MECHANICAL CHARACTERIZATION AND THERMAL MODELING OF A MEMS THERMAL SWITCH KEVIN RICHARD CRAIN

Transcription

1 MECHANICAL CHARACTERIZATION AND THERMAL MODELING OF A MEMS THERMAL SWITCH By KEVIN RICHARD CRAIN A thesis submitte in partial fulfillment of the requirements for the egree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING WASHINGTON STATE UNIVERSITY School of Mechanical an Materials Engineering December 005

2 To the Faculty of Washington State University: The members of the Committee appointe to examine the thesis of KEVIN RICHARD CRAIN fin it satisfactory an recommen that it be accepte. Chair ii

3 ACKNOWLEDGEMENTS This research woul not be possible without the patient help an guiance of my avisor, Dr. Bob Richars. His involvement an support has mae this research successful. From him I have gaine wisom an knowlege that will carry me into a career that I know will continue with the success that began here with my grauate stuies. From my other committee members, Dr. Cill Richars an Dr. Dave Bahr, I have gaine new insight into research an engineering. Their knowlege an expertise in a variety of areas has been invaluable to me in my pursuits in grauate school, an I will carry that knowlege with me throughout my career. I also acknowlege the entire P3 MEMS group for their har work an eication to an extraorinary research project. Their example an never-ie attitue is what makes this research project successful. I specifically want to thank Jeong-Hyun Cho for his help an avice regaring thermal switch fabrication, Lelan Weiss for avice, suggestions, an help regaring experimentation, an Aireus Christensen an Travis Wiser for their work as fellow thermal switch researchers. I thank all my friens an family for their support an encouragement as I progresse through this challenging perio of my life. I especially thank my wife Cristin, who stoo by me uring struggles an rejoice with me in success. Finally, I thank Go for blessing me an guiing me through until the en. iii

4 MECHANICAL CHARACTERIZATION AND THERMAL MODELING OF A MEMS THERMAL SWITCH Abstract by Kevin Richar Crain, M.S. Washington State University December 005 Chair: Robert Richars This thesis summarizes the research involve in mechanically characterizing a liqui metal micro roplet array thermal switch for use with the P3 micro heat engine uner evelopment at Washington State University. The mechanical characterization of the thermal switch was complete with the evelopment of a thermal moel that preicts the thermal resistance of the roplet array when in contact with the P3 engine at various loaings. The thermal switch was mechanically characterize statically, ynamically, as well as statistically. Static eformation experiments of single large roplets of 00µm iameters provie a means for valiating the mechanical an geometrical aspects of the thermal moel, such as force, eflection, an contact iameter. Deflection an contact iameter were measure simultaneously uner static conitions with applie forces ranging from 0 to 0.1N. Dynamic roplet array behavior was experimentally observe by visualizing cyclic actuation of the roplet arrays against a rigi, glass surface. Actuation frequencies of 0Hz an 400 Hz were applie to the roplet arrays using a piezoelectric actuator stack, over varying lengths of actuation time, for total cycle spans of one, ten, an one hunre thousan cycles, as well as one million cycles. Statistical iv

5 characterization was obtaine using computer-assiste roplet iameter measurement of igital photographs of the roplet arrays. Total array population was also statistically inferre from sample population ata analysis. Analytical moels were erive for geometry, mechanical eformation, an thermal behavior. Geometrical relationships between contact raius an eforme roplet height were erive, assuming constant volume an contact angle of the liqui/soli/vapor interface. This was converte into contact iameter an eflection for comparison an valiation with experimental measurements. Experimental mechanical eformation ata was compare an valiate against a moel base on capillary pressure of the liqui roplet. This moel was use to obtain a corresponing relationship between force an eflection of a eforme roplet. These moels were then incorporate into a thermal moel which calculates an effective thermal resistance for a network of resistances of the roplets an gas gaps in the array. The geometric an force moels were use to calculate the theoretical thermal resistance of every roplet in an array uner a specific loaing. Forces between 0 an 1N were use to calculate the thermal resistance of a roplet array. Different interstitial gas environments of air, vacuum, an xenon, were applie to the thermal moel to investigate possible increases in performance of the roplet arrays. v

6 TABLE OF CONTENTS ACKNOWLEDGEMENTS...III ABSTRACT... IV TABLE OF CONTENTS... VI LIST OF TABLES... IX LIST OF FIGURES...X 1. INTRODUCTION Motivation Literature Review Thermal Switch Applications Thermal Switch Designs Thermal Contact Resistance Thermal Interface Materials Characterization of MEMS Mercury Micro Droplet Switch Research Objectives FABRICATION Overview Thin Film Deposition Ultra-Violet Photolithography Droplet Deposition THERMAL MODEL Overview Metho... 4 vi

7 3..1 Mechanical Behavior Geometry Force Deflection Droplet Array Statistics Thermal Behavior EXPERIMENTAL APPARATUS Overview Static Deformation Compliance Alignment Loa Cell Laser Positioning System Visualization Dynamic Actuation Visualization Piezoelectric Actuator EXPERIMENTAL PROCEDURE Statistical Analysis Static Deformation Dynamic Actuation RESULTS Overview vii

8 6. Statistical Characterization of Droplet Arrays Droplet Diameter Array Size Static Deformation Initial Contact Behavior Deformation Hysteresis Moel Valiation Geometrical Relationship Force vs. Deflection Thermal Resistance vs. Force Dynamic Actuation Droplet Stability Optical Alignment CONCLUSIONS Static Deformation Dynamic Actuation Thermal Moel APPENDIX REFERENCES... 7 viii

9 LIST OF TABLES Table 6.1: Initial Contact Behavior Di/Do Ratio Table 6.: Parameter Stuy ix

10 LIST OF FIGURES Figure.1: 1600 Droplet Array Gol Mask Figure.: 1600 Droplet Array Die Mask Figure.3: Photoresist Protection Layer Die Mask... 0 Figure.4: Mercury Deposition Chamber... 1 Figure 3.1: Two Dimensional, Axisymmetric Representation of Deforme Droplet... 6 Figure 3.: Principle Raii of Curvature for a Sphere... 8 Figure 3.3: Diagram of Droplet Height Calculation... 9 Figure 3.4: Thermal Resistance Network Figure 6.1: Die 884H Air Droplet Diameter Histogram Figure 6.: Die 884K Xenon Droplet Diameter Histogram Figure 6.3: Die 964O Vacuum Droplet Diameter Histogram Figure 6.4: Portion of 1600 Droplet Array... 5 Figure 6.5: Large Droplet Contact Hysteresis Figure 6.6: Geometric Moel Valiation Figure 6.7: Test Stan Compliance Figure 6.8: Force Deflection Valiation Figure 6.9: Thermal Resistance Comparison in Air Figure 6.10: Thermal Resistance Comparison in Xenon Figure 6.11: Thermal Resistance Comparison in Vacuum Figure 6.1: Moele Thermal Resistance for Die 884H Figure 6.13: Moele Thermal Resistance for Die 884K Figure 6.14: Moele Thermal Resistance for Die 964O x

11 Figure 6.15: Droplet Array Deterioration uring Actuation... 6 Figure 6.16: 10,000 Cycle Actuation Figure 6.17: 100,000 Cycle Actuation Figure 6.18: Million Cycle Actuation Figure 6.19: Misaligne Actuation Figure A.1: Two Dimensional, Axisymmetric Representation of Deforme Droplet xi

12 CHAPTER 1 INTRODUCTION 1.1 Motivation Micromechanical switches are fining applications in thermal MEMS research, which inclue thermopneumatic actuators an micro heat engines. A novel external combustion micro heat engine is being evelope at Washington State University (WSU) [1,], which requires the use of a thermal switch to conuct heat into an out of the engine. The thermal switch must function at the resonant frequency of the engine an be able to transfer appropriate amounts of heat into an out of the engine at particular times, in orer for the engine to run as efficiently as possible. The motivation of this research is to evelop a thermal moel that will preict the performance of a thermal switch to be use in conjunction with the P3 micro heat engine uner evelopment at WSU. The ultimate goal is to esign more efficient thermal switches that will increase engine performance. 1. Literature Review Thermal switches, also known as heat switches, are a popular area of research. The scope of thermal switch applications is broa an iverse. However, the consistent nee in inustry centers on thermal control. Two applications of thermal switches involve the areas of space exploration an cryogenics. A thir application inclues biomeical DNA replication (also known as polymerase chain reaction, or PCR). Other applications of micromechanically esigne thermal switches that are increasing in popularity an importance inclue low temperature physics, soli state thermoelectric 1

13 coolers, an micro heat engines. These applications will be iscusse in greater etail to provie conceptual unerstaning of the nee for thermal switches. In thermal switch esign, thermal resistance (or inversely, thermal conuctance) is the principle parameter of interest. In esigning an effective thermal switch, thermal resistance shoul be minimize when the thermal switch is activate, allowing the maximum quantity of heat to transfer across the switch. When the thermal switch is eactivate, thermal resistance shoul be maximize in orer to minimize heat transfer an conserve energy. Contact resistance is also an integral part of thermal resistance an must be consiere when esigning thermal switches. Several aspects of thermal switch esign will be iscusse below. Characterizing thermal switch behavior is also important. A thermal switch controls the flow of heat in a mechanical system. This is analogous to controlling electric current in electrical systems, such as an electrical switch for a light fixture in a house. At times, the light must be turne on to illuminate a room. When there is no longer a nee for illumination, turning the light off will conserve electricity. In similar fashion, some mechanical systems require heat transfer uring a specific, finite perio of time. When the thermal switch is activate, or turne on, heat is transferre across the switch as the thermal resistance is minimize. When heat transfer is no longer require, the thermal switch is eactivate, thereby increasing thermal resistance an minimizing heat transfer across the thermal switch. Characterizing the behavior of thermal switches is imperative to ensure functional performance of the esign an application of a thermal switch. For the thermal switch application an esign involve in this research, theoretical characterization of expecte performance will also be iscusse.

14 1..1 Thermal Switch Applications There is great interest in the ability to control heat flow in mechanical systems. Space applications have traitionally been one of the most important areas for thermal switching. In particular, thermal switches have been applie to the area of cryogenics for spacecraft. Spacecraft raiation sensors, such as infrare an gamma ray etectors [3], nee to function at extremely low temperatures. Thermal switches are use to couple these sensors to cryogenic refrigerators. When the sensor is operating, the thermal switch is activate to issipate heat prouce by the sensor through the switch to the refrigerator. When not operating, the sensor is isconnecte from the refrigerator. Likewise, parasitic heat loas from refrigerators in reunant cooling systems can be isconnecte using thermal switches. The thermal switch is eactivate to provie high thermal resistance to isolate the sensor [4]. Other reasons for ecoupling the sensor from the cryogenic cooler inclue cases of open cycle systems that use expenable cryogens as coolant. Conservation of the expenable coolants increases the lifespan of the system an elongates the mission uration capability of the evice. In aition, ecoupling the sensor from the cooler reuces contaminants that collect on the sensor uring cryogenic operation. Often these contaminants can be remove by the resulting graual warm up uring inactivity [3]. Another application is thermal control of spacecraft via raiative heat transfer between the craft an the environment. The traitional approach to spacecraft thermal control involves large raiators connecte to louver structures controlle by a thermostat [5]. However, in applications where satellites are very small (weighing less than 0 kg, known as nanosats or picosats), this approach is ifficult. Possible alternatives inclue 3

15 variable emissivity coatings (VEC) that can actively control heat transfer from the spacecraft in response to variations in thermal loa an raiative conitions. Along these lines, one promising option is the active raiator tile (ART) thermal valve, a new form of MEMS thermal switch [6]. The areas of research for thermal switch integration inclue low temperature calorimetry [7], nuclear emagnetization cryostats [8], aiabatic emagnetization [9], an Pomeranchuk cooling (which is soliification of liqui helium via aiabatic compression) [9]. In low temperature calorimetry, a sample is coole with a refrigerator an then isolate using a thermal switch. The measurement then procees by applying a controlle heat pulse an observing the associate temperature rise. Aiabatic emagnetization requires precooling the paramagnet an aitional materials in a magnetic fiel by a refrigerator. The thermal switch then isolates the specimens an the magnetic fiel is lowere aiabatically to zero [9]. Soli state cooler applications, such as thermoelectrics (TE s), have benefite from thermal switches. TE s have avantages of high reliability, low mechanical noise, an localize temperature control. However, they typically have low efficiency an frequently nee multiple stages to be effective. In orer to make soli state cooling competitive, implementation of thermal switches in the transient operation of thermoelectric coolers has been achieve. Application of short transient pulses on top of a steay state bias results in an aitional temperature rop over the performance of steay state TE cooling [10]. Sensors, etectors, an signal processing perform better in reuce temperature environments. Soli state coolers enable the system esigner to 4

16 tightly control the evice temperature to specific ranges over varying power issipation levels by using active sensing an feeback [10]. Biomeical research may appear unrelate to applications of a thermal switch, but polymerase chain reaction (PCR) is an area in which carefully controlle heat transfer is crucial. PCR is a process through which DNA is replicate millions of times. It is a process that is meiate by enzymes an consists of perioic repetition of three biological reaction steps which each occur at ifferent temperatures. The basic requirement for efficient DNA amplification is rapi heat transfer [11]. A evice with low heat capacity an high thermal conuctivity is esire for optimal PCR. With traitional PCR instruments, heating an cooling rates are slow, ue to the relatively large size of thermal components. Pulse resistance heaters have been successfully use in microchip PCR evices [11], but thermal switches coul potentially be use in these applications as an alternative to resistance heaters. MEMS-base thermal switches, with naturally higher surface area to volume ratios, may prouce faster heat transfer rates an thus coul accelerate the PCR amplification process. At this time, implementation of a MEMS thermal switch has not occurre, but the characteristics of thermal switches suggest possible benefits coul be gaine from application of thermal switches in PCR. 1.. Thermal Switch Designs There have been several thermal switch esigns applie to the requirements of space-base cryogenic systems [3, 4, 1]. A gas-gap thermal switch consists of two cylinrical pieces that are separate by a small gap fille with a conuctive gas. The thermal resistance varies with respect to the amount of gas that fills the gap. Reporte methos of pumping the gas into the cyliners have utilize cryogenic an charcoal 5

17 pumps. Actuation times are epenent on allowing the gap to fill with gas, an they are on the orer of minutes, making these thermal switches very slow. However, thermal resistance ratios have been reporte as high as 1500 [3] an 4000 [1]. Another thermal switch esign revolves aroun the ifferential thermal expansion of istinct metals [4]. Actuation times are epenent on the materials use. The ifference between the gas gap an issimilar metal switch esigns is the metho of actuation. The former is actively actuate, requiring external energy to operate. The latter is passively actuate as a function of the mean temperature of the switch. Other thermal switches inclue solenoi-activate, metal to metal contact switches. Single gallium crystal switches operate at temperatures of liqui helium an are switche by magnetic fiels. Heat pipes have also been use as thermal switches an operate relative to the elay times that allow the nitrogen working flui to transfer along the length of the pipe [4]. The ART (active raiator tile) thermal switch utilizes electrostatic actuation to control the thermal switch [6]. The ART is comprise of two material layers, separate by an evacuate gap. Thus, the two layers, the external raiator an the internal base plate, are thermally isolate. Insie the gap, the two opposing surfaces are coate with a low emissivity material to minimize raiation across the gap. The external surface of the tile is coate with a high emissivity coating to maximize the raiative heat transfer into space. The external raiator is fabricate out of silicon, which has high thermal conuctivity. A large membrane with a central contacting mass is etche into the silicon. When an electrostatic charge is applie to the ART, the membrane eflects into intimate, mechanical contact with the hot base plate. Heat is then conucte to the raiator an 6

18 raiate to the environment. The temperature ifferential across the 10µm gap in the switch was reporte as high as 145 C in the off state. The thermal resistance of the ART was not reporte. Spacecraft are not the only area of evelopment for thermal switch integration. The fiel of low temperature physics frequently employs exotic thermal switch esigns, such as superconucting [7, 8, 13] an cryogenic [9, 14] thermal switches, in research. Superconucting thermal switches rely on the fact that the thermal conuctivity of a superconucting material in the normal state is substantially larger than its conuctivity in the superconucting state [7]. Some superconucting materials use in thermal switches inclue inium, aluminum, tin, lea, zinc [7], as well as col-presse Cu-Al composites [8]. One cryogenic thermal switch relies on the thermal properties of liqui helium which can achieve a thermal conuctance similar to electrolytic copper [14]. Actuation is one using a self containe cryopump. Heating the cryopump to a temperature where the helium is esorbe activates the thermal switch, an cooling the cryopump reabsorbs the helium. The reporte ratio of on an off conuctance was greater than 10 4 with switching times on the orer of minutes Thermal Contact Resistance Contact resistance is an important factor to consier when iscussing thermal switches. Contact resistance arises from a non-ieal contact at the interface between two soli surfaces that are brought into contact. The purpose of this contact is typically for transferring heat or electricity from one boy to another through conuction. When the surfaces are in contact, the real contact area is only a fraction of the apparent contact area 7

19 ue to asperities an roughness of the two contacting surfaces. An interstitial meium or vacuum occupies the remaining space between the surfaces an this creates a resistance to heat or electricity transfer. Quantifying this contact resistance can be a complicate process an is frequently inaccurate. These contact resistances can be small, yet quite significant when highly accurate measurements must be mae. The magnitue of the contact resistance is a function of the force applie at the interface between the two contacting boies. As more force is applie, the pressure at the interface increases an the gaps between the two boies shrinks that prouces a lower thermal resistance of the gap. Much work has been one to characterize the behavior of contact resistance, with respect to loaing conitions, temperatures, an ifferent material interfaces [15]. Thermal contact conuctance of copper contacts was measure over a range of contact pressures of 1 to over 10 MPa, with corresponing thermal contact conuctances ranging from 5 to 130 kw/m K, respectively. Obviously, the pressure at the interface has a significant influence on the conuctivity, or inversely the resistance, of the contact. Thermal contact resistance has prove to be important in cryogenic engineering. Cryogenically coole superconucting magnets use high temperature superconuctors as power current leas. It is frequently necessary to electrically connect the high temperature superconuctors with copper leas, an the thermal contact resistance between these two materials is crucial to unerstan for proper operation [16]. The contact resistance was measure for superconucting polycrystals connecte to copper leas for a variety of connection methos an over a temperature range of 10 to 00K. 8

20 The thermal contact resistivity results varie wiely between 10 1 an 10 4 mm K/W throughout the temperature range. In this research, thin gol layers are use as conensation targets for the mercury vapor. At the interface between the silicon ioxie an the gol thin film, potential contact resistances exist. To optimize thermal switch operation, this contact resistance shoul be minimize. Thermal contact resistance has been stuie for gol coatings on ceramic substrates, for example Al O 3 [17]. Here, thermal contact resistance was stuie an correlate with ahesion an the nature of the interface omain. Lower thermal contact resistances an stronger ahesion were reportely obtaine by ion etching the substrate before eposition. The surface roughness of the substrate was reporte to be 78nm. Annealing of the gol film was performe after evaporation eposition. The contact resistance measurement was performe using a pulse laser proceure an measuring the electrical resistance of the metal layer as the metal coole. Over a range of metal thicknesses from 100 to 400nm, a minimum contact resistance was foun for a film thickness aroun 00nm, an the resistance measure was less than 1e-7 m K/W. Equally interesting to this research is the thermal contact resistance behavior of smooth, polishe surfaces in close contact. Theories have been evelope to preict this behavior but agreement with experiments has been inconsistent. Some of these theories have been summarize by Wolff [18]. One theory moele the contact as asperities touching at the interface. Conuction epene on contact pressure, thermal conuctivity, harness, surface finish, along with size an shape of the contact asperities. Lumpe parameter methos became highly useful in eveloping this theory. Actual measurement work then proceee by measuring the conuctivity across the interface of 9

21 iffering materials an several interstitial fluis. The variety of surface finishes as a egree of complexity to moeling this phenomenon. For example, bea blaste surfaces ten to have homogeneous istributions of asperities, but groun an sane surfaces have irectionally epenent roughness that make preiction more ifficult. It has been observe that for very smooth surfaces an very har materials, applie pressure has little effect on the contact resistance [18]. Pressure only tens to affect contact resistance for materials with rougher surfaces that can easily eform at either microscopic or macroscopic levels. Conclusions of experimentation [18] have lea to a belief that the ability of the interface material to conform to the opposing surface material is more important than the conuctivity of the materials themselves. Literature reports that thermal aging can affect the contact resistance of cobalt an nickel harene gol platings (calle har gols) on copper [19]. This may provie another avenue to explore for reucing contact resistance. Electroeposite gol containing nickel an cobalt were eposite an age at a variety of temperatures. At temperatures between 150 an 00 C, the aging effect actually cause the contact resistance of the har gols to increase over the contact resistance of pure gol. The hareners themselves increase the contact resistance of pure gol as well. Contact resistance was measure by a probing technique specifie in ASTM B-667. Longer aging uration also cause increases in thermal contact resistance of the har gols, where pure gol remaine constant. Measuring contact resistance is a ifficult process. However, characterizing the contact resistance in a thermal switch is very important. A laser-base, non-contact an non-estructive transient thermo reflectance (TTR) metho has been use to measure 10

22 thermal conuctivity of a variety of silicon types an their oxies, as well as thermal contact resistance between a blanket gol layer an the silicon oxie layer [0]. Specifically, the silicon-8 isotope in a purifie form was teste an compare with natural silicon, which has a mixture of all silicon isotopes. The results showe that silicon-8 has an increase thermal conuctivity, as well as a ecrease thermal contact resistance with a eposite gol layer, over natural silicon Thermal Interface Materials A variety of new thermal interface materials (TIMs) are being stuie that hol the promise of increasing performance of thermal switches. TIMs are use to reuce contact resistance in orer to optimize thermal switch performance. One TIM that is currently being stuie is carbon nanotubes (CNT). CNT s have high thermal conuctivities, high aspect ratios, as well as goo mechanical strength that provie attractive characteristics for improve thermal control applications. They can be grown from a catalyst thin film an usually form a surface structure like a forest or grassy turf [1]. CNT s coul provie a compliant, elastic interface for contact of a thermal switch, which has potential to reuce wear an fatigue of the contacting surfaces. CNT s have yet to be integrate into a thermal switch, but the mechanical an thermal properties of CNT s coul be avantageous. Densely grown CNT turfs coul provie a surface that woul conform well to asperities of soli contacting surfaces an reuce contact resistance. Another TIM, known as curable polymer gels, is also being stuie [] to replace more traitional thermal greases [3] in electronics. These gels have ifferent mechanical properties ue to ifferences in the rheology of polymers. Their behavior 11

23 transitions from a grease to a gel when cure. These TIMs are intene to be use at the interface between microprocessors an the heat sinks use to issipate the thermal power generate uring operation. Polymer-base-gel TIMs have high bulk thermal conuctivities an low thermal interface resistances. When applie to the heat sink assembly, these gels are in a grease form. They have low surface energies an conform well to surface irregularities, which minimizes thermal contact resistance. Once they cure, the gels crosslink into a fille polymer, allowing cohesive strength that avois the leaking issues exhibite by greases uring temperature cycling. The thermal contact resistances for these gels are typically measure between 1 an 5e-5 m K/W at pressures up to 700 kpa []. The characteristics of these materials may not len similar benefits to thermal switches like CNT s, but perhaps they coul be useful at the interface between a thermal switch an the connecte bulk thermal reservoir. Low contact resistance between the heat source an the thermal switch coul be beneficial in cooling applications as in spacecraft thermal control iscusse earlier. The TIM use in the thermal switch of this research is mercury. Mercury roplets form a compressible contact for the thermal switch because they are in a liqui state at room temperature. This compliant contact reuces the threat of physical wear on the thermal switch an contacting surface. Likewise, the liqui state of mercury allows the roplets to easily eform when in contact. Contact area is allowe to increase as separation istance ecreases, which both lower thermal resistance an increase thermal switch performance. Aitionally, the liqui mercury can more easily conform to the irregularities of the contacting surface, which ecreases contact resistance. 1

24 The thermal switch iscusse in this thesis utilizes arrays of mercury micro roplets that are eposite on a silicon substrate. The fabrication of the mercury micro roplet arrays has been previously evelope [4,5] Characterization of MEMS Mercury Micro Droplet Switch The evelopment an characterization of the mercury roplet array thermal switch was inspire by the application of mercury micro roplets in a MEMS electrical switch [6, 7]. The eposition process for forming microscale mercury roplets was evelope [6]. A moel of the mercury micro roplet s mechanical behavior was evelope an reporte by J. Simon [8]. cot V cos cot a ± sin 34sin 36sin 48 6sin This moel escribes the relationship between contact raius a, roplet height, contact angle θ, an volume V of a single mercury roplet. The force require to eform a single mercury roplet can be foun from the capillary pressure ifference across a liqui surface, which is given by N. Aam [9]: 1 1 P γ ( ) 1. R 1 R The capillary pressure ifference P is a function of the surface tension γ an the two principle raii of curvature R 1 an R, which efine the shape of a sphere. 1.3 Research Objectives This research investigates the mechanical an thermal behavior of a thermal switch base on arrays of liqui metal micro roplets eposite on silicon substrates. The roplet arrays provie a compliant contact between a heat source an a contacting surface. 13

25 Mechanical behavior involves both static an ynamic characterization of the roplet arrays. The static relationship between the force applie to eform the roplets, the contact area, an the eflection is investigate. Statistical characterization of the roplet arrays is also performe. Mechanical moels are then evelope to valiate the experimental characterization. Dynamic characterization of the micro roplet arrays is also performe. This consists of cyclic actuation of the thermal switch to characterize long term switching behavior an longevity. Thermal behavior is stuie by eveloping a thermal moel to preict the thermal resistance of the switch with respect to the force applie uring contact. The thermal moel is evelope from the mechanical an statistical characterization of the roplet arrays. Thermal resistance is calculate for the entire thermal switch at ifferent applie static contact forces. This moel is compare with experimental measurements of thermal resistance obtaine by T. Wiser through the use of a guar heate calorimeter [30]. 14

26 CHAPTER FABRICATION.1 Overview MEMS technology is built on the backbone of the IC inustry an the siliconbase fabrication techniques that have been evelope an use for the last 30 years. What has helpe make microprocessor technology so afforable has been the ability to batch manufacture these microprocessor chips. MEMS technology boasts the same capability to reuce costs an increase prouction of evices. Processing of a single wafer can prouce many iniviual evices that can be teste an use iniviually. The liqui metal micro roplet arrays use in the thermal switch are fabricate using a few techniques that have been the basis of IC fabrication for ecaes. While thin film metal eposition can occur in a variety of ifferent ways, magnetron sputtering is one traitional metho that is use in this research. Photolithography is the process where a pattern is transferre to the substrate from a mask. Selective etching of the metal thin film uring photolithography prouces various shape structures on the substrate. Finally, the liqui metal is eposite on the substrate via evaporation an selective conensation. The liqui metal use in this research is mercury, an the conensation targets are gol, to which mercury has a very strong chemical attraction. These fabrication processes will be further iscusse in etail below.. Thin Film Deposition Mercury roplet eposition occurs by preferential conensation of mercury vapor onto gol target pas that are fabricate on a silicon wafer substrate. The silicon wafer has been previously covere with a thermally grown silicon oxie layer. The gol layer 15

27 an a titanium-tungsten ahesion layer are eposite onto a silicon substrate by DC magnetron sputtering. The sputtering system consists of a seale, evacuate chamber where the silicon wafer is positione above the metal source targets. Once the chamber is evacuate to a prescribe pressure, argon gas is brought into the chamber. A voltage fiel is create which attracts argon ions. The argon ions then accelerate into the metal source target an etach metal atoms that spray up towars the silicon substrate. Longer eposition times allow for a thicker metal layer to be eposite on the silicon substrate. The TiW layer is eposite first for 51 secons then the gol is eposite for 1 minutes to obtain thicknesses of 5nm an 300nm, respectively..3 Ultra-Violet Photolithography Once the thin film layer of gol is eposite onto the silicon wafer, ultraviolet photolithography is use to efine the eposition target pas. A polymer photoresist, AZ514, is eposite on top of the gol by a spin coating technique at 3000 RPM for 30 secons an then harene by baking on a hotplate at 110 C for 1 minute. A transparency mask, shown in Figure.1, is then use to cover the wafer when expose to ultraviolet light for 1 secons. Figure. shows a magnifie image of the mask for a single square gri array on a ie with imensions of 10mm by 18mm. The mask is a printe image on a transparent polymer sheet that allows light to pass through an expose selecte areas of the wafer while masking light exposure from other areas of the wafer. When light passes through the transparency mask an exposes the photoresist layer, cross linking within the photoresist polymer breaks apart. 16

28 Figure.1: 1600 Droplet Array Gol Mask The expose areas of the photoresist are etche away when the wafer is immerse in a solution of one part photoresist eveloper, AZ400K, to four parts eionize (DI) water. The unexpose areas are unaffecte by the eveloper solution. The mask feature size is limite by printer resolution, so uring evelopment, the photoresist is overetche. This reuces the size of the eposition pas to a iameter between 5 an 10 microns. It has been etermine that this is an optimal gol target size to obtain consistent roplet growth uring mercury eposition. The evelope pa iameter is carefully controlle by monitoring the evelopment process with a microscope. If the photoresist pas are too large, the wafer is immerse again in the eveloper solution for short perios of time 17

29 until the pas are the proper size. The pa size is constantly monitore using a microscope. Figure.: 1600 Droplet Array Die Mask The result is a wafer with a blanket layer of gol an a patterne layer of photoresist. Some portions of the gol are covere by photoresist while other portions of the gol are expose to the environment. The wafer is then immerse into a gol etch solution to etch away the areas of expose gol. The gol areas covere by photoresist are unaffecte an thus remain after etching has complete. The wafer is rinse in DI water an is then immerse into hyrogen peroxie. This process step etches away the titanium-tungsten ahesion layer from the areas where gol was etche away. The silicon ioxie layer of the wafer is then fully expose. The remaining photoresist is easily washe away using a stanar five step acetone/ipa/di/acetone/ipa cleaning process. The remaining structure on the wafer is a pattern of the gol pa arrays on top of silicon ioxie, in the same pattern as the mask shown above. Another photolithography step is performe to protect the expose oxie layer from mercury eposition. The gol etching oes not always remove all remnants of gol from the expose areas. This can 18

30 potentially attract mercury vapor to eposit aitional roplets on the substrate, which are referre to as satellite roplets. Satellite roplets can be potentially hazarous to the operation of the roplet arrays when the thermal switch is actuate against the P3 micro heat engine. If a satellite roplet sits near another roplet on a gol pa, the two roplets can touch an quickly combine into a larger roplet when eforme with enough force uring operation. If these roplets continue to grow by combining with other roplets, eventually the roplet array can eteriorate into a large mercury pule that will wash over the entire array surface, engulfing all other roplets. Due to the limite actuation istance of the thermal switch, these large pules will never break contact with the P3 engine. The result is a thermal switch that never switches. In essence, there woul never be an off state, because the mercury woul always keep the engine an the switch surface in constant contact. This woul severely hiner the performance of the P3 engine, which nees cyclic heat aition in orer to run. Continuous heat aition will cause the mean temperature of the P3 engine to rise. The engine will not be able to reject heat fast enough to keep up with the heat aition. The engine will stop oscillating an remain in a perpetually expane shape. For this reason, a metho was foun to prevent satellite roplet formation uring mercury eposition. Mercury has shown little tenency to conense on harene photoresist. Photoresist is spun over the top of the wafer again. The photoresist acts as a protection layer over the oxie an minimizes satellite eposition. Using an inverte image of the mask use in the gol patterning process escribe before, holes in the photoresist are patterne to expose the previously forme gol pas. Figure.3 shows 19

31 the array section of the inverte mask. Overetching in the photoresist eveloper wiens the holes in the photoresist to a iameter slightly larger than the iameter of the gol pas. This is monitore with a microscope like the previous evelopment process until the gol pas are fully expose through the photoresist holes. Aligning this mask with the existing gol ots is important for this process. The mask aligner machine has a high resolution positioning system an microscope for this task. Figure.3: Photoresist Protection Layer Die Mask Once this final patterning step is performe, the wafer is cut into ie. Each ie has a single gol pa array centere in the mile. The ie cannot be cleane using the stanar five step acetone/ipa cleaning process, because the photoresist protection layer woul be washe away. So cleaning the ie prior to eposition consists of rinsing the ie uner DI water for minutes. The ie is then immeiately expose to mercury vapor to reuce contaminants on the surface of the ie. These can provie locations for satellite roplet formation which must be minimize. 0

32 .4 Droplet Deposition A cleane an patterne ie is expose to mercury vapor to eposit the micro roplet array. A seale chamber with a pressure release col trap attache is heate in an oil bath insie a fume hoo. A small pule of mercury sits at the bottom of the seale chamber. A Teflon plate covers the top of the chamber an is seale with o-rings. The ie is place over a hole in the Teflon plate on top of an o-ring to provie a seal. The ie is then clampe own against the Teflon plate with a thir o-ring, a metal bar, an two bolts. There is a shutter on the bottom sie of the Teflon plate which is controlle from the outsie by a magnetic clip. The shutter can slie lengthwise along the bar clamp, an it is hel in place beneath by a groove track. A iagram of the mercury eposition chamber is shown in Figure.4. Figure.4: Mercury Deposition Chamber 1

33 The eposition process is performe first by carefully placing the ie over the o- ring an hole of the Teflon plate. The gol pa array must be centere insie the o-ring to ensure optimal roplet eposition an consistency in size. If the array is offset in any irection, the gol pas closest to the o-ring will potentially have less mercury eposite. The ie is clampe own an the shutter is teste to ensure the magnetic contact with the clip is secure. The shutter is move over the hole to eflect any mercury eposition from occurring uring heating. The oil bath is quickly heate to 176 C. Once the oil bath has reache a steay state temperature, then the shutter is opene for a specifie amount of time. Different array sizes require ifferent amounts of time for eposition. With more gol pas present, more mercury must be eposite, so more time is require. For the stanar 1600 roplet arrays (40x40 square gris) use in this research, a eposition time of 60 minutes consistently prouces uniform roplet arrays. The eposition occurs by the evaporation of the heate mercury as it tries to achieve equilibrium. This is riven by ifferences in the equilibrium partial pressures of the mercury vapor an air atmosphere insie the chamber. When the mercury evaporates, it oes so in all irections. However, the hole in the Teflon plate is significantly smaller than the surface area of the mercury pule beneath in the chamber. The istance between the mercury source an the hole is also very large with respect to the iameter of the hole. This means the mercury vapor that is entering the hole an epositing on the ie on the other sie is iffusing vertically an very little in any other irection. For this reason, the gol pa array shoul be centere over the hole, both which are of similar

34 imension. If there is an offset, the gol pas not in irect line of sight of the mercury pule beneath will have very little mercury eposite. 3

35 CHAPTER 3 THERMAL MODEL 3.1 Overview The major goal of this research is to evelop a theoretical moel to preict the thermal resistance of a thermal switch as a function of applie loa. This moel coul then be use to esign an optimize an effective thermal switch. An optimize thermal switch woul transfer the maximum amount of heat into an out of the P3 micro heat engine at the appropriate times in orer to maximize engine performance an efficiency. When esigning an effective thermal switch, it is necessary to maximize the thermal resistance of the switch in the off position. This off position occurs when there is a gap between the thermal switch an the contacting surface. Likewise, the thermal resistance must be minimize in the on position, when the switch an the contacting surface make contact. Achieving the largest thermal resistance ratio of the off to on states will maximize the engine performance by optimally controlling the heat transfer into the engine. 3. Metho The theoretical moel escribe here incorporates three main factors that are use to preict thermal resistance as a function of applie force on a mercury micro roplet array thermal switch. First, analytical solutions of the mechanical behavior of a single roplet are foun. The mechanical behavior involves relating the geometric shape of a eforme roplet to the force require to cause the eformation. Secon, a statistical analysis of the roplet size istribution in the square gri roplet array accounting for roplet size, position, an population is escribe. Thir, the mechanical behavior an 4

36 the statistics of the roplet arrays are use to calculate thermal resistance for an entire roplet array. The mechanical behavior of a single roplet can be escribe by two equations, which will be presente an iscusse in more epth below. The first equation eals solely with geometry an escribes the relationship between roplet contact iameter an gap length. Gap length is equivalent to the eforme roplet height or the length of the heat path. The secon equation relates the internal capillary pressure to the two raii of curvature of a eforme roplet. Combining these two equations for capillary pressure an contact area, the force applie to eform the roplet to a given eflecte height can be foun. Droplet statistics are then employe to apply the single roplet results to an array of roplets with a istribution of iameters. Statistically characterizing the variation in roplet iameters enables accurate preictions of mechanical behavior for an entire roplet array. The thermal behavior of a roplet array is then characterize using the concept of a thermal network. Each roplet an the surrouning gas are represente by a parallel thermal resistance Mechanical Behavior Thermal behavior of the thermal switch is closely couple to the mechanical behavior of the roplets. Thus, it is imperative to unerstan the mechanical behavior in orer to preict the thermal behavior of the thermal switch. The thermal resistance of a roplet epens on the heat path length or roplet height, the cross sectional area of the heat path or the roplet contact area. Therefore, to calculate roplet thermal resistance at 5

37 any applie loa requires an analysis of the mechanical behavior of a eforme roplet. For this reason, the force applie to the roplet an its corresponing effect on the eflection an contact area of the roplet is characterize Geometry The geometry of a eforme mercury micro roplet is consiere first. The roplet is assume to be between two parallel rigi plates that are brought together. As the two plates come into contact with the roplet, the roplet is eforme. First, the height of the roplets ecreases as it is squeeze between the plates. Secon, the contact area between the roplet an the plates increases. Figure 3.1 represents the cross sectional geometry of the eforme roplet as it is squishe towars the y-axis. Figure 3.1: Two Dimensional, Axisymmetric Representation of Deforme Droplet 6

38 Rotating the area below the circular arc (between x0 an x) aroun the x-axis prouces the volume of a roplet eforme uner an applie loa between two parallel plates. The volume of this rotate region is given by: V 0 [ f ( x)] x 3.1 The profile of the eforme roplet f(x) is escribe by: f ( x) x a 3. sin s tan where the function f(x) is the equation for a circle, centere at (/, a-b) as shown in the appenix. Inserting Equation 3. into the integral in Equation 3.1 an evaluating gives: 3 3 V a a a a tan tan 9sin 4sin 1 3 cos 3 18sin 3.3 as shown in the appenix. Rearranging this solution in terms of a as a function of,, an V, yiels [8]: cot V cos cot a ± sin 34sin 36sin 48 6sin as shown in the appenix. Equation 3.4 gives a relation for a, the contact raius, in terms of, the eflecte roplet height, which is also equal to the gap length between the two parallel plates. In the erivation, constant volume V of the roplet an constant contact angle, θ, were assume. Constant volume V follows from conservation of mass. Constant contact angle θ follows from the fact that the contact angle is a property of the interface between a soli, liqui, an gas. In this case, the interface is between air, mercury, an SiO. The angle can be foun from θ using: 7

39 90 [180 θ ] 3.5 as shown in the appenix Force The force require to eform a roplet epens on both the internal pressure an the contact area of the roplet. The internal pressure of the roplet is ue to capillary forces. The capillary pressure in the roplet epens on the surface tension γ an the two raii of curvature of the spherical roplet, R 1 an R [9]: 1 1 P γ ( ) 3.6 R 1 R The pressure ifference P is the ifference between the pressures acting on the insie an outsie of the roplet surface, or the ifference between the internal capillary flui pressure of the roplet an the external atmospheric pressure. The surface tension γ for mercury is 0.48 N/m [31]. The two raii of curvature R 1 an R, are shown in Figure 3.. Figure 3.: Principle Raii of Curvature for a Sphere 8

40 The two raii of curvature can be mathematically calculate using trigonometry as shown in the appenix. Solving Equation 3.6 for the static pressure insie the roplet gives: P 1 1 γ ( ) 3.7 rop P atm R1 R The force applie to the roplet is calculate by multiplying the roplet pressure by the contact area: F Prop ( a ) Deflection Deflection δ is calculate by subtracting the eforme roplet height from the original roplet height h, which is a function the original roplet iameter D 0 : h D0 (1 sin ) 3.9 A graphical representation of Equation 3.9 is shown in Figure 3.3. Height is the sum of the two terms shown in the figure. Figure 3.3: Diagram of Droplet Height Calculation 9

41 3.. Droplet Array Statistics The thermal switches use in this research were fabricate with arrays of approximately 1600 micro roplets. Within each array, the micro roplet iameters varie aroun a mean nominal roplet size. The istribution of roplet iameters was characterize for each micro roplet array by measuring the iameters of a sample population of roplets. Droplet iameters were measure by capturing igital pictures of representative portions of the roplet array using an optical microscope an igital camera. Droplet iameters, as well as the number of roplets foun on a given Au target or eposition site were etermine. The mean roplet iameter was calculate for the sample using [3]: i i y y 3.10 n The stanar eviation of roplet iameters was calculate using [3]: s 1 n 1 i ( y i y) 3.11 where n was the sample population. The sample roplet iameters were plotte in histograms with bin sizes of microns. Histograms were normalize by iviing bin populations by the total number of roplets sample, to give percentages. The number of excess roplets in the sample was also foun. Since the expecte total population of the entire roplet array was 1600, the ratio of actual sample size over expecte sample size was multiplie by 1600 to estimate the actual array population. The same proceure was use to estimate the global population for each bin. 30

42 3..3 Thermal Behavior The thermal resistance across a micro roplet array is foun by constructing a thermal resistance network that accounts for 1) roplets that are squeeze between two plates an touch both plates, ) roplets touching one plate but not the other, an 3) the gas filling the gap between the two plates. A simplifie example showing two roplets an the associate thermal resistance network is given in Figure 3.4. Each of the above three cases is consiere separately. Then, a metho to account for the statistical istribution in roplet iameters is iscusse. Figure 3.4: Thermal Resistance Network The thermal resistance of a roplet epens on the conuction path length through the roplet, the thermal conuctivity, an cross sectional area of the roplet, which is given by: L R th 3.1 ka The thermal resistance of a roplet was etermine by approximating the roplet s eforme shape as a cyliner. However, since a eforme roplet is not a straight cyliner but rather has a curve barrel shape (ue to the constant contact angle property of the material interface), two thermal resistance calculations for the roplet is 31

43 mae for each plate position. First, the thermal resistance of the smaller cyliner base on the contact raius a of the roplet is calculate. Secon, the thermal resistance base on the largest raius of the barrel shape, R, is foun. These two values provie an inner an outer boun to the problem. The two values are then average to obtain an approximation of the real roplet array thermal resistance. Because there is a istribution of roplet heights, some roplets are in contact with both plates while other roplets are not in contact. Thus, there is a small gap of gas between some roplets an the contacting plate surface. This air gap thermal resistance, in series with the roplet beneath it, is inclue. The thermal moel assumes that the cross sectional area of this air gap is the same as the area of the roplet cyliner, epening on the case for which roplet cyliner is use. As mentione previously, it is equally important to inclue the thermal resistance of the gas gap in the moel calculation. While the roplets account for a majority of the change in thermal resistance with increasing force, the effects of the gas are inclue to obtain aitional accuracy in the preiction. Two factors are consiere in relation to the gas effects. First, the roplets o not cover the entire surface area of the thermal switch. Experimentally, the surface area of the 1600 roplets ranges from less than one percent initially up to five percent when eflecte by 1N of force. So a large proportion of the surface area is covere by air, which has a ifferent thermal resistance than mercury. When consiering an array of roplets with varying size, the path length an cross sectional area are calculate with respect to force for each statistical bin of similarly size roplets. The path length of the bin is the same as any single roplet in the bin at a given eflection. However, the cross sectional area of the bin is obtaine by multiplying the 3

44 contact area of a single roplet by the population of the entire bin. The thermal resistance is then calculate for each bin using the path length an the total cross sectional area of the bin by Equation 3.1. The value for the thermal conuctivity k of mercury is 8.54 W/mK [33]. These calculations are repeate for every bin over a range of ifferent eflections. Because the roplet size of each bin is ifferent from one bin to the next, the statistical variation of roplet size among all bins is important to inclue in the moel. Here, the variation in roplet height is consiere. At the start of the moel, the thermal resistance is calculate with a gap of microns separating the plate an the tallest bin of roplets. Next, the thermal resistance is calculate when the plate moves microns closer. Here, the plate makes contact with the tallest bin of roplets but oes not eform them. Again, the plate is move closer. The first bin of roplets is eforme until the secon bin of roplets is touche, which is shorter than the first. The thermal resistance is calculate again. Subsequent calculations of thermal resistance are performe in similar fashion through contact of each bin of roplets. As more roplets come into contact with the plate, the thermal resistance ecreases ue to a greater number of paths for the heat to transfer through. Likewise, the taller bins of roplets continue to eform, ecreasing path length an increasing contact area, which also causes the thermal resistance to ecrease. Once all the requisite thermal resistances are accounte for, the single effective thermal resistance for the switch is foun using the techniques employe with the electrical resistance analogy. Resistances that are in series are summe together irectly (roplets not in contact with the secon plate, along with the gas gap between the roplet 33

45 an the plate) to form a single combine resistance. An equivalent thermal resistance for all parallel thermal resistances, R n, (roplets in contact, roplets not in contact, an the surrouning gas gap) is calculate by: R eq 1 R1 1 R R n 3.13 For each plate position, thermal resistance is plotte with respect to force applie to eform the roplet array. Thus, as the two parallel plates move closer together, a range of plate positions was use to calculate thermal resistance an force. Three separate curves are plotte, one base on each of the two cylinrical raii, an the thir base on the average of the two cylinrical approximations. 34

46 CHAPTER 4 EXPERIMENTAL APPARATUS 4.1 Overview A goal of this research was to characterize the mechanical behavior of mercury micro roplet arrays. Square gri arrays of 1600 roplets were characterize uner static an ynamic loas. Force, eflection, an contact iameter was measure an then use to valiate the moel for the parameters escribe in the previous chapter. The arrays were compose of nominal 30µm iameter roplets. A secon set of measurements were mae on large roplets with iameters on the orer of 00µm. Two sets of experiments were conucte for this research: 1) static characterization an ) ynamic characterization of the mercury roplet arrays. The goal of both of these experiments was the same, to visualize the roplets an characterize their behavior when eforme. The apparatus use for static characterization of the micro roplets is iscusse first. The apparatus use for the ynamic characterization of the micro roplets is iscusse next. 4. Static Deformation Mechanical characterization of the roplet arrays uner static eformation consiste of applying a known force to eform the roplets, an then measuring the resulting eflection (or ecrease in height), an the increase in contact area. A iagram of the static eformation apparatus use to make measurements is shown in Figure 4.1. The roplet arrays were mounte on top of an aluminum bracket, which was attache to the top of a loa cell an a z-axis optical positioning stage. A glass slie was mounte above the z-axis stage on the bottom of an aluminum plate with a slotte hole machine 35

47 into the center for optical access. The slot was mae as small as possible so that eflection of the glass woul be minimize. Figure 4.1: Static Deformation Apparatus The plate was bolte into four, 1 inch iameter steel optical posts that were attache to an optical air table. With the roplets an z-axis stage positione beneath the glass slie an aluminum plate slot, the z-axis stage micrometer was use to raise an lower the roplets. The roplets were brought into contact with a glass slie, which provie a flat, rigi, an transparent surface for visualization. A microscope an igital camera centere irectly above the slot was use to image the roplets. A loa cell, mounte in series with the roplet array, was use to measure the applie force. A laser an photo etector system was use to measure the isplacement of the roplet arrays. 36

48 4..1 Compliance In orer to obtain accurate measurements of the force-eflection relationship of the roplets, it was important to minimize the compliance of the test stan. A simple beam eflection analysis was performe on the top plate to etermine a plate thickness that woul eflect less than µm uner the applie loas in the roplet experiments. Maximum eflection v max of a simply supporte beam with a length of L, uner a loa of P locate at the center of the beam, with elastic moulus E an moment of inertia I, is given by[34]: v max PL EI The maximum eflection of the glass slie was foun by assuming that the loa applie to the glass slie was 0.15 inches away from one en of the slot, base on the position of the ie uner the slot. The maximum eflection woul then be foun by [34]: v max ( L b a ) Pba 4. 6EIL where b an a are the istances from the loa to either en of the beam. The loa applie to both the glass slie an the aluminum plate was taken to be 0.1 N, the maximum applie loa for the static eformation experiments. The length of the aluminum plate was 5 inches, the largest imension iagonally. The length of the glass slie was assume to be 0.5 inches, the length of the slot in the plate. The elastic mouli of the aluminum an the glass were both taken to be 70 GPa. The moments of inertia for aluminum an glass were calculate by [34]: 1 Lt I

49 an equalle 9.14x10-9 m 4 an 8.46x10-1 m 4, respectively, where L is the base length, an t is the height (or thickness of the plate). The thicknesses of the aluminum plate an glass slie were 9.55 mm an mm, respectively. The respective maximum eflections for the aluminum plate an the glass slie were foun to be 0.41µm an 0.055µm. 4.. Alignment An important issue consiere in the esign of these experiments was alignment. With a roplet height of 5µm an a ie imension of 10mm, alignment of the roplets an the glass slie the roplets comes into contact with was crucial. An alignment metho evelope by T. Wiser [30] was use. The metho involve using a bare silicon ie an thick, slow curing epoxy. A rop of epoxy was place on the top surface of the aluminum bracket an a bare silicon ie was place on top. Then, with the plate an glass slie mounte above the bare ie, the z-axis stage was raise until the bare ie was presse against the glass slie. The epoxy was able to flow unerneath the bare ie, allowing the ie surface to press evenly against the glass slie. The ie was hel in contact with the glass slie for 8 hours until the epoxy ha fully cure. Droplet array ies were then mounte on the top of the bare ie Loa Cell The loa cell use in the static eformation experiments was manufacture by Futek Avance Sensor Technology. The moel use, L331, was a 0.lb or ~90g capacity loa cell. The loa cell was connecte to a igital isplay, moel D501, also mae by Futek. The isplay ha a five igit reaout with ajustable ecimal place an tare button. With typical 1g maximum loaings use in the experiments, milligram 38

50 resolution was available with the isplay. However, ue to some vibration noise that coul not be ampe out by the air table mount, the thir ecimal place was not consistently reliable. As a result, a hunreth of a gram measurement resolution was use. The uncertainty was assume to be ±5 milligrams Laser Positioning System A combination of a laser an photo etector was use to measure the relative position of the roplet array. The laser was reflecte off a horizontal plane cut into the center of the aluminum bracket mount for the roplet array. The photo etector was positione on the other sie of the apparatus to intercept the reflecte laser. The photo etector signal was monitore with a multimeter that isplaye a voltage. As the test stan apparatus translate vertically, the reflecte laser beam image move across the photo etector. The relationship between voltage output an position was then calibrate. The multimeter was able to measure voltages with a reliable resolution of 10 millivolts. The assume uncertainty was ±5 millivolts. The corresponing uncertainty in position an isplacement was uniquely calculate from each position calibration curve Visualization Digital images were taken of the roplet arrays an large roplets uring eformation. These images were then use to statistically analyze the arrays. The measurement technique relie on a computer imaging program, Scion Image. Scion Image was use to count the number of pixels in a igital photograph along a userspecifie length. A micrometer scale bar was use as a calibration stanar. Using a photograph of the scale bar, the number of pixels was counte over a 100µm length. A calibration constant with units of pixels/micron was then etermine. Care was taken so 39

51 that all roplet pictures were taken with the same magnification an resolution settings. As a result, the same calibration constant was sufficient to convert all pixel measurements into lengths in microns. The assume uncertainty in these measurements was ±5 pixels. The corresponing uncertainty in length is calculate from the calibration constant base on five pixels. 4.3 Dynamic Actuation The characterization of the roplet array mechanical behavior uner ynamic actuation was limite to imaging the roplet arrays before an after actuation. The focus of these experiments was in obtaining qualitative information about the roplet array behavior, particularly roplet ahesion an roplet stability, uner cyclic loaing. As a result, these experiments i not inclue force, eflection, or contact area measurements as in the static eformation experiments. The apparatus use for ynamic actuation is shown in Figure 4.. Of particular interest in ynamic characterization experiments was the effect of roplet array alignment on roplet ahesion an stability. To control array alignment, a high precision, biirectional tilt stage was introuce into the apparatus. With this tilt stage, optical alignment of the roplet array was possible. Droplet array alignment was accomplishe by observing the array through a microscope while the roplets were slowly brought into contact with the glass. When one ege of the array was observe to touch the glass, the array was pulle back an then ajustments were mae to the tilt stage in the appropriate irection. The array was then raise again into contact an reajuste as many times as were require until all roplets across the array came into contact with the glass slie at the same time. 40

52 Figure 4.: Dynamic Actuation Apparatus It was possible to visually istinguish between roplets in contact an out of contact with the glass slie. The roplet arrays were front lighte using a fiber optic light source. Since the mercury roplets are metallic an spherical, light easily reflecte off the roplet surface which was visible in the microscope. When the spherical roplets came into contact with the glass slie an flattene out, the amount of light reflecte back to the microscope increase. This increase in reflecte light was clearly visible through the microscope. A piezoelectric actuator riven with an AC voltage signal was use to move the roplet array into an out of contact with the glass slie at specifie frequencies over require urations. Images were taken of the roplet arrays with a microscope an igital 41

53 camera. A vieo capture system was use to recor vieo clips of the roplets uring ynamic actuation Visualization The vieo capture system was similar to that use in the static eformation experiments. However, a microscope with a 50x magnification was use to image the roplet arrays. All vieos capture were 30s in length an were recore at the highest quality vieo setting, at a stanar vieo recoring spee of 30 frames per secon Piezoelectric Actuator The piezoelectric actuator use in the ynamic actuation experiments ha an effective operating range of frequencies from 0 to 500 Hz. The maximum amplitue of travel was 30µm. Most actuation experiments were run at 0 Hz for ease of vieo capturing. However, for high cycle actuation, experiments were run at frequencies of 400 Hz to shorten the uration of the experiment. 4

54 CHAPTER 5 EXPERIMENTAL PROCEDURE 5.1 Statistical Analysis Statistical characterization is use to obtain accurate measures of large populations when measuring an counting large populations is time consuming. For populations with thousans of items, such as a roplet array, it woul be time prohibitive to measure an count every roplet of many ifferent arrays. Statistics provie a means for obtaining information about such populations by analyzing a smaller, representative sample from the population. It is important to avoi introucing bias into a gathere sample of ata. Careful planning an consistency is require when selecting the representative sample. For the square gri pattern of the roplet arrays iscusse here, organizing an planning the ata collection proceure was as follows. The iagonals of the square gri were chosen as the locations of ata sampling from the roplet arrays. Any variation in the roplet array istribution was assume to be groupe together into quarants. Measuring along the iagonals was assume to cover all variations of roplet size. Pictures were taken in sequence along each iagonal, using the same magnification. A picture of a scale bar was also taken at the same magnification settings as a reference. Care was taken to not photograph any single roplet more than once. It was important to avoi measuring the same roplet multiple times to avoi potentially biasing the results. For each photograph, the file was converte into the TIFF format which coul be rea using the Scion Image program. The scale bar was analyze to obtain the conversion factor from pixels to microns. Each roplet picture was analyze to 43

55 etermine roplet iameters. The ata analysis package within Microsoft Excel was use to prouce a histogram of the roplet iameters for the sample. The histogram was ivie into statistical bins, each covering a iameter range of µm. The number of roplets in any bin was efine to be the number of roplets that have iameters between the current bin value an the next lower bin value. The number of total pictures taken along both iagonals range between 8 an 15. Each igital picture containe 0 to 100 roplets each, epening on the magnification an fiel of view. The time require to measure all of the roplets woul be great, so representative samples were chosen. To calculate a reasonable sample size, three parameters must be known: 1) the 100(1-α)% confience interval which ientifies the z value from the stanar normal istribution, ) the population stanar eviation σ which can be approximate from the sample stanar eviation, an 3) the uncertainty E which is chosen. Once these values are known, the sample size is calculate by [3]: n ( z ) ( σ ) α / 5.1 E A 99% confience interval was chosen, an thus α is equal to From a stanar normal istribution table, Z α/ is equal to.58. A sample stanar eviation of 3µm was initially use to approximate the population stanar eviation. The population stanar eviation for one array was later measure to be 3.47µm. The uncertainty E was chosen to be ±0.5µm. Inserting these values into Equation 5.1 prouces a sample size of 39. This is a minimum require sample size that must be taken to obtain 99% confience for the mean roplet size with an uncertainty of ±0.5µm. 44

56 For accurate statistical sampling, it is important to avoi creating any biases in the ata. Droplets were measure at even intervals across each picture, in the same manner for all pictures. Typically, one roplet was skippe between each roplet measure, or alternate rows woul be measure instea to reuce the time require. Satellite roplets were also counte an measure if their position was nearer to the target position than other ajacent positions. The average roplet iameter an stanar eviation were calculate for the sample. The number of excess satellite roplets was obtaine by subtracting the number of roplets foun by the planne number of roplets. If an array were perfect, there woul be a roplet on every gol pa an no roplets anywhere else. However, most arrays have extra roplets eposite on the substrate. These extra roplets were counte. A corresponing population for the entire roplet array was extrapolate by comparing the number of roplets counte with the number of targets. In this way, an actual population size was approximate. Tolerance intervals were calculate to obtain a range of the expecte array population base on the sample ata. To obtain this tolerance interval the sample stanar eviation s, the sample population average x, an the factor C T must be known. This factor states that a certain percentage B of the global population is inclue in a sample of etermine size n with a given level of confience level W. The interval is then calculate by [35]: ( ) TI x ± s * 5. C T ( B)( W ) n 45

57 5. Static Deformation Both single large roplets of ~00µm iameters an 1600 roplet arrays with 30µm iameter roplets were statically eforme using similar proceures. The first step for both experiments was to clean the glass slie, to ensure all particulates an organic films were remove from the glass. To o this, the glass slie was remove from the aluminum plate an cleane using a five step cleaning process. Only glove hans touche the eges of the glass slie after cleaning. Once cleane, the glass slie was centere an fixe over the visualization slot in the aluminum plate. Next, the bare silicon base ie was glue to the aluminum mounting bracket to achieve goo alignment [30]. When the epoxy ha cure, the air table was pressurize. The laser was positione in alignment with the photo etector, an the laser warme up for 1 hour prior to taking ata. The photo etector multimeter was turne on an the voltage output checke. The fiber optic light was positione for optimal lighting. The visualization system was aligne an focuse. To calibrate the position measurement using the laser photo etector system, metal shims of known thickness were use. First, the position of the bare ie against the glass slie was recore. Next, metal shims of ifferent known thicknesses were place between the bare ie an glass slie, an position measurements for each thickness were recore. A force of 90g was applie to the metal shims to ensure complete contact. The thickness of the metal shims was correlate to the voltage measurements to obtain a straight line calibration slope. Distances in microns were then calculate from the voltage reaing of the photo etector uring subsequent measurement. 46

58 The z-axis stage was retracte an the top plate remove. A roplet array ie was then place on the base alignment ie an the top plate was replace. For large roplets, a picture was taken of the roplet before contact to obtain the original roplet iameter. For roplet arrays, the roplet iameter istribution was foun via statistical characterization prior to testing. After the loa cell was zeroe out, the roplet array was slowly brought into contact with the glass slie. The initial contact position was obtaine by observing the array through the microscope as the z-stage was raise. When the first sign of contact was observe, the position voltage an loa cell reaing were recore. If a large roplet was being stuie, a picture was also taken using the igital camera. The z-axis stage was then raise a small amount. Force an position measurements were recore an pictures were also taken. This same process continue until the force applie was greater than 10g or 0.1 N. The initial contact point was recore as the zero eflection point. All subsequent changes in position were taken as eflection. For the large roplets, each picture taken was analyze to yiel contact iameter an contact area. Measurements were plotte in terms of force versus eflection, force versus contact iameter or contact area, an contact iameter versus eflection. For the large roplets, eforme roplet height (original height minus eflection) was plotte against contact iameter. Both eforme roplet height an contact iameter were normalize by the original roplet iameter. 5.3 Dynamic Actuation In preparation for the ynamic actuation experiments, the z-axis stage was fully retracte an the top plate was remove. The roplet array was fixe to the top surface of the mounting bracket with ouble sie ahesive. The top plate was replace an the 47

59 array was aligne using the tilt stage an visual monitoring. The roplet array was slowly brought into slight contact with the glass slie. If one portion of the array was in contact while another portion was not, the z-axis stage was lowere an the tilt stage was ajuste accoringly. This was repeate until the entire roplet array came into contact simultaneously. Once array alignment was establishe, the z-axis stage was retracte a few hunre microns. The function generator was set to generate a sine wave with the esire operating frequency. The signal was checke by an oscilloscope. The sine wave was then fe into the actuator amplifier an the actuator. The z-axis stage was then slowly raise until a blinking effect coul be seen as the roplet array came into an out of contact with the glass slie. By further raising the z-axis stage, the blinking effect coul be mae to isappear as soon as the roplets were continually in contact with the glass slie. The z-axis stage was set to ensure that the array was actuate into an out of contact with the glass slie. The roplet array behavior was then observe for ifferent numbers of cycles. Short, thirty secon vieo clips were recore to visually monitor the roplet array behavior uring actuation. 48

60 CHAPTER 6 RESULTS 6.1 Overview Results characterizing the mechanical behavior of mercury micro roplet arrays are presente. First, results of the statistical characterization of roplet iameter an array size are given. Secon, measurements of force, eflection, an contact iameter from static eformation experiments are iscusse. Thir, the results of ynamic actuation experiments performe to observe the ynamic response to cyclically actuate roplet arrays are presente. Finally, the results of the thermal moel in terms of thermal resistance are compare to measurements reporte by T. Wiser [30]. 6. Statistical Characterization of Droplet Arrays Three roplet arrays use to experimentally measure thermal resistance were statistically characterize. Both the roplet iameter istribution an the array size, or total number of roplets, were stuie Droplet Diameter A histogram of sample roplet iameters for a 1600 roplet array on ie 884H, is shown in Figure 6.1. Die 884H was use for experimentally measuring thermal resistance in an air environment at atmospheric pressure [30]. The average roplet iameter of this array was 6.4µm an the stanar eviation was 4.35µm. Die 884K was use for experimentally measuring thermal resistance in a xenon environment at atmospheric pressure. The histogram of sample roplet iameters for ie 884K is shown in Figure 6.. The average roplet iameter was measure to be 8.9µm with a stanar eviation of 4.9µm. 49

61 Frequency Droplet Diameter (µm) Figure 6.1: Die 884H Air Droplet Diameter Histogram Frequency Droplet Diameter (µm) Figure 6.: Die 884K Xenon Droplet Diameter Histogram A thir ie, 964O, was use to experimentally measure thermal resistance in a 0.5 torr vacuum environment. The histogram of sample roplet iameters for ie 964O is shown in Figure 6.3. The average roplet iameter measure was 9.9µm an the stanar eviation was 7.3µm. 50

62 50 40 Frequency Droplet Diameter (µm) Figure 6.3: Die 964O Vacuum Droplet Diameter Histogram 6.. Array Size An example of a roplet picture use to prouce the histograms shown above is shown in Figure 6.4. From the population of excess satellite roplets an total sample population etermine from the roplet array images such as that in Figure 6.4, a ratio or percentage was calculate for the amount of excess roplets sample. This ratio was use to preict the total array roplet population. The array size for the ie shown in Figure 6.1 was calculate to be 1537, with a confience interval of ±78. The array size for Figure 6. was calculate to be 1589±64. The array size for Figure 6.3 was calculate to be 1406 ±499. All calculations for the confience interval were mae base on a 95% confience level. 51

63 Figure 6.4: Portion of 1600 Droplet Array 6.3 Static Deformation Results of the mechanical characterization of roplet arrays subjecte to a static compressive force between two parallel plates (incluing the force applie uner static loaing conitions an the resulting increase in eflection an contact iameter) are presente. Initial contact iameter an eformation hysteresis are iscusse first. The results of the couple force, eflection, an contact iameter measurements are shown an use to valiate the mechanical moel. The results of the thermal moel are compare to experimental measurements obtaine from a guar heate calorimeter apparatus [30] Initial Contact Behavior The initial contact behavior of a single large roplet is shown in Table 6.1. The ratio of initial contact iameter D i to original roplet iameter D o, was use to characterize the initial contact behavior of a roplet. From Equation 3.4, inserting D o in for, the initial contact iameter D i can be calculate. As seen in the table, these values 5

64 were measure for a variety of large roplets, all varying in size. The comparison with moel preictions is also shown. The experimental ratios varie between 0.9 an 0.4. The moel preicte a ratio of Die Contact Diameter Outsie Diameter Di/Do Ratio BD BD3a BD3b BD4c BD BD BD BD Average 0.37 Stanar Deviation 0.05 Moel Table 6.1: Initial Contact Behavior Di/Do Ratio 6.3. Deformation Hysteresis Hysteresis in the eformation behavior was investigate for a large roplet with a iameter of 70µm. Results are shown in Figure 6.5. Negative eflections are apparent in the figure, which inicate the roplet remaine ahere to the glass slie in a state of tension. As seen in the figure, the roplet was pulle by the glass slie for almost 10µm before it broke contact an returne to its initial spherical shape. Subsequent attempts to come back into contact with the roplet resulte in ifferent initial contact iameters an starting positions, as inicate in the figure. Contact iameters an starting positions shown in the figure for subsequent initial contacts varie between 10 an 0µm from the original value. These measurement variations are small compare to the original roplet size. 53

65 Contact Diameter (µm) Deflection (µm) Figure 6.5: Large Droplet Contact Hysteresis Moel Valiation Measurements of force, isplacement, an contact iameter were obtaine for a large roplet with an original iameter of 197µm an a corresponing height of 174µm. The ifference in iameter an height is ue to the truncation of the liqui sphere as it sits on the substrate surface Geometrical Relationship Figure 6.6 shows measurements of contact iameter an eflection for the large (197 µm ia.) roplet. For comparison, results of the moel are also inicate with a soli line. The ata are presente in imensionless form by iviing the measurements of the eflection an the contact iameter by the original roplet size. The ata show goo agreement with the moel. 54

66 ..0 Contact Diameter/Size (µm/µm) Experiment Moel Deflection/Size (µm/µm) Figure 6.6: Geometric Moel Valiation Force vs. Deflection The compliance of the test stan was characterize to ensure accurate measurements of roplet eflection. Figure 6.7 shows the compliance characterization..5.0 Deflection (µm) Force (N) Figure 6.7: Test Stan Compliance The figure shows that the measure eflection oscillate between 1 an.5µm. 55

67 This eflection correspons to less than 10% of the roplet height of a 30µm roplet. Measurements of force versus eflection results for the large roplet are shown in Figure 6.8. Results of the force versus eflection moel are shown with a soli line on the same plot. 0.7 Deflection/Droplet Size (µm/µm) Correcte Moel Experiment Data Original Moel e-7 1.0e-6 1.5e-6.0e-6.5e-6 3.0e-6 Force/Droplet Size (N/µm) Figure 6.8: Force Deflection Valiation The ata were normalize with respect to roplet size. The moel an experimental ata show goo agreement over the range of eflection. Also shown is a ashe line that represents the force versus eflection moel prior to incluing a correction factor in the force ata. The correction was inclue because the moel of force versus eflection is a logarithmic function which can never reach zero force. However, in the experiment, zero force is obviously recore. Base on the initial contact stuy, when the roplet makes initial contact with the glass slie, the roplet seems to jump into contact with the glass slie. An initial contact area is present, even though no iscernable force has been applie to eform the roplet. Other factors must be at work to influence this behavior an len a egree of complication to the problem which this moel oes not fully 56

68 escribe. D. Packham [36] reports in his paper that this behavior can be explaine by surface tension an ahesion forces. Another argument inclues remembering the fact that the force is obtaine by calculating the capillary pressure of the liqui insie the roplet an multiplying by the contact area. This assumption fails for the moel near zero force. Even when the plate is not in contact, there is still an absolute pressure insie the roplet. Fortunately, the exact behavior of this relationship at very small forces oes not severely impact the behavior of the roplet as it is eforme at higher loas. This low force behavior was ignore Thermal Resistance vs. Force The parameter stuy shown in Table 6. was performe to characterize the behavior of the roplet array thermal resistance by changing physical parameters of the roplet array. Droplet Raius Effects (Hel Array Size Constant) Droplet Raius (um) Max Thermal Resistance (K/W) Min Thermal Resistance (K/W) at 0.1 N Difference (K/W) Smaller Droplet Baseline Larger Droplet Array Size Effects (Hel Droplet Raius Constant) Min Thermal Resistance (K/W) at 0.1 N Max Thermal Array Size Resistance (K/W) Smaller Array Baseline Larger Array Table 6.: Parameter Stuy Difference (K/W) Changing the roplet raius from 15µm to 16µm is a 6.3% change. The moele thermal resistance change by % (from 8.71 to 6.79). A similar 6.3% change in the array size (from 1600 to 1707) change the thermal resistance by 5.6% (from 8.71 to 8.). Clearly the roplet iameter is the parameter of most influence in the moel. 57

69 The thermal moel calculations were compare with experimental measurements of thermal resistance taken from T. Wiser [30]. The experimental ata of ie 884H in an air environment at atmospheric pressure are shown in Figure 6.9. A thermal conuctivity of W/mK was use in the air moel. 5 Thermal Resistance (K/W) Loa (N) Figure 6.9: Thermal Resistance Comparison in Air The air moel is shown as a soli line. Figure 6.10 shows the moel compare with experimental results of ie 884K in a xenon environment at atmospheric pressure. A thermal conuctivity of W/mK was use in the xenon moel. The xenon moel is shown as a soli line. Experimental results for ie 964O in a 0.5 torr air vacuum are shown in Figure A small iscrepancy between the experiments an the moel is apparent. A thermal conuctivity of W/mK was use in the vacuum moel. The vacuum moel is shown as a soli line. 58

70 5 Thermal Resistance (K/W) Loa (N) Figure 6.10: Thermal Resistance Comparison in Xenon 5 Thermal Resistance (K/W) Loa (N) Figure 6.11: Thermal Resistance Comparison in Vacuum The experimental results for both the vacuum an xenon environments show large increases in thermal resistance. The moel, in comparison, shows much smaller increases, especially at high forces. At low forces, the moel for vacuum an xenon preicts a y-axis intersection at much larger thermal resistances as compare to air at 59

71 atmospheric conitions. This follows what woul be expecte, since xenon an vacuum have much lower thermal conuctivities. However, the axis scales have been ajuste for clarity at lower thermal resistances, so this intersection is not shown. The moel oes not preict the results of the experiment very well. There is suspicion of experimental bias in these results, which may explain the iscrepancies. Aitionally, the moel was calculate for each ie in each gas environment. Three plots, one for each ie, are shown in Figures 6.1, 6.13, an Each plot shows the comparison of thermal resistance of a single roplet istribution in air, vacuum, an xenon gas environments Die 884H - Air Die 884H - Vacuum Die 884H - Xenon Thermal Resistance (K/W) Force (N) Figure 6.1: Moele Thermal Resistance for Die 884H 60

72 70 60 Die 884K - Air Die 884K - Vacuum Die 884K - Xenon Thermal Resistance (K/W) Force (N) Figure 6.13: Moele Thermal Resistance for Die 884K Die 964O - Air Die 964O - Vacuum Die 964O - Xenon Thermal Resistance (K/W) Force (N) Figure 6.14: Moele Thermal Resistance for Die 964O 6.4 Dynamic Actuation Droplet arrays were ynamically actuate repeately in an out of contact with a glass slie, an the array behavior was observe. This test simulate conitions that woul be similar to the cyclic switch operation expecte with the P3 micro heat engine Droplet Stability 61

73 Figure 6.1 shows a roplet array that was actuate 10,000 times. This array was eposite without a photoresist protection layer an with the silicon ioxie layer expose. Figure 6.15: Droplet Array Deterioration uring Actuation When the array was actuate, the roplets were seen to translate across the oxie substrate surface with relative ease an cause severe array eterioration. Figure 6.13 shows a picture of a roplet array, eposite with a µm photoresist layer over the silicon ioxie layer, after actuation for 30 minutes at a frequency of 0 Hz or 36,000 cycles. The roplets are still in contact with the glass slie. 6

74 Figure 6.16: 10,000 Cycle Actuation The roplets are seen to have remaine stably anchore to the gol pa positions in the array. There was no visible eterioration of the array. These same results were observe by actuating a similar roplet array for 90 minutes at 0 Hz, which correspons to over 100,000 cycles, shown in Figure Figure 6.17: 100,000 Cycle Actuation 63

75 A final actuation experiment involve a roplet array run at 400 Hz for 45 minutes, which equals over a million cycles in an out of contact with the glass slie. This is shown in Figure The roplets are in contact with the glass slie. Figure 6.18: Million Cycle Actuation 6.4. Optical Alignment Alignment of the array with the glass slie was investigate. An array with a misalignment of 0.6 was actuate at a frequency of 0Hz for 30 minutes. Figure 6.16 shows the results. As can be seen in the image taken towars the en of actuation, the roplets remaine stable an the array was unaffecte. 64

76 Figure 6.19: Misaligne Actuation 65