Introductory MEMS
Thomas M. Adams Richard A. Layton Introductory MEMS Fabrication and Applications 123
Thomas M. Adams Department of Mechanical Engineering Rose-Hulman Institute of Technology 5500 Wabash Ave. Terre Haute IN 47803 USA thomas.m.adams@rose-hulman.edu Richard A. Layton Department of Mechanical Engineering Rose-Hulman Institute of Technology 5500 Wabash Ave. Terre Haute IN 47803 USA layton@rose-hulman.edu ISBN 978-0-387-09510-3 e-isbn 978-0-387-09511-0 DOI 10.1007/978-0-387-09511-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009939153 c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedication For Diedre, whose love and companionship is no small thing. Thom To Gary, my first guitar teacher. Thanks, Dad. Richard
Contents Preface xiii Part I Fabrication Chapter 1: Introduction 3 1.1 What are MEMS? 3 1.2 Why MEMS? 4 1.2.1. Low cost, redundancy and disposability 4 1.2.2. Favorable scalings 5 1.3 How are MEMS made? 8 1.4 Roadmap and perspective 12 Essay: The Role of Surface to Volume Atoms as Magnetic Devices Miniaturize 12 Chapter 2: The substrate and adding material to it 17 2.1 Introduction 17 2.2 The silicon substrate 17 2.2.1 Silicon growth 17 2.2.2 It s a crystal 19 2.2.3 Miller indices 20 2.2.4 It s a semiconductor 24 2.3 Additive technique: Oxidation 35 2.3.1 Growing an oxide layer 35 2.3.2 Oxidation kinetics 37 2.4 Additive technique: Physical vapor deposition 40 2.4.1 Vacuum fundamentals 41 2.4.2 Thermal evaporation 46 2.4.3 Sputtering 51 2.5 Other additive techniques 57
viii Introductory MEMS: Fabrication and Applications 2.5.1 Chemical vapor deposition 57 2.5.2 Electrodeposition 58 2.5.3 Spin casting 58 2.5.4 Wafer bonding 58 Essay: Silicon Ingot Manufacturing 59 Chapter 3: Creating and transferring patterns Photolithography 65 3.1 Introduction 65 3.2 Keeping it clean 66 3.3 Photoresist 69 3.3.1 Positive resist 69 3.3.2 Negative resist 70 3.4 Working with resist 71 3.4.1 Applying photoresist 71 3.4.2 Exposure and pattern transfer 72 3.4.3 Development and post-treatment 77 3.5 Masks 79 3.6 Resolution 81 3.6.1 Resolution in contact and proximity printing 81 3.6.2 Resolution in projection printing 82 3.6.3 Sensitivity and resist profiles 84 3.6.4 Modeling of resist profiles 86 3.6.5 Photolithography resolution enhancement technology 87 3.6.6 Mask alignment 88 3.7 Permanent resists 89 Essay: Photolithography Past, Present and Future 90 Chapter 4: Creating structures Micromachining 95 4.1 Introduction 95 4.2 Bulk micromachining processes 96 4.2.1 Wet chemical etching 96 4.2.2 Dry etching 106 4.3 Surface micromachining 108 4.3.1 Surface micromachining processes 109 4.3.2 Problems with surface micromachining 111 4.3.3 Lift-off 112 4.4 Process integration 113 4.4.1 A surface micromachining example 115
Contents ix 4.4.2 Designing a good MEMS process flow 119 4.4.3 Last thoughts 124 Essay: Introduction to MEMS Packaging 126 Chapter 5: Solid mechanics 131 5.1 Introduction 131 5.2 Fundamentals of solid mechanics 131 5.2.1 Stress 132 5.2.2 Strain 133 5.2.3 Elasticity 135 5.2.4 Special cases 138 5.2.5 Non-isotropic materials 139 5.2.6 Thermal strain 141 5.3 Properties of thin films 142 5.3.1 Adhesion 142 5.3.2 Stress in thin films 142 5.3.3 Peel forces 149 Part II Applications Chapter 6: Thinking about modeling 157 6.1 What is modeling? 157 6.2 Units 158 6.3 The input-output concept 159 6.4 Physical variables and notation 162 6.5 Preface to the modeling chapters 163 Chapter 7: MEMS transducers An overview of how they work 167 7.1 What is a transducer? 167 7.2 Distinguishing between sensors and actuators 168 7.3 Response characteristics of transducers 171 7.3.1 Static response characteristics 172 7.3.2 Dynamic performance characteristics 173 7.4 MEMS sensors: principles of operation 178
x Introductory MEMS: Fabrication and Applications 7.4.1 Resistive sensing 178 7.4.2 Capacitive sensing 181 7.4.3 Piezoelectric sensing 182 7.4.4 Resonant sensing 184 7.4.5 Thermoelectric sensing 186 7.4.6 Magnetic sensing 189 7.5 MEMS actuators: principles of operation 193 7.5.1 Capacitive actuation 193 7.5.2 Piezoelectric actuation 194 7.5.3 Thermo-mechanical actuation 196 7.5.4 Thermo-electric cooling 201 7.5.5 Magnetic actuation 202 7.6 Signal conditioning 204 7.7 A quick look at two applications 206 7.7.1 RF applications 207 7.7.2 Optical applications 207 Chapter 8: Piezoresistive transducers 211 8.1 Introduction 211 8.2 Modeling piezoresistive transducers 212 8.2.1 Bridge analysis 213 8.2.2 Relating electrical resistance to mechanical strain 215 8.3 Device case study: Piezoresistive pressure sensor 221 Chapter 9: Capacitive transducers 231 9.1 Introduction 231 9.2 Capacitor fundamentals 232 9.2.1. Fixed-capacitance capacitor 232 9.2.2. Variable-capacitance capacitor 234 9.2.3. An overview of capacitive sensors and actuators 236 9.3 Modeling a capacitive sensor 239 9.3.1. Capacitive half-bridge 239 9.3.2. Conditioning the signal from the half-bridge 243 9.3.3. Mechanical subsystem 246 9.4 Device case study: Capacitive accelerometer 250
Contents xi Chapter 10: Piezoelectric transducers 255 10.1 Introduction 255 10.2 Modeling piezoelectric materials 256 10.3 Mechanical modeling of beams and plates 261 10.3.1 Distributed parameter modeling 261 10.3.2 Statics 262 10.3.3 Bending in beams 268 10.3.4 Bending in plates 274 10.4 Case study: Cantilever piezoelectric actuator 276 Chapter 11: Thermal transducers 283 11.1 Introduction 283 11.2 Basic heat transfer 284 11.2.1 Conduction 286 11.2.2 Convection 288 11.2.3 Radiation 289 11.3 Case study: Hot-arm actuator 294 11.3.1 Lumped element model 295 11.3.2 Distributed parameter model 300 11.3.3 FEA model 306 Essay: Effect of Scale on Thermal Properties 310 Chapter 12: Introduction to microfluidics 317 12.1 Introduction 317 12.2 Basics of fluid mechanics 319 12.2.1 Viscosity and flow regimes 320 12.2.2 Entrance lengths 324 12.3 Basic equations of fluid mechanics 325 12.3.1 Conservation of mass 325 12.3.2 Conservation of linear momentum 326 12.3.3 Conservation equations at a point: Continuity and Navier-Stokes equations 329 12.4 Some solutions to the Navier -Stokes equations 337 12.4.1 Couette flow 337 12.4.2 Poiseuille flow 339 12.5 Electro-osmotic flow 339 12.5.1 Electrostatics 340
xii Introductory MEMS: Fabrication and Applications 12.5.2 Ionic double layers 346 12.5.3 Navier-Stokes with a constant electric field 355 12.6 Electrophoretic separation 357 Essay: Detection Schemes Employed in Microfluidic Devices for Chemical Analysis 362 Part III Microfabrication laboratories Chapter 13: Microfabrication laboratories 371 13.1 Hot-arm actuator as a hands-on case study 371 13.2 Overview of fabrication of hot-arm actuators 372 13.3 Cleanroom safety and etiquette 375 13.4 Experiments 377 Experiment 1: Wet oxidation of a silicon wafer 377 Experiment 2: Photolithography of sacrificial layer 384 Experiment 3: Depositing metal contacts with evaporation 388 Experiment 4: Wet chemical etching of aluminum 392 Experiment 5: Plasma ash release 395 Experiment 6: Characterization of hot-arm actuators 397 Appendix A: Notation 405 Appendix B: Periodic table of the elements 411 Appendix C: The complimentary error function 413 Appendix D: Color chart for thermally grown silicon dioxide 415 Glossary 417 Subject Index 439
Preface We originally wanted to call this book Dr. Thom s Big Book about Little Things, but, apart from being perhaps too playful a title, we didn t like the word big in it. That s because the book was intended to be an introduction to the world of science and engineering at the microscale, not a comprehensive treatment of the field at large. Other authors have already written books like that, and they have done a wonderful job. But we wanted something different. We wanted an introductory MEMS text accessible to any undergraduate technical major, students whose common background consists of freshman level physics, chemistry, calculus and differential equations. And while a little book about little things might not suffice to that end, we at least desired a somewhat compact book about things micro. When we taught an introductory MEMS course for the first time in the spring of 2002 to just such an audience, it was, at least to our knowledge, a unique endeavor. We attempted to cover way too much material though, and we threw one of those big comprehensive books at the students. It nearly knocked them out. In subsequent installments, we cut back on the material and started using instructor notes in lieu of a text. Those notes, outlines, bulleted lists, and fill-in-the-blank handouts became the skeleton around which this text was formed. As creating microstructures requires such a different set of tools than those encountered in the macro-world, much of learning about MEMS rests squarely in learning the details of how to make them. Part I of this text therefore deals mainly with introducing the reader to the world of MEMS and their fabrication. Actuation and sensing are also treated from a generic standpoint, with MEMS devices used as examples throughout. In Chapter 7 of Part II, an overview of some of the most common MEMS transducers is given from a mainly qualitative, non-mathematical standpoint. Hence, the first seven chapters should suffice for the majority of introductory courses. Following Chapter 7 are specific treatments and modeling strategies for a handful of selected MEMS. The mathematical modeling is more detailed than in previous chapters, covering a number energy domains. Though the models given can be a bit involved, the necessary tools are
xiv Introductory MEMS: Fabrication and Applications developed for the reader. Part II is therefore better suited for a follow-up course, or perhaps a standalone course for students with the appropriate background. Alternatively, an introductory course covering Chapters 1-7 could culminate with one modeling chapter from Part II. The last chapter on microfluidics is in some sense a standalone treatment of the field. Just as no one is able to design a functioning power plant after having taken an introductory course in thermodynamics, no one will be able to design, build and test a successful MEMS device after only reading this text. However, the reader will have acquired the new skill of considering microtechnology-based solutions to problems, as well as the ability to speak intelligently about MEMS and how they are modeled. The text can therefore serve as both a springboard for further study or as an end in itself. One of the challenges in writing such a text is that it is a bit like writing a book entitled Introduction to Science and Engineering, as this is what MEMS really is science and engineering at the microscale, that is. It can therefore be quite difficult to keep it truly general. By making the intended audience an undergraduate technical major in any field, and therefore not assuming any other specialized background, we have avoided slanting the text in some preferred direction. That is to say, we have done our best to keep the text a true introduction to MEMS as a whole rather than an introduction to, say, dynamic systems modeling of MEMS devices, or materials engineering aspects of MEMS. The opposite danger, of course, is not including enough material to really understand MEMS. To address this, where needed we have included introductions to fields that are generally not part of the common experience of all technical majors. The introductions are kept brief, as they are intended to give the reader just enough background to understand the field in context of the MEMS device(s) at hand. Naturally these sections can be omitted when tailoring a course for specific majors. In reading the text, most readers will find themselves outside of their comfort zone at some point. At other times the reader may find themselves reading things that seem obvious. Which things are which will be different for different readers, depending on their backgrounds. What s more, readers may occasionally find themselves a trifle disoriented even within a field in which they have heretofore considered themselves well-versed. A prime example is Chapter 12 on microfluidics, in which electro-osmotic flow is treated. In electro-osmotic flow the traditional fields of fluid mechanics and electrostatics, topics usually thought of as having little to do with each other, are coupled and of equal importance. Throw in a smattering of mass transfer and chemistry and you have a topic in which very few of us can hit the ground running.
Preface xv Such is the world of MEMS. Scientists and engineers of all fields are necessarily drawn to one another in order to make things work. The cliché that the world is getting smaller has found new metaphorical meaning with the miniaturization of technology. It is for this very reason that we feel so strongly that this text and the types of courses it is designed to accompany are vitally necessary in the education of scientists and engineers. Gone are the days when technical professionals could pigeonhole themselves into not venturing outside of narrow areas of expertise. Multidisciplinary endeavors are all the buzz anymore, and rightfully so. For MEMS they are its very lifeblood. ACKNOWLEDGEMENTS Such a book is never truly the work of only it authors. Countless people have come together to make this happen. Many thanks go to the members of the Rose-Hulman MiNDS Group for their numerous selflessly given hours to make MEMS more assessable to a general audience: Jameel Ahmed, Daniel Coronell, Pat Ferro, Tina Hudson, Elaine Kirkpatrick, Scott Kirkpatrick, Michael McInerney, Daniel Morris, Jerome Wagner and Ed Wheeler. Thanks also to the students over the years with whom we ve worked and learned. We wish we had delivered you this text earlier. Special thanks to Azad Siahmakoun, director of the Micro-Nano Devices and Systems Facility at Rose-Hulman Institute of Technology, without whom undergraduate MEMS education would not exist at all at our institution, let alone a textbook. Thom extends extra special thanks to Diedre Adams for all the corrections and wonderful suggestions, and also for simply putting up with him. That s for both the little things and the big things. THOMAS M. ADAMS RICHARD A. LAYTON TERRE HAUTE, INDIANA