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Modeling and experimentation of micro-scale self-assembly processes
h [electronic resource] /
by Gary Hendrick.
[Tampa, Fla] :
b University of South Florida,
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Thesis (MSME)--University of South Florida, 2010.
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ABSTRACT: Self-Assembly in the context of micro-scale integration refers to a developing set of techniques which exploit phenomena resulting in the spontaneous integration of micro-scale components into designed systems. Self-Assembly may be leveraged most effectively in parallel assembly processes. This thesis studies the modeling of micro-scale self-assembly processes as stochastic processes. The researchers propose that self-assembly processes may be modeled as Markov chains. In order to develop these models a Self-Assembly test system was created and trials were conducted using this system. Initial tests into the hypothesis that variables contributing to the transition probabilities include the kinetic energy of the assembly interaction, the energy minimized during assembly, and the area fraction of bonding sites on the assembly surface are tested.
Advisor: Dr. Nathan Crane
x Mechanical Engineering
t USF Electronic Theses and Dissertations.
Modeling and Experimentation of Micro Scale Self Assembly Processes b y Gary Hendrick A thesis submitted in partial fulfillment of the requir ements for the d egree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Nathan Crane, Ph. D. Nathan Gallant, Ph. D. Alex Savachkin, Ph. D. Date of Approval: July 7 2010 Keywords : Assemblies, Micro I ntegration, Capillary Forces, Stochastic Processes Assembly Kinetics Copyright @ 2010 Gary Hendrick
ACKNOWLEDGEMENTS This work was conducted in part through funding from NSF grant CMMI 092637 and with the help of James Tuckerman, Brian Bertram, Mario Juha Sean Hollis and Nathan Crane, Ph.D
i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv ABSTRACT v i CHAPTER 1 : INTRODUCTION 1 1.1 Motivation 2 1.2 Scope 4 1.3 Outline 4 CHAPTER 2 : BACKGROUND 6 2.1 Surface Tension 6 2.2 Modeling Chemical Kinetics 9 2.3 Prior Art 16 2.3.1 Demonstrations of Self Assembly Process es 17 2.3.2 Modeling Self Assemblin g Systems 19 2.3.3 Application of Chemical Kinetics to Self Assembly 24 CHAPTER 3 : PROPOSED MODEL 29 3.1 System Model 29 3.1.1 Simulation of Stochastic Processes 31 3.1.2 Subject Model 32 3.2 Unit Cell Modeling 34 3.2.1 Modeling of Assembly Dynamics 34 CHAPTER 4 : SELF ASSEMBLY TEST SYSTEM 36 4.1 Requirements 36 4.2 Methods 37 4.2.1 Test Apparatus 39 4.2.2 Assembly Site Mount 40 4.2.3 Active Face Fraction 46 4.2.4 Assembly Component Fabrication 4 8 4.2.5 Bond Energy 50 126.96.36.199 Verification of Oil Deposition 52 4.2.6 Kinetic Energy Design 5 5 4.2.7 Energy Ratio: Kinetic Energy to Bond Energy 6 3
ii CHAPTER 5 : EXPERIMENTATION AND RESULTS 6 6 5.1 Experiment al Parameters 7 1 5.1.1 Energetic Relationships 7 1 188.8.131.52 Kinetic Energy in Trials 7 1 184.108.40.206 Bond Energy in Trials 7 2 220.127.116.11 Energy Ratio in Trials 7 3 5.1.2 Geometric Relationships 7 3 5.2 Experimenta l Results 7 8 5.3 Comparison to Hypotheses 7 8 5.3.1 Trial A 1 8 0 5.3.2 Trial B 1 8 1 5.3.3 Trial B 2 8 2 5.3.4 Trial B 3 8 3 5.3.5 Trial B 4 8 6 CHAPTER 6 : CONCLUSIONS 9 0 6.1 Future Work 9 1 LIST OF REFERENCES 9 4 APPENDICES 9 7 Appendix A: Assembly Mount 1 Drawing 9 8 Appendix B: Assembly Mount 2 Drawings 9 9 ABOUT THE AUTHOR End Page
iii LIST OF TABLES Table 4 1: Contact a ngles for c opper t reated with 1mM Octadecanethiol SAM at various interfaces ..................... 50 Table 4 2: Site contact angles by treatment ................................ .. 53 Table 4 3: Velocity m rts through H 2 O and 40% g lycerol s olution ................................ ..... 61 Table 5 1: Assembly t rial details ................................ .................. 68 Table 5 2: Kinetic energy for trials ................................ ............... 7 2 Table 5 3: Bond energy and associated parameters for assembly trials ................................ .......................... 7 2 Table 5 4: Energy ratio for assembly trials ................................ .... 7 3 Table 5 5 : Trial A 1 assembly geometry ................................ ........ 75 Table 5 6 : Trial B series assembly geometry ................................ .. 77 Table 5 7 : Assembly yield predictions ................................ ........... 77 Table 5 8 : Trial results and yield predictions ................................ .. 78
iv LIST OF FIGURES Figure 1 1: Assembly r ate v ariations with c omponent s ize ................ 3 Figure 2 1: One half of a spherical liquid drop with forces. ................ 7 Figure 2 2: Three p hases of f luid i nterface ................................ ...... 8 Figure 2 3: Young's l aw with planar geometry simplification .............. 9 Figure 2 4: First and second order reaction rate laws .................... 14 Figure 2 5: Possible assembly states for Hosokawa study. ............... 27 Figure 3 1: The two assembly states of the proposed model.. .......... 30 Figure 3 2: An illustration of the proposed Markov chain model.. ..... 33 Fi gure 3 3: The assembly unit cell ................................ ................ 34 F igure 4 1: Assembly e nvironment ................................ ............... 38 Figure 4 2 : Distribution of random parts a fter introduction ............. 40 Figure 4 3: Assembly mount.. ................................ ...................... 41 Figure 4 4: Original design of assembly mount.. ............................ 42 Figure 4 5: Sites with assembled parts ................................ ......... 45 Figure 4 6: Site p attern s chematic ................................ ............... 45 Figure 4 ....... 47 Figure 4 8: The geometric limit of assembly for a prismatic part ...... 48 Figure 4 9 : Goniometer i mage of a droplet of oil applie d to a site ..... 52 Figure 4 10 : Assembly site strip with oil bridging assembly sites ...... 52 Figure 4 11 : Oiled sites ................................ ............................... 53 Figure 4 1 2 : Contact a ngles for sites before washing with pipette .... 54 Figure 4 13: Contact angles for assembly sites after washing .......... 54 Figure 4 1 4 : Variati ons in terminal velocity ................................ ... 57 Figure 4 15: Stroboscope image of falling parts in fluid .................. 59 Figure 4 1 6 : Falling p art v elocity i mages ................................ ....... 61 Figure 4 1 7 : Linear r egression from time trial ................................ 62 Figure 4 18: Assembly c ondition in the grey region. ...................... 64 Figure 5 1: Fabricated parts ................................ ....................... 6 7 Figure 5 2: Assembly sites with bubbles ................................ ....... 69 Figure 5 3: Assembly array after purging of bubbles ....................... 70 Figure 5 4: Projected assembly area as a function of mount angle ... 75 Figure 5 5: Predicted yield curve with trial A 1 data point ............... 79 Figure 5 6 : Predicted and r esultant y ields for trials. ........................ 80 Fi gure 5 7 : Parts shown adhering to the copper site strips.. ............ 81 Figure 5 8 : Trial B 2 assembly results ................................ .......... 83 Figure 5 9 : Trial B 3 assembly. ................................ .................... 84 Figure 5 10 : Successfully bound part in assembly trial B 3 .............. 85 Figure 5 1 1 : An accretion of parts observed in assembly trial B 3. ... 86
v Figure 5 1 2 : Results of trial B 4 ................................ ................... 87 Figure 5 1 3 : Parts resting on assembly sites. ................................ 88 Figure A 1 : Original a ssembly mount design ................................ ... 9 8 Figure B1: Final design for assembly mount base ......................... 99 Figure B2: Final design of assembly mount shelves. ..................... 10 0
vi Modeling and Experimentation for Micro Scale Self Assembly Processes Gary Hendrick ABSTRACT Self Assembly in the context of micro scale integration refers to a developing set of techniques which exploit phenomena resulting in the spontaneous integration of micro scale components into designed systems Self Assembly may be leveraged most effectively in parallel assembly processes This thes is studies the modeling of micro scale self assembly processes as stochastic processes The researchers propose that self assembly process es may be modeled as Markov chains. In order to develop these models a Self Assembly test system was created and trials were conducted using this system. Initial tests into the hypothesis that variables contributing to the transition probabilities include the kinetic energy of the assembly interaction, the energy minimized during assembly, and the area fraction o f bonding sites on the assembly surface are tested
1 CHAPTER 1: INTRODUCTION The thesis presented here reports on work undertaken by the author in the University of South Florida micro integration lab This work focused on the development of predictive m odels for micro scale s elf a ssembly processes and the tools for verifying those models. Self Assembly is a promising new method for micro and nano scale integration processes The technology is not yet widely implemented in industrial processes and the maj ority of work in the field is in basic research. T his thesis likewise focuses on basic research into self assembly processes The following definition of Self Assembly, can be found in John Self Assembly: The Science of Things That Put Themse lves Togeth er : assembly refers to the spontaneous formation of organized structures through a stochastic process that involves pre existing components is reversible, and can be controlled by proper design of the components, the environment, and the driving  The term self assembly may be applied to behavior at any scale and its characteristics are observed in a wide variety of systems. The
2 research presented here focuses on the assembly of mechanical components at the micro scale. 1.1 Motivation The case for the need for means to integrate micro scale components through self assembly is made by Morris, et al.  In this work, the researchers synthesize data on assembly rates of various sized components in order to explore the relationship between component size and rate of assembly. The y make the argument that the rate of assembly using traditional assembly methods finds its global maxima at At this point component size has dropped to the point that inertial forces play a small part in the process. Assemblies conducted with traditi onal methods at this scale tend to result in simple 2D shapes. T he assembly rate decreases for c omponents smaller than 300 possibl y due to a greater difficulty in grasping parts or to the relatively high inertia of the assembly mechanisms in compariso n to the parts themselves. Figure 1 1 The potential of self assembly lies in the application of the technology to change the na ture of the curve throughout t he section indicated This section indicates the region of the rate/size relationship which may be realized
3 through the development of Self Assembly methodologies for micro s cale assembly. The widespread industrial application of self assembly technologies requires that predictive models for the processes be developed Through modeling self assembly processes may be accurately analyzed allowing process de signers to effectively predict the behavior of these processes With the maturation of self assembly techniques a wide range of constraints traditionally associated with modern robotic assembly processes will be lifted. The use of self assembly techniques in electronics packaging specifically will have implications to the fabrication of semi conducting devices allowing for improvements in a number of important performance parameters such as heat flux improvements due to new possibilities in the design of Figure 1 1 : Assembly r ate v ariations with c omponent s ize .
4 c omponent geometry and cost reductions due to reductions in loss of bulk material as component sizes may be reduced to take advantage of a greater capability to assemble components with smaller characteristic dimensions. 1.2 Scope This thesis presents basic research into capillary driven self assembly. Much of the work conducted throughout the course of the research period dealt with the development of the techniques required to run the self assembly trials presented in the section These techniques include the application of surface treatments, the measurement of key process parameters, and the use of automation technologies to aid in the repetition of tests. This document itself reports on relevant background, modeling, p reparation and experimentation with capillary driven self assembly processes 1.3 Outline Chapter 1 of th is document present s an introduction to the document, the motivations behind conducting this research and its scope. The second chapter, Background, expl ores the prior art of modeling applicable to self assembly These models includ e those
5 adopted from chemical kinetics surface energy modeling, and the modeling of stochastic processes. Chapter 3 Proposed Model, contains a description of the novel model of self assembly proposed in the thesis. The details of the stochastic model of the assembly system are presented along with a unit cell model describing the dynamics of individual interactions. The fourth chapter presents the testing methods developed by the researchers along with the results of the tests used to validate the models. The methods section includes descriptions of the test apparatus developed for this system. The results include an analysis of the test results and comparison to model predicti ons. The fifth and final chapter Conclusions, includes both conclusions drawn from the thesis, and plans for future works to be accomplished at the USF micro integration lab.
6 CHAPTER 2: BACKGROUND Self assembly is a broad topic. The application of self assembly to micro scale component integration may be achieved through the application of capillary forces to self assembly Th is chapter provides background necessary to understand the phenomena at wo rk during the assembly processes under investigation, general data on the nature of self assembling systems, and an exploration of prior art in the field. 2.1 Surface Tension Surface tension occurs at the interface between two immiscible fluids or at th e interface between a gas and a liquid. This tension is caused by unbalanced cohesive forces at the interface. Molecules at the surface of the fluid are subject to a net inward force while those within the fluid experience equal forces in all directions. These unresolved forces appear to create a hypothetical membrane at the interface which can be characterized by surface tension which has units of Force per L ength and is designated by the G reek symbol [21 ] This tension can be used in self assembly processes to bind assembly components, and has been demonstrated to be useful
7 for such purposes [11, 14, 22] These cases ar e discussed in greater detail below First, a more complete description of the mechanisms behind capillary binding and surface energy minimization follows. Due to surface tension an interface develops pressure This pressure can be used to determine the force at the interface. The force is balanced by the pressure differential between the internal and external pressures acting over the area of surface. For the spherical drop shown in F igure 2 1 the force at the edge of the drop is This force is balanced in the Equation 2 1 Surface energy is the work associated with the interface through the Greek sy Specific surface energy and surface tension are different terms for the same quantity and with the same magnitude. These quantities will be referred to as surface energy throughout this Equation 2 1 Figure 2 1 : One half of a spherical liquid drop with forces R p R 2
8 document. When a fluid wets a surface through capillary action it seeks a minimum surface energy. Figure 2 2 shows a three phase diagram of an interface. This interface is in equilibrium when the conditions of Equation 2 2 Equation 2 3 and Equation 2 4 are met. In equilibrium the net forces along each interface are equal to 0. Figure 2 2 : Three p hases of f luid i nterface Equation 2 2 Equation 2 3 Equation 2 4 in Figure 2 2 to that of a flat plane so that as is the case when a droplet is set upon a rigid surface. In the case that this model is phase is a surrounding gas or immiscible fluid, angle of the fluid interface. This permits the three surface tensions and single contact angle to describe the i nterface. The resulting forces can be illustrated as shown in Figure 2 3
9 The Young Dupre equation is shown in E quation 2 5 and is derived from E quation 2 3 using the above relationship for Within this relationship the contact angle o describe wettability such that interfaces resting on a solid, rigid plane the fluid is water, wettable solids a re referred to as hydrophilic while non wettable solids are referred to as hydrophobic. 2. 2 Modeling Chemical Kinetics Stochastic modeling for the dynamics of self assembly processes presents a promising avenue toward developing useful modeling tools for industrial adoption of self assembly processes. The application of accurate models to the design of self assembling systems at the micro scale will aid process designers and self assembly researchers to effectively scale successful self assembly systems and to apply these Equation 2 5 Figure 2 3 : Young's l aw with planar geometry simplification. LG SG SL
10 processes to new integration scenarios The yield problem, defined as problem of predicting the final amount of complete bodies in an arbitrarily given self assembling system  is an important question for the design of self assembling systems. The exploitation of existing models for the purpose of answering the yield problem has been undertaken by several research groups.  Ma ny of the models adapted for application to self assembling micro scale systems were originally developed for the analysis of molecular structures. The problem of applying these models to micro scale self assembly has to do with adapting the molecular models to micro scale systems. In a micro scale application the legacy of the science describing bulk chemical processes are only tangentially applicable and for similar tools to become available in micro scale self assembly the basis of the process models must be revised Some key differences which must be observed in scaling these processes up include a change in several order of magnitude for the concentration of reagents and the rate of reaction as well as large reductions in the complexity of shape and specificity in micro scale parts as compared to their molecular analogues. This section explores the scientific models used to describe chemical kinetics in order to identify the aspects of these models which are applicable to the kinetics of self assembly at the micro scale. An
11 exploration of rate equations for chemical reactions will provide the background for a review of several important studies. A reaction can be represented with the notation: Equation 2 6 Wherein the left side of the equation represents react ants and the right side of the equation represents products. The stoichiometric number for each component of the reaction is represented in the balanced equation above by a coefficient placed before the component symbol. The stoichiometric number for A in E quation 2 6 is a, for B it is b, and for the product X is c. The above notation also expresses the order of the reaction. The order of a reaction in respect to a reactant is the power to which that reactant is raise in the equation. The above reaction is a first order reaction with respect to A, a first order reaction with respect to B and it has the overall order of 2 which is found by summing the order of reaction for each reactants. reacti on moves forward, left to right in E quation 2 6 and negative if the reaction moves backward. Rate equations typically consider the concentration of reactants and products rather than quantities. This is accomplished by dividing both sides of the equation by the volume V, and these concentrations are r epresented by placing the component
12 products and positive for reactants and is equivalent to the rates of change of the concentration of each component divided by the reciprocal of the compone above, these rates balance as follows in E quation 2 7 Equation 2 7 The rate of the reaction may also be described through the use of a rate constant, k, and orders for the reaction signified by powers for the components of the reaction. The rate constant and the orders of the reaction with respect to each reactant must be determined experimentally. The orders of the reaction relative to the reactants are E quation 2 8 and may take the form of any number and is not necessarily an integer. Equation 2 8 It is clear that in chemical kinetics the rate of the reaction is dependent upon the order of that reaction. The order of the reaction with respect to A is expressed as The order of the reaction with respect to B is The overall order of reaction is e qual to + In the self assembly studies concerned with kinetics which are examined later in this chapter only first order reactions are considered The following discussion of reaction concentrations over time and rate equations follows the development from Alberty 
13 A reaction of the form A > products is a first order reaction with the rate equation Equation 2 9 Integrating the preceding with t 1 taken to be 0 and the initial concentration represented as [A] 0 yields the following Equation 2 10 In order to better understand the effect of reaction order upon the rate it is helpful to compare this first order reaction to a second order reaction. A second order reaction dependent upon the square of the reactant and taking the form follows the rate law Equation 2 11 Integrating the preceding with t 1 taken to be 0 and the initial concentration represented as [A] 0 yields the following Equation 2 12 A comparison of the concentration of reactants in the cases of first and second order reactions i s illustrated in F igure 2 4
14 Figure 2 4 : First and second order reaction rate laws In the case of a first order reaction the rate of reaction is proportional to only the concentration of a single reactant i.e. The rate constant, k, for the rate equation may be calculated by linearizing the plot of time vs. the concentration of the reactant and taking the negative of the slope of the line. Equation 2 13 In the case of a second order reaction, the rate of reaction is proportional to the product of the concentrations of two reactants, or to the square of a single reactant. In the case of a single second order reactant the rate equation will take the form be low Equation 2 14 [A] t 1st Order 2nd Order [A] 0 [A] 0 0
15 The rate constant for the reaction can be found through integration and rearrangement as in Equation 2 15 Equation 2 15 In the case of a second order reaction in which the rate of reaction is proportional to the product of the concentrations of two reactants the rate equation is shown in Equation 2 16 and the rate constant can be shown to be equal to Equation 2 17 Equation 2 16 Equation 2 17 Given these basic relationships for various reactions it is necessary to consider the methods by which the rate equation may be determined experimentally The description of this procedure follows the treatment by Alberty pp. 625 637 . For the reaction A + 2B = X, the rate equation takes the form seen in Equation 2 8 above In order to avoid complications in determining the rate due to the formation of the product X instantaneous rate measurements made before the product concentrations become significant and may be considered to be absent.
16 The process of determining the rate equation requires experimental data which, in the case of chemical kinetics, is often the result of successive measurements using methods such as light absorption to develop experimental points for c/ t And extrapolate that data back to t = 0. This data may be used to fit lines for the rel ationship [A] vs. time. If data on only the first 10% of the reactions are used, a linear regression to fit the concentration to the equation [X]/t = b + ct will be sufficient. The parameter b is the initial forward reaction rate of the reaction Usin g successive sets of measurements with variations in the initial concentration of the reactant in question [A] 0 will allow the relationship between and This relationship will reveal a slope equal to the order of the reaction. The preceding tools from the study of chemical kinetics have been applied to the study of micro scale self assembly . This will be addressed in greater detail in the section entitled 2. 3 Prior Art Micro Scale Self Assembly has been studied for some time and demonstrations of the application of self assembly processes have been conducted in an experimental setting and recently in a
17 commercialized process by Alien Technology Inc. The body of work available for review in literature includes a number of demonstrations of self assembly for micro scale integration as well as a several techniques for modeling these processe s These previous effor ts are described below 2.3.1 Demonstrations of Self Assembly Processes Parallel fluidic self assembly on the micro scale has been explored extensively over the course of the past two decades. Demonstrations of self assembly processes have typically accompanied exploration of the underlying principles of self assembly The techniques applied in these processes will be discussed immediately and the import ance of their underlying principles will be covered in following sections. One of the earliest explorations of micro scale self assembly was conducted by Yeh, et al. who demonstrated a technique in which GaAs light emitting diodes were fabricated with a sh aped features were introduced into a fluidic transport and washed over a silicon substrate containing complimentary shaped binding sites to control position and orientation [3, 4] This work rep orted a 90% fill ratio for the holes while immersed in carrier fluid, but degradation after evaporation due to surface tension reduced the yield to a fill ration between 30 and 70
18 percent This degradation in total yield is a direct result of relying exclu sively on gravity, a relatively weak force at this scale, to fix parts into place. The g ravitational forces were easily overcome by capillary forces during the drying process causing many parts to shift out of their previously stable positions. Yeh referred to th e process combining fluid transport and shape recognition between part and substrate as Fluidic Self Assembly (FSA). A later study from the same researcher group authored by Ashish Verma, provides a formal definition of FSA as follows. [Fl uidic Self Assembly] involves the placement of devices fabricated onto specifically material into similarly shaped receptacle holes made on a substrate of some other material.  FS A remains an important method in self assembly and has been improved upon and used successfully in numerous research endeavors exploring both modeling of self assembly and the techniques and methods necessary to implement self assembly industrially [3 9] The initial explorations into FSA inclu ded trapezoidal parts and holes which required novel fabrication processes. This would limit the ultimate applicability of the FSA process as any self assembly process must consider the integration of parts fabricated using traditional methods.
19 2.3.2 Mod eling Self Assembling Systems The exploration of self assembling behavior for the micro scale has led to a number of important observations. Simple mechanical assembly models conducted in two dimensions have been used for these purposes by Hosokawa, et al. Self  is section of this thesis. In this work solid triangles were vibrated on a surface and the emerging assembled structures were observed and used to validate a predictive model of the yield of the process. Hosokawa again employed these methods in 1999 to describe the behavior of a two dimensional self assembly for parts on a liquid air interface in which the parts were fabricated with a curved feature  In that study, Hosokawa also explored the effect of menisci upon assemblie s at a liquid liquid interface, demonstrating that parts with similar shapes but dissimilar menisci were mutually repulsive. The study of the two dimensional assembly at the interface between fluids and the behavior of components at these interfaces has b een explored by other research ventures. T he practice of controlling individual properties of otherwise shape identical assembly components has been successfully applied in several demonstrations of
20 two and three dimensional assembly at interfaces. These t echniques are capable of providing control over the shape and behavior of integrated structures of shape identical parts through the application of surface property patterning The Whitesides group, working out of the Department of Chemical Biology at Har vard University, has applied such principles in several noteworthy cases In 1999 they published works rega rding the two dimensional self assembly of micro scale components at a liquid liquid interface between an organic liquid and an aqueous liquid [12, 13] In both studies, they explored the potential of using capillary assembling components, and how variations in the bonding forces and the interaction environ ment affect the assembly structures. In order to mimic the behavior of biological systems in which specificity is governed by shape recognition and hydrophobic patterning t hey varied the patterning of hydrophobic hydrophilic areas on the assembly component s, the shape of the menisci at the edges of the parts through variations in density or surface energy of the part surfaces, and the densities of the three interacting phases of the organic liquid, aqueous liquid and polymeric solid. These studies demonstra ted how complex behavior can arise out of small variations in a limited set of building blocks [12, 13] In 2003, this laboratory continued its work on the application of c apillary
21 interactions thro ugh an exploration of interactions of hexagonal plates at a liquid liquid interface self assembling into two dimensional arrays  Again, the components of the assembly were shape identical PDMS hexagons they were prepared with five different permutations of hydrophobic and hydrophilic faces, and they were doped with varying degrees of aluminum oxide in order to affect their density and thus the shape of their menisci. This work compliments the 1999 [12, 13] work completed with similar parts but adds the complexity of having both positive and negative menisci associated with the assembly. Work such as that described above has continued to influence t he development of principles such as shape, and pattern recognition in self assembly. The Whitesides group has since continued to develop its work and extend their exploration of the principles of self assembly to observe new phenomena. In the year 2000 th ey published work on the three d imensional self assembly of micro scale hexagonal rods  between self assembling components. This new work is similar to pr evious studies in that it shares the quality of exploring the behavior of parts fabricated identically and agitated within a self assembly environment in order to express complex final structures through variations in surface properties. As de monstrated with the studies of
22 hexagonal plates at a liquid liquid interface [12, 13] this study successfully demonstrated a single shape of building block expressing numerous final structures with differences in size of section, structure, and stability Furthermore, alignment of the parts through capillarity was also observed, a strategy exploited in many capillary driven self assembly processes This work has continued to develop into further stu dies of the effect of capillary forces on the shape and structure of 3 D micro scale assemblies through self assembly processes I n 2002, more complex 3D structure s were integrated through self assembly including a helical electrical circuit modeled after t he tobacco mosaic virus In this study the researchers developed strategies for applying varied surface properties to control complex structures out of shape identical parts. The foc us in this case was to explore s ystems of orthogonal interactions in which the driving force for assembly was a capillary force from one of two interactions caused by the coalescing of either perfluorodecalin, PFD, or a molten solder, the pair of which do not interact with one another  Cylindrical Display by Patterned Assembly  in which they depart from the liquid liquid interfaces with lateral capillary action and instead assembl ed components onto a non planer substrate using low melting
23 point solder on the binding sites to act as both electrical and mechanical connections first to a lower electrode, then to a wafer of similarly patterned sites on an upper electrode. The process u sed first a set of 113 LEDs agitated in a bath with a cylindrical substrate onto which the LEDs fully assembled. The researchers then coated the top of the LEDs with solder and patter n ed solder to binding sites on a film containing the top electrodes for t he assembly. The entire assembly was heated again after hand placing the two sides in contact and the upper electrodes were bound to the assembled LEDs on the lower electrode successfully. The same procedure was applied to a larger assembly in which 1600 r eceptors and silicon blocks were assembled similarly with 98% coverage and an alignment accuracy of ~3 and was completed in roughly 3 minutes These assemblies illustrate strengths of self assembly including the speed of process through parallel self asse mbly and the capability to assemble functional non planar assemblies. The detailed descriptions of modeling and process design included in the cited literature are representative of the state of the art in research, and many of those processes include sta tistics for rate of assembly and other performance parameters in processes conducted as proof of concept. The Alien Technologies process is not available for review however, according to Mastrangeli, et al. the company claims
24 that its process is capable of assembling roughly two million parts per hour  This claim is very promising, however lacking published literature the author will focus upon the well documented applications of self assembly conducted experi mentally along with the published modeling techniques referenced above. 2.3.3 Application of Chemical Kinetics to Self Assembly Process parameters such as rate constants and order of reaction well developed in t he study of chemical kinetics, need renewed exploration if they are to be applied to the study of micro scale self assembly The application and demonstration of kinetic models to self assembly processes started with Verma et al who co nducted their experiments using a Fluidic Self Assembly (FSA) environment in which part to substrate SA systems were applied to test a rate equation model  The researchers in Verma, et al. 1995, were concerned with developing a set of rate equations using a steady state model in which the availability of parts and substrates is non diminishing. The work of Verma represents a first order system and was validated experimentally using a system which re circulated parts over a substrate patterned with holes into which parts could bind given a shape match. The nomenclature for this experiment follows:
25 Rate of Assembly Rate of Disassembly Assembly Constant Disassembly Constant Number of blocks Number of blocks left in Solution Number of Holes Number of Unfilled Holes Number of Filled Holes Associativity Ratio Fill Ratio These constants and parameters can be arranged algebraically to express the following relationships in which the rate of assembly and the rate of disassembly are leveraged to determine t he fill ratio. Equation 2 18 Equation 2 19 When the assembly reaches equilibrium the rate of assembly is equal to the rate of disassembly and the following equivalen ce is found. Equation 2 20 This equation can be rearranged as follows to find the fill ratio at equilibrium. In practice this relationship would need to be used in
26 order to ensure that the fill ratio is sufficiently close to 1 resulting in the assembly operat ing as expected. Equation 2 21 The fill ratio, x, can be effectively manipulated to reach 1 by increasing either K or In the thesis work we capitalize upon this relationship by reducing the probability that a hole will become unfilled, through manipulation of the surface energy to kinetic energy ratio involved in the binding process for the assembly process. This facet of the rese arch is explored in greater depth in later chapters. Th e application of the chemical kinetic analogy is continued in the work of Hosokawa et al with the intention of developing analogous yield and rate equations for micro scale systems and to clarify the dynamic evolution of self assembling systems  analogy includes a clear procedure for the application of his model to an assembling system. In this procedure the experimenter begins with a number of parts which may assemble with one another in multiple manners T he concentration of every intermediate product is a state variable. This reduces the degree of freedom of the system by forcing the model to only consider the stable intermediate products. After deriving the dynamics governing the state variables from the constraints of the processes being exp lored the variation of the states may be calculated.
27 In Hosokawa, et al 1996, a set of state variables representing the intermediate products of the assembly process is defined as The states considered in that research are states repre senting the integration of parts floating at a fluid interface into two dimensional structures. These states are illustrated in the following figure. Figure 2 5 : Possible assembly states for Hosokawa study The number of assemblies in state is represented as Time in this case is represented as a time step t which occurs at each collision of clusters. So that the number of assemblies in any state is altered at a collision according to Equation 2 22 Where F i represents the number of additional assemblies in state Xi after a collision and can be represented as the sum of the products of Where, stoichiometric number for the reactions producing Xi
28 and is the probability of the jth reaction occurring given the current state of the system. Equation 2 23 Equation 2 24 The quantity is a product of two other probabilities explored in greater depth in the thesis work, the probability of a reaction collision occurring and the probability of a reaction bond being formed, Their work concluded that the state of the self assembling systems can be used as state variables in stochastic analysis and that chemical kinetics and population dynamics can provide useful analogies for the self assembly of systems. The researchers use order to explore the means by which the probability of bonding, given a collision, can be made to approach 1 certainty. Avenues toward guaranteeing that the bond is formed are pursued through the exploitation of the relationship between the bond energy of a stable bond and the k inetic energy of a part and site in collision. By ensuring that the kinetic energy of the collision is low relative to the bond energy of an assembly a bond can be expected to form upon collisi on.
29 CHAPTER 3 : PROPOSED MODEL The following chapter presents the proposed model for this research. The modeling is conducted in two parts. The system model presents a Markov chain model of the parallel assembly method. The Unit cell model explores the dynamics of the assembly process. 3.1 System Model The model developed in this thesis concerns itself with the evolution over time of a self assembly process This model observes a state space in which assembly components may be exist in dif ferent states of assembly, i.e. assembled, unassembled, misassembled, etc. The individual states of the assembly process are represented by a set of random variables denoted by the vector The evolution of each state evolving over time, represents the number of assembly parts which have entered state i at time t. This collection of random variables evolving through time represents a time dependent stochastic process  For the purposes of modeling this stochastic system let the vector of random variables represent the state space for the process. The process is said to be in state i at time step
30 n when  The model considered in this research includes just two states for the assembly. These are states X 0 which represents an unbound part and X 1 in which a part is bound to an assembly site Figure 3 1 : The two assembly states of th e proposed model. These include state X 0 for unassembled parts on the left, and X 1 for assembled parts on the right. A stochastic process in which the conditional distribution of any future state is dependent upon only the present state is known as a Mark ov Chain. In the case of a Markov Chain, there is a fixed probability, that the process will move from state This statement can be expressed formally in Eq uation 3 1 Eq uation 3 1 A one step transition matrix, is composed of all probabilities of transition from i to j for all states within the state space X
31 Equation 3 2 For such a transition matrix, the following properties hold Equation 3 3 The statements of Equation 3 3 must be true.  3.1.1 Simulation of Stochastic Processes A Monte Carlo simulation may be used to approximate solutions for the expected value of a function operating upon the state space of a stochastic process. In general, if the state space denotes a random vector having a density function the ex pected value of an n dimensional function g may be approximated by solving the multiple integral from Equation 3 4  Equation 3 4 In situations in which it is difficu lt or impossible to solve E quation 3 4 it may be possible to approximate a solution to the system by means of a Monte Carlo Simulation. A Monte Carlo Simulation makes use of the strong law of large numbers to generate an average for the expected value of the n dimensional function g. This is done by generating random vectors having the joint density function For each value of compute
32 After having generated r, a fixed number of independent and identically distributed random variables for this formulation with, an approximation of the solution Equation 3 4 can be found as in Equation 3 5  Equation 3 5 3.1.2 Subject Model The assembly model considered in this study accounts for a state spac e including parts in a state space consisting of assembled and unassembled parts. These parts are free parts which are introduced into an assembly environment and bound to an assembly substrate wherein the parts find a stable state. Number of parts in a free state Number of parts in an assembled state Th e assembly process is initiated with all parts and sites in the free state and the value s of the vector of random variables evolves through time as a stochastic process as assembly proceeds Let P a represent the probability of transition from state 0, free, to state 1, assembled, indicates that a free part has encountered a binding site and successfully bound to it. Let a transition from state 1 to state 0 in which a part would undergo a disassembly from a previously bound
33 asse mbly site be represented by P u The process is represented by a Markov chain with the following one step transition matrix. Equation 3 6 This process model can be seen in Figure 3 2 consisting only of two states This model does not account for the possibility of bonding errors As a first step, this research seeks to determine a method for predicting P a In order to facilitate these measurements, a system in which the probability of disassembly P u is minimized will be used. Figure 3 2 : An illustration of the proposed Markov chain model This models the interaction of a ssembly for a part to site. In order to design the assembly process to allow for an absorbing state of assembly it is necessary to consider the dynamics of the interaction and develop a method by which the assembled state can be guaranteed to persist.
34 3 .2 Unit Cell Modeling 3.2.1 Modeling of Assembly Dynamics The researchers employ what we refer to as unit cell analysis. This is a method of s elf assembly process modeling on the basis of the dynamics of individual state transition interactions The unit cell is depicted in F igure 3 3 Figure 3 3 : The assembly unit cell This cell depicts process parameters important to the characterization of the assembly process This form of analysis depends on accurate charact erization of the dependence of the transition probability on the physical parameters of the system. site pair. In the case of part to substrate self assembly driven by
35 gravitational forces and bond thr ough capillary forces the unit cell interaction takes place as a part collides with a binding location. Analysis of parallel self assembly processes benefits from the analysis of global parameters affecting the dynamics of the unit cell. The stochastic self assembly process output is determined in part by the probability of binding after a successful collisi on has occurred. The thesis work explores how parameters such as bond strength and speed of approach during binding determine the transition probability of assembly. Accurate models require that controllable process parameters and their transition probabil ity be effectively analyzed.
36 CHAPTER 4: SELF ASSEMBLY TEST SYSTEM In order to test and validate models for specific assembly processes it is necessary to control parameters contributing to assembly performance. In order to do so efficiently a test syste m was developed for application to the assembly process. This system allows the researchers to vary specific parameters of the assembly process and report on assembly yield. 4.1 Requirements The requirements for the test system include spatial regularity and control over the energy involved in reactions. The sites must be fixed within an assembly environment in order to guarantee the repeatability of the experiments. The parts must be introduced in a repeatable manner These constraints guarantee the spatial regularity of the process. The control over the energy involved in the reactions requires control over both the kinetic energy of an interaction and the bond energy of a finished assembly. The magnitude of the kinetic energy involve d with the assembly interaction must be controllable. The exploration of the ratio of k inetic e nergy involved in an interaction to
37 the b ond energy of an assembled set is a key process parameter explored throughout this research. The bond energy of an assem bly must be controllable within the assembly environment. Within this system, this is achieved through the customization of surface properties for parts and sites and through the selection of bonding fluids. 4.2 Methods In order to design self assembling systems it is important to understand the complexity of the processes at work in the phenomena leveraged in these systems. A proper understanding of these processes may be used to inform stochastic models of self assembling systems working at the micro sc ale. Assembly interactions in such systems will include multiple interaction steps conducted with a variety of conditions. In capillary self assembly these conditions will include arrival angles and varied interaction activation and bonding energies. Thi s diversified set of assembly conditions results in a large and varied behavior. Experiments designed to understand these behaviors must allow control of at least some of these process parameters. Independent control of these process par ameters allow for the characterization of these processes
38 Figure 4 1 : Assembly e nvironment. The diagram on the left depicts the process parameters controllable through the assembly environment. The labeled process parameters from F igure 4 1 include height of the free fall of parts introduced to the assembly environment and the angle of approach of these parts. Other controllable parameters include the spatial distribution of parts, the constitution of the fluidic as sembly environment, and the pattern of available assembly sites within the environment. The selection of fluid will affect the surface energy of the assembly bonds. Furthermore, the viscosity of the fluid will alter the velocity of falling parts which cont rols the kinetic energy of the parts at the time of the reaction Many other parameter alterations are possible within the assembly environment. The means
39 by which these variables can be controlled are enumerated in the following sections along with an acc ount of an experiment making use of this test platform. 4.2.1 Test Apparatus In these experiments, free parts are introduced into the assembly environment through the fluid gas interface. Parts are placed on the fluid gas interface where they remain unle ss agitated to fall through the interface. This is a function of the scale of the parts and the surface tension of the environmental fluid. In order to pass through this interface it is necessary to agitate the parts. This is accomplished through dropping fluid onto the floating parts using an automated syringe pump. The syringe pump is attached to a Fab@Home system, which provides planar actuation of the pump over the surface of the fluid. Because the location of the syringe is controlled and the rate of d roplet introduction is also controlled the parts can be induced to enter the environment in a patterned manner. As a droplet strikes parts on t he surface they are forced parts fall into the assembly environment in a Gaussian distribution A nalysis of the assembly system relies on an ability to model the distribution of parts, which is better accomplished with a uniform distribution rather
40 than a Gaussian. A pseudo uniform distribution is simulated by overlapping the individual Gaussian distributions Given a uniform distribution of parts the probability of a collision occurring is equivalent to the area fraction of the sites distributed over the assembly field. Only through t his pseudo uniform distribution can probability y of collision be considered equivalent to the area fraction of sites. As shown in 4 2 the pseudo uniform distribution can be in good agreement with a truly uniform distribution Figure 4 2 : Distribution of random parts af ter introduction Two rows The grid lines above are spaced at 0.25 inches 4.2.2 Assembly Site Mount The assembly sites for this platform are fixed at the base of the assembly environment on a substrate mount the latest version of this mount is shown in F igure 4 3 The original version of the mounts are shown in F igure 4 4.
41 Figure 4 3 : Assembly mount. The geometry of the mount dictates the area fraction of asse mbly sites within the assembly environment. Through experimentation with the original mount design shown below, it was determined that the original design lacked flexibility and provided some obstacles to experimental setup which were addressed in the final design. Important improvements to the design include the use of slatted shelves rather than solid pedestal mounts. The slats allow sites to be pushed into place without overcon straint. The long shelves from the original design left sites subject to dislodging and required a high degree of manual dexterity to place the sites on the mounts. In both cases the mounts allow the sites to be spaced far enough from one another to permit parts which do not bind successfully to fall away into voids away from the assembly area.
42 Figure 4 4 : Original design of assembly mount. This milled aluminum sock holds sites in place at a 45 angle resting on shelves shown in detail on the bottom with dimensions in inches and degrees Mounting these sites provides a measure of control over several process parameters. The fixed location of the sites provides a constant fall distance for free parts d ropping from the fluid surface. The terminal velocity of the falling parts is controlled through the viscosity of the fluid, the shape and size of the parts, and the density of the parts. This allows the researchers to set upper limits to the interaction k inetic energy for the assembly. Furthermore, the area fraction of assembly sites is an important characteristic of the
43 environment. A uniform distribution of parts over the substrate mount will interact with sites with a probability equal to the area frac tion of sites distributed over the mount. Finally, the angle of the substrate mount surface can be varied by ma chining new mount shelves. This angle a ffects the arrival direction of the parts to the sites as well as the area fraction of sites exposed to th e part distribution. Complete drawings of the assembly mounts can be found in Appendix A. The parts are introduced through the air/fluid interface at the surface of the environmental fluid, a solution of Glycerol and water. As they fall they spread so that they land in a Gaussian distribution centered below the point at which they pass through the interface. In order to ensure that each binding site has a common likelihood of experiencing an assembly event, the drop point of the particle is varied over the surface of the fluid to provide a uniform distribution. With a uniform distribution the number of potential interactions is proportional to the area fraction of sites normal to the trajectory of falling parts. This ratio is a function of the patterning of binding sites as well as the angle of the substrate mounting. The function depends upon the patterning of the sites, however, given that A s represents the represents the angle of the subst rates to the direction of travel of parts, and A T represents the total area over which the parts are
44 distributed the area fraction, A f exposed to site interactions can be expressed with the following equation. Equation 4 1 The patterning of the binding sites must account for the interactions which will occur during assembly. It is important to space the sites far enough from one another so that a single part cannot span the empty space betw een sites If such a binding were to occur its state would need to be accounted for in the state space of the assembly process. Figure 4 5 parts assembled to two strips of the patterned assembly sites.
45 Figure 4 5 : Sites w ith assembled parts. This assembly was conducted through manual placement of the parts onto the sites using a pipette to move parts into position. Note that the top row misalignment does not interfere with neighboring assemblies. Figure 4 5 illustrates the important dimensions of the site patterning. Figure 4 6 : Site p attern s chematic Note that the square sites of side s are spaced at 1.75 s in distance to one another. This allows the cube sites to fall at their longest dimension between sites without interfering with more than one site.
46 4.2.3 Active Face Fraction The effects of the site and part fabrication upon the bond energy and the kinetic energy for a unit assembly are described in greater detail in the following sections. However, it is necessary also to consider the significant effect of part shape upon bond probability in order to use the unit cell model to effectively inform the stochastic model of the system. The initial requirement for an assembly process t o occur begins with the activation of the assembly interaction. This occurs when the part physically encounters the site, the probability of which is dependent upon the area fraction of sites available for interaction as discussed previously. However, in the case of capillary driven self assembly, it is necessary to consider that the orientation of the part upon entering the interaction is also important. The active assembly site through sur face energy minimization, has a direct effect upon the probability of assembly. The researchers propose the hypothesis that the geometric interaction occurring during the assembly process is equivalent to the probability that the part be oriented correctly at the time of the interaction to bind to an assembly site. This probability defines the geometric limit of assembly. As shown in Figure 4 7 and Figure 4 8 the
47 geometric contribut ion the probability of assembly is considerable. For a sphere in which the entire surface is an active assembly site this contribution is 1. For a long thin plate with only one active site the contribution would be 0.5. For a cube with one site valid for a ssembly, as used in the experiments to follow, the contribution is 1/6. This geometric based limit to assembly is multiplied by the area fraction of sites within the assembly area to generate the probability of an assembly interaction occurring. Figu re 4 7 geometric contribution to assembly probability due to the part to be 1.0
48 4.2.4 Assembly Component Fabricat ion The assembly parts may be customized by appropriate selection of materials to affect the surface energy of the parts Surface energy is affected through environmental fluid selection, material selection and surface treatments. In the case of the techniques explored in the course of this research and the experimental setup SiO 2 wafers were coated with copper and treated with an n octadecanethiol SAM to render copper coated regions hydrophobic. The SiO 2 wafers regions are not coated with the SAM as the active thiol head of the SAM is not adsorbed by silicon dioxide and so a difference in surface energy exists between the SAM coated copper regions and non coated SiO 2 regions. Figure 4 8 : The geometric limit of assembly for a prismatic part. With only 1 active face this contribution to assembly probability is 1/6.
49 The se surface characteristics determine the interaction bond energy of a bo und assembly The sites and parts were fabricated with silicon wafers. Initially, a themal oxide coating was grown on the wafers Next, Shipley 1813 Resist was spun onto SiO2 wafers then developed to expose the areas designated to be active. Using E beam deposition 200 angstroms of Chromium followed by 500 Angstroms of Copper were deposited. The parts were then rinsed in Acetone to complete the liftoff process. This same formula of deposition was used on bare wafers which were coated and then diced into in dividual prisms to serve as parts for assemblies. The patterned binding sites, thickness of the substrate, and diced size can be varied to achieve a variety of part aspect ratios and bond sizes to explore the effects of different sample cases upon the over all assembly process. Due to the application of dicing process and the strength of adhesion of the deposited materials to the substrate feasible part sizes using these methods range from several millimeters to approximately 100 microns. After dicing, t he Copper surfaces of the sites and parts were rendered hydrophobic by treat ment with a SAM solution. The site arrays and parts were rinsed with ethanol and submerged in a 1mM solution of 1 octadecanethiol in 99% ethanol within a reduced Oxygen
50 environment fo r 24 hours along with Cu samples used to measure contact angles after treatment. Contact angles on SAM coated parts were measured using a contact angle goniometer. Results for contact angle measurements are shown in Table 4 1 Table 4 1 : Contact a ngles for c opper t reated with 1mM Octadecanethiol SAM at various interfaces. Fluid Advancing Contact Angle De ionized water in air 114 60% w/w glycerol/ 40% water in air 117 n hexadecane in air 16 4.2.5 Bond Energy The bond energy of the assembly sites is an important process equation to the use of bond energy is important to understanding the effects of design choices on the system. The surface treatments app lied to the sites effect the wettability of fluids on the sites. The copper sections of the assembly sites are treated with the 1 octadecanethiol SAM and are rendered further hydrophobic. By applying an oil lubricant to the hydrophobic sites, a lubricating effect on the assembly can be observed, resulting in parts aligned more completely with the energy minima of the designed assembly site/part combinations. This oil is applied to the sites by passing the sites through a very thin layer of oil at the surface of the environmental fluid.
51 The hydrocarbon phase is composed of 0.4 mL of n hexadecane. It is sufficient to treat several 2 inch strips of sites before requiring that it be recharged. This volume of fluid is contained within a glass passageway at the surface of the environmental fluid. The working passageway is cylindrical and 2cm in diameter By passing the sites through the hydrocarbon phase and into the environmental fluid which in the case of these experi ments is either water or a solution of water and glycerol the sites may be collected in a transport vessel submerged within the environmental fluid and then transported into a working vessel without removal from the environmental fluid. The applied oil w ill bead over the sites initially, however agitation of the oiled sites with a fluid stream from a pipette will reduce the volume of fluid through shear and cause the sites to become more uniformly oiled.
52 18.104.22.168 Verification of Oil Deposition When the oil is deposited on the sites initially, it is possible for some bridging between sites to occur. This effect can be seen in the following image. Figure 4 10 : Assembly site strip with oil bridging assembly sites A strip of assembly sites treated with oil and agitated with the fluid flow from a pipette will create a regular array of oiled sites. The effects of this wa shing can be seen in the image below. Figure 4 9 : Goni ometer i mage of a droplet of oil applied to a site.
53 Figure 4 11 : Oiled sites Measur ements of the effects of pipette rinsing on the distr ibution of conta ct angles for oiled sites were made. These measurements indicate that the uniformit y of the oil coating on these sites is improved. Measurements site strips containing a total of 29 sites were made and histograms generated for pre rinsing and post rinsing were made. The Averages and Standard deviations of the contact angles measured in t hese tests were calculated These results are indicated in the following table. Table 4 2 : Site contact angles by treatment Pre Rinsed Sites Post Rinsed Sites Average Contact Angle 42.1 23.3 Standard Deviation 26.8 15.3 The table above indicates that the contact mean contact angle pipette washing. This is illustrated graphically in the following histograms.
54 Figure 4 12 : Contact a ngles for sites before washing with pipette Sites were dip coat ed through hydrocarbon phase into aqueous solution. Figure 4 13 : Contact a ngles for assembly sites after washing. The sites were dip coated through hydrocarbon layer into aqueous solution and washing with pipette flow of aquous solution This technique would improve greatly through the application of a pump to control the flow rate and volume of the fluid over the coated 0 1 2 3 4 5 6 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 More Pre Wash Contact Angles 0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 More Post Wash Angle Histogram
55 sites. A peristaltic pump sho uld be applied to this procedure in order to avoid contamination of the fluid within the pump. The current state of the technique is sufficient to ensure that individual sites are coated with oil while the regions outside of the copper assembly sites are f ree of oil. Without this washing, some bridging of oil from site to site is observed. The removal of oil from the inter site regions is necessary to apply the current methods to test for the geometric assumptions of the model in which the area fraction of active assembly area is an important process characteristic. The bridge of oil, being hydrophobic, contributes additional assembly area to the overall assembly process. The trials presented in the results section include trials conducted without the appli cation of oil to the assembly surfaces. The assembly sites used in those tests are solid copper surfaces with no pattern ing As lubrication of the assembly for proper site alignment has little meaning without patterned assembly sites, the oil patterning te chnique is not applied to these systems. However, the technique described above is important for future research. 4.2.6 Kinetic Energy Design The kinetic energy of the interaction is controlled by the velocity of parts approaching assembly sites. This pa rameter can be controlled by designing the assembly environment to limit the part velocities to
56 the ter minal velocity of the particles. The viscosity of the environmental fluid within the assembly structure can be used to set this limit because of the rela tionship between terminal velocity and kinetic energy The parts will reach terminal velocity if the parts fall from sufficient height Fluid v iscosity for the assembly environment can be varied by controlling the composition of the fluid as well as the temperature of the environment. This control is exercised over a continuum In the assembly environment used for the purposes of this research this is accomplished by varying the percentage of a glycerol to water in the environmental fluid mixture at room temperature. A significant change in viscosity can be achieved with only a modest change in surface energy (~10 mN/m) due to the variation in the relative interfacial energy between the capillary fluid and different compositions of environmental flui d Interaction kinetic energy is also adjusted through manipulation of the solution and composition of the parts. The range of kinetic energies achievable through this approach can be examined through calculations with spherical parts. The terminal velocit y of spherical parts falling through a viscous medium is given by Equation 4 2 Equation 4 2
57 In Equation 4 2 g is the acceleration due to gravity, is the order to illustrate a range o f terminal velocity values, Figure4 14 shows values for spheres of several diameters passing through a glycerol/water solution of varied concentration. These spherical terminal velocities are slightly higher than those found for flat plates at the same siz e and are useful, simple calculations for a limiting case. Figure 4 14 : Variations in terminal velocity These variations may be achieved through particle size, density and fluid viscosity variations. These diameters range from .25 mm to 2 mm The parts are composed of Silicon.
58 The component size, density, and shape all contribute to the terminal velocity of the components. The estimations of terminal velocity found through calculation of the spherical case provide limiting cases for design However, these calculations should be compared to empirical measurement of the terminal velocity of the components falling through the fluid. A stroboscope was employed in order to conduct these measurements. Sample parts were introduc ed into a water fluid at 60:40 weight to weight proportions the same composition used within the assembly environment. The figure below shows a trial image for a prismatic part of with dimensions of 1mm X 1mm X .5 5 mm composed of an SiO 2 wafer coated on two sides with Chromium and Copper as described in the assembly part fabrication section above. A camera was mounted on a tripod and exposed for one second while a strobe light flashed at 600 RPM within the field of focus The falling parts reflected light back to the camera and calculations of the terminal velocity of the particles were made. The room was darkened during testing to improve the image contrast.
59 Figure 4 15 : Stroboscope image of falling parts in fluid. W hite circles indicate the location of the part at a frequency of 600 Hz. The measured terminal velocity for the displayed trial displayed in Figure 4 15 was 6.60 cm/s measured with a strobe at 600 RPM, wh ich provided the clearest pictures of the strobe rates attempted The spherical parts were calculated to have a terminal velocity of 14.1 cm/s. The Lack of uniformities in the parts will result in error in the approximation of the terminal velocity extrapo lated from measurements of individual parts
60 A second method for the measurement of velocity of falling parts was developed in order to help improve the quality of analysis These tests were conducted with a set of parts smaller than those used previously having the dimensions 0.5X0.5X0.55 mm diameter and composed of silicon with one face coated in copper The fabrication of these parts is discussed in the following section. These parts were dropped through a fluid as a function generator triggered an Edw Optics EO 2 013C CMOS camera to capture images. The hardware signal provided an echo to a computer on which t he system clock was correlated with the image capture to calculate the part velocity as the slope between the fall distance and time to fall Multiple sequential images were analyzed for part location and timing and the velocity of the falling parts compared. The terminal velocity of the subject parts falling through a 40% glycerol to H 2 O w/w solution was found to be 2. 82 cm/s. The parts fallin g through de ionized water fell with a velocity of 7.13 cm/s.
61 Figure 4 16 : Falling p art v elocity i mages These trials were conducted five times for a 40% glycerol to H 2 O solution at 25.7 C and five times for parts falling through water. The results are reported in Table 4 3 It can be seen there that the variation in velocities is relatively small between trials Table 4 3 : Velocity m parts through H 2 O and 40% g lycerol s olution Fluid Velocity Average Velocity Standard Deviation H 2 0 at 21.4 C 0.072 5 m/s 0.0021 m/s Glycerol at 21.0 C 0.0277 m/s 0.0005 m/s Furthermore Figure 4 17 shows a linear regression for a plot of the distance fallen to the measured time. The coefficient of determination 0f 0.9902 shows a good fit to the linear regression indicating that the points fall very closely to a line. The linear fit of the distance to time measurements indicates that the parts are fall ing at terminal velocity and not accelerating through the fluid.
62 Figure 4 17 : Linear r egression from time trial The velocity of the parts is related to the kinetic energy of the interaction through the relationship shown in Equation 4 3 Equation 4 3 Relative variations in the velocity will have the greatest effect on the kinetic energy of the parts due to the square proportionality between kinetic energy and velocity. In studying the effects of the kinetic energy to bond energy ratio described in the next section of this thesis it is important to ensure that these variations do not interfere with the resultant picture of the relationship. In order to do so, the researchers conducted experiments wherein the parts were y = 0.0733x 0.0006 R = 0.9902 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.5 1 Distance (m) Time (s) Sample Points Linear (Sample Points)
63 structured and the viscosity of the fluid was selected so that the terminal velocity of the parts was well below or above the kinetic energy to bond energy ratio of 1:1 4.2.7 Energy Ratio: Kinetic Energy to Bond Energy The ratio of kinetic energy to bond energy for an assembly interaction may be an important process parameter. With many parallel assembly processes occurring without feedback based control systems it is important to ensure that the parts engage in the bind ing process with a lower kinetic energy than the energy minimized through binding. In this way, the bonds may be formed without immediate release from the bond. Furthermore, additional interactions between free floating parts and bound parts will not resul t in assembled parts being dislodged from their position. Through the control of assembly velocity and capillary bond energy, the ratio of these two parameters can be ensured. The kinetic energy of the assembly interaction between a falling particle and a fixed substrate can be varied with the terminal velocity as illustrated above.
6 4 Figure 4 18 : Assembly c ondition in the grey region. This region is below the 1:1 Kinetic to Bond Energy Ratio. Figure 4 18 graphically demonstr ates the region in which assembly conditions are favorable while disassembly conditions are unfavorable. Curves indicate the energy ratio for arrangements of process characteristics for the assembly of cubic parts over a range of glycerol concentrations w ithin the proposed assembly environment. The lines marked with squares indicate assemblies using n hexadecane as the assembly binding fluid with a su r face energy density of 0 .025 J/m 2 The lines marked with circles indicate assemblies with a higher energy density fluid, a low melting point solder with a su r face energy density of 0.5 J/m 2 The dashed lines indicate smaller parts with 0.25 0 25 50 75 100 Kinetic Energy: Bond Energy Glycerol Concentration E BE < E KE E BE >E KE Assembly Condition: E BE > E KE
65 mm squares while the large parts indicate parts with 2mm square profile areas The large parts, solid lines, can exceed t he KE:BE energy ratio at Unity for The majority of glycerol concentrations for either binding fluid. However, there are regions in which even these large parts can be used in assembly. For either composition of fluid and part size t here exists a wide range of process parameters which may be selected to favorably affect bond stability however it is important to apply an appropriate analysis before attempting assembly. The bond energy for a thin film of capillary fluid between components of equal size can be approximated as the b ond for the case of a small amount of fluid as shown in E quation 4 4. This relationship between surface energy density and the profile area of the bonded between the components is important to the design of the assembly parts and as sembly sites The composition of the liquid/assembly medium and solid/assembly medium determines the interfacial surface energies for the bond while A is the bond area Equation 4 4
66 CHAPTER 5: EXPERIMENTATION AND RESULTS Several trials of self assembly processes have been conducted with the previously described assembly environment. These trials have been, in large part, conducted with the intention of refining new techniques for application within the micro scale integration lab. The results do however reveal some relationships which may be exp lored in greater detail in further studies conducting using the methods under development here. The researchers hypothesi ze that the assembly yield may be predicted through appropriate application of a Markov chain model of self assembly. Several process variables are under investigation. The geometric contribution to assembly should dictate the assembly yield when the kinetic energy to bond energy ratio is near zero. Furthermore, because the assembly bond action is driven by surface energy, the bond energy parameter may be applied with the assumption of path independence and part approach angle will not affect the assembly, though projected area of assem bly due to angular variations in the site mounting will make a contribution to the assembly yield.
67 Five trials are reported upon. These were conducted using the self assembly test system developed for research into self assembly modeling The tests were co nducted with the intention of evaluating the state of processes available currently and to identify process weaknesses, model applicability at the current time, and further direction in the application of these processes to self assembly research These trials were conducted using parts described in C hapter 4 of this thesis The faces of these parts are shown in the image below. Figure 5 1 : Fabricated p arts. F rom l eft to r ight: The SiO 2 face of an assembly part the diced edge of an assembly part and t he Copper coated face of a part The parts, in all trials, were diced and coated with a 1 octadecanethiol solution as discussed previously in C hapter 4 under This treatment renders t he copper
68 face of the sites hydrophobic, while the SiO 2 face of the part remains hydrophilic. The part and site pairings for each trial are summarized in Table 5 1. The notation for the bonding fluid, C8 SAM, refers to the SAM n octadecanethiol. Table 5 1 : Assembly t rial d etails Trial Part Dimensions Site Structure Fluid Environment Bonding Fluid A 1 1 X 1 X 0.55 mm 3 Patterned Cu 1 X1 mm2 sites on SiO 2 60% Glycerol: H 2 O hexadecane B 1 0.5 X0.5 X0.55 mm 3 Cu Faced strips 40% Glycerol: H 2 O C8 SAM B 2 0.5 X0.5 X0.55 mm 3 Cu Faced strips H 2 O C8 SAM B 3 0.5 X0.5 X0.55 mm 3 Cu Faced strips H 2 O C8 SAM B 4 0.5 X0.5 X0.55 mm 3 Cu Faced strips H 2 O C8 SAM The pattered Cu assembly sites for trial A 1 are discussed in detail in c hapter 4. The Cu Faced strip assembly sites for the B series of assembly tests can be seen in Figure 5 2. These sites are 1.88 mm wide strips of silicon wafers with Copper deposited on SiO 2 as described i n C These depositions were made onto the entire face of SiO 2 wafers without patterning the surface through the photolithography and liftoff process used to create the patterned Cu assembly sites used in trial A 1 In all trials the sites were treated with the same 1 mM 1 octadecanethiol SAM solution used for the parts rendering the copper face hydrophobic. These sites were then mounted within the assembly
69 fixture, placed in the assembly environment, and the environmental fluid for the trial was added. The introductio n of fluid to the environment, in the current process, may introduce bubbles to the environment. These bubbles can be seen in Figure 5 2. Figure 5 2 : Assembly sites with bubbles In order to prevent these bubbles from interfering with the assembly a vacuum is pulled on the fluidic environment to remove gas from the fluid Any r emaining bubbles are washed free with a pipette. The resulting surfaces are clear of contamination and bubbles which would otherwise interfere wi th the uniformity of surface properties within the assembly environment.
70 Figure 5 3 : Assembly array after purging of bubbles The preceding steps were repeated for each trial. The trial s A 1 and B 1 conducted included the application of the assembly process to site strips mounted at 45 degrees within a glycerol solution to control The remaining trials were conducted with deionized water as the environmental fluid and with sites mounte d at 45 degrees in trial A 2, 60 degrees in Trial A 3, and 30 degrees in Trial A 4. These angles are relative to the incoming part trajectories and used with the intention of observing the effects of
71 change in projected area to the stream of incoming parts upon the final yield of the system. 5.1 Experimental Parameters The following sections present the geometric and energetic parameters for the experimental trials conducted using the self assembly test system. 5.1.1 Energetic Relationships The assumpti on of a near zero energy ratio of kinetic energy to bond energy must be verified discussed in the section on modeling allows for the yield predictions to be made at the geometric limit of assembly. 22.214.171.124 Kinetic E nergy in T rials I n order to use this as sumption, the velocimeter measurements described in section 4.2.6 Kinetic Energy Design were used to calculate the kinetic energy for the parts These were calculated and are tabulated below in Table 5 2
72 Table 5 2 : Kinetic e nergy for t rials Trial Fluid Part dimensions Part mass (kg) Velocity (m/s) Kinetic Energy (J) A 1 60% glycerol:H 2 O 1X1X 0 .55 mm 3 1.0E 6 5 01 E 2 1.26E 9 B 1 40% glycerol:H 2 O 0.5X0.5X 0 .55 mm 3 2.5E 7 2 77 E 2 9.65E 11 B 2 H 2 O 0.5X0.5X 0 .55 mm 3 2.5E 7 7 25 E 2 6.58E 10 B 3 H 2 O 0.5X0.5X 0 .55 mm 3 2.5E 7 7 25 E 2 6.58E 10 B 4 H 2 O 0.5X0.5X 0 .55 mm 3 2.5E 7 7 25 E 2 6.58E 10 126.96.36.199 Bond Energy in T rials To find the Energy ratio for these trials it is necessary to calculate the bond energy for each trial. The bond energy calculations are described under section 4.2.5 Bond Energy The results of the bond calculations and the parameters associated with the calculation of bond energy are tabulated below. These calculations were carried out with the assumption that the n hexadecane bonding fluid was of sufficiently small volume that its surface area could be assumed to be equal to the area that it wets. The notation for the bond fluid C8 SAM refers to n octadecanethiol self assembled monolayer. The total bonded area is the area of the site area of a single active part face and the area that that part face makes contact with in the assembly. Table 5 3 : Bond e nergy and associated parameters for assembly trials Trial Environmental Fluid Bond Fluid Bonded area (m 2 ) Bond Energy (J) A 1 60% glycerol:H 2 O n hexadecane 2.00E 6 2.10E 8 B 1 40% glycerol:H 2 O C8 SAM 5.00E 7 2.79E 8 B 2 H 2 O C8 SAM 5.00E 7 2.79E 8 B 3 H 2 O C8 SAM 5.00E 7 2.79E 8 B 4 H 2 O C8 SAM 5.00E 7 2.79E 8
73 188.8.131.52 Energy R atio in T rials The energy ratio for the trials must be calculated in order to determine if the zero energy ratio assumption can be held. The results of these calculations are shown in Table 5 4 The energy ratios found through these calculations are well below 1:1 and so, if the assumption of a near zero energy ratio is valid then the yield for these assemblies should be predictable based upon the geometric limitations to assembly. Table 5 4 : Energy ratio for assembly trials Trial Kinetic Energy (J) Bond Energy (J) Energy Ratio A 1 1.26E 9 2.10E 8 0.059 B 1 9.65E 11 2.79E 8 0.003 B 2 6.58E 10 2.79E 8 0.023 B 3 6.58E 10 2.79E 8 0.023 B 4 6.58E 10 2.79E 8 0.023 5.1.2 Geometric Relationships The assembly interaction includes a collision between introduced parts and stationary assembly sites. In order for an assembly to occur, the hydrophobic faces of the parts must come into contact with the hydrophobic region of the assembly sites whether the y be patterned sites as in trial A 1 full faced assembly strips as in the B series of trials. When this interaction does occur, capillary forces associated with surface energy minimization will attempt to bind the assembly part to the assembly site. Howeve r, if the kinetic energy of the interaction is too great these forces may be overcome as the parts
74 break free of the sites. Therefore, it is expected that there should be a peak assembly yield value at zero kinetic energy. At this limiting value, everythi ng that contacts favorably will bond. The area fraction of available binding area to the total assembly environment depends upon the orientation of the binding sites as well as to the geometry of the assembly mounts. The total assembly area represents the area over which the parts are uniformly distributed, i.e. the full assembly environment bounded by the acrylic walls of the assembly chamber. The area of interest within the assembly environment is the region in which assembly sites are mounted and betw een the mount edges. Parts are distributed outside of this area, however, this is the only area in which assemblies may take place. For each assembly trial, the active fraction of the assembly environment in which assemblies may take place is proportional to the cosine of the orientation of the sites
75 For the assembly trial A 1 assembly sites were composed of 1mm 2 regions. The trials were conducted in an early version of the assembly environment with the following geometric characteristics Table 5 5 : Trial A 1 assembly geometry Assembly Area Geometry Trial A 1 Total Area of Uniform Part Distribution 2823 mm 2 Total Mounted Strips 21 Sites per strip Average 14 Area Fraction of Cu 1mm 2 sites on patterned strips 0.0793 Area fraction of strip projected parallel to fluid surface 0.0740 Area Fraction of sites projected parallel to fluid surface 0.06 Geometric limit to assembly 0.03 For the assembly trial series B, t he re are a total of 25 assembly strips in each trial. The assembly site area is multiplied by the cosine of the tilt angle resulting in the projected area of the assembly sites. Equation 5 1 Figure 5 4 : Projected assembly area as a function of mount angle A N A p = A N cos(
76 This area is divided by the total area of the environment to find the area fraction of active assemblies. The Area fraction is later multiplied by 1/6 as each part is a cube in which one of the six faces is a valid assembly location.
77 Table 5 6 : Trial B series assembly g eometry Assembly Area Geometry Trial Series B Area Fraction Total Area of Assembly Environment 5642 mm 2 1 Area of Interest within environment 2157 mm 2 0.3823 Number of site strips in each trial 25 Active Area of site strip 68.3 mm 2 Total Active Area 1707.5 mm 2 0.3026 Trial B 1 Active Area at 45 1207.1 mm 2 0.2139 Trial B 2 Active Area at 45 1207.1 mm 2 0.2139 Trial B 3 Active Area at 60 853.5 mm 2 0.1513 Trial B 4 Active Area at 30 1478.5 mm 2 0.2621 1/6 active area for prismatic parts 0.16667 Trial B 1 Geometric limit to assembly .036 Trial B 2 Geometric limit to assembly .036 Trial B 3 Geometric limit to assembly .025 Trial B 4 Geometric limit to assembly .044 As described within the section on unit cell dynamics for the assembly interactions, the yield predictions for this model include the active area fraction of the surface of the assembly parts. The total yield prediction includes a function describing the e ffect of the KE:BE ratio. However, in the following experiments all trials are assumed to be conducted with a near zero energy ratio, kinetic energy:bond energy. With this assumption in place the predicted yields are at the geometric limit to assembly. Tab le 5 7 : Assembly yield predictions Assembly yield predictions for Trial sets A and B Trial A 1 Yield : 60% glycerol at 45 to normal .03 Trial B 1 Yield : 40% glycerol at 45 to normal 0.0357 Trial B 2 Yield : Deionized H2O at 45 to normal 0.0357 Trial B 3 Yield : Deionized H2O at 60 to normal 0.0252 Trial B 4 Yield : Deionized H2O at 30 to normal 0.0437
78 5.2 Experimental Results The trial results and predicted yield are tabulated below in Table 5 8 : Trial results and yield predictions Table 5 8 : Trial results and yield predictions Trial Predicted Yield at Zero KE limit Parts Dropped Parts Bound Resultant Yield Trial A 1 Yield : 60% glycerol to H2O at 45 to normal 0.03 170 5 0.029 Trial B 1 Yield : 40% glycerol to H 2 O at 45 to normal 0.0357 2664 107 0.0402 Trial B 2 Yield : Deionized H 2 O at 45 to normal 0.0357 3126 33 0.0106 Trial B 3 Yield : Deionized H 2 O at 60 to normal 0.0252 3268 11 0.0034 Trial B 4 Yield : Deionized H 2 O at 30 to normal 0.0437 3282 189 0.0575 5.3 Comparison to Hypotheses The results of the trials show mixed results in comparison to the experiment hypothesis. Trial A 1 shows the closest yield to the predicted yield. This trial included fewer parts dropped onto a patterned substrate The predicted yield is shown as a function of substrate mount angle The hypoth esis for these trials is that for syste ms in which the kinetic energy of the assembly interaction is low in comparison to the bond energy of an assembly the predicted yield will be at the geometric limit to assembly. With the self assembly test system all parameters of the assembly are fixed fo r a given trial,
79 however, within a trial series the substrate mount angle may be changed or fluid altered. In the case of trial A 1 the first prototype of the test system was in use and so the geometric limit of assembly, i.e. the predicted assembly yield, is different than the B series of trials. Trial A Figure 5 5 The curve and results for Trial series B are shown in Figure 5 6. Figure 5 5 : Predicted yield curve with trial A 1 data point. The predicted yield is a function of the substrate angle as the tilt of the substrate will alter the area of active assembly projected normal to the travel of parts. 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0 15 30 45 60 75 90 Predicted Yield Substrate Angle Predicted and Resultant Yields for trial A 1 Predicted Yield Trial A 1
80 Figure 5 6 : Predicted and r esultant y ields for trials Trial B 1 was conducted in 40% glycerol to H 2 O and is depicted using a square data point marker. The remaining tests were conducted in de ionized H2O and are depicted with circular data point markers. The substrate angle affects the geometric limit of assembly. 5.3.1 Trial A 1 This trial was conducted in an 60% glycerol to de ionized water environment with sites oriented at 45 to the direction of travel of the sites. 170 parts were dropped over the assembly environment and 5 successfully bound to the patterned assembly sites. The yield in this case was 0.029 of the total dropped parts. This trial was conducted near the zero ene rgy limit wherein the geometric parameters dominated the assembly model. This outcome is in good agreement with the predicted 3% yield. Unlike the other trials, this trial was 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 15 30 45 60 75 90 Predicted Yield Substrate Angle Predicted and Resultant Yields for series B Predicted Yield Trial B 1 Trial B 2 Trial B 3 Trial B 4
81 conducted with few parts. This may account for the high accuracy of the predicte d yield as the number of part interactions interfering with the assembly would be reduced. 5.3.2 Trial B 1 The first trial of this series conducted in an 40% glycerol to de ionized water environment with sites oriented at 45 to the direction of travel of the sites. 2664 parts were dropped over the assembly environment and 107 remained attached to the assembly area. The yield in this case was 0.04016 of the total dropped parts. This trial was conducted near the zero energy limit at which the geometric p arameters of the assembly model dominate yield. Figure 5 7 : Parts shown adhering to the copper site strips. The strip on top shows two parts bunching together from the continued addition of parts to an occupied area.
82 The y ield in this trial is somewhat higher than the predicted value of 0.0357. The grouping of parts at successful assemblies may be the cause. Parts landing on the surface, but in the wrong orientation, could simply remain in place due to contact with a proper ly attached part. The current setup is insufficient to test this speculation however, as it is unclear if the parts gathered as they fell or after falling to the surface. 5.3.3 Trial B 2 The second trial was conducted in de ionized water with assembly st rips oriented at 45 to the direction of part travel. 3126 parts were introduced to this environment with 33 parts assembling to the face of the copper in a recognizable fashion. A total of 88 parts remained on the surface, however most of these formed acc retions which are difficult to analyze and point to a necessity for some modification to part design or assembly process to prevent these formations from developing.
83 Figure 5 8 : Trial B 2 assembly results The yield of Trial 2 is found to be 0.0106, well below the predicted yield of 0.0357. This result is in part due to the difficulty of accounting for the accretions of parts, and also due to the anticipated effect of the higher energy interactions encountered in a pure H 2 O environment in which the kinetic energy of the parts exceed the bond energy of the parts. 5.3.4 Trial B 3 The third trial was conducted in de ionized water with assembly strips oriented at 60 to the direction of part travel. 3268 parts were
84 introduced to this environment with 11 parts assembling to the face of the copper in a recognizable fashion. A total of 46 parts remained on the surface, however many of these formed accretions which are di fficult to analyze as discussed previously. Figure 5 9 : Trial B 3 assembly. The sites are oriented at 60 degrees to the direction of travel of parts The yield of Trial 3 is found to be 0.00336, well below the predicted yiel d of 0.02521. This result is in part due to the difficulty of accounting for the accretions of parts, though, even accounting for all accreted parts as successful bonds the yield would remain low. The anticipated effect of the higher energy interactions en countered in a
85 pure H 2 O environment in which the kinetic energy of the parts is an additional factor which would interfere with the clarity of these results. A successfully bonded part is shown below as well as an image of the accretions encountered in all of the assembly trials. Figure 5 10 : Successfully bound part in assembly trial B 3. Note that this part suffers from a fabrication flaw due to dicing error. The parts reflection on the substrate makes ita appear like two p arts.
86 Figure 5 11 : An accretion of parts observed in assembly trial B 3. 5.3.5 Trial B 4 The fourth trial was conducted in de ionized water with assembly strips oriented at 30 to the direction of part travel. 3282 parts were introduced to this environment with 189 parts assembling to the face of the copper in a recognizable fashion. The yield of this trial was 0.05758, exceeding the predicted yield of 0.04368.
87 Figure 5 12 : Results of trial B 4 The high yield in this trial indicates that a simple geometric model for the interaction may be insufficient to describe the dynamics of the assembly interactions. With the sites at 30 to the direction of travel of the parts, the parts are lik ely encountering the sites and coming to rest on the sites whether they bind or not due to the low contribution of gravity to the motion of the parts in contact with the copper sites. The following picture shows several parts resting on the assembly sites without their copper faces binding to the strips as a result of the failure to move beyond the binding region.
88 Figure 5 13 : Parts resting on assembly sites These parts remain in place without binding to them properly and wi thout accreting to one another in trial B 4. Because the parts which strike the area of interest, but in the wrong orientation are capable of resting on the site, then the potential area of interest assembly is six times the assembly for parts striking in the correct orientation. The higher pitched substrates used in the other trials may permit the parts to slide off of their resting places if not successfully bound to the sites. In this trial, parts remain in place no matter their initial contact orientat ion or the result of a successful or unsuccessful binding. The results of this trial emphasize the necessity for a repulsive force within the self assembly environment. If the assembly had been conducted with a force of sufficient magnitude to repel parts from the
89 resting state in which they lie if unassembled, then the final yield count would be reduced to include only parts that approach the assembly in an orientation to bind to the site.
90 CHAPTER 6: CONCLUSIONS The application of the test environment to the initial assembly trials has revealed some important test design parameters. These conclusions will be acknowledged in the design and implementation of future experimentation plans using the system presented he re. The high relative accuracy of the trial A 1 compared to the B series of trials indicates a need to design tests using fewer parts, or to modify the system to prevent part interactions. This follows with the background from chemical kinetics in which ra te law models are created through the application of test data acquired during the first 10% of a reaction, as described in the background section of this work. Future trials will be conducted with fewer parts so that a sparse distribution assumption for n on interaction will be valid. The lack of a repulsive force within the environment can result in difficulties modeling and evaluating the performance of an assembly. The chemical kinetics models do not account for near chemical reactions in the way that ma y be seen in micro scale mechanical interactions between parts. The trial B 4 showed that parts may remain in the assembly space even without successfully binding if the repulsive force for disassembly of misaligned parts is too low to
91 remove them from the region. In this case, the repulsive force would be gravitational and the tilt of the assembly sites was insufficient to allow the gravitational parts to overcome the friction found resting on the assembly sites, even without a capillary bond in place. Som e promising results have been seen from the application of the Self Assembly test system developed for the purposes of this research. The modeling, which still requiring a great deal of fleshing out, appears at an initial assessment to reflect the assembly performance when the appropriate assumptions are observed. 6.1 Future Work In the short term it is the recommendation of this researcher that further trials be conducted exploring the near zero energy ratio limit assumption. A sequence of test conducted with varied fluid viscosity would greatly help to gather the sample data necessary to develop a proper functional model of the contribution of higher kinetic energies to the overall assembly yield. Furthermore, test repetitions using controlled forces for free part rejection may improve the clarity of assembly yield results. The automation of such a system would be ideal as consistency and repeatability should be observed in these trials. A peristaltic pump
92 connected to the assembly environment would provide a consistent flow however, pulsations in the flow may be desirable. The interference of individual parts within the assembly trials may be reduced or eliminated by changing the spacing of assembly sites and the s patial distribution of part drops. The interference of parts is a difficulty which affects analysis adversely and should be addressed as soon as possible. In a high throughput industrialized processes it seems likely that part interference may be unavoidab le. Modifying the predictive model to account for interference would, for this reason, be desirable. Further characterization and evaluation of the part and site fabrication process could be fruitful. The researcher and his colleagues have observed flaws i n the copper surfaces of the sites and parts, as well as residual copper left after the copper liftoff process has been completed for patterned assembly areas. Surface energy for assembly bonds may be increased by employing a silane SAM treatment to the Si surfaces of the assembly components. A hydrophilic silane wou l d reduce the surface energy for the Si portions of the assembly environment. Because the assembly surfaces are bounded by silicon regions the reduction in surface energy of the silicon regions would increase the gradient of energy between the assembly surfaces and the non active assembly regions, improving
93 the bond strength and increasing the capillary forces at play during bonding.
94 LIST OF REFERENCES  Pelesko, J. A., 2007, "Self assembly: the science of things that put themselves together," Taylor & Francis, Boca Raton.  Morris, 2005, "Self Assembly for Microscale and Nanoscale Packaging: Steps Toward Self Packaging," IEEE Transactions on Advanced Packaging, 2 8(4) pg. 600.  Hsi Jen, Y., 1994, "Fluidic self assembly of microstructures and its application to the integration of GaAs on Si," pg. 279.  Yeh, H. J., 1994, "Fluidic Self Assembly for the Integration of GaAs Light Emitting Diodes on Si Substrate s," IEEE Photonics Technology Letters, 6(6) pg. 706.  Verma, A. K., 1995, "Fluidic self assembly of silicon microstructures," pg. 1263.  Bohringer, K. F., 2001, "Modeling of Capillary Forces and Binding Sites for Fluidic Self Assembly," pg. 369.  Greiner, A., Lienemann, J., Korvink, J. G., 2002, "Capillary forces in micro fluidic self assembly," 2002 International Conference on Modeling and Simulation of Microsystems MSM 2002, Apr 21 25 2002, Anonymous Computational Publications, Cambridge, M A 02139, United States, San Juan, Puerto Rico, pp. 198 201.
95  Scott, K. L., 2004, "High Performance Inductors using Capillary Based Fluidic Self Assembly," Journal of Microelectromechanical Systems, 13(2) pg. 300.  Srinivasan, U., 2002, "Fluidic Sel f Assembly of Micromirrors Onto Microactuators using Capillary Forces," IEEE Journal of Selected Topics in Quantum Electronics, 8(1) pg. 4.  Hosokawa, 1994, "Dynamics of Self Assembling Systems Analogy with Chemical Kinetics," pg. 172.  Hosokawa, K., 1996, "Two Dimensional Micro Self Assembly using the Surface Tension of Water," Sensors and Actuators.A, Physical, 57(2) pg. 117.  Hongkai, W., 1999, "Selectivities among Capillary Bonds in Mesoscale Self Assembly," Applied Physics Letters, 75(20 ) pg. 3222.  Bowden, N., 1999, "Mesoscale Self Assembly of Hexagonal Plates using Lateral Capillary Forces: Synthesis using the Capillary Bond'," Journal of the American Chemical Society, 121(23) pg. 5373.  Wolfe, D., 2003, "Mesoscale Self Assembly: Capillary Interactions when Positive and Negative Menisci have Similar Amplitudes," Langmuir, 19(6) pg. 2206.  Oliver, S. R. J., Bowden, N., and Whitesides, G. M., 2000, "Self Assembly of Hexagonal Rod A rrays Based on Capillary Forces," Journal of Colloid and Interface Science, 224(2) pp. 425 428.
96  D. H., G., M., B., O., O., 2002, "Biomimetic Self Assembly of Helical Electrical Circuits using Orthogonal Capillary Interactions," Applied Physics Letter s, 80 pg. 2802.  Jacobs, H. O., Tao, A. R., Schwartz, A., 2002, "Fabrication of a Cylindrical Display by Patterned Assembly," Science, 296(5566) pp. 323 325.  Mastrangeli, M., 2009, "Self Assembly from Milli to Nanoscales: Methods and Applicatio ns," Journal of Micromechanics and Microengineering, 19(8) pg. 083001.  Alberty, R. A., and Silbey, R. J., 1992, "Physical chemistry," Wiley, New York.  Ross, S. M., 2003, "Introduction to probability models." Academic Press, San Diego,Calif. [2 1] Munson, B. R., Young, D. F., and Okiishi, T. H., 2006, "Fundamentals of fluid mechanics," J. Wiley & Sons, Hoboken, NJ.  Srinivasan, U., 2001, "Microstructure to Substrate Self Assembly using Capillary Forces," Journal of Microelectromechanical Sys tems, 10(1) pg. 17.
98 Appendix A: Assembly Mount 1 Drawing Figure A 1 : Original assembly mount design The long milled shelves held assembly sites
99 Appendix B: Assembly Mount 2 Drawings Figure B1: Final design for assembly mount base
100 Appendix B (continued) Figure B2: Final design of a ssembly mount shelves. Two are cut with sawed in slats and finally inserted into the base
ABOUT THE AUTHOR Gary Hendrick is a Mechanical Engineering student at the University of South Florida where he received his BSME in 2008 and plans to graduate with his MSME at the summer of 2010 In addition to his research at the micro scale integration laboratory he has been an activ e member and leader within the USF chapter of Engineers Without Borders.