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Analysis of capillary forces in electrowetting and precision self assembly

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Analysis of capillary forces in electrowetting and precision self assembly
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English
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Ramadoss, Vivek
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Preload force
Surface evolver
Repeatability
Alignment constraint
Dielectric layer
Dissertations, Academic -- Mechanical Engineering -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

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ABSTRACT: Developments in micro and nano technology have great potential in many applications. Two applications that will be addressed in this work are self assembly of microdevices and Electrowetting in microfluidics. Capillary forces are the most critical factor in both of these techniques and need proper characterization. This thesis describes a detailed study of these forces and explains how they were utilized as an effective source of drive in high end applications. Self assembly is a promising alternative to conventional pick and place robotic assembly of micro components. Its benefits include parallel integration of parts with low equipment costs. Various approaches to self assembly have been demonstrated, yet demanding applications like assembly of micro-optical devices require increased positioning accuracy. This thesis proposes a new method for design of self assembly bonds that addresses this need.Current methods have zero force at the desired assembly position and low stiffness. The proposed method uses a substrate assembly feature to provide a high accuracy alignment guide to the part. The capillary bond region of the part and substrate are then modified to create a non-zero positioning force to maintain the part in the desired assembly position. Capillary force models show that this force aligns the part to the substrate assembly feature and reduces the sensitivity of part position to process variation. Thus, the new configuration analyzed proves substantial improvement in positioning accuracy of capillary self assembly. Guidelines are proposed for the design of an effective assembly bond using this new approach. Electrowetting is another application that has been successfully demonstrated as a means of drop manipulations in digital micro-fluidic devices.These demonstrations show that electrowetting actuation holds great promise, but there are also reports of erratic behavior and system degradation. While a method for electrowetting force measurement to track the degradation of the electrowetting response was demonstrated, this thesis analyzes some adverse effects in the electrowetting response due to variations during measurement of electrowetting forces, specially the variation of volume, the tilt in the part considered for measurements, and defective layer response.
Thesis:
Thesis (M.S.M.E.)--University of South Florida, 2008.
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by Vivek Ramadoss.
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1 Analysis of Capillary Forces in Electrowetting and Precision Self Assembly by Vivek Ramadoss A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Nathan Crane, Ph.D. Craig Lusk, Ph.D. Wilfrido Moreno, Ph.D. Date of Approval: March 19, 2008 Keywords: Preload Force, Surface Evolver, Repeatabi lity, Alignment Constraint, Dielectric Layer Copyright 2008, Vivek Ramadoss

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2 DEDICATION To my Parents

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i ACKNOWLEDGEMENTS I wish to acknowledge the gracious support of many people for their contributions towards this work both directly and indirectly. Fir stly, I thank my advisor Dr. Nathan Crane who patiently guided me through all phases of this work. He is a true role model, and a best professor I have ever seen. The time and effort of Dr. Craig P. Lusk and Dr. Wilfrido Moreno as committee members are greatly ap preciated. I would like to thank my brother, Balaji Ramadoss f or his support, suggestions and invaluable encouragement that have always made me a better man and have indirectly prepared me to tackle challenges that I came across. Without my parents support and encouragement, I never would have made it this far. Additionally, I would like to thank all my friends and my friends especially from the research group Pradeep Mishra, Jeff Murray, and Jairo Chimento for having always motivated and accompanied me throughout the challen ges of research. Without their help, this thesis would have been much more difficu lt. This work has been supported in part through the Un iversity of South Florida Research Education Initiative Program under grant n umber FMMD04.

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i TABLE OF CONTENTS LIST OF TABLES .................................... ................................................... ...................... iv LIST OF FIGURES ................................... ................................................... ...................... v LIST OF EQUATIONS ................................. ................................................... ............... viii ABSTRACT .......................................... ................................................... ....................... ix CHAPTER 1 INTRODUCTION ............................ ................................................... ....... 1 1.1 Thesis Statement .............................. ................................................... ........ 1 1.2 Background .................................... ................................................... .......... 2 1.2.1 Self Assembly ............................... .................................................. 2 1.2.2 Types of Self Assembly ...................... ............................................ 5 1.2.3 Self Assembly Forces ........................ ............................................. 5 1.2.3.1 Assembly by Capillary Force................ ........................... 5 1.2.3.2 Assembly by Electrostatic Force ........... .......................... 6 1.2.3.3 Assembly by Magnetic Force ................ .......................... 7 1.2.4 Capillary Self Assembly – Our Concern ....... ................................. 8 1.2.5 Characteristics Influencing Capillary Self As sembly ..................... 9 1.2.5.1 Surface Tension ........................... .................................... 9 1.2.5.2 Binding Site Shape ........................ ................................. 11

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ii 1.2.5.3 Liquid Volume ............................. .................................. 12 1.2.6 Modeling Capillary Forces in Self Assembly .. ............................. 12 1.2.7 Electrowetting .............................. ................................................. 1 3 1.3 Research Benefits.............................. ................................................... ..... 16 1.4 Thesis Outline ................................ ................................................... ........ 17 CHAPTER 2 LITERATURE REVIEW ....................... .................................................. 18 2.1 Self Assembly ................................. ................................................... ....... 18 2.1.1 Optimization of Self Assembly Process ....... ................................ 18 2.1.2 Achievements Towards Precision Self Assembly ........................ 23 2.1.3 Surface Evolver in Self Assembly ............ .................................... 24 2.2 Electrowetting Review ....................... ................................................... 27 CHAPTER 3 DESIGN OF FLUIDIC SELF ASSEMBLY BONDS FOR PRECISE COMPONENT POSITIONING ..................... ......................... 30 3.1 Introduction .................................. ................................................... .......... 30 3.2 Basic Concept ................................. ................................................... ....... 32 3.3 Simulation .................................... ................................................... .......... 37 3.4 Results and Discussion ........................ ................................................... .. 39 3.4.1 Force Variations with Displacements for Diffe rent Dimensional Offsets................................ ...................................... 40 3.4.2 Potential Error Sources ..................... ............................................ 41 3.4.3 Dimensional Offset in Two Axes .............. ................................... 42

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iii CHAPTER 4 FORCE ANALYSIS ON ELECTROWETTING ........ ............................. 45 4.1 Electrowetting Forces ......................... ................................................... ... 45 4.2 Electrowetting Force Analysis ................. ................................................. 4 8 4.3 Results and Discussion ........................ ................................................... .. 49 4.3.1 Effect of Tilt .............................. ................................................... 50 4.3.1.1 Z Tilt .................................. .......................................... 51 4.3.1.2 X Tilt................................... ......................................... 54 4.3.1.3 Y Tilt................................... ......................................... 56 4.3.2 Effects of Volume ........................... .............................................. 57 4.4 Conclusions ................................... ................................................... ......... 58 CHAPTER 5 CONCLUSION AND FUTURE WORK .............. ................................... 60 5.1 Self Assembly ................................. ................................................... ....... 60 5.2 Electrowetting Force Variation ................ ................................................. 6 2 REFERENCES ........................................ ................................................... ...................... 64 APPENDICES ........................................ ................................................... ....................... 70 Appendix A: Program to Support the Analysis of Capi llary Forces .................... 71

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iv LIST OF TABLES Table 1 Comparison of best line fits for perfect a lignment with those with different values of x-tilt .................................................. .............................. 55 Table 2 Comparison of best line fits of those for perfect alignment with those with different values of y-tilt .................................................. ...................... 56

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v LIST OF FIGURES Figure 1 Schematic representation to illustrate a generic self assembly process ......... 4 Figure 2 Representation of the system at different positions.. ..................................... 4 Figure 3 Schematic of assembly by capillary forces .................................................. .. 6 Figure 4 Part assembled on to the binding site wit h assembly fluid in between them............................................... ................................................... .............. 9 Figure 5 Contact angle ( q ) due to surface tensions at interface ............ ..................... 10 Figure 6 Representation of low wettability and the ir variation with applied voltage ........................................... ................................................... ............ 14 Figure 7 Most commonly employed configurations in Electrowetting ...................... 15 Figure 8 (a) Typical self assembly system (b) prop osed self assembly system (c) mass-spring system representing typical self as sembly system.. ........... 35 Figure 9 Representation of error corresponding to force disturbances in selfassembled components............................... .................................................. 35 Figure 10 Proposed self assembly system to establi sh force-closure concept in micro-scale.. ..................................... ................................................... ......... 36

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vi Figure 11 Surface Evolver predictions of force ver sus y-displacement for different values of dimensional offset............. ............................................. 39 Figure 12 Impact of dimensional offset on part for ces.. ............................................. 41 Figure 13 Representation of dimensional offsets in two dimensions.. ......................... 43 Figure 14 (a) Force in (x, y and z directions) ver sus displacement with 100 m m dimensional offset in both x and y axis... ........ ............................................ 44 Figure 15 Variation in the preload force with dime nsional offsets.. ............................ 44 Figure 16 Surface Evolver model for force analysis on electrowetting ....................... 47 Figure 17 Surface Evolver predictions for comparin g normal configuration and the configuration with hole on the dielectric layer on one of the sides.............................................. ................................................... ............. 50 Figure 18 Comparison of y-force vs. y-offset at 10 0V for normal configuration and one with short ................................ ................................................... ..... 50 Figure 19 Surface Evolver model to detail tilt in different axis (a) z-axis (b) xaxis (c) y-axis ................................... ................................................... ......... 51 Figure 20 Comparison of y-force vs. y-offset at 10 0V for different tilt in z-axis ........ 51 Figure 21 Illustration to predict edge length with the tilt in z-axis .............................. 52 Figure 22 Comparison of simulation results and pre dicted results using equation for y-force vs. y-offset at 100V ......... ............................................ 54

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vii Figure 23 Comparison of y-force vs. y-offset at 10 0V for different tilt in x-axis........ 55 Figure 24 Comparison of y-force vs. y-offset at 10 0V for different tilt in y-axis........ 57 Figure 25 Comparison of (a) z-force and (b) y-forc e vs. y-offset for different volume............................................. ................................................... .......... 58 Figure 26 Schematic illustration of wedging in the proposed self assembly model.............................................. ................................................... ........... 62

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viii LIST OF EQUATIONS Equation 1 Young condition to show the contact ang le dependence in the surface tension of different medium ............... ............................................. 11 Equation 2 Young Lippman equation to show the depe ndence of contact angle with applied electric field........................ ................................................... .. 15 Equation 3 Prediction of preload force for one-dim ensional offset ............................... 40 Equation 4 Prediction of preload force for two-dim ensional offset ............................... 43 Equation 5 Prediction of induced voltage on either side of the electrodes .................... 46 Equation 6 Predition of critical y-offset based on z-tilt .................................................. 52 Equation 7 Prediction of edge length of the top pl ate when y-offset is below the critical y-offset value ........................... ................................................... ..... 52 Equation 8 Prediction of edge length of the top pl ate when y-offset exceeds critical y-offset value ........................... ................................................... ..... 53 Equation 9 y-force calculation based on surface en ergy difference and edge length variation .................................. ................................................... ....... 53

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ix Analysis of Capillary Forces in Electrowetting and Precision Self Assembly Vivek Ramadoss ABSTRACT Developments in micro and nano technology have grea t potential in many applications. Two applications that will be addres sed in this work are self assembly of microdevices and Electrowetting in microfluidics. C apillary forces are the most critical factor in both of these techniques and need proper characterization. This thesis describes a detailed study of these forces and explains how t hey were utilized as an effective source of drive in high end applications. Self assembly is a promising alternative to convent ional pick and place robotic assembly of micro components. Its benefits include parallel integration of parts with low equipment costs. Various approaches to self assemb ly have been demonstrated, yet demanding applications like assembly of micro-optic al devices require increased positioning accuracy. This thesis proposes a new me thod for design of self assembly bonds that addresses this need. Current methods ha ve zero force at the desired assembly position and low stiffness. The proposed method us es a substrate assembly feature to provide a high accuracy alignment guide to the part The capillary bond region of the part and substrate are then modified to create a no n-zero positioning force to maintain the part in the desired assembly position. Capillary f orce models show that this force aligns the part to the substrate assembly feature and redu ces the sensitivity of part position to

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x process variation. Thus, the new configuration ana lyzed proves substantial improvement in positioning accuracy of capillary self assembly. Guidelines are proposed for the design of an effective assembly bond using this new approach. Electrowetting is another application that has been successfully demonstrated as a means of drop manipulations in digital micro-fluidi c devices. These demonstrations show that electrowetting actuation holds great promise, but there are also reports of erratic behavior and system degradation. While a method for electrowetting force measurement to track the degradation of the electrowetting resp onse was demonstrated, this thesis analyzes some adverse effects in the electrowetting response due to variations during measurement of electrowetting forces, specially the variation of volume, the tilt in the part considered for measurements, and defective lay er response.

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1 CHAPTER 1 INTRODUCTION 1.1 Thesis Statement The thesis will address the applied capillary force s in self assembly and electrowetting applications. Modeling methods are u sed to investigate the impact of variation on the reliability of two different syste ms based on capillary forces. The first system is a fluidic self assembly process. This wo rk will show how the forces can be optimized in the process of self assembly to meet p recision assembly standards at the micro scale. The second system to be modeled is an electrowetting force measurement system. A nanoindenter has been adapted for measur ement of the electrowetting forces under an applied voltage. This thesis models the f orces induced by electrowetting and analyses their sensitivity to variation to determin e the usefulness of these methods in characterizing the substrate’s electrical and surfa ce properties. This chapter will review the background, overall co ncept, and critical factors involved in each application. For improved use of t he capillary force, a novel design is proposed and analyzed for accuracy.

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2 1.2 Background 1.2.1 Self Assembly Complex systems available in the market today are m ade by integration and interconnection of various components to create an object that performs the required functions. Assembly is the key manufacturing proces s of many such integrated systems. In macro-scale applications, assembly requirements have relied on robotic pick and place assembly lines to integrate and interconnect compon ents at all complexities. The evolution of micro-manufacturing has led to compone nts to the micro & nano scale with various functionalities integrated onto a single de vice. In the pick and place methods, a major concern at s maller size scales is the sticking effect due to the attraction forces such a s the Van der Waals and electrostatic forces. Also, pick and place methods lose their adv antage when assembling large numbers of micro parts of diverse sizes due to lack of a parallel assembly process. To address these limitations, technologies such as micromanipulator based assembly [1], and wafer to wafer devices transfer [ 2] have been developed in order to integrate micro components. Special micromanipulato rs were designed to aid micro assembly requirements, yet these manipulators prove d to be less efficient due to the inline assembly approach. These difficulties necessitated the need for a novel assembly technique thus leading to the concept of self assem bly. Self assembly is a promising alternative technique to conventional assembly methods. Its advantages include a parallel assembl y approach, 3D integration compatibility, cost effectiveness, and feasibility in the assembly of components of different sizes and characteristics.

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3 Self assembly concepts originated in organic chemis try at the molecular scale. Recent works in the field have proven that this tec hnique has potential in the assembly of components on the micro and nano scale. This techni que offers simplicity and economy in processes that work on components which are too small or too numerous to be manipulated by other means. Self assembly can be defined as a process where a s ystem of disordered components forms an organized structure without the necessity of grasping and placing the components. An external input is needed to obta in a series of random interactions usually through agitation. A driving force must be created in the system for the system to reach a state of minimum global energy. If parts ar e to be assembled to a substrate by self assembly, the substrate must be defined with bindin g sites that create the energy minima. When the substrate is brought into contact with the parts as by immersing in a fluid medium with suspended parts, the parts will bond to the substrate. In such a case, when a substrate is immersed in a medium where the parts a re agitated or randomly moved, the parts tend to fill the substrate binding sites. Fig ure 1 illustrates self assembly through agitation in a fluidic medium. Self assembly is a process of assembling parts toge ther driven by the minimization of various energies. These include gra vitational, magnetic, electrostatic and interfacial energies. Figure 2 shows the energy pro file in a generic capillary self assembly system, where the energy of the system as a functio n of the part position is detailed. The final assembly position is the one with the lowest energy thus demonstrating the concept of energy minimization.

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4 Figure 1 Schematic representation to illustrate a g eneric self assembly process. Figure 2 Representation of the system at different positions. The numbered positions start at the assembled position and then move to the disasse mbled state. In general, self assembly takes place in an agitate d fluidic medium as it facilitates 3D motion and interaction of the components. The ad vantage of self assembly in the fluidic medium is that it provides a constant suppl y of parts to the binding sites and removes all the parts from the site that are not bo und. Parts that are fully bound are not displaced by the fluid force as their attractive fo rces are stronger than the agitation forces.

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5 Self assembly in the fluidic medium is usually comb ined with other techniques of self assembly in [3-5]. 1.2.2 Types of Self Assembly In general there are two types of self assembly: st atic self assembly & dynamic self assembly [6]. In static self assembly, the sys tem does not require an external force/energy to create the global equilibrium state because it is a position of energy minimum within the system. Static self assembly req uires a source of external energy to help the components reach the minimum energy positi on. Once the components reach their minimum energy position, the energy input may be removed and the system remains stable. Dynamic self assembly can be applied to a system th at attains its equilibrium state when an external force/energy is applied. The appli ed energy is continuously dissipated in the system to create a minimum energy configurat ion that only exists while the energy is being dissipated [6]. 1.2.3 Self Assembly Forces There have been numerous energy and force types use d to drive the self assembly process. All these sources have different constrain ts and limitations although every method proves to be effective. Some of the chief me thods are described below. 1.2.3.1 Assembly by Capillary Force Many self assembly techniques rely on the concept o f a capillary or surface tension bond. Figure 3 gives a schematic representa tion of assembly of a part to the binding site by capillary forces.

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6 Figure 3 Schematic of assembly by capillary forces. Capillary forces are very effective due to the fact that the surface tension forces dominate the gravitational forces when the part siz e is small (<1mm). Hence assembly in such a case is done by the hydrophobic and hydrophi lic interactions, reactions due to the difference in the surface energy. Greiner et al. [ 7] demonstrated a case in which the energy difference was nearly two orders of magnitud e. The solid-fluid interface and the solid-assembly liquid interface provide the driving force for assembly. This process of self assembly is our major concern and hence a deta iled review on the works done and results obtained using this method is summarized in Chapter 2. 1.2.3.2 Assembly by Electrostatic Force Although capillary force bonding is an efficient me thod in self assembly, an alternate source with a longer range of interaction is sometimes favorable. This type of long range interaction in self assembly can be achi eved by the electrostatic force that is obtained by the polarization of the micro parts in electric fields. This assembly technique is by the principle of Coulomb’s law which states t hat the attraction or the electrostatic force is inversely proportional to the square of th e distance between unlike charges.

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7 Using this approach, attraction towards components can be increased by increasing the electric field intensity. Tien et al. [8] proposed the technique of micro-fab rication using electrostatic self assembly. The longer range of interactions provided by electrostatic force compared to the hydrophobic or hydrogen-bonding interactions fa cilitated the proposed method. Overlaps (two parts gets assembled on to a single l ocation) in this assembly technique were eliminated by designing parts with approximate ly 1:1 aspect ratio. The work detailed convenient methods to generate charged mic rostructures using a self-assembled monolayer. 1.2.3.3 Assembly by Magnetic Force Magnetic forces are another possible driving potent ial for self assembly. By the principle of magnetism, two magnetic surfaces alway s attract each other provided they belong to opposite poles. When a system is designed in such a way that the site is of the opposite polarity of the part, mere agitation of th e system would assemble the part on the assembly location. Yet this method has its own draw back of just being attracted to the site and does not deal with the accuracy in positio ning or orientation. This assembly technique is feasible for short range interactions and three-dimensional integration of microstructures. Shet et al. [9] proposed a simple assembly model us ing the magnetic field to assemble nano scale semiconductor devices. This pro cess consisted of two assembly steps assisted by the magnetic field. This work als o addressed the advantages over other methods including elimination of damage to pre-exis ting devices on the substrate, elimination of blocking of sites for assembly proce sses and a clean and dry assembly

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8 environment because the proposed method does not re quire any fluid medium as in the case of fluidic self assembly process. Love et al. [10] demonstrated a process of assembly of sub-micron sized metallic rods using magnetic field forces. This demonstratio n proved that the stabilization and formation of ordered 3D structures can be obtained by the magnetic profile of individual components. Emphasis was made on combining capillar y interactions with the magneticforce fields due to long range interaction requirem ents. The work addresses the problem of a chain of particles formed as a result of the m agnetic dipole interactions and suggested a possible solution for the problem. Whil e there have been few unexpected results in the self assembly of metallic rods, poss ible suggestions have been detailed and the final bundle of rods assembled is shown to be w ell ordered, neglecting the dipole interactions as they were comparatively weaker. The advantages of magnetic self assembly include making unnecessary the surface che mistry requirements and that the forces act both in water and air medium thus provid ing flexibility of the assembly process. 1.2.4 Capillary Self Assembly – Our Concern Self assembly dictates all the required assembly ch aracteristics in individual components. These characteristics determine the int eractions between the components. The main feature of the component is to align and o rganize among them as they have the ability to move with respect to each other. Once th ey reach a steady state position, there is a balance between the force of attraction and re pulsion. The focus of our work is the assembly of components by capillary-driven self assembly. Figure 4 shows a part assembled to the bi nding site on the substrate by

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9 capillary-driven self assembly. This is done by an assembly liquid in between them to drive the assembly process. Here the binding site i s defined as the surface that is highly wettable while other surfaces are non-wettable. Hen ce the assembly liquid and the parts are attracted towards this binding site location wh en the parts are agitated. Figure 4 Part assembled on to the binding site with assembly fluid in between them. 1.2.5 Characteristics Influencing Capillary Self Assembly There are critical factors that can affect the accu racy/effectiveness of the self assembly process. These include binding site shape surface tension of the fluid, and liquid volume. 1.2.5.1 Surface Tension Surface tension is the intermolecular attraction fo rce that acts on a liquid medium to change its shape. This force pulls the liquid in all the directions by the neighboring molecules which make the resulting net force to be zero. At the surface of the liquid there is a force of attraction by the molecules deeper in side the liquid although the force is not as intense as the molecules from the neighboring me dium. So all liquid molecules are acted on by an inward force of attraction that caus es the liquid to be compressed. This is

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10 the reason for the liquid to be compressed together till they reach a minimum surface energy level. This parameter is responsible for shaping of liquid volumes that plays a major role in self assembly. Surface tension is a proper ty of the fluid and it is often sensitive to parameters such as surface contamination and temper ature. The binding of the liquid to the binding site is by the surface tension force that acts on the liquid, which enables proper alignment of the micro part on the liquid. This liquid being a specific chemical has to be analyzed for its properties and formulated for an efficient approach. There can be two wetting reg imes that can be originated due to surface tension (complete wetting and partial wetti ng). In complete wetting, the liquid phase spreads out on the entire solid phase forming a three layer system (solid, liquid and surrounding medium). In partial wetting technique, the liquid phase stays in a finite region to a form a specific contact angle at a spec ific contact line [11]. Medium Solid LiquidgSLgLMgSMq Figure 5 Contact angle ( q qq q ) due to surface tensions at interface. Figure 5 shows an illustration to explain the depen dency of contact angle due to surface tensions at the interface of three differen t medium. This can be effectively explained with the equation supporting Young condition as

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11q g g gCosLM SL SM+ = Equation 1 Young condition to show the contact angl e dependence in the surface tension of different medium. Thus, surface energy of different mediums can be me asured by measuring the contact angle made between these mediums. By the im plementation of fluidic self assembly, the partial wetting technique can be expl oited where the resulting forces due to minimization are due to the driving effect of the f luidic medium [12]. Any change in the surface area due to energy minimization would resul t in a derivative of work that is proportional to a surface change. This depends on t he material that is in contact with the interface. When a surface element is displaced by a small area derivative, the pressure on either side of the interface changes in the medium accompanied by a volume change which also accounts for the change in energy patter n. Surface tension becomes more important when conside ring micro scale objects. For this type of assembly using surface tension, a substrate is prepared with surfaces of different surface tensions. The liquid wets the hyd rophobic patterns due to these differences in the surface tension values. After th e liquid settles on the surface, the system is suspended in the fluidic medium of differ ent surface energy where the liquidsurface interface starts attracting the parts towar ds them as the result of capillary force ensuring proper alignment. 1.2.5.2 Binding Site Shape The magnitude and directions of the capillary force s are determined by the shape of the binding site and the micro part as they have a significant role in the uniqueness of the assembly. The unique dependence of assembly in regards to orientation and accuracy

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12 is explained by Xiong et al. in [13] based on first order approximation energy model. This explains the crucial dependence of capillary s elf assembly technique on the binding site design employed. 1.2.5.3 Liquid Volume Liquid volume plays a significant role in accurate alignment of micro components by self assembly process. Unpredictable changes in the required volume have capabilities to affect the accuracy of alignment by either a til t or a lateral displacement of the component. Thus appropriate control of volume of th e liquid to be used is necessary for a precise alignment [7]. 1.2.6 Modeling Capillary Forces in Self Assembly K. A. Brakke came up with an interactive program ca lled the Surface Evolver. The program is used for the analysis of surface sha pes affected by surface tension, interfacial energy and other defined physical const raints. The evolution of the surface is by driving motion of the nodes on the surface to th e minimum energy position. The software has the capability of defining surface ten sion, gravity, crystalline integrand, square mean curvature and other user defined integr als to represent the energies of the system. The program has capability to have a Rieman nian metric so as to operate in space of arbitrary dimensions. It also has provisions to define spatial constraints and fixed constraints like fixed volume. The graphical output makes error identification easier and gives an idea on the iteration step involved. Each vertex is defined and when the iterations take place they form small union of triangles for the evolution procedure. The vertices take in to consideration the degree of

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13 freedom and the global scaling factor. The energy is calculated for each step. Numerous analyses are done on electrowetting and self assemb ly by using Surface Evolver [7, 1416]. 1.2.7 Electrowetting Miniaturization increases surface to volume ratios bringing more challenges in control of surface and surface energies [17]. In mi crosystem engineering, microfluidics has tremendous opportunities with its capability to handle liquids in Micro optical switching devices, Micro RF switches, Micro fluid p umps, Digital Micro Total Analysis System (micro-TAS) and more [18]. A fundamental iss ue in microfluidics is the movement of fluid volumes as desired. Micro pumps o ffer one solution. However micro pumps require a variety of lithography steps for fa brication and helps in only a continuous flow. Another promising option is the p henomenon of electrowetting for the manipulation of individual drops. In 1875, Gabriel Lippmann demonstrated a relationsh ip between electrical and surface tension phenomenon. This relationship allow s efficient control of shape and motion of a liquid meniscus by applying a voltage. The liquid changes shape when a voltage is applied in order to minimize the total e nergy of the system (sum of surface tension energy and electrical energy). Today, this effect, known as electrowetting, has seen potential importance in many applications.

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14 Figure 6 Representation of low wettability and thei r variation with applied voltage. For efficient control of shape of the droplet, the surface energy of the surface over which the droplet is located should be controlled. The surface energy of this surface can be varied by varying the temperature, varying the c hemical and topographical structure of the surface [19]. In miniaturized fluidic systems, electrowetting is an important source of electrical surface modification representing one of the best methods to control the liquid droplet. The idea behind electrowetting is to make the surfa ce highly wettable by an applied electric field. In electrowetting on a diel ectric, the change of contact angle as a function of the applied voltage can be related to t he dielectric thickness (d) and dielectric strength (e0,eR) as proposed by the Young Lippman equation [17]. The system energy is found by modeling the fluid us ing the contact angle data and the Young-Lippman equation. The forces acting on th e droplet are calculated by differentiating the energy with respect to the disp lacement of interest.

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15 These predictions are computed with numerical model ing of surface forces using Surface Evolver [15, 16] in order to determine the sensitivity of the forces to variations. d g e e q qlv r o oV 2 cos cos2 1+ = Equation 2 Young Lippman equation to show the depen dence of contact angle with applied electric field. Electrowetting is a unique method to realize the mo tion, dispensing, splitting and mixing of single droplets in a microfluidic system without the need of any mechanical or fault prone components. It employs control of volta ge that changes the interfacial energy of the liquid-solid interface [17]. By alternativel y applying voltage across an electrode, the fluid can be efficiently moved as desired, by c hanging contact angle of the liquid on the surface. This is proved by many works done so f ar by applying large voltage on dielectric called Electrowetting on Dielectric (EWO D) that provided large changes in the contact angle [20, 21]. FLOATINGDROPLET G R O U N D E D D R O P L E T Figure 7 Most commonly employed configurations in E lectrowetting. Figure 7 shows two most common configurations emplo yed in the electrowetting phenomenon. In the grounded droplet method, the liq uid is grounded while in the floating droplet, the droplet floats across two electrodes w ith applied voltage across them. Both of these configurations produce an effective force on the liquid both in the lateral and

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16 normal direction. This force induced is used to mov e the droplet through micro and nano tubes by alternatively applying voltage. Crane et al. [22] demonstrated that a nanoindenter could be adapted to measure these fluid forces with a custom tip. This work is concerned with the sensitivity of such a measurement system to system factors including vari ation in liquid volume, angular alignment of the part and substrate and displacemen t of the part relative to substrate features. 1.3 Research Benefits Self assembly is a promising alternative to convent ional pick and place robotic assembly of micro components. Its benefits include parallel integration of parts with low equipment costs. Various approaches to self assemb ly have been demonstrated, yet demanding applications like assembly of micro-optic al devices require increased positioning accuracy. This thesis implements a new method for design of self assembly bonds that addresses this need. Current methods ha ve zero force at the desired assembly position and low stiffness. This allows small dist urbance forces to create significant positioning errors. The proposed method uses a sub strate assembly feature to provide a high accuracy alignment guide to the part. The cap illary bond region of the part and substrate are then modified to create a non-zero po sitioning force to maintain the part in the desired assembly position. Capillary force mod els show that this force aligns the part to the substrate assembly feature and reduces sensi tivity of part position to process variation. Thus, the new configuration can substan tially improve positioning accuracy of capillary self assembly. This will result in a dra matic decrease in positioning errors in the micro parts.

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17 Electrowetting is considered to be one of the most efficient methods to manipulate fluids through micro and nano tubes and in other hi gh end applications. The forces induced in a system due to electrowetting can be me asured through a nano-indenter thus making it an electrowetting force measurement syste m. This thesis will address the potential variations that can be caused in the forc e values obtained due to variations in liquid volumes, tilt of the part and lateral displa cement. Influencing factors including voltage, methodology of voltage applied, changes in the liquid volume and effects due to the tilt in the component are considered in a detai led analysis. This analysis predicts the electrowetting behavior in different conditions und er all factors that might affect the process so that guidelines for accurate measurement s can be determined. 1.4 Thesis Outline This thesis proceeds as follows. Chapter 2 reviews the previous works done in self assembly and electrowetting processes and summarize s their outcome. Chapter 3 details the analysis of capillary forces in a self assembly process and implementation of a new design approach of the fluidic self assembly bond f or precision positioning of micro components. Chapter 4 is involved in analysis of ca pillary forces in electrowetting process and the sensitivity of the process to varia tions due to influencing parameters. Chapter 5 concludes the work done and recommends fu ture aspects for improvement and optimization of the processes.

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18 CHAPTER 2 LITERATURE REVIEW 2.1 Self Assembly The concept of self assembly has been formulated si nce (1930). This is emphasized by many famous landmarks with those incl uding the theory of universal Computation by Alan Turing (1930), The theory of au tomata replication by John Von Neumann (1950) and James D Watson and Francis Crick in the discovery of the structure of DNA [23]. While self assembly has been implemented in multidi sciplinary fields since then, the potential of the concept came to lime light whe n Kazuo Hosokawa’s group [23] demonstrated micro-scale self assembly using surfac e tension (1996). Since then there has been many research initiated in employing the c oncept of self assembly in the assembly of micro and nano parts. Following those initial works, there were numerous efforts to validate, optimize and achieve a high precision assembly using self as sembly process. This section details few of those important works under each category. 2.1.1 Optimization of Self Assembly Process Zheng et al. [24] proposed the use of low temperatu re melting solder for assembly of functional LED micro components having three dim ensional structures. The structure containted an LED component, an encapsulation body with solder bumps and a chip

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19 carrier. The proposed technique contained an assemb ly sequence that shows the process involved in self assembly. This method combined the shape recognition and solder directed method of self assembly together to realiz e the necessity in multicomponent, multimaterial, three-dimensional microsystems. This method explored the option of assembling heterogeneous microsystems, three dimens ional integration and ensured electrical connections. However the method was a se quential feed technique of feeding different sized components sequentially. Cannon et al. [25] proposed the self assembly of mi llimeter scale parts into 5mm cubes of polymethylmethacrylate. This work describe s about the local and the global energy minima in assembly and as to how the capilla ry forces acts as the driving force to ensure self alignment. The proposed method reports the self assemblies of parts with variety of functions being assembled in to three di mensional structures, enabled through a standard interconnect. An assembly rate of 0.125 co mponents per second was recorded with a 93% yield. The problem of selective self ass embly was reported. Process improvements such as using density stratified solut ion or molding alignment features so as to accept or reject parts by design were discuss ed. Gracias et al. [26] demonstrated the phenomenon of self assembly to form interconnects in electronic devices especially in t he circuits. The stages of series and parallel assembly in 3D electrical networks were es tablished. By making the wires substantially narrower (approx 150m) the height of the solder film was also limited. The width of the solder dots is 1mm. To ensure correct registration of parts, pattern to pattern registration was enabled by proper design of solder dots on the face of the part.

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20 Xiong et al. [27] demonstrated a method of controll ed multi-batch self assembly of micro components using capillary forces. An arra y of gold binding sites was patterned on the oxidized silicon substrate and once these si tes are exposed to an alkanethiol solution, they become hydrophobic. The self assembl y process was executed in an aqueous environment with a hydrophobic adhesive as the bonding fluid. Without a Self Assembled Monolayer (alkanethiol solution), the gol d sites are inactive as the sites are hydrophilic. Hence the self assembly process is don e by the principle of hydrophobic/hydrophilic interactions. The de-activa tion of Self assembled Monolayer is also discussed by application of an electrochemical potential between the gold and the aqueous solution. By this method the sites were abl e to be selectively assembled by selective activation and de-activation and thus obt ained controlled multibatch assembly of parts. LED arrays were assembled on to the subst rate with the heat polymerizable adhesive, and the electrical connections to the sub strate were formed by electroplating tin and lead. Fang et al. [14] proposed an assembly process based on shape recognition and capillary-driven mechanisms. The capability of this assembly towards various factors those including high dense assembly, peg free micro components, process in air environment, different modes of part mounting, uniq ue face orientation of parts, assembly of different types of components with even similar dimensions and high surface coverage on the surface were considered and achieve d using the proposed technique. For this proof of concept 790m diced square silicon co mponents were used. A parallel assembly strategy of the assembly sequence is detai led and the surface treatment of the diced parts to achieve the required assembly is als o provided. Two different cases were

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21 considered in terms of part dimensions (flat-edged parts and the step-edged parts) and the assembly strategy methods including vertical mode a nd the horizontal mode are considered. The process achieved 1000 densely packe d parts in approximately 2 min and the defect rate is mentioned to be approximately 1% A single batch proposed a surface coverage of 31% while the second batch doubled the same. Another class of processes referred to as self asse mbly is the alignment of computer chips by the surface tension of solder dur ing solder reflow. Vivek [28] proposed the analytical prediction of the shape and solder heights of equilibrium joints formed due to the solder re-flow in surface mount c omponents. This is done for the application of the components to the printed circui t boards. For this analysis the two dimensional joints with negligible solder density e ffects are considered. Experimentations were done on the same and the results agree with ea ch other. The sensitivity of the solder joint to the geometric and physical properties is a nalyzed numerically. Any smaller changes in these properties have larger potential h eights at constant solder volume. The reliability of the solder joints is closely related to the characteristic properties. This proposed technique is highly helpful in prediction the shape of the solder and the standoff heights when considering solder-based assembly. Scott et al. [29] proposed a batch fabrication proc ess to create a micron-sized helical and toroidal inductors with Q values greate r than or equal to 50 at multi-GHz frequencies. In order to increase the value of Q th e aspect ratio must be high as Q is directly proportional to the aspect ratio of the in ductor. The self assembly process allows multiple interconnects to the inductor. A proper de sign of inductor was required so as to minimize the losses between the substrate and the c onductor and increase Q and

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22 operating range. The part and the substrate are sel ectively processed for hydrophobic/hydrophilic interactions. Such a design and assembly had led to an inductor with Q approximately 60 at 5 GHz and with a resonan t frequency of 9 GHz. Such an inductor when assembled provides an increase by a f actor of approximately three as compared to a traditional lithographically fabricat ed inductor. Zheng W [30] proposed a novel assembly process to i ntegrate and connect semiconductor dies on surfaces with Single-Angular Orientation and Contact-Pad Registration. In this proposed technique major conc erns were to avoid overlaps in assembly, uniquely orient components and enabling a ssembly of parts of various dimensions. An experimental approach and results of the assembly process are detailed. A unique method of protecting five spots of gold su rface with Shipley 1813 photoresist was necessary to ensure correct angular orientation The fabrication procedure is detailed as part of the proposed technique and the assembly orientation and alignment issues are discussed by images of SEM and a standard deviation was measured for the lateral distance and the angular deviation for the proposed methods. The final results were an angular orientation of 0.3r and contact pad registr ation with an accuracy of 19m for heterogeneous dimensions from (500m – 2mm). Most self assembly of micro components relies on th e fluidic medium due to the fact that the handling of such small devices become s highly difficult in air/dry environment. Yeh and Smith in 1994 [31], proposed a technique on fluidic self assembly based on shape matching between micro components an d receptors with recess on them. The ability of the parts to recirculate across the receptor holes by constant agitation until they fall in to the receptors is the success of the fluidic self assembly. Integration of GaAs

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23 surface-emitting laser components on silicon substr ate was demonstrated using this technique. The substrate had etched holes in a trap ezoidal shape with those similar to the parts. The GaAs along with the fluid medium is disp ensed on the substrate. The required orientation is obtained due to the trapezoidal shap e of the part and the site. Random mechanical vibration was performed to give the nece ssary agitation so as to position the parts in to the receptor sites. According to the pr oposed method more than 90% of the holes were filled with the GaAs blocks. 2.1.2 Achievements Towards Precision Self Assembly Srinivasan et al. [5] demonstrated the self assembl y of parts with submicrometer positioning accuracy. The lateral alignment and the rotational misalignment have been dealt with in the paper and the proposed method of fluidic self assembly. Different sized parts ranging from 150 x 150 x 15 m3 and 400 x 400 x 50 m3 were used in the assembly process and were directed towards the subs trate using a pipette. The constraint of accuracy in the assembly process is attributed t o the patterning of the hydrophobic shapes and thus the positioning depends on the reso lution of these hydrophobic shapes. The substrate has been lubricated in the proposed m ethod so as to eradicate binding of parts to each other as a result of capillary forces between them. A quartz substrate was used to assemble microparts so that the accuracy ca n be determined by picturing the parts through the transparent substrate. The proposed sha pe matching occurred in approximately 1 sec in the experimental verificatio n of the proposed technique and the self assembly step is slowed by increasing the visc osity of the lubricant. The advantages of self assembly over wafer to wafer transfer were detailed and the maximum precision of 0.2m and rotational misalignment of approximately 0.3r were reported with the

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24 assembly rate of 98 part arrays in 1 minute with th e yield of 100% is recorded by the proposed method. Srinivasan et al. proposed a similar method of flui dic self assembly technique using capillary forces to assemble micro parts [32] with high alignment precision. For this purpose, a heat curable acrylate adhesive was used to provide capillary forces and is polymerized in a bath of water at 80rC for 16 hours with continuous nitrogen bubbling. The fill factors were measured to be 95% and the as semblies were measured to be flat to within 6nm rms. Further improvement of the process are discussed with those including reducing the mass of the assembly parts, characteri zing the adhesives and proper tune of bind site area to produce different levels of adhes ion. Singh B. P. et al. [33] proposed a technique to ass emble laser diodes using a guided fluidic assembly with reduced problems of mi sorientation. Unassembled Laser diodes are guided through a 150 m thick nickel met al mask in to the recess. Thus the assembly process is done in two steps. The first st ep is to guide the parts through the mask to the recess and the second step is the fine precision of the part under fluidic as well as gravitational force. Different sizes of Las er Diodes are assembled successfully with a precision of 2m and 100% efficiency. A flow chart to detail the automation capabilities of the guided fluidic self assembly is provided. Once the parts are assembled, wafer heat treatment is done before performance cha racterization. 2.1.3 Surface Evolver in Self Assembly Surface Evolver by K. A. Brakke is a powerful and f lexible system to represent and solve for equilibrium surface profiles and ener gies. This program can be used to analyze liquid surfaces shaped by various energies including surface tension and can be

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25 subject to defined physical constraint. Surface Evo lver drives the defined surface towards minimum energy and calculates force induced within the surface as a derivative of the energy. Numerous works were done using Surface Evol ver to predict the assembly liquid shape, to determine the characteristics of the proc ess at different parameters and to analyze the process at different volumes. This sect ion details a few of those works done using Surface Evolver which proves this program to be an efficient source for simulation and analysis of self assembly systems. Andreas et al. [7] proposed a parallel assembly in the fluidic phase. The proposed technique was by controlling the hydrophobic and hy drophilic interactions between the part and the site. The considered geometry is a squ are shaped part and a similar binding site and the sites are coated with a hydrophobic al kanethiol layer. The principle of the assembly was by the difference in the surface energ y of different medium in the assembly which acted as a driving force. A Surface Evolver m odel was simulated by giving the part a shift, a lift, a twist motion and a tilt. Results were generated and the assembly height corresponding to a volume of 200 nl is 0.174mm. The critical importance of the lubricant volume was portrayed in this work and a tilt deform ation in the part was shown with increased volume. The concept of increase of restor ing force with various shifts and then attaining a saturation value was proved. The Surfac e Evolver model was proved to be effective in predicting the final assembly shape an d location to characterize the self assembly process. Harsh et al. [34] explored the use of liquid solder to move a MEMS mirror from its planar fabrication position to an out-of-plane operational position. They developed a Surface Evolver model to predict the final assembly equilibrium angle of the solder,

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26 which was proved to be within an error of +/2 deg rees based on experiments. The modeling of the same obtained better results on the se error values giving high potential of Surface Evolver to aid in designing innovative 3D M EMS devices assembled using solder. This process of assembly of MEMS devices us es surface tension of solder. As stated earlier in [7], there is a crucial dependenc e of solder volume in the assembling accuracy. Hence the proposed technique explains the importance to develop and design models for solder at demanding precision requiremen ts. A comparison of geometry based model and a surface energy-based model are also pre sented. Various model aspects were considered and corresponding details are predicted for geometry based model and Surface energy based model. The need for a static a nalysis to consider potential energy was stated. The paper demonstrated the proposed tec hnique with 15 test assemblies. Sean et al. [12] proposed a two stop process with a finite element model to predict the hydrodynamic forces that would move the part to wards the substrate and the Surface Evolver program to determine the efficient assembly of the part once it comes into contact with the binding site. For the proposed mod el the binding site is designed with 10m and 20m deep recess and contains a low meltin g point solder on metal pads at the bottom of wells. Silicon shapes carrying matching p atterns were used for assembly testing procedure. A simulation is performed in the FEMLAB model to identify if the viscous fluid forces would be sufficient to move th e component to the desired location. Once the component reached the desired location, mo deling is done to predict the alignment of the component in the well. The results showed that the fluid forces induced were very small (between 2.5 and 2nN) for the compo nent dimensions of 10m x 50 m x 300m. The results also predict a decrease in the fluidic force once the liquid reaches

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27 the desired location. The Surface Evolver model giv es a prediction of the force at various lateral distance and heights once it is in the site The simulation results were confirmed with those of the experiments. 2.2 Electrowetting Review Recent emphasis on microscale phenomena and devices has resulted in many microscale fluidic systems. Most of the devices an d methodologies developed focus on continuous motion of fluid medium on a solid surfac e through a closed channel. However, recent advancements have paved the way to individually manipulate liquid droplets [17, 35, 36] in a process termed digital microfluidics (DMD). Electrowetting is the primary tool for manipulation of individual mic roscale liquid droplets. In this section, we review recent works that focuses on droplet moti on and control and the force induced in the method. Lienmann et al. proposed [15], a simulation using S urface Evolver to study the detailed behavior of a droplet for a given electrod e geometry and voltage curve. The proposed work mainly dealt with the simulation to p redict the electrowetting effects on a droplet and a methodology to calculate the shape of electrodes and optimization of the same was predicted. The results were compared with those of the analytical model. The simulations are integrated to a user-friendly simul ation tool based on Surface Evolver code. The application was focused towards four oper ations including creation, motion, splitting, mixing/merging of droplets. The proposed work helped in understanding the electrowetting behavior and proved the reliability of the process. Baird et al. proposed [37], a method to examine ele ctrostatic force on microdroplets transported via Electrowetting on Die lectric (EWOD). The force

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28 distributions on advanced and receding fluid faces are detailed in each case. Dependence of the force distribution and its integral on syste m geometry, droplet location and material properties are described. A comparison of scaling p roperties and force distribution for both the cases are given. The effect of the diverge nt charge density on possible explanations for contact angle saturation such as c harge trapping, local dielectric breakdown, and corona discharge are also studied. B oth analytic results for integrated total forces and numeric results for the force dist ribution are compared and are proved to be in agreement with results over the other. Walker et al. [38] discussed the modeling and simul ation of a parallel electrowetting on dielectric device that studies dr oplet movements through surface defects. The simulations are compared to that of th e experiments for a splitting droplet. Various factors affecting electrowetting effects ar e considered and the details on their influence are described in detail. The governing fl uid equations and boundary conditions along with contact hysteresis are developed. A nume rical simulation is described which uses a level set method for tracking the droplet bo undary. Peykov et al. [39] developed a model to study the c ontact angle changes and the limit at which the contact angle saturation occurs. The model proposed in this work predicts that for an electrowetting device in which an aqueous droplet can be forced to completely wet a hydrophobic surface, a surface wit h the same surface energy as the liquid is required. Indeed the work presented a mor e detailed consideration of electrowetting taking in to account the detailed st ructure of the double layer. Berthier et al. proposed [40] a technique to find to investigate minimum and maximum actuation voltages in electrowetting. He fo rmulated maximum voltage as a

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29 threshold beyond which there is no more gain in the capillary effect due to the saturation effect. Calculation was done to determine the elect rowetting force on a EWOD system considering the contact angle hysteresis and an ana lytical relation was obtained to derive the minimum actuation potential.

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30 CHAPTER 3 DESIGN OF FLUIDIC SELF ASSEMBLY BONDS FOR PRECISE COMPONENT POSITIONING 3.1 Introduction Assembly is essential to the production of most man made products. The challenges of design, engineering, manufacturing an d logistics come together as individual components are combined to make a functi oning system. In macro-scale applications, assembly processes have relied on hum an and robotic assembly to place, interconnect and integrate components at all comple xities. Robots are efficient for the accuracy and repeatability that were achieved and h ence high precision assembly was possible at the macro-scale. With the evolution of micro-manufacturing in recent years, part size has been greatly reduced. Although Robotic assembly is highl y efficient at the macro-scale, it loses its efficiency at the micro-scale due to increased positioning control challenges and difficulties in grasping and releasing micro-scale components. This is due to the fact that the surface tension, Van der Waals, and electrostat ic forces dominate the gravitational force at the micro-scale. Moreover such a serial as sembly by robots may not be time efficient and there are more complications while co nsidering 3D integration of components especially at the micron level. This cre ates a tremendous demand for new micro-assembly techniques in both packaging and int egration of complex microsystems.

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31 Recent developments in micro assembly technologies include micromanipulator based assembly [1], pick and place method [41] and wafer to wafer devices transfer [2]. The limitations of these methods included challenges of precision assembly, poor performance on non-planar surfaces in cavities and in fabrication of 3D systems and lack of a parallel assembly approach. While wafer to waf er transfer achieves parallel integration, yields can be decreased due to integra tion of potentially defective components with functional components. Self assembly is a promising alternative technique to conventional micro assembly methods. It is a parallel assembly approa ch with 3D integration compatibility and it requires limited specialized equipment. This can be applied to known good parts and unused or misassembled parts could be recovered and recycled to improve the assembly yields. In self assembly, components are brought together through random interactions. Over time, the system minimizes its energy by bonding together in the desired configuration. Self Assembly processes are often classified by the dominant interactions. These include electrostatic [8], mag netic field [9], and surface tension driven self assembly [13, 26, 42]. Surface tension-driven self assembly is achieved by the reduction of surface energy of an assembly fluid. Common assembly fluids include water, adhesive, and solder [7, 14, 29]. The surfaces of the parts to be assembled are patterned to create regions with differential wetting characteristics. An assembly fluid is introduced onto the well-wetted surfaces. These are dispersed in an im miscible fluid and agitated. The system energy is minimized when the assembly fluid contacts other well-wetted surfaces and the parts are bonded together. The physical lo cation of the minimum energy

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32 configuration depends on parameters such as the sur face tension, shape of the wetting regions, and the volume of the assembly fluid. In general, these must all be managed to assure accurate part positioning [7]. The promise of self assembly has motivated a variet y of trials. These have shown that it is possible to assemble significant numbers of parts successfully in short periods of time. Fang et al. [14] demonstrated assembly of 10 00 densely packed receptor sites with micro parts in about 2 minutes with a defect rate o f approximately 1%. Many studies have not measured the positioning accuracy of the c omponents, but Srinivasan et al. [5] demonstrated assembly with a precision of less than 0.2m and a rotational misalignment less than 0.3r. Singh et al. [33] assembled laser d iodes of two different sizes with 2m precision. Zheng et al. [30] proposed a novel techn ique to assemble different sized components with 0.3r rotational precision and a pot ential method to avoid some common assembly errors. The eventual range of self assembl y applications will depend on the accuracy with which parts can be assembled and the process control that is required to achieve these levels. Demanding applications requi ring precise optical alignment or electrical connections with a small pitch require f urther improvements in positioning accuracy. This work presents a concept for improv ing the accuracy and repeatability of positioning through self assembly and analyzes one method of implementation. A particular advantage of this method is its ability to reduce sensitivity of part accuracy to many sources of process variation. 3.2 Basic Concept All systems evolve towards their minimum energy con figuration. S elf assembled systems are designed so that, the perfect alignment position is coincident with the global

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33 energy minimum. The system evolution toward this po sition is driven by an effective force that is equal to the derivative of the system energy with respect to displacement. The net force at the alignment/equilibrium position is zero since the energy is at a minimum. Although this phenomenon of energy minimi zation drives assembly, accuracy is limited by the change in the energy landscape du e to process variation. These include variations in surface energies, dimensions, liquid volumes, and disturbance forces such as gravity, inertia, and electrostatics that can affec t both the minimum energy position and the part sensitivity to variation. Figure 8(a, b) illustrates a basic prismatic part a ssembled to a substrate via surface tension driven self assembly. The impact of proces s variations can be seen by analyzing the surface tension bond as a combination of spring s connecting rigid parts (Figure 8(c)). The position is a function of the disturbance force s and the spring stiffness—both of which can vary. Together, these can create signifi cant errors and uncertainty in the part position. Figure 9(a) illustrates the errors that result from a disturbance force and the uncertainty in the error motion due to variation in the spring stiffness. Accuracy improvement requires that all of these variations b e minimized or that the system sensitivity to the variations be reduced. Even w eak forces or torques can introduce positioning error by changing the position of the e nergy minimum. Macro-assembly systems utilize stiff alignment feat ures to assure accurate positioning despite variations in some parameters. Springs or other compliant parts are then used to hold the part against the alignment gu ide. This can be implemented in the spring model of Figure 8(c) by introducing a physic al constraint that displaces the part from its equilibrium position as illustrated in Fig ure 8(d). A restoring force of magnitude

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34 k d y is obtained. This force pushes the part towards t he energy minimum while the high stiffness of the rigid constraint prevents movement Due to the large difference in stiffness between the alignment guide and the sprin g, the alignment guide is considered a rigid body. Disruptive forces below this restoring force, referred to as the preload force will not displace the part. The magnitude of the p reload force will be a function the effective spring constant and the global equilibriu m position, but the part position is independent of these variations over a significant range. The resulting force-displacement error relationships are similar to the schematic sh own in Figure 9(b). Thus, the accuracy of the part position is a functi on of the accuracy and repeatability of the alignment feature alone. The spring’s sole function is to hold the part against the positioning constraint. Variations in s pring stiffness and the zero force position of the spring over a significant range now have no impact on the part position. The system should be designed so that the preload f orce is greater than any expected disturbance forces and the accuracy of the alignmen t feature should be within the required positioning accuracy. Under these conditio ns, the part position can be considered independent of these system variations a s in Figure 9(b). This is the concept of “force closure” articulated by Whitney [43]. This insensitivity to variation would be of particu lar value in self-assembled systems at the micro-scale. Many sources of process variations are difficult to control. For example, surface energy affects both the effect ive spring stiffness and equilibrium position and can be very sensitive to surface conta mination. Also many current methods of applying the assembly fluid require tradeoffs in control of the fluid volume versus

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35 speed of application. Further, self assembly proce sses rely on random interactions to generate the assembly which can also be a source of process variation. Figure 8 (a) Typical self assembly system (b) propo sed self assembly system (c) mass-spring system representing typical self assembly system. All disturbance forces deflect the springs and move the part. (d) mass-spring system represe nting proposed self assembly system. An alignment constraint displaces the part to create a preload force. Only disturbance forces above this preload can displace the part. Figure 9 Representation of error corresponding to f orce disturbances in self-assembled components. (a) Typical self assembly bond. In the typical self-assembled cases, all disturbances create variation in the part location. (b) Force-closure part positioning. The introduction of a rigid alignment feature decreases the error and uncertainty in position for disturbance forces below the preload force. This force-closure concept can be implemented in se lf assembly systems to reduce the sensitivity of micro self-assembled part positioning to process variation. In a capillary self assembly system, this can be accompl ished by introducing a rigid alignment feature to constrain the part. The wetting pads of the assembly fluid are then designed to

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36 reach their minimum energy position at a point that is blocked by the alignment feature just as the feature in Figure 8(d) prevents the spr ing from reaching its undeflected position. The fluid will apply a continual preload force against the alignment feature. In this work, the preload force is created by introduc ing a difference in dimensions of the substrate with respect to the part. The magnitude of this dimensional difference is referred to as the dimensional offset Figure 10 Proposed self assembly system to establis h force-closure concept in micro-scale. The wetted region on the part is larger than the we tted region on the substrate. Without the alignment constraint, these part would move to the left so that the center of the two regions were aligned. However, the alignment constraint pr events this motion and thus creates a preload force against the constraint. The alignment feature can be any rigid feature that provides the appropriate constraint. In the 2-D case, this can be a simple block as shown in Figure 10. One or more alignment features can also be used to provide constraint in multiple degrees of freedom. If the fluid bonds are appropriately desi gned, a preload force can be created that maintains the part position against the constr aint in all the required degrees of freedom. For the planar case, this can be accomplis hed by creating a dimensional offset in both the x and y axes. The forces and equilibri um positions have been analyzed for dimensional offsets in both one and two dimensions. The results are presented below.

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37 3.3 Simulation The simulation of a basic self assembly bond is don e in Surface Evolver; a powerful and flexible system for representing and s olving for equilibrium surface profiles and energies. The program analyzes the liquid surfa ces shaped by various energies including surface tension subject to defined physic al constraints. The program drives the defined surface towards minimum energy by the gradi ent descent method. Numerous works have been done using Surface Evolver to predi ct critical parameters of the self assembly process including positions and forces [4, 7, 13]. Due to the small sizes of the components and the re lative strength of the capillary forces, the inclusion of gravity in the simulation has negligible impact on the analysis under the conditions studied in this work except wh ere noted below. Therefore gravity is neglected in the analysis unless otherwise indicate d. The interfacial energy values defined in the system for Liquid-vapor ( gLV), Solid-vapor ( gSV) and Liquid-solid ( gLS) are 46e-3 J/m2, 52e-3 J/m2 and 1e-3 J/m2 respectively to represent an interfacial energy sy stem analyzed by [7]. Dynamic effects such as kinetic en ergy and viscous losses are not considered in the simulation. The model defines a fixed wetting region that repre sents the assembly substrate. The part is represented by a square pad with six de grees of freedom (three translational and three rotational motions). A liquid surface is defined between these two. Boundary constraints are defined to constrain the liquid wit hin the contact regions and the appropriate surface energies are applied to each su rface. The Surface Evolver is used to find the equilibrium shape and energies of the liqu id surface. Forces and torques are found from the Surface Evolver energy calculations by taking the derivative of energy

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38 with respect to the position variables of interest using the central difference method. An optimization routine within the Surface Evolver mod el finds the equilibrium position of the part relative to the substrate. This is done b y iterating on the z-displacement and rotational degrees of freedom of the part to minimi ze the surface energy of the system for a specified position in x and y. The desired assem bly position is defined as the origin of the coordinate system. Force-displacement relation ships are obtained by applying displacement offsets and solving for the forces at each position. The Surface Evolver models do not directly include the effects of align ment features. These are modeled by assuming that the part motion is limited at some di splacement level. In this work, the alignment features are positioned to prevent negati ve x and y displacements. However, force results are calculated for these negative pos itions to illustrate the overall fluid response. The parts analyzed in this study are 900 m m x 900 m m. The assembly fluid is assumed to wet the entire bottom face of the part w hile the substrate has a rectangular wetted region that is varied in size to create diff erent dimensional offsets. The fluid volumes used in this study created fluid heights fr om approximately 100 to 250 m m. When comparing designs with different dimensional o ffsets, the volume was scaled with the size of the substrate pad. These models were u sed to study the impact of varying position, fluid volume, and dimensional offsets bet ween the pad and substrate to characterize the proposed fluidic assembly system. The impact of dimensional offsets on restoring forces and tilt errors are analyzed to id entify their relative sensitivity to disturbance forces and volume variation.

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39 3.4 Results and Discussion The Surface Evolver models were used to predict the force-displacement relationships of self-assembled parts with differen t values of dimensional offset in the ydirection. Figure 11 shows that the forces in the x and z directions are zero to within the limits of the Surface Evolver convergence while the y-force varies both with displacement and dimensional offset. In the typica l self assembly configuration, dimensional offset=0, Figure 11(a) shows that the y -force is zero at the desired assembly location (dy=0 ). A 100 micron dimensional offset creates a resto ring force of approximately 27.6 m N at the assembly position Figure 11 Surface Evolver predictions of force vers us y-displacement for different values of dimensional offset. (a) Dimensional Offset = 0. At the desired assembly position, there is no reaction force. (b) Dimensional Offset = 100 m mm m m. At the desired position, the liquid applies a force of approximately 27.6 m mm m N. Forces below this critical force will not introd uce any positioning error. This would be the preload force for the selected pa rameters. Disturbance forces below the preload force will not cause any motion i n the parts. The force reaches zero at approximately -40 m m displacement. This point would be the energy min imum location, but this position is not attainable in practice due to the alignment features. Thus, the zero displacement position is the actual minimum energy location achievable in practice.

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40 3.4.1 Force Variations with Displacements for Different D imensional Offsets As seen in Figure 12, the preload force continues t o increase with increasing values of the dimensional offset until it reaches a pproximately 37 m N. The variation in tangential force with displacement can be estimated from simplified representations of the capillary force. The liquid will exert a force on the part equal to the surface energy times the perimeter length. The force will be orie nted tangent to the liquid surface. The y-force is then given by the perpendicular edges of the rectangular part. If the surface is modeled as a plane, there is no horizontal force co ntribution from the left side of the fluid because its tangent is vertical. The out-of-plane ( z) component of the force is balanced by the internal pressure in the fluid. The maximum fo rce is obtained when the fluid is tangent to the part and the angle q goes to zero and is approximately 41 m N for this case. The planar force can be estimated as a function of the dimensional offset as n =-V h L Fpyd g1tan cos Equation 3 Prediction of preload force for one-dime nsional offset. Where FPy Preload Force in the y-direction ( m N) L Width of the part ( m m) g Surface tension ( J/m2) h Height of the liquid ( m m) d V Dimensional offset in y-axis ( m m) Figure 12(b) shows that these relationships provide adequate estimates of the limits and trends of the preload force. Preload for ce increases with increase in the dimensional offset up to approximately 200 m m dimensional offset. Beyond this offset no further increase in preload force is observed. Howe ver, the accuracy is limited because

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41 the actual fluid is not well-approximated by a plan e. For analyzing the model for the effects of forces and tilt, a dimensional offset of 100 m m is considered. Figure 12 Impact of dimensional offset on part forc es. (a) Variations in the forcedisplacement relationship for four different values of dimensional offsets. Larger dimensional offsets increase the preload force but with diminishing benefits above 100 m mm m m (b) Variation in the preload force with dimensional offsets. Equation 1 provides an adequate estimate of the preload force over the range of dim ensional offsets analyzed. 3.4.2 Potential Error Sources The introduction of a dimensional offset disrupts t he symmetry of the self assembly bond and could introduce additional angula r errors into the part position. This was evaluated by calculating the equilibrium angula r orientations using Surface Evolver. According to the analysis, the tilt errors in the p art ranged to a maximum of 1 0.2 in a typical self-assembled system. Greiner et al. [7] s howed that in capillary self assembly, the flat position is an unstable equilibrium. Thus the parts tend to tilt about one axis to reach a stable energy minimum. When a 100 m m dimensional offset is introduced, these tilt errors are unchanged. This estimate of angular error was obtained while o nly considering the impact of alignment position on the location of the part cent er. An actual alignment feature like the one illustrated in Figure 10 would constrain both t he y-position and the rotation about the z-axis. Thus, it is expected that rotational error s in the x-y plane will be very small. If

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42 large x-axis or y-axis rotational errors were obser ved for parts under some circumstances such as parts with large mass, these could be reduc ed by the introduction of additional alignment features to constrain these axes. Gravita tional forces do not significantly change the rotational errors at the desired assembl y position, but do have larger effects with increased part displacements, larger dimension al offsets, and or larger assembly fluid volumes. Under these circumstances, gravitat ional effects should be considered. Previous research has shown that the part positioni ng can be sensitive to the assembly fluid volume [7]. For both the typical ass embly configuration and the forceclosure configuration, the part height varies linea rly with fluid volume over most volumes of interest. The preload force also varies significantly with the volume of the assembly fluid. For the 100 m m dimensional offset, the preload force decreases f rom 32.0 m N to 19 mN when the volume doubles from 63 nl to 126 nl. Howe ver, if the nominal preload is maintained greater than the expe cted disturbance forces, the part position can still be insensitive to the fluid volu me variations. 3.4.3 Dimensional Offset in Two Axes The results presented above explain the characteris tics due to dimensional offset in one dimension (y-axis) of the part. This concep t can be extended to include dimensional offsets along both x and y axis of the part to produce a resultant force in both directions. This preload force acts along the resul tant direction of the defined dimensional offsets. By implementing dimensional offsets in bot h the dimensions, disturbances forces in both axes can be overcome and stability can be i mproved further. Figure 13 illustrates how this could be implemented. The force-displace ment relationships vary depending on the direction of motion. Figure 14 shows how the forces compare for motion along the

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43 y-axis alone and for equal displacements in the x a nd y-axis. The two-offsets respond similarly to the one dimensional case and they act nearly independent of each other. When displaced along the y-axis (Figure 14(a)), the x-axis force remains constant while the y-axis has a similar trend to the one-dimension al offset case. When the part is displaced at 45 degrees, both the xand y-forces a re of equal magnitude as shown in figure 7(b). Figure 13 Representation of dimensional offsets in two dimensions. By creating dimensional offsets in two directions, preloads are created aga inst the alignment constraints in both directions. However, there is a significant difference in the c hange of the preload force with increased dimensional offset. Now, larger dimensio nal offsets decrease the contact angle of the fluid on the part, but they also decrease th e length of the wetted region. Equation (1) is modified to obtain a revised preload force r elationship of n =-V h U L FPyd g d1tan cos ) ( Equation 4 Prediction of preload force for two-dime nsional offset. Where dU is the dimensional offset in the x-axis ( m m). A similar equation can also be written for the preload in the x-direction. Now the preload force is maximized at an intermediate value of the dimensional offset. A t larger dimensional offsets, the benefit of a reduced angle of the fluid is offset by the sm aller wetted length. Figure 15 shows

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44 that this simple model provides an adequate represe ntation of the variation in the preload force with dimensional offset for most design calcu lations. Figure 14 (a) Force in (x, y and z directions) vers us displacement with 100 m mm m m dimensional offset in both x and y axis. The forces are the sa me in both directions. (b) Force in (x, y & z directions) versus y-displacement with 100 m mm m m dimensional offset in xand y-axes. The xforce is constant as the part is displaced in the y -direction. 0 10 20 30 40 0100200300Dimensional offsets ( m mm m m)Force ( m mm m N) Simulation Numericalapproximation Figure 15 Variation in the preload force with dime nsional offsets. The preload force reached a peak and then decreases with increased dimensiona l offset. Equation 4 provides an adequate prediction of the preload force.

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45 CHAPTER 4 FORCE ANALYSIS ON ELECTROWETTING Electrowetting is an effective method to manipulate droplets in Digital Microfluidics. The forces induced due to the princi ple of electrowetting is the main source of control of these droplets by causing an a pparent change in the surface energy due to the voltage applied across the substrate on which the droplet is located. These forces induced can greatly affect the performance o f electrowetting devices. Therefore, force measurement and optimization are critical to process improvements. A novel method has been developed to measure these forces i n two-dimensions. This chapter analyzes the sensitivity of this force measurement method to variations in those parameters that affect actual measurements. The res ults obtained gives great insight to guide the design towards an improved measurement me thod and to estimate the measurement errors that could be caused due to the variations discussed. 4.1 Electrowetting Forces In the case considered here, the droplet is positio ned over two substrate electrodes with an applied voltage across the electrodes that can be varied. This creates a circuit with two capacitors in series. At steady state, the resistance of the fluid can be neglected so that the electrical circuit consists of just the capacitors. This setup was used in the force measurements from nano-indentor by Crane et a l. in [22]. With a constant voltage across the electrodes, the voltage between each ele ctrode and the droplet will depend on

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46 the capacitance of the two capacitors. The capacita nce is a function of the area of overlap of the drop and electrode which changes with positi on. Two different voltages are obtained on the left and right of the electrode. If the dielectric layer has a constant thickness and dielectric constant, the voltage indu ced on the left and right electrode can be calculated from TOTAL RIGHT LEFT LEFT RIGHT TOTAL RIGHT LEFT RIGHT LEFTV A A A V V A A A V + = + = Equation 5 Prediction of induced voltage on either side of the electrodes. Where VTOTAL is the total voltage applied to the system, ALEFT and ARIGHT are area of the electrode under the droplet on left and right electrodes respectively. The area influenced by the applied voltage depends on the po sition of the droplet. Hence voltage on each side of the electrode is a function of area which in turn depends on droplet position. Another behavior that can be observed dur ing electrowetting is by the presence of a hole in the dielectric layer. A hole would sh ort the capacitor on one side so that no voltage will be applied across the region of the dr oplet over the shorted electrode. There will be full voltage drop across the other side. I n this case, the electrowetting force will be constant with displacement. The geometry conside red for the analysis of the basic configuration of electrowetting force measurement i s similar to [22] as shown in Figure 16.

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47 Figure 16 Surface Evolver model for force analysis on electrowetting. In the previous work, Electrowetting forces were me asured using a custom tip in a Hysitron Triboindenter in [22]. The top plate in F igure 16 was fixed to a nanoindenter. A small liquid drop is introduced between the plate a nd the substrate. The liquid and substrate materials are chosen so that the liquid c ompletely wets the top plate. When the space between the plate and the substrate is small, the liquid is constrained by the shape of the top plate. When a voltage is applied, the equilibrium position of the plate changes. Since the plate is restrained by the tip holder, the flui d applies a force on the plate in the direction of the minimum energy configuration. Due to the symmetry of this arrangement, the forces should be predominately in the ‘Y’ and ‘Z’ directions. The magnitude of these forces as predicted by numerical models can be closely approximated with simple formulas for the ideal case as demonstr ated [22]. However, errors in alignment or changes in droplet volume by evaporati on can cause variation in these electrowetting forces and depart from the ideal cas e. This Chapter will consider the impact of these variations on the force measurement s. Electrowetting forces in both the

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48 normal (two capacitors in series) case and one with the short (a single capacitor) are analyzed. The required standards and accuracy at wh ich measurement needs to be taken in order to achieve precise measurements are detail ed with the results obtained to support the explanation. 4.2 Electrowetting Force Analysis Although the experimental setup measured the electr owetting forces, the alignment accuracy of the top plate to the substrat e is unknown. There are always force variations that might cause variations/deviations f rom actual measurements. Also methods employed for control of liquid volumes were not very efficient and hence the force predictions due to minimal changes in volumes have to be considered. The test configuration was modeled using Surface Evolver and a detailed analysis is reported based on the predicted results. The model used for simulation has a part and the su bstrate with the liquid in between them as shown in Figure 16 above. There is a gap between the electrodes. The gap between these two capacitors is typically 2mm a nd the height defined between the part and substrate is 580 m m. The volume of the liquid used in the simulation is 47 m l. The size of the part considered is 9x9mm in dimension a nd assumed to be a rigid body for ease of modeling. The substrate is defined based on the parameters of electrowetting and the part above the liquid is defined in a local fra me of reference with six degree of freedom (three translational and three rotational). The translational motion of the part defined in our analysis is termed as offset and the rotation as tilt throughout the section. Both these motions can be defined to some constant value and force induced on the part due to electrowetting can be analyzed from the ener gy gradients as before. At the initial

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49 position (0mm y-offset), the part center is positio ned over the center of the gap between the electrodes. The voltage on each side is calcula ted using Equation 5 where the areas are calculated numerically in Surface Evolver. Typi cally in the floating case the voltage induced due to the applied voltage should be equal on both the sides as area under the droplet on the substrate is equal on both sides. 4.3 Results and Discussion To begin with, simulation is run to analyze force i n the y-axis against different values of voltage at 0 mm y-offset. With such a set up, in the normal configuration, the yforce is zero as the voltage is increased. But if t here was a hole in the dielectric layer, the response is changed. A zero offset can induce y-fo rce even at the 0mm y-offset as shown in Figure 17(a). This distinct difference permits easy detection of defects in the dielectric layer. Similar analysis is done at 3mm y-offset and the configuration with short on one side generates greater force than that of the norma l configuration. The y-force varies linearly with y-offset in the no rmal configuration as seen in Figure 18. This is because the voltage generated is dependent on the area of the droplet under the electrode. While a normal configuration g ives a linear force variation with displacement, the force of that in a shorted setup is a constant with offset. This is due to the fact that the voltage is not applied to one of the side of the electrode and hence force induced is not linear with offset.

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50 Figure 17 Surface Evolver predictions for comparing normal configuration and the configuration with hole on the dielectric layer on one of the sides. (a) comparison of y-force vs. voltage at 0mm y-offset. (b) Comparison of y-fo rce vs. voltage at 3mm y-offset. Figure 18 Comparison of y-force vs. y-offset at 100 V for normal configuration and one with short. 4.3.1 Effect of Tilt When force measurements are done in the electrowett ing setup, the alignment of the top plate with respect to x, y and z axis are a ssumed to be parallel to the substrate. In reality this may not be true and hence there might be variations in the measured value of force due to misalignment of the top plate with res pect to the substrate. The sensitivity of the force measurements due to misalignment in the p late is detailed in this section with results to support the analysis. Tilt about the th ree axes will be considered separately. Figure 19 illustrates tilt about each axis using ou tput from a Surface Evolver model.

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51 Figure 19 Surface Evolver model to detail tilt in d ifferent axis (a) z-axis (b) x-axis (c) y-axis. 4.3.1.1 Z Tilt Tilt in the x and y-axis are defined to be zero whi le the z-tilt is increased in steps to measure force variation. Figure 20 Comparison of y-force vs. y-offset at 100 V for different tilt in z-axis. The force measurements are not highly sensitive wit h varied tilts in z-axis for small y-offsets. The variation is due to increase i n the edge length of the top plate across the junction of the electrodes as illustrated in Fi gure 21.

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52 gapELECTRODE1ELECTRODE2 YC WW-EdgeLengthofthetopplateYc-Criticaly-offsetbeyondwhich edgelength(W)varieswithy-offset Figure 21 Illustration to predict edge length with the tilt in z-axis. The term Yc in Figure 21 is to denote the distance from the edge of the gap to the corner of the top plate. The value of Yc varies dep ending on the tilt in the z-axis. When the top plate has a z-tilt of value q then the value of Yc can be calculated as 2/ ) 45( 45 2 gap Cos Cos L Ycn n + =q Equation 6 Predition of critical y-offset based on z-tilt. Where Yc is the critical y-offset for tilt q in z-axis and gap is the distance between the two electrodes. When a part with the z-tilt is offset from the mean position the edge length (W) of the top plate over the electrode can be determined by qCos L W = Equation 7 Prediction of edge length of the top pla te when y-offset is below the critical yoffset value. Where L is the side length of the top plate and q is the z-tilt This value (W) is a constant till an offset value of Yc (determined ear lier). Once the offset exceeds the value of Yc, the edge length varies with offset and the v alue of the edge length in such a case is determined from

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53 ( ) =q q qCos Sin Yc y Sin L Woff* Equation 8 Prediction of edge length of the top pla te when y-offset exceeds critical y-offset value. Where q value of tilt in z-axis yoff actual offset defined to displace the top plate (m) Yc Critical offset value for a particular tilt (m) Gap gap between electrodes (m) The surface energies required for the calculation w ere obtained from the Surface Evolver prediction based on the area of electrode o ver each pad. Once these values are calculated, y-force can be calculated from ( ) [ ] Y R LF W = *g g Equation 9 y-force calculation based on surface ene rgy difference and edge length variation. gL Surface tension on the left pad (N/m2) gR Surface tension on the right pad (N/m2) W Edge length of the cover plate (m) FY Force in the y-direction (N) It is necessary to align the part within 5 tilt t o z-plane to limit the variation to 3% of the measured value, however for highly precise r esults it is recommended to ensure alignment within 1 error thereby ensuring approxi mately the force values to vary within 0.3% of the actual value.

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54 In order to compare the force results from Surface Evolver predictions with those of hand calculations 20 z-tilt is chosen at a random. The results for force in th e ydirection are predicted and compared with that of t he results of Surface Evolver as shown in Figure 22. This procedure captures the expected variation at large displacements. Comparison of y-force -310 -210 -110 -10 0123 y-offset (mm)y-force ( N) simulation equation Figure 22 Comparison of simulation results and pred icted results using equation for y-force vs. y-offset at 100V. 4.3.1.2 X Tilt Analysis was done with 0 tilt in the y and z-dire ction while the tilt in the x-axis is increased in steps and forces were analyzed for different y-offsets and a constant 100 V across the electrodes. Even minute tilt in the x-axis causes greater varia tion in the measured force values. A 0.5 tilt in the x-axis displaces the pa rt with a force of approximately 90 m N at 0mm y-offset. Hence theoretically, the tilt in the x-axis has to be maintained at 0 tilt in order to obtain accurate forces due to electrowetti ng.

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55 Figure 23 Comparison of y-force vs. y-offset at 100 V for different tilt in x-axis. Table 1 Comparison of best line fits for perfect al ignment with those with different values of x-tilt. However, the rate of change of force with offset is less sensitive to the x-tilt errors. From the graph shown in Figure 23, the slo pe of the results looks to be similar. Table 1 compares the best fit lines for perfect ali gnment to those with 0.5 , 1 , and 5 tilt in the x-axis. For 0.5 degree tilt, the slope error is 3.2%. Poss ible methodologies can be derived to predict the tilt errors by detecting offset, how ever it would be preferred to minimize the tilt errors as the force measurements prove to be highly sensitive to minute tilt errors in the x-axis. X-tilt Slope Intercept Slope Error 0 100.13 0.7376 NA 0.5 96.9 89.9 3.2% 1 91.4 178.9 8.7% 5 34.4 852.6 65.6%

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564.3.1.3 Y Tilt Analysis towards sensitivity of measurements with t ilt in y-axis was done at 100V applied voltage. The tilt values of y-axis were inc reased in steps while the part was accurately aligned to x and z axis (0 tilt). The resulting y-forces are shown in Figure 24. The y-force is very sensitive to y-tilt but less sensitive than to x-tilt The best fit line of perfect alignment condition is compared with those with 0.5, 1 and 5 degree tilt in y-axis in Table 2. Table 2 Comparison of best line fits of those for p erfect alignment with those with different values of y-tilt. The alignment of the part along the y-axis is very important for consistent force measurements. Similar to those variations in the xaxis, 0.5 tilt in the y-axis could offset a part with approximately 10 m N of force in positive direction of the y-axis when at 0mm y-offset. However, the slope of the force change wi th offset varies just 1% for this tilt so that the error is less significant at higher offset s. Y-tilt Slope Intercept Slope Error 0 100.13 0.7376 NA 0.5 100.02 9.5221 0.109% 1 99.864 19.085 0.265% 5 93.658 131.89 6.46%

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57 Figure 24 Comparison of y-force vs. y-offset at 100 V for different tilt in y-axis. From the analysis and comparison of the results fro m the Surface Evolver predictions, alignment requirements gain equal impo rtance in both x and y axis for accurate force measurements. 4.3.2 Effects of Volume A Liquid volume of 47 m l was defined for the liquid on all simulations don e and results compared. The drop volume is controlled by dispensing the drop with a micrometer syringe. The liquid volume is selected to provide a thin layer between the substrate and top plate. This ensures that the con tact area on the substrate to closely approximate the area of the top plate. The microme ter syringe dispenses drop to approximately 1% accuracy. After dispensing and du ring the test, the drop volume may be decreased by evaporation. Therefore, it is impo rtant to consider the impact of drop volume variation.

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58 Figure 25 Comparison of (a) z-force and (b) y-force vs. y-offset for different volume. Analysis was run for three different drop volume le vels at a constant electrode voltage of 100 V as summarized in Figure 25. While change of volume does not affect force measurements in the lateral direction, it has great significance when normal force measurements are considered. The variations accordi ng to the results show approximately 18% decrease from the actual force measurements for a 3 m l increase from the actual volume, while a 3 m l decrease has great influence on force measurement s to increase by a factor of 100. Thus volume needs high control and c onsistency between measurements in order to compare z-force magnitudes. However, if t he analysis is based on y-forces, then volume control is not critical. 4.4 Conclusions The Surface Evolver model was used to find the elec trowetting force measurements under a predetermined condition and an alyzed for variations in these measurement values for changes in critical paramete rs. The range of variation is specified by comparing hand calculation and Surface Evolver p rediction and the critical parameters to be controlled while measurements are taken. The tilt in the x-axis is found to produce high variations followed by y-tilt Z-tilt introduce lesser variation compared to that of x and y-tilt Volume had very negligible effect in the lateral force measurement and hence

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59 volume is not a critical factor when lateral forces are considered. This analysis helps to predetermine the variation in the force measurement s that might occur with possible reasons to support them. Since tilt causes the maxi mum possible variation from the actual value of electrowetting forces, one possible soluti on can be to align the part using the substrate surface as a fixture in itself so that th e part is aligned parallel when compared to the substrate so as to avoid measurement errors.

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60 CHAPTER 5 CONCLUSION AND FUTURE WORK Capillary forces have vast potential at the micro a nd nano scale applications. This work generated novel techniques to measure these ca pillary forces in two important applications and proved that optimization of these forces based on the proposed technique provides great potential in the field. By optimizin g these forces in the applications detailed in this thesis, there are high possibiliti es of these processes to meet commercial requirements. 5.1 Self Assembly Self assembly methods have the potential to achieve fast, parallel, low cost assembly of micro and nano-components. However, the accuracy of the current assembly methods is limited by the ability to control the pr ocess variables. This work has drawn from techniques employed to achieve accurate positi oning in macro-scale assembly and applied them to the case of capillary self assembly Analysis of self assembly systems in the typical case and the proposed case are done. Cr itical force optimization and variations in the critical force with liquid volumes are also detailed. This analysis demonstrates that a modified capillary self assembly method based on this approach can reduce sensitivity of component positioning to process variation throu gh a force-closure method. In the ideal case, the accuracy of the self assembly parts is only a function of the accuracy of a rigid alignment feature. Under this system, assemb ly bonds should be designed to ensure

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61 that under expected variations, the preload force r emains greater than the expected disturbance forces. Simple models are presented to provide adequate estimates of these forces as an aid in the component design. This dram atically simplifies the challenge of developing a robust, high yield process that can ac hieve high accuracy placement of microscale parts. Future work will characterize the sources and magni tude of variation. One significant source of variation is in the volume of the assembly fluid. The magnitude of this variation for the common “dip coating” procedu re would be measured. These measurements will be applied to the models develope d in Chapter 3 to better assess their ability to maintain accurate positioning under unce rtainty. This method will also be extended to self assembly processes based on other assembly forces. The analytical methods developed in this work must be tested experimentally. The parts will be fabricated by evaporating chrome and copper to a plain silicon wafer and dicing them to the required part dimensions. Al ignment feature as detailed in the proposed technique would be fabricated by standard photolithography technique using SU-8 2150 photoresist and the binding sites would b e patterned by evaporating chrome and copper for the required patterns through lift-o ff technique. The optimization of liquid volume by dip coating procedure detailed earlier ca n be a good start to decide on the height on the alignment feature required. Based on these results, characterization of photoresist SU-8 2150 would be done based on the he ight of the alignment feature required for the proposed technique.

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62 AlignmentFeature Part Bindingsite (a) (b) Figure 26 Schematic illustration of wedging in the proposed self assembly model. These models have analyzed parts in or near the ass embly position as illustrated in Figure 26(a). However, during assembly, the part s may contact in other locations. Ideally, the liquid will create a continuous drivin g force towards assembly. However, under some conditions, the parts will contact the b arriers as illustrated in Figure 26(b). “Wedging” could occur if capillary forces that prom ote assembly cannot overcome the frictional forces against the alignment feature as shown in Figure 26(b). Future work will characterize those forces that are responsible for wedging and will identify the part dimensions and friction ranges in which wedging may occurs. Based on those results, a solution can be developed. This problem will be cha racterized by determining the actual force/agitation required to overcome wedging issue in the proposed assembly technique. 5.2 Electrowetting Force Variation Electrowetting is a promising technique for droplet transport, mixing and control in applications related to microfluidics. There are numerous applications with those including micro optical switching devices and micro fluidic pumps that give tremendous opportunities to microfluidics. From many previous research works, the potential of

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63 electrowetting was proven but proper knowledge and prediction of the force variations will enable efficient control of droplet by electro wetting. Further, process improvement is possible by optimizing the force induced. These for ces were measured by Crane et al. in [22] using a nanoindenter. This analysis validated the measurement accuracy fr om the nanoindenter. Further, results are obtained for those variations in the me asurement system due to possible error sources with those including part tilt and excess l iquid volumes. These results are compared to identify the range of measurement varia tions and their sensitivity expected under such conditions. Current analysis is done bas ed on certain assumptions with those including assuming the part as a rigid body and thu s neglecting the deflections induced in them. In future, the part defined in the analysis c ould be analyzed in Ansys by defining the force equivalent to that induced by the liquid along the edges of the part and apply pressure through the area beneath the part with tho se values from the Surface Evolver to predict the deflection and force variations produce d by these deflections.

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64 REFERENCES [1] K. P. Ellis., “Optimizing the performance of a surface mount placement machine”. IEEE transactions on electronics packagin g manufacturing 24(3), pp. 160. [2] A. Singh, D. A. Horsley, M. B. Cohn, A. P. Pisa no and R. T. Howe, "Batch transfer of microstructures using flip-chip solder bonding," J Microelectromech Syst, vol. 8, pp. 27-33, 03. 1999. [3] K. Verma, M. A. Hadley and J. S. Smith, "Fluidi c self-assembly of silicon microstructures", 1995. [4] K. F. Bohringer, U. Srinivasan and R. T. Howe, "Modeling of capillary forces and binding sites for fluidic self-assembly”, 14th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2001), Jan 2 1-25 2001, 2001, pp. 369-374. [5] U. Srinivasan, D. Liepmann and R. T. Howe, "Mic rostructure to substrate selfassembly using capillary forces”, J Microelectromec h Syst, vol. 10, pp. 17-24, 2001. [6] G. M. Whitesides and B. Grzybowski, “Self-assem bly at all scales", Science, vol. 295, pp. 2418-2421, MAR 29. 2002. [7] A. Greiner, J. Lienemann, J. G. Korvink, X. Xio ng, Y. Hanein and K. F. Bohringer, "Capillary forces in micro-fluidic selfassembly", 2002, International Conference on Modeling and Simulation of Microsyste ms MSM 2002, Apr 21-25 2002, 2002, pp. 198-201.

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65 [8] J. Tien, A. Terfort and G. M. Whitesides, "Micr ofabrication through electrostatic self-assembly", Langmuir, vol. 13, pp 5349-5355, OCT 1. 1997. [9] S. Shet, V. R. Mehta, A. T. Fiory, M. P. Lepsel ter and N. M. Ravindra, "The magnetic field-assisted assembly of nanoscale semic onductor devices: A new technique", JOM, vol. 56, pp. 32-34, OCT. 2004. [10] J. C. Love, A. R. Urbach, M. G. Prentiss and G M. Whitesides, "Threedimensional self-assembly of metallic rods with sub micron diameters using magnetic interactions", J. Am. Chem. Soc., vol. 125, pp. 126 96-12697, OCT 22. 2003. [11] J. Lienemann, A. Greiner and J. G. Korvink, "M odeling, Simulation, and Experimentation of a Promising New Packaging Techno logy: Parallel Fluidic SelfAssembly of Microdevices”. [12] S. A. Stauth and B. A. Parviz, "Modeling of fl uidic self-assembly for integration of silicon components on plastic", 19th IEEE International Conference on Micro Electro Mechanical Systems, 2006, pp. 194-197 [13] Xiaorong Xiong, Sheng-Hsiung Liang and K. F. B ohringer, "Geometric binding site design for surface-tension driven self -assembly", IEEE International Conference on Robotics and Automation, 26 April, 20 04, pp. 1141-8. [14] J. Fang and K. F. Bohringer, "Parallel micro c omponent-to-substrate assembly with controlled poses and high surface cov erage", J Micromech Microengineering, vol. 16, pp. 721-730, APR. 2006. [15] J. Lienemann, A. Greiner and J. G. Korvink, "Modeling, Simulation, and optimization of electrowetting", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 25, pp. 234-4 7, 02. 2006.

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66 [16] K. Brakke, "The Surface Evolver", vol. 2007, S eptember 13, 2005. 2005. [17] F. Mugele. (2005, “Electrowetting: From basics to applications”, Journal of physics. Condensed matter 17(28), pp. R705. [18] Chang-Jin Kim, “http://www.research.ucla.edu/t ech/ucla00-270.htm”. [19] J. C. Berg, "Wettability”, Basel and Hong Kong : Marcel Dekker Inc., 1993. [20] J. L. Lin, G. B. Lee, Y. H. Chang and K. Y. Li en, "Model description of contact angles in electrowetting on dielectric laye rs", Langmuir, vol. 22, pp. 484-489, JAN 3. 2006. [21] S. Walker and B. Shapiro, "Modeling the fluid dynamics of Electrowetting on Dielectric (EWOD)", 2004 NSTI Nanotechnology Con ference and Trade show NSTI Nanotech 2004, pp. 391-394. [22] Nathan Brad Crane, Alex A Volinsky, Vivek Rama doss, Michael Nellis, Pradeep Mishra, Xiaolu Pang, "Analysis and Measurem ent of Forces in an Electrowetting-Driven Oscillator", 2007. [23] John A. Pelesko, “Self assembly, the Science o f Things that Put Themselves Together”, Taylor & Francis Group, 2007. [24] W. Zheng, P. Buhlmann and H. O. Jacobs, "Seque ntial shape-and-solderdirected self-assembly of functional microsystems", Proc. Natl. Acad. Sci. U. S. A., vol. 101, pp. 12814-12817, AUG 31. 2004. [25] A. H. Cannon, Y. M. Hua, C. L. Henderson and W P. King, "Self-assembly for three-dimensional integration of functional ele ctrical components", J Micromech Microengineering, vol. 15, pp. 2172-2178, NOV. 2005

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67 [26] D. H. Gracias., “Forming electrical networks i n three dimensions by selfassembly”, Science 289(5482), pp. 1170. [27] X. R. Xiong, Y. Hanein, J. D. Fang, Y. B. Wang W. H. Wang, D. T. Schwartz and K. F. Bohringer, "Controlled multibatc h self-assembly of microdevices", J Microelectromech Syst, vol. 12, pp. 117-127, APR. 2 003. [28] V. Jairazbhoy, "Prediction of equilibrium shap es and pedestal heights of solder joints for leadless chip components", IEEE T ransactions on Components, Packaging, and Manufacturing Technology. Part A, vo l. 19, pp. 224, 1996. [29] K. L. Scott, T. Hirano, H. Yang, R. T. Howe an d A. M. Niknejad, "Highperformance inductors using capillary based fluidic self-assembly", J Microelectromech Syst, vol. 13, pp. 300-309, APR. 2004. [30] W. Zheng and H. O. Jacobs, "Self-assembly proc ess to integrate and connect semiconductor dies on surfaces with single-angular orientation and contact-pad registration", Adv Mater, vol. 18, pp. 1387, JUN 6. 2006. [31] H. J. Yeh and J. S. Smith, "Fluidic assembly f or the integration of GaAs light-emitting diodes on Si substrates", IEEE Photo n. Technol. Lett., vol. 6, pp. 706, 1994. [32] U. Srinivasan, M. A. Helmbrecht, C. Rembe, R. S. Muller and R. T. Howe, "Fluidic self assembly of micromirrors onto microac tuators using capillary forces", IEEE Journal of Selected Topics in Quantum Electronics, vol. 8, pp. 4-11,FEB. 2002. [33] B. P. Singh, K. Onozawa, K. Yamanaka, T. Tojo and D. Ueda, "Novel high precision optoelectronic device fabrication techniq ue using guided fluidic assembly", Optical Review, vol. 12, pp. 345-351, AUG. 2005.

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68 [34] K. Harsh, "Modeling for solder self-assembled MEMS", Proceedings of SPIE--the International Society for Optical Enginee ring, vol. 3289, pp. 177, 1998. [35] V. Cristini and Yung-Chieh Tan, "Theory and nu merical simulation of droplet dynamics in complex flows a review", Lab on a Chip, vol. 4, pp. 257-64, 2004. [36] Y. Fouillet, D. Jary, A. G. Brachet, J. Berthi er, R. Blervaque, L. Davous, J. M. Roux, J. L. Achard and C. Peponnet, "EWOD digita l microfluidics for lab on a chip", 4th International Conference on Nanochannels, Micro channels and Minichannels, ICNMM2006, pp. 1255-1264, 2006. [37] E. Baird, P. Young and K. Mohseni, "Electrosta tic force calculation for an EWOD-actuated droplet", Microfluidics and Nanofluid ics, vol. 3, pp. 635-644, 2007. [38] S. W. Walker and B. Shapiro, "Modeling the flu id dynamics of Electrowetting on Dielectric (EWOD)", J Microelectr omech Syst, vol. 15, pp. 986-1000, 2006. [39] V. Peykov, A. Quinn and J. Ralston, "Electrowe tting: a model for contactangle saturation", Colloid & Polymer Science, vol. 278, pp. 789-93, 2000. [40] J. Berthier, “Actuation potentials and capilla ry forces in Electrowetting based Microsystems”, Sensors and actuators. A, Physical 134(2), pp. 471. [41] J. A. Thompson and R. S. Fearing, "Automating microassembly with orthotweezers and force sensing", Proceedings of RSJ/IEE E International Conference on Intelligent Robots and Systems, pp. 1327-34, 2001. [42] A. Terfort, “Self-assembly of an operating ele ctrical circuit based on shape complementarity and the hydrophobic effect”, Advanc ed materials 10(6), pp. 470, 1998.

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69 [43] D. E. Whitney, “Mechanical Assemblies: Their D esign, Manufacture, and Role in Product Development”, 1st ed.New York: Oxfo rd University Press, pp. 517, 2004.

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70 APPENDICES

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71Appendix A: Program to Support the Analysis of Capi llary Forces //program to automate the analysis run_program.cmd printf "">>> "x_loc.dat" printf "">>> "y_loc.dat" printf "">>> "z_loc.dat" printf "">>> "x_rot.dat" printf "">>> "y_rot.dat" printf "">>> "z_rot.dat" printf "">>> "xforce.dat" printf "">>> "yforce.dat" printf "">>> "zforce.dat" printf "">>> "xphiforce.dat" printf "">>> "yphiforce.dat" printf "">>> "zphiforce.dat" printf "">>> "totalenergy.dat" printf "">>> "volume.dat" printf "">>> "pressure.dat" printf "">>> "ti_log.txt"

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72Appendix A (Continued) // Postscript options gridflag off ; labelflag off ; pscolorflag on; tt :=0; // g until glue has calmed down cgl_TOL := 6e-8; calm_glue := { //printf "cgl: %15.15g -> ",total_energy >> "ti_log .txt"; conj_grad off; g10; conj_grad on; g20; do { cgl_old_e := total_energy; g 10; } while (abs((cgl_old_e-total_energy)/total_energy)> cgl_TOL); printf "%15.15g -> %15.15g\n",cgl_old_e,total_energ y >> "ti_log.txt"; };

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73Appendix A (Continued) fz_TOL := 6e-9; fz_movlim:=1e-6; fz_maxit:=15; find_zmin := // by Newton-Raphson { fz_it :=0; do { fz_it += 1; fz_old_CZ := z_loc; fz_old_energy := total_energy; // save old values calc_zf ; // calculate derivative fz_hstr := dEdz; fz_alpha := -dEdz/d2Edz2; // Newton // Apply motion limit if ( fz_alpha > 0 ) then fz_alpha:=minimum(fz_alpha ,fz_movlim) else fz_alpha:=maximum(fz_alpha,-fz_movlim);

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74Appendix A (Continued) // Shift micropart new_z_loc := fz_old_CZ + fz_alpha; change_z_loc; calm_glue; // Backtracking scheme, if Newton failes if ( total_energy>fz_old_energy) then { fz_alpha := fz_hstr *fz_alpha^2/(2*(total_energy -fz_hstr*fz_alpha-fz_old_energy)); new_z_loc := fz_old_CZ + fz_alpha; change_z_loc; calm_glue; }; printf "fz %g: z_loc: %10e, l: %10e, old_z_loc:%10e \n", fz_it ,z_loc,fz_alpha,fz_old_CZ >> "ti_log.txt"; } while (abs(fz_old_CZ-z_loc)>fz_TOL) and (fz_it
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75Appendix A (Continued) fp_maxit := 20; find_phimin:= // using Newton’s Method { fp_iter := 0; do // while Sum Delta CfX,Y,ZgPHI > TOL { fp_iter += 1; fp_CX_old := x_rot; // save x,k fp_CY_old := y_rot; fp_CZ_old := z_rot; fp_old_energy := total_energy; // get gradient calc_phif ; fp_g1 := dEdphix; fp_g2 := dEdphiy; fp_g3 := dEdphiz; fp_a := d2Edphix2; fp_b := d2Edphixy; fp_c := d2Edphixz;

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76Appendix A (Continued) fp_d := d2Edphiy2; fp_e := d2Edphiyz; fp_f := d2Edphiz2; // invert Hessian fp_idiv := -fp_c^2*fp_d + 2* fp_b*fp_c*fp_e fp_a* fp_e^2 fp_b^2* fp_f + fp_a*fp_d* fp_f ; fp_ai := (-fp_e^2 + fp_d* fp_f )/ fp_idiv ; fp_bi := ( fp_c*fp_e fp_b* fp_f )/ fp_idiv ; fp_ci := (-fp_c*fp_d + fp_b*fp_e )/ fp_idiv ; fp_di := (-fp_c ^2 + fp_a* fp_f )/ fp_idiv ; fp_ei := ( fp_b*fp_c fp_a*fp_e )/ fp_idiv ; fp_fi := (-fp_b^2 + fp_a*fp_d )/ fp_idiv ; // Newton step fp_step := ( fp_g1* fp_ai + fp_g2* fp_bi + fp_g3* f p_ci )*fp_nr_damping; if fp_step>0 then fp_step := minimum(fp_step,fp_mov lim) else fp_step := maximum(fp_step,-fp_movlim); new_x_rot := x_rot fp_step; fp_step := ( fp_g1* fp_bi + fp_g2* fp_di + fp_g3* f p_ei )*fp_nr_damping; if fp_step>0 then fp_step := minimum(fp_step,fp_mov lim) else fp_step := maximum(fp_step,-fp_movlim);

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77Appendix A (Continued) new_y_rot := y_rot fp_step; fp_step := ( fp_g1* fp_ci + fp_g2* fp_ei + fp_g3* f p_fi )*fp_nr_damping; if fp_step>0 then fp_step := minimum(fp_step,fp_mov lim) else fp_step := maximum(fp_step,-fp_movlim); new_z_rot := z_rot fp_step; change_rot; calm_glue; //printf "fp%g after Newton: x_rot: %10e, y_rot: %1 0e, z_rot: %10e, E: %10e\n", fp_iter ,x_rot,y_rot,z_rot,total_energy >> "ti_log.txt"; if ( total_energy>fp_old_energy) then { new_x_rot := fp_CX_old fp_backstep_damping* (x_r ot-fp_CX_old); new_y_rot := fp_CY_old fp_backstep_damping* (y_ro t-fp_CY_old); new_z_rot := fp_CZ_old fp_backstep_damping* (z_ro t-fp_CZ_old); change_rot; calm_glue; printf "fp_%g Newton failed: x_rot: %10e, y_rot: %1 0e, z_rot: %10e, E: %10e\n", fp_iter ,x_rot,y_rot,z_rot,total_energy >> "ti_log.txt"; };

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78Appendix A (Continued) } while ( abs(fp_CX_old-x_rot)+ abs(fp_CY_old-y_rot )+ abs(fp_CZ_old-z_rot) > fp_cgTOL) and (fp_iter> "ti_log.txt"; // -----lateral shift and stiffening effect ---------do { find_zmin; find_phimin; find_zmin; ti_iter+=1; } while (abs(fz_old_CZ-z_loc)>fz_TOL and (ti_iter
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79Appendix A (Continued) calc_xf ; calc_yf ; calc_zf ; // write out data printf "ti: dEdx: %10e, dEdy: %10e, dEdz: %10e\n",d Edx,dEdy,dEdz >> "ti_log.txt"; printf "ti: x_loc: %10e, y_loc: %10e, z_loc: %10e\n ",x_loc,y_loc,z_loc >> "ti_log.txt"; printf "%17.15g\n", x_loc >> "x_loc.dat"; printf "%17.15g\n", y_loc >> "y_loc.dat"; printf "%17.15g\n", z_loc >> "z_loc.dat"; printf "%17.15g\n", x_rot >> "x_rot.dat"; printf "%17.15g\n", y_rot >> "y_rot.dat"; printf "%17.15g\n", z_rot >> "z_rot.dat"; printf "%17.15g\n", xforce >> "xforce.dat"; printf "%17.15g\n", yforce >> "yforce.dat"; printf "%17.15g\n", zforce >> "zforce.dat"; printf "%17.15g\n", -dEdphix >> "xphiforce.dat"; printf "%17.15g\n", -dEdphiy >> "yphiforce.dat"; printf "%17.15g\n", -dEdphiz >> "zphiforce.dat"; printf "%17.15g\n", total_energy >> "totalenergy.da t"; printf "%17.15g\n", body[1].volume >> "volume.dat"; printf "%17.15g\n", body[1].pressure >> "pressure.d at"; printf "%17.15g %17.15g %17.15g\n", x_loc,y_loc,tot al_energy >> "X-Y-E.dat";

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80Appendix A (Continued) // -----lateral shift -------------------------------new_x_loc := x_loc + ti_CXstep; change_x_loc; new_y_loc := y_loc + ti_CYstep; change_y_loc; g 30; // vertex averaging and equiangulation V; u; V; calm_glue; }; calc_force.cmd calc_xf := { f_dx := pad_xdim1/1000; // small shift new_x_loc := x_loc + f_dx; change_x_loc; energy_hi := total_energy body[1].pressure*(body[ 1].volume-body[1].target); new_x_loc := x_loc 2*f_dx; change_x_loc; energy_lo := total_energy body[1].pressure*(body[ 1].volume-body[1].target); new_x_loc := x_loc + f_dx; change_x_loc; energy_mid := total_energy body[1].pressure*(body [1].volume-body[1].target); dEdx := (energy_hi energy_lo)/(2*f_dx ); d2Edx2 :=( (energy_hi 2*energy_mid + energy_lo)/( f_dx)^2); xforce := -dEdx;

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81Appendix A (Continued) //printf "xforce: %17.15gnn",xforce; } calc_yf := { f_dy := pad_ydim1/1000; // small shift new_y_loc := y_loc + f_dy; change_y_loc; energy_hi := total_energy body[1].pressure*(body[ 1].volume-body[1].target); new_y_loc := y_loc 2*f_dy; change_y_loc; energy_lo := total_energy body[1].pressure*(body[ 1].volume-body[1].target); new_y_loc := y_loc + f_dy; change_y_loc; energy_mid := total_energy body[1].pressure*(body [1].volume-body[1].target); dEdy := (energy_hi energy_lo)/(2*f_dy ); d2Edy2 := ((energy_hi 2*energy_mid + energy_lo)/( f_dy)^2); yforce := -dEdy; //printf "yforce: %17.15gnn",yforce; } calc_zf := { f_dz := ( z_loc-part_zdim/2)/1000; // small shift new_z_loc := z_loc + f_dz; change_z_loc; energy_hi := total_energy body[1].pressure*(body[ 1].volume-body[1].target); new_z_loc := z_loc 2*f_dz; change_z_loc; energy_lo := total_energy body[1].pressure*(body[ 1].volume-body[1].target); new_z_loc := z_loc + f_dz; change_z_loc;

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82Appendix A (Continued) energy_mid := total_energy body[1].pressure*(body [1].volume-body[1].target); dEdz := (energy_hi energy_lo)/(2*f_dz ); d2Edz2 := ((energy_hi 2*energy_mid + energy_lo)/( f_dz)^2); zforce := -dEdz; //printf "zforce: %17.15gnn",zforce; } calc_phif := { f_dpx := 0.0005; f_dpy := 0.0005; f_dpz:=0.0005; cp_x_rot:=x_rot; cp_y_rot:=y_rot; cp_z_rot:=z_rot; new_x_rot := cp_x_rot+f_dpx; change_rot; pxenergy_hi := total_energy body[1].pressure*(bod y[1].volume-body[1].target); new_y_rot := cp_y_rot+f_dpy; change_rot; pxyenergy_hi := total_energy body[1].pressure*(bo dy[1].volume-body[1].target); new_x_rot := cp_x_rot; change_rot; pyenergy_hi := total_energy body[1].pressure*(bod y[1].volume-body[1].target); new_x_rot := cp_x_rot-f_dpx; new_y_rot := cp_y_rot; change_rot; pxenergy_lo := total_energy body[1].pressure*(bod y[1].volume-body[1].target); new_y_rot := cp_y_rot-f_dpy; new_x_rot := cp_x_rot; change_rot; pyenergy_lo := total_energy body[1].pressure*(bod y[1].volume-body[1].target);

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83Appendix A (Continued) new_y_rot := cp_y_rot; new_z_rot := cp_z_rot + f_dp z; change_rot; pzenergy_hi := total_energy body[1].pressure*(bod y[1].volume-body[1].target); new_x_rot := cp_x_rot + f_dpx; change_rot; pxzenergy_hi := total_energy body[1].pressure*(bo dy[1].volume-body[1].target); new_x_rot := cp_x_rot; new_y_rot := cp_y_rot+f_dpy; change_rot; pyzenergy_hi := total_energy body[1].pressure*(bo dy[1].volume-body[1].target); new_y_rot := cp_y_rot; new_z_rot := cp_z_rot-f_dpz; change_rot; pzenergy_lo := total_energy body[1].pressure*(bod y[1].volume-body[1].target); new_x_rot := cp_x_rot; new_y_rot := cp_y_rot; new_z _rot := cp_z_rot; change_rot; energy_mid := total_energy body[1].pressure*(body [1].volume-body[1].target); dEdphix := (pxenergy_hi-pxenergy_lo)/(2*f_dpx); dEdphiy := (pyenergy_hi-pyenergy_lo)/(2*f_dpy); dEdphiz := (pzenergy_hi-pzenergy_lo)/(2*f_dpz); d2Edphix2 := ((pxenergy_hi 2*energy_mid + pxenerg y_lo)/(f_dpx)^2); d2Edphiy2 := ((pyenergy_hi 2*energy_mid + pyenerg y_lo)/(f_dpy)^2); d2Edphiz2 := ((pzenergy_hi 2*energy_mid + pzenerg y_lo)/(f_dpz)^2); d2Edphixy := (pxyenergy_hi-pxenergy_hi-pyenergy_hi+ energy_mid)/(f_dpx*f_dpy); d2Edphixz := (pxzenergy_hi-pxenergy_hi-pzenergy_hi+ energy_mid)/(f_dpx*f_dpz); d2Edphiyz := (pyzenergy_hi-pyenergy_hi-pzenergy_hi+ energy_mid)/(f_dpy*f_dpz); };

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84Appendix A (Continued) read "calcinertia.cmd" calc_planes.cmd calc_normals:= { c_sx := sin(x_rot*pi/180); c_sy := sin(y_rot*pi/180); c_sz := sin(z_rot*pi/180); c_cx := cos(x_rot*pi/180); c_cy := cos(y_rot*pi/180); c_cz := cos(z_rot*pi/180); // multiply with Rˆ-1 = RˆT c_Axp1 := (c_cy*c_cz); c_Axp2 := (c_sx*c_sy*c_cz+c_cx*c_sz); c_Axp3 := (-c_cx*c_sy*c_cz+c_sx*c_sz); c_Axn1 := (-c_cy*c_cz); c_Axn2 := (-(c_sx*c_sy*c_cz+c_cx*c_sz)); c_Axn3 := (-(-c_cx*c_sy*c_cz+c_sx*c_sz)); c_Ayp1 := (-c_cy*c_sz); c_Ayp2 := (c_cx*c_cz-c_sx*c_sy*c_sz); c_Ayp3 := (c_sx*c_cz+c_cx*c_sy*c_sz); c_Ayn1 := (c_cy*c_sz);

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85Appendix A (Continued) c_Ayn2 := (-(c_cx*c_cz-c_sx*c_sy*c_sz)); c_Ayn3 := (-(c_sx*c_cz+c_cx*c_sy*c_sz)); c_Azp1 := c_sy; c_Azp2 := (-c_cy*c_sx); c_Azp3 := (c_cx*c_cy); c_Azn1 := (-c_sy); c_Azn2 := (c_cy*c_sx); c_Azn3 := (-c_cx*c_cy); c_Pxp1 := x_loc + c_Axp1 part_xdim/2; c_Pxp2 := y_loc + c_Axp2 part_xdim/2; c_Pxp3 := z_loc + c_Axp3 part_xdim/2; c_Pxn1 := x_loc + c_Axn1 part_xdim/2; c_Pxn2 := y_loc + c_Axn2 part_xdim/2; c_Pxn3 := z_loc + c_Axn3 part_xdim/2; c_Pyp1 := x_loc + c_Ayp1 part_ydim/2; c_Pyp2 := y_loc + c_Ayp2 part_ydim/2; c_Pyp3 := z_loc + c_Ayp3 part_ydim/2; c_Pyn1 := x_loc + c_Ayn1 part_ydim/2; c_Pyn2 := y_loc + c_Ayn2 part_ydim/2; c_Pyn3 := z_loc + c_Ayn3 part_ydim/2; c_Pzp1 := x_loc + c_Azp1 part_zdim/2; c_Pzp2 := y_loc + c_Azp2 part_zdim/2;

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86Appendix A (Continued) c_Pzp3 := z_loc + c_Azp3 part_zdim/2; c_Pzn1 := x_loc + c_Azn1 part_zdim/2; c_Pzn2 := y_loc + c_Azn2 part_zdim/2; c_Pzn3 := z_loc + c_Azn3 part_zdim/2; } change.cmd define vertex attribute dist real calc_dists := { calc_normals; foreach vertex vv do { if ( on_constraint 1 or on_constraint 2 or on_const raint 3 or on_constraint 4 or on_constraint 5 or on_constraint 6 or on_constraint 13 ) then vv.dist := 1 else if fixed then vv.dist := 0 else { chipdist := maximum (0,c_Axn1*(x-c_Pxn1)+c_Axn2*(y-c_Pxn2)+c_Ax n3*(z-c_Pxn3))+ maximum (0,c_Axp1*(x-c_Pxp1)+c_Axp2*(y-c_Pxp2)+c_Ax p3*(z-c_Pxp3))+

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87Appendix A (Continued) maximum (0,c_Ayn1*(x-c_Pyn1)+c_Ayn2*(y-c_Pyn2)+c_Ay n3*(z-c_Pxn3))+ maximum (0,c_Ayp1*(x-c_Pyp1)+c_Ayp2*(y-c_Pyp2)+c_Ay p3*(z-c_Pxp3))+ maximum (0,c_Azn1*(x-c_Pzn1)+c_Azn2*(y-c_Pzn2)+c_Az n3*(z-c_Pzn3))+ maximum (0,c_Azp1*(x-c_Pzp1)+c_Azp2*(y-c_Pzp2)+c_Az p3*(z-c_Pzp3)); if (( z+chipdist)!=0) then vv.dist := z/(z+chipdist) else vv. dist :=0.5; } }; } // change x,y and z position of micropart new_x_loc := x_loc change_x_loc := { calc_dists ; change_dx := new_x_loc x_loc; x_loc := new_x_loc; set vertex x x+dist*change_dx; recalc; }

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88Appendix A (Continued) new_y_loc := y_loc change_y_loc := { calc_dists ; change_dy := new_y_loc y_loc; y_loc := new_y_loc; set vertex y y+dist*change_dy; recalc; } new_z_loc := z_loc change_z_loc := { calc_dists ; change_dz := new_z_loc z_loc; z_loc := new_z_loc; set vertex z z+dist*change_dz; recalc; } // declare variables so that evolver knows them... new_x_rot:=x_rot new_y_rot:=y_rot new_z_rot:=z_rot

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89Appendix A (Continued) // rotate micropart change_rot := { calc_dists ; change_dxphi:= new_x_rot-x_rot; x_rot := new_x_rot; change_dyphi:= new_y_rot-y_rot; y_rot := new_y_rot; change_dzphi:= new_z_rot-z_rot; z_rot := new_z_rot; sdx := sin(change_dxphi*pi/180); sdy := sin(change_dyphi*pi/180); sdz := sin(change_dzphi*pi/180); cdx := cos(change_dxphi*pi/180); cdy := cos(change_dyphi*pi/180); cdz := cos(change_dzphi*pi/180); r11 := cdy*cdz; r12 := -cdy*sdz; r13 := sdy; r21 := ( sdx*sdy*cdz+cdx*sdz);

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90Appendix A (Continued) r22 := ( cdx*cdz-sdx*sdy*sdz); r23 := -cdy*sdx; r31 := (-cdx*sdy*cdz+sdx*sdz); r32 := ( sdx*cdz+cdx*sdy*sdz); r33 := cdx*cdy; foreach vertex vv do { dx := x-x_loc; dy:=y-y_loc; dz:=z-z_loc; set vv x x_loc + (1-dist) dx + dist ( r11*dx + r12*dy + r13*dz ); set vv y y_loc + (1-dist) dy + dist ( r21*dx + r22*dy + r23*dz ); set vv z z_loc + (1-dist) dz + dist ( r31*dx + r32*dy + r33*dz ); }; recalc; }

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91Appendix A (Continued) //program for analysis of self assembly //Dimensions of part parameter part_xdim = 900e-6 // [m] parameter part_ydim =900e-6 // [m] parameter part_zdim = 500e-6 // [m] // reference location parameter x_loc =0 // [m] parameter y_loc = 0 parameter z_loc = 350e-6 // to implement rotation parameter z_rot = 0 parameter x_rot = 0 parameter y_rot = 0 parameter TMOBILITY = 1 // dimensions of pad (defined in two divisions to c hange dimensions along the midline parameter pad_xdim1 = 900e-6 // [m] parameter pad_xdim2 = 700e-6 // [m]

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92Appendix A (Continued) parameter pad_ydim1 = 900e-6 // [m] parameter pad_ydim2 =700e-6 // Physical properties parameter TENSLW = 46e-3 // [J/m^2] parameter TENSSW = 52e-3 // [J/m^2] parameter TENSLS = 1e-3 // [J/m^2] #define sx sin(x_rot*pi/180) #define sy sin(y_rot*pi/180) #define sz sin(z_rot*pi/180) #define cx cos(x_rot*pi/180) #define cy cos(y_rot*pi/180) #define cz cos(z_rot*pi/180) //vector representation of parts to enable translat ion and rotation along the local frame of reference #define Axp1 (cy*cz) // r11 #define Axp2 (sx*sy*cz+cx*sz) // r21 #define Axp3 (-cx*sy*cz+sx*sz) // r31 #define Axn1 (-cy*cz) // -r11 #define Axn2 (-(sx*sy*cz+cx*sz)) // -r21

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93Appendix A (Continued) #define Axn3 (-(-cx*sy*cz+sx*sz)) // -r31 #define Ayp1 (-cy*sz) // r12 #define Ayp2 (cx*cz-sx*sy*sz) // r22 #define Ayp3 (sx*cz+cx*sy*sz) // r32 #define Ayn1 (cy*sz) // -r12 #define Ayn2 (-(cx*cz-sx*sy*sz)) // -r22 #define Ayn3 (-(sx*cz+cx*sy*sz)) // -r32 #define Azp1 (sy) // r13 #define Azp2 (-cy*sx) // r23 #define Azp3 (cx*cy) // r33 #define Azn1 (-sy) // -r13 #define Azn2 (cy*sx) // -r23 #define Azn3 (-cx*cy) // -r33 // a reference point on the part #define Pxp1 (x_loc + Axp1 part_xdim/2) #define Pxp2 (y_loc + Axp2 part_xdim/2) #define Pxp3 (z_loc + Axp3 part_xdim/2) #define Pxn1 (x_loc + Axn1 part_xdim/2) #define Pxn2 (y_loc + Axn2 part_xdim/2) #define Pxn3 (z_loc + Axn3 part_xdim/2) #define Pyp1 (x_loc + Ayp1 part_ydim/2)

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94Appendix A (Continued) #define Pyp2 (y_loc + Ayp2 part_ydim/2) #define Pyp3 (z_loc + Ayp3 part_ydim/2) #define Pyn1 (x_loc + Ayn1 part_ydim/2) #define Pyn2 (y_loc + Ayn2 part_ydim/2) #define Pyn3 (z_loc + Ayn3 part_ydim/2) #define Pzp1 (x_loc + Azp1 part_zdim/2) #define Pzp2 (y_loc + Azp2 part_zdim/2) #define Pzp3 (z_loc + Azp3 part_zdim/2) #define Pzn1 (x_loc + Azn1 part_zdim/2) #define Pzn2 (y_loc + Azn2 part_zdim/2) #define Pzn3 (z_loc + Azn3 part_zdim/2) // Constraints for part and pad (for display only) constraint 1 // x+ formula: -(x Pxp1) Axp1 (y Pxp2) Axp2 ( z Pxp3) Axp3 = 0 constraint 2 // xformula: -(x Pxn1) Axn1 (y Pxn2) Axn2 ( z Pxn3) Axn3 = 0 constraint 3 // y+ formula: -(x Pyp1) Ayp1 (y Pyp2) Ayp2 ( z Pyp3) Ayp3 = 0 constraint 4 // yformula: -(x Pyn1) Ayn1 (y Pyn2) Ayn2 ( z Pyn3) Ayn3 = 0

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95Appendix A (Continued) constraint 5 // z+ formula: -(x Pzp1) Azp1 (y Pzp2) Azp2 ( z Pzp3) Azp3 = 0 constraint 6 // zformula: -(x Pzn1) Azn1 (y Pzn2) Azn2 ( z Pzn3) Azn3 = 0 // Constraints for liquid ( for calculation ) constraint 7 // keep glue above pad formula: z = 0 energy: e1: 0 e2: (TENSLS TENSSW) *x e3: 0 constraint 24 nonnegative // keep glue above substr ate formula: z constraint 25 nonnegative // keep glue above substr ate formula: z-(z_loc-part_zdim/2) constraint 13 // zof chip z+ of glue formula: -(x Pzn1) Azn1 (y Pzn2) Azn2 ( z Pzn3) Azn3 = 0 energy: e1: (TENSLS-TENSSW) (Azn3) y e2: (TENSLS-TENSSW) (Azn1) z e3: (TENSLS-TENSSW) (Azn2) x

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96Appendix A (Continued) content: c1: 0 c2:-((Pzn3 + Azn1/Azn3 Pzn1 + Azn2/Azn3 (Pzn2 y)) x Azn1/Azn3 x^2/2) c3: 0 // One-sided constraints for liquid on part. constraint 14 nonpositive // keep glue within pos x bound formula: (x Pxp1) Axp1 + (y Pxp2) Axp2 + (z Pxp3) Axp3 constraint 15 nonpositive // keep glue within neg x bound formula: (x Pxn1) Axn1 + (y Pxn2) Axn2 + (z Pxn3) Axn3 constraint 16 nonpositive // keep glue within pos y bound formula: (x Pyp1) Ayp1 + (y Pyp2) Ayp2 + (z Pyp3) Ayp3 constraint 17 nonpositive // keep glue within neg y bound formula: (x Pyn1) Ayn1 + (y Pyn2) Ayn2 + (z Pyn3) Ayn3 // One-sided constraints for liquid on pad (substra te). constraint 19 nonnegative //one-sided x-constraint on pad formula: x-(0-pad_xdim1/2) constraint 20 nonpositive //one-sided x-constraint on pad formula: x-(0+pad_xdim2/2) constraint 21 nonnegative //one-sided y-constraint on pad formula: y-(0-pad_ydim1/2)

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97Appendix A (Continued) constraint 22 nonpositive //one-sided y-constraint on pad formula: y-(0+pad_ydim2/2) //geometry definition starts here vertices //vertices of pad 1 -pad_xdim1/2 -pad_ydim1/2 -1e-7 fixed 2 pad_xdim2/2 -pad_ydim1/2 -1e-7 fixed 3 pad_xdim2/2 pad_ydim2/2 -1e-7 fixed 4 -pad_xdim1/2 pad_ydim2/2 -1e-7 fixed //vertices of part 5 (x_loc-part_xdim/2) (y_loc-part_ydim/2) (z_loc-pa rt_zdim/2) fixed constraint 13 14 15 6 (x_loc+part_xdim/2) (y_loc-part_ydim/2) (z_loc-pa rt_zdim/2) fixed constraint 13 14 15 7 (x_loc+part_xdim/2) (y_loc+part_ydim/2) (z_loc-pa rt_zdim/2) fixed constraint 13 14 15 8 (x_loc-part_xdim/2) (y_loc+part_ydim/2) (z_loc-pa rt_zdim/2) fixed constraint 13 14 15 9 (x_loc-part_xdim/2) (y_loc-part_ydim/2) (z_loc+pa rt_zdim/2) constraint 13 14 15 10 (x_loc+part_xdim/2) (y_loc-part_ydim/2) (z_loc+p art_zdim/2) constraint 13 14 15 11 (x_loc+part_xdim/2) (y_loc+part_ydim/2) (z_loc+p art_zdim/2) constraint 13 14 15 12 (x_loc-part_xdim/2) (y_loc+part_ydim/2) (z_loc+p art_zdim/2) constraint 13 14 15

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98Appendix A (Continued) //vertices of liquid 13 (x_loc-part_xdim/2) (y_loc-part_ydim/2) 0 constr aint 7 19 20 21 22 14 (x_loc+part_xdim/2) (y_loc-part_ydim/2) 0 const raint 7 19 20 21 22 15 (x_loc+part_xdim/2) (y_loc+part_ydim/2) 0 const raint 7 19 20 21 22 16 (x_loc-part_xdim/2) (y_loc+part_ydim/2) 0 const raint 7 19 20 21 22 17 (x_loc-part_xdim/2) (y_loc-part_ydim/2) (z_loc-p art_zdim/2) constraint 13 14 15 16 17 18 (x_loc+part_xdim/2) (y_loc-part_ydim/2) (z_loc-p art_zdim/2) constraint 13 14 15 16 17 19 (x_loc+part_xdim/2) (y_loc+part_ydim/2) (z_loc-p art_zdim/2) constraint 13 14 15 16 17 20 (x_loc-part_xdim/2) (y_loc+part_ydim/2) (z_loc-p art_zdim/2) constraint 13 14 15 16 17 edges 1 1 2 no_refine fixed 2 2 3 no_refine fixed 3 3 4 no_refine fixed 4 4 1 no_refine fixed

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99Appendix A (Continued) 5 5 6 constraint 4 6 no_refine 6 6 7 constraint 1 6 no_refine 7 7 8 constraint 3 6 no_refine 8 8 5 constraint 2 6 no_refine 9 5 7 no_refine 10 9 10 constraint 4 5 no_refine 11 10 11 constraint 1 5 no_refine 12 11 12 constraint 3 5 no_refine 13 12 9 constraint 2 5 no_refine 14 9 11 no_refine 15 5 9 constraint 2 4 no_refine 16 6 10 constraint 1 4 no_refine 17 7 11 constraint 1 3 no_refine 18 8 12 constraint 2 3 no_refine 19 5 12 no_refine 20 6 9 no_refine 21 7 10 no_refine 22 8 11 no_refine

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100Appendix A (Continued) 23 13 14 constraint 7 19 20 21 22 24 14 15 constraint 7 19 20 21 22 25 15 16 constraint 7 19 20 21 22 26 16 13 constraint 7 19 20 21 22 27 17 18 constraint 13 17 28 18 19 constraint 13 14 29 19 20 constraint 13 16 30 20 17 constraint 13 15 31 13 17 32 14 18 33 15 19 34 16 20 faces 1 1 2 3 4 fixed no_refine color red 2 15 -13 -19 constraint 2 no_refine tension 0 color green 3 8 19 -18 constraint 2 no_refine tension 0 color g reen 4 6 21 -16 constraint 1 no_refine tension 0 color g reen 5 17 -11 -21 constraint 1 no_refine tension 0 color green 6 16 -10 -20 constraint 4 no_refine tension 0 color green 7 5 20 -15 constraint 4 no_refine tension 0 color g reen

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101Appendix A (Continued) 8 7 22 -17 constraint 3 no_refine tension 0 color g reen 9 18 -12 -22 constraint 3 no_refine tension 0 color green 10 -8 -7 -9 constraint 6 no_refine tension 0 color green 11 9 -6 -5 constraint 6 no_refine tension 0 color g reen 12 10 11 -14 constraint 5 no_refine tension 0 color green 13 12 13 14 constraint 5 no_refine tension 0 color green 14 26 31 -30 -34 tension TENSLW 15 24 33 -28 -32 tension TENSLW 16 23 32 -27 -31 tension TENSLW 17 25 34 -29 -33 tension TENSLW bodies 1 14 15 16 17 volume (0.7*(pad_xdim1)*(pad_ydim1)*( z_loc-part_zdim/2)) //commads executed when running the program read //references to other cmd files related with this m odeling read "calcplanes.cmd"// normal vector calculations read "change.cmd" // shift and rotate read "calcforce.cmd"// calculate forces, torques an d hessian

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102Appendix A (Continued) target_tolerance := 1e-17 // because of small volum e //display liquid only liquid_only := { set facet color clear where color == red or color == green} read "run_program.cmd" prepare:= { r;g10;r;g10;r;g20; g10; conj_grad; g20; }; logfile "selfassembly.log" ti_angle:= 90; quiet on; showq; prepare; find_zmin; new_x_loc := -40e-6*cos(ti_angle/180*pi); change_x_ loc; new_y_loc := -40e-6*sin(ti_angle/180*pi); change_y_ loc;

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103Appendix A (Continued) ti_CXstep := 20e-6*cos(ti_angle/180*pi); ti_CYstep := 20e-6*sin(ti_angle/180*pi); ti 6; ti_CXstep *= -1; ti_CYstep *= -1; //ti 21; quiet off ;

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104Appendix A (Continued) //main program for electrowetting force analysis //dimension of the plate parameter PART_XDIM = 9e-3 // [m] parameter PART_YDIM =9e-3 // [m] parameter PART_ZDIM = 1e-3 // [m] // location of plate ( midpoint) parameter X_LOC = 0// [m] parameter Y_LOC = 3e-3 parameter Z_LOC = 1.08e-3 // chip rotation parameter Z_ROT = 1 parameter X_ROT = 0 parameter Y_ROT =0 parameter TMOBILITY = 1 // dimensions of pad parameter PAD_XDIM = 20e-3 // [m] parameter PAD_YDIM = 20e-3 // [m]

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105Appendix A (Continued) // Physical properties parameter TENSLW = 46e-3 // [J/m^2] parameter TENSSW = 52e-3 // [J/m^2] parameter TENSLS = 1e-3 // [J/m^2] parameter height = Z_LOC-PART_ZDIM/2 parameter GAMMA_LV = 0.072 parameter E_r = 2.1 parameter E_o = 8.854e-12 parameter distance = 2.1e-6 parameter VOLTAGE = 100 parameter angle = 110 parameter topangle = 20 parameter GAP = 0.002 #define sx sin(X_ROT*pi/180) #define sy sin(Y_ROT*pi/180) #define sz sin(Z_ROT*pi/180) #define cx cos(X_ROT*pi/180) #define cy cos(Y_ROT*pi/180) #define cz cos(Z_ROT*pi/180)

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106Appendix A (Continued) // Nomenclature: // x,y,z : face perpend. to x,y,z axis // p: positive orientation n: negative orientatio n // 1,2,3: x,y and z component of vector // Axp = R (1,0,0), Axn = R (-1,0,0) #define Axp1 (cy*cz) // r11 #define Axp2 (sx*sy*cz+cx*sz) // r21 #define Axp3 (-cx*sy*cz+sx*sz) // r31 #define Axn1 (-cy*cz) // -r11 #define Axn2 (-(sx*sy*cz+cx*sz)) // -r21 #define Axn3 (-(-cx*sy*cz+sx*sz)) // -r31 // Ayp = R (0,1,0), Ayn = R (0,-1,0) #define Ayp1 (-cy*sz) // r12 #define Ayp2 (cx*cz-sx*sy*sz) // r22 #define Ayp3 (sx*cz+cx*sy*sz) // r32 #define Ayn1 (cy*sz) // -r12 #define Ayn2 (-(cx*cz-sx*sy*sz)) // -r22 #define Ayn3 (-(sx*cz+cx*sy*sz)) // -r32

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107Appendix A (Continued) // Azp = R (0,0,1), Azn = R (0,0,-1) #define Azp1 (sy) // r13 #define Azp2 (-cy*sx) // r23 #define Azp3 (cx*cy) // r33 #define Azn1 (-sy) // -r13 #define Azn2 (cy*sx) // -r23 #define Azn3 (-cx*cy) // -r33 // a reference point on the face #define Pxp1 (X_LOC + Axp1 PART_XDIM/2) #define Pxp2 (Y_LOC + Axp2 PART_XDIM/2) #define Pxp3 (Z_LOC + Axp3 PART_XDIM/2) #define Pxn1 (X_LOC + Axn1 PART_XDIM/2) #define Pxn2 (Y_LOC + Axn2 PART_XDIM/2) #define Pxn3 (Z_LOC + Axn3 PART_XDIM/2) #define Pyp1 (X_LOC + Ayp1 PART_YDIM/2) #define Pyp2 (Y_LOC + Ayp2 PART_YDIM/2) #define Pyp3 (Z_LOC + Ayp3 PART_YDIM/2) #define Pyn1 (X_LOC + Ayn1 PART_YDIM/2) #define Pyn2 (Y_LOC + Ayn2 PART_YDIM/2) #define Pyn3 (Z_LOC + Ayn3 PART_YDIM/2) #define Pzp1 (X_LOC + Azp1 PART_ZDIM/2)

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108Appendix A (Continued) #define Pzp2 (Y_LOC + Azp2 PART_ZDIM/2) #define Pzp3 (Z_LOC + Azp3 PART_ZDIM/2) #define Pzn1 (X_LOC + Azn1 PART_ZDIM/2) #define Pzn2 (Y_LOC + Azn2 PART_ZDIM/2) #define Pzn3 (Z_LOC + Azn3 PART_ZDIM/2) #define GAMMA_SL (-GAMMA_LV*(cos(angle*pi/180))) // virtual tension of facet on plane #define VOLT_LEFT (((Arightq.value+Aleftq.value)<1e -12)? 0.0:((Arightq.value/(Aleftq.value+Arightq.value))*V OLTAGE)) #define VOLT_RIGHT (((Arightq.value+Aleftq.value)<1 e-12)? 0.0:((Aleftq.value/(Aleftq.value+Arightq.value))*VO LTAGE)) #define GAMMA_LEFT (GAMMA_SL-(((E_o*E_r)/(2*distanc e))*(VOLT_LEFT^2))) #define GAMMA_RIGHT(GAMMA_SL-(((E_o*E_r)/(2*distance))*(VOLT_RIGHT^2))) #define left ((y<-GAP/2)? (y+GAP/2) : (0)) #define right ((y>GAP/2)? (y-GAP/2) : (0)) #define BTENS ((y<-GAP/2)?((GAMMA_LEFT*(y+GAP/2))-( GAP/2*GAMMA_SL)) : (y>GAP/2)?((GAMMA_RIGHT*(y-GAP/2))+(GAP/2*GAMMA_SL) ) : (y*GAMMA_SL))

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109Appendix A (Continued) #define UPPERT (-cos(topangle*pi/180)*GAMMA_LV) quantity Arightq INFO_ONLY method edge_vector_integ ral vector_integrand: q1: -(right) q2: 0 q3: 0 quantity Aleftq INFO_ONLY method edge_vector_integr al vector_integrand: q1: -(left) q2: 0 q3: 0 // Constraints for chip and pad (display only) constraint 1 // x+ formula: -(x Pxp1) Axp1 (y Pxp2) Axp2 ( z Pxp3) Axp3 = 0 constraint 2 // xformula: -(x Pxn1) Axn1 (y Pxn2) Axn2 ( z Pxn3) Axn3 = 0 constraint 3 // y+ formula: -(x Pyp1) Ayp1 (y Pyp2) Ayp2 ( z Pyp3) Ayp3 = 0

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110Appendix A (Continued) constraint 4 // yformula: -(x Pyn1) Ayn1 (y Pyn2) Ayn2 ( z Pyn3) Ayn3 = 0 constraint 5 // z+ formula: -(x Pzp1) Azp1 (y Pzp2) Azp2 ( z Pzp3) Azp3 = 0 constraint 6 // zformula: -(x Pzn1) Azn1 (y Pzn2) Azn2 ( z Pzn3) Azn3 = 0 constraint 30 nonnegative formula: z // Constraints for liquid ( calculation ) constraint 7 // keep glue above pad formula: z = 0 energy: e1: ( -BTENS) e2: 0 e3: 0 constraint 24 nonnegative // keep glue above substr ate formula: z constraint 25 nonnegative // keep glue above substr ate formula: z-(Z_LOC-PART_ZDIM/2) constraint 13 // zof chip z+ of glue formula: -(x Pzn1) Azn1 (y Pzn2) Azn2 ( z Pzn3) Azn3 = 0

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111Appendix A (Continued) energy: e1: (UPPERT) (Azn3) y e2: (UPPERT) (Azn1) z e3: (UPPERT) (Azn2) x content: c1: 0 c2:-((Pzn3 + Azn1/Azn3 Pzn1 + Azn2/Azn3 (Pzn2 y)) x Azn1/Azn3 x^2/2) c3: 0 // One-sided constraints for glue on chip. constraint 14 nonpositive // keep glue within pos x bound formula: (x Pxp1) Axp1 + (y Pxp2) Axp2 + (z Pxp3) Axp3 constraint 15 nonpositive // keep glue within neg x bound formula: (x Pxn1) Axn1 + (y Pxn2) Axn2 + (z Pxn3) Axn3 constraint 16 nonpositive // keep glue within pos y bound formula: (x Pyp1) Ayp1 + (y Pyp2) Ayp2 + (z Pyp3) Ayp3 constraint 17 nonpositive // keep glue within neg y bound formula: (x Pyn1) Ayn1 + (y Pyn2) Ayn2 + (z Pyn3) Ayn3 // One-sided constraints for glue on pad. constraint 19 nonnegative //one-sided x-constraint on pad formula: x-(0-PAD_XDIM/2)

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112Appendix A (Continued) constraint 20 nonpositive //one-sided x-constraint on pad formula: x-(0+PAD_XDIM/2) constraint 21 nonnegative //one-sided y-constraint on pad formula: y-(0-PAD_YDIM/2) constraint 22 nonpositive //one-sided y-constraint on pad formula: y-(0+PAD_YDIM/2) vertices 1 -PAD_XDIM/2 -PAD_YDIM/2 -1e-7 fixed 2 PAD_XDIM/2 -PAD_YDIM/2 -1e-7 fixed 3 PAD_XDIM/2 PAD_YDIM/2 -1e-7 fixed 4 -PAD_XDIM/2 PAD_YDIM/2 -1e-7 fixed //vertices of plate 5 (X_LOC-PART_XDIM/2) (Y_LOC-PART_YDIM/2) (Z_LOC-PA RT_ZDIM/2) constraint 13 14 15 16 17 6 (X_LOC+PART_XDIM/2) (Y_LOC-PART_YDIM/2) (Z_LOC-PA RT_ZDIM/2) constraint 13 14 15 16 17 7 (X_LOC+PART_XDIM/2) (Y_LOC+PART_YDIM/2) (Z_LOC-PA RT_ZDIM/2) constraint 13 14 15 16 17 8 (X_LOC-PART_XDIM/2) (Y_LOC+PART_YDIM/2) (Z_LOC-PA RT_ZDIM/2) constraint 13 14 15 16 17

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113Appendix A (Continued) //vertices of Liquid 13 (X_LOC-PART_XDIM/2) (Y_LOC-PART_YDIM/2) 0 constr aint 7 19 20 21 22 30 14 (X_LOC+PART_XDIM/2) (Y_LOC-PART_YDIM/2) 0 const raint 7 19 20 21 22 30 15 (X_LOC+PART_XDIM/2) (Y_LOC+PART_YDIM/2) 0 const raint 7 19 20 21 22 30 16 (X_LOC-PART_XDIM/2) (Y_LOC+PART_YDIM/2) 0 const raint 7 19 20 21 22 30 17 (X_LOC-PART_XDIM/2) (Y_LOC-PART_YDIM/2) (Z_LOC-P ART_ZDIM/2) constraint 13 14 15 16 17 18 (X_LOC+PART_XDIM/2) (Y_LOC-PART_YDIM/2) (Z_LOC-P ART_ZDIM/2) constraint 13 14 15 16 17 19 (X_LOC+PART_XDIM/2) (Y_LOC+PART_YDIM/2) (Z_LOC-P ART_ZDIM/2) constraint 13 14 15 16 17 20 (X_LOC-PART_XDIM/2) (Y_LOC+PART_YDIM/2) (Z_LOC-P ART_ZDIM/2) constraint 13 14 15 16 17 edges 1 1 2 no_refine fixed 2 2 3 no_refine fixed 3 3 4 no_refine fixed 4 4 1 no_refine fixed

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114Appendix A (Continued) 5 5 6 constraint 4 6 no_refine 6 6 7 constraint 1 6 no_refine 7 7 8 constraint 3 6 no_refine 8 8 5 constraint 2 6 no_refine 23 13 14 constraint 7 19 20 21 22 30 Aleftq Arigh tq 24 14 15 constraint 7 19 20 21 22 30 Aleftq Aright q 25 15 16 constraint 7 19 20 21 22 30 Aleftq Aright q 26 16 13 constraint 7 19 20 21 22 30 Aleftq Aright q 27 17 18 constraint 13 17 28 18 19 constraint 13 14 29 19 20 constraint 13 16 30 20 17 constraint 13 15 31 13 17 constraint 30 32 14 18 constraint 30 33 15 19 constraint 30 34 16 20 constraint 30 faces 1 1 2 3 4 fixed no_refine color red 2 5 6 7 8 no_refine tension 0 color green

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115Appendix A (Continued) 14 26 31 -30 -34 constraint 30 tension GAMMA_LV 15 24 33 -28 -32 constraint 30 tension GAMMA_LV 16 23 32 -27 -31 constraint 30 tension GAMMA_LV 17 25 34 -29 -33 constraint 30 tension GAMMA_LV bodies 1 14 15 16 17 volume 4.7e-8//(PART_XDIM*PART_YDIM*( Z_LOC-PART_ZDIM/2)) read read "calcplanes.cmd"// normal vector calculations read "change.cmd" // shift and rotate read "calcforce.cmd"// calculate forces, torques an d hessian read "xyz.cmd" target_tolerance := 1e-17 // because of small volum e //new_X_LOC := -40e-6*cos(ti_angle/180*pi); change_ X_LOC; //new_Y_LOC := -40e-6*sin(ti_angle/180*pi); change_ Y_LOC; //ti_CXstep := 20e-6*cos(ti_angle/180*pi); //ti_CYstep := 20e-6*sin(ti_angle/180*pi);

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116Appendix A (Continued) doinit:= { r;g 10; r; g10; conj_grad; g10; refine edges where on_cons traint 1; g10; g10; } dostep:= { conj_grad on; g10; conj_grad off; g 50; {V;u;V} 4; g50; conj_grad on; g10; conj_grad off; g50; } // g until glue has calmed down cgl_TOL := 5e-7; calm_glue := { //printf "cgl: %15.15g -> ",total_energy >> "ti_log .txt"; conj_grad off; g10; conj_grad on;

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117Appendix A (Continued) g20; do { cgl_old_e := total_energy; g 10; } while (abs((cgl_old_e-total_energy)/total_energy)> cgl_TOL); //printf "%15.15g -> %15.15g\n",cgl_old_e,total_ene rgy >> "ti_log.txt"; }; Vout:= { printf "VLeft %15.15g\n", ((Arightq.value+Aleftq.va lue<1e-12)? 0.0:(Arightq.value/(Aleftq.value+Arightq.value))*VO LTAGE); printf "vright %15.15g\n", ((Arightq.value+Aleftq.v alue<1e-12)? 0.0:(Aleftq.value/(Aleftq.value+Arightq.value))*VOL TAGE); };

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118Appendix A (Continued) gout:= { printf "GLeft %15.15g\n", ((-GAMMA_LV*(cos(angle*pi /180)))(((E_o*E_r)/(2*distance))*(((Arightq.value+Aleftq.v alue)<1e-12)? 0.0:((Arightq.value/(Aleftq.value+Arightq.value))*V OLTAGE)^2))); printf "Gright %15.15g\n", ((-GAMMA_LV*(cos(angle*p i/180)))(((E_o*E_r)/(2*distance))*(((Arightq.value+Aleftq.v alue)<1e-12)? 0.0:((Aleftq.value/(Aleftq.value+Arightq.value))*VO LTAGE)^2))); printf "Gsl %15.15g\n", (-GAMMA_LV*cos(angle*pi/180 )); }; run_analysis:= { doinit; dostep; calm_glue; } run:= { doinit;

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119Appendix A (Continued) dostep; calm_glue; forces; v; vout; gout; } fz_TOL := 1e-9; fz_movlim:=0.01e-3; fz_maxit:=30; find_zmin := // by Newton-Raphson { fz_it :=0; do { fz_it += 1; fz_old_CZ := Z_LOC; fz_old_energy := total_energy; // save old values calc_zf ; // calculate derivative fz_hstr := dEdz;

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120Appendix A (Continued) fz_alpha := -dEdz/d2Edz2; // Newton // Apply motion limit if ( fz_alpha > 0 ) then fz_alpha:=minimum(fz_alpha ,fz_movlim) else fz_alpha:=maximum(fz_alpha,-fz_movlim); // Shift micropart new_Z_LOC := fz_old_CZ + fz_alpha; change_Z_LOC; calm_glue; // Backtracking scheme, if Newton failes if ( total_energy>fz_old_energy) then { fz_alpha := fz_hstr *fz_alpha^2/(2*(total_energy -fz_hstr*fz_alpha-fz_old_energy)); new_Z_LOC := fz_old_CZ + fz_alpha; change_Z_LOC; calm_glue; }; printf "fz %g: Z_LOC: %10e, l: %10e, old_Z_LOC:%10e \n", fz_it ,Z_LOC,fz_alpha,fz_old_CZ >> "ti_log.txt"; } while (abs(fz_old_CZ-Z_LOC)>fz_TOL) and (fz_it

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Analysis of capillary forces in electrowetting and precision self assembly
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by Vivek Ramadoss.
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[Tampa, Fla] :
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2008.
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Thesis (M.S.M.E.)--University of South Florida, 2008.
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ABSTRACT: Developments in micro and nano technology have great potential in many applications. Two applications that will be addressed in this work are self assembly of microdevices and Electrowetting in microfluidics. Capillary forces are the most critical factor in both of these techniques and need proper characterization. This thesis describes a detailed study of these forces and explains how they were utilized as an effective source of drive in high end applications. Self assembly is a promising alternative to conventional pick and place robotic assembly of micro components. Its benefits include parallel integration of parts with low equipment costs. Various approaches to self assembly have been demonstrated, yet demanding applications like assembly of micro-optical devices require increased positioning accuracy. This thesis proposes a new method for design of self assembly bonds that addresses this need.Current methods have zero force at the desired assembly position and low stiffness. The proposed method uses a substrate assembly feature to provide a high accuracy alignment guide to the part. The capillary bond region of the part and substrate are then modified to create a non-zero positioning force to maintain the part in the desired assembly position. Capillary force models show that this force aligns the part to the substrate assembly feature and reduces the sensitivity of part position to process variation. Thus, the new configuration analyzed proves substantial improvement in positioning accuracy of capillary self assembly. Guidelines are proposed for the design of an effective assembly bond using this new approach. Electrowetting is another application that has been successfully demonstrated as a means of drop manipulations in digital micro-fluidic devices.These demonstrations show that electrowetting actuation holds great promise, but there are also reports of erratic behavior and system degradation. While a method for electrowetting force measurement to track the degradation of the electrowetting response was demonstrated, this thesis analyzes some adverse effects in the electrowetting response due to variations during measurement of electrowetting forces, specially the variation of volume, the tilt in the part considered for measurements, and defective layer response.
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Advisor: Nathan Crane Ph.D.
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