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Experimental Investigation and Numerical Simulation of Composite Electrical Contact Materials for Microelectromechanical...


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EXPERIMENTAL INVESTIGATION AND NUMERICAL SIMULATION OF COMPOSITE ELECTRICAL C ONTACT MATERIALS FOR MICROELECTROMECHANICAL SYSTEMS APPLICATIONS By DANIEL JOHN DICKRELL III A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Daniel John Dickrell III

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This document is dedicated to my wife Pamela.

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Invictus Out of the night that covers me, Black as the Pit from pole to pole, I thank whatever gods may be For my unconquerable soul. In the fell clutch of circumstance I have not winced nor cried aloud. Under the bludgeonings of chance My head is bloody, but unbowed. Beyond this place of wrath and tears Looms but the Horror of the shade, And yet the menace of the years Finds, and shall find, me unafraid. It matters not how strait the gate, How charged with punishments the scroll, I am the master of my fate: I am the captain of my soul. -William Ernest Henley, 1849-1903

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v ACKNOWLEDGMENTS I thank my advisors, Dr. W.G. Sawyer a nd Dr. M.T. Dugger, for their sagacious guidance. I thank my laboratory associates in Gainesville for their assistance in assembling this document: Luis Alvarez, Nate Mauntler, Nick Argibay, Vince Lee, Dr. Jerry Bourne, Ben Boesl, Jason Bares, A lison Dunn, Dave Burris and Matt Hamilton. I would also like to thank my co-workers at Sandia National Laborat ories in New Mexico for their assistance in conducting the rese arch: Rand Garfield, Liz Sorroche, Tom Buchheit, John Franklin, Tony Ohlhausen, Wayne Buttry, Ron Goeke, Jon Custer, Paul Vianco, Jim Knapp, Dave Follstaedt, and John Jungk.

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vi TABLE OF CONTENTS page ACKNOWLEDGMENTS...................................................................................................v LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix ABSTRACT.......................................................................................................................xv CHAPTER 1 INTRODUCTION........................................................................................................1 2 BACKGROUND..........................................................................................................9 MEMS Electrical Contacts...........................................................................................9 Fundamental Concepts................................................................................................11 Contact Area........................................................................................................11 Contact Resistance...............................................................................................17 Contact Size Effects............................................................................................19 Adhesion..............................................................................................................20 Thermal Effects of Electrical Current.................................................................22 Surface Contamination........................................................................................26 3 EXPERIMENTAL APPARATUS.............................................................................29 Bulk-Film Electrical Contact Testing.........................................................................29 Modified Nano-indentation System....................................................................29 Data Acquisition..................................................................................................33 Single Contact Cycle...........................................................................................34 MEMS Electrical Contact Device..............................................................................35 Device Fabrication Process.................................................................................36 Device Design.....................................................................................................38 MEMS Experimental Testing..............................................................................40 4 CONTACT MODELING...........................................................................................45 Rough Surface Contact Modeling..............................................................................45 Real Surface Contact Simulation................................................................................51

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vii Electrical Current Modeling.......................................................................................54 Combined MEMS Electrical Contact and Current Modeling.....................................60 Thermal Modeling......................................................................................................66 Adhesion Modeling....................................................................................................67 5 COMPOSITE ELECTRICAL CONTACT MATERIALS........................................72 Percolation Threshold.................................................................................................72 Experimental Investigati on of Composite Films........................................................79 Film Deposition...................................................................................................79 TEM Imagery......................................................................................................82 Experimental Results...........................................................................................84 Composite Current Flow Simulation..........................................................................86 6 DISCUSSION.............................................................................................................92 7 CONCLUSIONS........................................................................................................97 APPENDIX A HOT-SWITCHED ELECTRICAL CONTACT RESISTANCE DEGRADATION.99 Carbonaceous Surface Contamination Effects...........................................................99 Silicone Oil Contamination Effects..........................................................................114 B MODIFIED NODAL ANALYSIS...........................................................................125 LIST OF REFERENCES.................................................................................................130 BIOGRAPHICAL SKETCH...........................................................................................138

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viii TABLE Table page 3-1 ECR nano-indentation system capabilities...............................................................31

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ix LIST OF FIGURES Figure page 1-1 Example of a MEMS device......................................................................................1 1-2 Taxonomy chart of MEMS devices grouped by tribological complexity..................2 1-3 Illustration of the operational frequency range of MEMS switches..........................4 1-4 Rockwell RSC MEMS metal-metal switch................................................................5 1-5 Metal contact interface of a series-switch in the up and down device state...............5 2-1 Previous low-force electri cal contact resistance studies..........................................10 2-2 Experimental MEMS devices with electrical contacts.............................................11 2-3 Example of MEMS elec trical contact surface..........................................................12 2-4 Atomic force microscopic image of the surface roughness of a deposited gold contact surface..........................................................................................................13 2-5 The difference between mechan ical and metallic contact area................................14 2-6 Illustration of the Greenwood-Williams on model and required input parameters...16 2-7 Illustration of a cont act constriction caused by in teracting rough surfaces.............18 2-8 The combination of constriction and contamination film resistance.......................19 2-9 Adhesion map for elasti cally contacting spheres.....................................................22 3-1 Nano-indentation system used in low force ECR testing.........................................30 3-2 Contact zone schematic............................................................................................30 3-3 Coated wafer sample dimensions.............................................................................31 3-4 Deposited film stack for bulk film ECR testing.......................................................32 3-5 White-light interferometry topographi c scans of the as-deposited primary gold layers on the sphere and flat contact samples..........................................................32

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x 3-6 Diagram of the mechanical and electrical data-acquisition system constructed to time synchronize the experiments............................................................................33 3-7 Example of one experime ntal contact cycle for a gol d-gold sphere-flat contact.....34 3-8 Optical micrograph of electrical contact MEMS device..........................................36 3-9 SEM micrograph of the contact dimple on the underside of the cantilever beam device.......................................................................................................................36 3-10 Electroplating deposition process fo r MEMS contact device fabrication................37 3-11 Cantilever MEMS device in up and down-states.....................................................38 3-12 Electrostatic actuation force dependen ce removal from the contact force using the pull-down landing pads to geom etrically constrain the device..........................39 3-13 Finite-element analysis of the ge ometrically constrained cantilever beam..............40 3-14 MEMS electrical contact devi ce probed in the Wyko NT1100 DMEMS instrument.................................................................................................................41 3-15 Height profiles of up and down-state devices..........................................................42 3-16 Results of hot-switched electrical contact resistance testing of the MEMS cantilever device.......................................................................................................43 3-17 Example of resistance degradation for hot-switched contact in the same location..44 4-1 An example of an optical su rface profilometer, a Wyko NT-1100..........................46 4-2 Discretized surface scan obtai ned from optical profilometry..................................46 4-3 A voxel surface constructed from a profilometer-obtained data scan......................47 4-4 Two separated voxel surfaces..................................................................................48 4-5 Voxel contact interaction.........................................................................................48 4-6 Rigid, perfectly-plastic constituativ e material model used for voxel contact interactions...............................................................................................................49 4-7 Histograms of the surface height data about the mean plane taken from Fig. 4-2...51 4-8 Gold-coated Si3N4 ball bearing voxel surface..........................................................52 4-9 Gold-coated silicon wafer voxel surface..................................................................53

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xi 4-10 Predicted contact area using rigid-pe rfectly plastic voxel rough surface contact model, Hertzian contact model, and Greenwood-Williamson statistically-based model for the same gold-gold contact surfaces under a 60 mN load.......................53 4-11 Focused ion-beam cross section of a gold-gold MEMS electrical contact..............55 4-12 Magnified view of the MEMS electrical contact.....................................................55 4-13 Schematic of electrical contact formed from the contacting members of Fig. 412............................................................................................................................. .56 4-14 Idealized model of a MEMS electrical contact........................................................56 4-15 Composite thin-film electrical contac t showing the effect of interfacial constituents on adhesion on intern al constituent on resistance................................57 4-16 Random resistor network approach to compute the resistance of a composite electrical contact material.........................................................................................58 4-17 Simplified representation of the RR N used to solve for the resistance....................59 4-18 Contact window created by voxel surface method...................................................60 4-19 AFM scan of surface topography for the electroplated gold contact dimple...........61 4-21 Contact area for a 1.25 N normal load applied to the contact dimple and signal layer surfaces............................................................................................................62 4-22 Depiction of the three-dimensional RRN used to calculate contact resistance........63 4-23 Current map for the contact shown in Fig. 4-21. The highest currents are concentrated at the periphery of the contact.............................................................64 4-24 Current maps of the layers 1-5 of th e 3-D RRN as the current descends toward the contact layer and forced through the constriction..............................................65 4-25 Discretized heat conduction model..........................................................................66 4-26 Temperature rise map for the Ohmic hea ting due to the electr ical current passage of Fig. 4-21...............................................................................................................67 4-27 Population of an discretized cont act island with an array of atoms.........................69 4-28 TEM image of gold nanowire forma tion from unloading of AFM contact experiments..............................................................................................................70 5-1 Different electrical composite mode ls, series-addition, parallel-addition, and randomly distributed................................................................................................73

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xii 5-2 Normalized composite resistivity as a function of decreasing gold percentage for series-addition, parallel-addition, and randomly distributed models.......................75 5-3 TEM image of a co-sputtere d gold-MoS2 composite film......................................76 5-4 Numerical simulation of the curr ent flow through a 10% gold composite..............76 5-5 Numerical simulation of the curr ent flow through a 35% gold composite..............76 5-6 Numerical simulation of the curr ent flow through a 45% gold composite, percolation threshold occurs in between Fig 5-5 and 5-6........................................77 5-7 Numerical simulation of the curr ent flow through a 66% gold composite..............77 5-8 Numerical simulation of the curr ent flow through a 93% gold composite..............77 5-9 Normalized composite resistivity of the contract-modulated TEM images showing percolation threshold of 37%.....................................................................78 5-11 TEM image of 90% gold, Au-Al2O3 PLD composite..............................................83 5-12 TEM image of 50% gold, Au-Al2O3 PLD composite.............................................83 5-13 TEM image of 20% gold, Au-Al2O3 PLD composite..............................................84 5-14 Normalized PLD composite film electrical contact resistance and adhesive force nano-indentation results...........................................................................................85 5-15 Resistance of PLD Au-Al2O3 composite films.........................................................86 5-16 Current maps for a 50 % gold composite.................................................................88 5-17 Normalized composite resistivity for 3,750 total contact current simulations as a function of gold percentage and hi gh-resistivity phase resistivity...........................89 5-18 Difference between uniform random a nd graded random distribution of highresistivity phase filler particles as a function of depth away from the contact interface....................................................................................................................90 5-19 Effects of high-resistivity phase dist ribution on percolation threshold for the uniform and graded random distributions................................................................91 6-1 Potential composite material location in the MEMS electrical contact device fabrication process....................................................................................................95 6-2 Regions of acceptable and undesirable resistance for gold-alumina composites approaching and beyond the percolation threshold..................................................96

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xiii A-1 Schematic of the nano-indentation appa ratus and the contact zone used in hotswitched cyclic contact testing...............................................................................100 A-2 Single hot-switched expe rimental contact cycle....................................................102 A-3 Cyclic electrical c ontact resistance degrad ation of Au-Pt contact.........................103 A-4 Inert environment and reduced current testing.......................................................104 A-5 Cyclic resistance degradation for inert environment testing with momentarily increases peak load to 1 mN for cycles 198-208, up from 150 N for all other cycles......................................................................................................................105 A-6 Resistance vs. time for individual contact cycles from Fig. A-5 with the grey area denoting the peak-load hold period................................................................106 A-7 Magnified views of cycle 1 and cycl e 200 from Fig. A-6 showing the amount of force required to obtain low resistance for non-degraded and degraded contacts.107 A-8 Dependence of resistance degr adation on hot-switched contact............................110 A-9 Dependence of resistance degrad ation on capacitive-quench presence.................111 A-10 Oscillograms showing the change in vo ltage transients at moments of close surface contact after capacitive-q uench circuit is removed....................................112 A-11 Auger Electron Spectra of suspec ted contamination region and of the surrounding metal surface......................................................................................113 A-12 Schematic of the contact zone w ith silicone oil introduced between the electrodes................................................................................................................116 A-13 Resistance degradation of silicone oil contaminated gold-gold contact................116 A-14 Resistance and load history fo r contact cycle 14 from Fig. A-13..........................117 A-15 Resistance degradation dependence on gap closure rate for an applied voltage of 3.3 V.......................................................................................................................118 A-16 Resistance degradation on contact gap vo ltage for an approach rate of 86 nm/s...118 A-17 Cycles to failure (R > 50 Ohms) depe ndence on time spent in the critical gap distance of 30 nm...................................................................................................121 A-18 Oscillograms of contact voltages at closure rates of 400 to 40 nm/s.....................122 A-19 Mechanical load required to attain at least 1 after degradation occurred (zero load required at 1 V sinc e no degradation occurred).............................................123

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xiv B-1 Example circuit for A matrix construction.............................................................127

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xv Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EXPERIMENTAL INVESTIGATION AND NUMERICAL SIMULATION OF COMPOSITE ELECTRICAL C ONTACT MATERIALS FOR MICROELECTROMECHANICAL SYSTEMS APPLICATIONS By Daniel John Dickrell III August, 2006 Chair: W.G. Sawyer Major Department: Mechanic al and Aerospace Engineering The performance and reliability issues a ssociated with microelectromechanical system (MEMS) electrical contact devices have precluded the wi despread adoption of MEMS devices employing electri cal contacts. Composite elec trical contact materials, gold-alumina, gold-titanium n itride, and gold-nickel, were developed to address the issues that plague MEMS electrical cont acts by reducing the am ount of interfacial adhesion while maintaining acceptable levels of electrical conductivity. The composite materials were experimentally investigated and compared to numeri cal simulations which predicated how the novel materials would perform. Experimental and numerical simulation results found that composite electr ical contact materials could enhance the performance of low-force electrical contact s if the ratio of high-conductivity to lowconductivity phases of the compos ite remained larger than a critical ratio, referred to as the percolation threshold.

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1 CHAPTER 1 INTRODUCTION Microelectromechanical Systems or MEMS, are microsc opic structures that combine mechanical and electronic elements into complex small machinery. Figure 1-1 shows an example of a MEMS device fabricat ed at Sandia National Laboratories. These devices, often the size of a grai n of sand, act as links between digital electronics and the physical world. The device pictured in Fig. 11 is a good illustration of the combination of mechanical elements (the gears) and el ectrical elements (the electrostatic drive actuators), into a functional system. Figure 1-1. Example of a MEMS device. The driv e actuators rotate the gears of the gear train which pushes a rack and causes a hi nged mirror to rise and redirect an incident laser beam [www.mems.sandia.gov] MEMS technology has been demonstrated in research and development facilities for about 25 years, but has been in production for almost 20 years as accelerometers in

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2 the automotive sector, one of the most wi dely used applications for MEMS devices today. Current MEMS products span a wi de range of applications including environmental sensors, micro-switches, a nd medical devices. From a tribological standpoint, the degree of surface interaction in a MEMS device relate s to how successful the device will be at attaining widespread adoption in the world outside of the laboratory. Figure 1-2 shows a taxonomy chart illustrating the increas ing degrees of tribological complexity inherent in a MEMS device [1]. Figure 1-2. Taxonomy chart of MEMS devices grouped by tribological complexity [1] The most widespread use of MEMS t echnology has occurred in the automotive sensor field. The reason for this successful deployment lies in the nature of the MEMS structures used for automotive accelerometers, and gyroscopes are fabricated as planar, monolithic structures with no interacting surf aces, typified by Class I device in Fig 1-2. Since no surfaces of the devices touch, the ope rational lifetime of these devices is not

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3 affected by problems originating from tribologic al effects, such as friction or wear, but solely by the material proper ties of the MEMS device. As the tribological complexity of MEMS de vices increases, the amount of attention paid to the interaction of the device interf aces becomes more important. To date, only a few Class III devices have been successfully deployed outside the laboratory. The most well-known example of a successful Class III device is the device at the heart of Digital Light Processing (DLP) television displays, the Texas Instruments Digital Micro-mirror Device (DMD). The tribological sources of failure in the DMD, friction, wear, and adhesion, were all eventually overcome after a large expenditure of research capital. In all of the examples of successful commercial adoption of MEMS tec hnologies the ability to mass-produce devices with well-contro lled physical properties, repeatable performance, and long lifetimes has been critical. Of all of the potential applications wh ere Class III and IV MEMS devices could, but as of yet have not, made an impact, el ectrical switching and relaying is an area of intense development. The goal of MEMS sw itches and relays is to replace legacy electronic switching components w ith smaller, more efficien t micro-system components. However, applications where electrical energy must be diverted, interrupted, or otherwise modified represent a challeng ing operational environment for any device to operate effectively for a long period of time. As it stands, MEMS devices with dynamically operating electrical contacts have had limited success in supplanting larger switches for use in commercial or defense applications due to performance and reliability limitations. Figure 1-3 shows the frequency spectrum in which MEMS switches operate. The main difference between switch types in Fig. 1-3 is the contact material used to affect the

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4 system electrical signal. Meta l-metal contact devices are us ed as series-switch devices, while non-metallic capacitive materials are us ed in capacitive-coupled shunt-switches. Metal-metal contact switches possess contact interfaces that carry electrical current, whereas capacitive-coupled switches only change the capacitance of the transmission line the signal is carried on and do not directly carry current. Figure 1-3. Illustration of the operational frequency range of MEMS switches An example of a metal-metal series switc h is shown in Fig. 1-4. When the movable middle switch-plate with electr ical contacts is brought down in to contact with the signal lines, a continuous conductive metal path is made between the two signal lines via the contact pads. This enables the electrical si gnal to flow through the switch. The signal is blocked when the middle plate is raised. Figure 1-5 shows a simplified schematic of how the metal contact interface of an metal-metal contact MEMS device is used to mo dulate electrical signal. In the up-state, a small gap of approximately 1~2 m exists between the movable device surface and the signal transmission line. When the device is actuated, either by electrostatic or thermal

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5 actuators or by environmental acceleration, the m ovable surface is forced into the signal line and electrical signal current is ca rried through the c ontact interface. Figure 1-4. Rockwell RSC MEMS metalmetal switch [www.rockwell.com] Figure 1-5. Metal contact interface of a seri es-switch in the up and down device state. The contact interface is responsible for electrical current signal transmission and is the source of pr emature device failures

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6 The advantage of metal-metal contact devi ces over capacitive-coupled devices is that the insertion loss, the decrease in transmitted signal power, associated with lowfrequency operation is much smaller for metalmetal contacts versus capacitive contacts. Due to the reduced losses incurred during low-frequency operation, metal-metal contact series-switch devices allow a higher-bandwid th operational envelope than capacitivecoupled devices. The broadband capabiliti es of metal-metal MEMS switches is however offset by the tribologi cal problems associated with metal contact interfaces. The electrical contact in terface formed between the moving metal surface and the stationary metal surface shown in Fig. 1-5 pr imarily determines how the MEMS switch performs. Almost all of the mechanisms that affect performance and cause device operational failure originate at the metallic contact interface. Segregating the failure mechanisms into distinct categories, two predominant failure modes arise which cause MEMS electrical contact devices to fail pr ematurely: unacceptably high electrical contact resistance and excessively high metallic adhesion. The first common failure mode of a MEMS electrical contact device is that the electrical resistance of the contact interface exceeds an acceptable resistance threshold. This is caused by a non-conductive material being formed or migrating into the region of contact and inhibiting electri cal current flow. These forei gn surface species may be native oxides, in the case of copper or silver contacts, or adsorbed contaminants, such as carbonaceous films, that originate from the ambient atmosphere or other sources of contamination. The solution to th is failure mechanism is to keep the electrical contact interface and surrounding environment as cl ean as possible, ensuring that the any contaminants are separated from the contact interface for as long as possible. This also

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7 includes choosing contact materials which will remain stable and not decompose or oxidize during storage and operational lifetime. The second common failure mode occurs wh en the metallic contact surfaces adhere so strongly that the surface cannot be separated and the MEMS device becomes permanently closed in the down-state, disallow ing further operational cycles. If the real contact area in the electri cal contact interface becomes la rge enough, the adhesive surface forces may overwhelm the devices ability to separate the contact. Electrical contact materials form very strong metallic bonds and a large metallic contact area can precipitate excess adhesion in the device. The el astic restoring force of the device is most often the only means of separating the contac t interface surfaces. The generally compliant nature of MEMS device structures means th at adhesive forces must be minimized for extended device operation. Excessively high co ntact interface adhe sion can also occur from thermally-induced contact welding, but mo st incidents of contact sticking originate from the metallic-bond adhesive forces existing between the MEMS electrode surfaces. The solutions to improving the performance of MEMS electrical contacts lie in the three device design parameters which can be altered: applied normal load, contact geometry, and contact material selection. The applied normal load range available from MEMS actuators, typically of electrostatic, thermal, or magnetic origin, are limited on average to only a few hundred micro-Newtons. Mechanical disruption of oxide layers and tenacious surface contaminants can require larg er force than this, removing the capability of the MEMS actuator to produce a conductive surface contact. The contact geometry of MEMS contacts is frequently limited to plan ar contacts due to th e fabrication methods used to created the devices. While intenti onal contact surfaces ar e achievable through the

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8 patterning of contact dimples, even these ar e planar contacts dominated by the surface roughness of the contact material. From the electrical and adhe sion standpoint, contact materi al selection remains as the best and most diverse me thod of addressing the predomin ant failure modes that occur in MEMS electrical contact devices. The mate rials that compose the electrical contact interface of MEMS devices are usually chosen from a set of specific materials, most often noble metals, because of their beneficial material properties like electrical and thermal conductivity, and resistance to form ation of surface films. MEMS electrical contact materials can be deposited separately from the structural ME MS device material, affording the choice of what and how much mate rial is used in the contact layer. This amount of control over the composition of th e contact material is an advantage that MEMS electrical contact devices has over macro-scale electrical contacts. From a problem-solving standpoint, devising a c ontact material which is simultaneously conductive and non-adhesive and able to be integrated into th e MEMS fabrication process, appears as the most promising solu tion to addressing MEMS electrical contact failures. This document describes an approach to model the characteristics of deposited electrical contact materials for use in MEMS electrical contacts that addresses both the goals of high conductivity and low adhesion, an d efforts to fabricate and evaluate such materials in low-force electrical contacts.

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9 CHAPTER 2 BACKGROUND MEMS Electrical Contacts There have been many previous investigations of electrical contacts at low applied contact forces, with research ers employing various experiment al techniques to study the behaviors and phenomenon associat ed with electrical contacts at force levels under 1 N [2-19]. Some of these studies are directly relatable to MEMS device contacts as they deal with the same materials, precious metals like gold and platinum, and applied force levels, under a milli-Newton, seen in microscale com ponents. Figure 2-1 summarizes the results for previously conducted contact resistance stud ies at force levels below 1 N for varied contact materials. The notable trend in Fig. 2-1 is that acro ss a sampling of independent investigations of low-force electrical contact s, the measured resistance in creases substantially as the contact load decreases. Figure 2-1 is easily constructed since most studies cite normal force applied. A figure depicting the depe ndence of contact re sistance on apparent contact pressure is more challenging to obtain since the exact experimental contact geometry is often not as clearly stated in the literature. Figure 2-2 shows a contact resistance vs. applied force plot for experi mental MEMS electrical contact devices [2030]. The applied force range shown in Fig. 22 is limited by the maximum amount of force applied by devices (~ 10 mN) and on th e low end the minimum force required to

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10 attain stable resistance (~ 100 N). The narrow operational force window for MEMS electrical contact devices cr eates a challenge to obtain lo w resistance for low contact force and still enable device release u nder the available restoring force. Figure 2-1. Previous low-force elec trical contact resistance studies MEMS electrical contact devices possess performance and reliability limitations stemming from the low operational contact fo rce, and this directly impacts their widespread acceptance for use as replacements for established commercial components. The performance and reliability, and inhere ntly the success of switches and relays, depends critically on the behavioral constanc y of the electrical contact interface which is the critical aspect of the switch. Unfortunately, the susceptibility of an el ectrical contact in terface to become degraded increases as the size of the contact decreases. This is due to the fact that surface effects become more pronounced at smaller lengt h-scales, as the ratio of surface area to volume increases with microsystem devices For MEMS electrical contacts, where

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11 interactions occur between only a small number of surface contacts, obtaining a stable, clean interface between two su rfaces over many repetitive operational cycles requires an understanding the fundamental concepts aff ecting the electrical resistance of MEMS device contacts. Figure 2-2. Experimental MEMS de vices with electrical contacts Fundamental Concepts Contact Area The current-carrying area of a contact inte rface is an important parameter affecting MEMS electrical contact performance. The bul k geometries of MEMS electrical contact interfaces resemble planar c ontacts, stemming from the de vice fabrication processes. Planar contacts emphasize the effects of surface roughness and distribution of surface asperities in determining the contact area, wh ich in chemically micro-machined devices is produced in a narrow range of variability. Figure 2-3 shows an example of a MEMS

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12 electrical contact surface [12]. The scanning-electron micrograph (SEM) in Fig. 2-3 shows the characteristic roughness of a MEMS device contact dimple. MEMS electrical contacts are typically fabricated by coating the structural sili con substrate material with a conductive metal, most often gold, that serves as the current carrying material. Electrical contacts deposited by sputtering or evapor ation retain the roughness of the silicon substrate metal, while contacts deposite d by electroplating have surface roughness determined by the plating process employed. Figure 2-3. Example of MEMS elec trical contact surface [12] A closer view of the characteristic ro ughness of a gold MEMS electrical contact surface is shown in Fig. 2-4. Instead of SE M imagery, atomic force microscopy (AFM) was used to obtain the surface topographic da ta for the gold contact surface. The characteristic roughness of the deposited gold material is visible in detail. The rough surface topography is responsible for the re sulting interfacial c ontact area when two device surfaces are pressed together. The measured average and root-mean-squared roughness for the surface shown in Fig. 2-4 are 1.37 nm and 1.71 nm, respectively. While the surface shown in Fig. 2-4 looks very rough, there is almost a 700: 1 ratio between the

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13 lateral scale and the measured roughness of the surface, and it is in fact a very smooth contact surface. An important distinction exists between the apparent, mechanical, and electrical contact areas for a MEMS device interface. Fi gure 2-5 shows the differences between the different types of contact area. The apparent area of contact is th e total amount of area where probable contact exists for a device. Th e real area of mechan ical contact is the actual amount of the apparent area where mechanical load is reacted between the interacting surfaces. The electrical, or me tallic, contact area depends on the surface contamination state of the ar eas in mechanical contact. Figure 2-4. Atomic force microscopic image of the surface roughness of a deposited gold contact surface If the mechanical area of contact is clea n, with no other spec ies other than the electrode material in the interface, then th e electrical contact area is the same as the mechanical contact area. Otherwise, if a nativ e oxide layer or alien surface contaminant is

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14 present in the contact interface, the amount of electrical cont act area that conducts current in a metallic fashion is less than that of th e mechanical contact area. If the non-metallic material covers the entire mechanical cont act area, the electrical contact resistance for that area increases, often to the severe detr iment of device operation. It is possible for very thin contaminant layers on the order of several nanom eters thick, that cover the entire area of contact to conduct current via quantum t unneling [31]. The effects of tunneling current is usually neglected how ever due to the significant conduction difference present between metallically-conducti ng contacts and contacts covered with very thin films. Figure 2-5. The difference between mechanical and metallic contact area The amount of mechanical contact that ex ists between two electrode surfaces must be determined before the effects of surface contaminants can be factored in to how

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15 electrical surfaces perform. A survey of previously developed rough surface contact models shows a multitude of approaches that attempt to resolve the mechanical contact area. The earliest calculation of the mechani cal area formed from two interacting bodies was developed by Hertz (32). The well-known Hertzian contact model assumed that the area formed by two spherical bodies in c ontact was dependent on the material elastic properties, geometry of the contact bodies and the force pressing the bodies together. The expression for the contact radius of the circular contact area is shown in Eq. (2.1), where the combined radius and elastic modulus are 1212'/ R RRRR and 1 22 1122'1/1/ EvEvE respectively. 1/3 '3 4nFR a E (2.1) A different contact modeling approach a ssumed that the local stresses at the asperity level, instead of elastic, always exceeded the elastic limit of the material and plastically deform. This assumption implied that real contact area was only related to the applied load and the material indentation ha rdness and independent of geometry [33]. This approach also ignored any effects surf ace roughness contributed to the contact area calculation. Equation (2.2) shows the expres sion for contact area assuming only plastic deformation of the surfaces. n cF A H (2.2) Later modeling incorporated the eff ects of surface roughness on contact area calculation. Greenwood and Williamson (GW) pr oposed a statistically-based asperity contact model based on the separation of a deformable rough surface and an ideally smooth, rigid plane [34]. From the relative interference between the rigid plane and the

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16 rough surface, it was possible to compute resultant contact area and load supported by knowing the height-wise distribut ion of surface asperities, th eir overall shape, and their material composition. The key assumptions of this model were that all asperities in contact were spherical and had the same radi us of curvature, there was no interaction between neighboring asperities, and that th e asperity heights followed a continuous, statistical distributi on (assumed to be normally distri buted). Figure 2-6 depicts the assumptions of the GW model. Figure 2-6. Illustration of the Greenw ood-Williamson model and required input parameters Equations (2.3 2.5) show the develope d expressions for contact area, load supported, and asperity height probability dist ribution as a function of asperity number, N, average asperity radius of curvature, composite elastic modulus, E height distribution standard deviation, and normalized surface separation, / hd 1 c A NSh (2.3) 1/23/2 3/24 3nFNESh (2.4) 21 21 () 2s n n hShsheds (2.5) While initially assuming purely elastic Hertzi an surface contact, a primary result of the GW model was the plasticity index. This index determines in which regime the

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17 predominance of individual asperi ty contacts reside, elastic or plastic, for various contact material and geometries. The plasticity index formula is shown in Eq. (2.6). Values of >1 correspond to predominantly plastic contacts, while <1 show increasing amounts of elastic contacts. The variable H represents the indentatio n hardness of the softer material. E H (2.6) Succeeding refinements to the popular GW model relaxed some of the key assumptions used in its formulation. Numerically simulated surface contacts incorporated anisotropically distributed, el liptically paraboloidal asperi ties. These simulation results differed only slightly from that produced by the GW model [35, 36]. Another study found that for two rough surfaces in contact, even if the contacts do not occur exactly at the asperity peaks, the resulting contact area is ne gligibly different from that of a composite rough surface touching a smooth rigid plane [37] These subsequent studies demonstrated that the GW model was a good approximati on for two contacting rough surfaces even though the assumptions it is based upon are not overly complex, as long as the asperityheight distribution is stat istically valid for the su rfaces under consideration. Contact Resistance The ability of rough surfaces to conduct el ectric current throu gh a contact interface is closely linked to the contact area calculatio ns outlined in the previous section. It is through these finite contact in terfaces that the entire am ount of electrical energy is constrained to flow. Ragnar Holm is most ofte n credited for the resistance calculation of a mono-metallic contact constriction,c R shown in Eq. (2.7). In Eq. (2.7), is the resistivity of the material and a is the radius of the contac t area which is assumed to be

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18 circular [33]. Figure 2-7 depicts how the contact area formed between two bodies in contact constricts current moving from th e top surface to the bottom. A detailed derivation of this equation is given by Jones [38]. 2cR a (2.7) Figure 2-7. Illustration of a contact constriction caused by interacting rough surfaces If dissimilar metals are in contact, an approximation for the constriction resistance is to use the average resistivity of the two contacting materials in the equation, 12/4c R a. The contribution to the total contact resistance by the interaction of many small contact areas was calculated previo usly [39,40]. The approximate formula for the constriction resistance in cluding the contribution from n parallel contact spots separated by a distance d is shown in Eq. (2.8). 21 2c ij iijR and (2.8) The constriction resistance equation fo r a single interface was derived assuming completely clean metallic contact. If contamin ation exists between metallic contacts, then the resistance of the contamin ant film must be added to the constriction resistance. An

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19 approximate equation for the contact resistan ce including contaminant films is shown in Eq. (2.9). The resistivity of contaminant ma terial is usually much greater than the resistivity of the contact materials. If contact surfaces are contaminated, the overall resistance may be dominated by the contaminant film resistance and totally irrespective of the constriction resistance [19]. Figure 211 depicts how interfacial contaminants can affect current flow in a metal contact. 12 24 f ilm ct R aa (2.9) Figure 2-8. The combination of constric tion and contamination film resistance Contact Size Effects The mechanism responsible for the electrica l resistance in metals is the diffusive scattering of electrons trave ling through the latti ce structure of the conducting material. Contacts below a certain size thre shold begin to experience a di fferent type of resistance, called ballistic conduction resistance, as the size of the constriction becomes the same order as the mean-free-path of electrons in the conductor, ~ 10 nm. This resistance, often called the Sharvin resistance, is shown in Eq. (2.10). It has been cited as a reason for observed deviations in expected behavior of electrical contact resistance studies for contacts on the order of te ns of nanometers [17, 41].

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20 24 3e sR a (2.10) Interpolation equations were developed th at enabled the calculation of combined electrical constriction resistance in the in termediate regions between nanometer-scale ballistic resistance and diffusive el ectron-scattering resistance [42,43]. Adhesion The adhesion between the metal contact su rfaces of MEMS de vices is also of concern because too much adhesion can cause de vices to become stuck in the down state, which renders the device inoperative. Howeve r, the GW model used the purely elastic Hertzian contact model to express contact area and load as a function of surface separation, and adhesive effect s on the contact area size were neglected. Se veral studies sought to remedy this oversight by including the effects of adhesive forces in contact area calculation. Johnson, Kendall, and Roberts (JKR) found the solution of an adhesive elastic contact between two spheres using an energy balance approach [44]. The JKR pull-off force required to separate the contact is shown in Eq. (2.11), where 1212 is the Dupre equation for the ener gy of adhesion between two surfaces, and R is the effective radius of the spheres. The JKR-modified contact radius, shown in Eq. (2.12), includes the adhesive surface for ce contribution to the contact area. As the surface energy diminishes, 0 Eq. (2.12) reverts back to the classical Hertzian equation for contact radius, Eq. (2.1). '3 2poFR (2.11) 22 2 3''' 12 1211 3 363 4nnaRFRRFR EE (2.12)

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21 Derjaguin, Muller, and Toporov (DMT) sepa rately solved the same problem using a thermodynamic approach and determined the pull-off force to be slightly different, shown in Eq. (2.13) [45]. The DMT approach assumed that the Hertzian contact area is not altered by the surface force and only th e pull-off force required to separate the surfaces is affected. '2poFR (2.13) The discrepancy between the two models conc erning the pull-off force was resolved later [46]. It was proposed that the JKR and DMT solutions were both accurate, but existed on opposite ends of the same solution space. An adhesion parameter was introduced, shown in Eq. (2.14), which linked the two s eemingly disconnected theories. The quantity 0z is the interatomic distance between the surfaces in cont act, typically less than a nanometer depending on the material. 1/3 '2 23'oR Ez (2.14) The adhesion parameter represented the ratio of the elastic displacement of the surfaces at the point of separation to the effective range of the surfaces forces. The parameter value 1 corresponded to large compliant spheres, as in the JKR theory. The DMT model corresponded to small rigid spheres and adhesion parameter values of 1 The JKR and DMT models do not depend on the exact form of the surface force potential immediately outside the contact region. However, Maugis developed an analytical solution for the a dhesive contact of elastic sphe res, using a Dugdale squarewell surface force potential (M-D), which spa nned the intermediate region between the JKR and DMT extremes [47]. The M-D mode l also contained a transition parameter which was almost equivalent to 1.16 A numerically-fit transition equation was

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22 developed that very accuratel y fit the M-D analytical solution and allowed for easier analysis of contacts in the JKR-DMT tran sition [48]. A graphical adhesion map was created that could be used to determine in which adhesive regime a contact resided as a function of and the ratio of the applied load to the adhesive pull-off force, '/ PPR [49]. Figure 2-9 shows the adhesion map. W ith the development of these models, the adhesive contribution to the area of contact for spherica l contacts could be calculated to account for adhesive effects on the contact area and pull-off force of rough surface contacts. Figure 2-9. Adhesion map for elas tically contacting spheres [49] Thermal Effects of Electrical Current The conventional treatment of electrically heated cont acts assumes that the only dissipation path for resistive heat produced within a contact is by conduction out through the bulk materials in contact. Within this constraint, the lines of equal potential for electrical current and heat flow within the conductor happe n to coincide. Consequently, the lines of current and heat flow also coinci de. Kohlrausch was the first to recognize this relation and derived Eq. (2.15), now called th e Kohlrausch voltage-temperature relation

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23 for electrical contacts [50]. Equation (2.15) relates the maximum temperature rise above the bulk material temperature in the contact, to the voltage-drop across the contact, the mean electrical resistivity, and the mean thermal conductivity, k. 28 V k (2.15) A more rigorous derivation of the voltage-t emperature relation that includes the temperature-dependent variation of electrica l resistivity and ther mal conductivity in the final result was derived [51]. If the contact temperature rise calculated with Eq. (2.15) appreciably affects the material electrical resistivity and thermal conductivity, then the more rigorous formulation, shown in Eq. (2. 16) is the more valid method of determining contact temperature rise. 2 08Vkd (2.16) The voltage-temperature re lation only gives a steadystate calculation of the contact temperature. A numerical model was de veloped to solve for the transient thermal response of two bodies communicating through a small circular contact area [52]. Those results reiterated earl ier calculations that the time c onstant required for stationary electrical contacts to reach near-equilibrium temperatures at locations adjacent to the contact is very short, on the order of microseconds depending on the material. The temperature rise was calculated for a circul ar constriction of two semi-infinite bodies [50,53]. The time constant for the solution was found to be 2/4 cak where c is the heat capacity per unit volume of the material, ais the radius of the constriction, and k is the thermal conductivity of the contacting bodies From these findings, thermal transient effects are only considered in applications of rapidly moving contacts, such as brush

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24 contacts, or in high-frequency power connec tions, otherwise the steady-state conditions for contact heating are primarily considered. A common simplification of the voltage-t emperature relation can be made by utilizing the correlation betw een electrical and thermal c onductivities and temperature, known as the Wiedemann-Franz law. This la w is shown in Eq. (2.17) and holds if electrical resistivity and th ermal conduction arise from elect ron transport in metals. The constant L is known as the Lorentz constant and has a value of 2.45E-8 V2 K-2. kLT (2.17) The voltage-temperature relation in Eq. (2.15) can be recast as Eq. (2.18) using the Wiedemann-Franz law expression. Its use is su itable in the temperatur e range of ordinary electrical contacts [50]. 24V L (2.18) However, the applicability of the voltage-tempe rature relations of Eq. (2.15) and Eq. (218) has been questioned for contacts smalle r than a micrometer. Although the voltagetemperature relation of Eq. (2.15) is irrespec tive of contact size, the resistance of small contacts with characteristic dimensions well under 1 m experimentally deviate from its predicted behavior [41]. This is due to th e assumption of a perfectly insulated contact being less valid with shrinking contact si ze as the conductive effects of oxide or contaminant films become more pronounced, as the second term in Eq. (2.9) begins to dominate the interfacial current conduction. The resistance mechanism, mentioned in th e previous section, also determines the degree of resistive heating e xperienced by a contact. Contact s with sizes well above the ballistic-conduction threshold ge nerate heat from diffusive sc attering of lattice electrons, otherwise known as Ohmic heating. Since the ballistic-conduction mechanism originates

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25 from boundary scattering instead of conduc ting electron interact ions, Ohmic heating within the contact is negligible for ballistic electron conduction. Hence the contact will not generate heat in the manner of Eq. (2. 15) or (2.16) for contacts in the ballisticconduction regime [54]. Contacts with complicated geometries and layered contacts, common to MEMS devices where a conductive layer is usually deposited on a semi-c onductive structural layer, make using analytical electro-thermal solutions tenuous. Finite-element simulations for thermal MEMS modeling have shown prom ise in predicting where high-temperature failure events would occur [55], but the anal ytical approaches provi de rapid first-order evaluations of local temperature rise that can determine if an exhaustive computer simulation is necessary. Thermal effects from electrical current passage are governed by the required operational parameters of the MEMS devi ce. Ohmic heating caused by large currentcarrying contacts can cause melting and catas trophic surface damage in MEMS devices [8,10]. For a specified current load, larger contact areas will have a lower current densities but also be subject to larger me tallic adhesive forces. Smaller contacts reduce surface adhesion, but increase the current density in the contact and increase the susceptibility to thermal effects. Also, signi ficant non-catastrophic re sistive heating can over time drive material diffusion and segregation within multilayer films that affects contact resistance [56-58]. From a device desi gn standpoint little can be done to mitigate the affects of contact melting or diffusion if the system requirements dictate that the contact current exceed what the MEMS contact interface can handle.

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26 Surface Contamination The derivations of the cla ssical electrical contact resi stance models are based upon the assumption of clean metallic contact at the interface. If the contact surface conductivity changes enough to cause the perfor mance of the contact interface to fail to meet operational specifications, then the contact is considered to be degraded. To this end, many varied physical phenomenon such as native oxides, particles, carbon films, or mechanical damage can affect the surface c onductivity of MEMS contact interfaces and cause resistance degradation. Device surfaces exposed to regular laboratory envir onments are covered with various forms of contaminants which can aff ect contact resistance [59]. Surfaces can only be considered strictly clean when they are completely devoid of atomic species other than that of the bulk material. Since this c ondition is only obtainable on surfaces carefully prepared in ultra-high vacuum, some amount of contamination will otherwise be present on MEMS contact surfaces [ 60]. Aside from hydrocarbon or oxide surface contaminants, the presence of adsorbed water vapor had pr eviously plagued MEMS reliability due to excessive meniscus forces overwhelming the restoring force ability of MEMS devices [59]. However, the developm ent of surface water-removal methods during fabrication, such as super-critical CO2 drying, have reduced packaged device susceptibility to watermeniscus force stiction failures. This brings about a paradoxi cal problem: the cleaner th e surface, the lower the contact resistance but the higher the adhesion. It has been theorized that monolayers of carbonaceous surface contaminants actually enhance device performance by preventing cold welding of metallic contac ts without significantly imp acting contact resistance [18]. Noble metals in particular, while having ex cellent electrode material properties, are

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27 capable of forming strongly bound adsorbed contam ination layers that are highly resistant to cleaning [61]. Beyond the effects of adso rbed contaminant monolayers, the reduction of bulk contact contamination lessens the chan ce that a MEMS elec trical contact will become operationally impaired. The contact load determines to what extent surface contamination will impact contact resistance. Interfacial contaminants have been shown to adversely alter the cyclic contact resistance of low-force metal contac ts, but the influence of contaminants on electrical contact resistance is diminished as contact force is increased [62]. Lower contact forces provide less of an opportunity for contaminant films to be mechanically disturbed or ruptured in the absence of shear from interf acial sliding. Consequently, undesirably high resistances arising from pollu ted surfaces affect el ectrical performance and reliability of MEMS switches and relays to a larger extent than macro-scale components [18]. Surface contaminant presence has been s uggested as a cause for the higher-thanexpected contact resistance regime seen in metal contacts at MEMS-scale force levels. The quasi-metallic contact regime is mark ed by unstable and unusually high values of resistance at loads below 100 N for a nominally conductive contact [16]. These high resistance values, however, converge to lower, mo re expected resistance levels as load is increased [8]. Surface contaminants may also grow and evolve with cyclic contact, causing degradation in the quality of the elec trical contact resistance at higher force levels [19]. The non-uniformity of surface c ontamination layers also creates spatial variability in both the resistance and adhesi on measured on metal surfaces [4]. The ability

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28 of carbonaceous contamination to impair elec trical contacts can be reduced by altering the contact environment [63]. It is clear from the review of the various factors affecting MEMS electrical contact performance that definite trade-offs exist between the need for large, low-resistance electrical interfaces and small, non-adherent mechanical interfaces. Of the controllable design aspects of MEMS fabricat ion (contact geometry, load, and material), the choice of contact material possesses the most possibl e avenues for creating a surface that is simultaneously low-adhesion and high-conductivity This type of cont act material does not currently exist, but by using the thin -film deposition techniques common to MEMS fabrication, an optimal low-adhesion, hi gh-conductivity contact material should be producible which solves the most common failure mechanisms seen in metal-metal contact MEMS devices.

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29 CHAPTER 3 EXPERIMENTAL APPARATUS Bulk-Film Electrical Contact Testing Modified Nano-indentation System A low-force electrical contact resistance apparatus was constructed to investigate composite electrical contact materials fo r MEMS applications without having to physically integrate the mate rials into devices. This ability allowed for quick investigation of assorted cont act materials, the integration of which into MEMS devices would have been prohibitively time-intens ive. The apparatus consisted of a nanoindentation system augmented with electri cal contact resistance measuring abilities. A picture and schematic of the nano-indentation apparatus is shown in Fig. 3-1. The nanoindentation system was used to apply and m easure the normal load between the contact samples, the displacement into the samples, a nd the pull-off force required to separate the contacts. The electrical measurements were acquired via a 4-wire measurement technique to remove influence from the measurement lead resistances [6]. A schematic of this set-up is shown in Fig. 3-2. A current source provide d the current passing through the contact. The current source was constrained to a sourced upper-threshold voltage when the contact was open, called the compliance voltage or open-circuit voltage limit.

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30 Figure 3-1. Nano-indentation system used in low force ECR testing Figure 3-2. Contact zone schematic An ammeter measured the amount of current actually passing through the circuit, while a voltmeter in parallel with the contact meas ured the voltage drop across the both contact samples. The contact resistance was calcu lated from the ratio of the voltage drop measured across the contact to the measured sourced current. The capabilities of the ECR nano-indentation system are shown in Table 3-1.

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31 Table 3-1. ECR nano-indentation system capabilities Capabilities Limits Measurement Uncertainty Normal Force 10 N 60 mN 1 N Sourced Voltage 0 20 V 1 V @ 2 V Sourced Current 0 1 A 10 nA @ 1 mA The nano-indentation apparatus accommodate d coated flat samples with linear dimensions up to 10 x 20 mm. The flat sample s consisted of a silicon wafer substrate coated with a titanium adhesion layer and a primary gold electrical contact layer. The dimensions of the coated flat samples are s hown in Fig. 3-3. The composite electrical contact material to be tested was depos ited on top of the primary gold layer. The electrical contact resistance measurement lead s would be connected to the primary layer to prevent additional resistances originat ing from through-film resistance from influencing the results. In all tests the contact coating for the sphere sample remained the same, a silicon nitride (Si3N4) substrate coated with a tita nium adhesion layer and a gold primary contact layer. The deposited film st ack for contact samples is shown in Figure 34. Figure 3-3. Coated wafer sample dimensions

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32 Figure 3-4. Deposited film stack for bulk film ECR testing Figure 3-5. White-light interferometry t opographic scans of the as-deposited primary gold layers on the sphere and flat contact samples White-light interferometry topographic scans of the prim ary gold contact material for both sphere and flat samples are shown in Fig. 3-5. Root-mean-squared roughness for the sphere and flat samples were 7.5 and 2.4 nm respectively, indicating that the primary gold coatings were smooth and replicated th e topography of the silicon substrate well.

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33 Data Acquisition Time-synchronized data acquisition of cont act force, displacement, and electrical contact resistance was enabled by adding a sign al-triggered electrical source meter, a Keithley 2400, and a data-logging computer communicating with the Keithley 2440 via GPIB. A diagram of the set-up is shown in Fig. 3-6. Figure 3-6. Diagram of the mechanical and el ectrical data-acquisition system constructed to time synchronize the experiments When the nano-indenter first se nses a change in contact stiffness, as the sphere and flat sample are first touching, a digital I/ O channel on the nano-indenter drops a trigger voltage from 5 V to 0 V. When the contac t trigger is detected by a LabView program monitoring the trigger channel, the contact voltage drop, sourced current, and calculated contact resistance data being continuously stored in the Keithley 2400 buffer is timestamped as time zero in the final data file. The contact forc e and displacement,

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34 separately monitored by the nano-indenter data acquisition system, is also time-stamped zero in the output file when the contact tr igger condition is met. Post-processing of the separate data files searches for the comm on zero times, then knits the data files together into one data file. This enabled the inference of time-dependent electrical phenomenon to be made during moments of very close surface proximity. Single Contact Cycle An example of a data file taken from the ECR nano-indenter for a single experimental contact cycle is shown in Fig. 3-7. Figure 3-7. Example of one e xperimental contact cycle for a gold-gold sphere-flat contact The sphere sample was moved towards the contact until the contact stiffness exceeded a user-defined threshold of 100 N/m. At the moment of contact, the normal load was zeroed and the test cycle began. The load was increased at a constant rate until the maximum load was reached. The load was then held briefly at the peak value for an

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35 averaged resistance measurement, then unloa ded at a constant rate until the surfaces separated. The force at which the surfaces separated was recorded as the pull-off or adhesive force. MEMS Electrical Contact Device A complementary experimental apparatus developed to investigated composite electrical contact materials was a MEMS elect rical contact device. The purpose of this device was to provide an expe rimental platform on which promising materials identified in bulk film testing could be studied in a true microsystem environment. The advantage of such a device is that the number of contact cycles achievable is many orders of magnitude higher than the nano-indentation approach, with contact cycle times on the order of milliseconds instead of 30 seconds for the nano-indentation apparatus. The MEMS electrical contact devi ce is also sensitive to the failure modes, such as contaminant film formation and contact st icking, that the composite materials are intended to address. Electrical contact resistance testing of microsystem contacts was performed by employing a MEMS device designed specifically to study low-force electrical contacts. The device, a simple cantilever with a single electrical contact interface, is shown in Fig. 3-8. A SEM micrograph of the contact dimple which serves as one of the electrical contact surfaces is shown in Fig. 3-9. Th e single contact dimple provided a reduced apparent contact area for surface analyti cal techniques such as Auger Electron Spectroscopy (AES) or Time-of-Flight Sec ondary Ion Mass Spectroscopy (TOF-SIMS) to identify failure mechanisms re sponsible for device malfunction.

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36 Figure 3-8. Optical micrograph of electrical contact MEMS device Figure 3-9. SEM micrograph of the contact dimple on the underside of the cantilever beam device Device Fabrication Process The devices were fabricated using a electroplating pr ocess which enabled a gold plated layer to be used as the primary stru ctural layer. Figure 310 shows the deposition process for the contact devices.

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37 Figure 3-10. Electroplating deposition pro cess for MEMS contact device fabrication The device fabrication pro cess proceeded as follows: 1. A substrate was selected for device fabrica tion. The chosen substrate for the current devices was gallium arsenide wafer coated with an insulating SiON over layer to prevent current leakage into the GaAs. 2. A 100 nm thick layer of TaN was deposite d to serve as the pull-down electrode material. 3. A 800 nm thick layer of evaporated gold wa s deposited to serve as the signal lines. 4. A polymer, polymethylglutarimide (PMGI), was deposited, masked and etched to make the contact dimples and anchor for the cantilever. 5. A thin gold seed layer was deposited to serve as a plating layer initiator. 6. Photoresist was deposited, patterned and etched to serve as a guide for the electroplated gold. 7. The structural gold layer is electropl ated on top of the gold seed layer. 8. The photoresist and PGMI layers are etched away, releasing the device.

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38 Device Design The cantilever in Fig. 3-8 will deflect towards the substrate when sufficient actuation voltage difference is applied betw een the actuation pad and the cantilever. Figure 3-11 shows the up state and down stat e of the cantilever switch. The expression for the electrostatic force felt by the cantilever is shown in Eq. (3.1). 2 0 21 2c eA FV gw (3.1) Figure 3-11. Cantilever MEMS device in up and down-states In Eq. (3.1), cAis the area of electrostatic interaction between the pull-down electrode and the bottom of the cantilever. The variables gand ware the gap distance between the bottom of the cantilever and the actuation pad, and the distance the cantilever has moved from its equilibrium position, respectively. The applied voltage Vis the voltage difference between the actuati on pad and the cantileve r. As the actuation voltage increases, the displacement w increases, causing an increase in electrostatic pulldown force. The greater the force, the more the cantilever displaces downward, creating a positive feedback and an eventual instabilit y at the voltage where the elastic beam

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39 restoring force can no longer oppose the elect rostatic force. The voltage where the instability occurs causes the beam to snap into contact is called the pull-in voltage. It is evident from Fig. 3-11 that the contact force cF is a function of the electrostatic pull-down force, the geometric dimensions of the beam, and the elastic properties of the beam material. One me thod of removing the electrostatic force dependence from the contact force is to incor porate raised landing pa ds on both sides of the electrostatic actuation area in the plated gold layer. These pull-down landing pads enable the cantilever beam to be pulled into contact with the subs trate without shorting the actuation voltage gap. If the pad closest to the electrical contact dimple is pulled into contact with the substrate, the contact force no longer depends on the electrostatic actuation force, but on the deflected beam geom etry and material properties. Figure 3-12 shows how this premise works. Figure 3-12. Electrostatic actuation force de pendence removal from the contact force using the pull-down landing pads to geometrically constrain the device Equation (3.2) shows the expression for th e contact force in terms of elastic modulus, E, beam width, length, thic kness and beam deflection, a y The calculated contact force for the device shown in Fig. 3-8 was 97.6 N using an elastic modulus for

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40 gold of 88.2 GPa, a beam thickness of 8.1 m, beam width and length of 25 and 140 m, and a displacement of 1 m. 34caEwt Fy l (3.2) Finite-element analysis of the beam wa s performed using ANSYS to verify the contact force calculation from simple beam equations. A predicted contact force of 110 N was obtained when the beam length, widt h, thickness, material properties and the expected deflection were i nput to the finite-element simulation. A maximum bending stress of 89.2 MPa was predicted at the root of the beam, well below 548 MPa, the yield stress for gold [64]. Figure 3-13 shows the finite-element analysis output for the geometrically-constrained beam. Figure 3-13. Finite-element an alysis of the geometrically constrained cantilever beam MEMS Experimental Testing Experimental testing of the MEMS de vices was performed using a Wyko NT1100 DMEMS profilometer. The NT1100 profilometer was equipped with tungsten-tipped micro-positioners that were used to make el ectrical contact to the signal and actuation pads of the device. Figure 3-14 shows a white -light interferometry scan of the device with the four probes, actuation, ground, and signal on the device.

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41 The actuation voltage required by the device to first overco me the elastic restoring force of the cantilever was 112 V. For subsequent electric contact cycl ic testing, a voltage of 150 V was applied so that the pull-in landing pad would be pulled down into the substrate, giving a contact force of know n magnitude. Figure 3-15 shows white-light interferometry height data of cross-se ctions passing through the beam showing the differences between up (un-actu ated) and down (actuated) st ates of the device for an actuation voltage of 150 V. Figure 3-14. MEMS electrical contact de vice probed in the Wyko NT1100 DMEMS instrument In the up state, the beam profile is not pa rallel with the substrate, which is caused by residual stresses formed in the gold laye r during the plating process. However, the change in beam curvature due to residual stre ss is several orders of magnitude less than the change in curvature caused by device actu ation tip deflection. This means that the change in contact force due to residual stre ss is negligible, but th e affect on actuation

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42 voltage is significant due to the change in the gap between the pull-down electrode and bottom surface of the cantilever. Figure 3-15. Height profiles of up and down-state devices Electrical contact resistance was measured by recording the voltage drop across the low and high signal probes and dividing it by the measured sourced current. Cyclic contact testing was performed by repeated ly actuating the device with a potential difference across the signal line and the cantilev er. Two sets of tests were performed, one with a sourced current of 1 mA and 1 V compliance voltage. The other test was performed with a 3 mA sourced current and a 3.3 V voltage compliance. The 3 mA and 3.3 V test condition was the same as a ME MS accelerometer operating condition. All tests were performed in laboratory air envir onment. The results of these hot-switched tests are shown in Figure 3-16.

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43 Figure 3-16. Results of hot-swi tched electrical contact resi stance testing of the MEMS cantilever device It is clear from Fig. 316. that the MEMS cantile ver ECR device experienced contact resistance degradation with cyclic ho t-switched actuation. An order of magnitude decrease in device lifetime betw een the 1 V and 3.3 V tests is due to the effects of hotswitching on the electrical cont act surface. Hot-switching is es pecially hard on low-force electrical contacts. Re peated contact cycling in the same location, without translating the sample, can cause detrimental behavior in the contact surfaces. The trend in contact resistance with contact cycle is similar to th e degradation seen in previous work [65]. The resistance degradation shape is also seen in hot-switched bulk film nano-indentation experimental results, shown in Fig. 3-17.

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44 Figure 3-17. Example of resistance degrada tion for hot-switched contact in the same location In Fig. 3-17, the contact resi stance was initially low, 965 m for a gold-platinum contact pair for an app lied contact force of 150 N. As the contact was repeatedly brought in and out of contact the contact resistance incr eased by several orders of magnitude within 25 cycles. While the resistance trend is the same in Fig. 3-16 and 3-17, the number of cycles at the onset of the degradation was three times higher for the MEMS test device than the nano-indentat ion experiments. Hot-switched contact resistance degradation is an important topic to consider for MEMS el ectrical contacts, but is tangential to the discussion of the effect of composite electri cal materials on contact resistance and adhesion. Investigation of the phenomenon responsible for hot-switched electrical contact resistance degradation of low-force metal contacts is presented in Appendix A.

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45 CHAPTER 4 CONTACT MODELING The previous chapter discussed the expe rimental apparatus employed to study lowforce electrical contacts. In addition to the experimental e ndeavor, significant effort was expended on the development of computer mode ls to simulate the effects of composite contact material on low-force electrical cont acts using real measured surface data. The two main thrusts of the modeling effort were i) a rough surface contact calculator, and ii) a three-dimensional random resistor network electrical current cal culator with contact surface temperature-rise capabilities. In addi tion to the contact and current modeling, a model to determine the adhesion of cont acting rough surfaces was also developed. Rough Surface Contact Modeling An novel approach to calculating rou gh surface contact area is to use threedimensional discretized surface data obtained from surface microscopy, instead idealized surface topography models, to di rectly calculate th e interfacial contact area. Quantitative discretized surface data is most often obt ained from stylus profilometry, optical profilometry or atomic force microscopy, de pending on the scan area size and range of surface heights to be measured. An example of an optical profilometer, a Wyko NT-1100, is shown in Fig. 4-1. Such a device is capab le of accurately measuring surface height data quickly and without extensive sample prep aration and experimental set-up time.

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46 Figure 4-1. An example of an opti cal surface profilome ter, a Wyko NT-1100 The surface data generated by optical prof ilometry is a two-dimensional X-Y array of pixels with Z height distance associated w ith each pixel. An example of a surface scan with a 640 X 480 pixel lateral sa mpling interval taken from a gold-coated steel sphere is shown in Fig. 4-2. Figure 4-2. Discretized surface scan obtained from optical profilometry

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47 The resulting surfaces can be treated as a collection of voxels, or volume pixels, shown in Fig. 4-3. The voxel rough surface model is composed of a collection of individual of voxels, with each voxel representi ng a X,Y, and Z value. Each voxel in the array is independent of its neighbor voxels and the material response of each voxel to mechanical load does not comm unicate to neighboring voxels. Figure 4-3. A voxel surface constructed fr om a profilometer-obtained data scan To calculate interfacial c ontact area, two voxel surfaces are placed a distance far away from each other. The su rfaces are then advanced towards one another until at some surface separation the voxel elements begi n to interfere. Figure 4-4 shows a representation of two voxel su rfaces about to be brought in to contact. As the surface separation is decreased furthe r, the interaction between voxe ls in each surface increases. Surface contact is composed of the summation of all of the indivi dual voxel interactions occurring at a given surface interference. An individual voxel interaction is shown in Fig 4-5.

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48 Figure 4-4. Two separated voxel surfaces Figure 4-5. Voxel c ontact interaction

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49 The voxels have a uniform differential area of 2 L and a for voxels in contact, an interference depth d. Different material constituative m odels elastic, plastic, or elastoplastic may be used to rela te voxel interference de pth (strain) to pressure (stress) and load-carrying capacity. The simp lest approach is to assume a rigid-perfectly plastic material model for the voxel interactions. This assumption states that no elastic strain is built-up as the voxels are pressed together and the contact pressure is equal to the material indentation hardness. Figure 4-6 shows the stress-strain relation for the rigid, perfectly-plastic material assumption. The indentation hardness assump tion circumvents the need to define the elastic strain for each indivi dual element with respect to a gage-length. Each voxel in contact contributes the same increment of load support, regardless of the degree of deformation of the voxel. A more rigorous contact modeling approach would include volumetric redistribution as the material disp laced inside the cont act plastically flows outwards to non-stressed areas. However, this model refinement is neglected due to the small amount of error introduced into the contact area calculation, perhaps several percent for low-force MEMS contacts. Figure 4-6. Rigid, perfectly-p lastic constituative material model used for voxel contact interactions

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50 The contact force generated from a single voxel interaction is calculated from the material indentation hardness and the area of the voxel. This is shown in Eq. (4.1). The total contact force is calculated by summing the force contributions from N interacting voxel pairs, shown in Eq. (4.2). 2*contactFHL (4.1) 1iN ncontact iFF (4.2) The treatment of contacting rough surfaces as a collection of independently-acting voxels is particularly suited to low-force contacts, such as MEMS devices, where the number of load-bearing points in the contact interface are very few compared to the overall surface size. The use of a analytical function to fit the surf ace height distribution, such as a Gaussian fit in the widely -used Greenwood-Williamson model, becomes increasingly erroneous as the contact load is decreased. Figure 4-7 illustrates how the Gaussian fit is an adequate approximation for the entire histogram of surface heights about the mean plane for the surface shown in Fig. 4-2. However, the further away the Gaussian fit is examined from the surface mean plane (and closer to the highest points in the hei ght distribution) the more poorly matched the fit becomes to the actual su rface height data. This poor fit is negligible for macroscale loads, as the deformation is sufficien tly large enough to bring surface points away from the poorly-fit surface point s into contact, causing the error introduced in the contact area calculation to be small. However, fo r MEMS contacts the forces are small enough that the poorly-fit outlying surface points are able to support the en tirety of the load, making the Gaussian fit or any analytical fits to the surface height distribution ill-suited for contact area calculation.

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51 A B C D Figure 4-7. Histograms of the su rface height data about the m ean plane taken from Fig. 42. A) is a histogram of the entire surf ace, B) is a closer view of the surface histogram, C) shows the tail of the as perity distribution and D) shows a magnified view of the tallest asperities most likely to be involved in surface contact Real Surface Contact Simulation The computational advantage of this cont act area calculation method is that since the voxels in one surface are di rectly registered to the voxe ls in the opposing surface, no computationally-expensive searching is requ ired to locate contacting voxel elements. This computational economy allows for almost real-time calculations of contact areas for relevant engineering surfaces. Contact area calculation for two real rough surfaces wa s performed by applying the above method to a 0.79 mm radius gold-coated Si3N4 sphere, shown in Fig. 4-8, and a

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52 gold-coated Si wafer, shown in Fig. 4-9. The indentation hardness used for the contact force calculation was 2 GPa, which was de termined from nano-indentation hardness testing of the same deposited material Contact simulation was performed by decrementing the distance between the surfaces until the calculated contact force became non-zero. The surface separation was then stepped in small increments until the calculated contact force became e qual to the target contact force. When the target contact force was reached, the contact area was de termined from the interacting voxels responsible for the contact lo ad. The predicted contact area for a 60 mN normal load is shown in Fig. 4-10. Also shown in Fig. 4-10 is the Hertzian contac t area calculated using the material and geometric properties of the scanned surfaces for the same applied load. The Hertzian contact model neglects surface roughness effects and assumes a completely elastic material response. Figure 4-8. Gold-coated Si3N4 ball bearing voxel surface

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53 Figure 4-9. Gold-coated silicon wafer voxel surface Figure 4-10. Predicted contact area using rigid-perfectly plastic voxel rough surface contact model, Hertzian contac t model, and Greenwood-Williamson statistically-based model for the same gold-gold contact surfaces under a 60 mN load

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54 The contact simulation method outlined above is superior to statistical contact area methods, such as Greenwood-Williamson, due to the absence of any assumptions based on perfectly spherical asperities and ambiguity about their statistic al distribution. The quantitative topographic data ta ken from two surfaces of interest directly compute the predicted contact area using straightforwardl y obtained material constants and simple constituative models. The voxel rough surface co ntact model also allows for predictions in contact area shape, an ability completely lacking in statistically-based models. The resulting prediction of contact area can be used to help explain low-force electrical contact phenomena. Electrical Current Modeling The modeling of MEMS electrical cont acts can be accomplished by understanding how MEMS electrical contact s are composed. Figure 4-11 shows a focused ion-beam (FIB) cross-section of an elec trical contact dimple fabricat ed using the same process as the device shown in Fig. 3-9. The contact ge ometry of the electrical contact surface, where the cantilever dimple touches the signal lin e, can be seen in the bottom of Fig. 411. A closer look at the cont act dimple region in Fig. 4-12 shows the coarse-grained structure of the electroplated gold cantilever, and the evaporated gold signal line. When the switch is actuated the contact dimple is pressed against the signal line, creating a metal contact and enabling current to flow. A schematic of the electrical contact is shown in Fig. 4-13. When the electrical contact bridge is ma de between two gold contact members, the sputter-deposited gold seed-layer deposited to initiate the electroplate growth will be interposed between the movabl e cantilever and the stationary signal line. The seed-layer can be seen in Fig. 4-12 as the thin, bright outline on the bottom of the top electroplated

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55 layer. An idealized electrica l contact model showing the s eed layer in between two gold contacts is shown in Fig. 4-14. Figure 4-11. Focused ion-beam cross secti on of a gold-gold MEMS electrical contact Figure 4-12. Magnified view of the MEMS electrical contact

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56 Figure 4-13. Schematic of elect rical contact formed from th e contacting members of Fig. 4-12 Figure 4-14. Idealized model of a MEMS electrical contact The amount of current passing through the interf ace is a function of the voltage difference between the contact surfaces and the resistance of the interface. The resistance of the interface is a function of the size of the contact ar ea and the resistivity of the interfacial material. In a homogenous contac t material layer, the resistance of the interface is straightforward to calculate if the contact ar ea and material are known. The resistance of a composite material is more complicated.

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57 In the calculation of the current flowi ng through a composite film, similar to the one shown in Fig. 4-15, the relative distri bution of the composite material constituents plays an important role. The boundary interface of the composite controls the adhesion between the bulk MEMS surfaces, but the condu ctive pathways through the interior of the composite determine the resistance of the interface. The calculation method of interfacial adhesion is straightforward. Th e amount of adhesion between the composite and the top electrode is typifi ed by a linear-rule of mixture relationship. The relative ratio between the amount of gold and non-gold fille r in the composite is proportional to the amount of adhesion present between th e composite and the top contact. Figure 4-15. Composite thin-film electrical c ontact showing the role of the interface on adhesion and the bulk of the film on resistivity The calculation of the composite materi al resistance can be accomplished by employing a random resistor network (RRN) to model the electrical transport in the composite. In the RRN, the composite material is discretized as a simp le cubic lattice of two different materials, a conductive and f iller phase, which are randomly distributed through the material. A nodal network is over-l aid on the composite with nodes laying at the center of each material element. Electri cal resistors connect the nodes, with the

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58 resistance determined by the resistivity of the connected material elements. Figure 4-16 shows the nodal connectivity and the assignment of resistance for a resistor based on the material between the nodes. The resistance be tween a pair of nodes is calculated by the equation h R wt where is the average resistivity of the materials between the nodes, h is the distance between the nodes, and wt is the product of the element width and thickness. Figure 4-16. Random resistor ne twork approach to compute th e resistance of a composite electrical contact material After the nodal mesh and inter-node resist ances are determined, the computation of the resistance of the RRN is performed. Fi gure 4-17 shows the RRN constructed from the electrical composite of Fig. 4-16. The voltage at the top and bottom nodes, corresponding to the equipotential surfaces of the top an bottom contacts, is prescribed. Equation (4.3) shows the mathematical equation fo r the current entering into the ith node in the RNN. The ith node is assumed to have an equipotential with voltage iV. If ijg is the local

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59 conductance between the ith and jth node, the current i I entering the ith node is the sum of the currents entering into (or leavi ng from) the other nodes connected to the ith node. For a simple cubic lattice structure the maximum number of n earest bonding sites or coordination number, N, is 4 for a two-dimensional lat tice and 6 for a three-dimensional lattice. N iijij j I gVV (4.3) Figure 4-17. Simplified representation of the RRN used to solve for the resistance The application of Eq. (4.3) for every node in the RRN creates a linear system of equations. Modified Nodal Analysis (MNA) wa s employed to solve for the nodal currents by applying Eq. (4.3) to the nodal mesh shown in Fig. 4-17. A detailed outline of the MNA algorithm is presented in Appendix B. Once the current flowing through the nodal mesh is known, the total current passing through the RRN can be found. Dividing the total current by the prescribed voltage differe nce across the RRN yiel ds the resistance of the contact material, whether homogenous or inhomogeneous composite, without distinction.

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60 Combined MEMS Electrical Contact and Current Modeling The combination of the voxel surface approach to rough surface contact area calculation with the RRN electrica l resistance calculation met hod can be used to estimate the contact resistance for MEMS devices us ing real rough surfaces and material data obtained from the devices. Using the voxel su rface method, the inte rfacial contact area for two rough surfaces is obtained, shown in Fig. 4-18. Figure 4-18. Contact window created by voxel surface method Figure 4-19 and Fig. 4-20 show surface topography of the contact dimple and signal layer for the MEMS electrical cont act device obtained using an atomic force microscope (AFM). AFM surface data was used to obtain the topographic data instead of a white-light interferometer be cause the minimum spatial reso lution of the interferometer is too large and the size-scal e of the surface features on th ese samples is too small to obtain sufficient surface data required to co mpute contact area for MEMS-scale contact forces. A white-light interferometer at its highest magnification of 100 X, will produce a

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61 computed contact area that consists of only several pixels for a 100 N normally-loaded gold contact surface. The spatial resolution of the input surface scans must be at least several orders of magnitude sma ller than the contact size to ob tain accurate data with the RRN electrical contact resi stance calculation method. The surfaces shown in Fig. 4-19 and Fig. 4-20 were input into the voxel surface contact calculator. A 2 GPa hardness for the gold surfaces was input into the calculator program. Hardness values for thin-film deposite d gold range from 1-3 GPa [66,67]. As an example of the ability of the method to analy ze very low-force contacts, a target contact load of 1.25 N was input into the contact program The calculated contact area that supported the target load is shown in Fig 4-21. The pixels within the contact area become the contact window used in the RRN calculation shown in Fig. 4-18. Figure 4-19. AFM scan of surface topography fo r the electroplated gold contact dimple

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62 Figure 4-20. AFM scan of surface topography for the evaporated gold signal layer Figure 4-21. Contact area for a 1.25 N normal load applied to the contact dimple and signal layer surfaces The contact window shown in Fig. 4-21 de termines the nodal connectivity between the surfaces at the inte rface. The contact connectivity was used in the three-dimensional

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63 RRN, shown in Fig. 4-22. The 3-D RRN simula tes the current flow traveling through the electrical bodies in a fashi on identical to the pr ocess outlined above, the main difference being the three-dimensional nodal mesh and se vered nodal connectivity at the pixels not in contact. A voltage drop was specified acro ss the contact bodies and the current flowing through the contact was calculated. After the 3-D RRN cont act resistance calculation was completed, a map of the current passing th rough the contact was constructed. Figure 4-23 shows the current map in the contact area of Fig. 4-21. The largest nodal current within the contact was 23.4 A. The total integrated curren t passing through the contact was 2.32 mA for a prescribed voltage drop of 10 mV, giving a calculat ed resistance of 4.31 This resistance is reasonable for a contact with characteristic dimensions under 100 nm. Figure 4-22. Depiction of the three-dimensiona l RRN used to calculate contact resistance.

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64 Figure 4-23. Current map for the contact show n in Fig. 4-21. The highest currents are concentrated at the periphery of the contact The total number of thickness layers used in the 3-D RRN simulation was ten. Figure 424 shows the current passing down through the top 5 layers of the 3-D RRN. The total current in layer 1, the top-most layer of vertical resistors attached to the equipotential boundary surface, is highly distributed among the all of the resistors in the layer. As the current descends through the resistor network and gets closer to the contact elements, the resistors closest to the contact spot begin to carry more and more current as the current is forced through the contact constriction. In layer 5, only the elements in contact determined by Fig. 4-21 have current passi ng through them. Since the contact modeled is homogenous gold, the current maps for the bottom layers 6-9 are symmetric about the contact as the current spreads away from th e contact constriction. The variations in material resistivity and the effects on curre nt constriction are investigated in the following chapter.

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65 Figure 4-24. Current maps of the layers 15 of the 3-D RRN as the current descends toward the contact layer and forced through the constriction

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66 Thermal Modeling Once the current in each resistor element is known, a heat flux based on the Ohmic resistive heating was applied in a discre tized half-space heat conduction model [68]. Figure 4-25 shows a single element in the mode l. For all of the elements in the contact layer, in contact or not, Eq (4.4) is applied in order to determine the temperature rise in each element. Equation (4.4) combines the te mperature rise for an element with an Ohmic heat flux over it, the first half of the Eq. (4.4), with the temperature rise from conductive heat flow from neighboring elemen ts. Equation (4.5) shows the equation for the heat flux for a single current-carrying element. This basic modeling does not incorporate any scale-dependency on the heat conduction mechanism. ; 01.12 2ni ii tti iqaqA kkr (4.4) 2 24 I R q a (4.5) Figure 4-25. Discretized heat conduction model Figure 4-26 shows the result of the heat conduction mode l applied to the current map of Fig. 4-23. The maximum temperature rise within the contact for a total current of 2.32 mA is only 0.034 degree K. The reason for th e very modest temperature rise is that

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67 gold is both an excelle nt electrical (2.2e-8 *m) and thermal conductor (317 W/m*K). A quick check of the thermal modeling is to use the Kohlrausch voltage-temperature relation, Eq. (2-15), to compute a maximum temperature rise. Using the electrical and thermal conductivities given above and using the contact voltage drop of 10 mV in the Kohlrausch relation gives a maximum temp erature rise of 0.018 degree K. The two values agree within a factor of two. Figure 4-26. Temperature rise map for the Oh mic heating due to the electrical current passage of Fig. 4-21 Adhesion Modeling Traditional calculation of adhe sive force involves the use of approaches like JKR or DMT described in Chapter 2. Depending on the contact geometry and interfacial material, the adhesive force calculation using these methods is uncomplicated. The ambiguity in using these approaches arises when deciding what constitutes the asperity radius for rough surface contact. The JKR equation, '2poFR assumes spherical

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68 asperity contact and requires an estimate of effective radius to cal culate the adhesive force. For low-force rough surface contacts like the one shown in Fig. 4-21 the assumption of a spherical asperity is questionable. Instead of using JKR or DMT approach, an alternative method to compute the adhesive force of two metal lic surfaces using real surf ace topography is presented here. To calculate the adhesive force, the total number of atoms inside the predicted contact area must be calculated. This can be calcula ted by finding the number of atoms inside a single pixel, and then summing the number of pixels within the contact surface. Once the total number of atoms in the contact is know n, the adhesion force contribution for each atomic contact can be summed, yielding a pul l-off force prediction for a clean metallic contact. Assuming two gold surfaces are brought into contact using the voxel contact calculator, the resulting contact area will be a subset of the entire image pixel-field. The pixels in contact will have characteristic length, p L based on the input surface scan length, divided by the scan resolution. For ex ample, the side length of a single pixel in the 512 x 512 pixel, 5 m x 5 m AFM surface scan would be 5 m / 512, or 0.98 nm. Each individual pixel within the contact ar ea would be then sub-divided into a square array, with each cell within the array havi ng a linear dimension equal to the atomic diameter, atomD, of the surface material. Figure 4-27 illustrates how the sub-division into an atomic array of a single contact is land within contact area is performed. Computing the ratio of the pixel length to the atomic cell dimension, / p atomLD, gives how many atomic cells will fit along one di mension of the pixel. For the self-mated gold contact area shown in Fig. 4-21, with gold having an atomic diameter of 0.2884 nm,

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69 the ratio of pixel length to atomic cell length is /9.776/0.28843patomLD The total number of atomic cells within a single pixel is therefore 2/11.5patomLD Multiplying the total number of pixels in co ntact with the number of atomic cells per pixel gives the total number of atoms in contact, 725*11.58,371 atoms for a 1.25 N applied force. Figure 4-27. Population of an discretized contact island with an array of atoms Once the total number of atoms in contact is known, the individual adhesive force contribution from each gold-gold contact can be summed together to predict the total force required to separate the mated surf aces. Several references exist which have measured the magnitude of adhesive fo rce for gold nanowires with a speciallyinstrumented AFM apparatus [69-71]. Figur e 4-28 shows a picture of the nanowire formation upon unloading of the AFM apparatu s [69]. The adhesive force for a single gold-gold atomic contact was ex trapolated from the nanowire adhesive force experiments and was determined to be 1.6 nN. This va lue is supported by theo retical studies which

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70 predicted the adhesive force of the same contact to be in the range of 1 to 2.2 nN [72]. It is arguable whether this value is a cohesive fo rce or an adhesive fo rce. A distinction is usually made between an adhesive force, wh ich acts to hold two sepa rate bodies together (or to stick one body to another) and a cohesive force, which acts to hold together the like or unlike atoms, ions, or molecules of a single body. In this particular case, both situations are seemingly appropriate, but for clarity the term adhesive force is used. Figure 4-28. TEM image of gold nanowire fo rmation from unloading of AFM contact experiments [69] Multiplying the number of atoms in contact with the adhesive force contribution of a single atomic gold contact, the adhesive force of the simulated contact is calculated to be, 8371*1.613,394 nN, or 13.4 N. This value is almost eleven times greater than the applied load of 1.25 N. The adhesive force calculated using JKR for the same contact, assuming a composite radius of 100 nm and an adhesion energy for gold-gold contact of 2.2 J/m2, is 1.04 N. While the JKR figure for adhesi ve force appears reasonable, the arbitrary nature of choosing a 100 nm based on a spherical asperity assumption makes its use questionable.

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71 The seemingly large adhesive force value of 13.4 N using the voxel-contact surface is in fact supported by experiment al evidence of cold-welding of gold-gold contacts in ultra-high vacuum [18]. Extremely high adhesive forces due to strong metallic bonding can be generated between metal contac ts when the surfaces are devoid of any contaminants. The assumption that every atom contributes to the adhesive force, as shown in Fig. 4-27, is akin to assuming that the contact interface is atomically clean. In reality, adventitious contaminan t surface films and material de fects will reduce the actual adhesive force by preventing strongly-bondi ng metal-metal contact to occur. The adhesive forces of these interfering entitie s are many orders of magnitude less than the metallic contact forces and the contribution of non-metallic substances are effectively negligible in the total force summation unless their presence is overwhelmingly predominant. Appropriate reductions in the num ber of atoms in contact, by a factor of three at least, would represen t the effects of low surface en ergy contaminant species on the surfaces in a non-vacuum device environment. Overall, the use of real surface topography to calculate contact area is pivotal in estimating MEMS contact properties, such as electrical contact resistance, Ohmic temperature rise and adhesive force, that are dependent on interfaci al contact area size and distribution.

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72 CHAPTER 5 COMPOSITE ELECTRICAL CONTACT MATERIALS Percolation Threshold The computation of composite electrical contact material resistivity can be accomplished using analytical expressions. Fi gure 5-1 shows three different structural models of a composite electrical contact mate rial. A simple linear rule of mixture model is analogous to the leftmost composite in Fi g. 5-1. Alternating layers of material perpendicular to the current direction o ffer no preferred conduction path through the material, hence the electrical current transp ort capability of the composite is dominated by the most poorly conducting species, analogou s to resistors in series. In the opposite case, the middle composite in Fig. 5-1 verti cally orients the two ma terials parallel to current flow, creating a composite material which is instead dominated by the most conductive phase. The rightmost composite in Fig. 5-1 is unique from the first two models. In a composite whose constituent phase s are randomly distribu ted, the resistivity depends on not only the resistivity of the c onstituent phases, but the orientation of the phases with respect to each other. The resist ivity of this composite structure can be described using a percolation model which is a function of constituent resistivity and relative interconnectedness. Electrical conduction in an inhomogeneous medium using a percolation model was first proposed in 1957 [73]. In the percolation m odel, a structural lattice is composed of an array of locations, or sites, which are in terconnected. Each site has a probability of whether the site is low-resistivity or high-resi stivity and that probability is independent of

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73 the state of its neighbors. Electrical conduction can only o ccur from one site to its immediately neighboring sites. The current ev entually propagates through the composite solid. At a critical volume fraction of the conducting pha se, called the percolation threshold, a continuous path of conductive site s is formed from one equipotential surface to the other. When the percolation threshold is reached, the resistivity of the composite greatly decreases and behaves more like the parallel-addition composite. Figure 5-1. Different electrical composite models, series-add ition, parallel-addition, and randomly distributed Equation (5.1), called the logarithmic mixi ng rule, can be used to calculate the resistivity of a electrical contact composite, m as a function of the high resistivity and low resistivity phases, h and l the volume fraction of the low resistivity phase and an exponent n[74]. The series-addition composite resi stivity, or linear rule of mixture equation, can be obtained with 1 n while the parallel-additi on composite resistance can be obtained with 1 n 111 1nnn mhl (5.1) Equation (5.2), called the General Effec tive Media (GEM) equation, was developed to calculate the resistivity of a randomly distributed composite material [75]. The GEM equation can be used to calculate the compos ite resistivity for structures like the one shown in the rightmost composite of Fig. 5-1, given the resistivities of the low-resistivity

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74 and high-resistivity phases. The variable c is the critical fraction of low-resistivity phase where the composite material percolates and the transition from high-resistivity to lowresistivity occurs. 1/1/1/1/ 1/1/1/1/1 0 11tttt mhml tttt cc mhml cc (5.2) Figure 5-2 shows the normalized resistivity for each of the respective mixing rules, series-addition, parallel-addition, and GEM e quations. The resistivity models are plotted as a function of gold percentage in the co mposite and normalized by the resistivity of gold, 82.210 x m The resistivity difference between the high-resistivity phase and gold was chosen to be 100,000 which is typical of the resistivity of fillers used in gold composites [76] In Fig. 5-2 the series -addition normalized composite resistivity increases almost immediately with inclusion of high-resistivity pha se. In contrast, the parallel-addition normalized resistivity remain s within an order of magnitude of pure gold up to high-resistivity phase percentages of 90%. From an engineering standpoint the parallel-addition composite material structure is most optimum if the goal is to keep the resistivity as low as possible while maximi zing the amount of filler in the composite. An example of how the percol ation threshold affects resistivity in a real composite material is shown in Figs. 5-3 through 5-8. A transmission electron micrograph of a goldMoS2 co-sputtered nano-composite film is show n in Fig. 5-3 [77]. The darker, banded grains are gold, while the lig hter, unstructured bands ar e molybdenum disulphide. By modulating the contrast in Fi g. 5-3, the contact resistan ce calculator outlined in the previous chapter was used to determine the re sistivity of each image in Figs. 5-4 through 5-8. Each image in Figs. 5-4 through 5-8 c onsists of a site-lattice structured image

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75 constructed from Fig. 5-3. Modulation of th e image contrast create d a variation in lowresistivity phase (black pixels) in a matrix of high-resistivity phase (white pixels). The binary composite image for each volume fractio n was then fit with a random resistor nodal mesh and given a voltage difference acro ss the mesh. The resulting current flow map adjacent to each binary composite image shows the most conductive pathway through the composite. The darkest pathway in the current map corresponds to the highest magnitude current within the com posite. This method of taking real crosssectional material microscope images enable s direct assessment of composite material electrical transport capabilities, al though the limitation of two-dimensional imagery reduces its usefulness in dea ling with contact simulations. Figure 5-2. Normalized compos ite resistivity as a function of decreasing gold percentage for series-addition, para llel-addition, and random ly distributed models

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76 Figure 5-3. TEM image of a co-sputte red gold-MoS2 composite film [77] Figure 5-4. Numerical simula tion of the current flow through a 10% gold composite Figure 5-5. Numerical simula tion of the current flow through a 35% gold composite

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77 Figure 5-6. Numerical simula tion of the current flow through a 45% gold composite, percolation threshold occurs in between Fig 5-5 and 5-6 Figure 5-7. Numerical simula tion of the current flow through a 66% gold composite Figure 5-8. Numerical simula tion of the current flow through a 93% gold composite

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78 Figure 5-9 shows the normalized resistivity of each of the numbered composite current simulations. As the high-resistivity phase percentage (white pixels) is decreased, the composite resistivity decreases gradually until the percolation th reshold is reached. When the critical conductive phase percenta ge is reached, at continuous path of conductive (black) pixels bridges the entire co mposite and the composite resistivity drops by over three orders of magnitude. As the hi gh-resistivity phase percentage is reduced further, the normalized composite resist ivity again drops at a gradual rate. Figure 5-9. Normalized composite resistiv ity of the contrast-modulated TEM images showing percolation threshold of 37% It is clear from Fig. 5-9 that to create an useful electrical composite material the filler percentage must remain less than the critical percentage near the percolation threshold, otherwise the penalty paid in increased resistivity will be too great.

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79 Experimental Investigation of Composite Films Film Deposition With the theoretical framework for predic ting and analyzing co mposite electrical contact materials established, thin-film electrical composite material were created for experimental testing. Three different composite film compositions, Au-Al2O3, Au-TiN, and Au-Ni, were made using a pulsed-lase r deposition (PLD) t echnique. Figure 5-10 shows a schematic of how the PLD system operated. Figure 5-10. Pulsed-laser deposition The composite materials were deposited in vacuum using a KrF excimer laser, with a wavelength of 248 nm, a 34 ns full-width hal f-maximum pulse width, and operated at a pulse rate of 35 Hz. The pure gold and filler phase ablation targets and sample substrates were mounted in an all-metal vacuum chamber with a base pressure of 2x10-7 Torr. The laser light was directed through a UV-transpar ent window to a fixed position in the plane of the target. The targets were continuously rastered in that plane over several square

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80 centimeters during deposition. Th e laser energy density at the target was in the range of 1-2 J/cm2. The deposition rates were material de pendent: gold deposited at a rate of 0.106 /shot, corresponding to 500 nm th ick film deposited in 30 minutes. A particle filter was mounted between the targets and the sample to eliminate the slow, non-plasma components of the laser ablation plume, wh ich would otherwise lead to a rough, non-ideal film. The in terposed velocity filter consisted of a 15 cm diameter wheel with two 5 cm wide slots around the peri phery. The filters were spun at a speed of 2100 rpm during the deposition with a wheel to target spacing of 2 cm and the laser synchronized to the wheel position. The lase r was fired when one of the openings was positioned between the target and sample substrate, allowing the fast (~105 cm/s) plasma component of the plume to pass through to the substrate, while blocking the slower moving (~103 cm/s) particle component. This produced a smooth, uniform film on the sample ~1 cm wide with very few large particles incorporated into the film. The composition of the composite film was varied by alternating gold and filler phase targets. The ablation of each material by the laser produced a short burst of plasma that is quenched on the substrate to be coat ed; alternating between targets allows the composition of the resulting film to be prec isely controlled, while the amount of each material deposited in a cycle is kept low enough (< 1 monolaye r) that the final material is approximately uniform in composition. Indivi dual deposition cycle layers were typically less than 10 each, but incomplete in areal coverage. The PLD film s were deposited on top of a 500 nm thick pure gold evaporated laye r. The final desired thickness of the PLD composite films was 50 nm.

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81 The filler phase materials for the PLD process were chosen for several reasons. Alumina was chosen as a filler phase becau se it is a chemically stable, thermally invariant, additive phase for gold films that was known to block dislocation motion, and to be compatible with the PLD process [78]. Gold-alumina cermet films had been previously fabricated using PLD, as well as by co-sputtering [7880]. The hypothesized advantage of the Au-Al2O3 composite over a pure gold el ectrical contact was that the alumina-filled material would have a re duced contact area and limited the amount of gold-gold contact adhesion, but without significant affects on the electrical resistivity. Similarly, titanium nitride was chosen because of its stability and increased hardness over pure gold. Au-TiN composites have been fabr icated using co-sputtering, increasing the measured Vickers microhardness of the composite over pure gold films by 300% [81]. It was hoped that Au-TiN composite s would be significantly more conductive than the alumina composites while still achieving similar hardening and adhesion reducing effects in the gold-alumina composites. Nickel-hardened gold composite material s are well known and widely used for electrical contact materials, most commonl y in macro-scale electrical switches and breakers. Alloys of Au-Ni have been invest igated previously for low-force electrical contacts [16,64]. The advantage of nickel is that its electrical resi stivity is only about 5 times greater than gold, unlike alumina or tita nium nitride, whose resistivities are many orders of magnitude higher than gold. Even for a very low gold percentage composite, the composite film resistivity shoul d remain in the range of nomi nally metal contacts for the Au-Ni films. The potential risk associated wi th nickel is the possibility of material

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82 segregation and surface oxidation of the nickel creating an insulating film on the surface of the gold. A concern with composite material co-depos ition is the scalabili ty of the deposition process with regard to large-volume device fabrication. Pulsed-l aser deposition is a versatile and powerful technique for deposit ed very specific thin-film structures. However, PLD is costly and does not scale well for large-scale de position schemes used in an industrial setting. Physical vapor deposition (PVD) techni ques, such as RFmagnetron sputtering, are capable of produc ing thin-film compos ites similar to PLDproduced materials, but at a lower cost a nd scalable to large-volume device production [82]. However, the difference in the fi nal resulting film between PLD and PVD techniques are not substantia l, as both techniques involve the physical impingement of atomic species onto the coated target. TEM Imagery Figs. 5-11 through 5-13 show cross-sectiona l TEM images of three different PLD Au-Al2O3 films, with 90%, 50%, and 20% gold volu me percent. The first TEM image of the 90% gold composite shows very subtle changes in the 50 nm thickness of the PLD film. The grain structure of the evaporated gold substrate is slightly larger than that of the PLD film deposited on top of it. The 50% gold composite shown in Fig 5-12 shows significant change in grain stru cture between the composite f ilm and the gold substrate. A definite boundary between the substrate and composite film is beginning to form. Three stratified layers can also be seen in the film In Fig. 5-13, the 20% gold film is starkly different from the gold substrat e underneath. Columnar grain structure and a very defined boundary between the composite and substrate are visible.

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83 Figure 5-11. TEM image of 90% gold, Au-Al2O3 PLD composite Figure 5-12. TEM image of 50% gold, Au-Al2O3 PLD composite

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84 Figure 5-13. TEM image of 20% gold, Au-Al2O3 PLD composite Experimental Results Experimental investigation of these films was performed using the ECR nanoindenter described in Chapter 3. A normal load of 100 N was applied while 1 mA of current was sourced with a 1 V compliance limit set. Figure 5-14 shows the normalized results of the three different type s of PLD composite coatings, Au-Al2O3, Au-TiN, and Au-Ni. Each resistance and pull-off data point is averaged from 10 repeated contacts. The mean normalization values for resistance and pull-off force were 533 7 m and 253 36 N, respectively for a baseline gold-gold co ntact. The variability of the resistance and pull-off force results originated from cha nges in the contact, as the experimental uncertainty for the electrical measurement and force measurement was 0.9 m and 1 as determined from Table 3-1. It is appa rent from Fig. 5-14 th at large increases in resistivity were realized with modest increase s in filler volume percentage. Also apparent is that the trade-off between increased com posite resistivity and decreased pull-off force

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85 was not directly related. Almost an order of magnitude reduction in pull-off force was achieved for the 50% gold films without a similar magnitude increase in composite resistivity. Figure 5-14. Normalized PLD composite film electrical contact resistance and adhesive force nano-indentation results Further experimental investigation of the electrical percolation threshold in AuAl2O3 composites was performed with similarly produced PLD films. Starting with pure gold, additional PLD film samples with incr emental additions of 7.5 % alumina were created to provide more compositional resoluti on than what is seen in Fig. 5-14. The results of the additional testi ng is shown in Fig. 5-15. Pu re PLD gold resistance was 637 10 m at 100 N normal load and 1 mA current, higher than the 533 m resistance of the PLD films tested in Fig. 5-14. As the gold film percentage decreased, the resistance

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86 increased slightly until a gold percentage of 40 % was reached. For film compositions less than 40 % gold, the resistance increas e began to accelerate until at 5 % gold the measured resistance was over 200 k The GEM equation fit to the data is also plotted Fig. 5-15. A percolation th reshold of 16 % gold and a t exponent of 1.05 was determined by a GEM equation fit to the experimental data The additional data supports the results shown in Fig. 5-14 and s uggests that for PLD Al2O3 films a gold percentage of 50 % or higher will not detrimentally affect cont act resistance for ap plied loads of 100 N. Figure 5-15. Resist ance of PLD Au-Al2O3 composite films Composite Current Flow Simulation To gain insight as to the effects of f iller on the electrical transport within a lowforce metal contact, the 3-D current calcula tor shown in the Chapter 4 was used to

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87 simulate how the introduction of a high-resis tivity phase affected bul k resistivity. Figure 5-16 shows the current maps for each succes sive layer of a 50% gold percentage composite. Moving from left-to-right, th e most energetically economical pathway through the film is no longer norma l to the image. The current disperses as it tries to find the most conductive pathway through the film The increased dist ance traveled by the current through the material, as well as the increased probability to encounter a highresistivity phase as the percolation threshold is approached, increases the resistivity of the composite. The advantage of using the 3-D contact cu rrent computer simu lation is that many different scenarios can be explored that would be prohibitively expensive and timeconsuming to investigate experimentally Figure 5-17 shows the results of 3,750 simulations of randomly distribut ed composites, similar to Fig. 5-16, for the same contact area shown in Fig. 4-22. For 30 different gol d percentages in Fig. 5-17, 25 repeated simulations were run for 5 di fferent resistivity values of the less conducting phase. The error bars shown in Fig. 5-17 represent the st andard deviation from the mean for the 25 simulations at each gold percentage. The percolation threshold shown in Fig. 5-17 in the randomly distributed composite simulations lies at a gold per centage of 33%, which corresponds to the theoretical critical filler percentage for a three-dimensional cubic array of filler sites [74]. As the highresistivity phase resistivity approaches the resistivity of gold, the magnitude of the change in composite resistivity at the perc olation threshold decreas es. The magnitude of the standard deviation from the mean also beco mes smaller with reduced resistivity of the filler phase.

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88 Figure 5-16. Current maps for a 50 % gold co mposite. The current starting in the upper left image, moving left to right, travels down through the bulk gold until it meets the contact constriction. After the current passes through the contact constriction, the current diffusively travels through the composite along the most energetically economic pathways allowed by the microstructure If the simulation in Fig. 5-17 is repeat ed for the largest high-resistivity phase resistivity with both a uniform random distribution and a graded random distribution of high-resistivity phase, th e beneficial effects of grading the compos ite material become apparent.

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89 Figure 5-17. Normalized composite resistivit y for 3,750 total contact current simulations as a function of gold percentage a nd high-resistivity phase resistivity Figure 5-18 shows the difference be tween uniform and graded random distributions.. The difference between the uni form and graded random filler particle distributions is the probability of filler site population as a function of film thickness. For the uniform random distribution, the probability of a filler site being populated with a high-resistivity particle remains constant as the depth within the composite film increases. In the graded random distribution, the probability of a high-resistivity phase populating a filler site decreases with increa sing composite depth away from the contact surface. The function used in Fig. 5-18 was expf p tft where the probability of filler site population, p t, was the product of the desired filler fraction at the interface,

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90 f f and a decaying exponential function of th e depth moving away from the interface, t The purpose of the non-uniform filler distri bution is to maximize the amount of highconductivity phase in the sub-surface bulk while also maximizing the amount of harder, low-adhesion phase at the surface. Some gol d must remain at the interface however as total coverage of the contact surface with high resistivity pha se inhibits efficient current flow through the contact. Figure 5-18. Difference between uniform ra ndom and graded random distribution of high-resistivity phase filler particles as a function of depth away from the contact interface Figure 5-19 shows the simulation results for uniform random and graded random distributions. Also depicted in Fig. 5-19 is the series -addition and parallel-addition resistance mixing rules of Eq. (5-1). The eff ect of the graded random distribution is clear: the percolation threshold for the graded random distribution falls at 9 % gold versus 33 % gold for the uniform random distribution. The graded random distribution normalized resistivity was also lower than the parall el-addition mixing rule for gold percentages larger than the 9 % percolation threshold. De position kinetics may also affect where the

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91 percolation threshold exists for composite fi lms, as evidenced by the results for the Al2O3 films shown in Fig. 5-15. The practical use of this result is that a highly conductive composite with low gold contents and a lo w adhesion interface may be deposited if sufficient attention is paid to how the constituent materials are distributed. Figure 5-19. Effects of high-re sistivity phase distribution on percolation threshold for the uniform and graded random distributi on. The gold percentage reflects the amount of gold at the interface whic h for the graded random simulation.

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92 CHAPTER 6 DISCUSSION The experimental efforts and numerical simulation work summarized in the previous chapters have potential beneficial impact on the performance and reliability of future MEMS electrical contact devices. Gene rally, the creation of a low-adhesion, highconductivity electrical interface would be the ideal optimum for MEMS electrical contact devices expected to functi on for extended operational life times. However, the knowledge of how to create such an interface and w hy a properly crafted interface would benefit MEMS devices has been hereto fore lacking in the larger MEMS community. This work has assembled experimental techniques a nd numerical modeling efforts in order to provide an understanding of the underlying phys ics of MEMS electrical contacts and to guide the development of composite electrical contact materials for MEMS applications. The experimental efforts successfully dem onstrated that a low-force mechanical testing apparatus could be combined with elec trical contact resistance measuring ability to simulate MEMS electrical contacts. The in tegration of an electrical contact resistance measurement system with a nano-indentation apparatus did not exist previously, either as a commercially available produc t or earlier constructed tes ting platform. The developed testing capability, using bulk film material samples to evaluate low-force electrical contacts intended for MEMS a pplications, provided a time-efficient, low-cost alternative method to direct on-die device testing of ca ndidate contact materials. This capability

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93 allowed for rapid investigation of promis ing contact materials created by thin-film deposition. In parallel with the nano-i ndentation experimental appa ratus, a MEMS electrical contact resistance test device was designed and fabricated to perform electrical contact material testing in a microsystem environmen t. The experimental device was successfully actuated and was capable of measuring the cont act resistance of the interfacial contact area formed during actuation. The MEMS test vehicle also enable d cyclic testing of electrical contacts for cycle numbers many orde rs of magnitude larger than achievable with the nano-indentation a pparatus. The creation of th e MEMS electrical contact resistance test vehicle produced a device-level testing capability for composite electrical contact materials deemed worthy of further investigation. The reduced size of the apparent area of contact in the MEMS device contact dimple also assisted in searching for evidence of degradation, such as cont act sticking damage or surface contamination. The numerical modeling efforts merged two previously unconnected concepts: rough surface contact area modeling and thre e-dimensional random resistor networking, creating a computational simulation ability which allowed assessment of composite electrical contact performa nce in MEMS electrical cont acts. The voxel-surface contact area modeling provided a straightforward estima tion of interfacial area from real surface topographic data. The direct registration of surface topographies avoided the use of traditional contact area modeling assumptions, such as spherically-radiused asperities and normally-distributed peak asperity distribu tions, the use of which becomes tenuous at MEMS contact force levels. The use of a th ree-dimensional random resistor network to simulate the electrical resist ance of a composite contact mate rial correlated well with the

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94 experimental results of composite films for varying filler fractions. In addition to composite material electrical properties, the utility of random resist or network simulation of composite material transport behavior is also applicable to ot her physical properties such as thermal conductivity, through the use of thermal resistor elements, or mechanical deformation response, using lin ear spring elements [83]. Both the experimental and modeling e fforts established that multiple-phase electrical contact materials are promisi ng for addressing failure modes in MEMS electrical contact applicati ons. The large reduction in measured pull-off force was achieved without a similar magnitude increase in contact resistance extending up to filler fractions approaching the perc olation threshold of the composite. The balance between conductivity and adhesion was due to the abil ity to create a film with the desired composite contact material phase ratio via thin film co-deposition methods. The codeposition of composite electrical contact material is also attractive because the technology exists within the larger framewo rk of the device fabrication process. For example, during the fabrication of th e MEMS electrical contact test device described in Chapter 3, the gold electropl ate seed layer shown in Fig. 6-1 could incorporate a graded gold-filler distribution as the electrical contact interface between cantilever and signal line. The biphasic seed layer would not substantially affect the electroplating process la yer since the composition of the film is predominately gold at the interface of the seed layer a nd electroplated material. Alternatively, the composite material could be deposited on top of the sign al layer instead of the electroplate seed layer, but this would require an additional mask layer and deposition step in the MEMS fabrication process.

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95 Figure 6-1. Potential composite material location in the MEMS electrical contact device fabrication process The main contribution of this work to the larger body of knowledge of MEMS electrical contacts is the eluc idation of how com posite electrical materials can enhance MEMS device performance by reducing me tallic adhesion without unduly impacting contact resistance. The effects of includi ng low-adhesion filler phases in a highlyconductive gold matrix were demonstrated e xperimentally and simulated numerically. The key finding was that the ra tio of high-conductivity to lo w-conductivity phases in the composite electrical material should remain larger than the ratio defined by the percolation threshold of the film structure. A composite material with a composition too close to the percolation threshol d will experience a large increase in film resistivity that overshadows any modest decrease in the adhere nce of the interface. Figure 6-2 illustrates this point. If the composite film composition remains in the gold-rich region, incremental increases in film resistivit y (and correspondingly contact resi stance) remain modest as

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96 gold percentage decreases. At the percolat ion threshold, small decreases in gold percentage cause large incremental increases in film resistivity. Figure 6-2. Regions of acceptable and undesirable resistance for gold-alumina composites approaching and beyond the percolation threshold Numerical modeling of potenti al composite electrical co ntact materials can assist the down-selection of candidate s films for experimental tes ting in both nano-indentation and actual devices. The ability to computati onally evaluate materi als before expending substantial effort in sample fabrication a nd testing is a useful capability for MEMS designers concerned with improving electrical contact device performance and reliability.

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97 CHAPTER 7 CONCLUSIONS The main conclusions of this document ar e listed below. These points are the most notable ideas and concepts de veloped concerning composite electrical contact materials for MEMS applications. 1. MEMS electrical contacts may be experime ntally simulated using a combined lowforce mechanical test platform and electri cal contact resistance measuring means. This capability enables rapid assessment of potential composite electrical materials for MEMS applications. Specifically, comb ined high-resolution measurements of contact force, displacement, and cont act resistance provides insight into degradation processes an d variation with cha nging contact conditions. 2. An electrical contact resistance MEMS devi ce was designed and fa bricated to allow for microsystem testing of composite electr ical contact materials. The design of the device removed the dependence of the electrostatic actuation force on the interfacial contact fo rce and enabled cyclic testing of low-force metal contacts for cycle numbers much greater than attainable in nano-indentation testing. Also, the single contact dimple increas ed the likelihood of resistan ce degradation mechanism identification with surface analytical techniques, impr oving the ability to relate observed resistance changes to physical phenomena. 3. The contact resistance of hot-switched, lo w-force metal contacts degraded rapidly in both nano-indentation and MEMS de vice settings. Hot-switched contact resistance in the electrical contact MEMS device degraded after a period of several thousand cycles, while the nano-indentati on contact resistance degraded after 25-75 cycles. The onset of the degradation was dependent on the voltage and current in the contact as well as the rate at the which the contacts closed (see Appendix A). 4. The combination of rough surface contact modeling using real surface topography with electrical current simulation usi ng a three-dimensional resistor network allowed for a numerical recreation of ME MS device composite material contacts. This methodology allowed for estimations of contact area size, contact resistance, interfacial adhesion, and contact temperature rise. 5. The simulated results for low-force composite material device contacts demonstrated that composite materials near their percolation threshold quickly lose their conductivity and therefore their usefulness as electri cal contact materials. The

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98 experimentally measured contact resist ance of pulsed-laser deposited composite films also showed a strong dependence of film conductivity on filler percentages near percolation threshold. Functional composite electri cal contact materials must be created with high-con ductive phase percentages su fficiently removed from the percolation threshold, at least 10 to 20% more conductive phase than at the percolation threshold. 6. Thin film co-deposition methods, such as pulsed-laser depositi on or physical vapor deposition sputtering, afford large control over the selectable composite constituent phase materials as well as the deposited phase distribution within the composite. The capability to tailor the contact material composition is a useful ability in the fabrication of microsys tem electrical contacts. 7. The selection of a highly-conductive f iller phase, over a less-conductive filler phase, reduces the severity of the percol ation threshold penalt ies on the composite conductivity for filler percentages near the percolation threshold. 8. The distribution of the filler particles in th e gold matrix affected the location of the percolation threshold. Numerical si mulation found that by using a graded distribution of filler particles with resp ect to the contact in terface instead of a uniformly random through-thickness dist ribution reduced the minimum gold percentage by a factor of two. The critical concept is that conductive channels must exist through the film, otherw ise the current will be una ble to percolate through the low-conductivity phase and the overall film conductivity will be severely reduced.

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99 APPENDIX A HOT-SWITCHED ELECTRICAL CONTACT RESISTANCE DEGRADATION Carbonaceous Surface Contamination Effects Hot-switched electrical contact resistance testing of a metal coated sphere-on-flat geometry was performed using a modified nano-indentation te st platform. The experimental objective was to examine how hot-switched cyclic contact affected the contact resistance and adhe sion of low-force metal c ontacts indicative of MEMS electrical contacts. The test conditions mimi cked the contact geometry and contact load of a silicon-micromachined environmental sensing switch. The electrical contact materials in the experiment matched the materials in the MEMS device. Schematic diagrams of the experimental apparatus and contact zone are depicted in Fig. A-1. The apparatus measured the force applied to, and displacement of, the sphere, while simultaneously recording the re sistance determined from the voltage drop measured across the contact. The source voltage established across the contact was set to 3.3 V, the operational specifica tion of a MEMS environmentalsensing switch. Instead of using a source-meter to simultaneously supply current and measure contact voltage drop, a current-limiting potentiomete r with a range of 1-200 k was used to limit the maximum amount of current in the circ uit, similar to a voltage-divider.

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100 Figure A-1. Schematic of the nano-indentati on apparatus and the contact zone used in hot-switched cyclic contact testing The sphere contact samples we re 3.2 mm diameter Cerbec Si3N4 balls. The spheres were sputter-coated with a 100 nm thick titanium adhesion layer followed by a 1000 nm gold contact layer. Silicon wafer flats were sputter coated with a mixed titanium-titanium

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101 nitride adhesion/barrier laye r that was 120 nm thick. The adhesion/barrier layer deposition started as pure titanium. Then nitrogen was gradually admitted into the chamber to form a reactively-sputtered titanium nitride layer. The nitrogen concentration was then gradually reduced until pure tit anium was again deposited on the surface. Lastly, a 200 nm thick platinum contact laye r was deposited. Before experimental testing the contact surfaces were cleaned with an ultrasonic acetone wash, followed by an ultrasonic methanol wash, and then a postwash UV-ozone clean to remove any bulk contaminants. The as-deposited root-mean-square roughne ss of the spheres and flat contact samples were measured by white-light interfer ometry to be 15 nm and 3 nm, respectively, and were reproduced over all samples tested. The stainless steel a nd Pyrex environmental enclosure isolated the ar ea immediately around the cont act and attained an oxygen concentration of 3 ppm when filled with fl owing nitrogen. Otherwise, laboratory air experiments were run in a cl ass 1,000 clean room at 22 3 C and 30 10% relative humidity. Figure A-2 is an example of a single cont act cycle, in this case the first contact cycle for the Au-Pt contact pair. The coated sp here and flat were brought into electrical contact at a constant load rate until a maximum target mechanical load of 150 N was reached. The maximum load was held for seve ral seconds for an averaged measurement of contact resistance at peak load. Then, the contact was unloaded at the same rate until the surfaces separated, denoti ng the amount of adherence fo rce required to complete surface separation. Force, displacement, and resistance were sampled at 5 Hz throughout

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102 the contact cycle. This cycle would be re peated many times at the same location to investigate changes of contact resistance a nd adhesion behavior with cyclic contact. Figure A-2. Single hot-switched experimental contact cycle Figure 3 is a plot of the average contact resi stance at peak load and pull-off force as a function of cycle number for a Au-Pt contact c ouple tested in laborato ry air. Initial tests resulted in an averaged contact resistance of 930 m for a force level of 150 N with an initial pull-off force of 45 N. The experimentally measured resistance was larger than the predicted resistance using a simple plastic contact model given by Holm, /2/()nRFH, suggesting that the metal surf aces were covered with some contamination. This initial resistance rema ined roughly constant until cycle 20, at which point the resistance rapidly in creased by many orders of magni tude to a highly degraded resistance level.

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103 Figure A-3. Cyclic electri cal contact resistance degr adation of Au-Pt contact An examination of Fig. A-3 shows th e onset and magnitude of the resistance degradation in laboratory ai r. The resistance trend in Fig. A-3, a sharp increase in resistance that approaches an asymptotic value, is very similar to the results of Neufeld who concluded that the formation of carbona ceous surface contamination was the cause [62]. The actual pull-off force decreased from 45 N at the first cycle to an average of 7 N from cycle 10 to the end of the experiment, which is close to the detection limit of the apparatus. The decrease of pull-off force co mbined with the increased contact resistance suggested that the contact surfaces were b ecoming covered with non-metallic species that were inhibiting electrical conduction and decreasing the a dherence of the contacts. Inert environment combin ed with reduced-current tests were performed to ascertain the sensitivity of the contaminati on to different environments and electrical loads. These results are shown in Fig. A-4. Reduced current tests we re run in both inert and laboratory environments at maxi mum electrical currents of 3 mA, 300 A, and 30 A. Resistance degradation occurred w ithin 75 cycles at 3 mA and 300 A currents in

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104 laboratory air, but was not seen for up to 200 cycles for 30 A of current regardless of environment. Figure 4 shows that as the re lative isolation of the contact from the laboratory environment increases, the cont act resistance degradation decreases in magnitude. Reduced current test results establis hed that there is also a current threshold below which the onset of degradation is eliminated or significantly delayed. Figure A-4. Inert environment and reduced current testing The composition of the ambient air a nd controlled environment chamber was analyzed using an automated thermal deso rption/gas chromatography/mass spectrometry (ATD/GC/MS) system. The purpose of the anal ysis was to determine the abundance of hydrocarbon species surrounding the contact zone in the two environments. Sampling results of the gaseous environment inside th e flowing-nitrogen chamber showed a four order-of-magnitude reduction in measured hydrocarbon content versus the ambient laboratory air environment. That difference correlates with th e change in the resistance degradation from air to nitrog en environments seen in Fig. A-4. The largest source of

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105 hydrocarbon contamination in the flowing n itrogen environment or iginated from the plastic tubing used to connect the environment chamber to the nitrogen source. Figure A-5 shows the cyclic resistance for a current of 3 mA in an inert nitrogen environment. The contact resistance values we re the average over the time period at peak load, per each cycle as depicted in Fig. A6. It appeared that a somewhat conductive contamination layer evolved w ith repeated contact in Fig. A-6. The layer grew until between cycles 60 and 75, when a higher stea dy-state resistance was achieved. At cycle 198 the maximum load was increased to 1 mN a nd the contact resistance returned to the initial values, implying that the contamination layer was breached by the added force. When the maximum load is reduced back to 150 N in subsequent cycles, the resistance returned to its higher value. Figure A-5. Cyclic resistance degradation for inert environm ent testing with momentary increases in peak load to 1 mN for cycles 198-208, up from 150 N for all other cycles

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106 Figure A-6. Resistance vs. time fo r individual contact cycles fr om Fig. A-5 with the grey area denoting the peak-load hold period An alternate hypothesis is that upon application of a higher load, fresh nondegraded asperities are bei ng brought into contact. Th ese new contacts are then responsible for the lower cont act resistance, not the ruptur e of a contaminant layer. However, for the cycles immedi ately following the increased load cycles when the load is returned to 150 N, the resistance does not instantaneous ly return to the degraded state as it would if the original asperities were pe rmanently degraded. Instead, several contact cycles are required for the resi stance to return to the degr aded state. Presumably, the process that created the surf ace layer re-contaminated the contact sites over several cycles. Figure A-7 shows magnified views of cycle 1 and cycle 200. The applied force required in cycle 200 to obtain a similar resistance to cycl e 1 is approximately 20 times larger than the applied force in cycle 1.

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107 Figure A-7. Magnified views of cycle 1 and cycle 200 fr om Fig. A-6 showing the amount of force required to obtain low resi stance for non-degraded and degraded contacts The experimental results s uggest that a load-bearing c ontaminant film was formed by repeated hot-switched elec trical contact. A possible c ontaminant creation mechanism involves the production of non-conductive carbonace ous surface films in the presence of low-energy contact arcs. S ub-micrometer gap arcing has been proposed to cause breakdown due to field emissi on currents in contacts wher e conventional atmospheric breakdown is not possible [84]. These arcs ex ist below the predicte d level of breakdown,

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108 as obtained from Paschens law, but still pr ovide an energetic stim ulus at moments of close surface contact to create non-conductive carbonace ous surface films. These conclusions were also drawn by Wallash who st udied the effective ranges of different arc phenomenon using an etched metal microscale test apparatus [85]. Alternatively, metalbridge evaporation on contact break can pyrol yze surface contaminants into insulating layers and precipitate resistance degradation. While the steady-state cu rrent in the contact was constant during contact, th e current in the separating me tal bridge originating from transient inductive voltage spikes is sufficien t to rupture the bri dge and energetically decompose carbonaceous species in the immedi ate vicinity of th e contact. Repeated occurrence of this process would eventually eliminate any conductive pathway between the surfaces and cause the re sistance of the system to be governed by the surface contaminates. Compared to the conductivity of bulk metals, this contaminating process would lead to a degraded contact resistance. Transient arc phenomena have long been recognized as problematic to hotswitched electrical contacts for large-scale contact devices. Gray analyzed degraded switch contact surfaces retrieved from opera tional telecommunication environments and compared them to similar contacts degraded experimentally [86]. The combined presence of carbonaceous surface contamination a nd contact arcing produced non-conductive surface films. Also, the produc tion of surface contamination enhanced arcing processes on subsequent cycles, thereby further accelerati ng degradation of the contact resistance. This feedback process was referred to as contact activation. The arc-initiated production of an insulating SiO2 film from adsorbed silicone vapor in micro-relays was examined by Tamai whose results bear a str ong resemblance to the trends observed in

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109 this work, although carbonaceous contaminati on is suspected in the present case. The dependence of resistance degrad ation on electrical power was also investigated in [87]. Smaller amounts of electrical power altered the arcing m echanism and enabled longer non-degraded cycle times. This trend is consiste nt with the results of this study showing a current-dependent resistance degradation. The me chanical load is also an important factor that changes the onset of degradation fo r low-power contacts where contaminant production is present. Therefore, the proposed explanation for the observed resistance degradation is that in the presence of lo w energy arcs, load-su pporting insulating films are formed from adsorbed contaminants at the contact surfaces, which impede conduction. At some critical contamination th reshold, the electrical contact interface becomes completely covered, causing a sudden and large increase in resistance. Further experiments examining the dependence of hot-s witched contact resistance on arcing were performed to support this hypothesis. Figure A-8 shows the results of cold-sw itched vs. hot-switched contacts for the Au-Pt contact. For the first 150 cycles of the cold-switched cont act, the voltage was manually switched on just as the peak load was reached and switched off as the load began to decrease from the peak value. The measured resistance did not increase at all during this cold-switched period. The cont act was then hot-sw itched by leaving the voltage supply on after cycle 151. The resistance degraded in a similar period to previous hot-switched tests, indicating that the presence of voltage bias at moments of close surface contact is the likely source of the obs erved degradation. Furthermore, if the contact resistance degradation was indeed caused by arc events at moments of close

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110 surface proximity, then similar experiments usi ng a modified experimental circuit, which is designed to specifically suppress arcing, would confirm this hypothesis. Figure A-8. Dependence of resistance degradatio n on hot-switched contact Holm describes how a capacitive-quench circuit can alleviate the detrimental effects of voltage transients at moments of surface contact [33]. The capacitive-quench circuit consists of a resistive and capacitive el ement in series, which is placed in parallel to the contact. As the current-carrying cont act surfaces suddenly separate, any inductance in the non-quenched circuit will act to maintain current flow by increasing the voltage across the contacts. The arc-quenching RC ci rcuit element allows for an alternative discharge path, effectively r obbing the energy available for arc formation in the gap. Figure A-9 shows the contact resistance versus cycle for hot-switched contacts with and without the capacitive quench circuit in parallel to the contact. The values used for the resistor and capacitor were 1000 and 0.1 F, respectively. It is apparent that

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111 when the capacitive quench circuit was rem oved from the circuit the contact resistance degraded as in the previous hot-switched tests. Figure A-9. Dependence of resistance degradation on capacitive-quench presence Oscillograms supporting this arc-quench ing hypothesis are shown in Fig. A-10. The cycles where the capacitive que nch circuit is in parallel with the contact have few, if any, voltage transients at the moment of contact make and break. As soon as the quench is removed at cycle 150 the number of voltage transients increases. The difference is especially significant at cont act break, where no transients were observed at all from cycles 1 to 149. From cycle 150 on, the numbe r and frequency of the voltage transients, now attributed to arcing, in creases rapidly along with the degrading contact resistance. These results provide sufficient evidence th at the contact resistance degradation was caused by transient electrical arc events at the instances of contact make and break. Specific examination of the relative importa nce of contact make-arc and break-arcing was not performed.

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112 Figure A-10. Oscillograms showing the change in voltage transients at moments of close surface contact after capacitive -quench circuit is removed The hypothesis of micro-arc induced cont aminant growth correlated very well with the observed experimental trends. Howeve r, it was not possible to directly correlate observed surface contaminants to the exact area of contact in these bulk-film experiments. For the experimental conditi ons and materials, a simple contact size calculation using Hertzian el astic-contact theory placed an upper-bound on the contact spot diameter at roughly 2 m. Surface roughness effects fu rther reduced the size of the contact area and hindered detec tion of the exact points of co ntact on a large, bulk contact sample.

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113 However, post-test examination of severa l test surfaces showed large, blackened regions on the contact surfaces, sim ilar to that witnessed by Tamai [87]. The AES spectra and accompanying SEM of the analyzed regions is shown in Fig. A-11. Auger Electron Spectroscopy (AES) examination of the large blackened region (Point 2) showed almost pure carbon in these spots. Th e spectra for a nominally un-contaminated surface location (Point 1) showed trace contam inants like sulfur and carbon, as well as the contact metal platinum. The observation of blackened car bon residue on the post-test surfaces was supportive of the hypothesis of decompos ed carbon species during hot-switched operation, but until the contact su rfaces can be directly analy zed before and after testing, such as in a MEMS electrical contact device, further work is required to definitively link the formation of carbon to the meas ured resistance degradation. Figure A-11. Auger Electron Sp ectra of suspected contam ination region and of the surrounding metal surface

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114 Silicone Oil Contamination Effects The presence of silicones in electronic equipment is a well known source of electrical contact contamination in switches and relays [88]. Silicone oil, or dimethyl silicones, is the name given to a family of synthetic polymers composed of a repeating SiO backbone and carbon-linked side-groups expressed by the chemical formula [(CH3)2SiO]n. Despite the beneficial pr operties of silicones, such as chemical stability and friction reduction of slidi ng contacts, their presence has been shown to impair the performance of electrical contacts thr ough insulating surface film formation and accumulation. This insulating film is produced by the energetic decomposition or oxidization of surface-adsorbed silic one oil and is composed of SiO2 or amorphous carbon [87]. These compounds are electrically insulating and gr eatly impair the conductivity of contact interfaces. The origins and effects of silic one oil contamination originating from evaporation or direct surf ace diffusion has been extensively studied on macro-scale electrical relays [89-90]. Hotswitching, or making a nd breaking electrical contact with potential bias present, prom otes silicone oil decomposition due to the presence of electrical arci ng between contacts. The effect s of hot-switching on electrical contact resistance degradation has also been investigated [90]. While there have been numerous studies investigating the effects of silicone oils on macro-scale switches and relays, the impact of silicone oil contamination on low-force electrical contacts, as in MEMS has not been previously studie d. It is expected that the effects of insulating film formation will be magnified in MEMS electrical contacts as the surface forces present are several orders of ma gnitude less than in the electrical relays studied previously [89]. The effects of silicone oil contamination on hot-switched gold contacts at forces representative of MEMS devices was investigated experimentally. The

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115 dependence of contact closure rate and app lied electric field on observed resistance degradation was also investigated. Low-force electrical testing of self-mat ed gold surfaces was performed using the modified nano-indentation a pparatus described above. All experiments were performed inside the stainless steel a nd Pyrex environmental enclosure that isolated the area immediately around the contact. The atmosphere inside the enclosure attained an oxygen concentration of 3 ppm when filled with flowing nitrogen. In all tests, a Si3N4 sphere, having a nominal radius of 0.8 mm and sputte r-coated with 500 nm of gold metal, was brought into contact with a silicon wafer, also sputter-coated with 500 nm of gold, until a maximum target load of 100 N was reached. The measured r.m.s. surface roughness of the spherical and flat contacts were 11.6 nm and 3.2 nm, respectively. The electrical circuit was run with a maxi mum sourced current of 3 mA and a non-contact voltage constrained to 3.3 V. Before the onset of hot-switche d contact experimentation, a 2 L volume of 10 cSt. silicone oil (Dow Corning DC200) wa s deposited into the gap upon the spherical contact as pictured in Fig. A-12. This amount of silicone oil served to fully coat the electrode surfaces during cyclic contact. The oi l spot was inspected after each experiment to ensure the silicone oil wa s still present within the contact zone, and in all tests it remained in excess. The electrical contact resist ance behavior for repeated contact in the same location for gold-gold contacts compared to those cont aining silicone oil is shown in Fig. A-13. Each data point in Fig. A-13 is composed of the contact resistance averaged for five seconds while the load is held at the peak value. For the silic one oil contaminated

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116 contact, the peak-load resistance increased al most 10 orders of magnitude within 25 hotswitched contact cycles. The uncontaminated contact did not experience an increase in measured resistance over the same number of contact cycles. The degradation onset seen in Fig. A-13 was reproducib le over a range of c ontact cycles for the same experimental conditions. The onset variabil ity stemmed from su rface roughness effects on contact between differing coated sphere and flat samples. Figure A-12. Schematic of the contact zone with silicone oil introduced between the electrodes Figure A-13. Resistance degradation of s ilicone oil contaminated gold-gold contact

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117 The resistance-time histor y of contact cycle number 14 taken from Fig. A-13 (occurring just prior to the sharp resistance increase) is shown in Fig. A-14. While the peak-load, averaged contact resistance in Fig. A-14 appears to be non-degraded, examination of the resistance change with c ontact force prior to p eak loading exhibited resistances of 100 and greater. The resistance decreased below 10 only after the load surpassed approximately 90 N. With increased numbers of contact cycles, the peak-load resistance minimum decreased in width unt il the periods of increased resistance continuously spanned the contact force-time history. Once this o ccurred, the peak-load contact resistance exhibited a sharp increase as seen in Fig. A-13. Figure A-14. Resistance and load history for contact cycle 14 from Fig. A-13 The dependence of the contact resistance degradation on contact closure rate was also investigated. The cyclic contact e xperiments were repeated using the same conditions, except that the rate at which the surfaces come into contact was varied. The results of the contact closure ra te variation is shown in Fig. A-15. It is clea r from Fig. A15 that the slower the electrodes come togeth er, the more rapidly the contact resistance increased. Figure A-16 shows the dependen ce of the resistance degradation on the

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118 potential bias across the contact gap for a fixed closure rate. By simply reducing the open-circuit voltage to 1 V, the degradati on was not observed within 100 closures, while a 10 V bias resulted in almost immediate degradation. Figure A-15. Resistance degrad ation dependence on gap closure rate for an applied voltage of 3.3 V Figure A-16. Resistance degrad ation dependence on contact ga p voltage for an approach rate of 86 nm/s

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119 Most often, the reason for hot-switched contact failures is arc damage that destructively alters the electrode surfaces. Th is arcing occurs predominately at voltages higher than those used in MEMS electrical contact devices, on the order of hundreds of volts. However, other investigat ors suggest that non-contact voltage levels thought to be safely underneath the atmospheric ionization th reshold referred to as the Paschen Law limit, may also negatively affect electrode surfaces through an arci ng process similar to vacuum breakdown [84]. Instead of the nonlinear Paschen Law contact gap-voltage relationship, the voltage breakdown threshol d in this process for gaps less than 6 m has been experimentally determined to be propor tional to the gap di stance, shown in Eq. (A.1) [91]. This equation allows for an estimate to be made of the contact gap distance at which electrical transient activ ity will begin to affect the contact surfaces for a given electrode bias. The conser vative value assigned to K based on the measured data was 110 V/ m [91]. BDgapVKd (A.1) The hypothesized degradation mechanism respons ible for the behavior seen in Fig. A-13 is the decomposition of surface contam inants into insulating compounds by field emission current excitation, occurring during times of close surface proximity where the electric field is largest. Significant non-c ontact field emission curre nts, on the order of milliamps, have been experimentally measured in 5 nm 5 m gaps for sub-Paschen limit voltages [85]. An expression for the field-em ission current is shown in Eqs. (A.2-A.3) [85]. 3/2 2 exp B IAE FE E (A.2)

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120 V E d (A.3) The variable is the material work-function and E is the electric field in the contact gap. The electric field is a function of the applied voltage V, the gap distance d, and the constant which is a geometrical field enhan cement factor that includes surface roughness effects on local field strength. The constants A and B are 6 6.210/ xa and 93/2 6.67x10, respectively, where a is the electron emitting area. A more thorough explanation of the quant ities contained in Eq. (A.2-A .3) is given by Slade [84] and Wallash [85]. Equations (A.2-A.3) neglect any influence of the silicone oil on the electric field or field-emission current. However, Eqs. (A.2-A.3 ) are still useful in examining the trends seen in Figs. A-15 and A-16. The electric fiel d at very small gap distances can be on the order of 10 MV/cm or higher. A large electric field would cr eate a large field emission current in the contact gap, similar to a colu mn of ionized gas molecules in atmospheric arcing. However, if the contact gap can be qui ckly closed, the time the electrode surfaces spend within the critical gap distance wher e field emission current s become significant will be decreased, limiting the degrading effects on the silicone oil. Fig. A-17 shows the number of cycles fo r the measured contact resistance to become greater than 50 plotted against the time at which the contacts are within the critical gap distance of 30 nm for an applied voltage of 3.3 V. The 50 limit was chosen as a value above which the contact was comp letely degraded by a contaminant film for the maximum load applied in the experiment.

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121 Figure A-17. Cycles to failure (R > 50 Ohms ) dependence on time spent in the critical gap distance of 30 nm Figure A-18(a-d) shows oscillos cope traces for the first co ntact cycle at each of the respective rates. The time fo r which electrical transient activity is present in each oscillogram is related to the calculated time that the contact spends within the critical gap. These electrical transients, in this cas e field emission curren t-induced arcing, are hypothesized to be energetically decomposi ng the silicone oil into insulating surface products. The more time the contaminated surfac es are exposed to th ese transients during contact make and break, the more quickly the contact resistance will degrade due to interfacial contaminants bei ng formed. Also plotted in Fig. A-18 is the calculated gap distance as a function of time, based on the closure rate. Within the critical gap distance of 30 nm, the measur ed transient activity peri od corresponds well with the amount of time the contact surfaces spend with in the gap distance. The true gap distance varies around this calculated value due to mechanical vibration and oscillation of the spherical contact as it appro aches the flat. The non-contact vibration-noise amplitude of the nano-indentation apparatus was measured to be less than 5 nm.

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122 A B C D Figure A-18. Oscillograms of contact volta ges at closure rates of 400 to 40 nm/s The formation of surface contaminant la yers suggests that the resistance degradation process would be affected by in creasing contact force, as any interposed contaminant materials would mechanically ru pture as contact force was increased. Figure A-19 shows the effect of increasing contact load after degradation has occurred for the experiments shown in Fig. A-16. The amount of load required to regain metallic contact, denoted by a return to 1 increases with increasing appl ied voltage. This suggests that at higher electric fields, decomposition occurr ed more rapidly creating a thicker layer, and more mechanical deforma tion was required is break th rough the contaminant layer. This effect is detrimental considering that MEMS devices can only apply a limited amount of contact force, and therefore at some point are unable to break through contaminant layers.

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123 Figure A-19. Mechanical load re quired to attain at least 1 after degrada tion occurred (zero load required at 1 V si nce no degradation occurred) Surface analysis of post-degradation d ecomposition products was attempted using Auger Electron Spectroscopy (AES) and Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) to ascertain the co mposition of the insulating layer. However, unlike the insulating layer formation witne ssed in other studies, the products formed during low-force contact were either too sma ll to be visually located, or were removed during cleaning of the excess silicone oil to permit surface analysis [87]. Subsequent AES and TOF-SIMS analysis of the location wher e contact was suspected showed traces of silicone oil, but no SiO2 or other reaction product. Like all surface contamination, the pr esence of silicone oil in dynamically operating MEMS electrical contacts should be minimized to prevent degradation and extend operational device life. This is challengin g give the mobility of silicone oil in both the vapor and liquid phase, allowing for even small amounts of silicone oil to migrate to contact surfaces inside an otherwise clean environment. The rate of contact closure determined the period during which the contac t surfaces are subjected to high electrical

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124 fields. The faster the operation, the more cy cles required for silicone oil degradation to occur. It is possible that th rough sufficiently rapid actuation, the critical gap distance may be traversed while allowing minimal transf ormation of surface contaminants. However, hot-switching real MEMS devices in the pr esence of bulk fluid will be limited by fluid decomposition to some degree. Similar to th e contact closure rate, the applied voltage across the contacts influenced the onset of degradation. Lo wer applied voltages extended operational lifetime, and in one case elimin ated degradation for the duration the of testing. The degradation products formed we re mechanically disp laced with increased contact force. Overall, it is clear that the combination of silicone oil and low-force MEMS electrical contacts pr esents a challenge to desi gners aiming for extended, nondegraded device lifetimes.

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125 APPENDIX B MODIFIED NODAL ANALYSIS The mathematical technique us ed to solve for the current and voltage distributions within a random resistor network is called Modified Nodal Analysis (MNA). The application this techniqu e can be summarized as follows for a circuit with n nodes and m voltage sources [92]: 9. Select a reference node (usually ground) and name the remaining n-1 nodes accordingly. 10. Assign a name to the current passing through each voltage source. 11. Apply Kirchoffs current law to each node. 12. Write an equation for the voltage supplied by each voltage source. 13. Solve the system of equations for the n-1 unknown nodal voltages. When MNA is applied to a circuit network with only passive elements (resistors) and independent sources, the resulting syst em of equations is shown in Eq. (B.1). A xz (B.1) The A matrix is nmnm in size and is composed of only known quantities. The nn region in the upper left of A is populated only with passive resistances. In this region resistors connected to gr ound appear only on the diagonal whereas elements not connected to ground a ppear in both the dia gonal and non-diagonal terms. The rest of the A matrix is composed of values that are 1, 0, or -1. These values are for relating which nodes are connected to sources and whether those sources are connected to ground.

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126 The x matrix is a 1 nm vector that contains the unknown nodal voltages and the currents passing through the inde pendent voltages sources. The top n elements are the nodal voltages while the bottom m elements are the currents. The z matrix is a 1 nm vector that holds only kn own quantities. The top n elements are the sum of the any current sources, while the bottom m elements are the voltage sources present in the network. The circuit network is solved by simple matrix inversion shown in Eq. (B.2). 1 x Az (B.2) After the solution of Eq. 2, the voltage at each node is known as well as the total current supplied by the supply. From this the current distri bution within the network can be calculated as well as the to tal resistance of the network. This method is very methodic and highly amenable to computerization. It is because of this that MNA was chosen to compute the electrical resist ance of a composite medium, with the ultimate goal being to investigate how the compositional variations affected performance of MEMS electrical contacts. The use of MNA to solve for the electrica l resistance of the composite is very similar to using the finite-element method (F EM) in solid or fluid mechanics. Each node is connected to its neighbor nodes by a resist or. The application of MNA to solve for the nodal voltages and supply current is straightforward. The A matrix in Eq. (B.2) is composed of four sub-matrices, shown in Eq. (B.3). GB A CD (B.3) The G matrix, also called th e conductance matrix, is nn and is determined by the interconnections between resistors. The B matrix is nm and is determined by the

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127 connection of the voltage sources. If onl y independent sources are present, the C matrix is simply the transpose of the B matrix. The D matrix is mm and is a zero matrix if only independent sources are present. The creation of the G matrix is performed us ing the following steps: Each element in the diagonal of G matrix is the sum of the conductance (1/R) of each resistor connected to the corresponding node. The first diagonal element would therefore be the sum of all of the con ductances connected to node 1, and so on through all n nodes. 14. The off-diagonal elements are the negativ e conductance of the element connected to the pair of corresponding nodes. A resist or between nodes 1 and 2 is entered into the G matrix at location (1,2) and (2,1) as a value of 1,21 R The B matrix is composed only of 0, 1, and -1 elements. If the positive terminal of the ith voltage source is connect to node k, then the element (i,k) in the B matrix is 1. If the negative terminal of the ith voltage source is connect to node k, then the element (i,k) in the B matrix is -1. Otherwise, elements of the B matrix are zero. As stated previously, if only independent sources are used, the C matrix is simply the transpose of the B matrix and the D matrix is a zero matrix. Equation (B.4) shows an example A matrix constructed for the example circuit shown in Fig. B-1. Equations (B.5-B.8) show the individual sub-matrices that constitute the A matrix. Figure B-1. Example circuit for A matrix construction

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128 122 223111 1 111 0 100 RRR A RRR (B.4) 122 223111 111 RRR G R RR (B.5) 1 ,10,0 0 BCD (B.6-B.8) The construction of the x matrix for the circuit shown in Fig. B-1 is straightforward. Since 2 n and 1 m the x matrix is a 3x1 column vector containing the desired unknowns, shown in Eq. (B.9). 1 2 v x v iV (B.9) The z matrix is also simply constructed. The top n elements of the z matrix are populated with the sum of the current sources entering each respective node. If no current sources are present, as in Fig. B-1, then the n elements of the z matrix are zero. The bottom m elements of the z matrix are populated with th e amount of voltage produced by the source. The z matrix for Fig B-1. is shown in Eq. (B.10). 0 0 z V (B.10) Assembling the matrices from Eqs. (B.4),(B .9), and (B.10) and substituting them into Eq. (B.2), the final form of the MNA technique is obtained, shown in Eq. (B.11). The accuracy of the MNA technique was eval uated using a Simulation Program with

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129 Integrated Circuit Emphasis (SPICE) program. The example circuit of Fig. B-1 was constructed in the SPICE program and the output was compared to the results obtained from Eq. (B.11). If assembled correctly the result obtained from MNA will match the results obtained from the SPICE program. This process was repeated for several other simple circuits, all of which yielded th e same output for both SPICE and MNA nodal voltages and supply current. The applica tion of MNA to the composite medium resistance calculation is an uncomplicated endeavor using the rules outlined above. 1 122 223111 1 10 111 200 100 RRR v v RRR iVV (B.11)

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130 LIST OF REFERENCES 1. Romig Jr., A.D, Dugger, M.T., and McW horter, P.J, Material Issues in Microelectromechanical Devices: Scien ce, Engineering, Manufacturing, and Reliability Acta Materialia, 51, No. 19, 2003, p. 5837-5866 2. Beale, J., and Pease, R.F., 1992, Appa ratus for Studying Ultra-Small Contacts, Electrical Contacts 1992. Proceedi ngs of the Thirty-Eighth IEEE Holm Conference on Electrical Contacts, Philadelphia, PA. pp. 45-49. 3. Bowden, F.P. and Williamson, J.B.P., 1958, Electrical Conduction in Solids. I. Influence of the Passage of Curre nt on the Contact between Solids, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 246(1244), London, pp. 1-12. 4. Cohen, S.R., Neubauer, G., and McCle lland, G.M., 1990, Nanomechanics of AuIr Contact Using a Bidirectional Atomic Force Microscope, Journal Vacuum Science and Technology, 8(4), pp. 3449-3454. 5. Crane, G.R., 1981, Contact Resistan ce on Surfaces with Non-Uniform Contaminant Films, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 4(1), pp. 5-9. 6. Hannoe, S., and Hosaka, H., 1996, Electrica l Characteristics of Micro Mechanical Contacts, Microsystem Technologies, 3, pp. 31-35. 7. Hosaka, H., Kuwano, H., and Yanagisawa, K., 1994, Electromagnetic Relays: Concepts and Fundamental Characteris tics, Sensors and Actuators A, 40, pp. 4147. 8. Hyman, D., and Mehregany, M., 1999, Cont act Physics of Gold Microcontacts for MEMS Switches, IEEE Transactions on Components and Packaging Technology, 22(3), pp. 357-364. 9. Koidl, H.P., Rieder, W.F., and Salzmann, Q.R., 1998, Parameters Influencing the Contact Compatibility of Organic Vapour s in Telecommunication and Controls Switching, Electrical Contacts 1998. Proceed ings of the Forty-Fourth IEEE Holm Conference on Electrical Contacts, Arlington, Va. pp. 220-225 10. Kruglick, E.J.J., and Pister, K.S.J., 1999, Lateral MEMS Microcontact Considerations, Journal of Micromechanical Systems, 8(3), pp. 264-271.

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131 11. Maddock, A.J., Fielding, C.C., Batchelo r, J.H., and Higgins, A.H., 1957, British Journal Applied Physics, 8(12), pp. 471-476. 12. Majumder, S., McGruer, N.E., Adams, G.G., Zavracky, P.M., Morrison, R.H., and Krim, J., 2001, Study of Contacts in an Electrostatically Actuated Microswitch, Sensors and Actuators A, 93, p. 19-26. 13. Pruitt, B.L., Park, W-T., and Kenny, T. W., 2004, Measurement System for Low Force and Small Displacement Contacts, Journal of Microelectromechanical Systems, 13(2), pp. 220-229. 14. Rieder, W.F. and Salzmann, Q.R., A Tw o Step Procedure to Evaluate Contact Compatibility of Organic Materials, , Electrical Contacts 1995. Proceedings of the Forty-First IEEE Holm Conf erence on Electrical Contacts, Pittsburgh, PA. pp. 267-273. 15. Rohde, R.W. and Pope, L.E., 1983, The E ffect of Surface Prep aration and Heat Treatment on Interfacial Resistance, Fr iction, and Wear of Precious Metal Electrical Contact Alloys, IEEE Trans actions on Components, Hybrids, and Manufacturing Technology, 6(1), pp. 15-20. 16. Schimkat, J., 1999, Contact Measuremen ts Providing Basic Design Data for Microrelay Actuators, Sensors and Actuators A, 73, pp. 138-143. 17. Schneegans, O., Houze, F., Meyer, R ., Boyer, L., 1998, Study of the Local Electrical Properties of Me tal Surfaces Using an AFM with Conducting Probe, IEEE Transactions on Components, Packaging, and Manufacturing Technology Part A, 21(1), pp. 76-81. 18. Tringe, J.W., Uhlman, T.A., Oliver, A. C., and Houston, J.E., 2003, A Single Asperity Study of Au/Au Electrical C ontacts, Journal of Applied Physics, 93(8), pp. 4661-4669. 19. Wang, B., Saka, N., and Rabinowicz, E ., 1992, The Failure Mechanism of LowVoltage Electrical Relays, Electrical Contacts 1992. Proceedings of the ThirtyEighth IEEE Holm Conference on Electrical Contacts Philadelphia, PA. pp. 191202. 20. Gretillat, M-A., Gretillat, F., and de Rooij, N.F., 1999, Micromechanical Relay with Electrostatic Actuation and Metallic Contacts, Journal of Micromechanical Microengineering, 9, pp. 324-331. 21. Kataoka, K., Itoh, T., Okumura, K., and Suga, T., 2002, Proceedings of IEEE ITC International Test Conference, Baltimore, MD. pp. 424-429. 22. Larsson, M.P., and Syms, R.R.A., 2004, Self-Aligning MEMS In-Line Separable Electrical Connector, Journal of Microelectromechanical Systems, 13(2), pp. 365376.

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132 23. Lee, H-S., Leung, C.H., Shi, J., Chang, SC., Lorincz, S., and Nedelescu, I., 2002, Integrated Microrelays: Concepts and Initial Results, Journal of Microelectromechanical Systems, 11(2), pp. 147-153. 24. Liu, Y., Li, X., Takashi, A., Haga, Y., and Masayoshi, E., 2001, A Theromechanical Relay with Microspri ng Contact Array, Technical Digest. MEMS 2001. 14th IEEE International C onference on Micro Electro Mechanical Systems, pp. 220-223. 25. Peroulis, D., Sarabandi, K., and Katehi L.P.B., 2002, Low Contact Resistance Series MEMS Switches, IEEE MTT-S Digest, pp. 223-226. 26. Qiu, J., Lang, J.H., Slocum, A.H., and Strumpler, R., 2003, A High-Current Electrothermal Bistable MEMS Relay, PROCEEDINGS: IEEE Microelectro Mechanical Systems Workshop Kyoto, Japan. pp. 64-67 27. Schiele, I., and Hillerich, B., 1999, Comparison of Late ral and Vertical Switches for Application as Microrelays, Journa l of Micromechanical Microengineering, 9, pp. 146-150. 28. Schiele, I., Huber, J., Hillerich, B., and Kozlowski, F., 1998, Surfacemicromachined Electrostatic Microrelay, Sensors and Actuators A, 66, pp. 345354. 29. Taylor, W.P., Brand, O., and Allen, M. G., 1998, Fully-Integrated Magnetically Actuated Micromachined Relays, Journa l of Microelectrom echanical Systems, 7(2), pp. 181-191. 30. Wong, J., Lang, J.H., and Schmidt, M. A., 2000, An Electrostatically-Actuated MEMS Switch for Power Applications, IEEE Thirteenth Annual International Conference on Micro Electro Mechanical Systems, pp. 633-638. 31. Simmons, J. G., 1964, Potential Barrier s and Emission-Limited Current Flow Between Closely Spaced Parallel Metal Elec trodes, Journal of Applied Physics, 35(8), pp. 2472-2481. 32. Johnson, K.L., 1998, Contact Mechanics, Cambridge University Press, London. 33. Holm, R., 1967, Electric Contacts: Theory and Application Springer-Verlag, New York. 34. Greenwood, J.A., and Williamson, J.P. B, 1966, Contact of Nominally Flat Surfaces, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 295(1442), pp. 300-319. 35. McCool, J.I, 1986, Comparison of Models for the Contact of Rough Surfaces, Wear, 107, pp. 37-60.

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133 36. Bush, A.W., Gibson, R.D., and Thomas, T.R., 1975, The Elastic Contact of a Rough Surface, Wear, 35, pp. 87-111. 37. Francis, H.A., 1977, Application of Spherical Indentation Mechanics to Reversible and Irreversible Cont act between Rough Surfaces, Wear, 45, pp. 221269. 38. Jones, F.L., 1957, The Physics of Electrical Contacts Clarendon Press, Oxford. 39. Greenwood, J.A., 1966, Constriction Resist ance and the Real Area of Contact, British Journal of Applied Physics, 17, pp. 1621-1632. 40. Boyer, L., 2001, Contact Resistance Calculations: Generalizations of Greenwoods Formula Including Interf ace Films, IEEE Transactions on Components and Packaging Technology, 24 (1), pp. 50-58. 41. Timsit, R., 1983, On the Evaluation of Contact Temperature from Potential-Drop Measurements, IEEE Transactions on Components and Packaging Technology, 6 (1), pp. 115-121. 42. Wexler, G., 1966, The Size Effect and the non-local Boltzmann Transport in Orifice and Disk Geometry, Proceedi ngs of the Royal Physical Society, 89, pp. 927-941. 43. Mikrajuddin, A., Shi, F.G., Kim, H.K., and Okuyama, K., 1999, Size-Dependent Electrical Constriction Resistance for Contact s of Arbitrary Size: from Sharvin to Holm Limits, Materials Scien ce in Semiconductor Processing, 2, pp. 321-327. 44. Johnson, K.L., Kendall, K., and Roberts, A.D., 1971, Surface Energy and the Contact of Elastic Solids, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 324(1558), pp. 301-313. 45. Dejaguin, B.V., Muller, V.M., and T oporov, Y.P., 1975, Effect of Contact Deformations on the Adhesion of Particle s, Journal of Colloid and Interface Science, 53(2), pp. 314-326. 46. Tabor, D., 1975, Surface Forces and Surface Interactions, Journal of Colloid and Interface Science, 58(1), pp. 2-13. 47. Maugis, D., 1992, Adhesion of Sphere s: The JKR-DMT Transition Using a Dugdale Model, Journal of Co lloid and Interface Science, 150(1), pp. 243-269. 48. Carpick, D., Ogletree, D.F., and Salmeron, M., 1999, A General Equation for Fitting Contact Area and Friction vs. Load Measurement, Journal of Colloid and Interface Science, 211(3), pp. 395-400. 49. Johnson, K.L., and Greenwood, J.A., 1997, An Adhesion Map for the Contact of Elastic Spheres, Journal of Co lloid and Interface Science, 192(3), pp. 326-333.

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PAGE 150

135 63. Unemura, S., and Aoki, T., 1992, Effects of CO2 Atmosphere on Contact Resistance Characteristics of Noble Metal Contacts, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 15(2), pp. 258-265. 64. Coutu, R.A., Kladitis, P.E., Leedy, K.D ., and Crane, R.L., 2004, Selecting Metal Alloy Electric Contact Materials for MEMS switches, Journal of Micromechanics and Microengineering, 14, pp.1157-1164. 65. Cuthrell, R.E., and Jones, L.K., 1978, Surface Contamination Characterization Using Potential-Current Curves, IEEE Tr ansactions on Components, Hybrids, and Manufacturing Technology, 1(2), pp. 167-171. 66. Han, S.W., Lee, H.W., Lee, H.J., Kim, J.Y., Kim, J.H., Oh, C.S., and Choa, S.H., 2006, Mechanical Properties of Au Thin Film for Application in MEMS/NEMS Using Microtensile Test, Current Applied Physics, in press. 67. Lilleodden, E.T., and Nix, W.D., 2006, Mic rostructural Length-Scale Effects in the Nanoindentation Behavior of Thin Gold Films, Acta Materialia, 54, pp.15831593. 68. Sawyer, W.G., Hamilton, M.A., Fregly, B.J., and Banks, S.A., 2003, Temperature Modeling in a Total Knee Joint Replacement Using Patient Specific Kinematics, Tribology Letters, 15, pp. 343-351. 69. Erts, D., Lohmus, A., Lohmus, R., Olin H., Pokropivny, A.V., Ryen, L. and Svensson, K., 2002, Force Interactions and Adhesion of Gold Contacts Using a Combined Atomic Force Microscope and Transmission Electron Microscope, Applied Surface Science, 188, pp. 460-466. 70. Stafford, C.A., 2002, Metal Nanowires : Quantum Transport, Cohesion, and Stability, Physica Status Solidi (B), 2, pp. 481-489. 71. Rubio, G., Agrait, N., and Vieira, S. 1996, Atomic-Sized Metallic Contacts: Mechanical Properties and Electronic Transport, Physical Review Letters, 76(13), pp.2302-2305. 72. Blom, S., Gorelick, L.Y., Jonson, M., She khter, R.I., Scherbakov, A.G., Bogachek, E.N., and Landman, U., 1998, Magneto -optics of Electronic Transport in Nanowires, Physical Review B, 58(24), pp.305-314. 73. Broadbent, S.R. and Hammersley, J.M., 1957, Percolation Processes. I. Crystals and Mazes, Proceedings of the Cambridge Philosophical Society, 53, pp. 629-641. 74. McLachlan, D.S., Blaszkiewicz, M., a nd Newnham, R.E., 1990, Electrical Resistivity of Composites, Journal of the American Ceramic Society, 8, pp.21872203.

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PAGE 152

137 89. Tamai, T., 1995, Effect of Silicone Va pour and Humidity on Contact Reliability of Micro Relay Contacts Electrical Contacts 1995. Proceedings of the FortyFirst IEEE Holm Conference on Electrical Contacts Boston, MA. pp. 252-259. 90. Tamai, T. and Miyagawa, K., 1997, Effect of Switching Rate on Contact Failure from Contact Resistance of Micro Rela y Under Environment Containing Silicone Vapor, Electrical Contacts 1997. Proceedings of the Forty-Third IEEE Holm Conference on Electrical Contacts Philadelphia, PA. pp. 333-339. 91. Lee, R. T., Chung, H. H. and Chiou, Y. C ., 2001, Arc Erosion Behavior of Silver Contacts in a Single Arc Disc harge across a Static Gap, Proceedings of the Institute of Electrical and Electronics Engineer. vol. 148, no. 1, pp. 8. 92. DeCarlo, R. and Lin, P-M., 2001, Linear Circuit Analysis Oxford University Press

PAGE 153

138 BIOGRAPHICAL SKETCH The author was born in 1977 in Duluth, Mi nnesota, but has lived in Florida since 1978. Daniel J. Dickrell III gra duated with a Bachelor of Science degree in engineering science from the University of Florida in 2000. He obtained his mech anical engineering Master of Science degree in 2002 from the same institution. In 2006, he obtained his Doctor of Philosophy in mechanical engine ering from the University of Florida.


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Title: Experimental Investigation and Numerical Simulation of Composite Electrical Contact Materials for Microelectromechanical Systems Applications
Physical Description: Mixed Material
Copyright Date: 2008

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EXPERIMENTAL INVESTIGATION AND NUMERICAL SIMULATION OF
COMPOSITE ELECTRICAL CONTACT MATERIALS FOR
MICROELECTROMECHANICAL SYSTEMS APPLICATIONS















By

DANIEL JOHN DICKRELL III


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006

































Copyright 2006

by

Daniel John Dickrell III

































This document is dedicated to my wife Pamela.





















"Invictus"


Out of the night that covers me,
Black as the Pit from pole to pole,
I thank whatever gods may be
For my unconquerable soul.

In the fell clutch of circumstance
I have not winced nor cried aloud.
Under the bludgeonings of chance
My head is bloody, but unbowed

Beyond this place of i u/ th and tears
Looms but the Horror of the shade,
And yet the menace of the years
Finds, and shallfind, me unafraid.

It matters not how strait the gate,
How charged iith punishments the scroll,
I am the master of my fate:
I am the captain of my soul.

-- William Ernest Henley, 1849-1903















ACKNOWLEDGMENTS

I thank my advisors, Dr. W.G. Sawyer and Dr. M.T. Dugger, for their sagacious

guidance. I thank my laboratory associates in Gainesville for their assistance in

assembling this document: Luis Alvarez, Nate Mauntler, Nick Argibay, Vince Lee, Dr.

Jerry Bourne, Ben Boesl, Jason Bares, Alison Dunn, Dave Burris and Matt Hamilton. I

would also like to thank my co-workers at Sandia National Laboratories in New Mexico

for their assistance in conducting the research: Rand Garfield, Liz Sorroche, Tom

Buchheit, John Franklin, Tony Ohlhausen, Wayne Buttry, Ron Goeke, Jon Custer, Paul

Vianco, Jim Knapp, Dave Follstaedt, and John Jungk.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ........................................................................ .....................v

LIST OF TABLES .............. ........ ............ .................. viii

LIST OF FIGURES ......... ......................... ...... ........ ............ ix

A BSTRAC T ......... .............. ................................................ .. ........ xv

CHAPTER

1 IN TRODU CTION ................................................. ...... .................

2 B A C K G R O U N D ...................... .... .............................. .......... ........ ......... .. ....

M EM S Electrical C ontacts ........................................ ................................. 9
Fundamental Concepts ......................................... ........ .. ................. 11
Contact Area ......... ............ ....... ..... ...............11
Contact Resistance ..... ...... .. ...... ..................... ........... .. ........ .... 17
C contact Size E effects ......................... ..................................... .. .......... ..19
A d h e sio n ........................ ... ................................................ .... ............... 2 0
Thermal Effects of Electrical Current ................................. ..........................22
Surface C ontam nation .............................................. ................ ..............26

3 EXPERIM ENTAL APPARATUS ........................................ ........................ 29

Bulk-Film Electrical Contact Testing................................ ........... .. ............... 29
M modified N ano-indentation System ....................................... ............... 29
D ata A acquisition ...... ... ................. ......................... .. ... ........ ..... 33
Single Contact Cycle ............. .... ................ ........... ............. 34
M EM S Electrical Contact D vice ........................................ ......................... 35
D evice Fabrication Process ........................................ ........................... 36
D ev ic e D e sig n ............................................................................................... 3 8
MEMS Experimental Testing.. .. ...................................40

4 CON TA CT M OD ELIN G ........... .................................. ................... ...............45

Rough Surface Contact M odeling ........................................ ........................ 45
R eal Surface C contact Sim ulation.......................................... ........... ............... 51









E electrical C current M modeling .......................................................................................54
Combined MEMS Electrical Contact and Current Modeling............... ................ 60
Therm al M modeling .......................... ................ ... .... ...... .... ..... .. 66
A dhesion M modeling .......................... .............. ................. .... ....... 67

5 COMPOSITE ELECTRICAL CONTACT MATERIALS .......................................72

P ercolation T h resh old ............... .... ................................................... ......... .... .. 72
Experimental Investigation of Composite Films ................................. ...............79
F ilm D ep o sitio n .............................................................. ............... 7 9
T E M Im agery ......................................................................82
E x p erim ental R esu lts......................................... ............................................84
Com posite Current Flow Sim ulation................................... .................................... 86

6 D ISCU SSIO N ...................................................................... .......... 92

7 C O N C L U SIO N S ..................... .... ............................ ........... ...... ... ...... 97

APPENDIX

A HOT-SWITCHED ELECTRICAL CONTACT RESISTANCE DEGRADATION .99

Carbonaceous Surface Contamination Effects ............... ............ .....................99
Silicone O il C ontam nation Effects .................................. ..................................... 114

B MODIFIED NODAL ANALYSIS................................................................ 125

LIST OF REFEREN CES ........................................................... .. ............... 130

BIOGRAPHICAL SKETCH ............................................................. ............... 138
















TABLE

Table page

3-1 ECR nano-indentation system capabilities.................................... ............... 31
















LIST OF FIGURES


Figure page

1-1 Exam ple ofa M EM S device .......................... ....... ..................................... 1

1-2 Taxonomy chart of MEMS devices grouped by tribological complexity ..................2

1-3 Illustration of the operational frequency range of MEMS switches ......................4

1-4 Rockwell RSC M EM S m etal-m etal switch..................................... .....................5

1-5 Metal contact interface of a series-switch in the up and down device state ...........5

2-1 Previous low-force electrical contact resistance studies .......................................10

2-2 Experimental MEMS devices with electrical contacts...........................................11

2-3 Example of MEMS electrical contact surface ......................................................12

2-4 Atomic force microscopic image of the surface roughness of a deposited gold
co n tact su rface ...................................... ............................. ................ 13

2-5 The difference between mechanical and metallic contact area.............................14

2-6 Illustration of the Greenwood-Williamson model and required input parameters... 16

2-7 Illustration of a contact constriction caused by interacting rough surfaces ............18

2-8 The combination of constriction and contamination film resistance ..................... 19

2-9 Adhesion map for elastically contacting spheres ............................................. 22

3-1 Nano-indentation system used in low force ECR testing...................................30

3-2 C contact zone scheme atic ......... ................. ................... .................. ............... 30

3-3 Coated wafer sam ple dim ensions....................................................................... 31

3-4 Deposited film stack for bulk film ECR testing.................................................32

3-5 White-light interferometry topographic scans of the as-deposited primary gold
layers on the sphere and flat contact samples .................................. ............... 32









3-6 Diagram of the mechanical and electrical data-acquisition system constructed to
time synchronize the experiments ................................................................ 33

3-7 Example of one experimental contact cycle for a gold-gold sphere-flat contact.....34

3-8 Optical micrograph of electrical contact MEMS device........................................36

3-9 SEM micrograph of the contact dimple on the underside of the cantilever beam
d e v ic e ............................................................................ 3 6

3-10 Electroplating deposition process for MEMS contact device fabrication...............37

3-11 Cantilever MEMS device in up and down-states...............................................38

3-12 Electrostatic actuation force dependence removal from the contact force using
the pull-down landing pads to geometrically constrain the device ........................39

3-13 Finite-element analysis of the geometrically constrained cantilever beam..............40

3-14 MEMS electrical contact device probed in the Wyko NT1100 DMEMS
instrum ent ..................................... ................................. ........... 41

3-15 Height profiles of up and down-state devices .................................. ............... 42

3-16 Results of hot-switched electrical contact resistance testing of the MEMS
cantilever device ................................................ ................. 43

3-17 Example of resistance degradation for hot-switched contact in the same location..44

4-1 An example of an optical surface profilometer, a Wyko NT-1100..........................46

4-2 Discretized surface scan obtained from optical profilometry ................................46

4-3 A voxel surface constructed from a profilometer-obtained data scan...................47

4-4 Tw o separated voxel surfaces ............................................................................ 48

4-5 V oxel contact interaction .............................................................. .....................48

4-6 Rigid, perfectly-plastic constituative material model used for voxel contact
in te ra ctio n s ...............................................................................................................4 9

4-7 Histograms of the surface height data about the mean plane taken from Fig. 4-2...51

4-8 Gold-coated Si3N4 ball bearing voxel surface.................................... ...................52

4-9 Gold-coated silicon w afer voxel surface.............................................................. 53









4-10 Predicted contact area using rigid-perfectly plastic voxel rough surface contact
model, Hertzian contact model, and Greenwood-Williamson statistically-based
model for the same gold-gold contact surfaces under a 60 mN load .....................53

4-11 Focused ion-beam cross section of a gold-gold MEMS electrical contact ..............55

4-12 Magnified view of the MEMS electrical contact ...................................................55

4-13 Schematic of electrical contact formed from the contacting members of Fig. 4-
1 2 ...................................................................................... . 5 6

4-14 Idealized model of a M EM S electrical contact..................................................... 56

4-15 Composite thin-film electrical contact showing the effect of interfacial
constituents on adhesion on internal constituent on resistance.............................57

4-16 Random resistor network approach to compute the resistance of a composite
electrical contact m aterial............................................... .............................. 58

4-17 Simplified representation of the RRN used to solve for the resistance ..................59

4-18 Contact window created by voxel surface method .............................................60

4-19 AFM scan of surface topography for the electroplated gold contact dimple...........61

4-21 Contact area for a 1.25 [[N normal load applied to the contact dimple and signal
layer surfaces ..................................................................... .........62

4-22 Depiction of the three-dimensional RRN used to calculate contact resistance........63

4-23 Current map for the contact shown in Fig. 4-21. The highest currents are
concentrated at the periphery of the contact.............. ...........................................64

4-24 Current maps of the layers 1-5 of the 3-D RRN as the current descends toward
the contact layer and forced through the constriction ...........................................65

4-25 Discretized heat conduction m odel ............................................... ............... 66

4-26 Temperature rise map for the Ohmic heating due to the electrical current passage
o f F ig 4 -2 1 ...............................................................................................................6 7

4-27 Population of an discretized contact island with an array of atoms.........................69

4-28 TEM image of gold nanowire formation from unloading of AFM contact
experim ents ........................................... ........................... 70

5-1 Different electrical composite models, series-addition, parallel-addition, and
random ly distributed ...................... ................ ................. .... ....... 73









5-2 Normalized composite resistivity as a function of decreasing gold percentage for
series-addition, parallel-addition, and randomly distributed models .....................75

5-3 TEM image of a co-sputtered gold-MoS2 composite film ..............................76

5-4 Numerical simulation of the current flow through a 10% gold composite ..............76

5-5 Numerical simulation of the current flow through a 35% gold composite .............76

5-6 Numerical simulation of the current flow through a 45% gold composite,
percolation threshold occurs in between Fig 5-5 and 5-6 .....................................77

5-7 Numerical simulation of the current flow through a 66% gold composite ..............77

5-8 Numerical simulation of the current flow through a 93% gold composite .............77

5-9 Normalized composite resistivity of the contract-modulated TEM images
showing percolation threshold of 37% .................. ...........................................78

5-11 TEM image of 90% gold, Au-A1203 PLD composite .............. ............... 83

5-12 TEM image of 50% gold, Au-A1203 PLD composite .................. ..................... 83

5-13 TEM image of 20% gold, Au-A1203 PLD composite ........ .............. 84

5-14 Normalized PLD composite film electrical contact resistance and adhesive force
n an o-in dentation resu lts ........................................ .............................................85

5-15 Resistance of PLD Au-A1203 composite films .....................................................86

5-16 Current maps for a 50 % gold composite ...................................... ............... 88

5-17 Normalized composite resistivity for 3,750 total contact current simulations as a
function of gold percentage and high-resistivity phase resistivity ........................89

5-18 Difference between uniform random and graded random distribution of high-
resistivity phase filler particles as a function of depth away from the contact
interface ........... ..... ............................. ..... ......... .......... 90

5-19 Effects of high-resistivity phase distribution on percolation threshold for the
uniform and graded random distributions ..................................... .................91

6-1 Potential composite material location in the MEMS electrical contact device
fab rication p ro cess.......... ........................................................................... .. ....... .. 9 5

6-2 Regions of acceptable and undesirable resistance for gold-alumina composites
approaching and beyond the percolation threshold.......................................96









A-i Schematic of the nano-indentation apparatus and the contact zone used in hot-
switched cyclic contact testing................................ ............... 100

A-2 Single hot-switched experimental contact cycle .............................. .................102

A-3 Cyclic electrical contact resistance degradation of Au-Pt contact ....................103

A-4 Inert environment and reduced current testing .................... ........... ................ 104

A-5 Cyclic resistance degradation for inert environment testing with momentarily
increases peak load to 1 mN for cycles 198-208, up from 150 [[N for all other
cy c le s ...................................... .................................................. 1 0 5

A-6 Resistance vs. time for individual contact cycles from Fig. A-5 with the grey
area denoting the peak-load hold period ..................................... ............... ..106

A-7 Magnified views of cycle 1 and cycle 200 from Fig. A-6 showing the amount of
force required to obtain low resistance for non-degraded and degraded contacts .107

A-8 Dependence of resistance degradation on hot-switched contact ............................110

A-9 Dependence of resistance degradation on capacitive-quench presence .................111

A-10 Oscillograms showing the change in voltage transients at moments of close
surface contact after capacitive-quench circuit is removed ............. ...............112

A-11 Auger Electron Spectra of suspected contamination region and of the
surrounding m etal surface ............................................................... ............... 113

A-12 Schematic of the contact zone with silicone oil introduced between the
electrodes ................. .......... .... ................ ............ ......... 116

A-13 Resistance degradation of silicone oil contaminated gold-gold contact ................116

A-14 Resistance and load history for contact cycle 14 from Fig. A-13 ..........................117

A-15 Resistance degradation dependence on gap closure rate for an applied voltage of
3 .3 V .............................................................................. 1 1 8

A-16 Resistance degradation on contact gap voltage for an approach rate of 86 nm/s... 118

A-17 Cycles to failure (R > 50 Ohms) dependence on time spent in the "critical" gap
distance of 30 nm ....................... .. .... .................. ... .. ...... .... ........... 12 1

A-18 Oscillograms of contact voltages at closure rates of 400 to 40 nm/s .....................122

A-19 Mechanical load required to attain at least 1 Q after degradation occurred (zero
load required at 1 V since no degradation occurred) .......................................... 123









B-l Example circuit for A matrix construction............................... ..................127















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

EXPERIMENTAL INVESTIGATION AND NUMERICAL SIMULATION OF
COMPOSITE ELECTRICAL CONTACT MATERIALS FOR
MICROELECTROMECHANICAL SYSTEMS APPLICATIONS

By

Daniel John Dickrell III

August, 2006

Chair: W.G. Sawyer
Major Department: Mechanical and Aerospace Engineering

The performance and reliability issues associated with microelectromechanical

system (MEMS) electrical contact devices have precluded the widespread adoption of

MEMS devices employing electrical contacts. Composite electrical contact materials,

gold-alumina, gold-titanium nitride, and gold-nickel, were developed to address the

issues that plague MEMS electrical contacts by reducing the amount of interfacial

adhesion while maintaining acceptable levels of electrical conductivity. The composite

materials were experimentally investigated and compared to numerical simulations which

predicated how the novel materials would perform. Experimental and numerical

simulation results found that composite electrical contact materials could enhance the

performance of low-force electrical contacts if the ratio of high-conductivity to low-

conductivity phases of the composite remained larger than a critical ratio, referred to as

the percolation threshold.
















CHAPTER 1
INTRODUCTION

Microelectromechanical Systems, or MEMS, are microscopic structures that

combine mechanical and electronic elements into complex small machinery. Figure 1-1

shows an example of a MEMS device fabricated at Sandia National Laboratories. These

devices, often the size of a grain of sand, act as links between digital electronics and the

physical world. The device pictured in Fig. 1-1 is a good illustration of the combination

of mechanical elements (the gears) and electrical elements (the electrostatic drive

actuators), into a functional system.








gear

drive
actuators









Figure 1-1. Example of a MEMS device. The drive actuators rotate the gears of the gear
train which pushes a rack and causes a hinged mirror to rise and redirect an
incident laser beam [www.mems.sandia.gov]

MEMS technology has been demonstrated in research and development facilities

for about 25 years, but has been in production for almost 20 years as accelerometers in









the automotive sector, one of the most widely used applications for MEMS devices

today. Current MEMS products span a wide range of applications including

environmental sensors, micro-switches, and medical devices. From a tribological

standpoint, the degree of surface interaction in a MEMS device relates to how successful

the device will be at attaining widespread adoption in the world outside of the laboratory.

Figure 1-2 shows a taxonomy chart illustrating the increasing degrees of tribological

complexity inherent in a MEMS device [1].

Class I Class II Class III Class IV
no moving parts moving parts moving parts, moving parts,
no rubbing or impacting surfaces impacting and
impacting surfaces rubbing surfaces







accelerometers gyros TI DMD optical switches
pressure sensors comb drives relays shutters
ink jet print heads resonators valves scanners
strain gauge filters pumps locks
switches discriminators

material properties
adhesion, wear
friction

Figure 1-2. Taxonomy chart of MEMS devices grouped by tribological complexity [1]

The most widespread use of MEMS technology has occurred in the automotive

sensor field. The reason for this successful deployment lies in the nature of the MEMS

structures used for automotive accelerometers, and gyroscopes are fabricated as planar,

monolithic structures with no interacting surfaces, typified by Class I device in Fig 1-2.

Since no surfaces of the devices touch, the operational lifetime of these devices is not









affected by problems originating from tribological effects, such as friction or wear, but

solely by the material properties of the MEMS device.

As the tribological complexity of MEMS devices increases, the amount of attention

paid to the interaction of the device interfaces becomes more important. To date, only a

few Class III devices have been successfully deployed outside the laboratory. The most

well-known example of a successful Class III device is the device at the heart of Digital

Light Processing (DLP) television displays, the Texas Instruments Digital Micro-mirror

Device (DMD). The tribological sources of failure in the DMD, friction, wear, and

adhesion, were all eventually overcome after a large expenditure of research capital. In

all of the examples of successful commercial adoption of MEMS technologies the ability

to mass-produce devices with well-controlled physical properties, repeatable

performance, and long lifetimes has been critical.

Of all of the potential applications where Class III and IV MEMS devices could,

but as of yet have not, made an impact, electrical switching and relaying is an area of

intense development. The goal of MEMS switches and relays is to replace legacy

electronic switching components with smaller, more efficient micro-system components.

However, applications where electrical energy must be diverted, interrupted, or otherwise

modified represent a challenging operational environment for any device to operate

effectively for a long period of time. As it stands, MEMS devices with dynamically

operating electrical contacts have had limited success in supplanting larger switches for

use in commercial or defense applications due to performance and reliability limitations.

Figure 1-3 shows the frequency spectrum in which MEMS switches operate. The

main difference between switch types in Fig. 1-3 is the contact material used to affect the









system electrical signal. Metal-metal contact devices are used as series-switch devices,

while non-metallic capacitive materials are used in capacitive-coupled shunt-switches.

Metal-metal contact switches possess contact interfaces that carry electrical current,

whereas capacitive-coupled switches only change the capacitance of the transmission line

the signal is carried on and do not directly carry current.

Operational Frequency Spectrum
communication frequencies
DC RF MEMS
,' I radiowave ;
OHz 30 Hz 3 KHz 300KHz 30 MHz 3GHz 300GHz








DC contact switch Metal-Metal Capacitive-Coupled
RF Switch RF Switch

Figure 1-3. Illustration of the operational frequency range of MEMS switches

An example of a metal-metal series switch is shown in Fig. 1-4. When the movable

middle switch-plate with electrical contacts is brought down into contact with the signal

lines, a continuous conductive metal path is made between the two signal lines via the

contact pads. This enables the electrical signal to flow through the switch. The signal is

blocked when the middle plate is raised.

Figure 1-5 shows a simplified schematic of how the metal contact interface of an

metal-metal contact MEMS device is used to modulate electrical signal. In the up-state, a

small gap of approximately 1-2 |jm exists between the movable device surface and the

signal transmission line. When the device is actuated, either by electrostatic or thermal









actuators or by environmental acceleration, the movable surface is forced into the signal

line and electrical signal current is carried through the contact interface.


Figure 1-4. Rockwell RSC MEMS metal-metal switch [www.rockwell.com]


Up State


signal out
--->-


Moving Surface

S1-2 pm


signal in
-- Metal Contact Layer

Substrate



Down State
signal out
Moving Surface
signal in =
SMetal Contact Layer

Substrate


Figure 1-5. Metal contact interface of a series-switch in the up and down device state.
The contact interface is responsible for electrical current signal transmission
and is the source of premature device failures


m m









The advantage of metal-metal contact devices over capacitive-coupled devices is

that the insertion loss, the decrease in transmitted signal power, associated with low-

frequency operation is much smaller for metal-metal contacts versus capacitive contacts.

Due to the reduced losses incurred during low-frequency operation, metal-metal contact

series-switch devices allow a higher-bandwidth operational envelope than capacitive-

coupled devices. The "broadband" capabilities of metal-metal MEMS switches is

however offset by the tribological problems associated with metal contact interfaces.

The electrical contact interface formed between the moving metal surface and the

stationary metal surface shown in Fig. 1-5 primarily determines how the MEMS switch

performs. Almost all of the mechanisms that affect performance and cause device

operational failure originate at the metallic contact interface. Segregating the failure

mechanisms into distinct categories, two predominant failure modes arise which cause

MEMS electrical contact devices to fail prematurely: unacceptably high electrical contact

resistance and excessively high metallic adhesion.

The first common failure mode of a MEMS electrical contact device is that the

electrical resistance of the contact interface exceeds an acceptable resistance threshold.

This is caused by a non-conductive material being formed or migrating into the region of

contact and inhibiting electrical current flow. These foreign surface species may be native

oxides, in the case of copper or silver contacts, or adsorbed contaminants, such as

carbonaceous films, that originate from the ambient atmosphere or other sources of

contamination. The solution to this failure mechanism is to keep the electrical contact

interface and surrounding environment as clean as possible, ensuring that the any

contaminants are separated from the contact interface for as long as possible. This also









includes choosing contact materials which will remain stable and not decompose or

oxidize during storage and operational lifetime.

The second common failure mode occurs when the metallic contact surfaces adhere

so strongly that the surface cannot be separated and the MEMS device becomes

permanently closed in the down-state, disallowing further operational cycles. If the real

contact area in the electrical contact interface becomes large enough, the adhesive surface

forces may overwhelm the device's ability to separate the contact. Electrical contact

materials form very strong metallic bonds and a large metallic contact area can

precipitate excess adhesion in the device. The elastic restoring force of the device is most

often the only means of separating the contact interface surfaces. The generally compliant

nature of MEMS device structures means that adhesive forces must be minimized for

extended device operation. Excessively high contact interface adhesion can also occur

from thermally-induced contact welding, but most incidents of contact sticking originate

from the metallic-bond adhesive forces existing between the MEMS electrode surfaces.

The solutions to improving the performance of MEMS electrical contacts lie in the

three device design parameters which can be altered: applied normal load, contact

geometry, and contact material selection. The applied normal load range available from

MEMS actuators, typically of electrostatic, thermal, or magnetic origin, are limited on

average to only a few hundred micro-Newtons. Mechanical disruption of oxide layers and

tenacious surface contaminants can require larger force than this, removing the capability

of the MEMS actuator to produce a conductive surface contact. The contact geometry of

MEMS contacts is frequently limited to planar contacts due to the fabrication methods

used to created the devices. While intentional contact surfaces are achievable through the









patterning of contact dimples, even these are planar contacts dominated by the surface

roughness of the contact material.

From the electrical and adhesion standpoint, contact material selection remains as

the best and most diverse method of addressing the predominant failure modes that occur

in MEMS electrical contact devices. The materials that compose the electrical contact

interface of MEMS devices are usually chosen from a set of specific materials, most

often noble metals, because of their beneficial material properties like electrical and

thermal conductivity, and resistance to formation of surface films. MEMS electrical

contact materials can be deposited separately from the structural MEMS device material,

affording the choice of what and how much material is used in the contact layer. This

amount of control over the composition of the contact material is an advantage that

MEMS electrical contact devices has over macro-scale electrical contacts. From a

problem-solving standpoint, devising a contact material which is simultaneously

conductive and non-adhesive and able to be integrated into the MEMS fabrication

process, appears as the most promising solution to addressing MEMS electrical contact

failures. This document describes an approach to model the characteristics of deposited

electrical contact materials for use in MEMS electrical contacts that addresses both the

goals of high conductivity and low adhesion, and efforts to fabricate and evaluate such

materials in low-force electrical contacts.















CHAPTER 2
BACKGROUND

MEMS Electrical Contacts

There have been many previous investigations of electrical contacts at low applied

contact forces, with researchers employing various experimental techniques to study the

behaviors and phenomenon associated with electrical contacts at force levels under 1 N

[2-19]. Some of these studies are directly relatable to MEMS device contacts as they deal

with the same materials, precious metals like gold and platinum, and applied force levels,

under a milli-Newton, seen in microscale components. Figure 2-1 summarizes the results

for previously conducted contact resistance studies at force levels below 1 N for varied

contact materials.

The notable trend in Fig. 2-1 is that across a sampling of independent investigations

of low-force electrical contacts, the measured resistance increases substantially as the

contact load decreases. Figure 2-1 is easily constructed since most studies cite normal

force applied. A figure depicting the dependence of contact resistance on apparent

contact pressure is more challenging to obtain since the exact experimental contact

geometry is often not as clearly stated in the literature. Figure 2-2 shows a contact

resistance vs. applied force plot for experimental MEMS electrical contact devices [20-

30].

The applied force range shown in Fig. 2-2 is limited by the maximum amount of

force applied by devices (- 10 mN) and on the low end the minimum force required to










attain stable resistance (- 100 [[N). The narrow operational force window for MEMS

electrical contact devices creates a challenge to obtain low resistance for low contact

force and still enable device release under the available restoring force.

10
-stage Enviroimellt :Shield
6f minanedsr J --^ A-A P- PdA -
10 18 ,.u Shield #Contact
17 2 Au-Au,lr-Au
1i05- 1 1 'erM 8 3 Au-Au
DC ...4 r Au
4i X.Y-Z SOAnI R ael -Mn al 5Au-Au
1" 11 mciro er 6 Au-Au, Pd-Pd,Ag-Ag
n3 7Au-Au,Au-Pd
S10" 10 13 8Au-Au
0 2 2 18 9 Au-Au, Pd-Pd
S10 11 10 Au-Si
M 1 2 18 11 Au-Au
S10 4 11187 77 12 Au-Au
0 0 1613 77 13 Au-Au
S10 13 14 Au-Au
S. 8 15 Pd-Au
S10 12 16816 66 16AuNi-AuNi
L) 1617W-W
10-2 from[199] 1
5 149 1519 1 Au-Au
10 A 3
1 0i -4 ----A u
10 -10 10- 10" 10-5 101 103 102 10'1 10
Contact Force (N)

Figure 2-1. Previous low-force electrical contact resistance studies

MEMS electrical contact devices possess performance and reliability limitations

stemming from the low operational contact force, and this directly impacts their

widespread acceptance for use as replacements for established commercial components.

The performance and reliability, and inherently the success of switches and relays,

depends critically on the behavioral constancy of the electrical contact interface which is

the critical aspect of the switch.

Unfortunately, the susceptibility of an electrical contact interface to become

degraded increases as the size of the contact decreases. This is due to the fact that surface

effects become more pronounced at smaller length-scales, as the ratio of surface area to

volume increases with microsystem devices. For MEMS electrical contacts, where









interactions occur between only a small number of surface contacts, obtaining a stable,

clean interface between two surfaces over many repetitive operational cycles requires an

understanding the fundamental concepts affecting the electrical resistance of MEMS

device contacts.

107
106-


10 -
10 5- # Contact
1 20 Au-Ni
21 W-Cu
SMicrodevices 22 Ni-Au
1 j 23 Cu-Cu
S10o2 20 24 Au-Au
C 25 Au-Au
S101 26 Cu-Cu
S27 27 Au-Au
- 100 28 21 28 Au-Au
2524 29 Au-Au
r_ 10 "-1 30 Au-Au

10.4 302922 2
10


10' 10 10- 10 10- 104 10 10 10 10 100
Contact Force (N)

Figure 2-2. Experimental MEMS devices with electrical contacts

Fundamental Concepts

Contact Area

The current-carrying area of a contact interface is an important parameter affecting

MEMS electrical contact performance. The bulk geometries of MEMS electrical contact

interfaces resemble planar contacts, stemming from the device fabrication processes.

Planar contacts emphasize the effects of surface roughness and distribution of surface

asperities in determining the contact area, which in chemically micro-machined devices is

produced in a narrow range of variability. Figure 2-3 shows an example of a MEMS









electrical contact surface [12]. The scanning-electron micrograph (SEM) in Fig. 2-3

shows the characteristic roughness of a MEMS device contact dimple. MEMS electrical

contacts are typically fabricated by coating the structural silicon substrate material with a

conductive metal, most often gold, that serves as the current carrying material. Electrical

contacts deposited by sputtering or evaporation retain the roughness of the silicon

substrate metal, while contacts deposited by electroplating have surface roughness

determined by the plating process employed.


MEMS Electrical Contact Surface









1pm


Figure 2-3. Example of MEMS electrical contact surface [12]

A closer view of the characteristic roughness of a gold MEMS electrical contact

surface is shown in Fig. 2-4. Instead of SEM imagery, atomic force microscopy (AFM)

was used to obtain the surface topographic data for the gold contact surface. The

characteristic roughness of the deposited gold material is visible in detail. The rough

surface topography is responsible for the resulting interfacial contact area when two

device surfaces are pressed together. The measured average and root-mean-squared

roughness for the surface shown in Fig. 2-4 are 1.37 nm and 1.71 nm, respectively. While

the surface shown in Fig. 2-4 looks very rough, there is almost a 700:1 ratio between the









lateral scale and the measured roughness of the surface, and it is in fact a very smooth

contact surface.

An important distinction exists between the apparent, mechanical, and electrical

contact areas for a MEMS device interface. Figure 2-5 shows the differences between the

different types of contact area. The apparent area of contact is the total amount of area

where probable contact exists for a device. The real area of mechanical contact is the

actual amount of the apparent area where mechanical load is reacted between the

interacting surfaces. The electrical, or metallic, contact area depends on the surface

contamination state of the areas in mechanical contact.

x 10

6
0.2 4


0.4 2
E 0

0.6 -2
-2

0.8 -4
-6

0.2 0.4 0.6 0.8 1 Ipm
pim

Figure 2-4. Atomic force microscopic image of the surface roughness of a deposited gold
contact surface

If the mechanical area of contact is clean, with no other species other than the

electrode material in the interface, then the electrical contact area is the same as the

mechanical contact area. Otherwise, if a native oxide layer or alien surface contaminant is









present in the contact interface, the amount of electrical contact area that conducts current

in a metallic fashion is less than that of the mechanical contact area. If the non-metallic

material covers the entire mechanical contact area, the electrical contact resistance for

that area increases, often to the severe detriment of device operation. It is possible for

very thin contaminant layers, on the order of several nanometers thick, that cover the

entire area of contact to conduct current via quantum tunneling [31]. The effects of

tunneling current is usually neglected however due to the significant conduction

difference present between metallically-conducting contacts and contacts covered with

very thin films.


Apparent \
S Contact Area


0o 0
0





SReal Areas of
SMechanical
Contact



CEffective Metallic
Contact Area


Figure 2-5. The difference between mechanical and metallic contact area

The amount of mechanical contact that exists between two electrode surfaces must

be determined before the effects of surface contaminants can be factored in to how









electrical surfaces perform. A survey of previously developed rough surface contact

models shows a multitude of approaches that attempt to resolve the mechanical contact

area. The earliest calculation of the mechanical area formed from two interacting bodies

was developed by Hertz (32). The well-known "Hertzian" contact model assumed that

the area formed by two spherical bodies in contact was dependent on the material elastic

properties, geometry of the contact bodies, and the force pressing the bodies together.

The expression for the contact radius of the circular contact area is shown in Eq. (2.1),

where the combined radius and elastic modulus are R'= RR / (R1 +R2) and


E'= ((- v2)/E+ (1-v/E2 ,respectively.

1/3
a 4E' (2.1)
S 4E )
A different contact modeling approach assumed that the local stresses at the

asperity level, instead of elastic, always exceeded the elastic limit of the material and

plastically deform. This assumption implied that real contact area was only related to the

applied load and the material indentation hardness and independent of geometry [33].

This approach also ignored any effects surface roughness contributed to the contact area

calculation. Equation (2.2) shows the expression for contact area assuming only plastic

deformation of the surfaces.


Ac = (2.2)
H
Later modeling incorporated the effects of surface roughness on contact area

calculation. Greenwood and Williamson (GW) proposed a statistically-based asperity

contact model based on the separation of a deformable rough surface and an ideally

smooth, rigid plane [34]. From the relative interference between the rigid plane and the









rough surface, it was possible to compute resultant contact area and load supported by

knowing the height-wise distribution of surface asperities, their overall shape, and their

material composition. The key assumptions of this model were that all asperities in

contact were spherical and had the same radius of curvature, there was no interaction

between neighboring asperities, and that the asperity heights followed a continuous,

statistical distribution (assumed to be normally distributed). Figure 2-6 depicts the

assumptions of the GW model.

normal distribution
4- A=0, =1
2-
m d
0- - fr7 - -

-2

-4-
0.0 01 02 03 0.4
Probability

Figure 2-6. Illustration of the Greenwood-Williamson model and required input
parameters

Equations (2.3 2.5) show the developed expressions for contact area, load

supported, and asperity height probability distribution as a function of asperity number,

N, average asperity radius of curvature, P, composite elastic modulus, E height

distribution standard deviation, a, and normalized surface separation, h = d / .

Ac = NfrNaS, (h) (2.3)

,= 4NE', p/27 2S32 (h) (2.4)
3

S,(h) = (s -h ds (2.5)

While initially assuming purely elastic Hertzian surface contact, a primary result of

the GW model was the plasticity index. This index determines in which regime the









predominance of individual asperity contacts reside, elastic or plastic, for various contact

material and geometries. The plasticity index formula is shown in Eq. (2.6). Values of

f/>1 correspond to predominantly plastic contacts, while f/<1 show increasing amounts

of elastic contacts. The variable H represents the indentation hardness of the softer

material.

El.- (2.6)
H /
Succeeding refinements to the popular GW model relaxed some of the key

assumptions used in its formulation. Numerically simulated surface contacts incorporated

anisotropically distributed, elliptically paraboloidal asperities. These simulation results

differed only slightly from that produced by the GW model [35,36]. Another study found

that for two rough surfaces in contact, even if the contacts do not occur exactly at the

asperity peaks, the resulting contact area is negligibly different from that of a composite

rough surface touching a smooth rigid plane [37]. These subsequent studies demonstrated

that the GW model was a good approximation for two contacting rough surfaces even

though the assumptions it is based upon are not overly complex, as long as the asperity-

height distribution is statistically valid for the surfaces under consideration.

Contact Resistance

The ability of rough surfaces to conduct electric current through a contact interface

is closely linked to the contact area calculations outlined in the previous section. It is

through these finite contact interfaces that the entire amount of electrical energy is

constrained to flow. Ragnar Holm is most often credited for the resistance calculation of

a mono-metallic contact constriction, Rc, shown in Eq. (2.7). In Eq. (2.7), p is the

resistivity of the material and a is the radius of the contact area which is assumed to be









circular [33]. Figure 2-7 depicts how the contact area formed between two bodies in

contact constricts current moving from the top surface to the bottom. A detailed

derivation of this equation is given by Jones [38].

R (2.7)
2a
Current Flow

V+
< p j Bulk



.Constricti on
(Diameter = 2a)




V-
Current Flow

Figure 2-7. Illustration of a contact constriction caused by interacting rough surfaces

If dissimilar metals are in contact, an approximation for the constriction resistance

is to use the average resistivity of the two contacting materials in the equation,

Rc = (P + P2) / 4a. The contribution to the total contact resistance by the interaction of

many small contact areas was calculated previously [39,40]. The approximate formula for

the constriction resistance including the contribution from n parallel contact spots

separated by a distance d is shown in Eq. (2.8).


2a (2.8)
2 a n2 d,
The constriction resistance equation for a single interface was derived assuming

completely clean metallic contact. If contamination exists between metallic contacts, then

the resistance of the contaminant film must be added to the constriction resistance. An









approximate equation for the contact resistance including contaminant films is shown in

Eq. (2.9). The resistivity of contaminant material is usually much greater than the

resistivity of the contact materials. If contact surfaces are contaminated, the overall

resistance may be dominated by the contaminant film resistance and totally irrespective

of the constriction resistance [19]. Figure 2-11 depicts how interfacial contaminants can

affect current flow in a metal contact.


R =( + (2.9)
4a T-a2
Current Flow

Bulk
I Ia


Contarnminant-
%-- Constriction






Figure 2-8. The combination of constriction and contamination film resistance

Contact Size Effects

The mechanism responsible for the electrical resistance in metals is the diffusive

scattering of electrons traveling through the lattice structure of the conducting material.

Contacts below a certain size threshold begin to experience a different type of resistance,

called ballistic conduction resistance, as the size of the constriction becomes the same

order as the mean-free-path of electrons in the conductor, 10 nm. This resistance, often

called the Sharvin resistance, is shown in Eq. (2.10). It has been cited as a reason for

observed deviations in expected behavior of electrical contact resistance studies for

contacts on the order of tens of nanometers [17, 41].









4pAe
R 4 = (2.10)
Interpolation equations were developed that enabled the calculation of combined

electrical constriction resistance in the intermediate regions between nanometer-scale

ballistic resistance and diffusive electron-scattering resistance [42,43].

Adhesion

The adhesion between the metal contact surfaces of MEMS devices is also of

concern because too much adhesion can cause devices to become stuck in the down state,

which renders the device inoperative. However, the GW model used the purely elastic

Hertzian contact model to express contact area and load as a function of surface

separation, and adhesive effects on the contact area size were neglected. Several studies

sought to remedy this oversight by including the effects of adhesive forces in contact area

calculation. Johnson, Kendall, and Roberts (JKR) found the solution of an adhesive

elastic contact between two spheres using an energy balance approach [44]. The JKR

pull-off force required to separate the contact is shown in Eq. (2.11), where

y = Y7 + 2, 12, is the Dupre' equation for the energy of adhesion between two surfaces,

and R is the effective radius of the spheres. The JKR-modified contact radius, shown in

Eq. (2.12), includes the adhesive surface force contribution to the contact area. As the

surface energy diminishes, y -> 0, Eq. (2.12) reverts back to the classical Hertzian

equation for contact radius, Eq. (2.1).


Fr = YR, (2.11)

a3 =3R + 21 ( + 3rR + 6rRF+ 377(R ),T (2.12)
4 TE TE









Derjaguin, Muller, and Toporov (DMT) separately solved the same problem using

a thermodynamic approach and determined the pull-off force to be slightly different,

shown in Eq. (2.13) [45]. The DMT approach assumed that the Hertzian contact area is

not altered by the surface force and only the pull-off force required to separate the

surfaces is affected.

F =o = 27ryR (2.13)
The discrepancy between the two models concerning the pull-off force was resolved later

[46]. It was proposed that the JKR and DMT solutions were both accurate, but existed on

opposite ends of the same solution space. An adhesion parameter /u was introduced,

shown in Eq. (2.14), which linked the two seemingly disconnected theories. The quantity

z0 is the interatomic distance between the surfaces in contact, typically less than a

nanometer depending on the material.


l 1 2 (2.14)
E '2 z3
The adhesion parameter represented the ratio of the elastic displacement of the surfaces at

the point of separation to the effective range of the surfaces forces. The parameter value

u >> 1 corresponded to large compliant spheres, as in the JKR theory. The DMT model

corresponded to small rigid spheres and adhesion parameter values of << 1.

The JKR and DMT models do not depend on the exact form of the surface force

potential immediately outside the contact region. However, Maugis developed an

analytical solution for the adhesive contact of elastic spheres, using a Dugdale square-

well surface force potential (M-D), which spanned the intermediate region between the

JKR and DMT extremes [47]. The M-D model also contained a transition parameter A

which was almost equivalent to / A = 1.16/ A numerically-fit transition equation was









developed that very accurately fit the M-D analytical solution and allowed for easier

analysis of contacts in the JKR-DMT transition [48]. A graphical adhesion map was

created that could be used to determine in which adhesive regime a contact resided as a

function of A and the ratio of the applied load to the adhesive pull-off force, P = P / ryR

[49]. Figure 2-9 shows the adhesion map. With the development of these models, the

adhesive contribution to the area of contact for spherical contacts could be calculated to

account for adhesive effects on the contact area and pull-off force of rough surface

contacts.

10 ,-- II-I -- I 1 -



\ JKR





10Bradley b
10




(rigid) \

10-3 102 10-1 100 101 102
Elasticity parameter X = 1.16 .

Figure 2-9. Adhesion map for elastically contacting spheres [49]

Thermal Effects of Electrical Current

The conventional treatment of electrically heated contacts assumes that the only

dissipation path for resistive heat produced within a contact is by conduction out through

the bulk materials in contact. Within this constraint, the lines of equal potential for

electrical current and heat flow within the conductor happen to coincide. Consequently,

the lines of current and heat flow also coincide. Kohlrausch was the first to recognize this

relation and derived Eq. (2.15), now called the Kohlrausch voltage-temperature relation









for electrical contacts [50]. Equation (2.15) relates the maximum temperature rise above

the bulk material temperature in the contact, 0, to the voltage-drop across the contact, the

mean electrical resistivity, p, and the mean thermal conductivity, k .

V2
0 = (2.15)
8pk
A more rigorous derivation of the voltage-temperature relation that includes the

temperature-dependent variation of electrical resistivity and thermal conductivity in the

final result was derived [51]. If the contact temperature rise calculated with Eq. (2.15)

appreciably affects the material electrical resistivity and thermal conductivity, then the

more rigorous formulation, shown in Eq. (2.16) is the more valid method of determining

contact temperature rise.


V2 = 8 p()k(O)dO (2.16)
0
The voltage-temperature relation only gives a steady-state calculation of the

contact temperature. A numerical model was developed to solve for the transient thermal

response of two bodies communicating through a small circular contact area [52]. Those

results reiterated earlier calculations that the time constant required for stationary

electrical contacts to reach near-equilibrium temperatures at locations adjacent to the

contact is very short, on the order of microseconds depending on the material. The

temperature rise was calculated for a circular constriction of two semi-infinite bodies

[50,53]. The time constant for the solution was found to be ca2 /4k, where c is the heat

capacity per unit volume of the material, a is the radius of the constriction, and k is the

thermal conductivity of the contacting bodies. From these findings, thermal transient

effects are only considered in applications of rapidly moving contacts, such as brush









contacts, or in high-frequency power connections, otherwise the steady-state conditions

for contact heating are primarily considered.

A common simplification of the voltage-temperature relation can be made by

utilizing the correlation between electrical and thermal conductivities and temperature,

known as the Wiedemann-Franz law. This law is shown in Eq. (2.17) and holds if

electrical resistivity and thermal conduction arise from electron transport in metals. The

constant L is known as the Lorentz constant and has a value of 2.45E-8 V2 K2.

pk= LT (2.17)
The voltage-temperature relation in Eq. (2.15) can be recast as Eq. (2.18) using the

Wiedemann-Franz law expression. Its use is suitable in the temperature range of ordinary

electrical contacts [50].

V2
0=- (2.18)
4L
However, the applicability of the voltage-temperature relations of Eq. (2.15) and Eq. (2-

18) has been questioned for contacts smaller than a micrometer. Although the voltage-

temperature relation of Eq. (2.15) is irrespective of contact size, the resistance of small

contacts with characteristic dimensions well under 1 jtm experimentally deviate from its

predicted behavior [41]. This is due to the assumption of a perfectly insulated contact

being less valid with shrinking contact size as the conductive effects of oxide or

contaminant films become more pronounced, as the second term in Eq. (2.9) begins to

dominate the interfacial current conduction.

The resistance mechanism, mentioned in the previous section, also determines the

degree of resistive heating experienced by a contact. Contacts with sizes well above the

ballistic-conduction threshold generate heat from diffusive scattering of lattice electrons,

otherwise known as Ohmic heating. Since the ballistic-conduction mechanism originates









from boundary scattering instead of conducting electron interactions, Ohmic heating

within the contact is negligible for ballistic electron conduction. Hence the contact will

not generate heat in the manner of Eq. (2.15) or (2.16) for contacts in the ballistic-

conduction regime [54].

Contacts with complicated geometries and layered contacts, common to MEMS

devices where a conductive layer is usually deposited on a semi-conductive structural

layer, make using analytical electro-thermal solutions tenuous. Finite-element simulations

for thermal MEMS modeling have shown promise in predicting where high-temperature

failure events would occur [55], but the analytical approaches provide rapid first-order

evaluations of local temperature rise that can determine if an exhaustive computer

simulation is necessary.

Thermal effects from electrical current passage are governed by the required

operational parameters of the MEMS device. Ohmic heating caused by large current-

carrying contacts can cause melting and catastrophic surface damage in MEMS devices

[8,10]. For a specified current load, larger contact areas will have a lower current

densities but also be subject to larger metallic adhesive forces. Smaller contacts reduce

surface adhesion, but increase the current density in the contact and increase the

susceptibility to thermal effects. Also, significant non-catastrophic resistive heating can

over time drive material diffusion and segregation within multilayer films that affects

contact resistance [56-58]. From a device design standpoint little can be done to mitigate

the affects of contact melting or diffusion if the system requirements dictate that the

contact current exceed what the MEMS contact interface can handle.









Surface Contamination

The derivations of the classical electrical contact resistance models are based upon

the assumption of clean metallic contact at the interface. If the contact surface

conductivity changes enough to cause the performance of the contact interface to fail to

meet operational specifications, then the contact is considered to be degraded. To this

end, many varied physical phenomenon such as native oxides, particles, carbon films, or

mechanical damage can affect the surface conductivity of MEMS contact interfaces and

cause resistance degradation.

Device surfaces exposed to regular laboratory environments are covered with

various forms of contaminants which can affect contact resistance [59]. Surfaces can only

be considered strictly "clean" when they are completely devoid of atomic species other

than that of the bulk material. Since this condition is only obtainable on surfaces carefully

prepared in ultra-high vacuum, some amount of contamination will otherwise be present

on MEMS contact surfaces [60]. Aside from hydrocarbon or oxide surface contaminants,

the presence of adsorbed water vapor had previously plagued MEMS reliability due to

excessive meniscus forces overwhelming the restoring force ability of MEMS devices

[59]. However, the development of surface water-removal methods during fabrication,

such as super-critical CO2 drying, have reduced packaged device susceptibility to water-

meniscus force "stiction" failures.

This brings about a paradoxical problem: the cleaner the surface, the lower the

contact resistance but the higher the adhesion. It has been theorized that monolayers of

carbonaceous surface contaminants actually enhance device performance by preventing

cold welding of metallic contacts without significantly impacting contact resistance [18].

Noble metals in particular, while having excellent electrode material properties, are









capable of forming strongly bound adsorbed contamination layers that are highly resistant

to cleaning [61]. Beyond the effects of adsorbed contaminant monolayers, the reduction

of bulk contact contamination lessens the chance that a MEMS electrical contact will

become operationally impaired.

The contact load determines to what extent surface contamination will impact

contact resistance. Interfacial contaminants have been shown to adversely alter the cyclic

contact resistance of low-force metal contacts, but the influence of contaminants on

electrical contact resistance is diminished as contact force is increased [62]. Lower

contact forces provide less of an opportunity for contaminant films to be mechanically

disturbed or ruptured in the absence of shear from interfacial sliding. Consequently,

undesirably high resistances arising from polluted surfaces affect electrical performance

and reliability of MEMS switches and relays to a larger extent than macro-scale

components [18].

Surface contaminant presence has been suggested as a cause for the higher-than-

expected contact resistance regime seen in metal contacts at MEMS-scale force levels.

The "quasi-metallic contact" regime is marked by unstable and unusually high values of

resistance at loads below 100 [[N for a nominally conductive contact [16]. These high

resistance values, however, converge to lower, more expected resistance levels as load is

increased [8]. Surface contaminants may also grow and evolve with cyclic contact,

causing degradation in the quality of the electrical contact resistance at higher force

levels [19]. The non-uniformity of surface contamination layers also creates spatial

variability in both the resistance and adhesion measured on metal surfaces [4]. The ability









of carbonaceous contamination to impair electrical contacts can be reduced by altering

the contact environment [63].

It is clear from the review of the various factors affecting MEMS electrical contact

performance that definite trade-offs exist between the need for large, low-resistance

electrical interfaces and small, non-adherent mechanical interfaces. Of the controllable

design aspects of MEMS fabrication (contact geometry, load, and material), the choice of

contact material possesses the most possible avenues for creating a surface that is

simultaneously low-adhesion and high-conductivity. This type of contact material does

not currently exist, but by using the thin-film deposition techniques common to MEMS

fabrication, an optimal low-adhesion, high-conductivity contact material should be

producible which solves the most common failure mechanisms seen in metal-metal

contact MEMS devices.
















CHAPTER 3
EXPERIMENTAL APPARATUS

Bulk-Film Electrical Contact Testing

Modified Nano-indentation System

A low-force electrical contact resistance apparatus was constructed to investigate

composite electrical contact materials for MEMS applications without having to

physically integrate the materials into devices. This ability allowed for quick

investigation of assorted contact materials, the integration of which into MEMS devices

would have been prohibitively time-intensive. The apparatus consisted of a nano-

indentation system augmented with electrical contact resistance measuring abilities. A

picture and schematic of the nano-indentation apparatus is shown in Fig. 3-1. The nano-

indentation system was used to apply and measure the normal load between the contact

samples, the displacement into the samples, and the pull-off force required to separate the

contacts.

The electrical measurements were acquired via a 4-wire measurement technique to

remove influence from the measurement lead resistances [6]. A schematic of this set-up is

shown in Fig. 3-2. A current source provided the current passing through the contact. The

current source was constrained to a sourced upper-threshold voltage when the contact

was open, called the compliance voltage, or open-circuit voltage limit.



















Glass Contact
Environmental Zone
Chamber



Na no-indentation
Column


Figure 3-1. Nano-indentation system used in low force ECR testing

insulator
coated flat
coated
sphere


holder mmete




current source

Figure 3-2. Contact zone schematic

An ammeter measured the amount of current actually passing through the circuit, while a

voltmeter in parallel with the contact measured the voltage drop across the both contact

samples. The contact resistance was calculated from the ratio of the voltage drop

measured across the contact to the measured sourced current. The capabilities of the ECR

nano-indentation system are shown in Table 3-1.









Table 3-1. ECR nano-indentation system capabilities
Measurement
Capabilities Limits
Uncertainty

Normal Force 10 tN 60 mN 1 tN

Sourced Voltage 0 20 V 1 lV @ 2 V

Sourced Current 0 1 A +10 nA @ 1 mA



The nano-indentation apparatus accommodated coated flat samples with linear

dimensions up to 10 x 20 mm. The flat samples consisted of a silicon wafer substrate

coated with a titanium adhesion layer and a primary gold electrical contact layer. The

dimensions of the coated flat samples are shown in Fig. 3-3. The composite electrical

contact material to be tested was deposited on top of the primary gold layer. The

electrical contact resistance measurement leads would be connected to the primary layer

to prevent additional resistances originating from through-film resistance from

influencing the results. In all tests the contact coating for the sphere sample remained the

same, a silicon nitride (Si3N4) substrate coated with a titanium adhesion layer and a gold

primary contact layer. The deposited film stack for contact samples is shown in Figure 3-

4.

Au Contact Material


0.5 mm

I 1 mm

~ 20 mm


Figure 3-3. Coated wafer sample dimensions











coated flat


2


OA mm radius
500nm
Au (prima ry contact material)


coated sphere

Figure 3-4. Deposited film stack for bulk film ECR testing


Figure 3-5. White-light interferometry topographic scans of the as-deposited primary
gold layers on the sphere and flat contact samples

White-light interferometry topographic scans of the primary gold contact material

for both sphere and flat samples are shown in Fig. 3-5. Root-mean-squared roughness for

the sphere and flat samples were 7.5 and 2.4 nm respectively, indicating that the primary

gold coatings were smooth and replicated the topography of the silicon substrate well.












Data Acquisition

Time-synchronized data acquisition of contact force, displacement, and electrical

contact resistance was enabled by adding a signal-triggered electrical source meter, a

Keithley 2400, and a data-logging computer communicating with the Keithley 2440 via

GPIB. A diagram of the set-up is shown in Fig. 3-6.

Keithley2400
Keithley 0 Nano-indentation contact resistance test

ir.s ultor coated wafer &
coated sphere

4-Wire Measurement te
holder contact force




0-







NI DAQ-6008 U5B-B 5


Figure 3-6. Diagram of the mechanical and electrical data-acquisition system constructed
to time synchronize the experiments

When the nano-indenter first senses a change in contact stiffness, as the sphere and

flat sample are first touching, a digital I/O channel on the nano-indenter drops a trigger

voltage from 5 V to 0 V. When the contact trigger is detected by a LabView program

monitoring the trigger channel, the contact voltage drop, sourced current, and calculated

contact resistance data being continuously stored in the Keithley 2400 buffer is time-

stamped as time "zero" in the final data file. The contact force and displacement,









separately monitored by the nano-indenter data acquisition system, is also time-stamped

"zero" in the output file when the contact trigger condition is met. Post-processing of the

separate data files searches for the common "zero" times, then knits the data files

together into one data file. This enabled the inference of time-dependent electrical

phenomenon to be made during moments of very close surface proximity.

Single Contact Cycle

An example of a data file taken from the ECR nano-indenter for a single

experimental contact cycle is shown in Fig. 3-7.

125 -- 10'
Load
100-

75 103

50 -
2 C:
S10 -


0-10,








Time (s)
-25 -

-50 -1 0
Resistance
-75

-100 I I F I I I. 10
0 5 10 15 20

Time (s)

Figure 3-7. Example of one experimental contact cycle for a gold-gold sphere-flat contact

The sphere sample was moved towards the contact until the contact stiffness

exceeded a user-defined threshold of 100 N/m. At the moment of contact, the normal load

was zeroed and the test cycle began. The load was increased at a constant rate until the

maximum load was reached. The load was then held briefly at the peak value for an









averaged resistance measurement, then unloaded at a constant rate until the surfaces

separated. The force at which the surfaces separated was recorded as the pull-off or

adhesive force.

MEMS Electrical Contact Device

A complementary experimental apparatus developed to investigated composite

electrical contact materials was a MEMS electrical contact device. The purpose of this

device was to provide an experimental platform on which promising materials identified

in bulk film testing could be studied in a true microsystem environment. The advantage

of such a device is that the number of contact cycles achievable is many orders of

magnitude higher than the nano-indentation approach, with contact cycle times on the

order of milliseconds instead of 30 seconds for the nano-indentation apparatus. The

MEMS electrical contact device is also sensitive to the failure modes, such as

contaminant film formation and contact sticking, that the composite materials are

intended to address.

Electrical contact resistance testing of microsystem contacts was performed by

employing a MEMS device designed specifically to study low-force electrical contacts.

The device, a simple cantilever with a single electrical contact interface, is shown in Fig.

3-8. A SEM micrograph of the contact dimple which serves as one of the electrical

contact surfaces is shown in Fig. 3-9. The single contact dimple provided a reduced

apparent contact area for surface analytical techniques such as Auger Electron

Spectroscopy (AES) or Time-of-Flight Secondary Ion Mass Spectroscopy (TOF-SIMS)

to identify failure mechanisms responsible for device malfunction.





























Figure 3-8. Optical micrograph of electrical contact MEMS device


Figure 3-9. SEM micrograph of the contact dimple on the underside of the cantilever
beam device

Device Fabrication Process

The devices were fabricated using a electroplating process which enabled a gold

plated layer to be used as the primary structural layer. Figure 3-10 shows the deposition

process for the contact devices.









Subtiate Q)


SSubstrute TaNi (2)


II 1 0
Substrute TaNi






Au seed layer

Substrte td











Ecdtmrplat Au
I I-- I I
Substrate Tae I

Figure 3-10. Electroplating deposition process for MEMS contact device fabrication

The device fabrication process proceeded as follows:

1. A substrate was selected for device fabrication. The chosen substrate for the current
devices was gallium arsenide wafer coated with an insulating SiON over layer to
prevent current leakage into the GaAs.
2. A 100 nm thick layer of TaN was deposited to serve as the pull-down electrode
material.
3. A 800 nm thick layer of evaporated gold was deposited to serve as the signal lines.
4. A polymer, polymethylglutarimide (PMGI), was deposited, masked and etched to
make the contact dimples and anchor for the cantilever.
5. A thin gold seed layer was deposited to serve as a plating layer initiator.
6. Photoresist was deposited, patterned and etched to serve as a guide for the
electroplated gold.
7. The structural gold layer is electroplated on top of the gold seed layer.
8. The photoresist and PGMI layers are etched away, releasing the device.










Device Design

The cantilever in Fig. 3-8 will deflect towards the substrate when sufficient

actuation voltage difference is applied between the actuation pad and the cantilever.

Figure 3-11 shows the up state and down state of the cantilever switch. The expression

for the electrostatic force felt by the cantilever is shown in Eq. (3.1).

Fe 1 sAc V2 (3.1)
2 (gw)2
up state Fe




+V-


down state
r~n---g ----------___






+V
Fc _6

Figure 3-11. Cantilever MEMS device in up and down-states

In Eq. (3.1), Ac is the area of electrostatic interaction between the pull-down

electrode and the bottom of the cantilever. The variables g and w are the gap distance

between the bottom of the cantilever and the actuation pad, and the distance the

cantilever has moved from its equilibrium position, respectively. The applied voltage V is

the voltage difference between the actuation pad and the cantilever. As the actuation

voltage increases, the displacement w increases, causing an increase in electrostatic pull-

down force. The greater the force, the more the cantilever displaces downward, creating a

positive feedback and an eventual instability at the voltage where the elastic beam









restoring force can no longer oppose the electrostatic force. The voltage where the

instability occurs causes the beam to snap into contact is called the pull-in voltage.

It is evident from Fig. 3-11 that the contact force Fc is a function of the

electrostatic pull-down force, the geometric dimensions of the beam, and the elastic

properties of the beam material. One method of removing the electrostatic force

dependence from the contact force is to incorporate raised landing pads on both sides of

the electrostatic actuation area in the plated gold layer. These pull-down landing pads

enable the cantilever beam to be pulled into contact with the substrate without shorting

the actuation voltage gap. If the pad closest to the electrical contact dimple is pulled into

contact with the substrate, the contact force no longer depends on the electrostatic

actuation force, but on the deflected beam geometry and material properties. Figure 3-12

shows how this premise works.






pull-down
Fc landing pad

Ya




Figure 3-12. Electrostatic actuation force dependence removal from the contact force
using the pull-down landing pads to geometrically constrain the device

Equation (3.2) shows the expression for the contact force in terms of elastic

modulus, E, beam width, length, thickness and beam deflection, Ya. The calculated

contact force for the device shown in Fig. 3-8 was 97.6 tN using an elastic modulus for









gold of 88.2 GPa, a beam thickness of 8.1 itm, beam width and length of 25 and 140 |tm,

and a displacement of 1 |tm.


Fc = E fi Y (3.2)

Finite-element analysis of the beam was performed using ANSYS to verify the

contact force calculation from simple beam equations. A predicted contact force of 110

[[N was obtained when the beam length, width, thickness, material properties and the

expected deflection were input to the finite-element simulation. A maximum bending

stress of 89.2 MPa was predicted at the root of the beam, well below 548 MPa, the yield

stress for gold [64]. Figure 3-13 shows the finite-element analysis output for the

geometrically-constrained beam.












-88.6 MPa Bending Stress 8.2 MPa

Figure 3-13. Finite-element analysis of the geometrically constrained cantilever beam

MEMS Experimental Testing

Experimental testing of the MEMS devices was performed using a Wyko NT 1100

DMEMS profilometer. The NT 1100 profilometer was equipped with tungsten-tipped

micro-positioners that were used to make electrical contact to the signal and actuation

pads of the device. Figure 3-14 shows a white-light interferometry scan of the device

with the four probes, actuation, ground, and signal on the device.









The actuation voltage required by the device to first overcome the elastic restoring

force of the cantilever was 112 V. For subsequent electric contact cyclic testing, a voltage

of 150 V was applied so that the pull-in landing pad would be pulled down into the

substrate, giving a contact force of known magnitude. Figure 3-15 shows white-light

interferometry height data of cross-sections passing through the beam showing the

differences between up (un-actuated) and down (actuated) states of the device for an

actuation voltage of 150 V.























Figure 3-14. MEMS electrical contact device probed in the Wyko NT1100 DMEMS
instrument

In the up state, the beam profile is not parallel with the substrate, which is caused

by residual stresses formed in the gold layer during the plating process. However, the

change in beam curvature due to residual stress is several orders of magnitude less than

the change in curvature caused by device actuation tip deflection. This means that the

change in contact force due to residual stress is negligible, but the affect on actuation









voltage is significant due to the change in the gap between the pull-down electrode and

bottom surface of the cantilever.

14
up a
12

10 down 0



a 6

4-

2
signal layer
0 substrate
-2-----------------------------
-2
200 300 400 500 600 700 800 900 1000
distance (rnm)

Figure 3-15. Height profiles of up and down-state devices

Electrical contact resistance was measured by recording the voltage drop across the

low and high signal probes and dividing it by the measured sourced current. Cyclic

contact testing was performed by repeatedly actuating the device with a potential

difference across the signal line and the cantilever. Two sets of tests were performed, one

with a sourced current of 1 mA and 1 V compliance voltage. The other test was

performed with a 3 mA sourced current and a 3.3 V voltage compliance. The 3 mA and

3.3 V test condition was the same as a MEMS accelerometer operating condition. All

tests were performed in laboratory air environment. The results of these hot-switched

tests are shown in Figure 3-16.






43

io5-
106
e 3 mA, 3.3 V
s5 A 1mA, 1V /
10 /




10
S/
S10

101- / I
(,'











Figure 3-16. Results of hot-switched electrical contact resistance tes ting of the EMS
cantilever device

It is clear from Fig. 3-16. that the MEMS cantilever ECR device experienced

contact resistance degradation with cyclic hot-switched actuation. An order of magnitude

decrease in device lifetime between the 1 V and 3.3 V tests is due to the effects of hot-

switching on the electrical contact surface. Hot-switching is especially hard on low-force

electrical contacts. Repeated contact cycling in the same location, without translating the

sample, can cause detrimental behavior in the contact surfaces. The trend in contact

resistance with contact cycle is similar to the degradation seen in previous work [65]. The

resistance degradation shape is also seen in hot-switched bulk film nano-indentation

experimental results, shown in Fig. 3-17.









106


101 -



104-

I I
C 103









0 25 50 75 100 125 150 175

Cycle

Figure 3-17. Example of resistance degradation for hot-switched contact in the same
location

In Fig. 3-17, the contact resistance was initially low, 965 mQ, for a gold-platinum

contact pair for an applied contact force of 150 [[N. As the contact was repeatedly

brought in and out of contact, the contact resistance increased by several orders of

magnitude within 25 cycles. While the resistance trend is the same in Fig. 3-16 and 3-17,

the number of cycles at the onset of the degradation was three times higher for the

MEMS test device than the nano-indentation experiments. Hot-switched contact

resistance degradation is an important topic to consider for MEMS electrical contacts, but

is tangential to the discussion of the effect of composite electrical materials on contact

resistance and adhesion. Investigation of the phenomenon responsible for hot-switched

electrical contact resistance degradation of low-force metal contacts is presented in

Appendix A.















CHAPTER 4
CONTACT MODELING

The previous chapter discussed the experimental apparatus employed to study low-

force electrical contacts. In addition to the experimental endeavor, significant effort was

expended on the development of computer models to simulate the effects of composite

contact material on low-force electrical contacts using real measured surface data. The

two main thrusts of the modeling effort were, i) a rough surface contact calculator, and ii)

a three-dimensional random resistor network electrical current calculator with contact

surface temperature-rise capabilities. In addition to the contact and current modeling, a

model to determine the adhesion of contacting rough surfaces was also developed.

Rough Surface Contact Modeling

An novel approach to calculating rough surface contact area is to use three-

dimensional discretized surface data obtained from surface microscopy, instead idealized

surface topography models, to directly calculate the interfacial contact area. Quantitative

discretized surface data is most often obtained from stylus profilometry, optical

profilometry or atomic force microscopy, depending on the scan area size and range of

surface heights to be measured. An example of an optical profilometer, a Wyko NT-1100,

is shown in Fig. 4-1. Such a device is capable of accurately measuring surface height data

quickly and without extensive sample preparation and experimental set-up time.




































Figure 4-1. An example of an optical surface profilometer, a Wyko NT-1100

The surface data generated by optical profilometry is a two-dimensional X-Y array


of pixels with Z height distance associated with each pixel. An example of a surface scan


with a 640 X 480 pixel lateral sampling interval taken from a gold-coated steel sphere is


shown in Fig. 4-2.


nE 360

300

200

100

0

-100

-200

-300

-400

-500

61P -616
F61 cpm


Figure 4-2. Discretized surface scan obtained from optical profilometry









The resulting surfaces can be treated as a collection of voxels, or volume pixels,

shown in Fig. 4-3. The voxel rough surface model is composed of a collection of

individual of voxels, with each voxel representing a X,Y, and Z value. Each voxel in the

array is independent of its neighbor voxels and the material response of each voxel to

mechanical load does not communicate to neighboring voxels.

voxahl a volume plxel

uniform differential area


mean plane













Figure 4-3. A voxel surface constructed from a profilometer-obtained data scan

To calculate interfacial contact area, two voxel surfaces are placed a distance far

away from each other. The surfaces are then advanced towards one another until at some

surface separation the voxel elements begin to interfere. Figure 4-4 shows a

representation of two voxel surfaces about to be brought into contact. As the surface

separation is decreased further, the interaction between voxels in each surface increases.

Surface contact is composed of the summation of all of the individual voxel interactions

occurring at a given surface interference. An individual voxel interaction is shown in Fig

4-5.









surface A


distance
between
surfaces










surface B


Figure 4-4. Two separated voxel surfaces


Area = L2


separated
voxels


d1


contacting
voxels


Figure 4-5. Voxel contact interaction









The voxels have a uniform differential area of L2 and a for voxels in contact, an

interference depth d. Different material constituative models elastic, plastic, or elasto-

plastic may be used to relate voxel interference depth (strain) to pressure (stress) and

load-carrying capacity. The simplest approach is to assume a rigid-perfectly plastic

material model for the voxel interactions. This assumption states that no elastic strain is

built-up as the voxels are pressed together and the contact pressure is equal to the

material indentation hardness.

Figure 4-6 shows the stress-strain relation for the rigid, perfectly-plastic material

assumption. The indentation hardness assumption circumvents the need to define the

elastic strain for each individual element with respect to a gage-length. Each voxel in

contact contributes the same increment of load support, regardless of the degree of

deformation of the voxel. A more rigorous contact modeling approach would include

volumetric redistribution as the material displaced inside the contact plastically flows

outwards to non-stressed areas. However, this model refinement is neglected due to the

small amount of error introduced into the contact area calculation, perhaps several

percent for low-force MEMS contacts.

(7


H
j L






-H


Figure 4-6. Rigid, perfectly-plastic constituative material model used for voxel contact
interactions









The contact force generated from a single voxel interaction is calculated from the

material indentation hardness and the area of the voxel. This is shown in Eq. (4.1). The

total contact force is calculated by summing the force contributions from Ninteracting

voxel pairs, shown in Eq. (4.2).

Contact H*L2 (4.1)
N
Fn = Fcontact, (4.2)
i=1
The treatment of contacting rough surfaces as a collection of independently-acting

voxels is particularly suited to low-force contacts, such as MEMS devices, where the

number of load-bearing points in the contact interface are very few compared to the

overall surface size. The use of a analytical function to fit the surface height distribution,

such as a Gaussian fit in the widely-used Greenwood-Williamson model, becomes

increasingly erroneous as the contact load is decreased. Figure 4-7 illustrates how the

Gaussian fit is an adequate approximation for the entire histogram of surface heights

about the mean plane for the surface shown in Fig. 4-2.

However, the further away the Gaussian fit is examined from the surface mean

plane (and closer to the highest points in the height distribution) the more poorly matched

the fit becomes to the actual surface height data. This poor fit is negligible for macro-

scale loads, as the deformation is sufficiently large enough to bring surface points away

from the poorly-fit surface points into contact, causing the error introduced in the contact

area calculation to be small. However, for MEMS contacts the forces are small enough

that the poorly-fit outlying surface points are able to support the entirety of the load,

making the Gaussian fit or any analytical fits to the surface height distribution ill-suited

for contact area calculation.












20000 -
surface data surface data
l8000- -Gaussian fit Gaussian fit
16000- 1600
14000 1400
12000 1200
S 10000 1000-
woo I 1800-
6000- 600
4000. 400-
2000 200

0.0 0.2 0.4 0.0 0.2 0.4
distance (2mn) A distance (pn) B

200 20 -
180- surface data surface data
Gaussian fit Gaussian fit
160 16
140- 14
12



620

6 0



0.0 02 0.4 0.0 0.2 0.4
distance (pim) C distance (rim) D


Figure 4-7. Histograms of the surface height data about the mean plane taken from Fig. 4-
2. A) is a histogram of the entire surface, B) is a closer view of the surface
histogram, C) shows the tail of the asperity distribution and D) shows a
magnified view of the tallest asperities most likely to be involved in surface
contact


Real Surface Contact Simulation


The computational advantage of this contact area calculation method is that since


the voxels in one surface are directly registered to the voxels in the opposing surface, no


computationally-expensive searching is required to locate contacting voxel elements.


This computational economy allows for almost real-time calculations of contact areas for


relevant engineering surfaces.


Contact area calculation for two real rough surfaces was performed by applying the


above method to a 0.79 mm radius gold-coated Si3N4 sphere, shown in Fig. 4-8, and a









gold-coated Si wafer, shown in Fig. 4-9. The indentation hardness used for the contact

force calculation was 2 GPa, which was determined from nano-indentation hardness

testing of the same deposited material. Contact simulation was performed by

decrementing the distance between the surfaces until the calculated contact force became

non-zero. The surface separation was then stepped in small increments until the

calculated contact force became equal to the target contact force. When the target contact

force was reached, the contact area was determined from the interacting voxels

responsible for the contact load. The predicted contact area for a 60 mN normal load is

shown in Fig. 4-10. Also shown in Fig. 4-10 is the Hertzian contact area calculated using

the material and geometric properties of the scanned surfaces for the same applied load.

The Hertzian contact model neglects surface roughness effects and assumes a completely

elastic material response.


0.2
10

20

E 20
-0.2
30

-0.4
40


10 20 30 40 50 60 pm
pm

Figure 4-8. Gold-coated Si3N4 ball bearing voxel surface
















30
-0.01
40
-0.015
20 40 60 pm
pm

Figure 4-9. Gold-coated silicon wafer voxel surface


5






1 25

30

35

40

45
10 20 30 40 50 60
pm

Figure 4-10. Predicted contact area using rigid-perfectly plastic voxel rough surface
contact model, Hertzian contact model, and Greenwood-Williamson
statistically-based model for the same gold-gold contact surfaces under a 60
mN load









The contact simulation method outlined above is superior to statistical contact area

methods, such as Greenwood-Williamson, due to the absence of any assumptions based

on perfectly spherical asperities and ambiguity about their statistical distribution. The

quantitative topographic data taken from two surfaces of interest directly compute the

predicted contact area using straightforwardly obtained material constants and simple

constituative models. The voxel rough surface contact model also allows for predictions

in contact area shape, an ability completely lacking in statistically-based models. The

resulting prediction of contact area can be used to help explain low-force electrical

contact phenomena.

Electrical Current Modeling

The modeling of MEMS electrical contacts can be accomplished by understanding

how MEMS electrical contacts are composed. Figure 4-11 shows a focused ion-beam

(FIB) cross-section of an electrical contact dimple fabricated using the same process as

the device shown in Fig. 3-9. The contact geometry of the electrical contact surface,

where the cantilever dimple touches the signal line, can be seen in the bottom of Fig. 4-

11. A closer look at the contact dimple region in Fig. 4-12 shows the coarse-grained

structure of the electroplated gold cantilever, and the evaporated gold signal line. When

the switch is actuated the contact dimple is pressed against the signal line, creating a

metal contact and enabling current to flow. A schematic of the electrical contact is shown

in Fig. 4-13.

When the electrical contact bridge is made between two gold contact members, the

sputter-deposited gold seed-layer deposited to initiate the electroplate growth will be

interposed between the movable cantilever and the stationary signal line. The seed-layer

can be seen in Fig. 4-12 as the thin, bright outline on the bottom of the top electroplated










layer. An idealized electrical contact model showing the seed layer in between two gold

contacts is shown in Fig. 4-14.


Figure 4-11. Focused ion-beam cross section of a gold-gold MEMS electrical contact


Figure 4-12. Magnified view of the MEMS electrical contact


I









current Flow


current Flow

Figure 4-13. Schematic of electrical contact formed from the contacting members of Fig.
4-12


Figure 4-14. Idealized model of a MEMS electrical contact

The amount of current passing through the interface is a function of the voltage

difference between the contact surfaces and the resistance of the interface. The resistance

of the interface is a function of the size of the contact area and the resistivity of the

interfacial material. In a homogenous contact material layer, the resistance of the

interface is straightforward to calculate if the contact area and material are known. The

resistance of a composite material is more complicated.









In the calculation of the current flowing through a composite film, similar to the

one shown in Fig. 4-15, the relative distribution of the composite material constituents

plays an important role. The boundary interface of the composite controls the adhesion

between the bulk MEMS surfaces, but the conductive pathways through the interior of

the composite determine the resistance of the interface. The calculation method of

interfacial adhesion is straightforward. The amount of adhesion between the composite

and the top electrode is typified by a linear-rule of mixture relationship. The relative ratio

between the amount of gold and non-gold filler in the composite is proportional to the

amount of adhesion present between the composite and the top contact.

adhesion determined
at interface

equipotential surface



bulk film resistance
determined by
material resistivity
equipotential surface and orientation
composite thin-film electrical contact

Figure 4-15. Composite thin-film electrical contact showing the role of the interface on
adhesion and the bulk of the film on resistivity

The calculation of the composite material resistance can be accomplished by

employing a random resistor network (RRN) to model the electrical transport in the

composite. In the RRN, the composite material is discretized as a simple cubic lattice of

two different materials, a conductive and filler phase, which are randomly distributed

through the material. A nodal network is over-laid on the composite with nodes laying at

the center of each material element. Electrical resistors connect the nodes, with the








resistance determined by the resistivity of the connected material elements. Figure 4-16

shows the nodal connectivity and the assignment of resistance for a resistor based on the

material between the nodes. The resistance between a pair of nodes is calculated by the

ph
equation R = where p is the average resistivity of the materials between the nodes,
wt
h is the distance between the nodes, and wt is the product of the element width and

thickness.

equlpotential surface +


V

equlpotental surface




I =ph
/ h R -h
/-/ wt


Figure 4-16. Random resistor network approach to compute the resistance of a composite
electrical contact material
After the nodal mesh and inter-node resistances are determined, the computation of

the resistance of the RRN is performed. Figure 4-17 shows the RRN constructed from the

electrical composite of Fig. 4-16. The voltage at the top and bottom nodes, corresponding

to the equipotential surfaces of the top an bottom contacts, is prescribed. Equation (4.3)

shows the mathematical equation for the current entering into the ith node in the RNN.

The ith node is assumed to have an equipotential with voltage Vi. If gi is the local









conductance between the ith andjth node, the current Ii entering the ith node is the sum

of the currents entering into (or leaving from) the other nodes connected to the ith node.

For a simple cubic lattice structure the maximum number of nearest bonding sites or

coordination number, N, is 4 for a two-dimensional lattice and 6 for a three-dimensional

lattice.

N
I giy(.V -vi) (4.3)





2









0

Figure 4-17. Simplified representation of the RRN used to solve for the resistance

The application of Eq. (4.3) for every node in the RRN creates a linear system of

equations. Modified Nodal Analysis (MNA) was employed to solve for the nodal currents

by applying Eq. (4.3) to the nodal mesh shown in Fig. 4-17. A detailed outline of the

MNA algorithm is presented in Appendix B. Once the current flowing through the nodal

mesh is known, the total current passing through the RRN can be found. Dividing the

total current by the prescribed voltage difference across the RRN yields the resistance of

the contact material, whether homogenous or inhomogeneous composite, without

distinction.









Combined MEMS Electrical Contact and Current Modeling

The combination of the voxel surface approach to rough surface contact area

calculation with the RRN electrical resistance calculation method can be used to estimate

the contact resistance for MEMS devices using real rough surfaces and material data

obtained from the devices. Using the voxel surface method, the interfacial contact area

for two rough surfaces is obtained, shown in Fig. 4-18.

surface A







F






contact window



surface B

Figure 4-18. Contact window created by voxel surface method

Figure 4-19 and Fig. 4-20 show surface topography of the contact dimple and

signal layer for the MEMS electrical contact device obtained using an atomic force

microscope (AFM). AFM surface data was used to obtain the topographic data instead of

a white-light interferometer because the minimum spatial resolution of the interferometer

is too large and the size-scale of the surface features on these samples is too small to

obtain sufficient surface data required to compute contact area for MEMS-scale contact

forces. A white-light interferometer at its highest magnification of 100 X, will produce a








computed contact area that consists of only several pixels for a 100 [[N normally-loaded

gold contact surface. The spatial resolution of the input surface scans must be at least

several orders of magnitude smaller than the contact size to obtain accurate data with the

RRN electrical contact resistance calculation method.

The surfaces shown in Fig. 4-19 and Fig. 4-20 were input into the voxel surface

contact calculator. A 2 GPa hardness for the gold surfaces was input into the calculator

program. Hardness values for thin-film deposited gold range from 1-3 GPa [66,67]. As an

example of the ability of the method to analyze very low-force contacts, a target contact

load of 1.25 [[N was input into the contact program. The calculated contact area that

supported the target load is shown in Fig 4-21. The pixels within the contact area become

the contact window used in the RRN calculation shown in Fig. 4-18.

gold surface A
4

0.1 2

0.2 0
E
zl. -2
0.3
-4
0.4
-6
0.5
0.1 0.2 0.3 0.4 0.5 nm
pm

Figure 4-19. AFM scan of surface topography for the electroplated gold contact dimple










10


5


-10


U 5
0.1 0.2 0.3 0.4 0.5 pm
pm

Figure 4-20. AFM scan of surface topography for the evaporated gold signal layer

contact area


0.1 0.2 0.3 0.4 0.5
pm


Figure 4-21. Contact area for a 1.25 tN normal load applied to the contact dimple and
signal layer surfaces

The contact window shown in Fig. 4-21 determines the nodal connectivity between

the surfaces at the interface. The contact connectivity was used in the three-dimensional









RRN, shown in Fig. 4-22. The 3-D RRN simulates the current flow traveling through the

electrical bodies in a fashion identical to the process outlined above, the main difference

being the three-dimensional nodal mesh and severed nodal connectivity at the pixels not

in contact. A voltage drop was specified across the contact bodies and the current flowing

through the contact was calculated. After the 3-D RRN contact resistance calculation was

completed, a map of the current passing through the contact was constructed. Figure 4-23

shows the current map in the contact area of Fig. 4-21. The largest nodal current within

the contact was 23.4 pA. The total integrated current passing through the contact was

2.32 mA for a prescribed voltage drop of 10 mV, giving a calculated resistance of 4.31 0.

This resistance is reasonable for a contact with characteristic dimensions under 100 nm.










1 c f
bo d y A









body B

Figure 4-22. Depiction of the three-dimensional RRN used to calculate contact resistance.










current map xlo

0.01
2
0.02

0.03
15
0.04

0505



0 07
0_5
008


0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 A
pm

Figure 4-23. Current map for the contact shown in Fig. 4-21. The highest currents are
concentrated at the periphery of the contact

The total number of thickness layers used in the 3-D RRN simulation was ten. Figure 4-

24 shows the current passing down through the top 5 layers of the 3-D RRN. The total

current in layer 1, the top-most layer of vertical resistors attached to the equipotential

boundary surface, is highly distributed among the all of the resistors in the layer. As the

current descends through the resistor network and gets closer to the contact elements, the

resistors closest to the contact spot begin to carry more and more current as the current is

forced through the contact constriction. In layer 5, only the elements in contact

determined by Fig. 4-21 have current passing through them. Since the contact modeled is

homogenous gold, the current maps for the bottom layers 6-9 are symmetric about the

contact as the current spreads away from the contact constriction. The variations in

material resistivity and the effects on current constriction are investigated in the

following chapter.













x 10-5 x 10-5

0.01 001
2 2
002 002

O03 003
1.5 15
004 004

05 .005
11
O.0 006

007 0.07
05 05


O 09

001 002 0.03 0.04 0.05 006 0.07 00o A 001 0.02 0.03 0.04 0.05 006 007 o0 A
pm pm


x 10-5 x 10-5

001 001
2 2
002 002

003 003
15 15
0.04 0.O4

005 005
1 1
006 0.06

007 007
05 05
OB O.-B

0 009

001 0.02 0.03 0.04 0.05 006 0.07 0 08 A 001 0.02 03 0.04 0.05 006 0.07 o0 A
pm pm


x 10-5

001

002

00o3 3

004 4

00o5 5
1(1,


007
0.5


0.09 1 o F F F o F

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 A
pm



Figure 4-24. Current maps of the layers 1-5 of the 3-D RRN as the current descends

toward the contact layer and forced through the constriction









Thermal Modeling

Once the current in each resistor element is known, a heat flux based on the Ohmic

resistive heating was applied in a discretized half-space heat conduction model [68].

Figure 4-25 shows a single element in the model. For all of the elements in the contact

layer, in contact or not, Eq (4.4) is applied in order to determine the temperature rise in

each element. Equation (4.4) combines the temperature rise for an element with an

Ohmic heat flux over it, the first half of the Eq. (4.4), with the temperature rise from

conductive heat flow from neighboring elements. Equation (4.5) shows the equation for

the heat flux for a single current-carrying element. This basic modeling does not

incorporate any scale-dependency on the heat conduction mechanism.

~Z n1 n;i A
0/ =1.12 qa+ qA (4.4)
k i=O 2ikt (4.4
I2R
q= (4.5)
4a2









* Ohmic heatflux
[] conduction 2a



Figure 4-25. Discretized heat conduction model

Figure 4-26 shows the result of the heat conduction model applied to the current

map of Fig. 4-23. The maximum temperature rise within the contact for a total current of

2.32 mA is only 0.034 degree K. The reason for the very modest temperature rise is that










gold is both an excellent electrical (2.2e-8 Q*m) and thermal conductor (317 W/m*K). A

quick check of the thermal modeling is to use the Kohlrausch voltage-temperature

relation, Eq. (2-15), to compute a maximum temperature rise. Using the electrical and

thermal conductivities given above and using the contact voltage drop of 10 mV in the

Kohlrausch relation gives a maximum temperature rise of 0.018 degree K. The two

values agree within a factor of two.

Ohmic Temperature Rise (K)

0.01



0.03 0.025

0.04
0.02


0.06 0.015

0.07
0.01

0.09
S0005
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
pm

Figure 4-26. Temperature rise map for the Ohmic heating due to the electrical current
passage of Fig. 4-21

Adhesion Modeling

Traditional calculation of adhesive force involves the use of approaches like JKR or

DMT described in Chapter 2. Depending on the contact geometry and interfacial

material, the adhesive force calculation using these methods is uncomplicated. The

ambiguity in using these approaches arises when deciding what constitutes the "asperity


radius" for rough surface contact. The JKR equation, Fo = 2~yR assumes spherical









asperity contact and requires an estimate of effective radius to calculate the adhesive

force. For low-force rough surface contacts like the one shown in Fig. 4-21 the

assumption of a spherical asperity is questionable.

Instead of using JKR or DMT approach, an alternative method to compute the

adhesive force of two metallic surfaces using real surface topography is presented here.

To calculate the adhesive force, the total number of atoms inside the predicted contact

area must be calculated. This can be calculated by finding the number of atoms inside a

single pixel, and then summing the number of pixels within the contact surface. Once the

total number of atoms in the contact is known, the adhesion force contribution for each

atomic contact can be summed, yielding a pull-off force prediction for a clean metallic

contact.

Assuming two gold surfaces are brought into contact using the voxel contact

calculator, the resulting contact area will be a subset of the entire image pixel-field. The

pixels in contact will have characteristic length, Lp, based on the input surface scan

length, divided by the scan resolution. For example, the side length of a single pixel in

the 512 x 512 pixel, 5 |tm x 5 |tm AFM surface scan would be 5 |tm / 512, or 0.98 nm.

Each individual pixel within the contact area would be then sub-divided into a square

array, with each cell within the array having a linear dimension equal to the atomic

diameter, Datom, of the surface material. Figure 4-27 illustrates how the sub-division into

an atomic array of a single contact island within contact area is performed.

Computing the ratio of the pixel length to the atomic cell dimension, L I/Datom,

gives how many atomic cells will fit along one dimension of the pixel. For the self-mated

gold contact area shown in Fig. 4-21, with gold having an atomic diameter of 0.2884 nm,








the ratio of pixel length to atomic cell length is L IDatom = 9.776/0.2884 = 3. The total


number of atomic cells within a single pixel is therefore (L, IDatom )2 11.5.

Multiplying the total number of pixels in contact with the number of atomic cells per

pixel gives the total number of atoms in contact, 725 *11.5 8,371 atoms for a 1.25 [tN

applied force.

Contact Area Single Pixel
Single Pixel





LV



Atomic
Datom
Cell


Figure 4-27. Population of an discretized contact island with an array of atoms

Once the total number of atoms in contact is known, the individual adhesive force

contribution from each gold-gold contact can be summed together to predict the total

force required to separate the mated surfaces. Several references exist which have

measured the magnitude of adhesive force for gold nanowires with a specially-

instrumented AFM apparatus [69-71]. Figure 4-28 shows a picture of the nanowire

formation upon unloading of the AFM apparatus [69]. The adhesive force for a single

gold-gold atomic contact was extrapolated from the nanowire adhesive force experiments

and was determined to be 1.6 nN. This value is supported by theoretical studies which









predicted the adhesive force of the same contact to be in the range of 1 to 2.2 nN [72]. It

is arguable whether this value is a cohesive force or an adhesive force. A distinction is

usually made between an adhesive force, which acts to hold two separate bodies together

(or to stick one body to another) and a cohesive force, which acts to hold together the like

or unlike atoms, ions, or molecules of a single body. In this particular case, both

situations are seemingly appropriate, but for clarity the term "adhesive" force is used.















Figure 4-28. TEM image of gold nanowire formation from unloading of AFM contact
experiments [69]

Multiplying the number of atoms in contact with the adhesive force contribution of

a single atomic gold contact, the adhesive force of the simulated contact is calculated to

be, 8371*1.6 -13,394 nN, or 13.4 [N. This value is almost eleven times greater than the

applied load of 1.25 [[N. The adhesive force calculated using JKR for the same contact,

assuming a composite radius of 100 nm and an adhesion energy for gold-gold contact of

2.2 J/m2, is 1.04 [[N. While the JKR figure for adhesive force appears reasonable, the

arbitrary nature of choosing a 100 nm based on a spherical asperity assumption makes its

use questionable.









The seemingly large adhesive force value of 13.4 [[N using the voxel-contact

surface is in fact supported by experimental evidence of cold-welding of gold-gold

contacts in ultra-high vacuum [18]. Extremely high adhesive forces due to strong metallic

bonding can be generated between metal contacts when the surfaces are devoid of any

contaminants. The assumption that every atom contributes to the adhesive force, as

shown in Fig. 4-27, is akin to assuming that the contact interface is atomically clean. In

reality, adventitious contaminant surface films and material defects will reduce the actual

adhesive force by preventing strongly-bonding metal-metal contact to occur. The

adhesive forces of these interfering entities are many orders of magnitude less than the

metallic contact forces and the contribution of non-metallic substances are effectively

negligible in the total force summation unless their presence is overwhelmingly

predominant. Appropriate reductions in the number of atoms in contact, by a factor of

three at least, would represent the effects of low surface energy contaminant species on

the surfaces in a non-vacuum device environment.

Overall, the use of real surface topography to calculate contact area is pivotal in

estimating MEMS contact properties, such as electrical contact resistance, Ohmic

temperature rise and adhesive force, that are dependent on interfacial contact area size

and distribution.














CHAPTER 5
COMPOSITE ELECTRICAL CONTACT MATERIALS

Percolation Threshold

The computation of composite electrical contact material resistivity can be

accomplished using analytical expressions. Figure 5-1 shows three different structural

models of a composite electrical contact material. A simple linear rule of mixture model

is analogous to the leftmost composite in Fig. 5-1. Alternating layers of material

perpendicular to the current direction offer no preferred conduction path through the

material, hence the electrical current transport capability of the composite is dominated

by the most poorly conducting species, analogous to resistors in series. In the opposite

case, the middle composite in Fig. 5-1 vertically orients the two materials parallel to

current flow, creating a composite material which is instead dominated by the most

conductive phase. The rightmost composite in Fig. 5-1 is unique from the first two

models. In a composite whose constituent phases are randomly distributed, the resistivity

depends on not only the resistivity of the constituent phases, but the orientation of the

phases with respect to each other. The resistivity of this composite structure can be

described using a percolation model which is a function of constituent resistivity and

relative interconnectedness.

Electrical conduction in an inhomogeneous medium using a percolation model was

first proposed in 1957 [73]. In the percolation model, a structural lattice is composed of

an array of locations, or sites, which are interconnected. Each site has a probability of

whether the site is low-resistivity or high-resistivity and that probability is independent of









the state of its neighbors. Electrical conduction can only occur from one site to its

immediately neighboring sites. The current eventually propagates through the composite

solid. At a critical volume fraction of the conducting phase, called the percolation

threshold, a continuous path of conductive sites is formed from one equipotential surface

to the other. When the percolation threshold is reached, the resistivity of the composite

greatly decreases and behaves more like the parallel-addition composite.

+ + +

V V V

linear rule of mixture vertically oriented randomly distributed
(series-addition (parallel-addition (percolation theory)
resistance) resistance)

Figure 5-1. Different electrical composite models, series-addition, parallel-addition, and
randomly distributed

Equation (5.1), called the logarithmic mixing rule, can be used to calculate the

resistivity of a electrical contact composite, p,, as a function of the high resistivity and

low resistivity phases, ph and pl, the volume fraction of the low resistivity phase q, and

an exponent n [74]. The series-addition composite resistivity, or linear rule of mixture

equation, can be obtained with n = 1, while the parallel-addition composite resistance can

be obtained with n = -1.


S(1-K+ ] (5.1)
P.j Ph A1
Equation (5.2), called the General Effective Media (GEM) equation, was developed

to calculate the resistivity of a randomly distributed composite material [75]. The GEM

equation can be used to calculate the composite resistivity for structures like the one

shown in the rightmost composite of Fig. 5-1, given the resistivities of the low-resistivity









and high-resistivity phases. The variable is the critical fraction of low-resistivity phase

where the composite material percolates and the transition from high-resistivity to low-

resistivity occurs.

(1O ^ ^) p l/_hl/t *pm/t _1/t)
+ = 0 (5.2)

"C ) "C )

Figure 5-2 shows the normalized resistivity for each of the respective mixing rules,

series-addition, parallel-addition, and GEM equations. The resistivity models are plotted

as a function of gold percentage in the composite and normalized by the resistivity of

gold, 2.2x10-8 (Q. m) The resistivity difference between the high-resistivity phase and

gold was chosen to be 100,000 which is typical of the resistivity of fillers used in gold

composites [76] In Fig. 5-2 the series-addition normalized composite resistivity

increases almost immediately with inclusion of high-resistivity phase. In contrast, the

parallel-addition normalized resistivity remains within an order of magnitude of pure

gold up to high-resistivity phase percentages of 90%. From an engineering standpoint the

parallel-addition composite material structure is most optimum if the goal is to keep the

resistivity as low as possible while maximizing the amount of filler in the composite.

An example of how the percolation threshold affects resistivity in a real composite

material is shown in Figs. 5-3 through 5-8. A transmission electron micrograph of a gold-

MoS2 co-sputtered nano-composite film is shown in Fig. 5-3 [77]. The darker, banded

grains are gold, while the lighter, unstructured bands are molybdenum disulphide. By

modulating the contrast in Fig. 5-3, the contact resistance calculator outlined in the

previous chapter was used to determine the resistivity of each image in Figs. 5-4 through

5-8. Each image in Figs. 5-4 through 5-8 consists of a site-lattice structured image









constructed from Fig. 5-3. Modulation of the image contrast created a variation in low-

resistivity phase (black pixels) in a matrix of high-resistivity phase (white pixels). The

binary composite image for each volume fraction was then fit with a random resistor

nodal mesh and given a voltage difference across the mesh. The resulting current flow

map adjacent to each binary composite image shows the most conductive pathway

through the composite. The darkest pathway in the current map corresponds to the

highest magnitude current within the composite. This method of taking real cross-

sectional material microscope images enables direct assessment of composite material

electrical transport capabilities, although the limitation of two-dimensional imagery

reduces its usefulness in dealing with contact simulations.

105


10 4 series random
t 0.88
c= 0.37

10
Pcomp10
PAu
102
101





100
I I I I I
Au 80% 60% 40% 20% 0%
Au Au Au Au Au

Figure 5-2. Normalized composite resistivity as a function of decreasing gold percentage
for series-addition, parallel-addition, and randomly distributed models
























Figure 5-3. TEM image of a co-sputtered gold-MoS2 composite film [77]

Binary Composite Image Current Flow







0 M
b






Figure 5-4. Numerical simulation of the current flow through a 10% gold composite










Figure 5-5. Numerical simulation of the current flow through a 35



Figure 5-5. Numerical simulation of the current flow through a 35% gold composite





















-I--


Figure 5-6. Numerical simulation of the current flow through a 45% gold composite,
percolation threshold occurs in between Fig 5-5 and 5-6








S- ---
















Figure 5-7. Numerical simulation of the current flow through a 66% gold composite







----------------------ii:::;"~r ii
-::: .....---------.
-------------- ::: : k= ------













m..
-- ---- -----'- -'-9 c----- o p i
"--- _- ..















:__V:: ::-------
---------------------
- - - - -

----- -------:: --- --


Figue 5-. Nuericl smulaion f th curentflowthrogh 93%goldcompsit






78


Figure 5-9 shows the normalized resistivity of each of the numbered composite

current simulations. As the high-resistivity phase percentage (white pixels) is decreased,

the composite resistivity decreases gradually until the percolation threshold is reached.

When the critical conductive phase percentage is reached, at continuous path of

conductive (black) pixels bridges the entire composite and the composite resistivity drops

by over three orders of magnitude. As the high-resistivity phase percentage is reduced

further, the normalized composite resistivity again drops at a gradual rate.

percolation
threshold

105


1044 series 2


S3 simulation
P comp10
102
101




10O


I II rIr
100

Au 80% 60% 40% 20% 0%
Au Au Au Au Au

Figure 5-9. Normalized composite resistivity of the contrast-modulated TEM images
showing percolation threshold of 37%

It is clear from Fig. 5-9 that to create an useful electrical composite material the filler

percentage must remain less than the critical percentage near the percolation threshold,

otherwise the penalty paid in increased resistivity will be too great.








Experimental Investigation of Composite Films

Film Deposition

With the theoretical framework for predicting and analyzing composite electrical

contact materials established, thin-film electrical composite material were created for

experimental testing. Three different composite film compositions, Au-Al203, Au-TiN,

and Au-Ni, were made using a pulsed-laser deposition (PLD) technique. Figure 5-10

shows a schematic of how the PLD system operated.

laserbeam

target heat ble
carousel sample
stage
substrate

=----





ablated plume


rotating
target

Figure 5-10. Pulsed-laser deposition

The composite materials were deposited in vacuum using a KrF excimer laser, with

a wavelength of 248 nm, a 34 ns full-width half-maximum pulse width, and operated at a

pulse rate of 35 Hz. The pure gold and filler phase ablation targets and sample substrates

were mounted in an all-metal vacuum chamber with a base pressure of 2x10-7 Torr. The

laser light was directed through a UV-transparent window to a fixed position in the plane

of the target. The targets were continuously rastered in that plane over several square









centimeters during deposition. The laser energy density at the target was in the range of

1-2 J/cm2. The deposition rates were material dependent: gold deposited at a rate of

0.106 A/shot, corresponding to 500 nm thick film deposited in 30 minutes.

A particle filter was mounted between the targets and the sample to eliminate the

slow, non-plasma components of the laser ablation plume, which would otherwise lead to

a rough, non-ideal film. The interposed velocity filter consisted of a 15 cm diameter

wheel with two 5 cm wide slots around the periphery. The filters were spun at a speed of

2100 rpm during the deposition with a wheel to target spacing of 2 cm and the laser

synchronized to the wheel position. The laser was fired when one of the openings was

positioned between the target and sample substrate, allowing the fast (-105 cm/s) plasma

component of the plume to pass through to the substrate, while blocking the slower

moving (~103 cm/s) particle component. This produced a smooth, uniform film on the

sample -1 cm wide with very few large particles incorporated into the film.

The composition of the composite film was varied by alternating gold and filler

phase targets. The ablation of each material by the laser produced a short burst of plasma

that is quenched on the substrate to be coated; alternating between targets allows the

composition of the resulting film to be precisely controlled, while the amount of each

material deposited in a cycle is kept low enough (< 1 monolayer) that the final material is

approximately uniform in composition. Individual deposition cycle layers were typically

less than 10 A each, but incomplete in areal coverage. The PLD films were deposited on

top of a 500 nm thick pure gold evaporated layer. The final desired thickness of the PLD

composite films was 50 nm.









The filler phase materials for the PLD process were chosen for several reasons.

Alumina was chosen as a filler phase because it is a chemically stable, thermally

invariant, additive phase for gold films that was known to block dislocation motion, and

to be compatible with the PLD process [78]. Gold-alumina cermet films had been

previously fabricated using PLD, as well as by co-sputtering [78-80]. The hypothesized

advantage of the Au-A1203 composite over a pure gold electrical contact was that the

alumina-filled material would have a reduced contact area and limited the amount of

gold-gold contact adhesion, but without significant affects on the electrical resistivity.

Similarly, titanium nitride was chosen because of its stability and increased

hardness over pure gold. Au-TiN composites have been fabricated using co-sputtering,

increasing the measured Vickers microhardness of the composite over pure gold films by

300% [81]. It was hoped that Au-TiN composites would be significantly more conductive

than the alumina composites while still achieving similar hardening and adhesion

reducing effects in the gold-alumina composites.

Nickel-hardened gold composite materials are well known and widely used for

electrical contact materials, most commonly in macro-scale electrical switches and

breakers. Alloys of Au-Ni have been investigated previously for low-force electrical

contacts [16,64]. The advantage of nickel is that its electrical resistivity is only about 5

times greater than gold, unlike alumina or titanium nitride, whose resistivities are many

orders of magnitude higher than gold. Even for a very low gold percentage composite, the

composite film resistivity should remain in the range of nominally metal contacts for the

Au-Ni films. The potential risk associated with nickel is the possibility of material









segregation and surface oxidation of the nickel, creating an insulating film on the surface

of the gold.

A concern with composite material co-deposition is the scalability of the deposition

process with regard to large-volume device fabrication. Pulsed-laser deposition is a

versatile and powerful technique for deposited very specific thin-film structures.

However, PLD is costly and does not scale well for large-scale deposition schemes used

in an industrial setting. Physical vapor deposition (PVD) techniques, such as RF-

magnetron sputtering, are capable of producing thin-film composites similar to PLD-

produced materials, but at a lower cost and scalable to large-volume device production

[82]. However, the difference in the final resulting film between PLD and PVD

techniques are not substantial, as both techniques involve the physical impingement of

atomic species onto the coated target.

TEM Imagery

Figs. 5-11 through 5-13 show cross-sectional TEM images of three different PLD

Au-A1203 films, with 90%, 50%, and 20% gold volume percent. The first TEM image of

the 90% gold composite shows very subtle changes in the 50 nm thickness of the PLD

film. The grain structure of the evaporated gold substrate is slightly larger than that of the

PLD film deposited on top of it. The 50% gold composite shown in Fig 5-12 shows

significant change in grain structure between the composite film and the gold substrate. A

definite boundary between the substrate and composite film is beginning to form. Three

stratified layers can also be seen in the film. In Fig. 5-13, the 20% gold film is starkly

different from the gold substrate underneath. Columnar grain structure and a very defined

boundary between the composite and substrate are visible.

































Figure 5-11. TEM image of 90% gold, Au-Al203 PLD composite






















Figure 5-12. TEM image of 50% gold, Au-A1203 PLD composite






























Figure 5-13. TEM image of 20% gold, Au-A1203 PLD composite

Experimental Results

Experimental investigation of these films was performed using the ECR nano-

indenter described in Chapter 3. A normal load of 100 [[N was applied while 1 mA of

current was sourced with a 1 V compliance limit set. Figure 5-14 shows the normalized

results of the three different types of PLD composite coatings, Au-A1203, Au-TiN, and

Au-Ni. Each resistance and pull-off data point is averaged from 10 repeated contacts. The

mean normalization values for resistance and pull-off force were 533 7 mQ and 253

36 [[N, respectively for a baseline gold-gold contact. The variability of the resistance and

pull-off force results originated from changes in the contact, as the experimental

uncertainty for the electrical measurement and force measurement was 0.9 mQ and 1

[[N, as determined from Table 3-1. It is apparent from Fig. 5-14 that large increases in

resistivity were realized with modest increases in filler volume percentage. Also apparent

is that the trade-off between increased composite resistivity and decreased pull-off force









was not directly related. Almost an order of magnitude reduction in pull-off force was

achieved for the 50% gold films without a similar magnitude increase in composite

resistivity.


1000 Au AuAI203 AuNi AuTiN



100



10 Normalized
Resistance


q 5-= -


Normalized
Pull-off Force
0.1 f T


Au% 100% 90% 50% 20% 75% 50% 25% 75% 50% 25%

Figure 5-14. Normalized PLD composite film electrical contact resistance and adhesive
force nano-indentation results

Further experimental investigation of the electrical percolation threshold in Au-

Al203 composites was performed with similarly produced PLD films. Starting with pure

gold, additional PLD film samples with incremental additions of 7.5 % alumina were

created to provide more compositional resolution than what is seen in Fig. 5-14. The

results of the additional testing is shown in Fig. 5-15. Pure PLD gold resistance was 637

+ 10 mQ at 100 |tN normal load and 1 mA current, higher than the 533 mQ resistance of

the PLD films tested in Fig. 5-14. As the gold film percentage decreased, the resistance