes massive parallel DNA analysis and PCR techniques available,resulting in a substantial analysis time reduction at limited costs [10,1,21,2,9].

Besides these benefits and successes of microsystem technology a big drawback,which makes the used techniques less accessible for companies and research institutes, is theneed of expensive conditioned cleanroom facilities and sophisticated cleanroom equipmentsuch as deposition and etching machines. In order to be able to obtain a good processcontrol, much specific knowledge about these processes is needed, which is often closely

Introduction 3

related to the used device geometries. Therefore the design and fabrication of microsystemsdemands for a close cooperation between different disciplines and people. These aspectsmake the microsystem technology is not as widely spread as other, “macro-mechanical”fabrication tools.

1.3 Project description

In 1990 the MESA+ Research Institute was established within the University of Twente tocombine common interests and funds to finance cleanroom facilities. At the university,microsystem research started at an early stage (1980). Main successes were obtained intechnology development applied to fabricate microfluidic components such as flowsensors[23] and pumps [25]. Since these components add more value by the combination andintegration with chemical sensors such as the ISFET [7], the µTAS orientation wasestablished under the supervision of Prof. Van den Berg. In 1994 the inter-disciplinary OSF(research stimulation fund) project named “Micro total analysis systems (µTAS), societalimpact and fundamental micromechanical, optical and chemical aspects” was started,consisting of technical research in the areas of micromechanics, chemistry and optics as wellas non-technical research in the influences and mechanisms of technical possibilities on law,political decision-making and external stakeholders. The aim is to combine the individualdiscipline-specific knowledge and facilities to make bigger steps forward in µTAS research.The work presented in this thesis has been performed within the micromechanics sub-project“Principles and methods for Micro Fluid Handling Systems (MFHS)” [5]. The aims are toexploit the available technologies to design micro fluid handling components that can beused in µTAS systems. From these components functional analytical and / or numericalmodels need to be derived and compared with experimentally obtained characterization data.Although technology development was not considered as a main issue in this project,microsystem design is closely related to the used fabrication processes [31,28], which oftenneed to be adapted in order to be able to make the design. Hence in chapter 5 a number oftechnological aspects will be treated in detail.

1.4 Outline

In the second chapter first a description will be given of microsystem technology which willshow that there is an overlap with the areas of nanotechnology and precision mechanics.After a historic treatise of the important developments of the research area and of µTAS inparticular, the role of modeling and design and the strong interaction and drive fromintegrated circuitry design will be discussed. Many similarities exist between microsystem

4 Chapter 1

designing and integrated circuitry design. However micromechanics-specific issues ask foradapted or new design tools. The chapter will end with a look at the expected bright future ofespecially µTAS.

The third chapter deals with the effects of downscaling on fluidics. Some physicaleffects will start to dominate when scale reduction is applied whereas other effects can beneglected. These aspects lead to a new consideration of fluidic system design since somephysical effects such as for instance turbulence cannot longer be used for fluid mixing but onthe other hand the channel surface / volume ratio for example increases which demands forother designs. By estimating the different physical mechanisms in the fluid flow equations, asimplification can be obtained for stationary flows. With this discussion the use of “macro”fluidic models in this thesis is argued. These models form the basis for the derivation of thehydraulic resistance for different channel geometries that can be made with micromachiningtechniques.

The following chapters are dedicated to applications. In the fourth chapter thedevelopment of the pressure-flow sensor will be described. The sensor is based on measuringpressures such that it can be used both to measure pressures and volume flow-rate. Simpledesign formulas are derived, the fabrication process will be described and measurementresults will be discussed.

Microvalves are described in chapter 5, 6 and 7. For modeling the resistance inespecially check valves, numerical routines are implemented such that the coupled fluid-dynamic induced forces and the resulting structural mechanical deformations can be solved.This theory is described in chapter 5, whereas chapter 6 describes passive and active valvedesigns and their fabrication processes. Established as well as new techniques are used. Animportant and very powerful technique is the use of selective fusion and anodic bonding toobtain moving valve spring structures. It is shown that recently developed fusion bondingtheories [17] can be successfully applied to obtain both, bonded and non-bonded areas.Besides bonding, much attention is paid to exploit the crystal orientations in monocrystallinesilicon in a more comprehensive way as been shown earlier in literature. Both <100> as wellas <111> oriented silicon is used. With the presented methods for example very thin, welldefined <111> oriented membranes can be made which are wafer thickness independent andfabricated in a simple wet chemical etching process. These membranes can be designed withdifferent geometries and dimensions which offers the possibility to make check valves withdifferent characteristics in one wafer. The seventh chapter deals with descriptive models forthese valves and measurement results to validate the analytical and numerical simulationdata. Finally, the last chapter gives an overview of the results described in more detail in thisthesis and provides an outlook for future research.

Introduction 5

References

[1] I. Amato, “Microchip arrays put DNA on the spot”, News focus in Science, Vol 282,(1998)

[2] R.C. Anderson, G,J, Bogdan, A. Puski, X. Su, “Advances in integrated geneticanalysis”, in: D.J. Harrison, A. van den Berg, Micro Total Analysis Systems, (1998),11-16

[3] E. Bassous, H.H. Taub, L. Kuhn, “Ink jet printing nozzle arrays etched in silicon”,Appl. Phys. Lett., vol. 31-2, (1977) 135-137

[4] C.A. Belsterling, Fluidic systems design, Wiley-Interscience, New York, (1971)[5] A. van den Berg, “Micro Total Analysis Systems (µTAS), Societal impact and

fundamental micromechanical, optical and chemical aspects”, OSF-program,MESA/CSTM, (1994)

[6] A. van den Berg, T.S.J. Lammerink, Micro Total Analysis Systems: Microfluidicaspects, integration concept and applications, in: A. Manz, H. Becker, MicrosystemTechnology in Chemistry and Life Science, Topics in Current Chemistry, Vol 194,Springer-Verlag, Berlin Heidelberg, (1998) 21-49

[7] P. Bergveld, “Development of an ion-sensitive solid –state device forneurophysiological measurements”, IEEE Trans. Biomed. Eng., BME-17 (1970) 70-71

[8] E.M. Blaser, W.H. Ko, E.T. Ton, “A miniature digital pressure transducer”, 24th

Annual Conf. On Eng. In Med and Biol., (1971) 211[9] L.A. Christel, K. Petersen, W. McMillan, M.A. Northrup, “Nucleic acid concentration

and PCR for diagnostic applications”, in: D.J. Harrison, A. van den Berg, Micro TotalAnalysis Systems, (1998), 277-280

[10] C.S. Effenhauser, “Integrated chip-based microcolumn separation systems”, in: A.Manz, H. Becker, Microsystem Technology in Chemistry and Life Science, Topics inCurrent Chemistry, Vol 194, Springer-Verlag, Berlin Heidelberg, (1998) 51-82

[11] M. Elwenspoek, T.S.J. Lammerink, R. Miyake, J.H.J. Fluitman, “Towards integratedmicroliquid handling systems”, J. Micromech. Microeng. 4, (1994) 227-245

[12] R.P. Feynman,“There’s plenty of room at the bottom”, J. Micromech. Systems 1-1,(1992) 60-66

[13] R.P. Feynman, “Infinitesimal machinery”, J. Micromech. Systems 2-1, (1993) 4-14[14] K. Foster, G.A. Parker, Fluidics: components and circuits, Wiley-Interscience, London,

(1970)[15] R. Fontana, “Magnetic Thin Film Heads, a Review on Processing Issues,” ECS Proc.

Symp. Magn. Mater. Process Devices 90-8, (1990) 205-219

6 Chapter 1

[16] P. Gravesen, J. Branebjerg, O.S. Jensen, “Microfluidics – a review”, J. Micromech.Microeng. 3, (1993) 168-182

[17] C. Gui, M. Elwenspoek, N. Tas, and J. G. E. Gardeniers, “The effect of surfaceroughness on direct wafer bonding”, J. Appl. Phys., Vol. 85-10, (1999) 7448-7454

[18] R. Hsiao, “Fabrication of magnetic recording heads and dry etching of head materials”,IBM Journal of Research and Development, vol. 43 no. 1/2, (1999) 89-102

[19] Pressure and airflow sensors, Product information catalog 15, Honeywell Micro SwitchDevision Sensing and Control, Freeport, Illinois 61032, USA, (1995).

[20] J.M.Kirshner, S.Katz, Design theory of fluidic components, Academic Press Inc., NewYork, (1975)

[21] M.U. Kopp, M.B. Luechinger, A. Manz, “Continuous flow PCR on a chip”, in: D.J.Harrison, A. van den Berg, Micro Total Analysis Systems, (1998), 7-10

[22] W. Kuehnel, S.J. Sherman, “A surface micromachined silicon accelerometer with on-chip detection circuitry”, Sensors and Actuators A45-1, (1994) 7-16

[23] T.S.J. Lammerink, N.R. Tas, M.C. Elwenspoek, J.H.J. Fluitman, “Micro-liquid flowsensor”, Sensors and Actuators A, (1993) 45-50

[24] BioChips, advances in DNA array and microfluidics technologies, A “Moore’s law”phenomenon in biotech, Report Lehman Brothers Inc., New York, November 21,(1997)

[25] H.T.G. van Lintel, F.C.M van de Pol, S.Bouwstra, “A piezoelectric micropump basedon micro-machining of silicon”, Sensors and Actuators 15, (1988) 153-167

[26] A. Manz, N. Graber, H.M. Widmer, “Miniaturized total chemical analysis systems: anovel concept for chemical sensing”, Sensors and Actuators B1, (1990) 244-248

[27] A. Manz, “Design secrets and new dimensions in field driven separations for micrototal analysis systems (µTAS)”, Proc. Solid-State Sensor and Actuator Workshop,Hilton Head, USA, (1996) 1-4

[28] K.W. Markus, “Developing infrastructure to mass-produce MEMS”, IEEE Comp.Science & Eng., Jan-Mar (1997) 49-54

[29] S. Middelhoek, “Quo vadis silicon sensors?”, Sensors and Actuators A41-42, (1994)1-8

[30] Nexus task force, Market analysis for microsystems 1996-2002, (1998)[31] E. Peeters, “Challenges in commercializing MEMS”, IEEE Comp. Science & Eng.,

Jan-Mar (1997) 44-48[32] S. Shoji, M. Esashi, “Microflow devices and systems”, J. Micromech. Microeng. 4,

(1994) 157-171

7

22 HHIISSTTOORRYY AANNDD LLIITTEERRAATTUURREE SSUURRVVEEYY OOFFMMSSTT AANNDD µµTTAASS

This second chapter sketches an overview of theachievements within the relative young “microworld”. Adescription of the work area of microsystems technology isfollowed by a short historical list of milestones. After thismicrosystem-oriented reflection, the micro total analysishistory will be discussed with some interesting successesreported in literature. Design and simulation tools becomemore important as microsystems technology matures.Developments and specific problems are discussed thatmainly relate on the differences with IC technology. Finallyfuture developments are treated such as achieved andpredicted market growth.

2.1 Classification of microsystems technology

The definition of microsystems technology (MST) is not very clear. Often the definition isassociated with the size of objects that are fabricated. In figure 2.1 an overview is given ofthe characteristic length scales of different species and physical effects in relation with thearea covered by different micro devices [66,37,91,39]. At the top the areas are showncovered by nanotechnology, microtechnology and precision mechanics respectively. Fromthis it can be observed that a big overlap exists between the different research areas. Figure2.1 indicates that characteristic length scales in the micrometer range are not unique for

8 Chapter 2

microtechnology. A better definition is found in relation with the fabrication techniquesused. In nanotechnology also referred to as molecular technology, the construction methodsconsist of building structures out of basic elements, molecules or atoms [20]. On the otherhand precision mechanics uses conventional techniques such as milling, stamping andelectro discharging. For microtechnology the basic fabrication tool is photolithography.Although other fabrication methods such as moulding methods like LIGA [10,21] also areput under the nominator of microsystems technology, lithography was involved in definingthe final sample dimensions. Concluding, the classification of nano-, micro- or precisionengineering fabricated samples is not always clear. In this thesis all applied microfabricationprocesses are based on lithography.

µ-technology

precision engineering

conventional pumps chemical plants

conventional reactorsµ-reactorsµ-motors& gears

nanotechnology

µ-roughness / etch pits / pyramids

µ-channel widths µTAS

ICchips

µ-pumps & valves

ICpads

ICdie printed circuit board

Röntgen radiation ultra violet visible infrared microwave radio frequency

hair

mist / fog spray raindroplet

smog smoke dust sand

metalions proteins long-chain molecules

coiled extended gas

molecules virus

cells red blood cellmean free pathoxygen at STA.

bacteria

atomicradii

ionicrange

molecularrange

macromolecular

microparticle

macroparticle

Å nm µm mm cm m km

10 m-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Figure 2.1 Typical dimensions and the application range of nanotechnology, microtechnology andprecision engineering [66,37,91,39].

Although research in microfabrication has earned an important place withinmanufacturing technology, the nomenclature is not unambiguous. Different names are usedto cover the research area such as “MicroElectroMechanical Systems”, abbreviated to“MEMS”, used in the United States, the European definition “MicroSystem Technology”(MST) and the Japanese “micromachine” [30]. Essentially, “MST” emphasis the technology

History and literature survey of MST and µTAS 9

side of making micron-sized devices. So a wide range of different engineering processes iscovered, related to precision- and nanoengineering as well. With “MEMS”, the close relationwith electronics and the system aspect is expressed, which is only true for devices such aselectrical sensors. The word “micromachine” arose from the idea making miniaturizedmachines independent of the applied fabrication tools. Since often the different names areused to indicate the same research area, no distinction will be made in this thesis.

2.2 Microsystem technology history

The history and development of microsystems technology is closely related to that ofelectronic circuit technology. In table 2.1 a chronological overview is given of importantevents. A milestone was the use of semiconductor properties to fabricate an electricalswitch. The bipolar transistor was born in 1947 [7,79]. For this invention, Shockley, Bardeenand Brattain of the Bell Telephone Laboratories were rewarded with the Nobel price in 1948.Not aware of the world-changing importance of this discovery, bulky but rather reliabletriode bulbs would still be used for many years. Only after it became clear thatsemiconductors like germanium and silicon opened a way to high-density integrated circuits(IC), a fast growing research in these materials and IC technology was started. C.S. Smith,employed at the Case Western Reserve University but spending his sabbatical leave onresearching the electromechanical characteristics of semiconductors at the Bell Laboratories,published about the piezo-resistive effects in silicon and germanium [82]. He found that thiseffect translated into a gage factor was 10 to 20 times higher than for metal strain gages. Thediscovery of this strong piezo electric effect has stimulated pressure sensor developments,which led to the start of microsystems technology. In 1958, more than ten years after the firstbipolar transistor, the first integrated circuit was made by J. Kilby at Texas Instruments aswell as the first planar silicon transistor by R. Noyce from Fairchild Semiconductor. Fromthis moment on it was clear that IC technology would cause an electronic revolution since itbecame possible to obtain huge electronic functionality per square mm. In the same yearKulite, Honeywell and Microsystem came with commercially developed strain gauges afterwhich Kulite further developed diffused resistors on thin silicon substrates that could be usedas membranes for measuring pressure differences. Honeywell improved this design by usingmilling to thin the silicon substrate to fabricate pressure sensor membranes (1966).

Since precision engineering techniques were used to obtain membranes, the firstmicromachined pressure sensor had yet to be made. In 1967 Finne and Klein [27] publishedthe first anisotropic etching technique in silicon. This technique still plays an important rolein bulk micromaching, fabrication of micromachined structures using the removal of wafer(bulk) material. The Kulite company was the first to fabricate pressure sensors with

10 Chapter 2

anisotropically etched silicon membranes (1976). At the same time this can be regarded asthe first (bulk) micromachined sensor. The start of microsystems technology however tookplace in 1967. Nathanson [58] published a transistor with a high quality bandwidth filter.

year event inventors – companies ref.194719541958195819581961196619671967

1969197019701971197119741975197619771977197919801982198619881988198819891990199119911993

First transistorPiezoresistivity of silicon and germaniumGermanium ICPlanar silicon transistorCommercially developed strain gaugeDiffused resistors on thin silicon substratesMilling in silicon to obtain sensor membranesAnisotropic etching of siliconThe resonant gate transistor: 1st surfacemicromachiningIntroduction of anodic bonding of glassISFETIsotropic etching in silicon to obtain membranesFirst microprocessor Intel 4004Monolithic integrated pressure sensorHigh-volume pressure sensorGas chromatography system on a waferAnisotropic etched pressure sensorMonolithic capacitive pressure sensorThermal printing headMicromachined accelerometerTorsional scanning mirrorFirst MOS integrated accelerometerLithography galvanoforming and plastic moldingSilicon fusion bonding in MSTPiezo electric micropumpMicromotorµTAS concept presentedThermopneumatic micropumpMicromachined capillary electrophoresis systemµTAS system using micro pumpsMicro-liquid dosing system + electronics

W. Shockley, J. Bardeen, W.H. Brattain – Bell LabsC.S. Smith – Bell LabsJ. Kilby – Texas InstrumentsR. Noyce – Fairchild SemiconductorKulite Inc., Honeywell Inc., Microsystem Inc.Kulite Inc.Honeywell Inc.R.M. Finne, D.L. Klein – Bell LabsH.C. Nathanson et al. – Westinghouse

G. Wallis, D. PommerantzP. Bergveld – University of TwenteKulite Inc.Intel Corp.E.M. Blaser et al. – Case Western Reserve Univ.National SemiconductorS.C. Terry – Stanford UniversityKulite Inc.C.S. Sander et al. – Stanford UniversityE. Bassous et. al - Texas InstrumentsL.M. Roylance, J.B. Angell - Stanford UniversityK.E. Petersen et al. – IBMK.E. Petersen et al.– IBME.W. Becker, et al. – KFZ KarlsruheK.E. Petersen et al. – Nova SensorH.T.G. van Lintel et al. – University of TwenteL.S. Fan et. al. – University of BerkelyA. Manz – Ciba Geigy GmbH.F.C.M van de Pol –University of TwenteD.J. Harrison, A. Manz – University of AlbertaB.H. van der Schoot et al. – University of NeuchâtelT.S.J Lammerink et al. – University of Twente

[7,79][82][50][50][50][50][50][27][58]

[90][11][50][50][12][50][85][50][70][8,9][68][62][63][10][64][45]

[24,25][46][65][35][72][41]

Table 2.1 List of important events in the history of microsystems technology and references topublished literature.

The design consists of a field effect transistor (FET) combined with a mechanicalelectrostatic oscillator driving the gate. To fabricate the mass-spring oscillator gate structure,a gold layer was plated over the diffused source and drain. A sacrificial layer of resist wasused as a spacer to define the gate insulation layer. In fact this is a very revolutionary devicesince it integrates micromaching with IC technology (integrated micromachining, iMEMS),it is the first surface micromachined structure and the first time that micromechanical


structures are used for their dynamical behavior to improve electronic characteristics.Recently the benefits of micromachined structures for implementing electronic functionsstarted to get attention again. Examples are voltage tunable capacitors, acoustic resonatorsand high quality factor coils patterned on glass [60,26] and microrelais [69,86,92].

Whereas IC technology is restricted to fabrication processes that do not destroy thefunctionality of the diffused transistor areas, microsystems technology explored newtechniques. Combinations of surface and micromachining techniques were applied usingboth ceramic materials as well as metals and polymers. Stacking different wafer layersoffered new possibilities. With bonding techniques caps and channels could be closed andstructures could be built by several bulk micromachined layers with high precision since nointermediate bonding layers were needed. First, anodic bonding was reported in 1969 by G.Wallis [90]. With use of a strong electric field, applied between a metal or semiconductorand a glass layer a strong bond was obtained. In 1988 K. Petersen presented the introductionof fusion bonding in microsystems [64]. Chemical mechanical polishing, used forplanarization of IC structures could also be used to reduce surface roughness to a level suchthat a fusion bond could be established [71,33].

Besides the combination of different materials with silicon technology, also processtechniques became in use, fully based on non-silicon materials such as ion-beam etching,thick resist and synchrotron radiation lithography of PMMA. The latter method wasoptimized to obtain a fast reproduction method by using the polymer structures forelectroplating a metal. After washing-out the polymer a metal mould is obtained which canbe used with casting resins, embossing, or injection moulding. This so called LIGA(LIthography GAlvanoforming) method was presented in 1986 [10] but due to the high costsof the synchrotron source it never became a generally available fabrication tool. Cheaperalternatives were proposed. Examples are the use of thick, UV-light sensitive photo-polymers like SU-8 (UV-LIGA) [19] and dry etching techniques, such as reactive ionetching in silicon (DEEMO) [23], for fabrication of the first mould for electroplating.Depending on the strategy and background of the research and production labs, ICcompatible processes with electronics integration are used or it is chosen for a modularconcept focussed on device optimization with separately connected electronic circuit dies.Within MESA+ the latter strategy is followed. These aspects will be discussed in theparagraph about future prospects.

2.3 Classification of µTAS

The name “Micro Total Analysis Systems” or abbreviated to µTAS originates from the ideasof A. Manz, N. Graber and H.M. Widmer, presented in 1989 and is described in the article

12 Chapter 2

“Miniaturized total chemical analysis systems: a novel concept for chemical sensing” [46].In this article the benefits of downscaling on chemical analysis are discussed such as fasterresponse times, more efficient chromatographic separations and reduction of chemicalsconsumption. To give a definition of a µTAS, three situations of an “ideal” chemicaldevice/system are discussed: the ideal sensor, the total analysis system (TAS) andminiaturized TAS (µTAS).

The ideal sensor is only capable to relate a specific chemical concentration to anelectric output signal (figure 2.2A). Separate electronics are needed to process these signals.In fact the sensor is a passive element in the sense that no sample treatment is involved. Inmany cases the sensor will be immersed directly in the sample solution which must bemanually pre-treated.

Figure 2.2 Schematic diagrams of an ideal chemical sensor versus total analysis system and µTAS

A total analysis system comprises besides sensors also sampling and sample pre-treatment equipment. All processing in a TAS occurs in a closed system. This means that afull analysis will take much less time and yield a better quality than in case a macro analysissystem is used. This quality is improved if shorter connections and less internal volume areused. Also analysis and cycling times are shortened. Miniaturizing of sample treatment andsensor components to a small hybrid or technological integrated system leads to a µTAS.Manz et al. stated that their aim of µTAS research is related to gaining better performancethrough miniaturization rather than obtaining a reduction of size. With use of sophisticatedmeasurements and sensing techniques, combined with modern electronics, a µTAS systemcan be extended towards a smart, self-calibrating piece of measurement equipment.


2.4 History of micro chemical analysis systems

Although Manz et al. presented the concept in 1989, the combination of chemical analysisand MST was utilized before. In 1970 a modified field effect transistor (FET) was publishedby Bergveld to measure ion concentrations [11]. This ion-sensitive FET (ISFET), developedat the University of Twente, can be regarded as the first chemical sensor made with ICtechnology processes. The gate layer of the FET is removed such that the electric double-layer, existing in an ionized solution at the interface of the silicon-dioxide gate insulationlayer, will build up an electric field, which steers the conduction of the FET channel. Doublelayers would play an important role later on in µTAS.

S.C Terry [85] presented for the first time a miniaturized system that meets thedefinition of µTAS. The system consisted of a gas chromatograph (GC) separation channel(1.5m x 200µm x 30µm) isotropically etched in monocrystalline silicon and sealed with ananodically bonded glass substrate. A modular mounted solenoid valve with a nickelmembrane (seat is etched in the silicon) and a modular thermal conductivity sensor (TCD),made with IC processes are integrated. The whole system fitted on a 2-inch wafer, whichmeans an enormous down scaling of outer dimensions. Compared to conventional GC’showever the performance was not improved due to the rather large, rectangular cross-sectionof the channel. With better separation channels the authors expected to reach a performanceimprovement of two compared to conventional systems.

In liquid flow control, a milestone was set by Van Lintel [45]. With a siliconmicromachined pump he demonstrated the possibility to pump liquid flows as might beneeded for integrated microanalysis systems. His design was based on two membrane checkvalves and a piezoelectric actuator for driving the pump membrane. An alternative actuatorwas reported by Van der Pol [65]. By heating up the air in a cavity above the pumpingmembrane, large displacements at high pressures could be obtained yielding higher pumpstrokes. After this many different actuator and valve principles were presented such aselectrostatic actuation [93] and valve-less pumps [83] using the direction-sensitive hydraulicresistance of diffuser nozzles for directing the flow.

After this period µTAS related research made big progress. An example is the high-pressure liquid chromatograph (LC), fitting on a 5x5mm die, presented by A. Manz et al.[47], although some problems existed with the integrated conductivity sensor. The pressuredelivery and switching of fluid streams still occurred with external, conventional equipment.B. van der Schoot et al. presented an example of a hybrid analysis system that demonstratedmaximum integration of components. It incorporated a potassium ion sensitive ISFET andtwo piezo pumps, one for sample delivery and one for washing the sensor. A similarprototype system with two pumps with feed-back control by two thermal mass-flow sensors,

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a light absorption cell and scaled electronics was demonstrated by T.S.J Lammerink et al.[41].

These mechanical pumps however were rather complex and would make theintegration with other sensors and separation channels not an easy task. Using longseparation channels with small cross-section diameters means high pressure drops and thusthe need for micro pumps that could deliver high pressures. An alternative electrokineticpumping mechanism, specially suited for small channels was used by D.J. Harrison [48,35].Due to a strong electric field of up to 1500V/cm over the channel length, flow velocities canbe obtained up to 1cm/s with electroosmotic pumping. This mechanism got more and moreattention due to its simplicity. With crossing channels with electrodes at the ends that can beindividually polarized a simple fluid switch is constructed. The need of high electric fieldsand the dependence on the charge of the double layer (pH) limits the application of thisprinciple. Electrophoresis, boosted by the fast-increasing DNA analysis became thedominating separation method. These methods will be treated in more detail in the nextchapter. At this moment electroosmosis and electrophoresis together with DNA sequencingmethods dominate the world of µTAS research.

2.5 Designing and modeling of microsystems

After existence of more than 25 years, microsystems technology is getting mature. Productslike pressure sensors, inkjet nozzles and airbag sensors are commercially sold for many yearsand expectations of µTAS systems are high [44]. Since time-to-market plays an importantrole [49] and test-runs to make prototypes are very expensive, there is a growing demand onmodeling and design tools [73,61]. At this moment these tools are still in their infancyalthough much effort is spent on development [74,75].

Since microsystems technology finds its roots in IC technology, links are made toVLSI (Very Large Scale Integration) when looking at tools to facilitate the design processsuch as the description language VHDL (Very High Speed Integrated Circuit HardwareDescription Language). The aim is to have a complete set of complementary design toolsthat will lead to the so-called “virtual microtransducer fab” [88,89]. Part of this set are masklay-out programs with design rule checkers, process simulators (Technology ComputerAided Design, TCAD), device simulators and system simulators. The flow scheme of figure2.3 distinguishes the different design stages that are followed during the development of amicrosystem. Although the arrows indicate a flow sequence, in practice, the process willshow an iterative behavior. First, product specifications are needed. At every design stage,the results will be compared with these specifications in order to check whether the design isok or changes should be made. After the specifications are clear, a first conceptual design is


made. Different concepts to meet the specifications are judged based on intuition andknowledge of the designer, with use of stored information in the form of solutions used inthe past, process and materials databases and design rules. In order to speed-up the decisionprocess about which solutions meet the requirements, simple analysis tools can be used suchas simple design formulas or simple numerical models. With use of design programs, thegeometries of the concept design can be drawn and initial mask and process designs can bemade. During this stage a close interaction between specialists in different disciplines isnecessary in order to get a compatible design between for example electronic circuitry,packaging and sensor design.

Since microsystem design is closely related and often strongly restricted by thefabrication processes, the fabrication processes must be determined in an early stage. Duringthe process development, small changes to the design can be made in order to improve themanufacturability without disturbing the functionality too much. Tools are materials andprocess databases, combined with process simulators. The results are improved processdescriptions and adapted geometrical layouts.

The further developed design will be modeled in more detail in the componentsimulation stage. Numerical simulation packages can be used, combined with analyticalmodels for optimization. These simulations will result in compact mathematical behavioraldescriptions of the components, to be used as input in the network simulation programs ofthe following system simulation stage. In this system simulation stage, the dynamicbehavioral descriptions of all components and subsystems, defined in the different domains(e.g. electronic circuitry, mechanical or chemical behavior of the sensor) will be coupled andtheir mutual interaction is analyzed.

When these stages are successfully passed, a prototype can be built. Together with thedeveloped process design and mask set, a first system is made for checking empiricallywhether the design meets the specifications. Process information, obtained duringmanufacturing must be passed on to the layout and process designers. During the last stagethe prototype is tested and characterized. A load database is used as input to test for examplethe endurance.

With this design trajectory, precious “trial and error” designing can be reduced and amore structural optimization of designs can be achieved. On the other hand a goodintegration with different disciplines is facilitated which is a constraint in especiallyintegrated CMOS compatible MEMS. Computer systems can be coupled and flexible dataexchange between the electronic and MST designers becomes possible [56].

16 Chapter 2

design geometriesmasksprocess designs

simulated device geometriesimproved process designs

I/O device behavior

I/O system behavior

prototype

device test datatesting & characterization

layout & design

process simulation

component simulation

system simulation

prototype fabrication

productspecifications

verification

intuitionknowledgedesign rules(mask) design programsanalysis toolsdevice databasesprocess databasesmaterials databases

process databasesmaterials databasesprocess simulators

simulation packagesanalytical modelsdomain coupled solversmaterials databases

network simulators

fabrication facility

testing & characterization tools

TOOLS STAGES DATA FLOW

Figure 2.3 Design stages and tools and data flow in microsystem development: the developmentprocess is an iterative process where backward steps might be needed. To save costs anddevelopment time, backward steps at later stages need to be avoided.

For micromechanical system development the IC implementation of a virtual fabcannot simply be copied. There are important differences to distinct [61]. The maindifference is the strong multi-domain nature of MST. Transducer systems always actbetween two or more physical domains. For fluid sensors such as the pressure / flow sensor,at least the hydraulic, mechanical and electrical domains are involved since a pressure drop,induced by a fluid flow deforms a membrane which causes an electrical resistance orcapacitance change. For electrical low-power and low-speed systems however only theelectrical domain needs to be taken into account. These domains need to be coupled in orderto be able to describe the total system. Practically, the more physical domains are involved,the more interfaces between the domains exist and thus the more complex the design andsimulation of the device becomes. The existence of many interacting domains requiresdesigner’s multidisciplinary knowledge about each of the domain. Often this knowledge


needs to be very specific. The small dimensional scale of the devices sometimes requires formore advanced mathematical models (e.g. non-linearity) and for example special sensing oractuation methods as will be discussed later on. An important issue in sensor design relatedto this is packaging [6]. With different domains, good solutions need to be found to solve thenon-electrical interfaces with the surroundings such as fluids interconnects [87,55].

Electrical components often can be easily translated into black boxes with only a fewin and output (I/O) ports. Resistors, capacitors and inductors only have one input and oneoutput port whereas transistors have three ports. Structures in the mechanical domain oftencannot be treated as lumped elements but must be modeled as a high-order discretisizedcontinuum, which means that the number of I/O ports or interfacing degrees of freedom ismuch larger than for electronic components. As will be shown in chapter 6 and 7 thedeformation shape of a valve membrane determines the three dimensional flow profilethrough the valve.

A third difference, related to this is the geometric difference between the IC and MSTstructures. Whereas IC structures are often planar and described with simple geometries,MST structures can be geometrically much more complex. The importance of the thirddimension and the complexity of the geometry results again in more degrees of freedom andthus in increasing computation times during simulations and a more complex way ofdescribing the geometries. Non-linear effects, caused by high mechanical aspect ratios willeven more increase the required amount of computation power. TCAD programs like 3Detch simulators [14,81,52,4] are needed to predict the geometries of (an-) isotropicallyetched structures out of the process conditions and the masks used or the other way around,masks are generated from the required 3D CAD models. Preferably these simulators arebased on physical models [84] and take changes or etching solution refreshment into account[78].

The functionality of micromachined components is closely related to the appliedfabrication processes [61,75,49]. For example due to thermal loads and intrinsic stresses indeposited layers the mechanical behavior is influenced. In extreme cases this can lead tobuckling and fracture of membranes and double-sided clamped beams. Especially surfacemicromachining techniques (depostion and removal of layers) suffer from these phenomena.Therefore not only a good understanding of the characteristics of the bulk materials isneeded but also characterization of the fabrication process. With multi domains, knowledgeof the influence of the process steps on each domain is necessary. Standardization ofcharacterized process sequences and device and material process databases [80] will help indealing with this matter. Since MST is not restricted to CMOS compatible materials but usesmore different materials including polymers and metals, knowledge of materialcharacteristics plays an important role.

18 Chapter 2

This overview makes clear that essential differences exist between the VLSI and MSTdesign. Therefore special tools need to be designed, adapted to the demands ofmicrotechnology. It is expected that development times will be longer than in VLSI [61].

2.6 Device and system simulation tools

Simulation of the properties of devices and system can be done in two different ways.Differential equations that govern the problem can be solved analytically or numerically inthe physical domain (continuum modeling) or the problem is split up into separate functionalelements for which the behavior can be described in terms of stimulus-response. The lattermethod is a standard tool used in electronic circuit development and often referred as “circuitanalysis software” or “network simulation software”. Making functional blocks out of acontinuum model is also called “lumped element modeling” or “macro modeling”. The“black boxes” with in- and output ports are called “lumped elements”, “macro models” or“behavioral models”. This way of modeling is very suitable for system design since we oftenregard a system as a composition of individual functions. These tools are mainly developedfor electrical circuit design. Therefore software packages like MicroSim’s Pspice [67] havestandard electronic components implemented such as voltage and current sources, passivecomponents as well as transistors etc. Besides these pre-defined component models, the usercan implement specific behavioral models. The energy lines (wires) between the componentsconsist of current flows and defined voltage levels at the ports. Additional signal lines forspecial purpose control are often available. In chapter 4, PSpice will be used to model asimple second order system. These programs are very convenient for designing electroniccircuits for reading-out sensors for example. The other physical domains however, must betranslated to the electrical domain. In case of the pressure / flow sensor this is not a problem.When the complexity of the microsystem increases and more different physical domains areinvolved, a general description would be more convenient. Instead of complementaryvoltage and current pairs, the generalized energy terms “effort” and “flow” can be usedrespectively. A structured graphical method to describe such systems is the use of bondgraphmodels [13]. An example of simulation software based on bondgraphs is 20-SIM [1]. Thedisadvantage of such programs is that for electronic design the user must build mostcomponents whereas electronic design kits have libraries containing network models of mostknown ICs. Another disadvantage is the higher level of abstractness of bondgraphs makingthe implementation of electronic circuits less transparent.

The descriptive models for the lumped elements needed in network simulation must beobtained from the differential or integral equations describing the physical problem.Sometimes these relations can be simplified and solved analytically such that closed


formulas can be obtained. Often there are no appropriate analytical solutions available. Areason for this can be the difficulty to meet boundary conditions due to for instance thecomplexity of the geometries. Other reasons can be the complexity of the equations or thenumber of dimensions involved. In micromechanics the differential equations for thedeflection of mechanical structures, such as double sided clamped beams and membranes,often get non-linear. Due to high aspect ratios of for example long, thin, double-sidedclamped beams and thin membranes with high diameters, the initial rather constant stiffnessdue to bending stresses increases with non-linear terms due to in-plane stretching effects forlarger deflections. For fluid mechanics the differential equations can be simplified byneglecting inertia terms at low Reynolds numbers as will be discussed in the next chapter.

Different numerical software packages are available for solving the domain governingdifferential equations, which can be distinguished by the types of the applied discretizationmethods. Often the choice of method is related to the characteristics of the physical problem.Deformation of material can be conveniently described with a numerical grid as shown isfigure 2.4A. This type of grid is obtained for example with finite element discretizations(FEM) [16]. On the other hand, flow problems can be conveniently described byconservation laws based flows through a grid of discrete boxes. This results in finite volume(FVM) grids as shown in figure 2.4B. Both methods use a full numerical grid covering thedomain space. For bounded problems where one is only interested to know the solutions atthe boundaries that enclose the mathematical domain such as electrostatic or capacitiveproblems [36], these methods need a large number of degrees of freedom (DOF). Rewritingthe differential equations on the interior can reduce the number of DOF. Internalconservation laws can be rewritten to flux relations over the boundaries using the Gaussianintegral relation. The resulting numerical solution methods are called boundary elementmethods (BEM) or panel methods. Numerical grids obtained with this method will look likefigure 2.4C. In chapter 3 a numerical solution method will be used based on fitting a generalmatching function on the mathematical domain such that boundary conditions will be met indiscrete points. Similar to BEM only a numerical boundary grid is needed. A drawback ofthese methods is that in contrast with FEM and FVM no sparse, symmetrical systemmatrices are obtained and that solving the matrix-vector equations will take morecomputation power. For sparse band matrices, special optimized routines are available.Whether the benefits of DOF reduction or the drawbacks of solving full matrices winsdepends on the specific application. For the user who is not interested in solutions on thedomain interior, the need of meshing only the boundaries might be the fact that counts. Afourth method of discretization is finite difference modeling (FDM). Numerous differentvariants exist. The numerical grids are generated similar to that of FEM but without thedefinition of elements.

20 Chapter 2

A B C

elements numerical grid points elements numerical grid points

Figure 2.4 Numerical grids meshed with A) finite element, B) finite volume and C) boundaryelement methods

Different software packages are commercially available for modeling continuum problems.Examples of structural mechanics and fluid mechanics software are listed in table 2.2 with adescription of the physical domains that can be modeled. In this thesis we used ANSYS 5.3since it can deal with multiple domains such as mechanics and fluid dynamics, has facilitiesto manipulate data internally using an APDL (ANSYS Parametric Design Language) and itcan run on a conventional Intel-based computer. None of these programs incorporates a bi-directional coupling between the structural mechanical and fluid mechanical domains asneeded for simulating the hydraulic resistance of valves for stationary flows, although Ansysprovides possibilities for acoustic-structural coupling. For stationary flows, these couplingfacilities need to be programmed by combining different programs like Cosmos and Fidap[40] or using a package like ANSYS combined with user programmed routines. This will betreated in more detail in chapter 6.

Currently, new software is being developed especially adapted to the domain couplingproblematic. An example is Microcosm’s MemCad [43], which consists of a set of domain-specific solvers like Abaqus, Fidap and FastCap (BEM for electronic capacitivecomputations) which are controlled by the MemCad shell. Unfortunately no fluid-structuralmechanics coupling has yet been implemented. For electro-hydrodynamic applications suchas capillary electrophoresis, Microcosm offers FlumeCad, a finite element solver based onFidap added with specially adapted user interfaces and numerical routines. SESES [77] fromNumerical modeling GmbH. as well as CFD-ACE+ [15] from CFDRC Inc. use a differentstrategy than Microcosm. Instead of combining existing solvers from other manufacturerswith a data management system, the packages are more integrated. With this strategy, itbecomes possible to solve the domain-coupled problems implicitly. CFDRC uses FEM,BEM as well as FVM discretizations, whereas SESES is based on FEM.


program manufacturer ref. disc. domainsAbaqusAnsys

Cosmos/MFluentFidapFlow3dNastran

Hibbitt, Karlsson & Sorensen, Inc.Ansys, Inc.

Structural Research and Analysis Corp.Fluent Inc.Fluent Inc.Flow Science Inc.MSC Inc.

[2][5]

[17][29][29][28][57]

FEMFEM

FEMFVMFEMFVMFEM

mechanical, thermal, acousticmechanical, thermal, fluid, acoustic,electric, magneticmechanical, thermal, fluid, electromagneticfluid dynamics, thermal, chemicalfluid dynamics, thermal, chemicalfluid dynamics, thermal, chemicalmechanical, thermal

Table 2.2 Examples of general purpose numerical continuum modeling packages and the applieddiscretization methods.

For system simulation, a link must be made between the continuum model simulatedwith one of previously described packages and the network simulator. Essentially there is adiscrepancy between the description of continuum models and distributed or lumpedmodels. A continuum model is described by I/O characteristics on an infinite number ofdegrees of freedom. With numerical discretization methods this number is limited althoughoften still very high. The system simulator needs lumped models of which the number ofDOF is reduced to a minimum. Currently much research is put into finding differentstrategies for achieving this [75,76]. For linear models different techniques can be appliedfor DOF-reduction, such as modal reduction with the use of system orthogonalization, usinga limited set of mode shapes and eigenvalues [51,76]. Non-linear models however showmore difficulties since no constant system matrices can be defined. In this thesis we aim atfinding analytical descriptions for the device properties. Numerical models are used to checkand if needed to upgrade the analytical descriptions. These formulas can be used to constructbehavioral models and are convenient to check the influence of different design parameterson the characteristics of the device.

2.7 Trends and prospects of MST and µTAS

Since microsystems technology is based on lithographic technologies comparable to thoseused in IC industry, the expectations of the growth of this new area have been high. It wasthought that Moore’s law [54] could be applied directly to micromechanical markets. Moorestated that every 18 months the transistor density on a chip would double which proved tohold for a long period and, although the law is slightly adapted, still does. This law wasdirectly translated to financial turnover of the IC industry. More than 25 years later, thesepromises could not be fulfilled for MST [61,6,53]. A reason for this is the fact that althoughMST has much simularities with IC technology, also a lot of differences exist as discussed inthe previous section, which increase the development time for MST products. Despite of

22 Chapter 2

this setback, MST is still very promising and growing. The 1998 Nexus Task Force MarketAnalysis MST [59] predicts a strong worldwide market growth from 14 billion US dollar in1997 to 38 billion by the year 2002. Currently hard disc drive heads followed by inkjetprinter heads dominate the MST market. The successful applications vary from low-costdisposable devices (e.g. inkjet printer heads) to automotive sensors (e.g. airbag sensors) andmedical devices (e.g. heart pacemakers).

During a long period products like pressure sensors and surface micromachined airbagsensors, made with mainly CMOS-compatible processes dominated [6,53]. Nowadays moreand more different non-CMOS compatible processes and non-silicon materials are used [59].Losing the compatibility restriction means more freedom to optimize the design of the MSTdevices. It also means that research in these new techniques becomes more important, suchas bonding methods and bulk etching. A cost reduction is achieved by introducing low-costreproduction methods. New materials such as polymers can be very favorable for disposableproducts.

Micro-chemical-analysis-system products are rather new in MST business. Howeverthese products cover the fastest growing MST markets [59]. The DNA analysis industry sawthe benefits from miniaturization and rapidly growing companies were established [3]. Overthe years from 1988 to 1995 DNA sequencing technology even showed a steeper slope indevelopment than the processor advances according Moore’s law [44]. Since electrophoresisand DNA sequencing techniques [38] can rather simply be implemented in a µTAS, this areais fast expanding. Successful companies are among others Affymetrix, founded in 1991,Caliper (1995), Genometrix (1993) Nanogen (1993) and Orchid BioComputer (1995).Regarding these developments observed at the µTAS conferences (1994-1996-1998), itshows that electrokinetically driven and controlled flows (electroosmosis) and separationmethods (electrophoresis) are of main interest [22,42]. Despite this overwhelming attentionto these research areas, conventional flow control with valves and pumps remains aninteresting field and might, due to the fast growing interest in µTAS, become more importantthan ever. Using high electrical fields in the electroosmosis and electrophoresis systemsrequires insulator materials such as nitrides, oxides and glass substrates. New materials andprocess technology research is pushed by these developments.

The success of electro-kinetic pumping has shown that for microsystems non-conventional physical mechanisms can be exploited which are not relevant to macrosystems.A further reduction of dimensions and internal volumes of µTAS will force designers to lookfor innovations, for example in the area of liquid transport, such as fluid manipulation usingcapillary forces. Recently examples for this have been published in Science [31,32,34].Electrically controlled hydrophilic “rails” on a hydrophobic surface along which a liquid canbe guided and propelled might give new possibilities for downscaling of micro fluid systems.


With a growing commercialization of MST and µTAS, modeling is getting more andmore important for the reasons given before. Funding by the U.S. government like theDARPA/ETO projects [18] will help to speed-up the evolution of the software tools. Thesuccess of airbag sensors and electro-kinetic pumping methods in µTAS has caused afocussing on sofware development on these markets. Products like MicroCosm’s FlumeCad[43] are a result of this.

In short it can be concluded that MST is now 32 years old and has made much progressup to the eighties. Unfortunately the developments stagnated up to the mid-nineties andcomparisons with the fast growing IC industry did not came true. Reasons for this can befound in the big differences in technology and design of MST devices with IC development.Therefore MST needs specially adapted, multi domain simulation software which iscurrently developed. Nowadays, micro total analysis systems research forms a positiveexception. A fast growing market for these systems arises and numerous successfulcompanies started since the mid-nineties. This success with the fast growing markets in otherworkspaces such as hard disk drive heads, inkjet nozzles and automotive and medicalapplication areas will push research in both CMOS compatible and incompatible processes.Development of design and simulation tools and research in understanding the physicalprocesses specially needed for microsystem design becomes of major importance.

24 Chapter 2

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26 Chapter 2

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30 Chapter 2

31

33 MMIICCRROO FFLLUUIIDD DDYYNNAAMMIICCSS

This chapter deals with the characteristics of micro fluidhandling systems. Miniaturization of microsystemsinfluences the functionality due to scaling laws as well aschanging physical effects. After a more qualitativediscussion of general scaling laws, using dimensionlessparameters, mathematical macro fluid dynamics equationsare described and adapted for miniaturized systems. Thephysical aspects of downscaling are treated in order tovalidate the further use of the macro-models in this thesis.With use of the simplified fluid dynamics theory, hydraulicresistances and velocity profiles in different channelgeometry shapes are derived. A very valuable tool for this isthe principle of virtual work and the torsion analogy withfluid dynamics.

3.1 Introduction

Miniaturization of analysis systems has several advantages. Portability and the possibility toreduce costs are two of them. The main goal of miniaturization is to exploit positivedownscaling effects to obtain for example faster and more accurate analysis results with lesspower and sample use. With downscaling new possibilities might become available thatcannot be obtained with macro systems. In order to find out about the positive scalingaspects, this chapter treats the quantitative and qualitative effects with an accent on thescaling properties of fluid dynamics. With quantitative aspects the effect of scaling on

32 Chapter 3

“macro” effects is meant. At a certain dimension level, physical effects appear that offer newdesign potentials. According to the generally accepted Murphy’s Law [30] there must bedrawbacks as well. These aspects will be treated in the next paragraph.

For modeling purposes of the fluid behavior in channels and for the designer ofmicroanalysis systems, knowledge is needed about the physics of flow in small channels.Questions need to be answered like “can we use macro models to simulate the resistance inchannels and valves?”. When are these models valid? In order to answer this, a start will bemade with the Navier-Stokes equations used in the “macro-world”. Assuming that thephysics are still valid for channels down-to a few microns, these macro models can besimplified.

After the quantitative discussion, the physics of liquid flows will be treated. Thisparagraph gives a validation for the use of the reduced macro-models that form the basis forthe proceeding chapters. Using these simplified Navier-Stokes equations for the stationaryflow situation, analytical solutions can be obtained for some simple channel cross-sectiongeometries. Etching profiles determine the number of cross-section geometries that can beused for microanalysis systems. Analytical models of the flow velocity for a range of mostcommon profiles are worked out. Hardly used, but very valuable for this is the introductionof the energy method on the basis of the virtual work principle, well known in the world ofsolid mechanics.

3.2 Quantitative down-scaling effects

In his famous speech at the California Institute of Technology in 1959 called “There’s plentyof room at the bottom” [7,8,40], Nobel price winner Richard Feynman predicted thepossibilities of micro systems. Feynman used the typical scaling laws combined with hisknowledge about physics to come to remarkable conclusions which largely became realitytwenty years later [33]. In this paragraph the consequences of the scaling laws on thefunctioning of microanalysis systems are discussed.

If we look at the downsizing, the area will be reduced to the power two and the volumeto the power three. This means that for small systems, the ratio area / volume will becomelarger than for macro systems. Diffusion related mechanisms such as thermal conduction andphysical dispersion are area related, thus micro systems offer possibilities to speed-updiffusion limited processes [4]. Good examples are the use of fast mixing in a micro mixer[29], and glass capillaries in chromatographs [25]. An increase of the percentage capillaryarea per volume of the chromatograph speeds up the binding of species to the walls such thatthe length of the column can be reduced and measurements can be performed much faster.Another benefit is the possibility for parallel processing. On the same workspace area for

Micro fluid dynamics 33

one macro analysis system, a series of miniaturized systems on a chip can be placed suchthat sequential analysis can be replaced by parallel processing.

Help in determining the influence of scaling is offered by the use of dimensionlessparameters. In table 3.2 a number relevant dimensionless parameters [16,44] is listed withthe used dimensional parameters listed in table 3.1. By looking at the power of the lengthdimension, the influence of scaling becomes apparent. The effect of the area / volume ratioscaling on the flow behavior is well described by the Reynolds number. This dimensionlessparameter, as well as the Bond, Knudsen and Weber number are also related to physicalphenomena which will be discussed in paragraph 3.4. Since the volume is scaled down to thepower three, also the inertance will be scaled down to the third power which means thatinertance effects become of minor importance and viscous effects start to dominant atsmaller scale. So the Reynolds number decreases for micro systems. Typical values for theReynolds number are around one or smaller. Although inertance effects like turbulence canbe neglected for these low values, locally, the effect of inertia of the fluid can still be presentin the form of for example the existence of vortices at sharp corners. This effect can beobserved in micro valves as will be demonstrated in chapter 7.

The other effect of a reduction of inertance is an increase in system speed. In RLCcircuits the response time is defined by the combination of inertance and capacity. Sinceboth capacity and inertance are scaled down, the net system times will be reduced whichmeans an increase in driving frequency of for example micro pumps. The friction coefficientindicates that the amount of energy dissipation relative to the stored kinetic energy in theflow will increase. Due to system size reduction the power consumption of a fluid handlingsystem reduces but due to a higher relative dissipation, the efficiency (relative differencebetween the total energy flow and by friction dissipated energy) of the fluid transportdecreases as well.

Thermal diffusion (conduction) as well as mass diffusion are enhanced by downscaling. Dimensionless parameters that give an indication of this are the thermal and massFourier numbers and the Peclet numbers respectively [22]. For thermal systems this meansthat high cooling-down speeds can be obtained since conduction increases. Mixing ofspecies due to diffusion is also improved which results in shorter reaction times. These twoaspects make miniaturization suitable to obtain better-controlled chemical reactions leadingto more pure reaction products. Due to fast temperature control, uniformly over the reactionchamber, reactions will be much more uniform. Explosive reactions with very short reactiontimes can be controlled and fast elapsing sub-reactions can be frozen, yielding reactionproducts which are hard to obtain with macro systems [17]. On the other hand forcedmixing is hampered. To obtain convection of species, inertance effects are needed. Due tolow Reynolds numbers only the diffusion mechanism will be left to obtain this.

34 Chapter 3

parameter description units

� thermal diffusivity m2s-1

� thermal expansion coeff. K-1

� dielectric constant C2N-1m-2

�ij ij oriented strain -

� flow rate m3s-1

µ dynamic viscosity Pas�ij ij oriented stress Pa

�surf surface tension Nm-1

� mass density kgm-3

� shear stress Pa

� angular coordinate -

� Zeta potential Va,b typical dimensions mcp spec. heat at const. pressure Jkg-1K-1

DAB mass diffusion coefficient m2s-1

e electron charge CE total applied potential V

E� power Js-1

g constant of gravity ms-2

hm convection mass trans. coeff. ms-1

hT convection heat trans. coeff. Wm-2K-1

Kb Boltzmann constant JK-1

ke specific conductance �m-1

kT thermal conductivity Wm-1K-1

l (characteristic) length mn0 average ion concentration -p pressure PaRhyd hydraulic resistance Pasm-3

r radius mT temperature Kt time sv velocity ms-1

x,y,z coordinates mz ion valence -Table 3.1 Used dimensional parameters and their units

From table 3.2 it can be concluded that small analysis systems have the potential to befaster than larger macro systems. This is both mechanically due to lower inertance andcapacitance and due to a faster thermal and mass diffusion. Forced convection withturbulence can no longer be used and must be compensated by this faster diffusion. Although


micro systems will generally consume less energy due to a reduction of the net masstransport, the efficiency will drop as viscous dissipation increases.

group abbreviation definition interpretation order lenghtBiot number Bi

T

T

klh Ratio of internal thermal resistance

of a solid to the boundary layerthermal resistance

-1

Mass transferBiot number

Bim

AB

m

Dlh Ratio of the internal species transfer

resistance to the boundary layerspecies tranfer resistance

-1

Bond number Bo�

��2)( lg vl �

Ratio of gravitational and surfacetension forces

2

Euler number Eu2

21 v

p�

Dimensionless pressure drop 0

Fourier number Fo2lt� Ratio of the heat conduction rate to

the rate of thermal energy storage ina solid; dimensionless time

-2

Mass transferFourier number

Fom2l

tDAB Ratio of the species diffusion rate tothe rate of species storage

-2

Grashof number GrL2

32 )(�

�� lTTg s �� Ratio of buoyancy to viscous forces 3

KnudsenNumber

K

ll free

Ratio of the mean free path of a gasand a characteristic length

-1

Lewis number Le

ABD� Ratio of the thermal and mass

diffusivities0

Nusselt number NuL

klhT Dimensionless temperature gradient

at the surface3

Peclet numbermass transfer

PeD

ABDlv Ratio of mass transport by

convection and by diffusion1

Peclet numberheat transfer

Pe�

�

vl Dimensionless independent heattransfer

1

Prandtl number Pr

T

p

kc � Ratio of the momentum and thermal

diffusivities0

Reynolds number ReL

�

� lv Ratio of the inertia and viscousforces

1

Schmidt number Sc

ABD�

� Ratio of the momentum and massdiffusivities

0

Weber number We

surf

lv�

�2 Ratio of inertia to surface tension

forces1

Table 3.2 Overview of dimensionless parameters and their relation to the dimension length(at constant velocity)

36 Chapter 3

3.3 Fluid dynamics

The fluid behavior in macro-systems is described by the mass conservation, forceequilibrium, energy and constitutive laws [16,44,12,10,3,20,49,18]. From the momentumequations and the constitutive relations, the general Navier-Stokes equations for constantmass density can be derived for a Newtonian fluid in vector form:

� � � �

� � � � � �� Fvvvv

vvvv

��

��

��

��

32

2312

�pDtD

(3.1)

Since bulk viscosity, �, only plays a role in fluids subjected to rapidly varying forces,simplification of this formula can be obtained. A further reduction of terms is achieved byassuming temperature- and pressure-independent behavior of viscosity. When no externalfields are present and when dimensions are small such that no substantial hydrostaticpressures can be built-up by gravity fields, the field term can be skipped. This leads to thesimplified form, referred to as Oseen’s equation or Navier-Stokes for incompressible flow:

vvvv 2��

��

��

�

�� p

t(3.2)

In addition to the differential equation, boundary conditions are needed. At the interface witha solid structure, for example the channel wall, this is the non-slip condition and thecondition that the wall is impermeable:

0v � (3.3)

These “macro” relations are based on the continuum assumption of the medium. Sincea medium consists of discrete molecules, this assumption might not be straightforwardapplied to micro-systems. Molecule transport in and out of a system can cause fluctuations inthe actual composition of the enclosed medium. For large volumes that contain manymolecules this effect will cancel out by the average state of the volume. If the continuumrelations no longer hold, statistical theory of free molecule flow must be applied [2,6].As reference length, the mean path is used that can be traveled by the molecules before acollision occurs with other fluid molecules or the wall (mean free traveling path). Thedimensionless Knudsen number relates characteristic length such as channel diameter to thismean free path. Streeter [44] gives a table in which the different flow regimes are visualized(figure 3.1). For Knudsen numbers smaller than about 0.01 the continuum assumption holds.At numbers larger than 10, free molecule flow must be assumed whereas the region inbetween is a transition state, called slip flow. In the latter region the continuum models


usually are applied with additional correction to allow slip at the walls. Since the mean freepath length of gas molecules is much bigger than of liquids the Knudsen number for gassesis much higher. The mean free path length can be computed with [19]:

abs

absbfree pa

TKl 22�

� (3.4)

where Kb is the Boltzmann constant of 1.381�10-23 J/K, Tabs and pabs the absolute temperatureand pressure of the gas respectively and a the diameter of the gas molecules. A typical meanfree path length of gasses at atmospheric pressure and room temperature is about 100nm.This means that for gasses under these circumstances, continuum dynamics will hold up tocharacteristic lengths of about one micron. At lower pressures the mean free path willrapidly increase. So care must be taken with applying macro theory to gas-flow inmicrochannels.

Reynolds number

Mac

h nu

mbe

r

0 10 -2 10 21 10 5 10 7�

0

0.4

0.91.1

5

�

Stokes Oseen laminar turbulent

inco

mpr

essi

ble

com

pres

sibl

e

subs

onic

supe

rson

ictra

nsso

nic

K < 0.01

K > 10

continuum flow

slip flow

free molecule flow

0.01 < K < 10

Figure 3.1 Flow regimes as a function of Reynolds and Mach numbers [44]. The regimes arebounded by Knudsen numbers 10 and 0.01. Note: in circular macro ducts flow isobserved to be stable (no turbulence) up to Reynolds values of 2100.

As shown in figure 3.1 the Knudsen number is related to the Mach (actual velocity /speed of sound) and Reynolds number. Mach numbers are only used for gas flows and canplay an important role in microchannels as demonstrated by Simões [41] and Furlan [11].

38 Chapter 3

Supersonic flows were observed in 20µm square channels using nitrogen at rather lowsupply pressures of 0.3 bar. In our experiments de-mineralized water and ethanol will beused which can be considered to follow the Newtonian behavior. The molecule sizes arevery small [21] (water ~1.3Å, ethanol ~3.2Å), which validates the applicability of continuummodels in channels with a cross section of more than a few microns. Hence fluid dynamics isgoverned by Oseen’s or Stokes’ equations. Relation (3.2) will be used in the numericalsimulations for the valves, reduced to the stationary situation where the time-derivative ofthe velocity is skipped. The second term on left side in this equation incorporates the inertialeffects of the fluid. For very small Reynolds numbers or flow through smooth straight tubesat a stationary situation, these effects can be neglected relative to the viscous effects modeledby the last term at the right hand side. The relation is simplified to:

v21��p

�(3.5)

This most elementary form is called Stokes flow or creeping flow regime. This relation isused in paragraph 3.5 to model the resistance of elementary channel shapes.

3.4 Surface effects in micro-flows

3.4.1 IntroductionAs noticed before, the surface / volume ratio is increased when dimensions are scaled-down.This means that the physical and chemical surface effects might start to play an importantrole. Together with the continuum assumption of the discussed models, the magnitude ofthese effects will justify or reject the use of the proposed Navier-Stokes derived flowmodels. There are three surface effects that will be discussed: the surface energy, doublelayers and surface roughness of the walls.

3.4.2 Surface energySurface energy plays can play a role in fluid mechanics when interfaces exist betweendifferent fluids or fluids and solids. In our case, the effect at the liquid-gas interface is ofimportance. The influence of the surface energy, causing surface tension effects, is expressedby the Bond and Weber number respectively (table 3.2). The Bond number relates theinfluence of the gravitational forces to the surface tension. Gravitational forces are reducedwhen scaling-down such that the Bond number will get smaller. The Weber number relatesthe inertia forces to the surface tension. Since also the inertia effects are reduced duringdownscaling, the Weber number drops, indicating that surface energy will become a


substantial factor in microsystems. A measure for the dominance of viscous or surfacetension effects can be obtained by dividing the Weber by the Reynolds number:

surf

vReWe

�

�� (3.6)

For small flow velocities in microchannels, this ratio becomes small, indicating that surfaceenergy becomes an important factor [28]. The

Surface free energy [1,36] is the cause for phenomena observed in daily life and called“surface tension”. Surface free energy is the energy needed to bring a molecule from theinterior to the surface of a fluid. This energy difference is caused by the differences in theVan der Waals forces between an atom and its surrounding atoms in the bulk of the fluid andat the surface. This means that the surface tension depends on the fluid and surroundingmaterials as well as the channel geometry. An additional pressure drop compensates the freesurface energy over meniscus of the fluid. The relation between this pressure drop, thegeometry described with two, perpendicular oriented radii r1 and r2 and the surface tension,�surf is described by the Young-Laplace [1, 36] equation:

��

��

��

21

11rr

σp surf (3.7)

Capillary pressures for different channel sizes

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1 10 100 1000

channel diameter (µm)

capi

llary

pre

ssur

e (P

a) Water

Ethanol

Figure 3.2 Capillary pressures in channels with different diameters for water and ethanol

40 Chapter 3

Typical values of the surface tension for water and ethanol at 20�C are: 72.7mN/m and22.3mN/m respectively. This means that for a circular, hydrophilic channel or tube, liquidwill flow-in in due to capillary forces, causing an under pressure as shown in figure 3.2. Asshown in this figure, the capillary pressures can become substantial and might cause damageduring filling (priming) of the system. The liquid will creep along the edges, whichminimizes the surface tension. This can hamper a full filling of the micro system.Techniques like filling the channels with fast soluble gasses like carbon dioxide have beenreported to get rid of the trapped gasses [50]. Surface tension problems are not over after thesystem is fully filled. Since the gas solubility is related to the pressure and temperature,degassing of the liquid causing trapped gas bubbles will still remain an issue. In-system builtventing units could be a solution for this [15] although not always beatific. During themeasurements of the passive check valves these phenomena will be discussed in more detail.

3.4.3 Double layersFor Newtonian and non-Newtonian liquid flows in microchannels Pfahler [34,35] observed areduction in the geometric friction factor as function of the channel size (ranging from 0.5 to10µm depth), translated to a reduction of the apparent viscosity of 77% for isopropanol. As asecond possibility for this reduction, the wall roughness and the corresponding slip along thewall is given. Due to uncertainties in the exact geometries of his channels, a clear answer isnot given. Differences with macro models [13] and similar influences of the temperature [48]have been reported which cannot be explained by the Navier-Stokes equations. Mala [23]stated that the importance of electric double layers might play in important role whenchannels become smaller. In fact fluid transport due to differently charged ions is used topump fluid as demonstrated in electrohydrodynamic pumps [37,14] and for electrophoreticseparations [26, 27]. Paul discussed the possibility to obtain extremely highelectrokinetically generated pressures with porous microstructures [32].

Basically, three charge-related effects can be distinguished [1]: Electrophoresis, whichis the charged ion transport due to the application of an electric field. For small molecularions this phenomenon is called ionic conductance, for larger species the word electrophoresisis used. Electroosmosis, also referred as electroendoosmosis, is the transport of the fluid dueto the drag of the moving, charged electric double layer. The streaming potential is thecounterpart of electroosmosis and refers to the charge displacement and consequently theexistence of an electric potential due to fluid transport.

Electroosmosis and streaming potential are two complementary phenomena. Theorigin of these effects is found in the charge distribution in the fluid near the walls. Mostsolid materials are naturally charged. Due to this charge, ions in the fluid are moved to thewall or to the center of the channel, depending on the polarity. At the walls a charged layer


exists, called the Stern-layer [42]. The structure of this layer is shown in figure 3.3. TheStern layer is rather immobile such that shear only occurs in the diffuse or shear layer. Sincethere is a net charge of the diffuse layer, flow will cause charge transport. Transport ofcharged ions (streaming current) will generate a streaming potential. To compensate for thischarge transport, a conduction current arises in the backward direction due to the generatedelectrical field. This electrical field causes an additional body force in the Stokes equationand finally an apparent viscosity term (increasing with flow-rate) for the flow-pressurerelation [23]. The other way around, if a potential is applied over the length of the tube, thediffuse layer will start to move, dragging the bulk fluid. If the tube is closed, a netelectroosmotic pressure will arise. Smoluchowski [43] derived equations to computestreaming potentials, equation (3.8) as well as the electroosmotic pressures, equation (3.9),for circular tubes:

egstrea kµ

εpζE�4min � (3.8)

22

rEεζposmosis

�

� (3.9)

with � the zeta potential as shown in figure 3.3, � the dielectric constant and ke the specificconductance of the fluid. Mala [23] computed a strong influence of the Debye-Hückelparameter �, equation (3.10) on the apparent viscosity: a reduction of the parameterincreases the apparent viscosity with possibly more than a factor two. In this definition e isthe electron charge, z the ion valence of the positive and negatively charged ions, n0 theaverage concentration of positive or negative ions, a the half distance between two platesand T the temperature.

TKezna

b��

2202

� (3.10)

From this definition it is seen that a reduction of the channel dimension reduces the Debye-Hückel parameter and thus would give rise to an increased apparent viscosity. As the zetapotential is increased, the net charge in the diffuse layer will increase. Due to this, thestreaming current is increased, inducing a higher friction factor. Experiments, performed byMala et al. [24], showed that for KCl solutions the effects in glass channels are much smallerthan in P-type silicon due to a smaller zeta potential of glass. On the other hand, an increaseof the ionic concentration will reduce the size of the charged part in diffuse layer and hencethe net current transport and so the friction factor is reduced.

42 Chapter 3

diffuse or shear layer

�0

0 d

Stern layer

distance from the wall

fluidwall

�po

tent

ial

Figure 3.3 Structure and potential level of the electric double layer (Stern layer)

Although influences of the electric double layer in the flow resistance for channelswhich cross-section dimensions of a few microns to more than hundred microns have beenmeasured, the influence was still rather small (<0.5%). Flockhart [9] did similar flowmeasurements with isopropanol on in <100>silicon etched trapezium KOH channels,covered with a glass plate with hydraulic diameters ranging from 50 to 120 and Reynoldsnumbers up to 600. He did not notice significant differences with macro theories. Theuncertainties due to fabrication techniques such as geometry tolerances easily dominate. Oneof these uncertainties is the influence of surface roughness due to etching. For flows inmacro pipes, roughness-friction tables are available for turbulent flows [10]. For laminarflows, the resistance is only related to the Reynolds number, not to the roughness. Formicrochannels no information is available about these roughness effects. Measurements ofwet chemical anisotropically etched {111} planes have shown pits [31] in the range of180nm peak to peak roughness. Small crystal misalignments can result in stepped channelgeometries. Also etch pyramids [5] might give rise to a substantial surface topology change.If channels are considered with dimensions in the order down to a few micron, this wouldmean that these roughness peaks are of the order of 10% or more. Even for laminar flow, thisroughness must cause considerable changes in resistance although the word roughness mightnot cover the load anymore. Keeping these uncertainties in mind, we will use Oseen’s andStokes’ fluid dynamics theory for modeling channel and valve resistance knowing thatdeviations can be expected.


3.5 Hydraulic channel resistance in stationary flows

3.5.1 IntroductionIn designing micro fluid handling systems it is very convenient to have simple analyticalformulas which predict the flow velocity in an arbitrary shaped channel. From this velocityprofile, the resistance and inertance can be calculated. In fluid dynamics literature only a fewanalytical solutions are known. Usually the resistance of a channel with a circular cross-section is used as a basis from which the resistance is derived for other channel geometries,using numerically calculated or empirically obtained data [10,49]. The adaptation of thevalues for the specific channel geometry to the known situation of a circular cross-section isdone with use of resistance coefficients as will be demonstrated in the next chapter. Thesecoefficients depend on for example the aspect ratio of the cross-section. The aim is togenerate a list of simple (approximating) formulas for typical channel geometries found inMST, without the need of look-up tables. In the next paragraphs the principle of virtual workis used for this. From the analogy with mechanical torsion of solid bars, interesting resultscan be derived for the hydraulic resistance as stated by Timoshenko [45], referring to thework of Boussinesq (1871). Although this analogy has been known for many years, noliterature was found with worked out channel examples.

3.5.2 Numerical solutions of the Laplace equationMicrochannels, which connect components on a channel board, usually are rather longcompared to the cross-section dimensions. Therefore the velocity profile will mainly bedefined as a fully developed, incompressible flow. For the stationary situation, in 3.3 theStokes relation was derived. For fully developed flow in a straight channel, shown in figure3.4, this equation is given by:

zpv

dd12

�� (3.11)

This relation can be rewritten to a Laplace equation. First, introduce v~ with the substitution:

zpvv

dd1~

�� (3.12)

This yields:

1~2�� v (3.13)

or written in terms of the x-y coordinates:

44 Chapter 3

1~~2

2

2

2

��yv

xv

�

�

�

� (3.14)

A further substitution of (3.15) in (3.14) results in the Laplace equation (3.16).

2

21~~ xvV �� (3.15)

xy

z

Figure 3.4 The channels axis system used in the computations

The boundary values are governed by the no-slip condition such that the velocity must bezero at the function values that describe the cross-section geometry. Thus the flow problemconsists of solving the system:

0~2�� V (3.16)

on the interior of the cross-section with

2

21~ xV �� (3.17)

on the channel cross-section edge.A simple numerical solution procedure is used by Flockhart [9]. For this the

differential equations are re-written in polar coordinates:

1~1~12

2

2 ��

��

��

�

��

�

��

�

�

�

�

� vrr

vrrr

(3.18)

and with substitution of (3.19) to equation (3.20).

2

41~~ rvV �� (3.19)

0~1~12

2

2 ��

��

��

�

��

�

��

�

�

�

�

� Vrr

Vrrr

(3.20)

The general solution of this equation can be written with the series:


� ��

��

N

nnn

n nbnaraV1

0 )sin()cos(~�� (3.21)

The constants a0, an and bn can be solved by taking a selection of discrete points (ri,�i) at theboundary of the channel cross-section. With the non-slip condition the relation (3.22) musthold which gives relation (3.23) to be solved.

2

41~

ii rV �� (3.22)

� � 2

10 4

1)sin()cos( i

N

ninin

ni rnbnara ��

�

�� (3.23)

This matrix-vector system can only be solved if the number of grid points on the boundaryequals 2N+1. After back-substitution the velocity field is computed from:

� �zprnbnarav

N

nnn

n

dd1

41)sin()cos( 2

10

��

��

��

��

(3.24)

-1.5-1

-0.50

0.51

1.5

x 10-4

00.5

11.5

22.5

x 10-4

0

0.5

1

1.5

2

2.5

x 10-9

u µ/

(dP/

dz)

(m

)

x-coordinate (m)y-coordinate (m)

2

Figure 3.5 Velocity profile in a triangular (54.7�) channel computed with the numerical method.Due to a limited number of boundary grid points, some vaulting occurs at the corners.Mesh refinement improves these boundary conditions.

46 Chapter 3

This procedure is implemented in a Matlab routine from which a result of the flow-profilethrough a triangular channel is shown in figure 3.5. A nice aspect of this numerical routine isthe fact that only a few grid points at the boundaries are needed. As a result of this, thematrix-vector system is very compact although the matrix is fully filled with elements andcan become bad conditioned due to low amplitudes of the high-frequency (large n) terms.This numerical method will be used to verify the analytically obtained results in the nextparagraphs.

3.5.3 Exact analytical solutionsAnalytical solutions for the velocity profile in channels are rare. Most analytical solutionsare for situations for which an exact solution can be derived. Examples of these are thePoiseuille flow between two plates [10,3] (2D), which gives:

� �22

21~ axv �� (3.25)

for a half the plate distance or in a circular pipe [10,49] (3D):

� �22

41~ arv �� (3.26)

With a the radius of the pipe. These solutions are easy to derive since the boundaryconditions are rather simple.

A more complicated shape is the ellipsoid. This shape could be obtained if a channel ismade by etching two wafers isotropically, after which they are bonded together [46]. Sincethe mask opening width will influence the aspect ratio of the cross-section, an ellipsoidshape might well approximate this situation. Batchelor [3] gives an equation for the velocityprofile in an ellipsoid channel. In order to find solutions for the Stokes problem, a 2-dimensional function needs to be found which meets the Laplace differential equation on theinterior (3.16) and the corresponding boundary conditions (3.17) at the edge. The boundaryconditions of equation (3.13) are simpler: the function value becomes zero at the edge.Hence this differential equation is preferred over the Laplace equation. For the ellipsoidcross-section solving this problem is simple since the function description of an ellipsoid canmeet the boundary conditions at the edges as well as the differential equation exactly:

��

��

�� 1~

2

2

2

2

by

axCv (3.27)


The constant c is found from the substitution of the shape function in the differentialequation. From this we find the velocity function:

��

��

��

�

��

�

� 1

)(2~

2

2

2

2

22

22

by

ax

babav (3.28)

For a = b we see that the profile reduces to the situation found before for the flow through acircular channel. The definition of the variables a and b are given in table 3.3 where theresults are summed of all geometries to be derived.

For a triangular channel the same procedure can be applied. The three lines boundingthe surface are multiplied to get a function that meets the boundary condition. Since onlyequilateral or triangles with two sides of the same length are observed in micro systems,these types will be considered only. If shape function (3.29) is substituted into thedifferential equation, relation (3.30) resultes, which states that an exact solution for thisgeometry can only be obtained for the equilateral situation (� = 60�). For such a triangulargeometry velocity function (3.31) is found.

� �� yaxyaxyCv �� )tan()tan()tan()tan(~�� (3.29)

constant3)tan()(tan 2 �� yay �� (3.30)

� �� yaxyaxayv ��

��

� )(3)(33

121~ (3.31)

For higher order polygons, exact solutions cannot be obtained such that seriesapproximations are needed. For a rectangular cross-section, a Fourier series expansion canbe used in order to meet the differential equation on the interior. This is demonstrated byBachelor [3]. With this method, expression (3.32) is obtained:

)2πcos(

)2πcosh(

)2πcosh(

1)1(1π

16~ )2

1(

..5,3,133

2

axn

abnayn

nav

n

n ��

�

�

��

�

�

��

�

�

� (3.32)

3.5.4 The virtual work principleA series solution like for the rectangular geometry cannot always be obtained. Thereforeadditional approximation methods are needed. From literature however no other solutionsare found. In structural mechanics however, more work is done in the analytical mathematicsarea. A popular method is minimization of energy terms. This method will be applied to the

48 Chapter 3

fluid dynamics problem according to the analogy with torsion of straight beams, as noticedby Timoshenko [45]. The method will be derived on the basis of the principle of virtual work(variational method).

Assume �v to be a virtual velocity in the z-direction of a particle. If there are is a netforce �Fz acting in the same direction, the total work per time (power) on the particle mustvanish if the particle is in equilibrium:

0Σ �zFv� (3.33)

Which states the equilibrium of the forces acting on the particle:

0Σ �zF (3.34)

Due to the stresses, a small cube will deform as shown in figure 3.6. The velocity strainincrements become:

vx

vz

vxxz ��

�

��

�

��

�

�

�

�

��

21

21

� vx

vx

vzzx ��

�

��

�

��

�

�

�

�

��

21

21

� (3.35)

vy

vz

vyyz ��

�

��

�

��

�

��

�

��

21

21

� vy

vy

vzzy ��

�

��

�

��

�

��

�

��

21

21

�

The virtual power for a volume element dxdydz is:

� � zyxzyxE dddddd zyzyyzyzzxzxxzxz ��

�� (3.36)

z

y

z

x

side top

�yz �xz

�yz �xz

�zx�zx�zy�zy

�yz �xz

Figure 3.6 Stresses and deformation of a (velocity) fluid element for Stokes flow

This virtual power dissipated by the viscous forces must be in balance with the powerexerted by the externally applied forces. For the channels this is the power from the pressureforces:


zyxvzpzyxE p ddd

ddddd ��

� (3.37)

So per unit channel length the net virtual power must be zero which yields the relation:

� � 0dddddd

zyzyyzyzzxzxxzxz �� yxyxvzp

�� (3.38)

In this relation there is only a variation of the velocity field, the forces and stresses remainconstant. Therefore the relation states that the first order variation of the total potentialenergy (power) must be zero:

� � 0dddd

zyzyyzyzzxzxxzxz ��

��

�� yxv

zp

�� (3.39)

Substitution of the Newtonian viscosity relations (3.40) and the equilibrium relations (3.41)of the stresses on the elements of figure 3.6 yields equation (3.42).

ijij �� (3.40)

zxxz �� yzzy �� (3.41)

� � � � 0dddd

zyyzyzzxxzxz ��

��

�� yxv

zp

�� (3.42)

and with the strain-velocity relations we finally find:

0dd21

dd

22

��

��

��

��

�

��

�

��

��

�

�

��

�

��

�

�

�� yx

yv

xvv

zp

�� (3.43)

With substitution (3.12) this relation can be rewritten to:

0dd~~

21~

22

��

��

��

��

�

��

�

��

��

�

�

��

�

��

�

�

�� yx

yv

xvv� (3.44)

Solving the differential equation on the interior of the channel geometry and theboundary conditions at the edge has now changed to finding a velocity function that meetsthe boundary conditions on the edge and minimization of the potential energy. This can bedone by taking a function that is built by a product of functions that individually meet theboundaries and an additional series with fitting coefficients:

50 Chapter 3

��

�

N

ii

M

ji

jiij yxyxCv

10,

),(~� (3.45)

In this series, Cij are the constants, which need to be determined such that the energyminimum is found. Functions �i describe the boundaries of the channel geometry. For thetriangular channel a first order term can be used:

� �� yxayxayCv �� )tan()()tan()(~�� (3.46)

The constant can be computed by solving the differentiated integral over the triangularsurface :

0~~~

212

0

)tan()(

0

22

��

��

�

��

��

�

�

��

��

��

�

�

��

�

�

��

��

�

�

��

�

��

�

�

�

�

��

�

�

dydxvyv

xv

C

a

x

xa

y

�

(3.47)

The solution for the velocity field found from this is:

� ��

��

��

�

��

��

��

3)(tan)tan()tan()()tan()(

23~

2��

�� yaxyaxayv (3.48)

For � = 60� the same function is found as the exact solution derived earlier.

As stated before, for other angles the solution is not exact. To investigate the error, theresidue value is plotted in figure 3.7. This value was computed as the difference between theleft and right hand side value of the differential equation according to:

� �2

22

11~

residue ��

v (3.49)

From this figure we see that at 60� the residue vanishes as was expected.A series approximation for the flow in a rectangular channel was already found. With

the energy method it is possible to obtain a more simple approximation. For a one-termquadratic approximation of a rectangular and square geometry the result is listed in table 3.3.Figure 3.8 shows that the residue is rather big which indicates that the order of the chosenshape function is rather low to obtain precise results for high aspect-ratios. Therefore also asecond order approximation is derived (table 3.3).


0

20

40

60

80

100

resi

due

(%)

30 40 50 60 70 80angle (degrees)

Residue as function of the triangle angle

�

Figure 3.7 Residue as function of the triangle angles: for an equilateral situation, the formulaexactly meets the differential equation.

0

50

100

150

200

250

resi

due

(%)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2aspect-ratio a/b

Residue as function of the rectangle aspect-ratio (b=1)

Figure 3.8 Residue as function of the aspect-ratio for a rectangle for b = 1. Note: the residue goes tozero for a/b = 0 since residue depends on a characteristic length.

Trapezium shaped channels can be made by different etching techniques. Thesimplest way is KOH etching of <100> oriented silicon with a time stop and bonding of asecond wafer on top. A differently shaped trapezium is obtained if a combination of directiveion etching and anisotropic wet chemical etching is used in <100> or <111> wafers. SEMpictures of two examples are given in figure 3.9. Figure 3.9A is obtained with the “buriedchannel” method [47], a combination of deep trench etching with RIE (Reactive Ion

52 Chapter 3

Etching), passivation of the walls with for example silicon nitride and wet chemical etchingin for example KOH. This process produces a perfect diamond shape. A similar shape,although not equilateral is obtained if trenched are etched with for example RIE in a <111>wafer after which the (111) planes are formed by wet anisotropic etching (figure B).

[001][111]

[11 ]1[ 1]11

A BFigure 3.9 Two examples of trapezium shaped channels with an angle of 70.6�. Channels fabricated

with the “burried channel” method (A) are equilateral, in <111> wafers etched channelscan have different aspect ratios (B).

For these shapes a first order approximation has been derived (table 3.3). The x-y coordinatesystem has the origin in one of the two sharp corners with one side parallel to the x-axis. Theresidue takes a minimum for a rectangular shape that was derived before. The relation for anin <100> wafer etched trapezium channel becomes rather elaborate even for a first orderapproximation.

Isotropically etched channels will result in elliptical geometries as discussed beforeor half-ellipsoid cross-sections. This geometry is defined by two profile functions y1 and y2

according to equations (3.50). For such a geometry, the next solution procedure can be used[45].

)(11 sKy �� (3.50)

)(22 sKy ��

with the s-coordinate defined as in figure 3.10 according to:

Lxs /� (3.51)


y

x

y (s)1

y (s)2

L

Figure 3.10 Definition of the shape functions

A new shape function can be constructed of the form:

� �qpm sss �� 1)(� (3.52)

A suitable velocity function that satisfies the boundary conditions is:

� �� )()(~21 sKysKyCv �� (3.53)

When the energy is minimized using this equation, the solution for the constant C will be:

� �212

22

12

2

21

KKKKLLC

��

�

�(3.54)

with:

� �

�

�� 1

0

3

1

0

23

d)(

d/)()(

ss

sdssds

�

��

� (3.55)

For the half-ellipsoid with the y-axis defined as shown in the figure, the two geometricfunctions are given by:

)1(21 ssby �� (3.56)

02 �y

Such that K1 = 2b, K2 = 0, m = 1/2, p = 1 and q = 1/2 and a new shape function defined by:

)1()( sss �� (3.57)

With these values, � becomes 1/3, which results in the velocity profile:

54 Chapter 3

� ��

��

��

��

�

22

2

3)1(2

23~

bassbyya

v (3.58)

For the x-axis moved over a distance a, such that the y-axis forms the symmetry axis of thehalf ellipsoid, the velocity profile is defined by:

��

��

��

�

��

�

� 22

22

2

323~ xa

aby

bayav (3.59)

shape geometry parameters velocity profileparallel infinitelylong plates

x

z2a � �22

21~ axv ��

circle (full) y

x

2a

� �22

41~ arv ��

circle (half) y

x

2a

� �22

83~ xayyv ��

ellipsoid (full) y

x

2a

2b��

��

��

�

��

�

� 1

)(2~

2

2

2

2

22

22

by

ax

babav

ellipsoid (half) y

x

2a

b��

��

��

�

��

�

� 22

22

2

323~ xa

aby

bayav

squareseries solution

y

x

2a

2a )2

cos()

21cosh(

)2

cosh(1)1(116~ )

21(

..5,3,133

2

axn

n

ayn

nav

n

n

�

��

�

�

��

�

�

�

�

��

�

�

�

�

squarefirst orderapproximation

y

x

2a

2a � ��

��

� �� 2

2222

165~

aayaxv


squaresecond orderapproximation

y

x

2a

2a

� �� 2210

2222~ yxCCayaxv ��

201

277259

165

aC � 41

127735

23

165

aC �

rectangleseries solution

y

x

2a

2b )2

cos()

2cosh(

)2

cosh(1)1(116~ )

21(

..5,3,133

2

axn

abn

ayn

nav

n

n

�

��

�

�

��

�

�

�

�

��

�

�

�

�

rectanglefirst orderapproximation

y

x

2a

2b � ��

��

�

�

�� 22

2222

85~

babyaxv

rectanglesecond orderapproximation

y

x

2a

2b

� �� 2210

2222~ yxCCbyaxv ��

88624426

642246

0 2525280498280569695

1635

bababababbabaaC

��

��

88624426

44

1 252528049828016525

bababababaC

��

��

triangle(equilateral)

y

x��

2a

�


��

� )(3)(33

121~

triangle y

x��

2a

(� around 60�)

� ��

��

��

��

��

� �

��

3)(tan)tan()tan()()tan()(

23~

2

yaxyaxayv

triangle54.7�

y

x��

2a


��

� )(412.1)(412.12126.0~

trapezoidy

x

2a

2b

�

� ��

� �

��

�

�

��

�

�

��

��

��

�

��

��

��

)(tan)(7)(tan)2(14

)(tan)1077()tan(9854

8)tan(10)(tan5)tan()3(

)tan()(3

87~

4222

322

2222

34

222

�

�

�

�

��

�

�

baabaabbab

abbbaba

xabyxabybyby

v

56 Chapter 3

trapezoid54.7�

y

x

2a

2b

��

� ��

� �432234

22

6.5910.631145211298.2225684.9882.69

)3(412.1)(412.13

bbabaabababa

xabyxabybyby

��

��

��

��

diamond y

x�

2a

2b� ��

� � 2222 )(tan)tan()2()tan(2

85~

bbaaxyxybyyv

��

��

diamond 70.6� y

x��

2a

2b� ��

� � 22206.8)2(84.284.22

85~

bbaaxyxybyyv

��

��

Table 3.3 Velocity profiles for different channel geometries with dzdpvv

��

1~

3.5.5 Channel resistanceThe channel resistance is calculated by integration of the velocity profile over the cross-section area such that the flow-rate as function of the pressure drop is known. Results of thisprocedure are listed in table 3.4. Another way to obtain convenient design formulas for theresistance is to look at the analogy with torsion mechanics of solid beams. A Prandtl stressfunction, �, [45] can be defined in order to make the torsion differential equation solvable.This equation and the boundary conditions are defined by:

�� G22�� (3.60)

on the interior of the beam cross-section and

0�� (3.61)

at the beam edge, with � the torsion angle per unit beam length and G the shear modulus.This equation and the boundary conditions can be translated to the flow problem bysubstituting:

vG ~2 �� (3.62)

The torsion stiffness, Ktorsion, relates the torsion angle per unit length with the appliedmoment Mtorsion:

�/torsiontorsion MK � (3.63)

Furthermore, the surface integral of the Prandtl stress function equals the applied moment:


�� dxdyM torsion �2 (3.64)

Since the flow-rate is defined as the integral of the velocity field over the cross-sectionsurface, the analogy gives a value for the hydraulic resistance from torsion stiffness solutionswith the substitution:

lGK

Rtorsion

hyd �41� (3.65)

with l the channel length.From the torsion stiffness, many design formulas have been published [38,39]. An

overview of formulas for microchannels is given in table 3.4.

shape geometry parameters resistanceparallel infinitelylong plates

x

z2a

baµl

323 , b = channel width

circle (full) y

x

2a

4

8aµl

�

circle (flattened side)0 � � � 90�

y

x

2a

�

1

54

324

)]cos(1[9299.0)]cos(1[0769.3)]cos(1[1595.4)]cos(1[6183.2

)]cos(1[0333.07854.02

�

��

��

�

��

��

�

��

��

��

��

��

�

aµl

circle (half) y

x

2a

43128

aµl

�

ellipsoid (full) y

x

2a

2b��

��

� �

� 33

224babaµl

ellipsoid (half) y

x

2a

b��

��

� �

� 33

22

3332

babaµl

square y

x

2a

2a 4916

al�

58 Chapter 3

rectangleseries solution

y

x

2a

2b

��

�

�

��

�

�

��

�

�

�)

2cosh(

)2

sinh(1)1(1128

)2

1(

..5,3,1355

3 2

abn

an

nnba n

n �

�

�

rectanglefirst orderapproximation

y

x

2a

2b1

4

4

3 12136.3

3164

�

��

��

��

�

�

ab

ab

abµl

triangle (equilateral) y

x��

2a

�

4320

aµl

triangle y

x��

2a

(� around 60�)

��

��

� �

)(tan)(tan310

3

2

4�

�

aµl

triangle 54.7� y

x��

2a

473.17a

l�

trapezoidy

x

2a

2b

��

� ��

1

22

2

33

22

2

3

4222

322

2222

3

4

3

)(tan5)tan(10

8*

)(tan5)(tan15

)tan(188

)(tan7)(tan214)(tan1077

)tan(9854

)tan(1445

�

��

�

�

��

�

�

��

�

�

�

�

�

��

�

�

�

�

�

�

�

��

�

�

��

�

�

��

��

��

�

�

aab

b

aba

abb

baabaabbab

abb

bl

trapezoid 54.7�y

x

2a

2b

��

1

2

2

3

2

2

3

4

3

22

3

4

3

247.1765.1

761.1740.3178.3

81.1576.440.1039.100

96.41 �

��

�

�

��

�

�

��

�

�

�

�

��

�

�

�

�

�

��

�

�

��

�

�

�

�

aab

b

aba

abb

ababa

abb

bl�

diamond y

x�

2a

2b)(tan

)(tan)(109

233

2222

�

��

bababl

diamond 70.6� y

x��

2a

2b33

222

06.8)(06.8

109

bababl ��

�

Table 3.4 Hydraulic resistance for different channel cross-sections


For rectangular channel geometries, a comparison of the resistance, computed withdifferent methods and formulas is made in figure 3.11. It shows that the first orderapproximation matches the higher order solutions quite well, especially for squaregeometries. For infinitely wide channels, the solution resembles the 2-dimensional situationexactly. For ratios in between, there is a small difference such that a second order or seriesapproximation with about 25 terms can be chosen. The numerical method starts to sufferfrom poor conditioned matrices, which caused the difference in figure 3.11 for a/b biggerthan 5.

Model comparison for a rectangular cross-section

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1.0 2.0 3.0 4.0 5.0 6.0 7.0aspect ratio a/b

series approximation1st-order approximation2nd-order approximationnumerical solution

system matrix gets poor conditioned

Ra

/µl

4

Figure 3.11 Comparison of the different resistance calculations: for a square channel all methods canbe used whereas for higher aspect ratios, the second order approximation shows a goodalternative to the series approximation. The numerical method suffers from poorconditioned matrices at high aspect ratios.

Since these effects will also occur for trapezium shaped channels, it is recommended touse the first order approximation formulas only for geometries small width / height aspectratios. An alternative would be to use the series approximation for rectangular geometries.Changing the wavelength of the cosine term as function of the y-coordinate can make thefunction suitable to meet the boundary conditions. Verifications with the numerical modelhowever showed a more than 100% too low flow resistance. Similar to the rectangular shape,better results might be obtained when using a second or higher order approximations.However these formulas will become rather elaborate.

A comparison of the first order approximation for the flow resistance of channels withrectangular cross-sections with empirically obtained friction factors (see chapter 4), found in

60 Chapter 3

literature [49] shows a 5.1% error for an aspect-ratio 1 and 13.8% for a/b=2. In the nextchapter, the empirically obtained formulas will be used to model the flow through thepressure / flow sensor.

3.6 Conclusions:

Downscaling of geometries provide new possibilities but also has its drawbacks. Diffusionrelated processes such as mixing by molecular diffusion and thermal conduction are speededup due to the increase of the amount of surface relative to the volume. This enables fasterthermal cycling in devices (heating-up and fast cooling down) and with this a faster chemicalanalysis or better quality of reaction products. On the other hand convection relatedprocesses such as turbulent mixing is no longer possible.

Besides these benefits and drawbacks, downscaling also puts new demands on fluiddynamics models. Since the ratio surface / volume increases and volume flows decrease,effects such as surface energy, the electric double layer and roughness start to play a moreimportant role than in macro mechanics. High capillary forces can arise in a micro systemwhen gas-liquid interfaces exist. This means that structures should not only be designed towithstand loads during the operation but also during the filling procedure. Carbon dioxidecan be used to speed-up the removal of gas-bubbles since it easily dissolves in water.Changes of temperature or pressure still can cause bubble forming during operation modes,which might give rise to malfunctioning of the micro fluid handling system.

Theoretically, the electric double layer on the flow resistance can become relevant formicro systems. Literature however showed that during experiments with microchannels thisinfluence was overruled by geometric uncertainties like etch deviations in channel height andwidth but also the surface roughness. Therefore a choice is made to use Oseen’s and Stokes’simplifications of the Navier-Stokes equations in the next chapters. A list of simple designformulas for describing the velocity profile and hydraulic resistance of Stokes flow throughtypical microchannel geometries has been derived. The use of variational or energy methodsand the analogy with mechanical torsion of straight bars, proved to be very successful.Although not for all geometries a precise matching and simple relation can be derived, theformula’s give a first order guess of the actual flow situation. A numerical method wasimplemented to check the analytical results.


References

[1] A.W. Adamson, A.P. Gast, Physical chemistry of surfaces, John Wiley & Sons, NewYork, 6th edition, (1997)

[2] T.Ariman, M.A. Turk, N.D.Sylvester, “Microcontinuum fluid mechanics-a review”,Int. J. of Eng. Sc. 11, (1973) 905-929

[3] G.K. Batchelor, An introduction to fluid dynamics, Cambridge University Press, NewYork, 2nd edition, (1970)

[4] J.P. Brody, P. Yager, “Low Reynolds number micro-fluidic devices”, Proc. Solid-StateSensor and Actuator Workshop, Hilton Head, USA, (1996) 105-108

[5] M. Elwenspoek, H.V. Jansen, Silicon micromachining, lecture notes University ofTwente, (1997)

[6] A.C. Eringen, “Theory of micropolar fluids”, J. Math. and Mech. 16-1, (1966) 1-18[7] R.P. Feynman,“There’s plenty of room at the bottom”, J. Micromech. Systems 1-1,

(1992) 60-66[8] R.P. Feynman, “Infinitesimal machinery”, J. Micromech. Systems 2-1, (1993) 4-14[9] S.M. Flockhart, R.S. Dhariwal, “Experimental and numerical investigation into the

flow characteristics of channels etched in <100> silicon”, ASME, J. Fluids Eng. 120,(1998) 291-295

[10] R.W. Fox, A.T. McDonald, Introduction to fluid mechanics, John Wiley & Sons, NewYork, 3rd edition, (1985)

[11] R. Furlan, J.N. Zemel, “Comparison of wall attachement and jet deflection microfluidicamplifiers”, Proc. IEEE MEMS’96, (1996) 372-377

[12] J. Happel, H. Brenner, Low Reynolds number hydrodynamics, Martinus NijhoffPublishers, The Hague, 2nd edition, (1973)

[13] J. Harley, H. Bau, J.N. Zemel, V. Dominko, “Fluid flow in micron and submicron sizechannels”, Proc. IEEE MEMS’89, (1989) 25-28

[14] D.J. Harrison, A. Manz, P.G. Glavina, “Electroosmotic pumping within a chemicalsensor system integrated on silicon”, Proc. Int. Conf. on Solid-State Sensors andActuators’91, (1991) 792-795

[15] K. Hosokawa, R. Fujii, I. Endo, “Hydrophobicmicrocapillary vent forpneumaticmanipulation of liquid in µTAS”, Proc. µTAS’98 Workshop, Banff Canada,(1998) 307-310

[16] F.P. Incropera, D.P. de Witt, Fundamentals of heat and mass transfer, John Wiley &Sons, New York, 3rd edition, (1990)

62 Chapter 3

[17] K.F. Jensen, S.L. Firebaugh, A.J. Franz, D. Quiram, R. Srinivasan, M.A. Schmidt,“Integrated gas phase microreactors”, Proc. µTAS’98 Workshop, Banff Canada, (1998)463-472

[18] S. Kim, S. Karrila, Microhydrodynamics: principles and selected applications,Butterworth-Heinemann, Boston, First edition, (1991)

[19] H. Kuchling, Taschenbuch der Physik, Carl Hanser Verlag, München Wien, 16th

edition, (1996)[20] H. Lamb, Hydrodynamics, Cambridge University Press, New York, 6th edition, (1975)[21] D.R. Lide, Handbook of chemistry and physiscs, CRC Press, London, 74th edition

(1993-1994)[22] W.E. van der Linden, “Miniaturization in flow injection analysis, practical limitations

from a theoretical point of view”, Trends in Analytical Chemistry 6-2, (1987) 37-40[23] G.M. Mala, D. Li, J.D. Dale, “Heat transfer and fluid flow in microchannels”, ASME,

Microelectromechanical Systems (MEMS), DSC-Vol. 59, (1996) 127-136[24] G.M. Mala, D. Li, C. Werner, J.J. Jacobasch, Y.B. Ning, “Flow characteristics of water

through a microchannel between two parallel plates with electrokinetic effects”, Int. J.Heat and Fluid Flow 18-5, (1997) 489-496

[25] A. Manz, Y. Miyahara, J. Miura, Y. Watanabe, H. Miyagi, K. Sato, “Design of anopen-tubular column liquid chromatograph using silicon chip technology”, Sensors andActuators B1, (1990) 249-255

[26] A. Manz, C.S. Effenhauser, N. Burggraf, D.J. Harrison, K. Seiler, K. Fluri,“Electroosmotic pumping and electrophoretic separations for miniaturized chemicalanalysis systems”, ”, J. Micromech. Microeng. 4, (1994) 257-265

[27] A. Manz, “Design secrets and new dimensions in field driven separations for micrototal analysis systems (µTAS)”, Proc. Solid-State Sensor and Actuator Workshop,Hilton Head, USA, (1996) 1-4

[28] H. Matsumoto, J.E. Colgate, “Preliminary investigation of micropumping based onelectrical control of interfacial tension”, Proc. IEEE MEMS’98, (1990) 105-109

[29] R. Miyake T. Lammerink M. Elwenspoek J. Fluitman. “Micro Mixer with FastDiffusion”, Proc. IEEE MEMS’93, (1993) 248-253

[30] E.A. Murphy Jr., Murphy’s Law, the original Murphy’s Law reads: “If there are two ormore ways to do something and one of those ways can result in a catastrophe, thensomeone will do it”, pronouncement quoted by Major J.P. Stapp at a news conferenceabout the test of human acceleration tolerances by the U.S. Air Force, (1949), thegeneralized version: “Anything that can go wrong, will” has been derived by L. Nivenand is called: “Finagle's Law of Dynamic Negatives”


[31] A.J. Nijdam, J.W. Berenschot, J. van Suchtelen, J.G.E. Gardeniers, M. Elwenspoek,“Velocity sources as an explanation for experimentally observed variations in Si{111}etch rates”, J. Micromech. Microeng. 9, (1999) 135-138

[32] P.H. Paul, D.W. Arold, D.J. Rakestraw, “Electrokinetic generation of high pressuresusing porous microstructures”, Proc. µTAS’98 Workshop, Banff Canada, (1998) 49-52

[33] K.E. Petersen, “Silicon as a mechanical material”, Proc. IEEE 70-5, (1982) 420-457[34] J. Pfahler, J. Harley, H. Bau, J. Zemel, “Liquid Transport in Micron and Submicron

Channels”, J. Sensors and Actuators, (1990) A21-A23, 431-434[35] J.N. Pfahler, Liquid transport in micron and submicron size channels, PhD. Thesis

Department of Mechanical Engineering and Applied Mechanics, University ofPennsylvania, (1992)

[36] R.F. Probstein, Physicochemical hydrodynamics, an introduction, John Wiley & SonsInc., New York, 2nd edition, (1994)

[37] A. Richter, A. Plettner, K.A. Hofmann, H. Sandmaier, “Electrohydrodynamic pumpingand flow measurement”, Proc. IEEE MEMS’91, (1991) 271-276

[38] R.J. Roark, W.C. Young, Roark’s formulas for stress and strain, McGraw-Hill Int.,New York, Sixth edition, (1989)

[39] A.S. Saada, Elasticity theory and applications, Pergamon Press Inc., New York, (1974)[40] S.D. Senturia, “Feynman revisited”, Proc. IEEE MEMS’94, (1994) 309-312[41] E.W. Simões, R. Furlan, J.N. Zemel, “Computational two-dimensional finite element

analysis flow behavior inside microfluidic amplifiers”, Proc. Int. Conf. Modeling andSimulation of Microsystems, Semiconductors, Sensors and Actuators, Santa Clara,USA, (1998) 480-485

[42] O. Stern, “Zur Theorie der Elekrolytischen Doppelschicht”, Zeitschrift fürelektrochemie, (1924) 508-516

[43] M. Smoluchowski, “Contribution à la théorie de l’endosmose électrique et de quelguesphénomènes corrélatifs”, Bulletin International de l’Académie des Sciences deCracovie, Classe des Sciences Mathématiques et Naturelles, (1901) 182-199

[44] V.L. Streeter, Handbook of fluid dynamics, McGraw-Hill, New York, 1st edition,(1961)

[45] S.P. Timoshenko, J.N. Goodier, Theory of elasticity, McGraw-Hill Int., Singapore, 3rd

international edition, (1970)[46] R.W. Tjerkstra, M.J. de Boer, J.W. Berenschot, J.G.E. Gardeniers, A. van den Berg,

M.C. Elwenspoek, “Etching technology for chromatography microchannels”,Electrochimica acta, 42-20, (1997) 3399-3406

64 Chapter 3

[47] R.W. Tjerkstra, M. de Boer, E. Berenschot, J.G.E. Gardeniers, A. van den Berg, M.Elwenspoek, “Etching technology for microchannels”, Proc. IEEE MEMS’97, (1997)147-152

[48] W. Urbanek, J.N. Zemel, H. Bau, “An investigation of the temperature dependence ofPoiseuille numbers in microchannel flow”, J. Micromech. Microeng. 3, (1993) 206-208

[49] F.W. White, Fluid mechanics, McGraw-Hill, New York, 3rd edition, (1994)[50] Zengerle, M. Leitner, S. Kluge, A. Richter, “Carbon dioxide priming of micro liquid

systems”, Proc. IEEE MEMS’95, (1995) 340-343

65

44 TTHHEE PPRREESSSSUURREE // FFLLOOWW SSEENNSSOORR,, AACCAASSEE SSTTUUDDYY**

The theory concerning fluid dynamics, treated in thepreceding chapters, will be applied to a device: the pressure/ flow sensor. This sensor, built with micromechanicalfabrication techniques, is an example of a simple, secondorder system that can be described with analytical formulas.The sensor design is worked-out and its performance andapplication areas are analyzed.

4.1 Introduction

In the area of integrated fluid analysis systems such as µTAS, liquid or gas flows need to bemeasured and controlled [2,6]. The flows can be dosed by using for instance regulatedmicropumps and active valves [9,7,13]. To adapt the flow delivery to changing impedancesand to know exactly the parameters, at which it is delivered, sensors are needed. For examplethe impedance (e.g. resistance) of the system can show fluctuations due to switching ofvalves or clogging up of channels due to pollution. The parameter of interest for feeding achemical detection system is mass flow. Pressure is the complementary parameter, needed tocompute the applied hydraulic power.

Different principles for flow measurement with use of microsensors have beenpresented. In table 4.1 the main principles are sketched. For gas flows, thermal sensors arevery suitable [13]. With use of a heater resistor a small increase in temperature of the gasflow is accomplished.

* Based on: R.E. Oosterbroek, T.S.J Lammerink, J.W. Berenschot, G.J.M. Krijnen, M.C. Elwenspoek,A. van den Berg, “A micromachined pressure / flow-sensor”, Sensors and Actuators A, 1999

66 Chapter 4

sensor description sensing principle principle sketch ref.

thermal flow sensor heat transportation due tothermal convection

flow

sensors

heater thermal boundary layer [13][20] [5][14][11][12]

shear stress sensor shear stress in the fluid at thewall due to viscosity springs

velocity profilesuspended plate

[17]

inertance drag sensor(beam type)

bending of a beam due todrag forces caused byinertance of the passing fluid flow

flexible beam [26]

viscous drag sensor pressure drop is sensed overa small channel by means ofpressure sensors

pressure sensors

flow

resistance channel [3] [16]

inertance drag sensor(membrane type)

bending of a membrane dueto drag forces caused byinertance of the passing fluid

orificemembrane

flow

[19]

lift force sensor lift forces on a wing due toinertance of the passing fluid

lift forceflow

wing

[23]

Prandtl Micro FlowSensor (PMFS)

forces on a plate due to thedifference between thestagnation pressure and thestatic pressure in a fluidflowing around a body

flow

stagnation point

static pressure

stagnant pressure

deflection [1]

Table 4.1 Overview of different flow measuring principles used in MST

At some distance from the heater a second resistor is heated up by the transported heatflow (convection), which depends on the flow-rate. This sensor can be used for DC flows aswell as AC and even acoustic flows as shown in a very nice application example, the“Micro-flown”, as developed by H.E. de Bree [4]. The driving conditions for this type ofsensor can be varied such that both range, accuracy, linearity and temperature sensitivity canbe changed [c]. E. Kälvesten et al. [11] presented an integrated system comprising twothermal flow sensors and a pressure sensor for measuring the flow rate and direction as well

The pressure / flow sensor, a case study 67

as pressure at a small location for turbulence analysis. A CMOS compatible sensor for onlinedetermination of blood flow is presented by R. Kersjens et al. [12]

A different type of flow sensing is that of measuring mechanical loads generatedduring fluid flow. Shear stresses in the fluid due to the viscosity of the fluid are related to thefluid flow over a plate. A. Padmanabhan et al. [17] presented a sensor based on this relation.An in-plane movable plate is used to transform the shear stresses into a displacement, whichis measured optically. A different way to measure the flow-induced drag is to put anobstruction in the flow path such as presented by A.J. van der Wiel [26] and M. Richter [19].Besides drag, lift forces on a sensor object can be registered such as demonstrated by N.Svedin [23]. By putting a small wing in the fluid with a certain angle of attack, a non-symmetric pressure distribution is obtained resulting in a net lift force. A related sensingmethod is used in the “Prandtl Micro Flow Sensor” by O. Berberig et al. [1] where thedifference between the stagnant pressure on one side of a plate and the static pressure on theother side results in a net force which varies the electric sensor capacity.

In this chapter the pressure / flow-sensor [16] is discussed which can sense bothflow-rate and pressure to deliver all relevant information for flow and pressure delivery in aµTAS. The pressure is measured with capacitive or piezo-resistive pressure sensors, whereasthe flow rate is computed from the pressure drop over a well-defined, hydraulic resistancechannel. Design formulas, the static and dynamic behavior and the resulting advantages anddrawbacks are discussed.

4.2 The flow sensing principle

The flow sensing principle of the pressure / flow-sensor is to measure the pressure drop overa hydraulic resistor. Deriving the flow-rate out of this differential pressure signal is wellknown. There are two ways to obtain a relation. A conversion of kinetic energy (speed) topotential energy (pressure) can be accomplished by leading the flow through a converging /diverging nozzle such that the speed is increased locally. Measuring the dynamic and staticpressure and using the relation between pressure and velocity according to Bernoulli givesthe fluid speed [10]. This principle is used in venturi type macro flow-sensors and is onlyapplicable when no substantial energy losses due to friction are expected. For microchannelswith liquid flows at low Reynolds values, this energy loss cannot be neglected. Therefore wechose for measuring the pressure loss over a hydraulic resistance [3]. This means that thesensor is passive and a small amount of hydraulic energy is extracted from the fluid flow andtransformed into a pressure drop signal. The principle is similar to the well-known use of anelectrical shunt resistor to convert current into a measurable voltage drop.

68 Chapter 4

4.3 Fabrication

The functional layout of the sensor is drawn in figure 4.1. To guarantee that the staticpressure instead of the dynamic pressure is measured, the fluid velocity in the resistor mustbe much higher than at the points where pressure is measured. Thus two chambers, one at theentrance and one at the exit, are needed. The space required for the pressure sensormembranes can be used for this.

For the micro pressure / flow-sensor we made two prototypes, one hybrid design,consisting of two piezo-resistive sensor dies, glued on top of a 10x5x0.9 mm glass-siliconsubstrate, embedding the resistor channel and a fully, 10x5x1.4 mm integrated design withcapacitive pressure sensors. Figure 4.2 shows a schematic view of the hybrid variant.

pyrex

flow in

capacitive pressure sensors

channel

P P1 2

flow out

silicon

pyrex

Figure 4.1 Schematic view of the lay-out of the integrated capacitive pressure / flow-sensor,fabricated with bulk micromachining techniques

With an-isotropic KOH etching, holes were made through <100> oriented silicon.After the resistor channels are isotropically etched in the glass wafer with HF, usingchromium as a mask layer, holes are created through the wafer, using a powder blastingprocess. With use of the anodic bonding process, the glass wafer is mounted on the siliconwafer. A stamping method is used to pattern glue accurately on the pressure-sensor dies(~100 µm precision), after which the dies are mounted on top of the glass-silicon sandwich.Finally the dies are mounted on a “system board” and electrical and fluidic connections are.A ready mounted sensor is shown in figure 4.3.


pyrex

flow in

piezo-resistive pressure sensors

channel

P P1 2

flow out

silicon

glue

Figure 4.2 Lay-out of the hybrid variant of the pressure / flow-sensor, using piezo-resistivepressure-sensors

Figure 4.3 Mounted hybrid pressure / flow-sensor with electrical connectors and tubing

Since the sensor principle is passive and needs no actuation power, a low powerversion is designed by replacing the piezo resistive pressure sensors by capacitivetransducers. For this, a fully integrated design has been made. Figure 4.1 and 4.4 show thecross-sections. The sensor is built in a glass-silicon-glass sandwich structure. In the bottomglass wafer the hydraulic resistors are etched, again using isotropic HF etching incombination with a chromium mask (figure 4.5, sequence C). After this, holes through theglass are created.

70 Chapter 4

glass

silicon

glass exit holeentrance hole

membrane

resistor channel

membrane

Figure 4.4 SEM picture of the cross-section of the integrated capacitive pressure / flow-sensor

The top wafer holds the upper, fixed electrodes for reading-out the membranedeformations as a function of the applied pressure. By depositing the electrodes in a cavity,the initial gap between the electrodes is defined. The process steps used for this are drawn infigure 4.5, sequence A. The first step (A1) consists of patterning a chromium mask layer bymeans of a wet chromium etching technique. After the glass is etched in HF such that thecavities have reached the required depth (A2), chromium and platinum are deposited (A3).Since the resist - chromium mask is under etched during the HF step, the mask is used as ashadow mask as well, such that the edges of the top electrode are well defined inside of thecavity. With this combined etch and shadow mask, the electrode material is only deposited atthe bottom such that short-circuiting of the electrical connections is avoided. After strippingthe resist / chromium layers in HNO3, the glass wafer with the top electrodes is finished.

The silicon wafer contains the membranes and counter electrodes for the pressuresensors. First, the membranes are etched anisotropically in a KOH solution, using siliconnitride as mask and defining the membrane thickness by a stop in time (steps B1-2). Afterthis, the silicon nitride at the membrane side is removed at areas that need to be bonded andthe lower electrodes are patterned with a lift-off technique.

For bonding the two glass wafers with the silicon wafer, the anodic bonding method isused. Because the distance between the upper and lower electrodes is rather small, theelectrostatic forces on the membranes during the bonding process could damage the sensor.


A top electrode C channel

1

2

3

4

5

B membranes

Figure 4.5 Process sequence of the integrated capacitive pressure / flow-sensor: (A) top electrodewith combined etch / shadow mask, (B) membrane + lower electrode fabrication, and(C) hydraulic resistor processing.

Therefore all upper and lower electrodes are connected to the same potential, resultingin a potential drop between the glass and silicon only. Dicing of the sensors is done such thatthe connections to the upper and lower electrodes become accessible. For this, a V-groove isetched in the silicon and the top and bottom glass wafers are partly diced at a shiftedposition. After breaking, the bond pads become accessible, as shown in figure 4.6.

close-up of the sawed lines before and after breaking

A B

C

Figure 4.6 Dicing method to free the entrance to the electrodes: (A) Top-view of half of the sensor(one pressure sensor only), (C) Combination of saw-lines and v-grooves. After breaking,the upper electrode becomes accessible as shown in the photos (B).

72 Chapter 4

4.4 Modeling of the stationary sensor behavior

4.4.1 Membrane deflectionVarying the resistors and / or the dimensions of the sensor membranes makes it possible toadapt the sensor for a specific flow and pressure range. To predict the effects of the differentdesign parameters, we derived simple design formulas for the fluid mechanical as well asstructural mechanical behavior. Only the fully integrated capacitive pressure / flow-sensorwill be discussed, since commercially available pressure sensor dies were used for the piezoresistive variant.

The used parameters are summarized in tables 4.2 and 4.3. The capacitance / pressurerelation of the sensors is defined by among others the stiffness of the membranes. For smalldeflections the dimensionless linear pressure / deflection membrane formula (4.1) can beused [24,18]:

0WKQ b� (4.1)

Q is a dimensionless load parameter, Kb the bending stiffness and W0 the centerdeflection of the membrane relative to the membrane thickness. Relation (4.1) fits well fordeflections W0, smaller than about 0.5. For values of W0 larger than 0.5, the in-plane stressesbecome important resulting in a non-linear load deflection relation. A simple approximationfor these situations with or without additional pre-stress is given by:

300 WKWKQ db �� (4.2)

membrane theory capacitanceparameter description units parameter description unitspww0

ha2*ar�

x,yE�

�0

pressuredeflectioncenter deflectionthicknessradiuslengthradius coordinate.angular coordinatex-y coordinatesmodulus of elasticityPoisson’s constant.pre-stress

Nm-2

mmmmmmrad.mNm-2

-Nm-2

c�0

�r

sdd0

rc1

rc2

xc

yc

Sc

capacitancedielectric constant of vacuumrelative dielectric constantareagap distancegap distance (unloaded)inner electrode radiusouter electrode radiusouter x-coordinate electrodeouter y-coordinate electrodeelectrode area

FC2N-1m-2

-

m2

mmmmmmm2

Table 4.2 Parameters used for the description of the membrane deflections and sensor capacity.


membrane theory capacitanceparameter description def. parameter description def.QWW0

R�

X,Y�0

loaddeflectioncenter deflectionradius coordinateangular coordinatesx-y coordinatespre-stress

pa4/Eh4

w/hw0/hr/a�

x/a, y/a�0a2/Eh2

CD0

Rc1

Rc2

Xc

Yc

specific capacitancegap distance (unloaded)inner electrode radiusouter electrode radiusouter electrode x coord.outer electrode y coord.

ch/�a2

d0/hrc1/arc2/axc/ayc/a

Table 4.3 Definitions of the introduced dimension-less membrane and capacitance parameters

membrane shape analysis Kb Kd ref.circular analytical

small deflectionsno pre-stress

)1(1264

2��

[24]

circular analyticallarge deflectionsno pre-stress

04��1

67.2 [24]

circular analyticallarge deflectionsno pre-stress

��

��

�

� 211

316

� 66155582850015010 2

�� [22]

circular analyticallarge deflectionspre-stress

04)1(3

4�

��

� )1(37

�

�

�

� [22]

circular FEMsmall deflectionsno pre-stress

)1(1264

2��

[18]

circular FEMlarge deflectionspre-stress

00.4 �

)233.0026.1)(1(67.2

��

[18]

square analytical /FEMsmall deflectionsno pre-stress

)1(126.49

2��

[24][18]

square analyticallarge deflectionspre-stress

004.3 �

�

�

�

�

140.047.1 [24]

square FEMlarge deflectionspre-stress

041.3 �

�

�

�

�

1585.098.1 [18]

Table 4.4 Analytically and numerically obtained deflection stiffnesses for circular and squaremembranes

74 Chapter 4

In this relation, K� is the pre-stress term whereas Kd represents the net stiffness constantwhen in-plane stresses become important. For circular and square membranes, thedefinitions of the stiffness constants differ. Analytical and numerical results, obtained fromliterature [24,18,[22] are summarized in table 4.4.

To compute the electric and hydraulic capacitance of the pressure sensor, thedeflection shape of the membrane in needed. For round membranes, the spherical relationgiven by:

220 )1( RWW �� (4.3)

For square membranes with the axis system origin oriented in the membrane center, cosinefunctions can be used according to:

��

��

��

�

��

�� YXWW π

21cosπ

21cos0 (4.4)

However, we experienced that the deflections of membranes with clamped edges are betterdescribed with the spherical relation:

22220 )1()1( YXWW �� (4.5)

4.4.2 Electric pressure-sensor capacitanceThe electric capacitance of the pressure sensor varies when pressure is applied on themembranes due to the changing gap geometry between the upper and lower electrode. Thispressure / capacitance relation can be approximated by the surface integral given in equation(6).

dsd

dsd

ccc S

rS

r ��

10

0��

�� (4.6)

With d the gap distance between the upper and lower electrodes as function of the positionand the electrode area. Substitution of the shape function of a round membrane results in thedimensionless deflection / capacity relation (4.7), where the circular electrode ranges fromR=Rc1 to Rc2.

� �� 00

21

22

2

022

00

1tan1tan)1(

0

0

0

02

1DW

RaRaRWD

RdRdC cDW

cDWR

RR

c

cc

��

�

��

� � ��

��

�

�

(4.7)


The center deflection, W0, can be replaced by one of the equations (4.1) or (4.2), dependingon the existence of large deformations and pre-stresses. For the square membranes, noanalytical solutions exist so that the integrals must be computed numerically.

4.4.3 The hydraulic resistanceA pressure drop, related to the flow-rate is obtained by energy dissipation in the resistancechannel between the two pressure sensors. In our design this is simply implemented by anarrowing of the channel cross-section. The pressure drop over a channel with an effectivediameter, deff, is given by equation (4.8) [8,25].

ldv

fpeff

eff

2

2�� (4.8)

A list of the used flow parameters and their units is given by table 4.5. In our applications,we assumed a rectangular shape of the resistor cross section. The correction factor for thisgeometry [25] results in:

lS

kRev

p dheff ��

��

� ��

��

�

2

81 �

� (4.9)

This equation shows the flow dependent and geometry dependent relation of the pressuredrop. With the definition of the Reynolds number according to equation (4.10), andsubstituting this in the flow dependent part, equation (4.11) is obtained.

�

� effeff dvRe � (4.10)

lS

kdv

p dh

eff

eff ��

��

� ��

��

� ��

81 (4.11)

It is shown that the flow-sensor will measure the volume flow and is sensitive to viscositychanges. These aspects will be discussed further on in this article.

The HF etched channels in our sensor were relatively long and wide compared to thedepth. In a first approximation we neglected the entrance and exit effects as well as therounded corners, created during the isotropic etching process. The channel cross-section wasassumed to be rectangular. For this situation, the resistance can be described with equation(4.12). The parameters a and b are the side lengths of the cross-section. The friction constantcan be obtained empirically and is found in literature [25]. Finally the volume flow-rate canbe extracted from the pressure drop with use of equation (4.13).

76 Chapter 4

lba

bakR dhhyd ��

��

��

� �� 33

22 )(512� (4.12)

hydRp�

� � (4.13)

description dimensional parameter unitsdisplaced volume � m3

volume flow-rate � m3s-1

kinematic viscosity � m2s-1

mass density � kgm-3

wetted perimeter � mpressure drop �p Nm-2

thermal expansion coefficient �T K-1

dynamic viscosity µ Nsm-2

channel width a mchannel depth b mhydraulic capacitance Chyd N-1m5

effective diameter deff mhydraulic diameter dh mhydraulic power consumption E� W

friction factor f -resonance frequency fhyd Hzhydraulic transfer function Ghyd -temperature-viscosity constant k� -volume expansion coefficient k� K-1

laminar friction constant kdh -minor loss coefficient km -specific heat capacity kT Jkg-1K-1

channel length l mhydraulic inertance Lhyd Ns2m-5

quality factor Qhyd -Reynolds number Re -hydraulic resistance Rhyd Nsm-5

cross-section area S m2

time t stemperature T Keffective velocity veff ms-1

Table 4.5 Used flow parameters and their units


In this case, the measured pressure signal is linearly related to the flow-rate. The entranceand exit effects however cause so-called minor losses, which introduce a non-linear behavioras is described by equation (4.14).

meffor kvp 221

min �� (4.14)

For the situation of the resistance channel, the minor loss coefficient, km, can be ashigh as 0.5. The relative influence of the minor losses compared to the constant channelresistance is expressed in equation (4.15). This non-linearity ratio represents the validity ofneglecting the minor losses.

� � lbaba

kk

pp

dh

m

major

or22

min 256�

�

�

��

�

� (4.15)

For flow-rates on the order of a few microliters per second, a kinematic viscosity of about10-6 m2s-1, an equal width and depth of the channel and a channel length of a fewmillimeters, the ratio will be less than one percent. Increasing the channel length can furtherreduce the non-linear effect of the minor losses. In figure 4.7 the measured and calculatedpressure drop are shown as a function of the flow-rate in case water is used. As expected, thenon-linearity is very small and not noticeable. The difference between the measured andcomputed resistance is substantial (21%). The reason for this might be found in the cross-section geometry and roughness of the resistor channel. We assumed a smooth, rectangulargeometry whereas pictures of the channel show a rounded trapezium shape. These roundedcorners reduce the net effective cross-section area, which means an increase in resistance.Since the cross-section parameter influences the resistance to the power four as was shownin equation (4.12), this substantial difference between the measurements and computedresistance can easily be obtained: a 21% resistance difference is caused by a net dimensiondifference of 4.8%

If only major losses are taken into account, the hydraulic energy dissipation per unittime (power) is:

2�� hydmajorhyd RpE �� (4.16)

This loss of hydraulic energy is converted to thermal energy and thus will rise the fluidtemperature. Under the assumption that the heat is only transferred uniformly to the fluidwithout losses to the channel walls, this temperature rise is given by:

T

hyd

kR

T�

�� (4.17)

78 Chapter 4

For a sensor design, used in combination with ethanol, resulting in a hydraulicresistance of 1.7*1012 Ns/m5, with a density of 787 kg/m3, heat capacity of 2.44*103 J/kgKand used to measure flows of 1 µl/s, the dissipated energy is 1.70 µW. Since this dissipatedenergy will heat up the liquid only 8.9*10-4 K, the effect is negligible. It shows that thepressure / flow-sensor can be designed to consume besides electrical power, little hydraulicpower as well.

Measured and computed pressure-drop vs. flow rate

flow-rate (µl/s)

pres

sure

-dro

p(Pa

)

-1 .0E +04

0 .0E +00

1 .0E +04

2 .0E +04

3 .0E +04

4 .0E +04

5 .0E +04

6 .0E +04

7 .0E +04

8 .0E +04

9 .0E +04

0 .0 0 .5 1 .0 1.5 2.0 2 .5 3.0 3 .5 4.0 4.5 5.0

measured: R = 1.74 .10 Ns/m

computed: R = 1.37 .10 Ns/m13

13

5

5

Figure 4.7 Measured pressure-drop / flow-rate relation of the sensor. The non-linear entrance andexit effects are negligible.

4.5 Modeling of the quasi-dynamic sensor behavior

When the sensor is operated in a system with fast fluctuating fluid speeds, it is important toknow the dynamics. An example of such application would be to sense the flow-rateproduced by a membrane pump. The dynamic behavior of the sensor is important to predictthe time dependent signal from the delivered flow and pressure. Due to the dynamicimpedance of the sensor, a frequency dependent amplitude change and phase shift of thepressure signal, described by the transfer function, can occur.

Transfer functions are based on the assumption of harmonic flows. In practice it isdifficult to obtain this situation, but if a linear system is assumed, other, non-harmonic flowscan be modeled by using Fourier series. A good indication about the dynamic behavior in thefrequency domain can be obtained which is used to estimate the working range of the sensor.Besides the computed hydraulic resistance of the channel, the sensor consists of hydraulic


capacities and inertance [15] as well. In figure 4.8, a schematic of the electronic analogy isdrawn.

Rhyd Lhyd

Chyd

pressure / flow-sensor

Psource Rload

Figure 4.8 Electric analogy of the pressure / flow-sensor, simulated with a PSPICE model: theresistance, capacitance and inertance of the sensor. The sensor is fed by a pressuresource and loaded by a resistance impedance.

The pressure sensors form the hydraulic capacities of the sensor. Due to the membranedeflection under a pressure load, liquid can be accumulated. In general, the hydrauliccapacity Chyd is described by:

dtdpChyd�� (4.18)

Since the flow rate is defined as the amount of transported volume per time, the capacitanceis defined as the volume change per unit pressure variation:

dpdChyd�

� (4.19)

The volume under a square membrane is given by integrating the dimensionless deflectionformula (4.5).

� � � �bb K

QdXdYYXKQ

22525611

1

1

1

1

2222��

� �

(4.20)

The capacity for the small deflections of a square membrane will be:

� �23

6

3

6

128.01225256

��Eha

KEhaC

bhyd (4.21)

80 Chapter 4

It is assumed that both pressure sensors are identical such that the capacities at both sides ofthe resistance channel are identical.

Inertance of the sensor is caused by the acceleration of liquid mass in the sensor.Because the fluid velocity under the sensor membranes is assumed to be much smaller thanthe velocity in the hydraulic resistor, the kinetic energy is regarded to be concentrated in theresistor. Therefore only the inertance in the resistor channel is taken into account. Thehydraulic inertance, Lhyd, is defined by equation:

dtdLp hyd�

� � (4.22)

According to Newton’s second law, the force per area needed to accelerate a plug of liquidwith length l and cross-section area S equals:

dtd

Slp ��

� � (4.23)

Hence the inertance of the filled channel with square geometry is defined by:

bal

SlLhyd

�� (4.24)

The lumped element analogy of the electric circuit indicates that a second order systemis to be expected. This electric equivalent circuit is shown in figure 4.8. The complextransfer function of a LRC circuit is expressed in (4.25). For the situation with a pressuresource, as shown in figure 4.8, only the capacitance of the downstream pressure sensor is ofimportance.

hydhydhydhydhyd CLCRj

G 211

��

� (4.25)

For this second order system, resonance is to be expected for the LC combination at afrequency fhyd that satisfies equation (4.26) with a quality factor Qhyd expressed by (4.27).

hydhydhyd CL

f�2

1� (4.26)

hyd

hyd

hydhyd C

LR

Q 1� (4.27)

The prototypes of the capacitive pressure / flow-sensor consist of square siliconmembranes of about 25µm thickness and a length and width of 1500 µm. The hydraulic


capacity of these membranes will be around 1.7*10-17 m5/N. For the channels, threedifferent widths are chosen: 200, 340 and 570µm. The length is 2900 µm and the depth 21µm. For the 340 µm wide channel, the resistance for ethanol becomes 1.7*1012 Ns/m5 withan inertance of 3.2*108 Ns2/m5. With these values, the resonance frequency is 2.2 kHz withquality factor 2.56. When the channel width is varied, the resistance as well as inertance willbe affected. Figures 4.9 and 4.10 show the computed amplitude and phase angle respectivelyof the transfer curves for the three different channel sizes.

Transferfunction of the pressure / flow sensor for different channel widths

570µm

340µm

200µm

frequency (Hz)

ampl

itude

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.00 1000 2000 3000 4000 5000 6000

Figure 4.9 Computed amplitude of the hydraulic transfer of the fabricated pressure /flow-sensor asfunction of the driving frequency

From the equations, derived for the dynamic transfer of the sensor, it can be concludedthat the current sensor design can be used dynamically with a fluid frequency up to about 1kHz. If a higher dynamic range is wanted, the resonance frequency must be increased. If welook at equation (4.26), this is possible by reducing the hydraulic capacity or the inertance.The first parameter depends on the pressure sensor design. A reduction of the hydrauliccapacity means that a stiffer membrane must be used which has consequences for the electricbehavior: smaller gap sizes are needed between the upper and lower electrodes to gain thesame pressure sensitivity. When commercial dies are used for the pressure sensors, as for thepiezo resistive variant, the resistance channel can be varied, causing a change of theinertance but hydraulic resistance as well. Variation of the channel dimensions such that theresistance is kept within a pre-defined range, defined by the sensitivity of the pressuresensors, and reducing the inertance can be the subject of optimization. A boundary condition

82 Chapter 4

in this is the length of the channel, which needs to be long enough to reduce the non-lineareffects of the entrance and exit resistance.

Although an estimation is made about the dynamic work range of the sensor, regardingthe impedances of the different parts of the sensor only, the work range will be stronglydetermined by the system surroundings. Long interconnects to and from the sensor willincrease the resistance (damping) as well as generate additional inertance. Due to thecombination of this inertance with the sensor capacities, additional resonnances can occur atlower frequencies.

Transferfunction of the pressure / flow sensor for different channel widths

frequency (Hz)

phas

e an

gle

(deg

rees

)

0

-20

-40

-60

-80

-100

-120

-140

-160

-180

1000 2000 3000 4000 5000 6000

570µm

340µm

200µm

Figure 4.10 Computed phase angle of the hydraulic transfer of the fabricated pressure / flow-sensoras function of the driving frequency

4.6 Accuracy and stability

Temperature changes can have strong influences on the stability of the sensor. The maininfluence of temperature variations on the sensor signal is due to a change of density andviscosity as temperature varies. For liquids, the absolute viscosity decreases with increasingtemperature. This temperature dependent viscosity change can be approximated for manyliquids with relation [25]:

��

��

��

�

� � 1293exp)(

293T

kT

K

�

�

�

�

(4.28)

Temperature viscosity constants, k�, vary for different liquids. For ethanol for example thisvalue is 5.72 [25]. Around 293 Kelvin, the relative change in viscosity will be about 2%/K.


This influence of temperature on the viscosity affects the sensor signal proportionally sincethe viscosity is linearly related to the pressure drop as was shown by equation (4.12). Thisinfluence has consequences for the stability of the sensor. For high accuracy, the temperatureof the liquid must be known or be controlled. For the first prototypes no high precision wasaimed at and thus no temperature regulation or sensing system was implemented. It can beconcluded that for an uncompensated sensor the sensor signal will give an underestimationof the ethanol volume flow rate of about 2 percent per Kelvin increase.

If we want to know the mass flow, the sensor volume flow signal must be multipliedwith the mass density of the fluid. This density varies with temperature according to [25]:

� �29311)(

293��

�

TkT

K ��

�

�

(4.29)

Specific values for the volume expansion coefficient, k�, are around 110.10-5 /�K for ethanol[25], so that the change in mass density will be about 0.1 percent per Kelvin. If temperaturerises, the density will decrease. The temperature induced density variation of ethanol willthus cause an underestimation of the mass flow rate of 0.1 percent per Kelvin temperatureincrease.

Besides the change in fluid properties, the geometry changes of the sensor also affectthe hydraulic resistance. Since the resistance is inversely related to the channel cross-sectionwith to the fourth power, small variations in channel size will affect the resistancesubstantially and thus give deviations in measured pressure drops. The influence of thechannel geometry can be expressed by the first derivative of the resistance to the geometryparameter. For simplicity the situation of a circular channel is taken such that the resistanceis inversely related to the fourth power of the diameter. The relative resistance change willthus be defined by:

hh

hyd

hyd ddR

R4

dd1

�� (4.30)

The linear thermal expansion coefficient �T of the used glass (Hoya SD-2) is 3.2*10-6 K-1.This means that the relative resistance change will be:

Td

hyd

hyd

hyd

hyd

hyd T

d

dR

RTTR

Rhyd

�4d

d1d

)(d1��

�

�� (4.31)

Substituting �T, gives a resistance change of only 1.28*10-3 percent. Hence the resistancechange due to temperature induced geometry variations is negligible compared to theviscosity and density changes of the fluid. Other mechanisms such as pollution of the sensor,

84 Chapter 4

causing coverage of the channel walls can give rise to serious malfunctioning. Alsoclogging-up of the channel when particles are involved is disastrous.

4.7 Viscosity versus inertance induced dissipation

In the introduction, different types of drag flow sensors were discussed. These sensors can bedivided into two main types: the viscosity-induced drag and inertance-induced drag sensors.The fabricated sensors and the shear-stress sensor [1] are of the first kind whereas sensorsfrom references [19,23,26] are of the inertance type. For the latter types, only minor lossesare measured which means that the sensor becomes insensitive to viscosity changes asshown in equation (4.14). An expression for the flow-rate as function of the measuredpressure is obtained by integrating this relation over the orifice area:

m

or

kpS�

�� min2� (4.32)

Since we found a strong temperature sensitivity of the viscosity, the inertance-inducedsensors are more temperature-stable than the viscosity-induced alternatives. However, it isdifficult to eliminate all viscous forces from the sensor [19]. For a resistance geometry like acircular orifice in a membrane for example, this means that the radius must be much largerthan the membrane thickness (length of the resistance). Therefore the working range of thistype of sensors is strongly limited by technology. Scaling-down of microsystems will worsenthis situation even more since Reynolds numbers will decrease and viscosity will more andmore dominate.

Another aspect of the use of minor losses is the fact that mass-flow is measured insteadof volume flow. For chemical analysis mass flow is of interest rather than the deliveredvolume. Equation (4.32) can be re-written in terms of mass-flow:

m

or

kpSm min2 ��

�� (4.33)

From this equation, it is shown that the mass-density of the fluid is still needed in order toobtain a value for the flow-rate. The number of material parameters however, is reducedfrom two to one since no viscosity terms are involved. The relation between the flow-rateand measured pressure is no longer linear. For small flow-rates the sensor becomes moresensitive than for larger flows.

These considerations lead to the conclusion that the both sensor types have advantagesand drawbacks. Minor losses can be used in order to reduce temperature influences but areless suitable for detection of flow-rates at low Reynoldsnumbers and give a non-linear sensor


output. Both sensor types are supplementary since viscosity can be measured with theviscosity drag sensor after the flow-rate is obtained from the inertance drag sensor.

4.8 Conclusions and discussion

A combination of a pressure and flow-sensor, based upon the principle of measuring theviscosity-induced pressure drop over a hydraulic resistor was discussed. The interestingaspect of this pressure / flow-sensor is that the principle is rather simple. It is comparable tomeasuring currents in an electrical circuit by sensing the voltage drop (pressure drop) over afixed resistance.

A few points make the sensor very suitable for micro fluid handling systems: unlikemany thermal mass flow-sensors, the electrical contacts of the pressure / flow-sensor arefully galvanically insulated from the fluid. There are no heater and sensor elements inelectrical contact with the medium due to which a voltage drop may occur between the fluidand ground. For drug delivery or some chemical analysis applications, this can be animportant requirement. It also facilitates integration with other components, which lackgalvanic insulation.

A second feature is the fact that no energy injection in the liquid is used. Only littleenergy (micro Watts) is extracted from the fluid stream due to friction. This means thatheating up of the fluid is negligible, which is an important issue for temperature sensitivematerials or chemical reactions. The fact that there is only little power consumed from theflow to obtain a pressure drop means that no additional electrical energy is needed togenerate an actuator signal. These signals, like the heat transfer to the fluid in a thermalflow-sensor, usually consume a lot of energy. Using a combination of capacitive pressuresensors further reduces the power consumption, which makes the sensor very suitable in lowpower applications.

The robustness of the sensor is high since there are no fragile bridges in the sensor, likethe structures needed in many thermal flow-sensors. Membranes are the weakest structuresused. They however are designed to withstand the maximum expected pressures and form noobstacle in the flow path. A final positive feature of the sensor is the reduction of theelectronics needed for read-out. The electronics needed to read-out the pressure is alsoneeded to measure the flow. So the same kind of electronics can be used or an additionalmultiplexer to read-out the second pressure sensor.

Besides these strong points, there are some weak points to consider. The mentionedpositive aspect of a passive sensor also has a drawback. If the sensor is used in a system withfor example micropumps to deliver flow at a certain pressure, these pumps must compensate

86 Chapter 4

the energy loss in the sensor due to friction. A good hydraulic resistance design, combinedwith sensitive pressure sensors can minimize this drawback.

With the principle of differential pressure flow sensing, the volume flow-rate insteadof mass flow-rate is measured. For chemical analysis however, knowledge of mass flow isneeded. Therefore the mass density must be known in order to compute the mass flow.Another parameter that must be known to be able to derive the volume flow out of thepressure difference, is the viscosity. Changing the concentrations of the medium might affectboth density and viscosity. These effects must be known in order to derive good volume flowvalues. Temperature changes of the fluid give rise to substantial fluctuations in viscosity.For ethanol at room temperature, this is 2 percent pressure change per Kelvin. Consequentlyfluid temperature measurements must be measured and / or controlled to reach a high flowmeasurement precision. On the longer term, the hydraulic resistance can change due topollution. Therefore, like many other flow-sensors, the functionality is hampered when thewalls get coated. Particles also form a severe threat because they can clog the resistancechannel.

For the micromachined sensor design, presented in this paper, formulas are derived topredict the static as well as dynamic behavior. Because of the presence of hydraulicresistance, inertance and capacitance, the device will act as a damped second order systemwith a resonance frequency in the range of a few kHz when ethanol is used as a fluidmedium. Optimizing the hydraulic pressure sensor capacitance and channel geometry canincrease this range.

These sensor aspects lead to the conclusion that the pressure / flow-sensor is simpleand low power consuming dynamic fluid sensing device, capable of measuring bothparameters, describing the hydraulic domain: pressure and flow-rate. If no temperaturecompensation is applied, the application area will be low precision flow rate measurements.When temperature is known or controlled, high precision is possible.


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[8] R.W. Fox, A.T. McDonald, Introduction to fluid mechanics, John Wiley & Sons, NewYork, Third edition, (1985)

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[11] E. Kälvesten, Ch. Vieider, L. Löfdahl, G. Stemme, “An integrated pressure-flow sensorfor correlation measurements in turbulent gas flows”, Int. Conf. on Solid-State Sensorsand Actuators, (1995) 428-431

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88 Chapter 4

[13] T.S.J. Lammerink, N.R. Tas, M.C. Elwenspoek, J.H.J. Fluitman, “Micro-liquid flowsensor”, Sensors and Actuators A, (1993) 45-50

[14] T.S.J. Lammerink, A. van den Berg, J.H.J. Fluitman, “Micro system array sensors”,Proc. Dutch Conf. on Sensor Tech. 1994, The Netherlands, (1994), 173-177

[15] T.S.J. Lammerink, N.R. Tas, J.W. Berenschot, M.C. Elwenspoek, J.H.J. Fluitman,“Micromachined hydraulic astable multivibrator”, Proc. IEEE MEMS’95, TheNetherlands, (1995) 13-18

[16] R.E. Oosterbroek, T.S.J Lammerink, J.W. Berenschot, A. van den Berg, M.C.Elwenspoek, “Designing, realization and characterization of a novel capacitive pressure/ flow sensor”, Int. Conf. on Solid-State Sensors and Actuators, Chicago, USA, (1997)151-154

[17] A. Padmanabhan, H.D. Goldberg, K.S. Breuer, M.A. Schmidt, “A siliconmicromachined floating-element shear stress sensor with optical position sensing byphotodiodes”, Int. Conf. on Solid-State Sensors and Actuators, Sweden, (1995) 436-439

[18] J.Y. Pan, P. Lin, F. Maseeh, S.D. Senturia, “Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films”, Tech. DigestIEEE Solid-State Sensors Workshop, (1990) 70-73

[19] M. Richter, M. Wackerle, P. Woias, B. Hillerich, “A novel flow sensor with high timeresolution based on differential pressure principle”, Proc. IEEE MEMS’99, OrlandoUSA, (1999) 118-123

[20] R.J. Ross, “Optimization of thermal mass-flow sensing principles”, Masters Thesis,University of Twente, (1998)

[21] S. Shoji, M. Esashi, “Microflow Devices and Systems”, J. Micromech. Microeng. 4,(1994) 157-171

[22] V.L. Spiering, Package stress reduction for micromechanical sensors: application in apressure sensor, Ph.D. thesis, University of Twente, (1994)

[23] N. Svedin, E. Kälvesten, E. Stemme, G. Stemme, “A new silicon gas-flow sensor basedon lift force”, J. Micromech. Systems, Vol 7-3 (1998) 303-308

[24] S.P. Timoshenko, S. Woinowsky-Krieger, Theory of plates and shells, McGraw-Hill,New York, second edition, (1970)

[25] F.W. White, Fluid mechanics, McGraw-Hill, New York, Third edition, (1994).[26] A.J. van der Wiel, M.A. Boillat, N.F. de Rooij, “A bi-directional silicon orifice flow

sensor characterised for fluid temperature and pressure”, Int. Conf. on Solid-StateSensors and Actuators, Sweden, (1995) 420-423

89

55 MMIICCRROOVVAALLVVEESS

This chapter is dedicated to microvalves. An overview ofthese fluid components, completed with examples ofdifferent types of valves found in literature will be given.The theory treated is restricted to working principlediscussions and fabrication technology. Special attention ispaid to the use of selective bonding processes, which playan important role in creating movable structures with bulkmicromachining techniques. A new theory, developed topredict the chance on fusion bonding, is successfully appliedon different valve types to define areas that need to bebonded and areas were fusion-bonding needs to be avoided.Another aspect that is highlighted is the more pronounceduse of the crystal orientation in anisotropic etching of <100>and <111> oriented silicon to create thin membranes andvalve spring structures.

5.1 Introduction

Microvalves form an important component within the area of µTAS. Since the typicaldifferences between total analysis systems and plain sensors consist of sample pre-treatment,fluid flows need to be directed. Furthermore sample fluid needs to be transported, forexample from the source to a reaction chamber where reagent chemicals will be injected. Forthis transport micropumps can be used [67,98,36,61,146,12,21].

90 Chapter 5

Two different types of valves are distinguished: passive or check valves and activevalves. Check valves can be regarded as the fluidic analogy of the electric diode. In the“open” direction a low hydraulic resistance will be obtained whereas in the opposite theresistance is substantially increased. This diode type fluid component can fulfill an importantrole in micro fluid handling systems. Since the check valve forces the liquid flow in onedirection, back flow can be prevented. For feeding elements such as reaction chambers, backflow of reacted products must be avoided for which check valves can give the solution(figure 5.1A). Another application is in pressure driven flows. By switching externallyapplied pressures on a system, fluid streams can be reversed. However with the use of checkvalves also junctions can be made such that a more complex switching system can be built(figure 5.1B). Currently valves are often used in membrane micropumps. A pulsating flow isusually generated by a membrane driven by an actuator. Two check valves at both sides ofthe pump chamber are used to change the fluctuating flow to a net one-way directed flow(figure 5.1C).

Figure 5.1 Applications for micro check valves: A) back flow prevention in a reaction chamber, B)fluid switching by pressure changing and C) check valves in micropumps.

A more sophisticated fluid switching can be obtained with active valves. Examples forapplications of these valves are injection switches in analysis systems such aschromatography channels [128], flow injection analysis channels [63] and fluid processors[54]. For highly integrated chemical systems that need to process a multitude of differentflows, active valves are much more convenient.

In this chapter first an overview will be given of passive and active valve typespresented in literature. For researching the flow behavior in especially check valves, a

Microvalves 91

selection is made of three different valve designs: the so-called bossed, membrane andduckbill valve. Technology and design aspects of these valves will be treated in thefollowing paragraphs. Important issues involved are the “tricks” to get free movable valveelements for which selective bonding techniques were used. Finally the discussion will befinished with etching techniques for <111> oriented silicon wafers.

5.2 Valve types

5.2.1 Passive valves

Passive valves can be split into two types: valves with and valves without moving parts.Valves with moving parts use the deformation of a spring element or the displacement ofballs to change the resistance. In table 5.1 an overview is given of different principles. Themost commonly used valve type is the flap valve 1. This valve is very popular especially inmicropumps and can be made out of monocrystalline silicon. All of these valves can be fullyprocessed with micromachining techniques except from the ball valve (figure 5.1-7).

Valves without movable elements obtain their flow direction-dependent hydraulicresistance (diode function) from the difference in velocity profiles in the different directions.Three types can be distinguished: the diffuser (figure 5.1-8), nozzle (figure 5.1-9), and Tesla(figure 5.1-10) type. The diffuser and nozzle valves consist of a simple converging ordiverging channel geometry. At small diverging angles, the pressure loss in divergingdirecting becomes lower than in the converging direction. However, when the divergingangle is increased, flow separation will occur in the diverging direction and a vortex flowwill arise. This vortex flow reduces the cross-section of the net flow path resulting in the so-called “vena-contracta” effect. Due to this induced flow-path obstruction, nozzle valves willshow a higher flow resistance in the diverging direction. The direction dependency of theresistance of the Tesla valve is due to the difference of intersection angle of both channels atthe two junctions. In the open-direction, the flow will split into two separate flows, which areinjected in the same direction at the second junction. When the flow direction is reversed,merging of both flow streams takes place in a less-fluent way, inducing a resistance increase.

Both the nozzle as well as Tesla-type valves function due to inertial effects of the flow.This means that rather high Reynolds numbers are needed to be able to exploit the resistanceeffects. The diffuser type also shows a good functionality at low Reynolds numbers at abetter efficiency than the diffuser type. The resistance selectivity however of the diffuser,nozzle and Tesla valves are rather low compared to the other listed valve types.

92 Chapter 5

nr. schematic type references1 flap [129] [66] [144] [145]

[146] [56] [57]

2 flap [125] [139]

3 membrane [113] [53]

4 membrane [67] [98] [61] [72]

5 membrane [111] [112]

6 bossed [120] [130] [1] [136][64] [14]

7 ball [28]

8 diffuser [127] [81] [82] [83] [84][85] [86] [51]

9 nozzle [85] [33] [34] [51]

10 Tesla [7]

Table 5.1 Summation of micro check valve principles and literature references.

5.2.2 Active valvesIn micro system technology, active valves have been made with different actuator principlesand layouts [36,121,21]. Since there is usually a stable state in which the valve needs not tobe actuated, these valves can be split into two groups: normally closed (NC) and normallyopen (NO) valve types. In the non-actuated state, NC valves have a high fluid resistancesuch that the valve is assumed to block the fluid flow. The normally open valve is thecomplement of the normally closed type. For this valve the fluid resistance is minimal whenno actuation occurs. In table 5.2 a list of different active valve types is given. This list gives

Microvalves 93

a good overview of different types of layout and actuation principles although it is notcomplete.nr. schematic actuation type reference1

lower electrode

upper electrode electrostatic NO1/2

[20] [6]

2

lower electrode

electrostatic NC [106] [135] [76] [42][43] [44] [24]

3

piezoelectric elements

piezoelectric NC [52] [125] [24]

4

heater elements

thermalbimetallic effect

NC [8] [99] [68] [69] [49][50] [75] [35] [24]

5

heater meander

thermalthermal expansion

NC [24]

6 + electrode - electrode electrochemical NO [78]

7 coil permanent magnet electromagnetic NO [74]

8 electro magnetsoft magnetic ball electromagnetic NC [59]

9 heater meander thermalthermal expansion

NO [30] [141] [142] [143][37]

10heater meander

thermalthermal expansion

NC [41]

11 top electrode

bottom electrode foil electrode

electrostatic NO [104] [105] [115][116] [117]

12 heater thermalthermo-viscous

NC [73]

Table 5.2 Overview of different active microvalve types.

94 Chapter 5

Besides these valves many different modular valve types have been presented consisting offor example a membrane valve body with a piezo stack [26,27,118,119,121], piezo bi-morph[126] or electromagnet [121,100] mounted with gluing techniques.

Not all listed valve types are suitable for both gasses and liquids. In the electrostaticactuated valve types 1 and 11, the electrodes are in contact with the medium that needs to beswitched. Hence these valves can only be used for dielectric fluids. On the other hand valve12 is based on temperature related viscosity changes. In order to get a good hydraulicresistance change between the actuated and non-actuated state, a high temperature sensitiveviscosity and for liquids high boiling temperatures are needed. Since this valve type has ahigh leakage, it was applied in micropumps [73], not as separate open / close switches.

Valves 2-5 are drawn in the configuration as patented by Robert Bosch GmbH [24]. Bya smart layout of the membrane surface relative to the valve plate size, the valve becomes“balanced” such that the actuation power needed to open or close the valve becomesindependent of the pressure at the valve inlet. The references cited at the correspondinglayouts do not all make use of balancing but use a similar actuation principle and forexample membrane or beam design.

5.3 The bossed valve

5.3.1 IntroductionThe bossed valve consists of plate suspended by flexible beams over the valve seat. It can beused as a check valve since a positive pressure drop will lift the boss from the seat such thata free flow channel arises whereas a negative pressure drop will press the boss against theseat such that the valve is closed. By using thin beams instead of a full membrane, thestiffness and thus the hydraulic resistance of the valve in the open direction can be reduced.In the close direction a large leak resistance still can be obtained. Surface micromachining aswell as bulk micromachining techniques can be used to make the valve. In the nextparagraphs both fabrication principles will be illustrated.

5.3.2 Surface micromachined bossed valvesFor the application in a micro analysis system for the detection of ammonium, based on flowinjection analysis (FIA), valves are needed to prevent back-flow of reaction products fromthe reaction chamber as sketched in figure 5.1A. These reaction products arise after goodmixing of sample fluids with reagents. As discussed in chapter 3, mixing in microsystems isstrongly diffusion related since, due to low Reynolds numbers, the turbulent mixing

Microvalves 95

mechanism cannot be used. This means that for a continuous flow FIA at a fixed flow-ratelong channels are needed in order to get a fully reacted product leading to long measurementtimes. The use of a laminar mixer is needed to solve these problems. Laminar mixers exploitthe benefit of fast diffusion in micro systems by increasing the interaction area between twofluid streams. One possibility is the use of a perforated membrane [77] to create a thinlaminate of fluid streams, which will rapidly diffuse. This perforated membrane can beintegrated with a valve such that a compact integrated reaction chamber system is obtainedwhich prevents back-flow. The principle of the integrated mixer-valve combination is shownin figure 5.2.

p < p1 2

p2

fluid 1 fluid 1+2

fluid 2perforated membrane

p > p1 2

p1fluid 1 fluid 1

fluid 2

p2

p1

Figure 5.2 Mixer-valve principle: for pressure levels p1 < p2 the valve will open and laminar mixingwill occur whereas for p1 > p2 the valve will close to prevent back flow of reactedproducts.

Fluid 1 will flow over the membrane. When the pressure level p2 is higher than p1, the valvewill open such that fluid 2 is flowing out over a long surface are. Fast diffusion into fluidstream 1 will result. If the pressure is reversed for instance due to an increase of pressure p1,the valve will instantly close.

In order to prevent the reaction product from flowing back to the channel of fluid 1,also check valves are needed in the other fluid supplies. Therefore an integrated system wasmade with two entrance channels, one with a normal check-valve for supply of fluid 1 andone with a mixer-valve. Figure 5.3 shows the layout of the complete combination and animpression of the cross-section layout.

Figure 5.3 Optical picture and cross-sectional view of the mixer-valve combination with additionalcheck valve for the main flow.

96 Chapter 5

The device is fabricated in a combined surface- [15,65]/ bulk-micromachining [58] process.LPCVD silicon rich, low stress silicon nitride is used for the membrane fabrication. Thislayer is patterned with reactive ion etching in a CHF3/O2 process. With anisotropic wetchemical etching in a KOH solution the entrance holes are etched through the wafer and adeepened channel is obtained under the perforated membranes and valve beams. Tounderetch the silicon nitride structures, a thin, LPCVD deposited polycrystalline silicon layeris patterned at places that will etched in KOH. One of the final steps in the valve fabricationsequence is the removal of the oxide ring that was patterned on the valve seat under thenitride, which frees the valve. To guide the fluids to the valve, HF-etched glass wafers areanodically bonded on top and bottom of the wafer. The final cross-section layout is shown infigure 5.4. The module has connection ports defined at a standard 2.5 mm pitch, whichfacilitates the integration with other components on a channel board.

Figure 5.4 Cross-section of the total mixer-valve module

The design of the valve can be very compact. Since the hole is etched from both thebottom and topside, influences from wafer thickness variations are eliminated [60]. Anotherbenefit of the valve is the freedom in shaping the silicon nitride beams. Instead of thestraight beams, spiral shaped beams can be used or even different type of valves can be madesuch as flap valves.

One of the drawbacks is the fragility of the silicon nitride. The thin beams and bossesare about 1 µm thick, which means that for bigger valve dimensions folding of the plate willoccur when the pressure is reversed. Another drawback is that the mechanical properties ofthe silicon nitride depend strongly on the parameters of the LPCVD process and followingprocessing steps. Although “low stress” nitride is used, it still incorporates a high level oftension. These rather uncertain parameters make these valves less suitable for model

Microvalves 97

validation. A third drawback is the use of time-stop etching with a KOH solution. Theoutside corners of the valve seat will be etched away if the process is not stopped in time. Onthe other hand, time is needed to properly etch away the silicon under the beams and theperforated membrane. Although corner compensation structures have been applied whichimprove the quality of the seat, the process remains critical. Finally the use of a sacrificialoxide layer for freeing the boss can be regarded as a negative aspect of this valve designsince an initial gap will arise and the possible chance on sticktion or bonding of valve to thevalve seat. Since polished wafers are used and a thin oxide layer is grown, the roughness ofthe tangent plane of the nitride boss with the valve seat is very low. Therefore the nitridemay easily form a fusion bond. This effect was observed during dry spinning of the wafersafter etching of the oxide ring. Due to capillary forces the boss was pulled against the silicon.This bonding effect is very crucial for valve fabrication and will be discussed in paragraph5.3.4.

5.3.3 Bulk micromachined bossed valvesThe alternative for the surface micromachined valves is using bulk micromachiningtechniques. With bulk micromachining, fabrication processes are meant that consist ofetching “bulk” material out of the silicon wafer [58,95,23]. In combination with waferbonding, different processed layers can be stacked. For the bossed valve these layers consistof a silicon wafer with valve seat, a wafer with bulk etched spring structures and boss andeventually a glass cover wafer to close the valve. In figure 5.5 a cross-sectional view is givenof an anisotropic wet chemically etched (KOH) type.

Figure 5.5 Layout and SEM picture of the bulk micromachined bossed valve, consisting of 2selectively fusion bonded and wet anisotropically etched wafers

Both <100> oriented silicon wafers are anisotropic wet chemically etched in a KOH solutionwith silicon nitride as masking material. First the beams and valve plate contours are etchedwith a time stop to obtain a defined thickness of about 20 µm. After this, nitride is grownand the back-side nitride mask is etched such that with KOH etching a cavity is created.When the deepened nitride layer at the valve side is reached, the process is stopped and the

98 Chapter 5

nitride is removed. In figure 5.6 the elementary process steps are shown. The bottom wafer isetched in a similar way.

This fabrication process can be extended to obtain more design freedom when theshallow KOH etching steps are replaced with cryogenic SF6/O2 reactive ion etching (RIE)steps [47,48, 23]. With this, no edge compensation structures are needed which facilitatesmask designing and provides a better geometric accuracy. A detailed process descriptionincluding process parameters is given in appendix A. With KOH etching only straight beamor hooked beam structures can be made to change the stiffness. With RIE, curved structuresand circular bosses, valve seats and entrance holes can be made. Besides, the number ofbeams to hold the plate can be reduced to three in order to get a determined system instead ofthe over-determination in case of four beams. Figure 5.7 shows a top and bottom view of aspiral shaped valve structure. The light pattern on one side of the beams and plate consists ofsilicon nitride, which is used to avoid bonding as will be explained in the next paragraph.

Figure 5.6 Essential process steps in the fabrication sequence of the full-KOH etched bossed valve.A) top wafer processing of the spring structure and boss, B) bottom wafer processing ofthe valve seat, C) fusion bonding of both wafers

Figure 5.7 Top (left) with zoom-in and bottom (right) view of the top wafer of the RIE / KOHetched bossed valve. The white patterns on the right picture are silicon nitride anti-bonding layers.

Microvalves 99

The circular entrance holes are etched with deep reactive ion etching (DRIE) with cryogeniccooling. By using DRIE [47,48,137], circular holes with small diameters can be made. Strictconstraints on the holes are a minimum underetch of the valve seat mask and a good etchuniformity over the wafer. The DRIE wafer-through etching is described by H. Wensink etal. [137]. Since helium gasses are used at the backside of the wafer as cooling medium,wafer-through etching will finally cause leakage of the helium such that the etch plasma andtemperature control will get seriously disturbed. To avoid this, the process uses polyimide asbackside protection layer. During this process, a thin, poorly defined silicon rim will be lefton the polyimide at the wall of the hole. Besides, mask under etch ratios of maximum 1 µmover 100 µm depth can be achieved with poor uniformity over the wafer, resulting in at least4 to 5 µm under etch but for most devices the result is even worse as shown in figure 5.8.

Figure 5.8 Left: mask underetch (part indicated with “undercut”) at the valve seat during deepreactive ion wafer-through etching due to radial ion impingement, leaving a thin, poorlydefined, perforated silicon rim. Right: contour after improved parameter settings, whichminimize mask underetching.

A reduction of mask underetching is obtained by increasing the ion energy and the wallpassivation with increased oxygen gas flow. To get a better etch selectivity at theseparameter settings and mask definition, chromium was used as mask material instead ofresist. However at a certain depth black silicon [47,48] arises. The conflicting demands of alow mask underetch, the avoidance of the creation of a thin silicon rim and wafer-throughetching for 600 µm diameter circular holes lead to the decision to use, similar to the topwafer, an additional LPCVD silicon nitride deposition step combined with KOH etchingfrom the backside. After bonding of the two silicon wafers, a glass cover plate wasanodically bonded to close the valve. The cross-section layout is shown in figure 5.9.

100 Chapter 5

Figure 5.9 Cross-section layout of the combined RIE / KOH etched bossed valve.

5.3.4 Selective fusion bondingA critical step in the fabrication process of reliable operating valves is to obtain a freemoving spring structure. For the surface micromachined valve a sacrificial oxide layer wasetched away to free the boss. This method has the drawback of creating an initial gap andthus an increase of leakage at low reversed pressure. But even more important is the risk ofsticktion of the valve to the seat.

The wafers of the bulk micromachined valves are assembled by fusion bonding.Bringing two polished and carefully cleaned surfaces in close contact, a fusion bond can bebrought about [96]. For this, no additional pressures like the strong electrostatic pressuresduring anodic bonding [132,133,134] are needed since the bonding mechanism is based onattracting Van der Waals forces. For the valve structures this means that besides the bulksilicon also the movable parts will bond to the valve seats. Therefore a technique isintroduced which allows control over areas of the wafer surface that bond in the fusionbonding process. With this selective bonding technique no initial gaps arise and risks onbonding during operation are avoided.

Fusion bonding consists of the formation of hydrogen bridges between two wafersurfaces. The process consists of two steps: an aligned pre-bonding at room temperature andan annealing step at about 1100�C for two hours. During the first stage, the cleaned wafersare carefully aligned and brought together, during which hydrogen bonds are formedbetween the thin water layers on the wafer surfaces [71,97]. During the high-temperatureannealing step these bonds are transformed to form bonds between the oxygen and siliconwhereas water is diffused out.

For this mechanism the surface morphology or roughness and the material parametersof the surfaces are of importance. It is known that a certain maximum roughness level isneeded in order to obtain a fusion bond and that some material combinations form a bondmore easily than others do. A model to describe the chance on obtaining a bond, calledbondability, is derived by C. Gui [38,39]. His model is based on bonding energy andelasticity as a measure of bondability. The higher the specific effective bonding energy, thebetter the chance on bonding.

Microvalves 101

The normalized specific effective energy needed for bringing surfaces together at adistance s is given by [38,39]:

*21-

21-2/3** dde2de)(

234

*

2

*

2

sxxsxRbS s

x

s

x

sb

b � ��

��

�

��

��

�

��

�

�� (5.1)

with � and �b the specific surface energy and specific effective bonding energy respectively.The specific bonding energy is defined as the amount of energy per unit area needed toseparate two bonded surfaces. Dimensionless parameter s* indicates the local distancebetween two surfaces divided by the standard deviation of the roughness, �. For a fulldescription of the surface roughness, the mean asperity top radius R and the asperity density�s (number asperities per area) are taken into account. The product of the three roughnessparameters: �, R and �s is a constant, which means that they are related. The integrationdomain is defined by sb, the distance at which equilibrium is found. For separations biggerthan sb, wafers need to be pushed together whereas for smaller separations additional pullingforces are needed to remain the gap distance. Value sb can thus be found from the zeroexternally applied pressure relation resulting in:

0de23)(

*

2

21-2/3* ��

�

��

��

�

bs

x

b xsx �� (5.2)

with

�/*bb ss � (5.3)

Equation (5.1) shows that there is a relation between the specific effective bonding energyand the dimensionless surface adhesion parameter �. This parameter is defined by (5.4) withE and � the effective modulus of elasticity and Poisson’s constant respectively.

RE 3

2

1)1(

�

��

�

� (5.4)

The relation between the specific effective bonding energy as function of the surfaceadhesion parameter is plotted in figure 5.10. With the adhesion parameter three differentregions can be distinguished for bondability: for � smaller than 1 the specific bonding energyis indicating that good fusion bonding capabilities are obtained without the need ofadditional pressure. Experimentally the non-bonding regime was found to be bounded by �larger than about 12 whereas for the range in between ( 1 < � < 12) adherence can occurwithout a real good fusion bond.

102 Chapter 5

Using this theory, surface parts can be selectively treated to have surface propertiesthat fit into bonding or non-bonding regime [40]. For this, the adhesion parameter needs tobe adapted. Surface energy or the roughness morphology are the most convenient designparameters to define. The influence of the surface roughness is of a higher power than thesurface energy and can be easily adapted. Since the product of the mean asperity radius withthe asperity density and the standard deviation is constant, the roughness deviation willinfluence the adhesion parameter to about the second order (see equation (5.4)).

For the bulk micromachined valves the roughness was changed by depositing a layerof silicon nitride on the boss. The nitride on the valve seat was fully stripped. After twoLPCVD depositions (1 µm + 200 nm) and fully removing the silicon nitride layer at areas tobe bonded and two times partially etching back of nitride layers from 1 µm down to 800 nmin 50% HF solution at the boss, the roughness of the silicon bonding area and the nitrideanti-bonding layer was measured. The atomic force microscopy pictures (AFM) are given infigure 5.11.

0.0

0.2

0.4

0.6

0.8

1.0 A B C

adhesion parameter �

norm

aliz

ed s

peci

fic e

ffect

ive

bond

ing

ener

gy �

b*

Figure 5.10 The normalized specific effective bonding energy as function of the adhesion parameter:in region A fusion bonding is always achieved whereas bonding in region C isprevented. In the adherence region B sticktion can occur. [38,39]

From these roughness measurements, the bonding adhesion parameters were calculatedto be about 4.8 before annealing (transition zone) and reduced to 0.24 (bonding zone) afterthe annealing step for the silicon to silicon bond and 529 (non-bonding zone) for the nitrideto silicon anti-bonding pattern. This means that a good fusion bond can be obtained at thesilicon-silicon interface and that bonding is prevented at the nitride-silicon interface. Filling

Microvalves 103

experiments of the valve, applying an ethanol flow and measuring the pressure drop over thevalve, showed that no sticktion of the valve occured during operation or after putting thevalve in vacuum and filling again. On the contrary the silicon-silicon bond strength was veryhigh. The membrane valve fractured in the bulk material instead of the bond interface.

RMS=0.8nm RMS=6.3nm

Figure 5.11 AFM surface morphology scans of (left) polished silicon after stripping LPCVD siliconnitride and (right) silicon nitride anti-bonding pattern after two times deposition andpartially etching back in 50% HF solution.

The 800 nm silicon nitride anti-bonding layer turns out to be thicker than necessary.Layer thickness will gives rise to a pre-stress in the valve and thus a small increase in openpressure. Knowledge about the relation between the surface morphology and for exampleetching and deposition times and process parameters is needed to optimize the layerthickness. Besides deposition of rough layers, etching such as RIE might be used to locallyroughen areas. Therefore it is expected that bonding and anti-bonding areas can be definedwithout the need of thick layers.

5.4 The membrane valve

5.4.1 IntroductionMembranes are often used in microcomponents. The reason is that membranes structures areeasily etched since all bulk etching processes are out-of-plane oriented. With time stops,boron dotation or by depositing for example a nitride layer, thin strong membranes can befabricated. With these membranes, simple passive and active valve types can be made bypositioning the membrane over an entrance hole such that the membrane will deflect when apositive pressure drop is applied over the membrane which lifts the membrane from thecavity or close when the pressure drop is reversed. In this paragraph, two types of activemembrane valves will be presented: a NO and NC type that can be used in analysis systems

104 Chapter 5

to actively switch flows. The valves are pressure-controlled which means that an externalpressure source is needed to activate the valves. Since the valves are pressure actuated andnot pressure balanced, its hydraulic resistance will also depend on the pressure built up in theflow. Therefore it is used as subject for investigating the flow-structure interaction in thenext chapter.

5.4.2 Membrane check / pressure actuated normally open valvesThe combined reactive ion / KOH etching technique described in paragraph 5.3.3 can beused to fabricate a pressure actuated normally open valve. Pressure actuation has severaladvantages. With pressure generation very powerful actuation mechanisms can be build suchas thermopneumatic [98] or with use of liquids which have a large thermal expansioncoefficient [41]. Another interesting actuation principle is the use of electrolysis [78]. Incontrast to the preceding methods, this pressure source only consumes little energy sinceonly for pressure changing energy is needed. This means that little or no energy is neededwhen a constant pressure is maintained in the actuation chamber. A second benefit of thepressure actuators is the possibility to generate the pressure externally and leading smallchannels to the actuator. The actual pressure source can therefore be positioned somedistance from the valve, which facilitates integration and scale reduction of the valves. Sincefor laboratory setups the internal volume is of more interest than the outer dimensions of thesystem, even external gas pressure switches can be used to switch the applied actuationpressure. Besides pressure actuation, the body of the NO valve can also be used incombination with for example piezo-elements [121].

For validation purposes of the models for the NO valve that will be derived in chapter7 the standard design of the valve is not provided with an actuator. The pressure chamber isleft open to atmospheric pressure. Without external pressure source the valve acts as a checkvalve for which the hydraulic resistance in back and forward directions depends on themembrane and valve seat dimensions. The hydraulic characteristics when applying actuationpressure are measured on a valve with a Plexiglas cover with pressure connection glued ontop for external pressure supply.

The design and fabrication process is similar to the circular bossed valve with thedifference that no spring structure needs to be etched and only a KOH cavity is etched fromthe top side of the top wafer and that an additional channel is needed in the bottom wafer toguide the fluid from the entrance to the exit. A schematic layout is shown in figure 5.11. Inthis design, direct wafer bonding is exploited to obtain circular silicon membranes withoutthe need of long time reactive ion etching. Reactive ion etching is only needed to pattern thelower wafer about 50 µm deep. KOH etching is used to create the membrane. After bonding,the strength of the bond is simply measured by applying a pressure drop over the membrane.

Microvalves 105

It turned out that the circular membrane bulged-out in a circular shape indicating that thebond was strong enough to provide a good circular clamping of the membrane. After apressure overload the membranes are blown-out leaving the bonded areas still intact. Thesetests show that high strengths can be obtained with fusion bonding of thin membranes to asolid substrate.

Figure 5.12 Schematic layout of the pressure actuated normally open membrane valve (the actuatorchamber is not closed), left: cross section, right: top views of the KOH etchedmembrane and RIE etched seat and channel.

5.4.3 Pressure actuated normally closed valvesThe normally closed type is the counterpart of the previously described valve. Pressureactuation is needed to open the valve [62]. Figure 5.13 outlines the principle of the design.Two bossed membranes of different size and stiffness are connected at the center. If apressure is applied between the two membranes, they will bulge out. However since bothmembranes are connected at the center, an additional force is exerted in the center whichpulls the membranes back. Since both membrane dimensions differ, an asymmetric situationarises such that the connected bosses will get a net translation in one of the both directions.

boss actuation chamber

flow entrance flow exit

membranesactuation pressure

connection

Figure 5.13 Principle sketch of the normally closed pressure actuated membrane valve

With this translation, a flow opening can be controlled such that an active NC valve isobtained. A pre-stress, which closes the valve in a deactivated situation, is created by a stepof the valve seat due to for example a silicon nitride layer. On the other hand, an under-

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pressure in the activation chamber will reverse the deflection and accordingly actively closethe valve as well.

vent bottom membrane top electrode for capacitivedisplacement read-out

actuationpressure supply flow entrance flow exit top membrane

glass

silicon

silicon

silicon

Figure 5.14 Layout of the KOH etched normally closed pressure-actuated valve.

For the fabrication of the valve, the selective fusion bonding method turns out to be anideal construction technique. With this method no additional forces are needed such that theflexibly suspended bosses can be fused by bringing the two surfaces into contact at at leastone spot. The remaining part of the surfaces is automatically attracted such that a full surfacebonding is established. Since we first bonded the lower to the second silicon wafer (figure5.14), the lower bossed membrane was deflected by 1 µm such that during the second fusionbonding step both bossed membranes were contacted without the need of additionalpressure. This process turned out to be very reliable resulting in a high yield.

Figure 5.15 Top (left) with the top membrane and (right) the bottom view with fluid connections ofthe 6 x 6 x 1.2 mm diced pressure actuated normally closed valve.

SEM pictures of the top and bottom of a bonded and diced silicon sandwich are shownin 5.15. For the fabricated valve, the top glass wafer has not been fabricated. This extensioncan be used in order to obtain a feed-back signal to measure the valve lift height for constanthydraulic resistance control or for safety checks to see whether the valve is not

Microvalves 107

malfunctioning. This signal is measured capacitively since the plate distance between theboss and the fixed top electrode on the glass is reduced when the valve opens, causing ameasurable increase in capacity.

5.5 The duckbill check valve

5.5.1 PrincipleThe above-mentioned and check valves presented in literature all work out-of-plane. Henceadditional entrance and exit channels are needed and vias through the wafers to guide theflow. Due to this, additional processed wafer layers and much channel volume is needed.A simple alternative can be obtained by using the typical crystal orientations of mono-crystalline silicon to fabricate thin membranes that can deflect under a defined angle. Theprinciple of such a valve is demonstrated in picture 5.16.

angle defined by thecrystal orientation

flow flow

Figure 5.16 Cross section view showing the principle of using a membrane oriented along crystalorientations for obtaining a check valve.

When a pressure drop is applied from the left to the right hand side, the membrane will bendopen creating a gap (left picture) whereas a reversed pressure drop will push the free side tothe bottom substrate (right picture).

Essential for the fabrication and functioning of this type of valve is the flexibility incombination with the strength of the membrane. Since the membrane is oriented under acertain crystal orientation angle with the substrate, the gap size is a fraction of the membranedeflection. Hence deflections are needed that are sufficient enough to give a reasonablehydraulic open resistance. Due to the small thickness of the membrane, a short channellength is obtained which reduces this resistance. The thickness is limited by the strength.

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5.5.2 Design and fabrication of thin <111> oriented membranesThin membranes oriented under a defined angle can be fabricated by anisotropic wetchemical etching. For a <100> oriented wafer the obtained angle will be 54.7 degrees withan additional wafer mis-cut angle. One way to create membranes is to etch a cavity startingat both sides of the wafer as shown in figure 5.17A. The thickness of the membranes etchedwith this double-sided etch method depends on the dimensions of the mask windows, therelative alignment of the top and bottom mask and the mask alignment relative to the crystalorientations. Since the relative alignment of both masks is of influence, the membranethickness variation is strongly related to the wafer thickness variations according to 1/tan(�)with � the crystal orientation angle of the {111} plane with the wafer surface. For <100>oriented silicon �=54.7� and thus this factor is 0.71 which means that for a wafer thicknessdeviation which can be in the order of ±15 micron for 3 inch wafers, a maximum precisionof the membrane of ±11 micrometer can be obtained. This precision is far to low since for agood performance (low open flow resistance) already a membrane flexibility is neededcorresponding to a thickness in the order of 5 micrometer.

A B

[100]

[011]

C

[011]1

3

2

4

5

6

7

convex hole

V-groove concave hole

rough vertical wall

Figure 5.17 Wafer thickness dependent technique A), full wet chemical {111} plane switchovertechnique B) and C) a combined DRIE – wet chemical etching method to create <111>oriented membranes in <100> silicon

A solution is found in the use of switching over of the <111> oriented planes(figure 5.17B) [11,8,60]. When two KOH cavities, etched from both sides of a wafer meet, asharp outer corner occurs, resulting in a convex hole as shown in figure 5.17B step 4. Thissilicon shape is not stable so that the sharp corner is etched away until a stable concave holeis formed along the {111} planes. The {111} planes switch over from a positive anglerelative to the wafer surface to a negative angle. For the etch stages between situation 4 andthe final structure 7 partly vertical walls will be etched with high roughness formed by etch

Microvalves 109

steps (step 5) [5,22,55,23]. After the stable situation of figure 5.17B step 7 is reached, theetch rate is drastically slowed down and defined by the mask under etch rate. We measured a<100> / mask under etch rate ratio in the order of about 100 (typical process parameters arelisted in appendix B).

An alternative to this wet chemical etching method is the combination of deep reactiveion etching after which an anisotropic wet chemical etch step is performed [32]. The processis illustrated in figure 5.17C. For this combined method no top mask is needed and noadditional wafer layer is needed to close the valve at the top. The maximum possible heightof the membrane however is reduced.

With the {111} plane switchover technique, two situations exist that define how themask dimensions, mask aligning and wafer thickness influence the final membranegeometry. In case the switched over corner of the concave hole is positioned exactly abovethe top of the triangular KOH cavity, the KOH cavity as well as the concave hole aredefining the dimensions of the membrane. When the masks are positioned such that thecorner moves towards the concave hole, as shown in figure 5.18-A1, the top mask and thusthe wafer thickness still influences the membrane dimensions.

switched over corner

Figure 5.18 Influence of the changing the mask positioning and dimensions on the definition of themembrane dimensions: A) variation of the top mask position th, B) bottom maskopening tm and C) mask window distance tw

Positioning the corner to the other side as shown in A3, makes the design independent of thetop mask. The bottom mask defines all dimensions whereas the top mask only serves forswitching over of the {111} planes. In this situation the design becomes independent of thewafer thickness which allows the fabrication of very thin membranes with high accuracy,defined by the distance between the two windows in the bottom mask. High precision of thedouble-sided mask alignment is no longer needed, since the only function left for the topmask is to initiate switching-over of the {111} planes. Crucial however is a highly accurate

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aligning of the masks relative to the crystal orientation. The alignment mask developed byVangbo et al. [131] can be used for this producing an angular accuracy of 0.05°. Since aslow mask under etch rate is present, the membrane thickness can be fine tuned by using atimed overetch. With this method membranes were made down to less than 1 µm thickness.

Figure 5.18 shows the design freedom to define the dimensions of the membranes.Since the membrane thickness, height and width are completely defined by the bottom mask,valves with different flow characteristics can be designed in one rather elementary mask,consisting of a collection of rectangular windows. Sequence A shows the effect of movingthe top mask relative to the bottom. The concave hole can be varied in shape from symmetric(situation 1) to strong asymmetric (situation 3). These pictures only show the 2 dimensionalsituation. In the third dimension however the position of the switched-over corner can alsobe changed independently. This means that “strange” intersection lines should arise of the{111} planes. This does not happen. In figure 5.19 facets planes are shown that form theintermediate region between the different <111> planes. In this situation the switched-overcorners are at the same heights. When the corners are at different heights, the facet planes aresplit into four sub-facets.

Figure 5.19 Picture of facet planes that arise at the intersection of 4 {111} planes. When the 2switched-over corners are at the same height, plane facets will arise as shown. When theswitched-over corners are at different heights, the facets will split into four differentfacet planes. For stability reasons the processed wafer is fusion bonded to a siliconsubstrate. The rounded corners of the membranes occurred due to pollution duringdicing.

Besides the mask window dimension of the concave hole also the relative positioning of theV-groove mask and the V-groove length can be varied. With these variations, different

Microvalves 111

membrane shapes can be made. The effects of the positioning and size of the mask windowson the membrane shape is shown in table 5.2. Many different membrane shapes can bemade. Together with the width, height and thickness variations the method offers manydesign possibilities.

The method for creating thin membranes is not limited to <100> oriented wafers. Inparagraph 5.6 etching possibilities in <111> will be illustrated. For these wafer typeshowever a pre-etch step is required and the functionality as a valve is worse. Since themembranes are oriented along the {111} planes, which form a 70.5� angle with the wafersurface, the net cross-section opening is reduced for a certain membrane deflection. Thismeans that the <111> valve is stiffer than with the <100> oriented valve. Anotheralternative, which might show a better performance is the use of <110> oriented wafers. Inthese wafers the membranes are oriented under a smaller angle of 35.3�. Of course otherorientations become possible when using special cut wafer types.

mask layout membrane shape mask layout membrane shape

Table 5.3 Influence of the mask windows positioning and size on the membrane shape. The topmask is indicated transparent with dotted lines whereas the bottom mask is drawn graywith solid lines.

5.5.3 Membrane taperingEtching of the membrane occurs along {111} planes. So the expectation is that plan parallelmembranes will be formed. The SEM pictures of figure 5.20 however shows a slighttapering of the membrane thickness [90]. For this specific situation of a 400 µm highmembrane the free edge is half of the thickness of the clamped topside. The reasons for thistapering can be found in a different etch mechanism at both sides of the membrane. As

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shown in figure 5.20 the mask underetch of a switched-over plane turns out to be larger thanat the V-groove planes [11].

Figure 5.20 Cross-section of a duckbill valve fusion bonded to a silicon substrate (left picture). Thepicture shows a zoom-in on the membrane showing a thickness tapering of about 1.3°.The right picture shows a difference in underetch of the silicon nitride mask for A) theswitched-over edge and B) the V-groove side.

This indicates that a faster nucleation of etch steps at the silicon-mask interface of theswitched-over plane occurs [22]. Indeed differential interference contrast microscopy imagesof both sides of the membrane surfaces show a different morphology as discussed by Nijdamet al. [79,80]. These pictures are shown in figure 5.21. Since the inclination angle of theswitched-over plane is smaller than that of the V-groove, apparently a faster attack of thesilicon occurs at the mask side of the switched plane which overrules the step initializationmechanism at etch pits. A further detailed etch research in these typical phenomena is doneby A.J. Nijdam.

Figure 5.21 Surface morphology of the {111} planes in a V-groove (left picture). Etch pits whichinitiate etch steps are covered all over the surface whereas for a switched-over plane,steps are initiated mainly at the mask interface (right).

Microvalves 113

5.5.4 ApplicationsAs demonstrated in figure 5.18 and table 5.2 there are many design possibilities with theproposed technique. Compact valve designs can be made which can be integrated in systemssuch as a check valve array for injecting fluids in a main stream as demonstrated in figure5.22. Connecting fused silica capillaries are easily glued into the V-grooved entrancechannels.

B C

valves

A

Figure 5.22 Functional (A), art (B) and SEM impression of a 2�5 check-valve array for capillaryfiber connections.

Other fluidics applications are injection valves for flow injection analysis systems, meanderchannels separated by thin membranes for heat exchangers, thin sacrificial structures used tocreate outer corners [89] and passive valve mixer modules [107]. With the thin membranesalso more complex structures can be constructed by positioning them at 90� angles.Examples are shown in figure 5.23. The first picture demonstrates a tray suspended by thinmembranes with the silicon nitride etch mask left at the bottom. The center can be reducedsuch that a fan structure is obtained as shown in the right hand side picture.

Figure 5.23 Possibilities with etching thin <111> oriented membranes: a tray suspended by thinmembranes (left) and a matrix of fan structures (right).

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5.5.5 Selective anodic bondingThe etched wafer can be mounted on another silicon or glass wafer by the previouslydescribed selective fusion bonding process. However we used a glass wafer (Hoya SD2 andCorning 7740) which was mounted with a selective anodic bonding process. With this glassbonding, the valve becomes transparent enabling visual inspection of the membrane seat.

The oxidation mechanism with blocking anodes is generally accepted to describe theanodic bonding process of glass to silicon [132,133,134,16,17,71,19,4]. By applying avoltage drop of about 500V at 450�C over a silicon-glass sandwich as shown in figure5.24A, a migration of positively charged sodium ions towards the negatively chargedelectrode induces a depletion layer at the silicon interface of about one micron thickness.The negatively charged oxygen ions are considered to be immobile. Since the silicon ispositively charged, a high electrostatic field is built over the depletion layer and the siliconinterface which causes an electrostatic attraction pressure between the two wafers in theorder of more than 6.5 MPa [132]. A second result of the depletion layer is a remainder ofreactive oxygen ions at the silicon interface such that oxidation at the silicon-glass interfacetakes place forming a tight silicon-glass bond.

Figure 5.24 Anodic bonding process without (left) and with (right) chromium anti-bonding layer.The chromium layer influences the field lines and thus the electrostatic pressuredistribution as well as the ion transport (indicated with arrows) and avoids bondinglocally.

Deposition of a patterned chromium layer, which acts as a conductor, influences theelectrostatic field and thus the pressure distribution [46]. At the chromium-silicon interfaceno attracting forces are present since locally, no depletion layer is created. Furthermore thechromium will react with available oxygen preventing oxidation of the silicon and shieldingthe silicon from the active oxygen ions in the glass.

For a proper closure of the valve the anti-bonding layer must be thin. A thick layerinduces stresses in the valve since the membrane bends over it. At the clamped membraneside edges, a gap might arise and the membrane edge is bent upward in the middle.Therefore the layer thickness must be reduced to a minimum to optimize the valveperformance. For a first batch of valves a 7.5 nm thick chromium layer was used. Anodic

Microvalves 115

bonding tests with different reduced chromium layers still showed no signs of bonding. Withincidence x-ray diffraction, the minimum layer thickness that was obtained after 1 secondsputtering time was estimated to be in the order of a (few) monolayer(s). Duckbill valveswith 1 nm chromium showed an improvement in closing resistance. The chromium surfacemorphology of the thinnest sputtered layer is not known but it is expected that no uniformclosed layer is formed. This aspect needs more research in future.

5.6 Micromachining possibilities in <111> oriented silicon

5.6.1 IntroductionIn microsystem design <111> oriented silicon wafers are used very rarely. The reason is thatthe <111> planes prevent direct etching with anisotropic wet chemical etch solutions such aspotassium hydroxide (KOH). However, by using an isotropic or directional pre-etching orusing the wafer off-axis cut, interesting new alternatives arise for designing in the moreconventional used <100> and <110> oriented wafers [10]. Especially for valve designswhere suspended or membrane structures are needed, <111> wafers can offer interestingpossibilities. We used <111> wafers to obtain duckbill type valves with a differentmembrane angle and a low dead volume alternative for the previously described bulkmicromachined bossed valves. With the combination of reactive ion etching and anisotropicetching, compact valve and pump designs can be made by reducing the number of neededwafers. In this paragraph practical etch results are presented that demonstrate the potential ofdesigning in <111> wafers related to fluid components. In reference [91] a more detaileddiscussion can be found about designing in <111> oriented silicon.

5.6.2 Crystallographic orientations in <111> wafersIn figure 5.25 the spatial positioning of the crystal octahedron in <100> and <111> waferorientations are shown. In contrast to <100> wafers where the {111} planes define arectangular intersection with the wafer plane, defined by the <110> directions, a hexagonalshape is obtained in <111> wafers [95]. The in-the-wafer-plane oriented directions that

define the sides of this hexagonal intersection are: �� 110 , �� 110 and �� 101 as shownin figure 5.26 The angle between the wafer surface and the {111} planes that define thehexagonal shape is 70.5�. These planes are inward and outward directed in an alternatingway.

116 Chapter 5

Figure 5.25 Spatial positioning of the crystal octahedron, built with {111} planes in a <100> (left)and <111> oriented (right) silicon wafer.

Since wafers are usually sold with a few degrees off-axis cut for better doping processcontrol, the anisotropic etch mechanism will occur as shown in figure 5.27. Etch steps willmainly start at the wafer edge. When these edges are protected with a mask material, etchingwill still occur due to the off-axis cut until the all non-bounded {111} planes by the mask arevanished.

Figure 5.26 Hexagonal contour formed by the projection of the atomic FCC structure on the {111}plane (left). The right picture shows the side view of the {111} plane orientations forthree plane intersections (see figure 1). The out-of-the wafer oriented {111} planes arein- and outward directed in an alternating way, with their intersection lines with the in-the-wafer-surface oriented {111} planes defined by two equilateral trianglesrespectively, forming an hexagon. The top triangle of figure 1 is accented.Anisotropicwet chemical etching of <111> wafers

Microvalves 117

The created tilted planes are bounded by the mask and the out-of-the-wafer plane oriented{111} planes. Since all left planes are <111> oriented a very low surface roughness isobtained which makes the process vary useful for optical applications [92,94] and highquality structures. The remaining roughness is determined by the spread nucleation of etchpits over the {111} surface. This etch mechanism (auto-polishing) can be used to create aperfectly crystal aligned wafer area with a smooth surface by applying a mask only at thewafer edge. By applying the process to both sides of the wafer a smooth plan-parallel waferarea is obtained.

Figure 5.27 Etching of <111> oriented wafers with use of the wafer off-axis cut. Left: partly etchedwafer with a rough stepped surface left. Right: fully etched, smooth surface bounded by{111} planes. The etching of steps is mainly initiated at the surface.

5.6.3 Pre-etching without wall coatingTo create structures into the wafer, first a cavity can be directionally etched. In combinationwith a top mask, thin <111> oriented membranes can be made as shown in figure 5.28. Theinitial trench can be made by many different techniques. For the situation of figure 5.28B themask is defining the trench width whereas the trench depth depends on the initial,directionally made trench. This means that different (non-precision) techniques can be usedsuch as mechanical and laser drilling [70], sawing, melting [2,3] or powderblasting. For the“pre-etching” steps we applied deep reactive ion etching and sawing.

Figure 5.28 Effect of the directionally etched trench and mask layout on the obtained anisotropicallyetched geometry and mask underetch. Thin <111> oriented membranes can be made byetching two closely spaced trenches.

After anisotropic wet chemical etching the walls become smooth, aligned according to the{111} planes. With this technique, similar to the <100> duckbill etching process the

118 Chapter 5

membrane thickness can be reduced to a minimum provided that a good mask to crystalalignment is obtained. The orientation of the membranes is along the hexagonal shape asshown before in figure 5.26, directed inward and outward in an alternating way.

5.6.4 Pre-etching with wall coatingWafers with <111> crystal orientation are very suitable for the fabrication of suspendedstructures by using an additional silicon nitride deposition step. In figure 5.29 differentprocess steps are shown. First a structure is directional etched with for example reactive ionetching (step 2). The etch depth equals the final thickness of the wanted free standingstructures. After this etch step the wafer is fully coated with for example silicon nitride oroxide. Next the bottom of the etched trenches is removed and the silicon is etched until thedepth is reached wanted for the final gap between the bulk silicon and the free structures(A5, B5, C5).

When these structures, coated with a wall protection layer, are anisotropic wetchemically etched, the unprotected silicon walls are attacked such that the dry etchedstructures are underetched bounded by the horizontal {111} planes. For shallow siliconstructures where step coverage with resist is possible, the bottom of the wall protection layercan be etched with a more narrow mask as demonstrated in figure 5.29 sequence A [25]. Fordeeper structures however a step-coverage is not feasible such that the bottom must beremoved by the high directionality of the reactive ion etching process. During this step themask edges of the trenches can easily be etched-trough. To avoid this, a slight maskunderetching during the first directional silicon etch step can be used (figure 5.29B) suchthat an overlap exists of the silicon nitride top mask [29,18]. Another alternative to obtain ahigher precision of the silicon structures is to use an oxide-silicon nitride sandwich for thefirst directional etch step after which the oxide is slightly etched. After the next depositionstep, a thick silicon nitride layer is formed at the trench edges such that a robust well-definedmask is obtained (figure 5.29C).

Method B was used to create the suspended valve structures with the result as shown infigure 5.30. Since the underetch-depth can be determined by the second directional etch step,the spacing and thus the amount of volume in the valve can be varied. The spiral shapedvalve element will always be released whereas straight beams will not be etched under whenthey are aligned along the {111} planes. This situation is shown in figure 5.30-C and D.Notice the fact that for this situation underetching of the circular plate will proceed untilsilicon walls have been formed along the intersection lines of the three beams. These beamsand circular plate can only be etched free when the second DRIE etch step is deeper than thebeam width times tan(70.5°). With deep reactive ion etching, a high aspect ratio mono-crystalline silicon structure can be created with a profile that is tuned to give a slightly

Microvalves 119

negative tapered structure. After applying the passivation layer, a mask-less directionaltrench bottom etch step and anisotropic wet chemical etching, an overhanging mask roof atde bottom of the initial trench is created due to the shadow effect (figure 5.30-D).

Figure 5.29 Three different processes for underetching of <111> oriented silicon: A) process forshallow structures where a good step coverage with resist can be obtained using siliconnitride and resist layers, B) process suited for thick structures using mask underetchingand C) slight etching of siliconoxide and successive silicon nitride growing to obtainrobust nitride mask edges.

The advantage of this method over the sacrificial layer etching techniques, is thefreedom in choosing the structure height and underetch depth (“sacrificial layer”) duringprocessing, like in micromachining techniques such as SCREAM [114]. Since SCREAMuses an isotropic reactive ion etch process with wall passivation to release the structures, thistechnique can only be applied when narrow structures need to be underetched. At highunderetch widths, long etching times are needed and thus much thickness variation willoccur. So this process is strong geometry limited. The <111> pre-etching method with wallcoating allows free etching of large structures without dimensional constraints.

Applying the previously described process sequence at both sides of a wafer, a smoothplan parallel membrane is obtained in the middle of the wafer. A cross-section of such astructure is shown in figure 5.31. The process of successive directional silicon etching, wallcoating, directional etching and anisotropic underetching can be done at different depthssuch that layered, high-quality suspended structures are obtained.

120 Chapter 5

A B

C DFigure 5.30 SEM pictures showing the silicon underetching in <111> oriented wafers applied to

spring element for micro check valves. Figure A shows a circular plate suspended bystraight beams, which are underetched only when a proper crystal (mis-) alignment isused. The spiral shaped beams of figure B will always be released. When the threebeams are oriented along the {111} planes, no underetching might occur as shown in C.Picture D shows a zoom-in of the slight negative tapering during DRIE and the resultingrim of mask material due to the shadow effect. The stepped bottom is caused by thewafer off-axis cut.

Figure 5.31 Cross-section of a buried, plan-parallel membrane structure fabricated by double-sidedunderetching of a <111> oriented wafer.

Microvalves 121

A B C

FED

<111><112>

Figure 5.32 Possible layered cross-section geometries of plan-parallel membranes usingunderetching in <111> wafers: A) A buried membrane, B) buried membrane created bytwo cavities that meet after which one big cavity arises, C) 2x6 layered 2 sided clampedtriangular membranes, D) combination of a closed, fully clamped membrane and atriangular membrane, E) two membranes with different size and a channel in betweenand F) entrance and exit slits positioned on top or at the bottom of the wafer.

In figure 5.32 a list of examples of possibilities are shown. These examples show thatalthough <111> wafers are rarely used in microsystem technology, many interesting, highquality monocrystalline structures can be made which open new and possibly more simpledesign for micro fluidic devices.

5.7 Conclusions

Different passive as well as active valve designs have been described. A bossed valve and anormally closed pressure actuated valve were made with conventional anisotropic wetchemical etching techniques. The combination however of reactive ion etching with wetchemical etching allows more freedom in design and improves the valve design sincecircular and spiral shapes become possible.

Selective fusion and anodic bonding are main keys in these designs. For the fusionbonding the adhesion parameter turns out to be a good and convenient design parameter topredict bondability or selective avoidance of bonding. To avoid bonding, depositing LPCVDsilicon nitride can easily increase surface roughness. With this method no sticktion wasobserved during the first filling sequence, during operation and after drying and refilling ofthe valves. With the technique of fusion bonding, circular membranes were made usinganisotropic wet chemical etching to obtain thin, square membranes and the reactive ionetching process in a second wafer to define the clamping edge and thus the geometry of thefinal membrane. Selectively avoiding of anodic bonding can be achieved by using achromium layer deposited on the glass substrate. Measurements showed no bonding even atlayers of a (few) monolayers thick.

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Exploiting the crystal orientations of <100> and <111> oriented silicon provides newinteresting possibilities. Examples are demonstrated with the thin <111> orientedmonocrystalline membranes and the suspended plan-parallel structures in <100> wafers.With a low cost wet etching method extremely thin membranes can be made with highprecision and wafer thickness independence although no high accuracy is needed for the topmask alignment. With the constructed membranes compact check valves can be made inonly a few fabrication steps for which only 1 crystal alignment mask, 2 etch masks and onechromium lift-off mask is needed. The simplicity and design freedom to define all membranegeometric information in one mask makes the proposed method very suitable for fluidiccomponents and integration purposes.

The same holds for the etching techniques that have been developed in <111> orientedwafers. Using this less-familiar wafer orientation provides many new design possibilities aswell as new structures that can be used to analyze etch mechanisms since plan parallel {111}oriented planes can be made with low surface roughness, which are fully bounded by other{111} planes.

The development of the duckbill valve initiated a lot of new design and researchinformation such as the formation of the facets and the tapering effects. These are aspectsthat need a closer look and might give new insights in the mechanisms that governanisotropic wet chemical etching. Another point that needs more clarification is the effect ofthe chromium layer thickness on the anodic bonding process.

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134 Chapter 5

135

66 FFLLOOWW--SSTTRRUUCCTTUURREE CCOOUUPPLLIINNGG

Fluid flows induce mechanical loads on for example channelwalls. When flow is applied through flexible structures,geometry changes of the channel cross-section will occur.This interaction between flows and mechanical deformationis treated in this chapter. Special attention is paid tonumerical tools to simulate the problem. Aspects related tothis, such as convergence will be discussed. This chapterwill serve as a general theoretical basis for the flow-structure coupling theory, which will be used, in the nextchapter to model the open resistance of various valves.

6.1 Introduction

The theory of modeling fluid flows through microcomponents has been discussed in chapter3. In that chapter models have been derived to describe flow profiles and hydraulicresistances in channels. For these situations, the outer geometry of the channels is assumedto be rigidly defined. For the checkvalves of chapter 5 however, movable elements are usedto create a direction-sensitive resistance. This means that an interaction exists between thefluid flow and the partly flexible channel geometry. In this chapter this flow-structureinteraction will be discussed. Additional to the formulas describing the flow-pressurerelations, structural mechanics equations will play a role.

The aim of the research on check valves is to obtain analytical design formulas that canbe used as input for behavioral models (see chapter 2) describing the valves in terms of inputand output parameters [28,6] which can be used as elements in for example the design and

136 Chapter 6

simulation of micropumps. On the other hand it can be used to investigate the effects ofdesign parameters on the performance of the valves.

Different approaches in the research on microvalves have been published, oftendirectly related to micropumps. Gerlach [12] published an analytical design study on themicrodiffuser type valve. Recently Olsson et al. [18] published a numerical lumped elementmodel of a pump using this type of valves. Park et al. [20] and Vandelli et al. [26] publishedfinite difference results for the flow-structure interaction in diaphragm valves. Van Kuijk[17] used coupled FEM models. By far the most research on valve and pump simulations andmeasurements, both statically and dynamically has been spent on flap type valves[29,30,31,24,25,14,15,13,10]. Other pump simulations were performed assuming “ideal”diode characteristics [27] or using empirical data [5].

In this chapter numerical tools will be described to help building analytical designformulas for the various valves discussed in chapter 5. With these numerical tools, the effectof design parameter changes on the valve behavior can be studied. Hence this chapter ismeant to form a general basis for the specific formulas which will be derived in chapter 7.First the functional layout of the check valve will be analyzed and the flow-structureinteraction will be explained in an abstract way. Different approaches of solving the couplingproblem between the fluid and structural domains will be treated. Two of these approacheswere implemented in the FEM package ANSYS. In order to get a good and fast convergencedifferent iteration schemes will be discussed. Finally an analytical stability analysis will beperformed to see whether the deflection of microvalves is uniquely defined or not.

6.2 Flow-structure interaction in check valves

Check valves show a hydraulic resistance, which depends on the direction of the flowthrough the valve. This directional sensitivity can be determined by the fixed shape of thechannels as exploited in diffuser-nozzle valves [22,11,3] or by using spring elements in theflow paths [14,21,19,26]. In fact check valves can be seen as the fluidic variant of theelectric diode. The latter type of valve mechanism will be analyzed in this chapter.

Check valves with spring elements such as membranes can be modeled with lumpedelements as shown in figure 6.1. In this electric analogy the behavior in open and closedirection is modeled separately by introducing two diodes Dopen and Dclose. The inductorsrepresent the inertia of the liquid. The capacitors are formed by the mechanical deflection offor example the valve membranes. In figure 6.1 the capacitor ports are connected to bothsides of the resistor, however for some valves, the output pin is connected to atmosphericpressure. All components can be expected to have variable impedance. The resistance isstrongly non-linear due to the interaction of the mechanical structure with the flow. In this

Flow-structure coupling 137

thesis we will look at the steady state valve characteristics. Consequently the research isfocussed on the variable hydraulic resistance.

inlet outlet

Dclose

Cclose

Rclose

Lclose

Lopen

Copen

Dopen

Ropenopen direction

close direction

Figure 6.1 Schematic electric analogy of a check valve. The upper branch, controlled by the idealdiode Dopen, models the flow in the open direction whereas the lower branch, controlledby Dclose, models the closing behavior.

When there is a fluid flow through a channel, pressure forces will be induced sinceenergy is dissipated by viscous drag. These pressure loads will change the geometry offlexible structures like the valve membranes etc. On the other hand, the change of theflexible valve structure will influence the cross-section of the flow channel and thus affectthe hydraulic resistance. This means that a bi-directional coupled system exists between thestructural mechanics and fluid mechanics domain. Pressure is the linking parameter asshown schematically in figure 6.2. In this diagram, the mechanical stiffness of the springelement is assumed to be dependent on the pressure, which is the case for large membranedeflections for example.

For a fixed resistance the pressure – flow rate relation is linear. Due to the control ofthe resistor, the system becomes non-linear. The non-linear deformation-resistance relationand possibly non-linear structural mechanics relation further increase this non-linearity. So asystem of coupled nonlinear partial differential equations needs to be solved.

There are three strategies. The differential equations for the mechanical andhydrodynamical domains can be solved at the same time, building one system matrixcontaining both the structural stiffness matrix [Mstruc(u)] as well as the part describing thefluid equations [Mfluid(v)] as shown in equation (6.1) [16]. These matrices can be dependenton the structural displacements, u, and flow velocities, v. The sub matrix [-I] is a negativeunity matrix.

138 Chapter 6

fluid flow hydraulicresistance pressure

mechanicalspring elementdeformation

� � �h K h p= ( ) K h( )�

R h( )� � � �p R h= ( )�

Figure 6.2 Flow diagram of the fluid mechanics – structural mechanics domain coupling in acheckvalve with a spring element. The lower diagram shows the relations in case of anon-linear spring element with stiffness K and a variable hydraulic resistance R.

Since the Navier-Stokes equations and (for large deflections) the structural equationsare nonlinear as well, iterative solving procedures such as Newton methods [2] are needed toobtain the velocity and deformation fields.

��

��

��

��

��

� �

}{}0{

}{}{

)]([]0[][)]([

vpu

vMIuM

fluid

struc (6.1)

This matrix system is solved on a fixed geometrical domain, split into a part on which thestructural equations are valid and a part on which the fluid domain is defined (direct domaincoupled solving). A one-directional coupling is obtained since the pressure {p} will induce amechanical deformation {u}. The pressure is thus computed on the geometrically non-deformed grid. For weakly coupled situations this computation can give a goodapproximation since the geometric deformations do not have much influence on the pressuredistribution. For convergence speed it is better to split-up the two domain computations tostart with the fluid domain after which the necessary loads are put on the mechanicaldomain. The resulting two separate system matrices are symmetrical and better conditionedwhich facilitates solving. In this strategy an open-loop situation, figure 6.2 without the arrowfrom “deformation” to “hydraulic resistance”, is regarded.

This open-loop approximation will not be suitable for valves where strong flow-structure coupling effects are present. For these situations the problem can be described bythe equations:


})({on}{}{)]([ upvvK fluidfluidfluid �� (6.2)

strucstrucstruc puuK �on}{}{)]([ �� (6.3)

with Kfluid and Kstruc the stiffness matrices of the fluidic and mechanical domainsrespectively. In equation (6.3) the load vector {pstruc} consists of values of {pfluid} fromdomain interfaces that are mechanical flexible. The fluid domain �fluid is described, byamong others, the from equation (6.3) resulting deformation vector {u}. To solve thisproblem consisting of two equations that are bi-directionally coupled by the loads andgeometry of the fluid domain, an iterative procedure is necessary to converge to self-consistence. During the iteration cycles the numerical grid of the fluid domains needs to beupdated. This procedure is called indirect coupled solving.

The third strategy can help to reduce the amount of computation time. Equilibriumiterations can be extremely computer time consuming. Fluid dynamic computations are non-linear and usually converge rather slowly, especially if strong local velocity gradients exist.An extra iteration loop therefore will increase the time substantially. Since the aim is toanalyze effects of geometry changes on the valve resistance it is important to avoid theadditional iteration loop. A degree of freedom (DOF) reduction opens the possibility to de-couple both domains although still a bi-directional coupled problem is solved. In the nextparagraph the implementation will be treated in more detail.

6.3 Numerical implementation

6.3.1 IntroductionOne of the aims of the research on check valves is to obtain design formulas that describe theeffects of the different parameters on the valve characteristics. This can be achieved bysolving the differential equations numerically. However exact solutions that meet thedifferential equations as well as boundary conditions cannot be found for most situations.Hence tradeoffs must be done to the precision of the model by reducing the problem to asimplified situation and finding approximating solutions. For valves, simplification of themodels will mean using simplified flow models such as Stokes’ flow description byneglecting inertia effects. In order to meet the boundary conditions, the geometry will besimplified towards flow in a narrow gap, neglecting flow though entrance and exit channelsand around the moving valve structures.

By solving the differential equations numerically with simulation programs, moreextended flow description models can be used which take inertia effects into account. In

140 Chapter 6

chapter 7 it will be shown that, although flows at low Reynolds numbers are observed,inertia effects can play a role on a local scale such as the existence of vortex flow at the exitof a valve. The results however are discretely known on a numerical grid, which makes itinconvenient to use for design purposes. The aim is to use the numerically obtained data toimprove the analytical design formulas.

Numerical simulations of the flow-structure-coupled problem can be done withdifferent programs for each domain [17]. We used the finite elements program ANSYS ver.5.3 [1], running on an Intel Pentium 120 based computer for both domains. It incorporatesfluidic elements as well as structural elements and different flow and structural models. Withthe use of the internal APDL (Ansys Parametric Design Language) commands a rather fastcoupling with data transfer between the two domains can be established.

6.3.2 Bi-directional coupled solvingIn ANSYS, a facility for fluid-structural coupling is implemented. It consists of the use ofdummy elements for modeling the structural mechanics domain during the fluid simulationafter which they are substituted for real structural elements and the pressure loads aretransferred. After the structural computation a one-directional simulation is obtained. Thenumerical grids that can be built are restricted to the use of 2D 4-node and 3D 8-node linearelements.

Since a bi-directional coupled simulation tool is needed and flexibility in thecombination of elements such as the use of shell elements for thin membranes, new routineshave been programmed. In figure 6.3 the process flow is drawn of the bi-directionalcoupling. The outer loop is used to compute the flow-structure interaction for differentparameters such as a varying valve geometry, the inner loop is used for the convergence tothe equilibrium situation by checking the differences in structural deformations betweensuccessive iteration loops.

Input for the program consists of the structural and fluidic geometry and materialparameters, boundary and start conditions, domain interfaces and convergence criteria. Forthe fluidic domain, a fixed geometry can be defined with interfaces to the flexiblemechanical structure that will deform.


structural mechanics solver

structural mechanics grid generator

structural mechanics boundary condition generator

fluid mechanics solver

fluid mechanics grid generator

fluid mechanics boundary condition generator

convergence checkon deformation

compute parameters, plots and save data

define: geometry, material, boundary and start conditions,domain interfaces, convergence criteria, grid dimensions

exit



NO

YES

next configuration?

YES

NO

start

structural mechanics boundary condition generatorinter-extrapolation of load data between domain interfaces

Figure 6.3 Flow scheme of the implemented numerical tool for indirect bi-directional coupledflow-structure interaction simulation for investigation of the effects of parameterchanges on the valve characteristics.

142 Chapter 6

To obtain a flexible program that can be used to quickly implement different valve types, alldefinitions in the program are done parametrically. For the start conditions an initial load onthe flexible structure is needed.

The coupling between the fluidic and structural mechanics domain consists ofaddressing fluidic pressures to the flexible mechanical structure and updating the fluidicgeometrical grid after a computed mechanical deformation. Transferring pressure loads canbe done in two ways: a one to one nodal transfer [17] or inter-/extrapolation of pressuresbetween the grids. Both principles are drawn in figure 6.4. The first method is ratherstraightforward, however it has several drawbacks. With the use of inter-/extrapolation ofnodal pressures between the domain grids, much flexibility is obtained in building models.Each individual domain grid can be built without taking care of the grids in other domains,which leads to a better individual numerical grid optimization.

In the fluidic domain local pressure gradients can occur that require a refinement of thegrid. For the mechanical structure however this refinement might not be necessary sincelocal pressure peaks will damp-out fast according to the principle of Saint Venant [23] pp.39. Averaging of the pressure peaks will still show identical effects on the mechanicalstructure. With the gained freedom in optimization of the fluidic and mechanical grids, abetter change on fast numerical convergence is obtained whereas unnecessary gridrefinement might cause a worsening of the matrix conditions and increasing the amount ofDOF. So flexibility in grid definition will reduce the needed computer power. Besides thesenumerical advantages, the definition of the grid by the programmer becomes much easiersince the number of constraints is reduced. A very important benefit for data transfer viainter-/extrapolation is the possibility to combine different element types such as for examplebi-linear and quadratic elements and combinations of membrane and 3D elements.Especially in micromechanics, structures such as membranes with high aspect ratios areoften present which are difficult to model with general 2D or 3D elements. These elementsresult in a too high stiffness, requiring special membrane elements. For fluidic computationshowever 2D or 3D brick or triangular elements are commonly used. Based on theseconsiderations the method of inter-/extrapolation was chosen.

To avoid losing information when transferring load data from a coarse to fine grid, acombination of integration and extrapolation is used as shown in figure 6.4B.


fluidic domain

structural mechanicsdomain

A B C

Figure 6.4 Load data transfer between domain grids: A) nodal one-on-one transfer, B) transfer withintegration and extrapolation from a fine to coarse grid, C) transfer with interpolationfrom a coarse to fine grid.

For assigning the nodal pressure values and to define the flexible interface, “components”are used. A component is a defined geometric area or line. Nodes covered by the “interfacecomponent” will be used in the inter-/extrapolation and fluid grid updating routines. Thismeans that the node selection in the transfer routines is fully automated which facilitates theimplementation of new models and grid refinements.

The convergence to the equilibrium situation is checked by monitoring the differencebetween the mechanical deformation of the flexible structure between successive iterations.Since a continuum model is used, the deformation of the structure is taken into account. It isexpressed as the sum of the relative change in displacements, u, of a selected set of DOF:

��

�

��

��

� �max

1

21k

kik

ik

ik

uuu (6.4)

With k the summation index over the amount of DOF to check convergence and i theiteration step. To define the selection of nodes that will be used in this check, a “convergencecomponent” is made. With the geometrical definition of the component in combination withthe convergence value, the criterion is set.

Convergence of the structural or fluid mechanics computations individually is stronglyrelated to the layout of the numerical grids. During the iteration sequence the geometry ofthe fluid domain is changed. Due to this, for each cycle a new grid must be generated whichincreases the risk of a bad layout [16]. To minimize this risk the fluid domain will be split indifferent sub regions that can be meshed individually. In combination with mapped mesheswith 4 or 8 node fluid elements, a good mesh condition can be preserved. The only risk thatexists lies in the aspect ratio of the formed elements. Since for example the gap-height undera valve will vary, different elements with different aspect ratios can arise. This problem is

144 Chapter 6

avoided by the implementation of routines for adapting the number of elements in such away that a fixed aspect ratio is maintained.

A simple direct transfer of load and deformation data will show a slow convergencebut more likely divergence as shown in figure 6.5. In this figure a one DOF system isregarded with a constant mechanical stiffness. Especially for low spring constantsdivergence is easily obtained. The condition for convergence in general can be describedwith:

0lim1

12�

�

�

�

��

��

ii

ii

i pppp

(6.5)

fluidics

structural mechanics

pressure

point of equilibriumdefo

rmat

ion

h4

h3h0

heq

h1h2

p5 p3 p1 peq p0 p2 p4

Figure 6.5 Graphical representation of the possibility on divergence when using a simple load anddeformation data transfer.

For a uniform, monotonous increasing deflection-load function of the structural mechanicscomputation and a uniform, monotonous decreasing flow function, this condition equals foreach step i:

iiiiiiii hhhhpppp �� 112112 (6.6)

The limiting situation for divergence is obtained when each new pressure iteration step anddeflection step size equals the preceding one. In this case a rectangular iteration path can bedefined as shown in figure 6.6. From this picture it can be concluded that convergence formonotonously increasing and decreasing functions on the domain:


],[ UL hhh� (6.7)

can be obtained when:

hp

hp fs

�

��

�

� (6.8)

for all

],[ UL ppp� (6.9)

With superscript f and s indicating the fluid and structural mechanics domains respectively.In practice, this condition will not hold for microvalves. Values for the fluid and structural“pressure stiffness” in the order of 1018 and 107 can be obtained respectively.

fluidics


pressure

defo

rmat

ion

diverging

divergingconverging

pL pU

hL

hU

Figure 6.6 The effect of curve changes on the convergence

Still, if convergence could be obtained, the efficiency of this iteration scheme is still ratherlow. During the iteration sequence the approximated results “spiral” towards the exactequilibrium answer. A faster and stable convergence can be guaranteed by taking precedingsteps into account using higher order Newton iteration schemes. However for higher orderNewton methods, derivatives are needed or additional function evaluations. These functionevaluations, especially for the fluid computations are expensive. Therefore different methodswere used that exploit the shape of the functions in both domains. Looking at figure 6.5 it is

146 Chapter 6

shown that the pressure and deformation equilibrium respectively can be found somewherebetween successive iteration points. If for the situation of figure 6.6 both relations would belinear, the intersection point could be found on 50% of the calculated step sizes. For the non-linear curves the intersection will be positioned at the left half of the bounded box. Hencetaking only a fraction kw of 50% of the incremental pressure step will yield convergence andspeed up the iterative process. This principle is shown in figure 6.7.

fluidics


pressure


rmat

ion

h0

h1

eqh2h

p2peq p1 p0

Figure 6.7 Fast convergence can be obtained by taking for example half of the successive predictedpressure step values.

Written in a mathematical form:

)~(f s1 ii ph �

�(6.10)

)(f f1 i

fi hp ��

(6.11)

fiwiwi pkpkp 11 )1(~~��

�� (6.12)

with kw = 50%.Since

],[ 1�� iie ppp (6.13)

and

eiei pppp ��1 (6.14)


convergence is guaranteed. With ff and fs the functional operators, describing the fluid andstructural mechanics domains respectively. The 50% value for the pressure step might beincreased to give more weight to the fluid computation steps. This will speed up the iterationsequence even more since the fluid computation is more non-linear. On the other hand thechance on divergence will be increased.

This weighing method does not take history into account. Since it is known that theequilibrium is bounded by the computed points (pi,hi) and (pi-1,hi-1) a better estimation of thenext iteration point can be obtained by calculating the intersection of the two lines definedby: (pi,hi) and (pi+2,hi+2) with (pi+1,hi+1) and (pi+3,hi+3). Combined with the method ofaveraging pressure predictions, the scheme of figure 6.8 is obtained. After two iterationsaccording to the previous scheme, a new prediction is made by computing the intersection ofthe linear approximation of the fluid model and structural mechanics model through points iand i+1 (lines through f0, f1 and s0, s1 respectively).

fluidics


pressure


rmat

ion

h0

h1

eqh2h

p2peq p1 p0

s0f0

f1 s1

e1

Figure 6.8 A fast and stable converging method: a combination of the iteration scheme of figure 6.7and a prediction (extrapolation) step (e1) using previous 2 flow and structural mechanicsiteration steps (s0,f0 and s1,f1).

This iteration method is fast since the fluid mechanical model is strongly non-linearcompared to the structural mechanics model. For a linear mechanics model the predictionwill lie on the pressure-deformation line as shown in figure 6.8. Mathematically the methodcan be described by:

��

��

�

�

�� s

if

i

si

si

fi

fif

ie hhphphhh

��

�� (6.15)

148 Chapter 6

sfxpphhh x

ixi

iixi or

1

1�

�

�

�

�

�

� (6.16)

)~(f s1 ii ph ��

(6.17)

)(f 1f

1 �� i

fi hp (6.18)

fiwiwi pkpkp 11 )1(~~��

�� (6.19)

6.4 Domain de-coupling

For equilibrium iterations, many flow and structural mechanics data are computed that willnot be used. The only data used are the finally converged values. Since the aim is toimplement routines to extract information that can be used to describe the characteristics ofvalves, an additional loop was implemented for parameter change. For each point in thedesign space an iteration procedure must be done. Splitting-up the structural and fluidcomputations will reduce this amount of time substantially. This is only possible when thenumber of DOF can be reduced to one without affecting the accuracy. For example for thebossed valve this is valid if the torsional stiffness of the valve is much larger than thetranslational stiffness such that no tilting of the boss occurs. With individual calculations ofthe fluid and structural mechanics characteristics, similar to the two lines in figures 6.5 to6.7, two data sets are obtained which can be fitted together to find the equilibrium point byintersection of the curve fits on both sets. Similar to the bi-directionally coupled problem,routines are implemented in ANSYS to compute the de-coupled situation. In figure 6.9 theflow diagram is shown.

6.5 Stability

In figure 6.2 the bi-directional coupling of the fluid and structural mechanics domains wasdrawn as a feedback loop. In this loop the fluid domain was treated as a resistance. Formicrovalves operating in the Stokes flow range (chapter 3) this assumption is justified sinceinertial effects will not play an important role. With only fluid dissipation by the hydraulicresistance, stability of the valve is assured. Stability in this case is meant that for eachapplied steady flow-rate a unique, time independent valve opening or gap is obtained. Forhigher flow-rates however inertial effects must be taken into account.




structural mechanics boundary condition generator


define: geometry, material, boundary conditions,grid dimensions

next configuration?

YES

fluid mechanics solver

fluid mechanics grid generator

fluid mechanics boundary condition generator

define: geometry, material, boundary conditions,grid dimensions

start


exit

next configuration?

YES

coupling of domain results via coupling parameters


NO NO

Figure 6.9 Data flow scheme for the domain de-coupled numerical simulation

Assuming no viscous effects, the equations are governed by Bernoulli’s law [9] whichdescribes the energy balance at different places in a non-dissipating flow, neglecting gravityfields etc. :

constant21 2

�� vp � (6.20)

Applying this relation to valves means that due to the flow under the valve, a local pressuredrop will occur which reduces the gap. Determined by the continuity laws, a certain gap sizeis needed in order to get the fluid flowing through. Bernoulli’s law can thus give rise to apositive or negative feedback loop and thus depending on the design causing instability. Thisphenomenon, researched in the world of aeroelasticity can be observed in for example flutterof airplane wings and swinging of badly designed bridges during storms [8,7].

150 Chapter 6

To see whether instability plays a role, a simple 2D-piston structure, shown in figure6.10 is investigated from which general conclusions will be drawn. For reducing the amountof parameters to a limited convenient set, the dimensionless groups of table 6.1 are used.

variable parameter dimension dim-less variable definitionh valve gap m

sK~ lvKs2

0/2 �

h0 entrance height m p~ 20/2 vp �

Ks spring stiffness N/m 0~p 2

00 /2 vp �

l valve length m v~ 0/ vv

p pressure in the valve Pa �h lh /p0 entrance pressure Pa �h0 lh /0

v flow velocity in valve m/s �w lw /v0 entrance flow velocity m/sw valve width m� flow-rate m3/s

� mass density Kg/m3

Table 6.1 Used dimensional and dimension-less parameters

With these parameters Bernoulli’s relation becomes:

20

~1~~ vpp �� (6.21)

The flow continuity law is rewritten to:

0

~h

hv�

�� (6.22)

And the load balance on the valve states:

w

hsKp�

�~~� (6.23)

Substitution of these relations yields the equation for the valve deflections:

� � 01~~ 20

20

3�� hwhwhs pK �� (6.24)


v0 p0

Ks

h0

wh

Figure 6.10 Piston model used for analyzing the effect of aeroelastic instability

This third order equation will give three solutions. Depending on the discriminant [4] ofequation (6.25) the number of real-valued solutions and thus of the equilibrium situations aregiven.

� ��

�

�

��

�

� ��

��

��

� 2

330

20

2

20 ~27

1~

4~s

wwh

s

wh

KP

KD �� (6.25)

For D > 0 the valve will be stable. For D < 0 however 2 positive real-valued solutions areobtained. In figure 6.11 the roots are plotted for different values of the stiffness and pressureparameters for realistic values of �w= �h0 = 1.

0

1

10

100

1000

0.0 0.5 1.0 1.5 2.0 2.5

defle

ctio

n pa

ram

eter

�

stiffness factor Ks

Valve deflections for different stiffness and pressure factors

P = 0~0 P = 1~

0 P = 2~0

~

h

Figure 6.11 Bifurcation plots showing the valve deflections for varying stiffnesses and pressures

152 Chapter 6

This figure shows that instability can be reduced by increasing the valve stiffness. This isrelated to the pressure and the velocity. At low flow-rates stability can be obtained whereaswith increasing flow velocities a sudden bifurcation occurs. However filling-in typicallengths, flow-rates and material parameters for microvalves, bifurcation will occur at a valvestiffness in the order of 10-6 N/m or less. In the next chapter it will be shown that typicalstiffnesses are in the order of 1 N/m or more which means that the valve operation is stableunder practical conditions. In addition, viscous damping in microvalves will be high suchthat the effect of instability can readily be neglected.

6.6 Conclusions

With the routines implemented in the FEM package ANSYS 5.3, fast and flexible numericaltools have been created to verify the analytical solutions and to investigate the effects, whichcan be neglected in analytical models. Flexibility is obtained on different points. With theuse of data inter-/extrapolation in combination with “components” both domain grids can beeasier implemented and optimized and automatic node relations are made.

The improvement of the numerical domain grids will speed up the convergence ofthe individual computations. Since the geometry of the domain grid of the fluid computationchanges during each iteration cycle, re-meshing is necessary. Automatic element numberadaptation will promote convergence since good aspect ratios of the fluid element sizes areguaranteed.

With simple load and deformation transfer between the domains convergence cannotbe obtained since the pressure-deformation relation in the fluid domain is strongly non-linearcompared to the more or fully linear structural mechanics domain. Therefore fast convergingmethods have been proposed. With these rather simple methods convergence is guaranteed.

With the FEM routines, insight in the relation between design parameter changes andthe stationary valve performance will be investigated in chapter 7. These simulations takemuch computer time. Therefore an additional de-coupled program was written that can beapplied to models which can be reduced to one degree of freedom. The structural mechanicsas well as the fluid domain are individually computed for different parameter changes afterwhich both data sets can be combined to give the valve behavior.

Finally an aeroelastic static stability analysis has been performed in order toinvestigate the effect of varying design parameters on the uniqueness of the valve deflection.It shows that for very flexible valves more than one equilibrium solution can be obtained.However realistic microvalve stiffnesses appear to be much higher such that no instability isexpected.


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154 Chapter 6

[17] J. van Kuijk, Numerical modeling of flows, Ph.D. Thesis University of Twente, TheNetherlands, ISBN 90-9010395-3, (1997)

[18] A. Olsson, G. Stemme, E. Stemme, “A numerical design study of the valveless diffuserpump using a lumped-mass model”, J. Micromech. Microeng. 9, (1999) 34-44

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[21] L. Smith, B. Hök, “A silicon self-aligned non-reverse valve”, Proc. Transducers’91,(1991) 1049-1051

[22] E. Stemme, G. Stemme, “A valveless diffusor/nozzle-based fluid pump”, Sensors andActuators A39, (1993) 159-167

[23] S.P. Timoshenko, J.N. Goodier, Theory of elasticity, McGraw-Hill Int., Singapore, 3rd

int. edition, (1970)[24] J. Ulrich, H. Füller, R. Zengerle, “Static and dynamic flow simulation of a KOH-etched

micro valve”, Proc. Transducers’95, (1995) 17-20[25] J. Ulrich, R. Zengerle, “Static and dynamic flow simulation of a KOH-etched

microvalve using the finite-element method”, Sensors and Actuators A53, (1996) 379-385

[26] N. Vandelli, D. Wroblewski, M. Velonis, T. Bifano, “Development of a MEMSmicrovalve array for fluid flow control”, J. Microelectromech. Syst. 7-4, (1998) 395-403

[27] P. Voigt, G. Schrag, G. Wachutka, “Microfluidic system modeling using VHDL-AMSand circuit simulation”, Microelec. J. 29, (1998) 791-797

[28] P. Voigt, G. Schrag, G. Wachutka, “Electrofluidic full-system modeling of a flap valvemicropump based on Kirchhoffian network theory”, Sensors and Actuators A66, (1998)9-14

[29] R. Zengerle, M. Richter, “Simulation of microfluid systems”, J. Micromech. Microeng.4, (1994) 192-204

[30] R. Zengerle, W. Geiger, M. Richter, J. Ulrich, S. Kluge, A. Richter, “Transientmeasurements on miniaturized diaphragm pumps in microfluid systems”, Sensors andActuators A46-47, (1995) 557-561

[31] R. Zengerle, J. Ulrich, S. Kluge, M. Richter, A. Richter, “A bidirectional siliconmicropump”, Sensors and Actuators A50, (1995) 81-86

155

77 VVAALLVVEE CCHHAARRAACCTTEERRIIZZAATTIIOONN

Hydraulic resistance models for the in chapter 5 describedvalve designs will be derived and compared withmeasurement data. Analytical approximations are derived toobtain simple design formulas. Using the numerical tools,which were described in chapter 6, these models can beextended to model the valve behavior in more detail. Bothstructural and fluid mechanical models will be discussed toget insight in the strength, deflection and domain-coupledcharacteristics of the passive and active valves.

7.1 Introduction

The functionality of the valves, discussed in chapter 5 will be analyzed by derivingsimplified analytical design formulas. The aim is to generate design formulas, which can beused in future component and system development and optimization. Due to the rathercomplex geometry of the valves, meeting the boundary conditions exactly is not possible inan analytical way. Therefore assumptions must be done which simplify these conditions suchthat analytical design formulas can be derived. Due to these simplifications, the model’spredictions will differ from reality. In order to analyze the effects of some of thesimplifications and to verify the analytical solutions, numerical models were implemented inthe ANSYS 5.3 finite element package. For the fluid-structural domain coupling, routineswere implemented, described in chapter 6. With these models, details such as entrance andexit effects in the flow computation can be visualized and analyzed in more detail. It will beshown that, although flow at low Reynolds numbers is present, kinetically induced flow

156 Chapter 7

patterns can be obtained at local scale. Other local effects that will be investigated are themechanical stress concentrations since these strongly limit the strength of the valves. Thecomputed results will be validated with data obtained from measurements.

7.2 Characterization setup

For validation of the models and to check the functionality of the fabricated valves, acharacterization setup is needed. Hydraulic characteristics of a valve are determined by theapplied and resulting pressures and flow-rates. This means that for measuring the stationarybehavior of the valve, a choice can be made between applying a pressure drop over the valveand measuring the flow-rate or the other way round, applying a flow rate and measuring theresulting pressure drop.

Since the measurement system has a flow resistance, defined by tubing, connectors,sensors etc., simply applying pressure and measuring the flow-rate is not suitable. Thepressure drop has to be measured directly over the valve. For this, a differential pressuresensor was used (Honeywell 26PCXFA1D [6]) of different ranges of 7.0�103, 3.0�104 and1.0�105 Pa respectively. We chose for a flow source: applying a volume flow using a syringepump. With a combination of a precision translation stage (Microcontrole-NewportUTMPE1 [10]), to generate translation speeds and stepper positions with a precision of 1 µmand a range of 50 mm, and a syringe of different stroke volumes, a flow range can be appliedfrom 10µl/s down to about 1 nl/s . Three sizes Hamilton GASTIGHT syringes [5] were used:10 µl, 100 µl and 1 ml stroke volume. At low stepper speeds, the translation does not show asmooth translation but moves with pulses, which limit the minimum flow-rate.

The system is designed as a modular architecture of tubes, connectors and polymerblocks for mounting devices, syringes and the differential pressure sensors. For theconnectors, the 062 MINSTAC system from The Lee Company [11] is used. Devices aremounted on the building blocks by using a clamping mechanism and sealing o-rings. Sincethe stroke of the syringe pump is limited, refill cycles are needed. Hence an electricalsolenoid valve (MINSTACK 062 LFYA05) is mounted, which is connected to the syringe atone side and switches between the reservoir and the rest of the system at the other side. Aschematic layout is shown in figure 7.1.

As discussed in chapter 3, surface tensions play a dominant role in miniaturizedsystems. Consequently, droplet formation at the exit tube of the measurement systemgenerates substantial measurable pressure pulses. To avoid these pulses, the tube exit mustbe kept under the liquid level such that the existence of a meniscus is prevented. Combiningthe “source” and “drain” reservoirs in one bottle with an additional venting hole, prevents a

Valve characterization 157

pressure offset over the system due to different reservoir liquid levels. Since small particlesin the tubing can cause severe malfunctioning of the valves, microfilters were applied.

> ERROR INSUFFICIENT DISK SPACE _

DUT

reservoir

filter filter

syringe pump solenoid valve device under test

pressure sensor

stepper controller power supply multimeter IEEE 488 GPIB bus

computer

Figure 7.1 Schematic overview of the valve characterization setup

The pressure sensors were read-out with a 10-channel multiplexed Keithley 2000multimeter [8]. The multimeter, stepper controller for the syringe pump and the powersupply for switching the valve were computer-controlled via the IEEE 488 GPIB bus.Programs written in the graphical programming language, HP-VEE version 3.2 [7] wereused to control the setup and perform data acquisition. An example of the user interface formeasuring the stationary hydraulic flow resistance is shown in figure 7.2. The program readsin an ASCII file with a list of flow-rate values to be generated. For every flow-rate, a definednumber of pressure measurements are performed at a given time interval. After this series ofpressure measurements is finished, the flow-rate is adapted to the next listed level, afterwhich the series of measurements is repeated. Since the measurement system has a certaincapacitance (flexibility of the tubing, pressure sensor and valve membranes etc.) time delayis needed to reach a stable, constant pressure signal. Routines are programmed to check forstability before measurements are started. Measured flow-rates, pressures and computedhydraulic resistance values are on-line plotted on the screen and written to files in ASCIIformat for further use in spreadsheet programs.

158 Chapter 7

Start Stop470.6 0 1.140E+003 0.000E+000 1

resistance (Ns/m^5) steps/spressure (Pa)flow-rate (µl/s)time (s)

Data plot in time

position (µm) sample nr.25667 10

12kpressure

200Tresistance

2E+003/ 20T/

0 050050/time (s)

00

resistance (Ns/m^5)

pressure (Pa)

flow (m^3/s)

flow50m/

0.3

Measurement cycle Duckvsb1_upd1.cle sample 4-9

resistance

pressure

pressure (Pa)2E+003/

12k

00

flow-rate (m^3/s) 50m/0.3

200mresistance (Ns/m^5)20T/

0

Pressure & resistance plot

Figure 7.2 User screen for the valve open-resistance characterization: the settings (sample timesactual pressure and flow-rate etc.) are listed on top, the flow-rate, pressure andcomputed resistance values versus time are plotted in the upper graph and the pressureand resistance values versus flow-rate are shown in the lower graph.

7.3 The bossed valve

7.3.1 Structural mechanicsThe design of the bossed valve has been treated in detail in section 5.3. The beams and platehave the same thickness such that both, beams and plate will bend under a pressure load. Inpractice however this plate bending is very limited as will be shown later on. As a result ofthis, the plate can be treated as a rigid boss.

Valves have been made with 3 and 4 straight or curved beams. Due to the diverselayouts, different rotation and translation stiffnesses can be obtained. The spring structurehas 3 mechanical degrees of freedom (DOF) as shown in figure 7.3. When a pressure isbuilt-up under the plate, the valve will lift in the z-direction (Wz). However due to therotational freedom around the x- and y-axis, the plate can also tilt. This would mean that fora correct prediction of the hydraulic resistance, all degrees should be taken into account. Areduction of DOF towards one would be favorable.


z

y

x �x

�y

wzXy

Z~

~~

Figure 7.3 Degrees of freedom of the spring structure of the bossed valve: two rotations around thex- and y-axis and one translation in the z-direction are possible.

To check whether a reduction is possible, first the load on the boss is considered. Asdiscussed in chapter 6, the valve can be thought of as a variable resistance. For the bossedvalve, the resistance is generated by the narrow gap that arises between the boss and thevalve seat. For small flow rates, the fluid velocity in this gap is much higher than at otherpositions in the valve such that only the flow in this gap is taken into account. A perfectvertical lift of the boss will generate a symmetrical gap opening and thus a pressure dropover the valve seat occurs in an axial-symmetrical way. On the other hand, a tilting of theboss will generate more resistance at the small gap side than at the opposite boss position.Since the valve seat is rather small (~20 µm) compared to its radius (~200 µm), the pressurewill be constant over a large part of the boss surface. Therefore a worst-case situation wasanalyzed which is strongly exaggerated but gives the limiting case: the distributed pressureload is thought of being concentrated in one point such that the distributed load changes intoa point force. The most tilting will be obtained when the resulting moment, generated by theforce is maximized. This is the case for a force on the boss edge, at the joining of one of thebeams.

An analytical model for predicting the boss deflection and tilting at the boss center, canbe derived by first looking at the deflection, rotation and torsion of one beam with arectangular cross-section. These forces and moments on the beams as function of the beam-tip deflection and rotations can be written in the following matrix-vector system:

��

��

�

��

��

�

�

�

��

�

�

�

��

��

�

��

��

�

�

iy

ix

iz

Ti

y

ix

iz W

llEIlk

l

lEI

MMF

�

�

�

�

�

�

�

�

~

~

~

2

3

3

~

~

~

406

00

6012

(7.1)

160 Chapter 7

Or written in terms of matrix variables:

izyx

izyx

izyx

��

~~~~~~~~~ WKF �� (7.2)

The indexes x~ , y~ and z~ indicates the local beam-oriented axis system as shown in figure

7.3. The used variables are listed in table 7.1. The moment of inertia for rectangular beamcross-sections [4] is given by:

3

121 btI � (7.3)

variable description unit

� tilt angle or angular coordinate rad

� beam orientation angle rad

� Poisson’s constant -

� mass density kgm-3

µ dynamic viscosity Nsm-2

a boss radius or membrane length mA surface area m2

aout outer radius of the spiral shaped beams mb beam with or membrane width mD flexural rigidity of a membrane NmE modulus of elasticity PaF force NFcoup coupling force between two bosses in a nc valve Nh valve lift height mI moment of inertia m4

kT torsion stiffness Nml length mM moment NmP pressure PaPact actuation pressure PaQ distributed shearing force per unit length Nm-1

r radius coordinate mrboss boss radius of a bossed membrane mRhyd hydraulic resistance Nsm-5

rin inner radius of a circular valve seat mrmem membrane radius mrout outer radius of a circular valve seat mt beam or membrane thickness mW deflection mx,y,z Cartesian coordinates mTable 7.1 Variable definitions and their dimensions


Variable kT incorporates the torsional stiffness of the beams. For rectangular cross-sections,an approximation is given by Roark [17]:

lGk

k geomT � (7.4)

with the shear modulus defined by:

)1(2 ��

�EG (7.5)

and the torsion constant for rectangular cross-sections:

��

��

��

��

��

��

��

��

��

�

��

��

43

121121.0

31

bt

bt

ltbkgeom (7.6)

These “element” matrices for each beam can be composed to one combined matrix:

��

zyxzyxzyx ~~~~~~~~~ WKF �� (7.7)

With rotation matrix T, consisting of the element matrices TI at the matrix diagonal, thebeam-oriented axis systems can be translated into terms of the global axis system.

��

�

�

��

�

�

��

)cos()sin(0)sin()cos(0

001T

ii

ii

��

�� (7.8)

��

zyxxyz ~~~FTF �� (7.9)

The forces and moments acting on the beams and the externally applied forces must be in

equilibrium, which is described by:

�

xyzFMF �� (7.10)

with the columns of matrix M formed by:

��

�

�

��

�

�

��

�

10)cos(01)sin(001

M

i

ii

aa

�

�� (7.11)

The relations can be combined to form a system force-deflection relation:

162 Chapter 7

WKWMTKTMF TT~~~ ��

�

zyx (7.12)

with K the system stiffness matrix. For a valve with three, 1 mm long and 80 µm widestraight beams with a boss diameter of 420 µm and a thickness of 18.8 µm, a deflection of3.71 µm and a tilt of 0.13� is obtained under a load of 1 mN at the boss rim at a beamconnection. ANSYS results are shown in figure 7.4. From this extreme loading situation it isobserved that the tilting effect is still small. The tilt angle obtained from the numericalsimulation resembles the angle obtained from the analytical calculation. However theanalytically computed deflection at the boss center (3.71 µm) differs from the numericalsimulation (4.40 µm). Due to the higher number of DOF of the numerical model moreflexibility is obtained. Stiffness measurements with an atomic force microscope (AFM) witha stiff needle gave a stiffness for the valve of 212�27N/m. Compared with the analytically(270N/m) and numerically (223N/m) obtained stiffnesses, the real valve is more flexible.Since the beam thickness/beam length ratio is related to the stiffness to the power 3, a smallvariation in the thickness uniformity will have large effects on the valve deflection. Hencegeometrical inaccuracies can explain the stiffness difference.

From the AFM measurements no tilting of the boss could be distinguished. In thesimulations, only bending and torsion was taken into account. For large deflections in theorder of the beam thickness, stretching effects will increase the stiffness and reducing thetilting effects. Besides, for larger lift heights, the effect of a tilting of the plate has lessinfluence on the resistance than for small lift heights. Since a gap reduction causes anincrease in resistance, a higher local pressure gradient will occur. This means that thedistributed force on the lower valve edge is smaller than the force at the larger gap opening.As a consequence, a symmetrically suspended valve with identical beams will show ahorizontal positioning of the valve boss.

These considerations lead to the conclusion that a reduction of three DOF down to oneout-of-plane deflection is allowed. With the elimination of tilting freedom, the deflectionstiffness of the valve is simply given by:

3

��

��

��

ltbnEK (7.13)

with n the number of beams (3 or 4).The assumption of a rigid boss instead of a deformable plate is valid as well. In the left

picture of figure 7.5, a zoom-in is given on the deformed plate when a uniform distributedpressure load is applied. The curvature of the plate is very small. In the right hand sidepicture, the effective stress distribution is shown.


ANSYS 5.3

NODAL SOLUTIONSTEP=4SUB =1TIME=4UZTOPRSYS=0DMX =.004853SEPC=5.088SMX =.004853

.758E-04

.303E-03

.607E-03

.834E-03

.001138

.001365

.001668

.001896

.002199

.002427

.00273

.002958

.003261

.003488

.003792

.004019

.004323

.00455

.004853

ANSYS 5.3


MX

.003423

.003491

.003583

.003651

.003742

.003811

.003902

.00397

.004062

.00413

.004221

.00429

.004381

.004449

.004541

.004609

.0047

.004769

.00486

Figure 7.4 Tilting of the valve when a force is applied at one of the beams. The boss is only slightlycurved and the tilting effect is limited. The top picture shows a view of the full valvewhereas the lower picture shows a zoom-in. The gray values indicate the deflectionlevels.

Since a linear model is used, the maximum uniform pressure load before failure isestimated to be about 11bar in the open direction, when a yield stress is assumed of 7.0GPa[16]. Due to stretching effects at large deflections, the real strength will probably be higher.Failure will occur at the stress concentrations at the beam-valve seat connection. In the closedirection a higher strength is obtained since the valve will be uniformly pressed against theflat seat such that a better edge support will arise without loading the beams.

164 Chapter 7

ANSYS 5.3


.005275

.005322

.005384

.00543

.005492

.005538

.0056

.005647

.005709

.005755

.005817

.005863

.005925

.005972

.006033

.00608

.006142

.006188

.00625

ANSYS 5.3

NODAL SOLUTIONSTEP=1SUB =1TIME=1SEQV (AVG)TOPDMX =.006228SMN =264410SMX =.622E+08SMXB=.889E+08

.786E+07

.105E+08

.139E+08

.165E+08

.199E+08

.225E+08

.260E+08

.286E+08

.320E+08

.346E+08

.381E+08

.406E+08

.441E+08

.467E+08

.501E+08

.527E+08

.562E+08

.588E+08

.622E+08

stress concentration

Figure 7.5 Valve boss deflection (top) and effective stress profile (bottom) for the situation of auniformly distributed pressure load of 0.1 bar. The deflection profile shows only a slightcurvature of the boss such that a rigid boss can be assumed. Stress concentrations at thebeam-boss connection indicate the points of failure initialization.

In order to reduce the stiffness of the valve to have a lower hydraulic open-resistance,the thickness and the length of the beams can be increased. As discussed in chapter 5, thethickness is limited by the etch process in combination with the wafer thickness variations.The length however can well be controlled in the mask design, using curved and hookedbeams, without increasing the valve size. For a hooked spring system consisting of two


perpendicular straight beams as drawn in figure 7.6, torsion as well as bending of the beamsoccurs. The total stiffness of this system with 4 beams is given by:

� �1

12

21222

221

212

121

32

31

2323448�

��

��

��

�

�

��

�

�

�

��

lClllCll

lClllCllllEIK (7.14)

with the torsion constant C according to:

Ik

C)1(2

geom

��

� (7.15)

When KOH etching is used to fabricate the valve, the beam cross-section will be trapeziumshaped. For kgeom, an approximation can be made by taking the value in case of a rectangularcross-section with a mean beam width (b1+b2)/2 (see figure 7.6). These widths are relatedaccording to:

)7.54tan()(2 12 �� bbh (7.16)

The moment of inertia, I, for the trapezium shape is defined by:

)(36)4(

21

2221

21

3

bbbbbbtI

�

��

� (7.17)

l1l3

b2

b1

t

Figure 7.6 Top view of the hooked spring structures (left) and the cross-section of the KOH-etchedbeams.

The spiral design allows for better shaped springs. The combination of torsion and bendingin combination with the spiral shape make an exact derivation of the stiffness rather complex[20]. Therefore an approximation can be found by only taking the bending into account.The radius of the spiral can be described by different radius functions. For the in chapter 5described valves a linear and cosine function was used:

166 Chapter 7

maaaR out π2

)()( �

� �� (7.18)

��

��

��

�

� ��

�

��

��

�

� �

mna

maR out

2π2cos1

22cos1

2)( ��

� (7.19)

with aout the outer radius of the spiral, a+l for the valves with straight beams as shown infigure 7.7.

a

aout

b

Figure 7.7 Spiral shape and the definition of the radii variables

The number of rotations of the spiral is given by m. Both spiral designs result the same beamlengths given by:

� �outaaml �� π (7.20)

For pure bending, the spring stiffness of the spiral valve with n beams of m rotations willthus be:

� �

3

π ��

��

�

��

outaamtbnEK (7.21)

For a spiral valve with 3, 80.1 µm wide, 14.6 µm thick beams of one revolution and a bossradius of 210 µm and outer valve radius of 725 µm, a stiffness of 5.0 N/m with the bendingmodel was computed whereas 4.2�0.29 N/m was measured. Thus a huge reduction instiffness can be obtained. Since torsion was neglected in the model (infinitely high torsionconstant) an overestimation of the modeled stiffness will result.

7.3.2 Flow-structure couplingWith the reduction of the degrees of freedom, the flow-structure computation is stronglysimplified. Since the flow area formed by the lift height of the boss is much smaller than theother channel cross-sections inside the valve, the hydraulic resistance is assumed to be


defined by this gap only. By neglecting the entrance and exit effects, the in chapter 3 usedmodels for fully developed flow can be used. For a circular valve seat with outer dimensionrout (see figure 7.8), the pressure drop over the valve seat as a function of the radius, r, andlift height h is:

��

��

��

rr

hµhrp outln

π6),( 3 (7.22)

As a result the hydraulic resistance as a function of the gap, is given by:

��

��

��

in

outhyd r

rhµhR ln

π6)( 3 (7.23)

Under the assumption that the pressure acts uniformly on the boss from r = 0..rin and dropsto zero from r = rin..rout, the total force acting on the boss becomes:

� �� 22

330

30

3lnπ6ln

π6)( inout

r

r

outr

in

outr

hyd rrh

Adr

rhµAd

rr

hµAdrpF

rout

rin

inout

��

��

��

�

��

�� (7.24)

Poiseuille flow

rin

rout

h

K

�

Figure 7.8 Cross-section geometry, used to model the bossed valve

Combined with the stiffness-deflection relations the lift height of the valve is described by:

� �4/1

223��

��

��

�inout rr

Kh (7.25)

In order to reduce the number of variables, dimension-less parameters can beintroduced. For the bossed valve types, 4 dimension-less parameters describe the coupling:The Reynolds number [3], describing the ratio of inertial to viscous forces:

inr r

Rein �

�� (7.26)

168 Chapter 7

The Euler number [3], representing a dimensionless pressure or, since kinetic energy is

dissipated by a hydraulic resistor, the amount of dissipated energy relative to the kinetic

energy of the fluid flow:

221

4

��

inr

rpEuin� (7.27)

Dimension-less stiffness parameter:

221

3

�� in

stiffrK

� (7.28)

Valve seat thickness ratio:

in

outgeom r

r�� (7.29)

With these parameters, equation (7.25) can be rewritten [12] to:

� �� 32

43

44

1

lnπ96

�

�

geom

geomstiffReEu

�

�� (7.30)

This relation is used to derive a design formula from the data, obtained from ANSYSsimulations. Since only one degree of freedom can was assumed, de-coupled routines can beused as discussed in section 6.4. To fit the numerical data onto equation (7.30), fit constant Cis introduced:

� �� 32

43

44

1

lnπ96

�

�

geom

geomstiffCReEu

�

�� (7.31)

For C = 1.18 a good fit was found, which shows that the analytical equation alreadydescribes the hydraulic resistance well. For validation of the model, measurements wereperformed on a KOH etched valve. Since only square geometries can be etched with thismethod, an adjustment must be made to be able to apply the axial-symmetric model to thesquare valves. Hence a translation from a square to a circular boss was achieved by using thesame circumference (hydraulic diameter):

π2widthinlet4 �

�inr (7.32)


π2widthoutlet4 �

�outr (7.33)

For this verification a KOH etched valve was used with a boss of 700x700 µm seat innerdimensions and 850x850 µm outer diameter. The beam length, width and thickness were800x200x21 µm. A comparison of the analytical, numerical and measured pressure versusflow-rate data is shown in figure 7.9.

Comparison of the analytical and numerical flow-pressure drop models with measurements

flow-rate (µl/s)

pres

sure

(Pa)

2.0E+3

4.0E+3

6.0E+3

8.0E+3

10.0E+3

12.0E+3

14.0E+3

16.0E+3

0.0E+3

measurements

analytical model

numerical model

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Figure 7.9 Comparison between the analytically, numerically and measured pressure-flow curvesof a KOH-etched bossed valve with 4 straight beams.

The graphs show a good similarity between the two models and the measured data. Moremeasurements were performed on RIE etched valves with circular bosses to see the effect ofdifferent spring designs. Figure 7.10shows the hydraulic resistance plots and the computedlift heights. Only small lift heights are obtained for both stiff and flexible valves. This meansthat micro valves can be very sensitive to pollution. Clogging of particles on the valve seatwill easily create a substantial leakage. Therefore filters and the use of fluids without coatingtendencies are essential. As a consequence of the small deflections, the linear spring modelsremain valid over the full flow range.

A second point, observed from the measured data, is the slightly different curvaturecompared to the models. This is better visualized in the double-logarithmic plot of figure7.11. The 4th order power relation between the Euler and Reynolds number seems to deviate

170 Chapter 7

slightly from the measurements. This effect is visible at large and small flow-rates whichindicates the presence of a hydraulic resistance in the flow.

Surprisingly the valves with spiral shaped springs gave a much higher resistance thantheir stiffer, straight beamed counterparts. The fitted beam thicknesses of the analyticalmodels in figure 7.10 were 60 µm for the spiral with 2 coils and 170 µm for 1 coil. This isfar from realistic since the beams were etched down to around 16 µm thickness, which meetsthe measurements of the valves with straight beams. A likely explanation for the largedifferences is the drag of the spiral beams in the fluid flow. According to this explanation,the spiral structure with two coils will show a larger resistance than with one coil. This isindeed observed from the plotted curves.

Valve resistance and deflection as function of the flow-rate

0.0E+00

1.0E+13

2.0E+13

3.0E+13

4.0E+13

5.0E+13

6.0E+13

7.0E+13

8.0E+13

9.0E+13

1.0E+14

0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.40.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

3.5E-06

4.0E-06

4.5E-06an. mod. beam 550x80x18x210 µml b t r = beam beam beam outx x x

an. mod. beam 1000x80x15x210 µml b t r = beam beam beam outx x x

an. mod. spiral 2 revs. 550x80x210 µmaout- x xa b r = beam out

an. mod. spiral 1 rev. 1000x80x210 µmaout- x xa b r = beam out

meas. beam 550x80x18x210 µml b t r = beam beam beam outx x x

meas. beam 1000x80x15x210 µml b t r = beam beam beam outx x x

meas. spiral 2 revs. 550x80x210 µmaout- x xa b r = beam out

meas. spiral 1 rev. - x x 1000x80x210 µma a b r = out beam out

flow-rate (µl/s)

hydr

aulic

resi

stan

ce (P

a s/

m )3

disp

lace

men

t (m

)

Figure 7.10 Measured and analytically computed hydraulic resistance (decaying curves) andcomputed lift heights (rising curves) as a function of the flow-rate for different bossedvalve designs. The legend gives the dimensions for the valve with 3 beams according to:l x b x t x rout and for the spiral valve: number of spiral coils (2 and 1) aout x b x rout withrin = 150 µm.

The thickness variations of the beams play a dominant role in the valve characteristics.In contrast, small variations of the valve seat width are of minor influence. From equations(7.21), (7.23) and (7.25) it is shown that the beam thickness is related to the power 9/4 to thehydraulic resistance whereas the valve seat radius is related to the power –3/2. This meansthat the valve design is very critical to etch depth inaccuracies and wafer thickness


variations. These variations can be easily in the order of several microns. Therefore aquantitative prediction of the valve behavior can only be done accurately enough if the exactgeometry is measured after the fabrication process.

Figure 7.11 clearly shows the effect of downscaling on the dissipation (see also chapter3). The Euler number scales the dissipated energy in terms of pressure drop with the netkinetic energy in the flow. Downscaled fluidic systems operate in a lower Reynolds numberrange than larger systems. This means that downscaling of fluidic systems is related to anincrease of the Euler number. Thus relatively more kinetic energy is dissipated indownscaled fluidic systems.

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0000E-01 1.0000E+00 1.0000E+01

an. mod. beam = 950x80x21x210 µml x b x t x rbeam beam beam out

an. mod. beam = l x b x t x rbeam beam beam out 650x80x17x210 µm




meas. beam 950x80x21x210 µml x b x t x rbeam beam beam out =

meas. beam 650x80x17x210 µm = l x b x t x rbeam beam beam out




Euler vs. Reynolds number for varying beam lengths

Reynolds number

Eule

r num

ber

Figure 7.11 Double logarithmic plots of the Euler vs. Reynolds number. The 4th power relationbetween the Euler and Reynolds numbers does not completely fit on the measured data.The legend gives the dimensions for the valve with 3 beams according to: l x b x t x rout

with rin = 150 µm.

7.4 The membrane valve

7.4.1 Membrane check / pressure actuated normally open valveThe derivation of the pressure-flow relation for the membrane valve is identical to the bossedvalve. There is a difference however due to the fact that not a rigid plate structure but a

172 Chapter 7

deformable membrane defines the gap. As a consequence, the pressure profile at the valveseat will change. For the numerical computations this means that the iteratively flow-mechanics coupled solver routines are used. The regarded situation is sketched in figure7.12.

For solving the deflection of the membrane analytically, a model is used that describesthe deformation due to a uniform pressure load on a selected area in the center. To model thepressure decay at the valve seat, a constant pressure is assumed over one-half of the rim.This approximation is valid for small valve seats. When the liquid is flowing from out of thehole at the center of the membrane (situation 1), load-deflection model (7.34) is used [19].When the flow is reversed (situation 2), a uniform pressure arises at the membrane exceptfrom the center towards halfway the valve seat. This load situation is described by equation(7.35).

� ��

� �p

rrr

rrrr

rrrrr

Drrprw

mem

mem

mem

inout

memmem

inout�

�

�

�

�

� �

��

�

��

�

�

��

�

��

�

�

��

��

��

� �

�

��

�

��

��

��

��

��

�

��

�

�

�

��

2

222

222

2

1

)1(21ln

4

ln213

64),( (7.34)

for center loaded and (rout + rin)/2 < r < rmem

� � � � � �

� �p

rrr

rrrr

rrrrrrrrr

Dprw

mem

mem

mem

inout

memmeminoutmem

�

�

�

�

�

� �

��

�

�

��

�

�

�

��

��

��

��

� �

�

��

�

��

��

��

��

��

��

��

��

�

�

��

�

2

222

222222

2

)1(21ln

4

ln213

641),( (7.35)

for outside loaded , (rout + rin)/2 < r < rmem and with D the flexural rigidity of the membrane:

)1(12 2

3

��

�

EtD (7.36)

For the resistance computation, equation (7.23) is used which means that a constant liftheight is assumed at the seat. Thus the model is only valid for small seats and smalldeflections. With the substitution of this resistance relation, the load-deflection equationsbecome for situation 1, expressed in dimension-less terms:

� �1lnπ

39321623

3

34

�� geomgeom

stiffrr inin

ReEu ��

�(7.37)


with the Reynolds and Euler numbers defined according to (7.26) respectively (7.27) and thestiffness and geometry parameters defined by:

221 ��

� instiff

rD� (7.38)

in

memgeom r

r�1� (7.39)

12 ��

in

outgeom r

r� (7.40)

� ��

�

��

�

��

�

�

�

��

�

�

� ��

1

222

1

222

22

12

23 ln1284641

geom

geomgeom

geom

geomgeomgeomgeomgeom

�

��

�

�� (7.41)

rin

rout

�

h

Poiseuille flowrmem

direction 1 direction 2

Figure 7.12 Geometric model of the normally open membrane valve: the pressure under themembrane is assumed to be constant at the inlet till halfway the valve seat. When theflow direction is reversed, the pressure is assumed to be constant at the complementarypart of the membrane.

For a small valve seat and a large membrane compared to the entrance hole, this geometryparameter simplifies to:

22

213 2

1geomgeomgeom �� (7.42)

resulting in the relation:

� �1ln1000.1 262

61

364

�� geomgeomgeom

stiffrr inin

ReEu ��

�(7.43)

174 Chapter 7

The fully coupled numerical simulation was used to iteratively solve the fluid-mechanicalcoupled problem. Since the membrane will deform, the shape of the flow channel willchange. To model this, the numerical fluid domain grid was split up into areas with a fixedgrid and areas, which were updated during the iteration steps. Since the membrane is circularand a symmetrical flow is expected, the axi-symmetrical, bi-linear fluid elements were usedin a mapped configuration and 2-node, axi-symmetric shell elements to model thedeformation of the membrane. The layout is shown in figure 7.13. Fitting the numericallycomputed data on the simplified model, results in equation:

� �1ln1037.1 262

61

364

�� geomgeomgeom

stiffrr inin

ReEu ��

�(7.44)

So an increase of hydraulic resistance is obtained of 8.1% compared to the simplifiedanalytical model.

Line 3

updated boundaries with splines fixed grid

updated grid

fixed wall boundaries

entrance conditions

exit

cond

ition

s

sym

met

ry c

ondi

tions

Figure 7.13 Top: definitions of the boundary conditions and fixed and updated grid areas of the fluiddomain. The lower picture shows the mapped mesh that arises after deflection of themembrane.

In figure 7.14 the analytically computed lift height and hydraulic resistance are showncompared with the measured resistance. The analytical model approximates the measuredresults for large flow-rates well, although the 1500 µm membrane shows 50% higherresistance than predicted. This effect can be caused an inaccuracy of the membranethickness, resulting in a stiffness variation to the third power. The differences betweenapplying the numerical model, analytically derived model or the analytical model with the


simplified geometry parameter, �geom3, is shown in figure 7.15. The numerical model showsa good similarity with the measured data. The difference between the results obtained withthe analytically derived model and its simplified form is small. For high flow-rates, thedirection of the computed Euler curves matches the measured data well. For small flow-rateshowever the difference is increasing. The reason for this difference is not clear since theanalytical models are based on viscous flow without inertance effects, which are verysuitable in the low fluid velocity range.

0.0E+00

1.0E+14

2.0E+14

3.0E+14

4.0E+14

5.0E+14

6.0E+14

7.0E+14

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

1.0E-06

1.2E-06

1.4E-06

1.6E-06

1.8E-06

2.0E-06meas. x x = 1800x450x25 µmr r tmem out

meas. 1500x450x25 µm x x = r r tmem out

meas. 800x450x24 µm x x = r r tmem out

ana. 1800x450x25 µm x x = r r tmem out






Valve resistance and deflection as function of the flow-rate

flow-rate (µl/s)

hydr

aulic

resi

stan

ce (P

a s/

m )

disp

lace

men

t (m

)

3

Figure 7.14 Hydraulic resistance and lift height as a function of the applied flow-rate.

The resistance of a reversed flow is described by:

� �1lnπ

314572823

4

34

�� geomgeom

stiffrr inin

ReEu ��

�(7.45)

with:

21

62

2

142

22

21

42

414 32

12ln

43

23

41

geom

geom

geom

geomgeomgeomgeomgeomgeomgeom

�

�

�

��

��

�

�

��

�

�� (7.46)

176 Chapter 7

Or simplified for a small valve seat to:

414 geomgeom �� (7.47)

1.0E+06

1.0E+07

1.0E+08

1.0E+09

0.10 1.00 10.00

meas. x x = 1800x450x25 µmr r tmem out

meas. 1500x450x25 µmr r tmem out x x =

meas. 800x450x24 µmr r tmem out x x =

ana. 1800x450x25 µmr r tmem out x x =



ana. app. 1800x450x25 µmr r tmem out x x =



num. 1800x450x25 µmr r tmem out x x =



Euler vs. Reynolds number

Reynolds number

Eule

r num

ber

Figure 7.15 Euler vs. Reynolds number for the measured data, numerically obtained formula,analytical formula and simplified analytical formula.

A plot of the directionality of the flow resistance is shown in figure 7.16, with index 1 and 2indicating the flow direction. With the approximations for small valve seats, the relation isdescribed by:

2/3

2

14

24

2

14

1

2

1��

�

�

��

�

��

geom

geom

rr

rr

inin

inin

ReEuReEu

RR

�

�

(7.48)

When a pressure is applied on top of the membrane, the net deformation of themembrane can be modeled by the superposition of linear deflection of a center-loadedmembrane and the uniform distributed actuation pressure, pact, operating in the oppositedirection. To simplify the model, the outlet pressure of the valve is assumed to beatmospheric such that the pressure difference applied over the membrane resembles theabsolute pressure level (relative to atmospheric pressure). For this situation the valve modelmust be extended with an additional dimension-less pressure term, indicated by Euact.


Although the dimensionless scaling of the actuation pressure is similar to the definition ofthe Euler number, it has no physical resemblance. With this additional term the analyticalmodel defined by:

� �1ln

81π

39321623

53

3

�

��

��

��

� geom

actgeomrgeom

stiffrr

EuEuReEu

in

inin�

��

�(7.49)

with:

22

22

15 41

��

��

�� geomgeomgeom �� (7.50)

0.01

0.1

1

10

100

0.1 1 10

Directionality of the hydraulic resistance

resi

stan

ce ra

tio

R /

R

�geom1 �geom2/

12

Figure 7.16 Directionality of the membrane valve resistance as function of the geometry: for smallgeometry ratios �geom1/�geom2 a higher resistance is obtained for flow direction 2whereas the resistance in direction 1 dominates for ratios larger than 1.

For given flow-rates and actuation pressures, a non-linear equation must be solved. This isdone for flow-rates of 0.01 µl/s and 0,025 µl/s and compared with measurements as shownin figure 7.17. These first measurements show that, in contrast with the precedingmeasurements, the differences between the model and measured results are very large. A

178 Chapter 7

large offset exists in the pressure level. The cause of this effect is unknown and will needfurther attention. The slope of the model resembles the measurements well.

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

0.0E+00 5.0E+03 1.0E+04 1.5E+04 2.0E+04 2.5E+04 3.0E+04 3.5E+04 4.0E+04

meas. 450x900x20 µm, 0.01 µl

meas. 450x900x20 µm, 0.025 µl

ana. 450x900x20 µm, 0.01 µl

ana. 450x900x20 µm, 0.025 µl

Hydraulic pressure drop as function of the actuation pressure

actuation pressure (Pa)

hydr

aulic

pre

ssur

e dr

op (P

a)

Figure 7.17 Measured and computed hydraulic pressure vs. actuation pressure of the normally openmembrane valve.

7.4.2 The pressure actuated normally closed valveThe actuation of the pressure actuated normally closed valve is based on a force balancebetween two bossed membranes [9]. In figure 7.18 the forces on the membranes areillustrated. The actuation pressure pushes the two membranes apart. Since the bosses arebonded, a coupling force Fcoup arises in the connection. The force, which can be exerted bythe individual membranes, depends on the size as well as the stiffness of the membrane. Alarger membrane surface will induce a higher force. On the other hand, a flexible membranewill easily bend back than a stiffer one. Calculating the net deflection of this system is doneby assuming two circular, bossed membranes 1 and 2, both with edges built-in. Thesemembranes are loaded by a uniform distributed pressure on the membranes, and forces at thebosses.

Linear bending (small deflections) of symmetrically loaded circular membranes isdescribed in cylindrical coordinates by [19]:

DQ

rWr

rrr��

�

��

��

��

dd

dd1

dd (7.51)


with Q the distributed out-of-plane acting shearing force per unit length. This differentialequation can be solved with the boundary conditions at the membrane and boss edges:

0d

)(d0d

)(d0)( �

�

�

�

��

rrrW

rrrWrrW bossmem

mem (7.52)

The shearing force depends on the type of load. For a force at the boss, equation (7.53)

must be used, whereas for a uniform distributed pressure at the membrane only, relation is

(7.54) used.

rFQF π2

� (7.53)

��

��

� ��

rrrPQ boss

P

22

21 (7.54)

2

1

rmem1

rboss1

Fcoup

Figure 7.18 The normally closed valve can be regarded as two coupled, bossed membranes. Thecoupling is established by the force Fcoup.

Solving these equations results in a deflection profile for the force load according to:

� ��

��

�� 322

12 )ln(

411)ln(

8)( FFFF CrCrCrr

DFrW�

(7.55)

with integration constants:

� ��

��

��

�� 1)ln()ln(22 22

22

1bossmem

bossbossmemmemF rr

rrrrC (7.56)

2222

2)ln()ln(2

bossmem

bossmembossmemF rr

rrrrC�

�

� (7.57)

180 Chapter 7

� �� 222

22

3 21)ln(21)ln()ln(

membossmem

membossmembossmemF r

rrrrrrrC �

�

��

� (7.58)

and for the pressure load:

� ��

��

�� 322

1224

81)ln(

21

41)ln(1

81

8)( PPPbossP CrCrCrrrr

DPrW (7.59)

� � � ��

��

��

��

�

�� 22

2222222

1)ln()ln(4

bossmem

bossmembossbossbossmemmembossP rr

rrrrrrrrC (7.60)

� �

��

��

�

�� 22

222

2)ln()ln(41

bossmem

bossmembossbossmemP rr

rrrrrC (7.61)

� ��

� ��

�

�

��

�

�

��

��

��

�

�

)ln()ln(4)ln(4

)ln(43242222

42222

22

2

3bossmembossbossmemmemboss

bossbossbossmembossmem

bossmem

memP rrrrrrr

rrrrrrrr

rC (7.62)

The total deflection is obtained by the superposition of the deflections for both load cases:

)()()( rWrWrW PF �� (7.63)

The coupling force, Fcoup , can be calculated from the constraint that both boss deflectionsare identical:

)()( 2211 bossboss rWrW � (7.64)

Taking the different load into account, the load-deflection relations for membrane 1 become:

)( 011 PPSW actPP � (7.65)

� �� 210

21

21011 π connconnbossactFF rPrrPPSW �� (7.66)

coupFcoup FSW 11 �� (7.67)

and for membrane 2:

)(22 outactPP PPSW �� (7.68)

� ��

��

��

��

�

��

��

��

�

��

��

��

��

22

22

2

22

222 22π inout

inconnbossactinout

bossoutFFrrPrrPrrrPSW (7.69)


coupFcoup FSW 22 �

with SF and SP defining the flexibility constants for both membranes found from equations(7.55) and (7.59):

FSrW FbossF �)( (7.70)

PSrW PbossP )( (7.71)

Pact

Pout

Pin

P0

rmem1

rmem1

rboss1

r =conn1 rboss2

routrin

Figure 7.19 Geometry parameters and loads to describe the deflection of the valve

-1.0E-05

-5.0E-06

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

1.0E-03 1.5E-03 2.0E-03 2.5E-03 3.0E-03 3.5E-03 4.0E-03

t2=15µm upper membrane

t2=15µm lower membrane

rboss1=1.25mm upper membrane

rboss1=1.25mm lower membrane

rmem2=3.5µm upper membrane

rmem2=3.5µm lower membrane

initial case upper membrane

initial case lower membrane

mem

bran

e de

flect

ion

(m)

radius coordinate (m)

Deflection curves of the pressure actuated NC valve for different designs

Figure 7.20 Deflection curves for different valve geometries. The initial case is a valve loaded at0.1bar with membranes of 20 µm thick and a top membrane radius of 4 mm, boss 2 mmand lower membrane radius 3 mm, boss radius 1 mm. In the legend the variations on thisinitial situation are indicated.

182 Chapter 7

For analyzing the effect of changing geometry parameters on the deflection of themembrane, simplifications were introduced. The inlet and outlet pressures are assumed to beat atmospheric level. Furthermore, the connection part of membrane 2 has the same width asboss. With these assumptions the deflection graphs of figure 7.20 have been computed.From this picture it can be observed that many design variations are possible. Thecombination of the “pressure stiffness” versus “force stiffness” of both membranesdetermines whether or not toroidal bulging of the thin membrane will occur.

Deflections of the KOH-etched valve have been measured at different actuationpressures as shown in figure 7.21, where a comparison was made with the model.

0 0.2 0.4 0.6 0.8 1 1.2 1.40

10

20

30

40

actuation pressure (bar) breakdown pressure

defle

ctio

n (µ

m)

model measured

Pressure-deflection curves for the pressure actuated NC valve

Figure 7.21 Measured and computed deflection curves as function of the actuation pressure for aKOH-etched valve with dimensions: upper membrane size: 9 x 9 mm, boss 4.5 x 4.5mm, thickness 40, lower membrane size: 4 x 4 mm, boss 2 x 2 mm and thickness 35µm.

Since large deflections were obtained in the order of the membrane thickness, stretchingeffects may not be neglected. This is observed from the non-linearity. Due to the presencerigid bosses, stretching will occur at even smaller deflections than for full membranes. Fromfigure 7.21 is shows that the order of magnitude can rather well be predicted. Once thedeflection of the membrane as function of the applied actuation pressure is known, thehydraulic resistance can be computed similar to the bossed valve using formula (7.23).


7.5 The duckbill valve

7.5.1 Membrane analysisIn chapter 5 the design possibilities were shown of the <111> plane switch-over technique tofabricate thin plates of various geometries for the fabrication of check valves. A diamondshaped geometry was chosen for a functional analysis. For many applications this geometrywill be used, since it is obtained when a V-groove entrance channel of limited length iscombined with a long concave exit channel. The layout is sketched in figure 7.22.

60o

a

b

y

zx

Figure 7.22 The diamond-shaped membrane geometry which is taken for analysis.

The typical 60� inclination angle is obtained, as a consequence of perpendicular, in-the-wafer-plane intersecting {111} planes:

� � � � ��

��

�� 60101011

21acos T

� (7.72)

To simplify the problem, a rectangular plate is chosen (�=90�) with three edges built-in and one edge free. The differential equation that governs the deflection of membranes,described relative to Cartesian coordinates as shown in figure 7.22 is given by [19]:

DzyP

zW

zW

yW

yW ),(2 4

4

2

2

2

2

4

4

��

��

�

�

�

��

�

� (7.73)

For plates, the boundary conditions for built-in edges defined by the relation y=a arestraight-forward defined by:

� � 0��ayW (7.74)

0��

��

�

�

�

�ayyW (7.75)

184 Chapter 7

The latter condition is replaced by (7.76) (no clamping moments at the edge) when a simplysupported edge is observed.

02

2

��

��

�

�

�

�ayyW (7.76)

The free edge however causes more trouble. According to Kirchhoff [19], the following twoconditions provide enough information:

0)2( 2

3

3

3

��

��

�

��

�

�

�

�ayyzW

zW

� (7.77)

02

3

2

3

��

��

�

�

�

�

�

�ayyW

zW

� (7.78)

Solving the differential equation exactly for three sides built-in and one edge free is notpossible. Van de Eb [2] gives an approximation, which meets the boundary conditions in afew discrete points. For special cases he calculated formula constants. Timoshenko [19]gives a series solution for the situation of simply supported side edges and a built-in topedge which can be used for parametric studies:

)sin()ˆ1(1π

4...5,3,1

55

4

iii

zYiD

aPw ��

�

(7.79)

)sinh()()cosh()1(ˆiiiiiiii yCyByyCY �� (7.80)

� �2222

22

)1()1(cosh)1)(3()1()sinh()1(cosh)1)(3(

��

��

��

��

�

ii

iiiiB (7.81)

� �2222

2

)1()1(cosh)1)(3()1(cosh)1(sinh)1(coshsinh)1)(3(

��

��

��

��

�

ii

iiiiiiiC (7.82)

byiyiπ

� (7.83)

aziziπ

� (7.84)


abi

iπ

�� (7.85)

For small a/b ratios, one summation term of this series approximation already gives a goodconvergence value since the simply supported edges force the membrane to a sinusoidalshape. The duckbill valve however will have a large aspect ratio, which demands a series ofterms [14]. Figure 7.23 shows an example of the function evaluation.

ab

z

y

wt

x

Figure 7.23 Analytically computed deflection profile of the duckbill valve

Since the membranes are oriented perfectly aligned along the {111} planes, the effectwas researched of the crystal orientations on the deflection and stresses. Due to the cubiclattice, monocrystalline silicon behaves mechanically like an orthotrope material [21].Orthotrope behavior can be described with the stress-strain relation [18]:

��

�

��

�

�

��

�

��

�

�

�

�

��

�

�

�

�

��

��

�

��

�

�

��

�

��

�

�

31

23

12

33

22

11

123123

31

23

12

33

22

11

2

2

2

00000

00000

00000

0002

0002

0002

�

�

�

�

�

�

��

��

��

�

�

�

�

�

�

G

G

G

G

G

G

εC (7.86)

in which G en � are the Lamé constants according to:

)1(2 ��

�EG (7.87)

)21)(1(E

��

�� (7.88)

186 Chapter 7

For mono-crystalline silicon the following stress-strain material constants are given [21]:C11 = 166GPa, C12 = 63.9GPa and C44 = 7.95GPa. The indices give the correspondingorientations, where 1 corresponds to the <100>, 2 to the <010> and 3 the <001> directions.A transformation of matrix C123 to describe the stress-strain equations in the membrane-plane orientation (figure 7.22) is obtained by pre- and post-multiplying with thetransformation matrices according to:

T123 TCTC ��xyz (7.89)

with the transformation matrix defined by:

123σTσ ��xyz (7.90)

The indices of this transformation matrix consist of combinations of the direction cosinesaccording to:

123pqjqip

xyzij RR �� (7.91)

||||),cos(

123

123123

xxxx

xxxyz

xyzj

xyziijR

�

�� (7.92)

The elements of the direction cosines can be written in a rotation matrix, which transformsthe original axis system along the crystal orientation towards the in-the-membrane-planeoriented sytem:

��

�

�

��

�

�

�

��

��

�

�

��

�

�

�

022333

666R

21

21

31

31

31

31

61

61

333231

232221

131211

RRRRRRRRR

(7.93)

With these transformation values, the new material constants become:Ex = 169GPa Ey = 188GPa Ez = 169GPa�xz = 0.26 �yz = 0.26 �yz = 0.18 Gxz = 66.9GPa Gyz = 57.8GPa Gyz = 57.8GPa

These material values indicate that the membrane will show a deflection behavior, whichwill not differ much from the situation of membranes made of isotropic materials. AnANSYS load-deflection plot, for a 1020 µm wide, 495 µm high and 5 µm thick membrane isshown in figure 7.24. For small deflections, the difference between orthotropic and isotropicmaterial behavior with a modulus of elasticity of 169GPa and a Poisson’s constant of 0.3


does not show substantial differences. At large deflections, the orthotropic, nonlinear modelshows a higher stiffness than the nonlinear isotropic model.

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

0.0E+00 2.0E+03 4.0E+03 6.0E+03 8.0E+03 1.0E+04 1.2E+04 1.4E+04 1.6E+04 1.8E+04 2.0E+04

flat, isotropic

flat, orthotropic

tapered, isotropic

linear analytical 5µm

linear analytical 10.5µm

Deflection of different duckbill membrane models

pressure (Pa)

defle

ctio

n (m

m)

Figure 7.24 Analytically and numerically computed load-deflection curves for a 1020 x 495 x 5 µmduckbill membrane: the influence of tapering is dominant whereas orthotropic materialbehavior is only of influence at large, non-linear deflections.

The effect of the built-in edges on the maximum deflection is clearly visible. Theoverestimation of the flexibility, predicted with the analytical model compared to thenumerical models with built-in edges increases when deflection increases. The clampededges cause an earlier dominance of stretching effects in the membrane. Tapering of themembrane due to etching effects, as discussed in chapter 5, is even more dominating [14].Since the tapering angle is independent of the membrane thickness, the effect becomes morepronounced when the membranes get thinner. To reduce the hydraulic resistance in the opendirection, the membranes must be thin, in the order of about 5 µm. This means that for a 500µm high membrane the thickness will vary from 5 µm at the free edge to about 16.2 µm atthe built-in edge. For the plotted load range of the tapered membrane, the linear model canbe used. With a suitable value for the “effective” thickness a reasonable approximation canbe obtained with the analytical model. However, this effective thickness depends on theaspect ratio of the membrane. Deriving an analytical model, which describes the membranedeflection including tapering and three built-in edges, seems to be impossible since the free-edge boundary conditions are hard or not to meet.

188 Chapter 7

ANSYS 5.3NODAL SOLUTIONSEQV (AVG)DMX =.152E-03SMN =589.755SMX =.500E+07

589.755208893417196625500833803.104E+07.125E+07.146E+07.167E+07.188E+07.208E+07.313E+07.333E+07.354E+07.375E+07.396E+07.417E+07.437E+07.458E+07.479E+07.500E+07

stress concentrationANSYS 5.3NODAL SOLUTIONSEQV (AVG)DMX =.024918SMN =260289SMX =.161E+10

260289.672E+08.134E+09.201E+09.268E+09.335E+09.402E+09.469E+09.536E+09.603E+09.669E+09.100E+10.107E+10.114E+10.120E+10.127E+10.134E+10.141E+10.147E+10.154E+10.161E+10

pressure = 10 mbar

pressure = 3.5 bar

Figure 7.25 Stress profile in the duckbill membrane loaded at 10mbar (top) and 3.5 bar (bottom)respectively. Due to the stretching effects, the stress profile changes for large deflectionsalthough a stress concentration remains in the 120� corner at the free edge.

Since the membranes are rather thin and comprising of sharp corners, a stress analysiswas performed to investigate the presence of stress concentrations that govern themechanism of failure. Von Mises stress [18] at the membrane surface was taken was taken asa criterion. In figure 7.25 a contour plot is shown of the ANSYS simulation. As indicated, astress concentration occurs at the 120� angle at the free side of the membrane. Roark [17]gives a relation to approximate the effective stresses at this point on the membrane for athree-sided fully clamped rectangular, flat plate:

ptb

eff

2

��

��

�� (7.94)


with constant � , depending on the aspect-ratio. For a 1020 x 572 x 5 µm membrane, theconstant is about 1.37 [17], which yields a relation between the pressure and effective stressof:

peff41079.1 �� (7.95)

Assuming a yield stress of 7.0GPa for silicon [16], the maximum pressure load for thissize duckbill valve is 3.92 bar. Destructive tests yielded a slightly smaller maximum pressureof 3.5bar in the open direction. In the close direction, a model for a three-sided clamped, oneside simply supported model overestimates the strength. For this situation Roark givesequation (7.94) with �=0.348 for a/b=2.25 which yields a maximum pressure of 25.4 barwhereas a test on a 1020 x 454 x 5.1 µm membrane showed could resist no more than 4.5bar. The mechanism of collapsing in the close direction probably is different from that of athree-sided clamped, one side simply supported membrane. The free edge of the membranecan still move over the glass substrate. The model for bending with one side free, yielding a�=1.76 for a/b=2.25 results in a maximum pressure of 5.0 bar.

7.5.2 Flow-structure couplingWhen bending, the membrane forms a kind of sinusoidal shaped flow opening. This meansthat the gap height and velocity profile are functions of the position along the free membraneedge. A fully coupled 3D fluid and membrane simulation is needed. However, for thenumerical and analytical modeling assumptions were done for simplification such that the 3-dimensional coupled problem is changed to a 2-dimensional de-coupled model. For the fluidflow description, a wide gap is assumed relative to the gap height. This means that a 2D-flowvelocity profile can be assumed over the gap height. Since small deflections are assumed, thetilting of the free membrane edge is neglected, such that no diffuser effects exist in the flowpath and, for the analytical model, a 2-dimensional parallel-plate flow profile can be taken.The flow profile is taken over an infinitesimal small part dz. Integration of the piecewise-calculated flow profiles over the gap width will result in a net flow through the curved gap.For the analytical equation this yields:

� ��

�

� a

z

hyd

dzpzW

tpR

0

3)7.54cos(),(12)(

�

�

�� (7.96)

with W(z,�p) the deflection of the free edge of the membrane as function of the z-coordinateand pressure drop. The reduced net flow opening due to the 54.7� tilted orientation of themembrane is modeled by the additional cosine term. Figure 7.26 shows the analytically

190 Chapter 7

computed pressure drop over a 500 µm wide, 5 µm thick membrane as function of the lengthand flow-rate through the valve. The plot shows that a reasonable open resistance can beobtained. With equation (7.79) for the membrane deflection description, the followingresistance equation is found if only one summation term is taken into account:

� � 313

3

3

1

3

16

)(ˆ1

1)7.54(cos

π649

paDh

bYRhyd

�

�� (7.97)

A comparison, made between the analytical and numerical models with measured data[13] of a 1000x368x5µm-sized valve is shown in figure 7.27. The numerical model, using an8µm thick flat plate to compensate for the thickness tapering shows a good approximation inthe low flow-range. For higher flows, the model becomes to stiff. The error made by usingthe analytical model with identical effective thickness is much worse. Due to taking simplysupported instead of fully clamped edges into account and using only one summation term,the membrane becomes too flexible, resulting in an underestimation of the hydraulicresistance.

Another neglected effect in the analytical model is the flow pattern at the entrance andexit of the valve. The ANSYS flow simulation gives insight in the streamlines as shown infigure 7.28. Although flows at small Reynolds numbers are regarded, the figure shows thatinertance effects can still be present on local scale as demonstrated by the arising vortex flowat the valve exit. This vortex flow will dissipate additional kinetic energy causing an increasein pressure drop.

00.2

0.40.6

0.81

x 10-9

0

0.5

1

1.5

x 10-3

3

3.5

4

4.5

5

5.5

6

flow-rate (m/s)length a (m)

Pressure drop over the duckbill valve

3

pres

sure

-dro

p lo

g

(Pa)

10

Figure 7.26 Pressure drop over a 500 µm wide (b) and 5 µm thick (t) duckbill valve in opendirection as function of the length (a)


Pressure-drop vs. flow-rate for the duckbill valve

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

3.0E+04

3.5E+04

4.0E+04

0 0.5 1 1.5 2 2.5 3 3.5flow-rate (µl/s)

numerical model 8µm

measurements

analytical model 8µm

pres

sure

dro

p (P

a)

Figure 7.27 Comparison between the measured and computed flow-pressure curves for a1000x368x5µm valve. To compensate for the approximation of the tapering with a flatmembrane model, 8µm thickness is chosen.

vortex region

Figure 7.28 Vector plot of the flow pattern through the duckbill valve. The circle shows the centerregion of the vortex flow.

192 Chapter 7

Similar to the bossed and membrane valves, the flow-pressure relation can be rewrittenin dimension-less terms. The characteristic length for expressing the Reynolds and Eulernumbers however is not unambiguous. The membrane length, a, was chosen since thisparameter is directly related to the flow opening. With the introduction of the new Reynoldsand Euler number definitions, the dimensionless equation becomes:

3

2

21

164 π329

��

�

�

��

�

��

geom

stiffgeomaa ReEu

�

�� (7.98)

221

4

��

apEua � (7.99)

aRea

�

�� (7.100)

221 ��

�tD

stiff � (7.101)

ha

geom �1� (7.102)

� � )7.54cos()(ˆ1 12 �� bYgeom� (7.103)

The leakage of the valve in the close direction was tested by reversing the flow direction.Due to the high close resistance of the valve, a flow-source is not suitable. Applying a flowwould result in very high pressures causing much leakage of in the system. Besides, we wantto know the leakage at pressures below one bar since future µTAS systems will operate inthis range. Hence an estimation of the leak resistance was found by using the capacity of themeasurement system. First, the capacity was “charged” in a relative short time with thesyringe pump until a pre-set pressure level was reached. After stopping the pump, thepressure “discharge” over the pressure-dependent valve resistor was measured until adefined lower pressure level was reached. From these RC-curves, the average resistance wasestimated. In figure 7.29 examples of these curves are shown. Although this method is alsoaffected by the small leakage present in measurement system, it can be used to estimate amaximum leakage. Typical close / open resistance ratios were found of 140 and more. Thisshows that the simple duckbill design can be well used to direct flows.


0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

1.0E+01 1.0E+02 1.0E+03 1.0E+04

pump 1020x572x8.8 µmpump 1020x500x3.7 µmpump 1020x427x4.8 µmpump 818x576x4.5 µmrelaxation 1020x572x8.8 µmrelaxation 1020x500x3.7 µmrelaxation 1020x427x4.8 µmrelaxation 818x576x4.5 µm

RC curves for leak resistance determination

time (s)

pres

sure

(Pa)

Figure 7.29 Pump and RC relaxation plots for the determination of the leak resistance of the duckbillvalve.

7.6 Conclusions

A series of design formulas have been presented to describe the structural mechanical andhydraulic resistance of active and passive microvalves. With these models, insight isgenerated in the behavior of fluid-structure coupling. In order to simplify the complexproblem of two coupled domains, degree of freedom reduction is a powerful tool. Theinvestigated valves showed that degree of freedom reduction can be applied in most caseswithout much loss on accuracy.

For a compact description of the valves, the Euler and Reynolds number wereintroduced. The Reynolds number is very suitable since it relates the influence of inertialeffects on the fluid flow whereas the Euler number indicates the amount of dissipation of thevalve due to friction. With these parameters, check valve resistance characteristics can bedescribed by: Eu4Re = constant. The stiffness and geometry of the valve determine the valueof the constant. From this relation it is shown that scale reduction will result in a higherrelative energy dissipation of the fluid flow. Although measurements were done in the flowrange around a Reynolds number of one where inertial effects can be neglected, on a localscale these effects can still be present. Simulations of the duckbill valve showed theexistence of a small vortex flow at the outlet side of the membrane.

194 Chapter 7

In general the models showed a good resemblance with the measurements except fromthe pressure actuated normally open valve and the analytical duckbill description. Predictedtrends in the valve behavior as function of the geometry and fluid flow all resemble themeasurement data. In order to obtain a good resemblance in a quantitative way, thedimensions of the devices must be accurately known. Although etch processes allow for thefabrication of very small structures with high absolute precision, the relative precision isoften poor. Thickness variations of a few micrometer of a membrane of a few tenmicrometer thickness cause large stiffness variations, related to the power 3. Another sourcefor inaccuracies is the wafer thickness variation, which can be even more. The inaccuracieslead to large variations in valve characteristics. As a result of this, realized valves can showlarge differences with the aimed, modeled behavior.

For the bossed valves, different models have been realized for describing the springstructures. Very flexible springs can be made by using curved beams, such as spirals.Measurements showed that although a lower hydraulic resistance was expected for thevalves with spiral shaped springs, a higher resistance was found. A possible explanation forthis is the increase of the resistance due to drag of the spiral beams on the passing fluid. Fora valve with 2 coils a higher resistance was found than for one coil. Design formulas forvalves with straight beams resemble the measured data well.

The pressure actuated normally open valve showed a linear relation between theresistance and the actuation pressure as predicted with the models. The models howevershowed a large pressure offset, resulting in an overestimation of the resistance. For the non-actuated situation, the numerical and analytical models show a good similarity. The newlydeveloped mechanism for actuating a pressure controlled normally closed valve, based onthe combination of two bossed membranes with different geometries turned out to workwell. The derived mechanical model gives a good estimation of the deflection and providesinsight in the deformation shapes of both membranes.

The new duckbill valve concept turns out function well. A clear direction dependentresistance is measured with a typical close / open resistance ratio of more than 140. Themeasured maximum strength was 3.5 bar in the open and 4.5 bar in the close direction,which is less than computed. The tapering of the valve membrane turned out to have a largeinfluence on the mechanical behavior. Mechanical models of flat plates with a thickness ofthe free edge of the membrane show a much too low stiffness, resulting in anunderestimation of the hydraulic resistance. An extension of the analytical model is neededtaking tapering and built-in side edges into account. However, deriving such a model seemsto be impossible due to the boundary conditions at the free edge. These can only beapproximately met in simplified cases, such as for simply supported side edges.


References

[1] Ansys, Ansys Inc., Southpointe, 275 Technology Drive, Canonsburg, PA 15317, USA[2] W.J. Van der Eb, Berekeningen van een plaat, welke aan 3 zijden ingeklemd en aan de

4e zijde geheel vrij is, De Ingenieur,Vol. 26, (1950) O.31-O.35[3] R.W. Fox, A.T. McDonald, Introduction to fluid mechanics, John Wiley & Sons, New

York, Third edition, (1985)[4] J.M. Gere, S.P. Timoshenko, Mechanics of materials, Van Nostrand Reinhold (UK) Co.

Ltd, 2nd SI edition, (1988)[5] Hamilton Bonaduz AG., P.O. Box 26, CH-7402 Bonaduz Switzerland[6] Pressure and airflow sensors, Product information catalog 15, Honeywell Micro Switch

Devision Sensing and Control, Freeport, Illinois 61032, USA, (1995).[7] HP-VEE, Visual Programming Language, Hewlett-Packard Co. , Test & Measurement

Division, 9780 S. Meridian Blvd. ,Englewood, CO 80112, U.S.A[8] Keithley Instruments Inc., 28775 Aurora Road, Cleveland, Ohio 44139 U.S.A[9] T.S.J. Lammerink, N. Olij, J.W. Berenschot, R.E. Oosterbroek, J.G.E. Gardeniers, C.

Neagu, A. van den Berg, M. Haller, G.J.M. Krijnen, M.C. Elwenpoek, “A normallyclosed active valve using bulk micromachining”, Proc. 6th Int. Conf. on NewActuators, Actuator’98, Bremen, Germany, (1998) 122-125

[10] Microcontrole, Newport, Motion Control catalog, (1997)[11] The LEE Company, Electro-fluidic systems, 2 Pettipaug Road, P.O. Box 424,

Westbrook, Connecticut 06498-0424, U.S.A. Component catalog, 1994.[12] R.E. Oosterbroek, S. Schlautmann, J.W. Berenschot, T.S.J Lammerink, A. van den

Berg, M.C. Elwenspoek, “Modeling and validation of flow-structure interactions inpassive micro valves”, Proc. Int. Conf. Modeling and Simulation of Microsyst.,Semiconductors, Sensors and Actuators, MSM'98, Santa Clara, (1998) 528-533

[13] R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J Lammerink, A. van denBerg, M.C. Elwenspoek, “In-plane oriented fluid control components, fabricated withnew etching techniques”, Actuator’98, (1998) 43-46

[14] R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J. Lammerink, G.J.M.Krijnen, M.C. Elwenspoek, A. van den Berg, “Characterization and optimization ofmono-crystalline in-plane operating check valves”, Proc. IEEE Transducers’99, (1999)1816-1819

196 Chapter 7

[15] R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, G.J.M. Krijnen, T.S.J Lammerink,M.C. Elwenspoek, A. van den Berg, “Designing, simulation and realization of in-planeoperating micro-valves using new etching techniques”, J. Micromech. Microeng. 8,(1999) 194-198

[16] K.E. Petersen, “Silicon as a mechanical material”, Proc. IEEE 70-5, (1982) 420-457[17] R.J. Roark, W.C. Young, Roark’s formulas for stress and strain, McGraw-Hill Int.,

New York, Sixth edition, (1989)[18] S.P. Timoshenko, J.N. Goodier, Theory of elasticity, McGraw-Hill Int., Singapore, 3rd

int. edition, (1970)[19] S.P. Timoshenko, S. Woinowsky-Krieger, Theory of plates and shells, McGraw-Hill,

New York, 2nd edition, (1970)[20] A.M. Wahl, Mechanical springs, McGraw-Hill Inc., 2nd edition, (1963)[21] J.J. Wortman, R.A. Evans, “Young’s modulus, shear modulus and Poisson’s ratio in

silicon and germanium”, J. App. Physics, vol 37-1, pp.153-156, 1965

197

88 CCOONNCCLLUUSSIIOONNSS && OOUUTTLLOOOOKK

In short a summary will be made of the results andconclusions of the preceding chapters. This summation willbe completed by reflections given on the future ofmicrofluidics development and important issues in this.

8.1 Overview

In this thesis different aspects of microfluidics have been discussed. For modeling fluidflows, the theory discussed in the third chapter about using variational techniques is veryvaluable. The principle of virtual work was used for obtaining flow velocity and hydraulicresistance models for simulating flows in microchannels. With this method it wasdemonstrated that for simple geometries such as KOH-etched V-grooves, good analyticalmodels can be obtained. For more complex geometries such as diamond-shaped channelshigher order terms need to be taken into account. Additional to the variational method, theanalogy with torsion of prismatic beams provided a direct relation for the hydraulicresistance.

The derived relations were all based on the assumption that “macro models”, such asStokes flow, can be applied on microchannels as well. For gas flows the application range isgiven by the Knudsen number, which indicates that macro theory can be used for gasses atatmospheric pressures down to about 1µm. For liquids continuum models can be used evenfor nanometer dimensions. However other effects like streaming potentials might start toplay a role, although a clear answer to this question is not yet found. Uncertainty in geometrydimensions during the fabrication process and the influence of the surface roughness of theetched channels make research in downscaling effects very difficult. This was endorsed by

198 Chapter 8

the results of the pressure / flow sensor and valve characterization measurements. For thechannel dimensions used in this thesis, Oseen’s and Stokes’ flow assumptions (see section3.3) seem to be valid. Surface tension plays a dominant role in microfluidic systems sincesubstantial positive or negative pressures can be generated during the filling of the systemand bubbles can be trapped.

A capacitive and a piezo-resistive pressure / flow sensor was developed to measureboth flow-rates and pressure levels. Models were derived to describe the flow sensorbehavior and stationary measurements were performed. Since no temperature compensationwas implemented, resulting in a temperature sensitivity due to viscosity changes, the sensorcan be used in systems were measurements with limited accuracy are needed or in welltemperature controlled environments. The nice aspect of these sensor types is that simplepressure sensors can be used and that the hydraulic power can be computed from thepressure and flow rate values.

Besides sensors, passive and active valves were modeled, designed, fabricated andcharacterized. The normally open, respectively normally closed valves are pressure-actuated.For these valves analytical formulas were derived that can be used to optimize the valvedesigns. In order to verify these formulas and be able to investigate the effects of neglectingthe device details, numerical routines have been implemented to obtain a full flow-structurecoupled finite element model with optimized iterative solver routines. It was shown thatdegree of freedom reduction helps to simplify and de-couple both domains, offering thepossibility to obtain simple analytical formulas and a faster solving of the numerical system.

An accurate prediction of the behavior of microfluidic components can be verydifficult due to the previously described inaccuracies of the fabrication processes. Theabsolute precision of micro fabrication processes can be very high. The relative precisionsuch as for example the relative thickness variation of wet chemically etched membranes canbe rather poor though. This means that especially for thin membranes big changes inmechanical stiffness can occur resulting in substantial deviations of the hydrauliccharacteristics of valves.

For some systems or devices this may not be a problem such as for switching valves.Sensors, hydraulic resistance control valves and some check valve applications demand forexact knowledge of the device characteristics. For these situations, calibration afterwardsand if possible electronic trimming can solve the problem. This however cannot be done incase of check valves. Therefore better control and knowledge of fabrication process andwafer variations is needed. For commercial, high-volume labs this is common use. In case ofresearch labs this is very difficult. Hence a solution can be sought in the design by using forexample the presented {111} plane switching over technique. With this technique thin

Conclusions & outlook 199

membranes can be anisotropic wet chemically etched in <100> oriented silicon without theproblem of wafer thickness dependence.

The demonstrated etching techniques in <100> and <111> oriented wafers show thatmonocrystalline silicon offers much more potential in micro system design than is oftenutilized. With thin <111> oriented membranes simple, well functioning check valves havebeen made as well as 3-dimensional structures. <111> wafers can be used very well as agood alternative for sacrificial layer etching and dry free etching techniques to obtainmonocrystalline suspended structures. With this technique spring elements were made forthe bossed-type check valve.

Selective bonding plays an important role in the fabrication of check valves. Withselective bonding, well-closing movable valve structures can be obtained without the risk onsticktion or bonding during operation. In this thesis two bonding techniques have beendiscussed: fusion bonding and anodic bonding. The fusion bonding process was used for thebossed check valve, membrane active / passive valve and the pressure actuated normallyclosed valve. For the fusion bonding process, the adhesion parameter proposed by Gui et al.proved to be an effective design parameter not only for predicting bonding but also to createpatterns with changed roughness to avoid bonding locally. Realized glass-to-silicon anodicbonding experiments, using sputtered chromium on glass to prevent bonding showed that thechromium layer thickness can be substantially reduced to much less than one nanometerwhile still avoiding the formation of a bond.

8.2 Outlook

Looking back at four years working in the µTAS research area, much has changed. First ofall, µTAS has attracted a lot of attention from both research institutes and companies. Thebenefits of scale reduction and using micromachining processes have proven to open newpossibilities in chemical analysis. Especially DNA analysis research stimulated the growth ofthe µTAS research area and a fast continuous growth is expected for the first coming years.

Besides a change in size, also the points of attention have changed. Much research hasfocussed the last years on electrophoresis separation techniques using simple channelgeometries whereas more complex designs such as integrated systems with pumps andswitching valve arrays seem still to be rather futuristic. My personal expectation is that thesuccesses with the electrophoretic separation channels has attracted much attention of theapplied science (chemistry) groups and will stimulate a further development of thesecomponents and systems as well although it will be less fast due to the complexity. Goodsimulation packages and libraries, fitted to the needs of micro system design will help inspeeding-up this development.

200 Chapter 8

For a further scale reduction however, “conventional” thinking in terms of valves,pumps and flow sensors might not be useful anymore. Valve-less switching techniques andtransport, using for example the in microsystems governing surface tensions [2,3,4] andelectro-hydrodynamic [6,1,5,8] or Lorentz forces [7] offer better opportunities in this case.

Research, meant for generating new (experimental) information and trying to find anexplanation for it. In this thesis some of the experiments generated a lot of information forwhich a good explanation could not yet be given. Like in case of the selective anodicbonding layers and differences in etch rate after switching over of {111} planes, someunsolved questions have arisen. Maybe that is the difference between engineering andresearch: engineering starts with more questions whereas research ends with more.

Conclusions & outlook 201

References

[1] A. van den Berg, “Arrangement for fluid flow control”, Dutch patent, NL-1010327,(1999)

[2] B.S. Gallardo, V.K. Gupta, F.D. Eagerton, L.I. Jong, V.S. Craig, R.R. Shah, N.L.Abbott, “Electrochemical principles for active control of liquids on submillimeterscales”, Science, Vol. 283, (1999 ) 57-60

[3] M. Gunze, “Driven liquids”, Science, Vol. 283 (1999), 41-42[4] H. Gau, S. Herminghaus, P. Lenz, R. Lipowsky, “Liquid morphologies on structured

surfaces: from microchannels to microchips”, Science, Vol. 283, (1999) 46-49[5] D.J. Harrison, A. Manz, P.G. Glavina, “Electroosmotic pumping within a chemical

sensor system integrated on silicon”, IEEE Transducers’91, (1991) 792-795[6] C.S. Lee, W.C. Blanchard, C.T. Wu , “Direct control of the electroosmosis in capillary

zone electrophoresis by using an external electric-field”, J. Anal. Chem. 62-14, (1990)1550-1552

[7] A.V. Lemoff, A.P. Lee, R.R. Miles, C.F. McConaghy, “An AC magnetohydrodynamicmicropump: towards a true integrated microfluidic system”, Proc. IEEETransducers’99, (1999) 1126-1129

[8] A. Manz, D.J. Harrison, J.C. Fettinger, E. Verpoorte, H. Lüdi, H.M. Widmer,“Integrated electroosmotic pumps and flow manifolds for total chemical analysissystems”, Proc. Transducers’91, (1991) 939-941

202 Chapter 8

203

AA BBOOSSSSEEDD VVAALLVVEE FFAABBRRIICCAATTIIOONNPPRROOCCEESSSS DDEESSCCRRIIPPTTIIOONN

The fabrication process of the bulk micromachined bossedvalve is described as discussed in chapter 5. Graphically, theessential steps are illustrated after which a list with processsettings are given. The described process uses a combinationof reactive ion etching and anisotropic wet chemical etchingin <100> oriented wafers with a potassium hydroxidesolution for defining the check valve geometry. Selectivefusion bonding with siliconnitride is used to obtain movablespring structures.

Design description

The bossed valve is a passive valve, used to investigate the numerical and analytical valvemodels that are derived in the OSF µTAS project. The valve has a direction-dependentresistance. The design consists of two fusion bonded (selective) <100> wafers and ananodically bonded glass cover plate. A combination of reactive ion etching (RIE) withanisotropic wet chemical KOH etching is used to obtain circular valve seats and bosses aswell as freedom in spring design. In the mask, two different spring designs are implemented:simple straight beam-suspended valves and spiral shaped springs. The mask design is suitedfor 4” bonding equipment. However, with some improvisation the process was run with 3”wafers.

204 Appendix A

Explanation of typical process steps

Top wafer� Fusion bonding of the two silicon wafers is used to obtain a zero initial gap and to

facilitate wafer scale processing.� To prevent the membrane from bonding during the fusion bonding process, a thin

siliconnitride layer is patterned (step t04).

Bottom wafer� Wet thermal oxidation is used to create the mask for reactive ion etching of the valve seat

and the channel.� Since a good definition of the thin seat is wanted, under etching of mask during step b11

must be reduced. An additional chromium mask is used in order to obtain a high etchselectivity between mask and silicon, to be able to etch with high ion energies and thuswith high directionality. This mask alignment step is critical.

� Due to cooling problems and low ion energies at the bottom of the holes long overetching times are needed to etch through the wafer with RIE in once. During this process,mask under etch is substantial. Hence a combination with KOH etching is applied.

� The resist stripping step b12 with 100% HNO3 is used in order to avoid the formation ofthe chemically stable chromium oxide on the chromium mask layer.

Mask description

The design uses 6 masks described in table A.1. In figure A.1 the orientation of the masks isshown, whereas figure A.2 shows a zoom-in on the mask layout.

position description code insideA boss and spring structuring mask for RIE BNS whiteB anti-bonding sin patterning ABO blackC beam thickness definition BOP whiteD valve seat definition SNK whiteE in-outlet holes (HOL) MemRie whiteF koh back-etching in-outlet holes BKE whiteTable A.1 Masks description with codes and development type (inside white or black). The

position numbering corresponds with the pictures in figure A.2.

Bossed valve fabrication process description 205

MemRIESNK

BKE

BNSABO

BOP

Figure A.1 Used masks for the top en bottom silicon wafers.

Figure A.2 A zoom-in on the masks used for the fabrication process. The device masks are shownfor the bossed valve with straight beams.

Process outline

Top wafer

step process description cross-section after processing

t01 LPCVD of SiN (1�m)

t03 Lithography back-side mask “ABO”

t04 RIE of SiN front and back-side (800nm)

t06 Lithography back-side mask “BNS”

t07 RIE of SiN front side (200nm)

206 Appendix A

t08 RIE of Si front and back-side (25µm)

t10 HF etching of SiN etching (200nm)

t12 LPCVD of SiN (200nm)

t13 Lithography front-side mask “BOP”

t14 RIE of SiN (200nm)

t17 KOH etching (wafer thickness-25�m)

t18 HF etching of SiN (200nm)

Table A.2 Process outline top wafer

Bottom wafer

step process description cross-section after processing

b02 Wet thermal oxidation thickness=400nm

b03 Standard photolithographymask “SNK”

b04 BHF etching of SiO2

b07 Evaporation of chromium

b08 Photolithography mask “MemRIE”

b10 Etch Chromium but leave resist on top

b11 RIE etching of Si depth=200�m

b12 b13

Strip resist and chromium


b15 RIE etching of Si depth=50�m(channel depth)

b16 BHF etching of SiO2

b18 LPCVD of SiN (150 nm)

b19 Photolithography mask “BKE”

b20 RIE pattern the bottom side SiN

b23 KOH etch (wafer thickness-250�m)

b25 Strip SiN in BHF

Table A.3 Process outline bottom wafer

Process parameters

Wafer preparation

step process process parameters specific settings

c01 Select wafers Silicon wafers:-orientation <100>-conductivity 5-10�cm-diameter 3 inch-thickness 360-400µm-curvature <10�m

a set consists of:1 top wafer (t) DSP1 bottom wafer (b) SSP1 Corning 7740 Pyrex glass

c02 Wafer curvaturemeasurement

-Sloan Dektak II-scan path 50mm

two times eachdouble sided polished

c03 Scribe ID-code on wafers -top wafers: Txx-bottom wafers: Bxx

c04 Thickness measurement -Lee wafer thickness probe at three points on the wafer c05 Ultra-sonic cleaning -time 20min

Table A.4 Wafer preparation steps

208 Appendix A

Top wafer processing

step Process parameters specific settings

t01 Introduction / LPCVDSiN cleaning

-fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S-boiling nitric acid (90�C), 15min-quick dump rinse, DI, <0.1�S-60s HF(1%)-dip-quick dump rinse, DI, <0.1�S-spin drying

cleaning directly beforeLPCVD step

t02 LPCVD SiRN -Tempress LPCVD Furnace program N6-SiH2Cl2 flow 70sccm-NH3 flow 18sccm-temperature 850�C-pressure 200mTorr-deposition rate 8.3nm/min

thickness 1�mtime 120min

t03 LithographyS&A 907/17-3”

-hot plate 120°C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/17, 4000rpm, 20s-prebake: hotplate 95�C, 90sec-maskaligner: Electronic Visions AL-6, contact: hard-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 30min

back-sidemask “ABO”

t04 Plasma etching of SiRN -Elektrotech PF 310/340 (Etske)-dirty chamber-styros electrode-electrode temp.: 10�C-CHF3 flow 25sccm-O2 flow 5sccm-pressure 10mTorr-power 75W-etchrate SiRN 60-90nm/min-etchrate Olin resist 95nm/min

back and front-sidedepth 800nmtime 14min


t05 Photoresist stripOxygen plasma

-oxygen plasma Nanotech Plasmaprep 100-O2 flow 55sccm-power 120W-electrode temperature 150�C-pressure 2.00mbar-time 20min

back-side


-hot plate 120°C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/12, 4000rpm, 20s-prebake: hotplate 95�C, 60sec-maskaligner: Electronic Visions AL-6, contact: hard-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 30min

back-sidemask “BNS”alignment precisionhigh

t07 Plasma etching of SiRN -Elektrotech PF 310/340 (Etske)-dirty chamber-styros electrode-electrode temp.: 10�C-CHF3 flow 25sccm-O2 flow 5sccm-pressure 10mTorr-power 75W-etchrate SiRN 60-90nm/min-etchrate Olin resist 95nm/min-profile: slightly tapered for PR-profile: directional for metal mask

back and front-sidedepth 200nmtime 4min

t08 Deep Plasma etchingof Si

-Oxford Plasma lab 100 ICP (Katharina)-temperature –110C�-SF6 flow 120 sccm-O2 flow 0 sccm-pressure 10 Torr-icp power 600WNative oxide removal:-power 7.5W-Vdc 41VSi etching:-power 2.5W-Vdc 16V-etchrate 4.5µm/min

front-side

time 1min

depth 25�mtime 10 min

210 Appendix A



back-side

t10 HF etching of SiRN -HF 50%-etchrate: 5nm/min-temperature 20�C

depth 200nmtime 40min

t11 Online cleaning -fuming nitric acid (I), 5min-fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S-boiling nitric acid (80�C), 15min-quick dump rinse, DI, <0.1�S-spin drying

t12 LPCVD SiRN-S&A -Tempress LPCVD Furnace program N6-SiH2Cl2 flow 70sccm-NH3 flow 18sccm-temperature 850�C-pressure 200mTorr-deposition rate 8.3nm/min

thickness 200nmtime 25min


-hot plate 120°C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/12, 4000rpm, 20s-prebake: hotplate 95�C, 60sec-maskaligner: Electronic Visions AL-6 contact: hard-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 30min

front-sidemask “BOP”alignment precisionnormal

t14 Plasma etching of SiRN -Elektrotech PF 310/340 (Etske)-dirty chamber-styros electrode-electrode temperature 10�C-CHF3 flow 25sccm-O2 flow 5sccm-pressure 10mTorr-power 75W-etchrate 80nm/min-etchrate Olin resist 95nm/min

front-sidedepth 200nmtime 3min



-oxygen plasma Nanotech Plasmaprep 100-O2 flow 55sccm-power 120W-electrode temperature 150�C-pressure 2.0 mbar-time 20min

front-side

t16 Native Oxide Strip -HF 1%-time 1min

t17 KOH etching of Silicon -500gr KOH-1500ml-temperature 75�C-stirr-etchrate <100> 1�m/min

depth = 360-25�mtime ~330min

Table A.5 Top wafer processing steps

Bottom wafer

step process parameters specific settings

b01 Introduction cleaning -fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S-boiling nitric acid (80�C), 15min-quick dump rinse, DI, <0.1�S-spin drying-60s HF(1%)-dip-quick dump rinse, DI, <0.1�S-spin drying

b02 Wet Thermal OxidationS&A-3

-Tempress Omega Junior III-gasses H2O+N2

-temperature 1150�C

thickness 500nmtime 25min(check chart)

b03 LithographyS&A-907/12-3”

-hot plate 120°C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/12, 4000rpm, 20s-prebake: hotplate 95�C, 60sec-maskaligner: Electronic Visions AL-6 contact hard, exposure 4s-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying

front-sidemask: “SNK”

212 Appendix A

-visual microscopic inspection-postbake: hotplate 120�C, 30min

b04 BHF etching of SiO2 -etchrate: 60nm/min-until etched patterns hydrofobic


b05 Photoresist stripOxygen plasma

-Nanotech Plasmaprep 100-O2 flow 55sccm-power 120W-electrode temperature 150�C-pressure 2.0mbar-time 20min

front-side

b06 Online cleaning -fuming nitric acid (I), 5min-fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S-boiling nitric acid (80�C), 15min-quick dump rinse, DI, <0.1�S-spin drying

b07 Evaporation of Cr -Varian 3117-voltage 9 kV-current 0.02 A-deposition rate 1 nm/min-base pressure < 2.10-6 Torr

front-sidethickness 50 nmtime 50 min

b08 LithographyS&A-907/12-3” on metal

-hot plate 120°C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/12, 4000rpm, 20s-prebake: hotplate 95�C, 90sec-maskaligner: Electronic Visions AL-6 contact hard, exposure 4s-after exposure bake 120�C, 1min-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 45min

front-sidemask “MemRIE”alignment precisionhighnotice: holes areslightly bigger thanmask “SNK”

b09 Annealing photoresist -Heraeus convection furnace 150�C, 15 min-cool-down to 30C�

b10 Cr etch -standard S&A Cr etch-time: 2 min

leave resist on top toavoid Cr sputteringduring RIE


b11 Deep Plasma etchingof Si

-Oxford Plasma lab 100 ICP (Katharina)-temperature –130C�-SF6 flow 150 sccm-O2 flow 5 sccm-pressure 10 Torr-icp power 600WNative oxide removal:-power 100W-Vdc 49VSi etching:-power 45W-Vdc 36V-etchrate 3.8µm/min

front-side

time 2min

depth 200�mtime 50min

b12 Photoresist strip (HNO3) -HNO3 100%-time 20 min.

to prevent formingchromium oxidemake new solution

b13 Cr etch -user Cr etch-time: 5min

strip Cr

b14 RCA-2 CleaningNH4OH/H2O/H2O2

procedure:-add H2O to H2O2 to NH4OH, 5:1:1-wait till temp. 80�C, switch on heater-time: 20min-quick dump rinse, DI, <0.1�S-spin drying

b15 Deep Plasma etchingof Si

-Oxford Plasma lab 100 ICP (Katharina)-temperature –110C�-SF6 flow 120 sccm-O2 flow 0 sccm-pressure 10 Torr-icp power 600WNative oxide removal:-power 7.5W-Vdc 41VSi etching:-power 2.5W-Vdc 16V-etchrate 4.5µm/min

front-side

time 1min

depth 50�mtime 10min

b16 BHF etching of SiO2 -standard S&A BHF (1:7)-etchrate 60nm/min-time 8min

depth 500nm

214 Appendix A

b17 Online cleaning -fuming nitric acid (I), 5min-fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S-boiling nitric acid (80�C), 15min-quick dump rinse, DI, <0.1�S-spin drying

b18 LPCVD SiRN -Tempress LPCVD Furnace program N4?-SiH2Cl2 flow 70sccm-NH3 flow 18sccm-temperature 850�C-pressure 200mTorr-deposition rate 8.3nm/min

thickness 200 nmtime 25min

b19 LithographyS&A-907/12-3”

-hot plate 120°C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/12, 4000rpm, 20s-prebake: hotplate 95�C, 60sec-maskaligner: Electronic Visions AL-6 contact hard, exposure 4s-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 30min

back-sideMask “BKE”alignment precisionnormal

b20 Plasma etching of SiRN -Elektrotech PF 310/340 (Etske)-dirty chamber-styros electrode-electrode temperature 10�C-CHF3 flow 25sccm-O2 flow 5sccm-pressure 10mTorr-power 75W-etchrate 80nm/min-time 3min-SiN profile: slightly tapered for PR-SiN profile: directional for metal mask

back-sidedepth 200nm

b21 Photoresist stripOxygen plasma

-Nanotech Plasmaprep 100-O2 flow 55sccm-power 120W-electrode temperature 150�C-pressure 2.0mbar

back-sidetime 20min

b22 Native Oxide Strip -HF 1% time 1mincheck for hydrofobic


b23 KOH etching of Silicon -500gr KOH-1500ml-temperature 75�C-stirr-etchrate <100> 1�m/min

depth= wafer thick.-250�mfor 360µm thickness:time appr. 110min

b24 RCA-2 CleaningNH4OH/H2O/H2O2

procedure:-add H2O to H2O2 to NH4OH, 5:1:1-wait till temp. 80�C, switch on heater-time: 20min-quick dump rinse, DI, <0.1�S-spin drying

b25 HF etching of SiRN -HF 50%-etchrate: 5nm/min-temperature 20�C


Table A.6 Bottom wafer processing steps

Aligned low temperature fusion bonding

All steps for top and bottom waferstep process parameters specific settings

f01 Introduction cleaning forfusion bonding

-fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S-boiling nitric acid (80�C), 15min-quick dump rinse, DI, <0.1�S-spin drying-60s HF(1%)-dip-quick dump rinse, DI, <0.1�S

immediately beforebonding step

check if hydrofobic

f02 RCA “Piranha” cleaningfor fusion bondingH2SO4/H2O2

procedure:-add H2O2 to H2SO4, 1:3

-wait till temp. 100�C, switch on heater-time 20min-quick dump rinse, DI, <0.1�S-store and transport wafers under water-spin dry just before bonding-spin parameters: time 1.5min, max speed

direct before bondingstep

F03 Pre-bonding maskaligner: Electronic Visions AL-6contact vaccuum, bottom bondcontact force 150/10 [10]NO seal rise and NO purging pre-bonding

Upper chuck

Bottom chuck

f04 IR-inspection -use IR setup to check the pre-bond

216 Appendix A

-use tweezers for additional pressure to promote bonding of not bonded spots

f05 Annealing -ZnO furnace-N2 ambient-time 120min

f06 IR-inspection -use IR setup to check final bondTable A.7 Aligned low temperature fusion bonding steps

Anodic bonding

step process parameters specific settings

g01 Clean glass -user HNO3 100% 15min.g02 Glass wafer aligning - use old bond chuck

- align by hand- fix position with spring

g02 Anodic bonding - bond oven floor 7- temperature 450�C- Vdc 500V

time 45min

Table A.8 Anodic bonding process steps

217

BB DDUUCCKKBBIILLLL VVAALLVVEE FFAABBRRIICCAATTIIOONNPPRROOCCEESSSS DDEESSCCRRIIPPTTIIOONN

The fabrication steps of the duckbill valve are described,integrated in a system of channels for flow injection analysisexperiments. Essentially, the processes consist ofanisotropic wet chemical etching in potassium hydroxide(KOH) and selective anodic bonding of silicon to glass. Thewet chemical etching method is used to create thin,monocrystalline <111> oriented membranes in <100>oriented silicon.

Design description

The duckbill valve is applied in a test system for flow injection analysis (FIA). The processuses three masks: two masks to pattern the siliconnitride (SiN) at both sides and one mask topattern the chromium anti-bonding layer under the valve membrane. An additional mask(UPP) however is needed to find the crystal orientation in the wafer as discussed in chapter5. A good alignment of the bottom (BOT) mask to the crystal orientation of the <100>silicon is needed in order to get well-defined thin plates. A small mis-alignment will result inetching-through the membranes. The alignment of the top mask (TOP) is not critical sincethis mask is only needed to etch through the wafer in order to switch-over the <111>oriented planes. The silicon wafer is wet anisotropical chemically etched in KOH at bothsides of the wafer at the same time. Mask underetch is used to determine the final thicknessof the thin {111} plates. Hence the membrane thickness as defined by the mask openings is

218 Appendix B

somewhat larger. At a concentration of 833g KOH on 1250ml water, an minimum underetchvelocity was found of 11nm/min at a <100> etch rate of 0.77µm/min. Double-side polished,4” wafers are used. With the thicker 4” wafers, deeper v-grooves can be etched than in 3”wafers such that larger, more flexible valves can be made.

Explanation of typical process steps

� The first step is needed to find the crystal orientation in the <100> wafer. Use the crystalorientation alignment mask for this, indicated by “UPP”.

� Chromium is used to prevent the glass wafer from (anodic) bonding with the silicon. Thethickness of this metal layer needs to be minimized to reduce stress and initial deflectionof the membrane. Experience showed that less than 1nm (extremely short sputter time) isenough.

Mask description

The design uses 4 masks (including the crystal alignment mask) described in table B.1. Infigure B.1 the position and the sequence of the masks is shown, whereas figure B.2 shows azoom-in on the mask layout.

position Description code insideA {111} plane switch-over mask (Si top) TOP whiteB Channel definition (bottom) BOT whiteC Anti bonding patterns (glass) MIL white- Crystal alignment mask (bottom) UPP whiteTable B.1 Masks description with codes and development type (inside white or black). The

position numbering corresponds with the picture in figure B.2.

TOP

UPP

SNKBOT

glass

glass

Si <100>

Figure B.1 Wafer layers and orientation of the used masks.

Duckbill valve fabrication process description 219

Figure B.2 A zoom-in on the masks used for the fabrication process. The left two masks are usedfor wet chemical etching of silicon, mask C is used for patterning the chromium anti-bonding layer.

Process outline

Silicon wafer

step Process description cross-section after processing

t01 LPCVD of SiN (1�m)

t04 Lithography backside alignment mask“UPP”

t05 RIE of SiN backside (1µm)

t09 KOH etching (15µm)

t11 Lithography frontside mask “TOP”

t12 RIE of SiN frontside (1µm)

t15 Lithography backside mask “BOT”

t16 RIE of SiN backside (1µm)

t20 KOH etching: wafer-through andswitching {111} planes

t22 HF etching of SiN (1µm)

Table B.2 Process outline of the silicon wafer

220 Appendix B

Step Process description cross-section after processing

b02 Lithography front side mask “MIL”

b03 Sputtering chromium(minimal layer thickness <<1nm)

b04 Resist lift-off

Table B.3 Process outline of the glass bottom wafer

Process parameters

Wafer preparation

Step Process parameters specific settings

c01 Select Si wafers Silicon:-orientation <100>-conductivity 5-10�cm-diameter 4 inch-thickness ~525µm-double sided polished

a set consists of:1 top wafer (t) DSP1 bottom wafer (b) SSP1 Corning 7740 Pyrexglass

c02 Scribe ID-code on wafers -number wafers c03 Thickness measurement -Lee wafer thickness measurement probe at three points on the

wafer c04 Ultra-sonic cleaning -time 20min

Table B.4 Wafer preparation steps

Silicon wafer processing

Step Process parameters specific settings

t01 Introduction / LPCVDSiN cleaning

-fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S-boiling nitric acid (90�C), 15min-quick dump rinse, DI, <0.1�S-spin drying

cleaning directly beforeLPCVD step

t02 Native oxide strip -60s HF(1%)-dip (check hydrofobic)-quick dump rinse, DI, <0.1�S-spin drying

removes native oxidebefore LPCVD SiN,can be combined withstep t01


t03 LPCVD SiRN -Tempress LPCVD Furnace program N4-SiH2Cl2 flow 70sccm-NH3 flow 18sccm-temperature 850�C-pressure 200mTorr-deposition rate 8.3nm/min

thickness 150nmtime 18min

t04 LithographyS&A-907/17-4”

-hot plate 120�C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/17, 4000rpm, 20s-prebake: hotplate 95�C, 90sec-maskaligner: Electronic Visions AL-6 contact hard, exposure 4s-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 30min

bottom sidemask “UPP”back-side protectionwith same type resist

t05 Plasma etching of SiRN -Elektrotech PF 310/340 (Etske)-styros electrode-electrode temp.: 10�C-CHF3 flow 25sccm-O2 flow 5sccm-pressure 10mTorr-power 75W-etchrate SiRN 60-90nm/min-etchrate Olin resist 95nm/min-profile: slightly tapered for PR-profile: directional for metal mask

bottom sidedepth 150nmtime 3min



2 times: both sides



222 Appendix B

t09 KOH etching of Silicon -833g KOH-1250ml H2O-temperature 75�C-stir-etchrate <100> 0.77�m/min

depth 15µmtime 35min.

t10 RCA-2 CleaningNH4OH/H2O/H2O2

procedure:-add H2O to H2O2 to NH4OH 5:1:1-wait till temp. 80�C, switch on heater-time 20min-quick dump rinse, DI, <0.1�S-spin drying


-hot plate 120�C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/17, 4000rpm, 20s-prebake: hotplate 95�C, 90sec-maskaligner: Electronic Visions AL-6,contact hard, exposure 4s-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 30min

backsidemask “BOT”front side protectionwith same type resist

alignment on crystalorientation with KOHetch pattern formed bymask “UPP”

alignment precisionhigh

t12 Plasma etching of SiRN -Elektrotech PF 310/340 (Etske)-styros electrode-electrode temp.: 10�C-CHF3 flow 25sccm-O2 flow 5sccm-pressure 10mTorr-power 75W-etchrate SiRN 60-90nm/min-etchrate Olin resist 95nm/min

backsidedepth 1µmtime 18min


t13 Photoresist strip(Oxygen plasma)


2 times: both sides



-hot plate 120�C, 5min-primer: HMDS (liquid), 4000rpm, 20s-resist: Olin 907/17, 4000rpm, 20s-prebake: hotplate 95�C, 90sec-maskaligner: Electronic Visions AL-6 contact hard, exposure 4s-after exposure bake 120�C, 60sec-development: OPD 4262, 45s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection-postbake: hotplate 120�C, 30min

front sidemask “TOP”backside protectionwith same type resist

double sided alignmenton mask “BOT”

alignment precisionnormal

t16 Plasma etching of SiRN -Elektrotech PF 310/340 (Etske)-styros electrode-electrode temp.: 10�C-CHF3 flow 25sccm-O2 flow 5sccm-pressure 10mTorr-power 75W-etchrate SiRN 60-90nm/min-etchrate Olin resist 95nm/min

backsidedepth 1µmtime 18min

t17 Photoresist strip(Oxygen plasma)


2 times: both sides

t18 Online cleaning -fuming nitric acid (I), 5min-fuming nitric acid (II), 5min-quick dump rinse, DI, <0.1�S

224 Appendix B

-boiling nitric acid (80�C), 15min-quick dump rinse, DI, <0.1�S-spin drying


t20 KOH etching of Silicon -388g KOH-1250ml H2O-temperature 75�C-stir-<100> etchrate <100> 0.77�m/min-mask underetch rate 11nm/min-<110> etch velocity 1.8-2.0µm/min

depth = wafer-through+ time for fullswitching-over of{111} planes.Fine tuning ofmembrane thicknesswith underetchingtime ~730min

t21 RCA-2 CleaningNH4OH/H2O/H2O2

procedure:-add H2O to H2O2 to NH4OH 5:1:1-wait till temp. 80�C, switch on heater-time 20min-quick dump rinse, DI, <0.1�S-spin drying

t22 HF etching of SiRN -HF 50%-etchrate: 5nm/min-temperature 20�C-quick dump rinse, DI, <0.1�S-spin drying


Table B.5 Silicon wafer processing steps

Bottom glass wafer processing


b01 Glass wafer cleaning -100% nitric acid 15min.-quick dump rinse, DI, <0.1�S-spin drying

user made

b02 Lithography-S&A907/12-4”

-hot plate 120�C, 5min-resist: Olin 907/12, 3000rpm, 20s-prebake: hotplate 95�C, 60sec-maskaligner: Electronic Visions AL-6contact: hard, exposure time 3.4s-after exposure bake 120�C, 60sec-development: OPD 4262, 60s-quick dump rinse, DI, <0.1�S-spin drying-visual microscopic inspection

front sidemask “MIL”


b03 Sputtering chromium -UT sputtergun system “Sputterke”-chromium target-pre-sputter vacuum pressure 1.0E-6 mbar-pre sputter Argon pressure 5.0E-3 mbar(~ Argon flow 45 sccm)-power 200W-sputter rate 13.5nm/min

thickness << 1nmtime: minimized to lessthan 1 sec.(only rotating shutter)

b04 Lift-off -acetone (dirty)-ultrasonic bath-time 15min-refresh acetone (new)-time 10min

user made

b05 Glass wafer cleaning -100% nitric acid 15min.-quick dump rinse, DI, <0.1�S-spin drying

user madecombine with step g01

Table B.6 Process steps of the glass bottom wafer

Cover glass wafer processing


g01 Glass wafer cleaning -100% nitric acid 15min.-quick dump rinse, DI, <0.1�S-spin drying

user madecombine with step b05

Table B.7 Cover glass wafer processing steps

Anodic wafer bonding


a01 Anodic bonding - bond oven floor 7- temperature 450�C- Vdc 500V

silicon + glass coverwafertime 45min

a02 Glass wafer aligning - use old bond chuck- align by hand- fix position with spring

a03 Anodic bonding - bond oven floor 7- temperature 450�C- Vdc 500V

+ bottom glass wafertime 45min

Table B.8 Anodic wafer bonding steps

Summary 227

Summary

During the last decades, miniaturization of electrical components and systems has assumedlarge proportions. The reason for these developments is the application of etch anddeposition techniques in the IC-production (integrated circuit), which allows a large amountof functionality per surface area. The IC-production techniques can also be used for thefabrication of functional elements, operating in other physical domains. This has led to theresearch area of micromechanics. With use of existing and to specific demands adapted ornewly developed etch and deposition techniques, miniaturized sensors and actuators can beobtained with typical dimensions in the order of microns to millimeters.

The described micromechanics research is carried out at the MicromechanicalTransducers Group of the Faculty of Electrical Engineering, University of Twente and tookplace within the fast growing area of µTAS: micro Total Analysis Systems. The aim of theresearch is to design miniaturized chemical analysis systems by applying micromechanicalfabrication methods to exploit the benefits from downscaling. These advantages can be:reduction of analysis costs, obtaining more compact, energy and reagents economicalsystems, performing a faster and / or more precise analysis, or performing of chemicalanalysis which are difficult or not possible with “macrosystems”.

The research is focussed in particular on modeling, designing and fabrication ofcomponents of a µTAS. The effects of downscaling on the influence of the different physicalmechanisms on the behavior of microcomponents can be well analyzed with use ofdimensionless numbers. In the considered microcomponents, the flow regime is in the rangeof Reynolds numbers around 1. Within this range, simplified models according to Stokes canbe used. For stationary, fully developed flow in straight channels with typical microchannelcross-section geometries, analytical expressions have been derived to describe the velocityprofile and the hydraulic resistance. The application of the virtual work principle (variationalmethod) and the analogy of the mathematical description for torque of beams turns out to bevery successful.

Stoke’s theory is applied to modeling both the quasi-dynamic behavior of the pressure/ flow sensor and the stationary, domain-coupled behavior of the valves. The hydraulicresistance of passive valves can be described well with use of the dimensionless relationEu4.Re = constant, in which Eu forms the Euler number and Re the Reynolds number. Agood prediction of the behavior of microvalves turns out to be rather difficult though. Therelative fabrication accuracy is poor, despite the used high absolute accurate fabricationprecision, such that substantial differences between the measured and aimed valve behaviorcan occur.

228

In this thesis different fabrication techniques and process designs are presented for therealization of the sensors and valves. For the manufacturing of a well-closing valve, selectivebonding is an essential step. To achieve this, two methods are presented: selective anodicbonding of silicon to glass, with use of a chromium layer of less than 1 nm thickness andselective silicon to silicon bonding with use of siliconnitride layers.

Besides waferbonding, much attention is paid to the application of anisotropic wetchemical etching of mono-crystalline silicon. By optimally using the crystal orientations indifferent wafertypes, combined with directional and anisotropic etching, powerful designsfor microstructures arise. An example is the possibility to etch thin plates with high accuracyby using the switching of {111} planes in <100> silicon during etching through the wafer, incombination with a suitable mask design. These plates can be used to create among otherspassive valve arrays with a limited number of process steps. For both <100> and <111>oriented silicon design rules are given for optimally using the possibilities offered by theanisotropic etch process. Precisely defined, suspended structures, thin plates, plan-parallelbeams and membranes can be made with anisotropic etching and a combination withdirectional etching and wall-protection. The presented techniques offer an interestingextension of the design possibilities within microsystem technology.

Samenvatting 229

Samenvatting

Miniaturisatie van elektronische componenten en systemen heeft de afgelopen decennia eengrote vlucht genomen. De verklaring voor deze vlucht ligt in de toepassing van ets- endepositietechnieken in de IC-fabricage (integrated circuit) die een grote functionaliteit pereenheid oppervlak mogelijk maakt. De IC-fabricagetechnieken kunnen eveneens gebruiktworden bij het produceren van functionele elementen, die in andere domeinen werken. Ditheeft geleid tot het ontstaan van het vakgebied micromechanica. Met behulp van debestaande en aan de specifieke eisen aangepaste of met behulp van nieuw ontwikkelde ets-en depositietechnieken kunnen bijvoorbeeld geminiaturiseerde sensoren en actuatorenworden verkregen die typische afmetingen hebben in de orde van microns tot millimeters.

Het beschreven micromechanica-onderzoek is uitgevoerd binnen de leerstoelTransductietechniek van de faculteit Elektrotechniek der Universiteit Twente en valt binnenhet snelgroeiende deelgebied µTAS: micro Total Analysis Systems. De doelstelling van hetonderzoek is geminiaturiseerde chemische analysesystemen te ontwerpen door het toepassenvan micromechanische fabricagemethoden en aldus de voordelen van schaalverkleining uitte buiten. Deze voordelen kunnen bestaan uit lagere analysekosten, het verkrijgen van meercompacte, energie- en reagenszuinige systemen, het doen van snellere en / of meernauwkeurige analyses, of het uitvoeren van chemische analyses die met ‘macrosystemen’niet of moeilijk te doen zijn.

Het onderzoek richt zich in het bijzonder op het modelleren, ontwerpen en fabricerenvan deelcomponenten van een µTAS. De effecten van schaalverkleining op de invloed vanverschillende fysische mechanismen ten aanzien van het gedrag van microcomponentenkunnen goed geanalyseerd worden met behulp van dimensieloze kentallen. In deonderzochte microcomponenten ligt het stromingsregime in het bereik vanReynoldskentallen rond 1. Binnen dit bereik kan voor vloeistofstroming gebruik wordengemaakt van de vereenvoudigde stromingsmodellen volgens Stokes. Voor stationaire,volledig ontwikkelde stroming door rechte kanalen zijn voor verschillendekanaalgeometrieën, die in de microsysteemtechnologie voorkomen, analytischeuitdrukkingen gevonden voor de beschrijving van het stromingsprofiel en de hydraulischeweerstand. Het toepassen van de virtuele arbeidsstelling (variatiemethode) en de analogievan de wiskundige beschrijving met de situatie voor torsie van balken blijkt hiervoor ergsuccesvol.

De theorie van Stokes is tevens toegepast op het modelleren van het quasi-dynamischegedrag van de druk- / debietsensor en van het stationaire, domein gekoppelde gedrag vankleppen. De hydraulische weerstand van passieve kleppen kan goed beschreven worden met

230

de dimensieloze relatie Eu4.Re = constant, waarin Eu het Euler- en Re het Reynoldskentalvormt. Een goede voorspelling van het gedrag van gefabriceerde microkleppen blijktevenwel moeilijk te zijn. De relatieve fabricage nauwkeurigheid is matig – ondanks degebruikte hoge absolute fabricage nauwkeurigheid – zodat er aanzienlijke afwijkingenkunnen ontstaan van het gemeten klepgedrag ten opzichte van het beoogde gedrag.

In dit proefschrift worden verschillende fabricage technieken c.q. procesontwerpengepresenteerd voor de realisatie van de sensoren en de kleppen. Voor het vervaardigen vaneen goed afdichtende klep is selectief bonden een essentiële stap. Hiervoor worden tweemethodes gepresenteerd: selectief anodisch bonden van silicium en glas met behulp van eenchroomlaag kleiner dan 1nm èn selectief silicium-silicium fusionbonding met behulp vansiliciumnitride lagen.

Naast waferbonding wordt vooral aandacht besteed aan het toepassen van anisotroopnat chemisch etsen in mono-kristallijn silicium. Door optimaal gebruik te maken van dekristaloriëntaties in verschillende wafertypes, gecombineerd met directioneel en anisotroopetsen, ontstaan krachtige ontwerpen voor microstructuren. Een voorbeeld is de mogelijkheidom met grote nauwkeurigheid dunne platen te etsen, door gebruik te maken van hetomklappen van {111} vlakken in <100> silicium bij het dooretsen van de wafer, incombinatie met een geschikt maskerontwerp. Deze platen kunnen gebruikt worden om onderandere compacte arrays van passieve kleppen te creëren in een beperkt aantal processtappen.Zowel voor <100> georiënteerd silicium als voor <111> silicium worden ontwerpregelsgegeven voor het optimaal benutten van de mogelijkheden die het anisotroop etsproces biedt.Nauwkeurig gedefinieerde, vrij hangende structuren, dunne platen, planparallelle balken enmembranen kunnen worden gemaakt door anisotroop te etsen en een combinatie metdirectioneel etsen en wandprotectie toe te passen. De gepresenteerde technieken bieden eeninteressante uitbreiding op de ontwerpmogelijkheden binnen de microsysteemtechnologie.

Bibliography 231

Bibliography

S. Schlautmann, R.E. Oosterbroek, T.S.J. Lammerink, M.C. Elwenpspoek, “A Surface- andBulk-Micromachined combination of a passive checkvalve and a mixer”, 1st Symposium onMicro Systems Technology in Practice, Enschede, The Netherlands, January 9-10, 1997

R.E. Oosterbroek, T.S.J. Lammerink, J.W. Berenschot, A. Van den Berg, M.C. Elwenspoek,“Fluid control for Micro Total Analysis Systems”, STW Workshop Sensortechnologie, Zeist,The Netherlands, March 12-13, 1997

R.E. Oosterbroek, T.S.J Lammerink, J.W. Berenschot, A. van den Berg, M.C. Elwenspoek,“Designing, realization and characterization of a novel capacitive pressure / flow sensor”,Proc. IEEE, International Conference on Solid-State Sensors and Actuators, Transducers’97,Chicago, U.S.A., June 16-19, 1997, pp. 151-154,

J.W. Berenschot, R.E. Oosterbroek, T.S.J. Lammerink and M.C. Elwenspoek,“Micromachining of {111} plates in <001> oriented silicon”, 8th Workshop onMicromaching, Micromechanics & Microsystems, Micromechanics Europe, MME’97,Southampton, England, August 31 – September 2, 1997, pp. 83-86

R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J Lammerink, A. van den Berg,M.C. Elwenspoek, “A new fabrication method for in-plane micro fluid handling componentsand analysis systems”, Proc. Dutch Sensor Conference, Enschede, The Netherlands, March2-3, 1998, pp. 85-90

R.E. Oosterbroek, S. Schlautmann, J.W. Berenschot, T.S.J Lammerink, A. van den Berg,M.C. Elwenspoek, “Modeling and validation of flow-structure interactions in passive microvalves”, Proc. International Conference on Modeling and Simulation of Microsystems,Semiconductors, Sensors and Actuators, MSM’98, Santa Clara, U.S.A., April 6-8, 1996,pp. 528-533

J.W. Berenschot, R.E. Oosterbroek, T.S.J. Lammerink and M.C. Elwenspoek,Micromachining of {111} plates in <001> oriented silicon, Journal of Micromechanics andMicroengineering, Vol. 8, 1998, pp. 104-107

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R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J Lammerink, A. van den Berg andM.C. Elwenspoek, “Designing, simulation and realization of in-plane operating micro-valves, using new etching techniques”, 8th Workshop on Micromaching, Micromechanics &Microsystems, Micromechanics Europe’98, Ulvik, Norway, June 3-5, 1998, pp. 104-107

R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J Lammerink, A. van den Berg,M.C. Elwenspoek, “In-plane oriented fluid control components, fabricated with new etchingtechniques”, Proc. 6th International Conference on New Actuators, Actuator’98, Bremen,Germany, June 17-19, 1998, pp. 43-46

T.S.J. Lammerink, N. Olij, J.W. Berenschot, R.E. Oosterbroek, J.G.E. Gardeniers, C. Neagu,A. van den Berg, M. Haller, G.J.M. Krijnen, M.C. Elwenpoek, “A normally closed activevalve using bulk micromachining”, Proc. 6th Int. Conference on New Actuators, Actuator’98,Bremen, Germany, June 17-19, 1998, pp. 122-125

S. Schlautmann, R.E. Oosterbroek, J.W. Berenschot, T.S.J Lammerink, A. van den Berg,M.C. Elwenspoek, “Modeling and validation of fluid structure interactions in passive microvalves”, Second Symposium on Microsystems in Practice, Gelsenkirchen, Germany, June18-19, 1998

R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J Lammerink, A. van den Berg,M.C. Elwenspoek, “Utilizing the {111} plane switch-over etching process for micro fluidcontrol applications”, Proc. 3rd International Symposium on Micro Total Analysis Systems,µTAS’98, Banff, Canada, October 13-16, 1998, pp. 137-140

R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J. Lammerink, G.J.M. Krijnen,M.C. Elwenspoek, A. van den Berg, “Characterization and optimization of mono-crystallinein-plane operating check valves”, Proc. IEEE International Conference on Solid-StateSensors and Actuators, Transducers’99, Sendai, Japan, June 7-10, 1999, pp. 1816-1819

R.E. Oosterbroek, J.W. Berenschot, A.J. Nijdam, G. Pandraud, M.C. Elwenspoek, A. vanden Berg, “New design methodologies in <111> oriented silicon wafers”, Proc. SPIE,Conferrence on Micromachining and Microfabrication, Micromachining andMicrofabrication Process Technology, Vol. 3874, Santa Clara, U.S.A., September 20-22,1999

Bibliography 233

R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, G.J.M. Krijnen, T.S.J Lammerink,M.C. Elwenspoek, A. van den Berg, “Designing, simulation and realization of in-planeoperating micro-valves using new etching techniques”, Journal of Micromechanics andMicroengineering, Vol. 9, 1999, pp. 194-198

C. Gui, R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J. Lammerink, A. van denBerg, M.C. Elwenspoek, “Selective fusion bonding by surface roughness control”, Proc. 5th

International Symposium on Semiconductor Wafer Bonding: Science, Technology andApplications, Joint International Meeting of The Electrochemical Society, Hawaii, U.S.A.,October 17-22, 1999

R.E. Oosterbroek, T.S.J Lammerink, J.W. Berenschot, G.J.M. Krijnen, M.C. Elwenspoek, A.van den Berg, “A micromachined pressure / flow-sensor”, Sensors and Actuators A:Physical, 1999, to be published

R.E. Oosterbroek, J.W. Berenschot, H.V. Jansen, A.J. Nijdam, G. Pandraud,M.C. Elwenspoek, A. van den Berg, “New design methodologies in <111> oriented siliconwafers”, Journal of Microelectromechanical Systems, to be published

C. Gui, R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J. Lammerink, A. van denBerg, M.C. Elwenspoek, “Selective fusion bonding by surface roughness control”, Journal ofThe Electrochemical Society, to be published

Dankwoord 235

Dankwoord

Dit proefschrift is een reflectie van de activiteiten rondom mijn project. Hieraan hebben velepersonen direct of indirect hun steentje bijgedragen, waarvoor ik ze hartelijk bedanken wil.Zonder jullie hulp was het niet gelukt. In willekeurige volgorde wil ik ten eerste mijnpromotoren, Albert van den Berg en Miko Elwenspoek en de overige commissieledenbedanken voor hun bijdrage. Albert’s enthousiasme voor en zijn kennis van het boeiendeµTAS vakgebied werkt erg stimulerend. De micromechanica groep, officieelTransductietechniek genoemd, maar in de wandelgangen beter bekend en berucht alsMicmec, is een uitstekende omgeving om onderzoek in te doen. Dit is voor een belangrijkdeel te danken aan Miko. Leuke mensen van allerlei pluimage, goede materiëlevoorzieningen, interessant onderzoek en de mogelijkheden om je werk regelmatig in hetverre buitenland te presenteren heeft mij destijds doen beslissen hier wel vier jaar te willenwerken.

De kennis en ervaring van Theo Lammerink zorgde voor een andere kijk op demodelleringsproblematiek en een verbreding van mijn werktuigbouwkundige kennis. Ik denkdat er zeker een ‘vonkje’ van jouw liefde voor de elektronica is overgesprongen, vooral ophet vlak van ‘sexy’ microcontrollers die uitstekend geschikt bleken voor de hobby. GijsKrijnen wil ik zeer bedanken voor het feit dat hij, ‘voor de leeuwen geworpen’ debegeleiding overnam, maar daardoor met een nuchtere en open blik de zaken volgde. Tevensben ik je erg dankbaar voor het vele papier werk dat ik bij je langs kon brengen omvervolgens weer nauwkeurig gecorrigeerd terug te krijgen.

Het dagelijkse Micmec ‘controle centrum’ Erwin en Meint (Berenschot - de BoerB.V.) wil ik bedanken voor hun grote steun, gezelligheid en input van kennis. Zonder dit duozou de Micmec niet kunnen functioneren. Zij zijn de chef-koks die steeds weertechnologische hoogstandjes laten zien en de sterren scoren voor de groep. Bedankt voorjullie technologische ‘trucks’, oplossingen en het processen van vele devices. Te samen metStefan ‘Schlauther Stef’ Schlautmann en Remco ‘Pino’ Sanders zijn zij de werkpaardengeweest die veel van de gepresenteerde resultaten voortgebracht hebben. Ik hoop dat ik dezenaar jullie wens gepresenteerd heb. Remco, bedankt voor het uitvoeren van de vele, somssaaie metingen waarbij de resultaten soms wat anders uitvielen dan gewenst. Stefan, bedanktvoor het simulatiewerk, maskers ontwerpen, cleanroomwerk en de gezelligheid gedurende jeperiode ‘achter de kast’.

Wat ik altijd erg tof heb gevonden is dat de micmec ook buiten werktijd een team is.Borrelen op de groene bank, “daghappen” op de markt of een bioskoopje pakken, altijd zijner wel micmeccers te vinden die meedoen. Bedankt voor deze Micmec gezelligheid, Han,

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Niels, Jasper, Theo, Hans, Stefan(San), Marko, Johannes, Pele, Martin, Wietze, Cees, Henk,Robert, Sandra, John en Hans-Elias. Willem wil ik in het bijzonder bedanken voor degezamenlijke ‘AIO survival’. Vaak zaten we op dezelfde lijn, maar over sommige zakenzullen we het wel nooit eens worden zoals bijvoorbeeld of donker harigen of blondinesknapper zijn en of je nu Linux of Windhoos op je computer moet zetten.

Verder zijn er vele AIO’s, OIO’s en TWAIO’s en overige micmeccers geweest wienskennis mij weer een stuk verder gebracht heeft. In het bijzonder wil ik noemen: Henri(e)‘miep miep Janneboer’, Cristina, Gui ‘Mr. Bond’, Vincent, Rob, Gert-Jan, Albert ‘Prakkie’,Edwin ‘Smullebul’, Thijs en Jan-Kees. Joost en Job ben ik erg erkentelijk dat ze meaangenomen hebben op het µBlast project tijdens mijn vervangende dienstplicht. Hierdoorben ik in aanraking gekomen met de kleine, maar boeiende wereld van de microsysteemtechnologie en de Micmec in het bijzonder. Er zijn nog vele Micmeccers en ex-Micmeccerswaarvan ik de namen niet allemaal kan opnoemen maar die hier zeker bij horen.

Naast onderzoek doen en schrijven, zijn er allerlei formaliteiten, declaraties en fax-problemen te overwinnen. Gelukkig hebben we een leuk stel secretaresses te weten: Judith,José, Simone, Ingrid, Sharron en Hermine, die hierbij een grote steun zijn. Ook als buurtjeswil ik jullie hartelijk bedanken. Het was altijd erg gezellig om jullie schaterende lachbuienover de gang te horen galmen. ‘Dicky’ Dick, en Henk bedankt voor jullie ondersteuning inhet lab op vloer 7. Onze ideeën zouden ook niet verwezenlijkt kunnen worden zonder defraaie MESA+ cleanroom faciliteiten. Hiervoor wil ik alle S&A medewerkers hartelijkbedanken, met in het bijzonder Kees, Stan, Gerard, Jonny, Nicole, Huib, Riel en Arie. Bert,ik bedankt jou in het bijzonder. Zonder jouw artistieke SEM plaatjes zou het proefschrift ertoch een stuk saaier uit hebben gezien. Dat wetenschap niet altijd serieus moet wordengenomen is wel bewezen met het µMussel project. Bedankt mussle-experts voor julliecreatieve bijdragen.

Het project is mogelijk gemaakt met behulp van de financiën uit het OnderzoekStimuleringsfonds van de Universiteit Twente. Daarvoor wil ik de universiteit van hartebedanken. Het OSF project was een boeiende samenwerking tussen een aantal, soms sterkverschillende disciplines. Dank voor jullie bijdrage Eelco, Simon, Geerten, Olivier enGregory. Ik denk dat dit project heeft aangetoond dat samenwerking tussen verschillendedisciplines een must is binnen µTAS.

Naast de mensen op UT wil ik tevens alle vrienden, kennissen en familie bedankenvoor hun support. Willem van de Logt wil ik bedanken voor zijn belangeloze medewerkingaan het boren van glas wafers, de Drienerlose Zweefvliegclub voor gezelligheid en hetbieden van de mogelijkheid om van tijd tot tijd “met het hoofd in de wolken” te verkeren.Pascal, Erwin, Eric en Patrick, jullie, als leden van Team Delta Yankee in het bijzonder dankvoor het starten van ‘een projectje’. Jullie verklaarden me altijd voor gek als ik zei geen tijd

Dankwoord 237

te hebben om mee te vliegen als de cumuls aan de hemel stonden te lonken. En inderdaad hetwaren moeilijke keuzes maar ik hoop mijn achterstand spoedig in te halen.

Tenslotte bedank ik de belangrijkste mensen in mijn leven: mijn ouders, Carin enHerbert en opa en oma’s. Pa en ma, jullie hebben me altijd gesteund met wijze adviezen enhulp. Zonder jullie steun was ik niet tot hier gekomen.

238 Biography

Biography

Rijk Edwin Oosterbroek, call name Edwin, was born at January 28, 1970 in Borne. Afterfinishing highschool, he started his study in mechanical engineering at the University ofTwente in 1988. Within this study, he chose for mechanics and mathematics as mainsubjects. His practical term and graduation work were done at the Structures and Materialsdepartment of the Dutch National Aerospace Laboratory, NLR, at the Noordoostpolder.During this period, he worked on optimization of dynamic finite element models by usingmeasured frequency response data to better resemble reality. In 1994 he graduated as anM.Sc. engineer at the Technical Mechanics and Tribology group, under supervision ofprofessor Tijdeman.

After his graduation, Edwin fulfilled his civil service at the micromechanics chair ofthe Transduction and Materials Science group of Prof. Fluitman, now known asTransduction Technology, Faculty of Electronics, under the supervision of Prof.Elwenspoek. At this group he worked for one year on the Brite-Euram project, called“µBlast”, to do research in polymer and silicon-related materials for the fabrication ofmicropumps. This acquaintance with the world of microtechnology excited him so much, hedecided to continue on the project “Principles and methods for Micro Fluid HandlingSystems (MFHS)”, part of the inter-disciplinary, OSF-financed project “Micro total analysissystems (µTAS), societal impact and fundamental micromechanical, optical and chemicalaspects”, under supervision of Prof. Van den Berg. The results of the promotion work arewritten in this thesis.

In his free-time, Edwin is engaged in soaring and doing the maintenance of the planes,trailers and other materials of the Drienerlose Zweefvlieg Club. Besides, he likes to playvolleyball, R.C. flying, electronics and computer work.

Levensloop 239

Levensloop

Rijk Edwin Oosterbroek, roepnaam Edwin, werd geboren op 28 januari 1970 in Borne. Nade middelbare school, begon hij in 1988 aan de studie Werktuigbouwkunde aan deUniversiteit Twente. Binnen deze studie koos hij voor mechanica en wiskunde alszwaartepunten. Zijn stage en afstuderen heeft hij extern uitgevoerd bij de afdeling Structuresand Materials van het Nationaal Lucht- en Ruimtevaart Laboratorium (NLR) in deNoordoostpolder. In deze periode werkte hij aan het optimaliseren van dynamische eindigeelementen modellen met behulp van gemeten frequentie responsie data om zo de modellenbeter met de werkelijkheid overeen te laten komen. In 1994 studeerde hij af als ingenieur bijde vakgroep Technische Mechanica en Tribologie onder supervisie van professor Tijdeman.

Na zijn afstuderen vond Edwin een plaats voor het verrichten van de vervangendedienstplicht bij de micromechanica groep van vakgroep Transductietechniek enMateriaalkunde van prof. Fluitman, later verzelfstandigd als Transductietechniek, onderleiding van prof. Elwenspoek aan de Faculteit der Elektrotechniek. Hier werkte hij voor eenjaar op het Brite-Euram project ‘µBlast’, met als opdracht materiaal onderzoek te doen voorhet fabriceren van micropompen in polymeren en silicium-gerelateerde materialen.

Deze kennismaking met de wereld van de microtechnologie boeide hem zozeer dat hijhierna koos voor een vervolg met het project ‘Principles and methods for Micro FluidHandling Systems (MFHS)’, vallende binnen het interdisciplinaire, OSF-gefinancierdeproject ‘Micro total analysis systems (µTAS), societal impact and fundamentalmicromechanical, optical and chemical aspects’, onder de supervisie van prof. Van den Berg.De resultaten van het promotieonderzoek staan beschreven in dit proefschrift.

In zijn vrije tijd houdt Edwin zicht vooral bezig met zweefvliegen en klussen aan devliegtuigen, aanhangers en het overig materieel van de Drienerlose Zweefvlieg Club.Daarnaast houdt hij van volleyballen, modelvliegen, met elektronica knutselen encomputeren.

modeling, design and realization of microfluidic components · the development of microfluidic...

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