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Magnetic Self-Assembly Of Small Parts

Permanent Link: http://ufdc.ufl.edu/UFE0024802/00001

Material Information

Title: Magnetic Self-Assembly Of Small Parts
Physical Description: 1 online resource (159 p.)
Language: english
Creator: Shetye, Sheetal
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: magnets, packaging, self
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Modern society s propensity for miniaturized end-user products is compelling electronic manufacturers to assemble and package different micro-scale, multi-technology components in more efficient and cost-effective manners. As the size of the components gets smaller, issues such as part sticking and alignment precision create challenges that slow the throughput of conventional robotic pick-n-place systems. As an alternative, various self-assembly approaches have been proposed to manipulate micro to millimeter scale components in a parallel fashion without human or robotic intervention. In this dissertation, magnetic self-assembly (MSA) is demonstrated as a highly efficient, completely parallel process for assembly of millimeter scale components. MSA is achieved by integrating permanent micromagnets onto component bonding surfaces using wafer-level microfabrication processes. Embedded bonded powder methods are used for fabrication of the magnets. The magnets are then magnetized using pulse magnetization methods, and the wafers are then singulated to form individual components. When the components are randomly mixed together, self-assembly occurs when the intermagnetic forces overcome the mixing forces. Analytical and finite element methods (FEM) are used to study the force interactions between the micromagnets. The multifunctional aspects of MSA are presented through demonstration of part-to-part and part-to-substrate assembly of 1 mm x 1mm x 0.5 mm silicon components. Part-to-part assembly is demonstrated by batch assembly of free-floating parts in a liquid environment with the assembly yield of different magnetic patterns varying from 88% to 90% in 20 s. Part-to-substrate assembly is demonstrated by assembling an ordered array onto a fixed substrate in a dry environment with the assembly yield varying from 86% to 99%. In both cases, diverse magnetic shapes/patterns are used to control the alignment and angular orientation of the components. A mathematical model is used to characterize part-to-substrate MSA. It is shown that the assembly rate and the yield are most dependent on the rotational symmetry of the magnet pattern. Simultaneous and sequential heterogeneous assembly of two types of parts with selective bonding is also demonstrated, with the average assembly yield of 93% in 60 s and 99% in 3.5 min respectively. Finally, MSA with functional electrical interconnects is also demonstrated with a yield of 90.5%.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sheetal Shetye.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Arnold, David.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024802:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024802/00001

Material Information

Title: Magnetic Self-Assembly Of Small Parts
Physical Description: 1 online resource (159 p.)
Language: english
Creator: Shetye, Sheetal
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: magnets, packaging, self
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Modern society s propensity for miniaturized end-user products is compelling electronic manufacturers to assemble and package different micro-scale, multi-technology components in more efficient and cost-effective manners. As the size of the components gets smaller, issues such as part sticking and alignment precision create challenges that slow the throughput of conventional robotic pick-n-place systems. As an alternative, various self-assembly approaches have been proposed to manipulate micro to millimeter scale components in a parallel fashion without human or robotic intervention. In this dissertation, magnetic self-assembly (MSA) is demonstrated as a highly efficient, completely parallel process for assembly of millimeter scale components. MSA is achieved by integrating permanent micromagnets onto component bonding surfaces using wafer-level microfabrication processes. Embedded bonded powder methods are used for fabrication of the magnets. The magnets are then magnetized using pulse magnetization methods, and the wafers are then singulated to form individual components. When the components are randomly mixed together, self-assembly occurs when the intermagnetic forces overcome the mixing forces. Analytical and finite element methods (FEM) are used to study the force interactions between the micromagnets. The multifunctional aspects of MSA are presented through demonstration of part-to-part and part-to-substrate assembly of 1 mm x 1mm x 0.5 mm silicon components. Part-to-part assembly is demonstrated by batch assembly of free-floating parts in a liquid environment with the assembly yield of different magnetic patterns varying from 88% to 90% in 20 s. Part-to-substrate assembly is demonstrated by assembling an ordered array onto a fixed substrate in a dry environment with the assembly yield varying from 86% to 99%. In both cases, diverse magnetic shapes/patterns are used to control the alignment and angular orientation of the components. A mathematical model is used to characterize part-to-substrate MSA. It is shown that the assembly rate and the yield are most dependent on the rotational symmetry of the magnet pattern. Simultaneous and sequential heterogeneous assembly of two types of parts with selective bonding is also demonstrated, with the average assembly yield of 93% in 60 s and 99% in 3.5 min respectively. Finally, MSA with functional electrical interconnects is also demonstrated with a yield of 90.5%.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sheetal Shetye.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Arnold, David.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024802:00001


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1 MAGNETIC SELF -ASSEMBLY OF SMALL PARTS By SHEETAL B. SHETYE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Sheetal B. Shetye

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3 To the loving memory of my father, Bhalchandra Shetye

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4 ACKNOWLEDGMENTS Financial support for this work was provided by National Science Foundation (NSF) grant DMI 0556056. I would like to take this opportunity to thank my advisor Dr. David P. Arnold for his guidance and motivation to bring out the best in me. His continuous encouragement and support made it possible for me to deal with all the techn ical as well as personal difficulties. I would also like to thank my committee members, Dr. Louis Cattafesta, Dr. Toshi Nishida, and Dr. Huikai Xie for their direction and supervision in the success of this project. I am extremely thankful for all the gre at friends I have made here at the Interdisciplinary Microsystems Group (IMG). I would like to thank Erin Patrick for being such a wonderful friend and for all the technical and non -technical discussions which played a significant role in the success of th is work. Brandon Bertolucci deserves special thanks for his help with the initial experimental set up and photography skills. I am thankful to Ilan Eskinazi for his help with the experimental set ups and data collection and analysis. I also thank Israel Bo niche for his help with solder dispensing set up, which helped me complete the final portion of this work. I am also grateful to Jeremy Sells, Naigang Wang, Vijay Chandrasekharan, Ben Griffin, Chris Bahr, Robert Dieme, and John Griffin for their insight an d helpful contributions. I am thankful for the ultimate frisbee Sundays, which helped me refuel for the rest of the week. I would also like to thank Al Ogden and Bill Lewis (UFNF staff) for their fabrication and clean room processing expertise. I am foreve r in debt to my father, Bhalchandra Shetye, who instilled this dream in me. I wish he was here to witness his dream come true and shower me with his blessings. I would also like to thank my mother, Madhuri Shetye, who puts her heart and soul into fulfillin g my dreams and desires before hers. I am thankful to my brother, Harshal Shetye, for his support. I am also

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5 thankful to my in -laws, Premchand and Madhuri Chaube, brother in law, Nilesh Chaube, and sister -in -law, Anju Pandey, for their love and support. Above all, I am grateful to my husband, Ritesh Chaube, for his unconditional love. He has been a very good listener and helped me through a lot of technical discussions. He is the pillar of my life, his patience and support through all the ups and downs, made this work possible.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 8 LIST OF FIGURES .............................................................................................................................. 9 ABSTRACT ........................................................................................................................................ 14 CHAPTER 1 INTRODUCTION ....................................................................................................................... 16 1.1 Motivation .......................................................................................................................... 16 1.2 Research Goals .................................................................................................................. 18 1.3 Research Contributions ..................................................................................................... 18 1.4 Thesis Organization .......................................................................................................... 19 2 BACKGROUND ......................................................................................................................... 20 2.1 Self -Assembly ................................................................................................................... 20 2.2 Self -Assembly Techniques ............................................................................................... 21 2.2.1 Gravitational Force Driven Self -Assembly .......................................................... 22 2.2.2 Capillary Force Driven Self -Assembly ................................................................ 26 2.2.3 Capillary Force Driven Assembly with Shape Recognition ............................... 34 2.2.4 Other Self -Assembly Techniques ......................................................................... 38 2.3 Drawbacks of Previously Demonstrated Self -Assembly Processes .............................. 51 2.4 Magnetic Self -Assembly (MSA) ...................................................................................... 54 2.5 Conclusion ......................................................................................................................... 57 3 MODELING ................................................................................................................................ 58 3.1 Magnetic Modeling ........................................................................................................... 58 3.1.1 Forc e Equations ..................................................................................................... 60 3.1.2 Finite Element Method .......................................................................................... 67 3.2 Self -Assembly Process Modeling .................................................................................... 73 3.2.1 Assembly Model .................................................................................................... 73 3.2.2 Model Validation ................................................................................................... 77 3.3 Conclusion ......................................................................................................................... 78 4 FABRICATION .......................................................................................................................... 79 4.1 Bonded Powder Magnets .................................................................................................. 80 4.1.1 Polyimide Capped Magnets .................................................................................. 80 4.1.2 Wax Bonded Magnets ........................................................................................... 80

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7 4.2 Magnetization .................................................................................................................... 82 4.3 Measurement of Magnetic Properties .............................................................................. 83 4.4 Part and Substrate Fabrication .......................................................................................... 85 4.4.1 Part and Substrate Singulation .............................................................................. 85 4.4.2 Preparation of Parts and Substrates for Bonding Selectivity Experiments ........ 86 4.4.3 Part and Substrate Fabrication for Magnetic Self -Assembly with Electrical Interconnects ......................................................................................................... 88 4.5 Conclusion ......................................................................................................................... 91 5 RESULTS .................................................................................................................................... 92 5.1 Evaluation of Magnetic Bonding Forces ......................................................................... 92 5.1.1 Evaluation of Size, Shape and Type of Magnets ................................................. 92 5.1.2 Evaluation of Force between Arrays of Magnets ................................................ 96 5.2 Bonding Force Measurement ......................................................................................... 100 5.3 Part to Part Magnetic Self -Assembly ............................................................................ 104 5.3.1 Experimental Setup ............................................................................................. 104 5.3.2 Experiments and Results ..................................................................................... 105 5.4 Part to Substrate Magnetic Self assembly .................................................................... 108 5.4.1 Experimental setup .............................................................................................. 108 5.4.2 Magnetic Self -Assembly of a Homogeneous Mixture of Parts ........................ 110 5.4.3 Magnetic Self -Assembly of a Heterogeneous Mixture of Parts ....................... 123 5.4.4 Magnetic Self -Assembly Demonstration with Electrical Interconnects .......... 129 5.5 Measurement of Alignment ............................................................................................ 132 5.6 Conclusion ....................................................................................................................... 133 6 CONCLUSION AND FUTURE WORK ................................................................................ 135 6.1 Conclusion ....................................................................................................................... 135 6.2 Key Issues ........................................................................................................................ 138 6.3 Recommended Future Work ........................................................................................... 142 APPENDIX: MATLAB FUNCTIONS ........................................................................................... 144 REFERENCES ................................................................................................................................. 149 BIOGRAPHICAL SKETCH ........................................................................................................... 159

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8 LIST OF TABLES Table page 2 1 Summary of previously demonstrated self assembly processes ......................................... 48 3 1 Assembly yield as function of t / T and redundant parts ........................................................ 75 4 1 Magnetic properties of Si embedded micromagnets ............................................................ 85 5 1 Comparison of measured bonding forces with the estimated FEM forces for various component types ................................................................................................................... 103 5 2 Force estimation for Si embedded SmCo magnets for part to -part magnetic self assembly ................................................................................................................................ 106 5 3 Part to part magnetic self assembly results ........................................................................ 107 5 4 Part to -substrate magnetic self assembly results ............................................................... 113 5 5 Statistical moments of the parameter T derived from the Monte Carlo simulation ......... 116 5 6 Part to -substrate magnetic self assembly characterization results .................................... 123 5 7 ANOVA table for T analysis ............................................................................................... 123

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9 LIST OF FIGURES Figure page 1 1 Comparison of (a) conventional robotic assembly and (b) self assembly process ............ 17 2 1 Previously dem onstrated approaches for self assembly of small parts (cross sectional views) ...................................................................................................................... 22 2 2 Self assembly of 1000 hexagonal parts in a t wo dimensional lattice using diaphragm vibration. ................................................................................................................................. 23 2 3 Self assembly of GaAs LEDs on Si substrate using shape recognition technique ............ 24 2 4 Part and substrate for selfassembly using interlocking pins .............................................. 25 2 5 Part and substrate design for in -plane orientation using interlocking pins ......................... 25 2 6 Demonstration of two dimensional arrays using lateral capillary forces. .......................... 26 2 7 Ca pillary force driven selective self assembly process ....................................................... 27 2 8 Formation of 3D electrical networks using capillary driven self assembly process .......... 27 2 9 Self assembly of cylindrical display using capillary force .................................................. 28 2 10 3D sequential self assembly of micro -scale components using hydrophobic interactions .............................................................................................................................. 29 2 11 Capillary force driven self assembly of micromirrors onto microactuators ....................... 30 2 12 Capillary for ce self assembly of microfabricated inductors ................................................ 31 2 13 Capillary force driven selective self assembly process ....................................................... 32 2 14 Capillary force driven self assembly in air assisted by diaphragm agitation ..................... 32 2 15 Programmable bo nding: Activation of solder coated receptor sites using embedded heaters on the backside of the substrate ................................................................................ 33 2 16 3 D self assembly using polymer adhesive for capillary force driven self assembly process ..................................................................................................................................... 33 2 17 Shape and solder directed heterogeneous assembly and packaging of functional Microsystems .......................................................................................................................... 35 2 18 Heterogeneous self assembly using shape recognition and capillary force ....................... 36 2 19 DUO -SPASS process using shape recognition and capillary force .................................... 37

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10 2 20 Capillary force driven vertical and horizontal assembly process ........................................ 38 2 21 Self assembly using surface tension of water ...................................................................... 39 2 22 Solder surface tension self assembly process ....................................................................... 40 2 23 Electrostatic self assembly .................................................................................................... 41 2 24 Electric field driven self assembly of surface mount capacitors and diodes. ..................... 42 2 25 Self assembly using bridging flocculation ........................................................................... 42 2 26 Micromanipulation on microparts using external magnetic field ....................................... 43 2 27 3 D self assembly of hinged structures using external magnetic field ............................... 44 2 28 3 D magnetic self assembly .................................................................................................. 45 2 29 Magnetic self assembly with the snow -globe set up ........................................................... 46 2 30 Folding of membranes using soft -magnetic array and external magnetic field ................. 47 2 31 Magnetic field assisted self assembly process ..................................................................... 47 2 32 Self assembly using permanent magnet array ...................................................................... 48 2 33 Magnetic self assembly concept ........................................................................................... 55 3 1 Typical hysteresis plot for a permanent magnet (M H loop) .............................................. 59 3 2 Typical B -H loop for a permanent magnet ........................................................................... 60 3 3 External magnetic field acting on a permanent magn et ....................................................... 62 3 4 Force between cuboidal and cylindrical magnets ................................................................ 64 3 5 M H loop and r v/s H plot for SmCo magnet .................................................................... 68 3 6 Example field solution for FEM simulation of two cuboidal magnets. .............................. 69 3 7 Axial force vs. axial and lateral displa cement for cuboidal magnets. ................................. 70 3 8 Lateral force vs. axial and lateral displacement. .................................................................. 71 3 9 Comparison of force between magnets and the chip weight force ..................................... 73 3 10 Assembly yield as function of t / T and redundant parts. ...................................................... 76 3 11 Experimentally measured progression of magnetic self assembly with respect to time for different numbers of redundant parts .............................................................................. 78

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11 4 1 Process flow for fabrica tion of Si embedded micromagnets ............................................... 81 4 2 Components fabricated using Si embedded bonded powder micromagnets. ..................... 82 4 3 Cross sectional view of Si embedded bonded pwder magnets ............................................ 82 4 4 Pulse magnetizer .................................................................................................................... 83 4 5 System diagram of VSM ........................................................................................................ 84 4 6 Ch ips with various magnet patterns ...................................................................................... 86 4 7 Transfer of parts from the dicing tape to the painter's tape ................................................. 87 4 8 Spray painted substrate and parts in black and white .......................................................... 88 4 9 Process flow for fabrication of parts and substrate for demonstration of magnetic self assembly with electrical interconnects .......................................................................... 89 4 10 Part and s ubstrate with three columns of receptor sites for demonstration magnetic self assembly with electrical interconnects. ......................................................................... 90 5 1 Analysis of size and type of magnet ..................................................................................... 93 5 2 Shape analysis ........................................................................................................................ 94 5 3 Magnetization direction analysis ........................................................................................... 95 5 4 Surface effects for electroplated magnets ............................................................................. 96 5 5 Array of magnets on part A and part B indicating magnet width, a and array spacing, d ................................................................................................................................ 97 5 6 Laterally displaced magnets with zero axial gap ................................................................. 97 5 7 Normalized axial force vs. normalized lateral gap for square magnets .............................. 9 8 5 8 Variation of force and force per unit area with respect to normalized array spacing ........ 99 5 9 Experimental set up for bonding force measurement ........................................................ 101 5 10 Compari son of axial force using FEM ideal, non ideal, experimental and analytical methods. ................................................................................................................................ 102 5 11 Part to part magnetic self assembly concept ...................................................................... 105 5 12 Experiment set up for part to part magnetic self assembly .............................................. 105 5 13 S i embedded SmCo magnets with 4 -fold symm etry and 2 -fold symmetry ...................... 106

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12 5 14 Part to part magnetic self assembly of free floating components .................................... 107 5 15 Part to -substrate magnetic self assembly concept ............................................................. 108 5 16 Schematic of the experiment set up for part -to -substrate magnetic self assembly .......... 109 5 17 Experiment set up for part to -substrate magnetic self assembly ...................................... 110 5 18 Components used in part -to -substrate magnetic self assembly demonstration................ 111 5 19 Demonstration of part -to -substrate magnetic self assembly where parts have assembled onto an inverted substrate .................................................................................. 111 5 20 Assembly vs. time data for Square1 pattern for 15 trial s ................................................... 114 5 21 Snapshot views of magnetic self assembly of oval pattern from t=0 to t=20s. ............... 114 5 22 Probability distribution function of T for oval_2 pattern. .................................................. 115 5 23 Part to -substrate assembly with some stacked components .............................................. 117 5 24 Variation of T with respect to the magnet pattern symmetry ............................................ 118 5 25 Variation of T with the numbe r of magnets in the bonding pattern .................................. 119 5 26 Variation of T with respect to the magnet surface area ..................................................... 119 5 27 Variation of T with respect to the bonding force ............................................................... 120 5 28 Variation of T with respect to the bonding force per unit area .......................................... 120 5 29 Latin square design with 3 levels and 3 -factors for characterization of magnetic self assembly process. ................................................................................................................. 121 5 30 Various components used in the characterization of magnetic self assembly experiments. .......................................................................................................................... 122 5 31 Magnetic self assembly (MSA) of two types of parts from a heterogeneous mixture of part s .................................................................................................................................. 124 5 32 Components used for sequential heterogeneous magnetic self assembly demonstration. ...................................................................................................................... 124 5 33 Demonstration of sequential magnetic self assembly of multiple component types from a heterogeneous mixture ............................................................................................. 126 5 34 Concept for sequential magnetic self assembly ................................................................. 126 5 35 Components used for simultaneous heterogeneous assembly. .......................................... 127

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13 5 36 Demonstration of simultaneous magnetic self assembly of multiple component types from a heterogeneous mixture ............................................................................................. 128 5 37 Concept for simultaneous magnetic self assembly ............................................................ 128 5 38 Part and substrate used for demonstration of magnetic self assembly with electrical interconnects ......................................................................................................................... 129 5 39 Demonstration of magnetic self assembly with electrical interconnects, substrate with assembled parts. ........................................................................................................... 130 5 40 Magnetic pattern used for alignment measurement ........................................................... 133 5 41 Substrate with 6 x 6 array of receptor sites used for alignment measurement ................. 133 6 1 Patterned magnets on back side and electrical interconnects on the front side of the components ........................................................................................................................... 141

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14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfill ment of the Requirements for the Degree of Doctor of Philosophy MAGNETIC SELF -ASSEMBLY OF SMALL PARTS By Sheetal B. Shetye August 2009 Chair: David P. Arnold Major: Electrical and Computer Engineering Modern societys propensity for miniaturized endus er products is compelling electronic manufacturers to assemble and package different micro -scale, multi -technology components in more efficie nt and cost -effective manners. As the size of the components gets smaller, issues such as part sticking and alignme nt precision create challenges that slow the throughput of conventional robotic pick n -place systems As an alternative various self assembly approaches have been proposed to manipulate micro to millimeter scale components in a parallel fashion without hu man or robotic intervention. In this dissertation, magnetic self assembly (MSA) is demonstrated as a highly efficient, completely parallel process for assembly of millimeter scale components. M SA is achieved by integrating permanent micromagnets onto comp onent bonding surfaces using wafer level microfabrication processes. Embedded bonded powder methods are used for fabrication of the magnets. The magnets are then magnetized using pulse magnetization methods, and the wafers are then singulated to form individual components. When the componen ts are randomly mixed together, self assembly occurs when the intermagnetic forces overcome the mixing forces.

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15 Analytical and finite element methods (FEM) are used to study the force interactions between the micromagnets. The multifunctional aspects of MS A are presented through demonstration of part to -part and part -to -substrate assembly of 1 mm x 1mm x 0.5 mm silicon components. Part -to -part assembly is demonstrated by batch assembly of free -floating parts in a liquid environment with the assembly yield o f different magnetic patterns varying from 88% to 90% in 20 s. Part to -substrate assembly is demonstrated by assembling an ordered array onto a fixed substrate in a dry environment with the assembly yield varying from 86% to 99%. In both cases, diverse mag netic shapes/patterns are used to control the alignment and angular orientation of the components. A mathematical model is used to characterize part to -substrate MSA. It is shown that the assembly rate and the yield are most dependent on the rotational sym metry of the magnet pattern. S imultaneous and sequential heterogeneous assembly of two types of parts with selective bonding is also demonstrated with the average assembly yield of 93% in 60 s and 99% in 3.5 min respectively. Finally, MSA with functional electrical interconnects is also demonstrated with a yield of 90.5%.

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16 CHAPTER 1 1 INTRODUCTION The goal of this research is to explore, understand, and optimize a novel self assembly technique for assembly and packaging of micro to millimeter scale components. This technique called magnetic self assembly (MSA) uses the magnetic fields from permanent magnets microfabricated on component surfaces as the driving force for assembly. MSA is expected to overcome the drawbacks of previously demonstrated self assembly process that use gravity, capillary, or electrostatic forces to drive the assembly process. If successful MSA will offer significant advantages and design flexibility for complex self assembly processes. 1 1 Motivation The idea of a miniaturized electronic world has spurred the development of complex, integrated microsystems for consumer electronics, sensor networks, biomedical devices, and so on. Si nce many of the new device fabrication technologies and materials are not compatible with each other, complex and multifunctional devices are made by heterogeneous integration of various subsystems. One example is a modern cellular phone, which tightly int egrates CMOS electronics, RF components, photonics, microelectromechanical systems (MEMS), passive discrete components, power supplies, and circuit boards to enable wireless communication, data processing/storage, and signal processing functionalities. To keep pace with market demands for smaller, cheaper, electronic systems with more functionality, device manufacturers are faced with great technological and economical challenges. Conventionally, all device subcomponents are manufactured separately in bulk and then assembled in serial fashion using robotic pick -n -place systems as shown in Figure 1 1 (a) However, as the size of these subcomponents diminishes the throughput is limited by precise manipulation requirements. Alignment and positioning tolerances scale with the component size.

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17 A t the microscale, electrostatic and Van der Waals adhesion forces between the components and the manipulator become promi nent making the handling and the release of the components difficult. Also, the number and the speed of the manipulators decide the assembly and packaging rate. Overall, the serial assembly and packaging of these bulk manufactured components is becoming a manufacturing bottleneck and a technological barrier for advanced microsystems. Hence the need for alternative assembly methods has risen where by the subcomponents can self assemble in parallel without any robotic or manual intervention as shown in Figure 1 1 (b). Figure 1 1 Comparison of (a) conventional robotic assembly and (b) self assembly process Potential appli cations of self assembly include the assembly of RFID integrated circuits onto larger planar substrate antennas ; 2D and 3D integration of different device technologies (e.g. integrated circuits, sensors, actuators, and power supplies) for highly functional ultra compact microsystems ; or the ability to self assemble reconfigure, or self -heal microrobots or other futuristic technologies

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18 1 2 Research Goals The objective of this research is to develop new, magnetically directed, self -assembly approaches to enable complex, three-dimensional structures to be formed in parallel from a heterogeneous mixture of parts of arbitrary size and shape. To achieve this goal, microscale magnets or array of magnets of different shapes and sizes are batch fabricated onto the surfaces of microcomponents using low -cost, wafer level embedded bonded magnet fabrication methods [1]. To enact assembly, t hese components are then mixed together in a random fashion either by fluidic motion (for wet assembly) or by bouncing the parts using a mechanical shaker (for dry assembly) The parts self assemble when the intermagneti c forces overcome the mixing forces thereby bonding components to one another By using diverse magnetic patterns, MSA is demonstrated to enable advance d self assembly features such as orientation uniqueness, inter part bonding and bonding selectivity. 1 3 R esearch Contributions Analytical and experimental evaluation of magnetic bonding forces for single magnets and arrays of magnets Development and characterization of microfabrication processes for wafer level integration of hard magnets onto microcomponent surfaces Experimental demonstration of part to -part magnetic self assembly with angular orientation Experimental demonstration of part to -substrate magnetic self assembly from a homogeneous mixture of parts with unique angular orientation and funct ional electrical interconnects Experimental demonstration of part to -substrate magnetic self assembly from a heterogeneous mixture of parts via selective/programmable bonding Characterization and modeling of magnetic self assembly processes

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19 1 4 Thesis Organization This dissertation consists of six chapters. Chapter 1 includes a brief introduction to self assembly, and research goals and contributions. Chapter 2 reviews previously demonstrated self assembly processes and introduces the magnetic self asse mbly concept. Chapter 3 discusses force equations for permanent magnets and also introduces an assembly process model used to model the MSA process. Chapter 4 presents various microfabrication techniques for permanent magnets on to silicon surfaces and pre paration of parts and substrates for various magnetic self assembly demonstrations. Magnetic self assembly demonstration and results are discussed in Chapter 5. The characterization results of MSA using the assembly model are also presented in this chapter Chapter 6 includes the conclusion some key issues and recommendations for future work.

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20 CHAPTER 2 2 BACKGROUND In this chapter the term self -assembly is first defined as applying to this thesis. P reviously demonstrated techniques of self a ssembly are explained in detail, and the results from these prior efforts are summarized. Finally the magnetic self assembly concept is introduced and its advantages over previously demonstrated approaches are discussed. 2 1 Self Assembly Self assembly i s seen in nature all the time, where intermolecular forces spontaneously assemble millions of subcomponents into ordered structures with great efficiency [2]. Self assembly is defined as the autonomous organization of components into patterns or structures without human intervention [2] The term self assembly is very well known in the field of molecular chemistry where molecules from ordered structures usually through non-covalent bonding [3]. In [3] the authors G.M. Whitesides and M. Boncheva draw parallels between molecular self assembly and mesoscopic and macroscopic self assembly. The concept o f self assembly is explained with the help of studies done on molecular self assembly. In the self assembly process presented here, assembly is focused on the directed organization and selective manipulation of several mechanically unconstrained small part s (micro to millimeter scale) in parallel. Here self assembly of discrete components to form an ordered stable structure by local energy minimization is considered. There are two main forces acting in the self assembly process; Bonding force: the short ra nge bonding force that result s in suitable interactions between components that cause the parts to assemble onto the substrate or one another. Mixing force: the mechanical force that causes random movement and mass transport of the discrete parts and enabl es them to self assemb le

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21 The mixing forces mix the parts randomly, bringing them in close proximity, while the short range bonding forces capture and trap the parts The combination of these two processes drives the self assembly in a random fashion Self assembly occurs when these short range bonding forces overcome the mixing forces and alignment is achieved by local energy minimization. Fluid flow, mechanical vibrations and stirring have been used as mixing forces in previously demonstrated self assembl y techniques. Numerous short range bonding forces, such as gravitational force, surface tension force, electrostatic force, capillary force, magnetic force and combination of some of these have been explored by various groups as the driving force for the s elf assembly process as discussed in the next sections. To be useful for manufacturing, self assembly must be capable of correctly assembling parts in well-controlled configurations. In addition to the forces driving the assembly, different passive and ac tive strategies have been used to help align the parts or enable specificity in the bonding. For example, the physical geometry of the component has been used to aid in alignment or orientation, a technique known as shape recognition. Or for capillary dr iven processes, embedded heaters have been used to selectively melt solder bumps to enable a degree of programmability. A later section describes all these processes in much detail. 2 2 Self Assembly Techniques Numerous research groups have devoted their eff orts towards demonstrating innovative and progressive self assembly techniques that could be used for homogeneous and heterogeneous, Two dimensional ( 2 D ) and three dimensional ( 3 D ) assembly of otherwise incompatible (fabrication wise) microdevices. Figure 2 1 illustrates some of the previously demonstrated self assembly processes which are discussed in this section.

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22 Figure 2 1 Previously demonstrated approaches for self assembly of small parts (cross sectional views) In 1991, A. P. Pisano et al. from University of California, Berk e ley were first to draw an analogy between crystal growth and self assembly of m to mm scale devices [4]. The y demonstrated the self assembly of 1000 identical hexagons 1 mm in diameter to achieve a regular two dimensional lattice in about a minute The hexagonal parts were dispensed on a vibrating concave diaphragm resulting in all the parts eventually lying fla t on the diaphragm and forming the two -dimensional lattice as shown in Figure 2 6 This group provoked the interest in self assembly concept and thus enabled the exp loitation of micromachining and microfabrication technologies to their advantage. Since then many self assembly demonstrations were made using the gravity and capillary driven processes and also the combination of the two. First these two major techniqu es will be d iscussed here, followed by discussion of the other techniques shown in Figure 2 1 2 2 1 Gravitational Force Driven Self Assembly In 1994, Yeh and Smith also from University of California, Berkley [5] first introduced the concept of fluidic self assembly that utilizes gravity fluid flow, and s hape recognition to drive the assembly of micro scale components. Their work mainly focused on assembly of trapezoidal shaped components into complementary holes in the substrates by gravity in fluidic medium as shown in Figure 2 3 The trapezoidal shape prevented the upside down falling components from

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23 assembling into the recesses on the substrate This process further became known as fluidic self assembly (FSA). Fig ure 2 2 Self assembly of 1000 hexagonal parts in a two dimensional lattice using diaphragm vibration [4] (Reprinted with permission [1991] IEEE). Yeh and Smith successfully integrated GaAs vertical emitting light -emitting diodes (LED s), GaAs/AlAs resonant -tunneling diodes (RTDs), vertical cavity surface emitting lasers (VCSELs), and optoelectronic devices onto Si wafers [6, 7 10] FSA technology has now been adopted by Alien Technology Corp oration for selfassembly of RFID tags at ra tes up to 2 million/hr and assembly of nanoblock ICs onto flexible substrates [6] Application of FSA for integration of electronic and optoelectronic devices with CMOS and MEMS devices was explored in [6, 7] A yield of 30 [5, 8] In [9] a systematic study of FSA integration efficiency was presented. Two sizes of blocks were explored: large blocks of dimension 1.0 mm x 1.2 mm x 0.235 mm and small blocks of dimension 150 m x 150 m x 35 m. A bubble pump apparatus was used to circulate the parts during the assembly. The authors reported 100% yield in 2.5 min in the case of la rge blocks and

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24 a yield of 70% in 15 min in the case of small blocks [9]. The number of redundant parts (the number of parts relative to the number of sites) used in the assembly of large blocks was about 2.7x and in the case of the smaller blocks was about 7x. GaAs LED Si substrate GaAs LED Si substrate Ethanol Figure 2 3 Self assembly of GaAs LEDs on Si substrate using shape recogniti on technique (Adapted from [8]). In [9, 10] issues related to self assembly of small devices were also reported. Small components tended to stick to the substrate surface due to their low mass as compared to the exposed surface area. Recommendatio ns like using roughing the substrate surface, stronger fluid flow or acoustic vibration under the substrate were suggested to mitigate the sticking of the parts to the substrate and to improve the agitation of the smaller parts to improve the assembly yiel d of the FSA process. Karl F. Bhringer now at University of Washington, has been working on self assembly process since 1997. In his most recent publications his group demonstrated a fully dry 2D and 3D self assembly process using gravity and shape recog nition. This was achieved by using complementary interlocking pins [11 13] The parts were fabricated with an interlocking pin

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25 similar to a nail, and the substrates were fabricated with the binding site having a large hole and a small interlock hole as see in Figure 2 4 When the parts were allowed to vibrate and move on the substrate, the parts fell into the large hole and then slid in to the small interlocking hole. 100% assembly yield in 5 min with 2 x redundant parts on the substrate with 18% packing density, and 81% with 1.5 x redundant parts on the substrate with 40% packing density was achieved [12] Figure 2 4 Part and substrate for selfassembly using interlocking pins (Adapted from [12] ). Using a similar technique in -plane orientation was achieved by introducing additional features on the parts and the substrates [11] as seen in Figure 2 5 In this case 95 % assembly yield was achieved with maximum rotational orientation error of 1.7 and maximum translational error of 5 m. Figure 2 5 Part and substrate design for inplane orientation using interlocking pins ( Adapted from [11 ]). In the most recent publication, a method to enhance the efficiency of the previously demonstrated dry self assembly processes was explored [13] A fe w non -participating mm -scale

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26 components (220.5 mm3) were added to the microcomponents (80080050 3). These mm scale components acted as catalysts resulting in 25 50 % reduction in acceleration and up to 4 times increase in the number of activated pa rts for the assembly process. Just by adding 3 catalysts in box with 30 parts the number of activated parts increased 5 fold at lower accelerations. 2 2 2 Capillary Force Driven Self Assembly G. M. Whitesides s group at Harvard demonstrated self assembly of mm -s cale objects (1 10 mm) into ordered two dimensional array using lateral capillary forces in 1997 [14] The parts with desired shapes were made from a hydrophobic polymer, polydimethylsiloxane (PD MS).Then certain surfaces (side faces ) of the parts were made hydrophilic by oxidation. These parts were then floated a t a perfluorodecalin and water interface, with the hydrophobic sides wetted by the perfluorodecalin. With appropriate mixing forces the wetted hydrophobic sides of adjacent part s created a contact by the lateral capillary force thus resulting in a self assembled two dimensional array as shown in Figure 2 6 Figure 2 6 Demonstration of two dimensional arrays using lateral capillary forces. A) Assembly of crosses, B) Assembly of Hexagons and C) Assembly of closed packed hexagons [14] From N. Bowden, A. Terfort, J. Carbeck, and G. M. Whitesides, "Self Assembly of Mesoscale Objects into Ordered Two Dimensional Arrays," Science, vol. 276, pp. 233235, 1997. Reprinted with permission from AAAS.

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27 Next, Whitesides group demonstrated formation of 3D aggregates from 1 mm size parts using capillary forces [15] In general the capillary force driven self assembly involves the chemical modification of the surface properties i.e. selectively making the surfaces hydrophobic or hydrophilic and then assembling the parts in liquid environment. The concept of capillary driven self assembly is shown in Figure 2 7 Hydrophobic area Lubricant Figure 2 7 Capillary force driven selective self assembly process ( Adapted from [16] ). Their next major accomplishment was demonstration of 3 D electrical networks with millimeter scale polyhedral parts [17] The surfaces of these parts were patterned with solder dots, wires and LEDs. On mixing these polyhedral components in an isodense liquid at the melting temperature of the solder, the solder dots fused together and resulted in self assembly through capillary action between the interfaces as seen in Figure 2 8 Figure 2 8 Formation of 3D electrical networks using capillary driven self -assembly process [17] From D. H. Gracias, J. Tien, T. L. Breen, C. Hsu, and G. M. Whitesides, "Forming Electrical Networks in Three Dimensions by Self -Assembly," Science, vol. 289, pp. 11701172, August 18, 2000. Reprinted with permission from AAAS.

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28 Later on this group demonstrated the formation of a cylindrical display [18] using microscale LEDs. The substrates in this case were patterned with solder -coated areas that acted as receptor sites for the semiconductor devices and as electrical contacts after the assembly. The parts and the substrate were mixed together in water that was heated to 90 C. At this temperature, the solder became molten and upon agitation the components self assembled as a result of minimization of free ene rgy at solder -water interface. The fabricated cylindrical display shown in Figure 2 9 contained 113 GaAlAs LEDs with chip size of 280 m x 280 m x 200 m. Also, abou t 1500 chips were shown to self assemble onto planar substrate with a defect rate of about 2% in less than 3 minutes with a total of about 5000 redundant components. Figure 2 9 Self assembly of cylindrical display using capillary force [18] From H. O. Jacobs, A. R. Tao, A. Schwartz, D. H. Gracias, and G. M. Whitesides, "Fabrication of a Cylindrical D isplay by Patterned Assembly," Science, vol. 296, pp. 323325, April 2002. Reprinted with permission from AAAS. Isao Shimoyamas group at University of Tokyo used capillary force driven assembly to demonst ra te 3 D sequential self assembly of 10 m components [19, 20] and closed link microcha in structures with selective bonding [21] They achieved this in two steps using hydrophobic interaction and Van der Waals (VDW) force as the interactive forces between the microcomponents. In the first step the microcomponents bound to each other on their

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29 hydrophobic surfaces in aqueous solution. In the second step the pH of the solution was changed to cause the partic les to bind on their hydrophilic surfaces. Figure 2 10 depicts the 3 D sequential micro self assembly process using hydrophobic interactions between microcomponents. In case of self assembly of the microchains, 70 % yield in 60 min was achieved in the first step and 10 % yield in 720 min was achieved in the second step. The maximum length of the self assembled microchain was 6 units. Figure 2 10. 3D sequential self assembly of micro -scale components using hydrophobic interactions [21] (Reprinted with permission [1991] IEEE). Roger Howe now at Stanford University has been working on self assembly of microdevices since 1997. T his group has demonstrated substantial results in self assembly of m scale parts using capillary force s They demonstrated self assembly of micromirrors onto surface-micromachined microactuators for use in an adaptive optics mirror array [22, 23] In this case, an acrylate based hydrophobic adhesive provided the capillary force for the assembly process. The part and the substrate binding sites we re photolithogra phically defined. Later the

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30 part surfaces were made hydrophobic by surface treatment and the substrate binding sites were coated with the hydrophobic adhesive. The parts were then dispensed onto the substrate under water. Once the hydrophobic part came in contact with the adhesive on the substrate, capillary forces held the part in place and permanent bonding was achieved by heat -curing the adhesive. The single -crystal 20 m -thick hexagonal mirrors were 464 m in diameter, and the binding sites were abo ut 200 m in diamete r. The micromirrors were assembled with fill factors up to 95% with the surface deformations lower than 6 nm rms. Figure 2 11 shows the assembled h exagonal micromirrors onto the unreleased microactuators. Figure 2 11. Capillary force driven self assembly of micromirrors onto microactuators [23] (Reprinted with permission [2002] IEEE). This group also demonstrated fluidic self assembly of micromachined silicon parts onto silicon and quartz substrates using capil lary force [24] with part sizes ranging from 150 x 150 x 15 m3 to 400 x 400 x 50 m3 using square binding sites. The final assembly resulted in rotational misalignment within 0.3 and assembly of 98 -part arrays in about 1 min with 100% yield. Other binding shapes not having rotat ional in -plane symmetry such as semicircles and commas indicated a yield of only about 30 40% [24] Their latest effort demonst rated the self assembly of micron sized helical and toroidal inductors [25] Hexadecane was used as the hydrophobic adhesive to provide the capillary force

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31 and the solder bumps provided electrical interconnects between the parts and the substrate. The inductor chiplets (450 x 950 m2) were assembled onto CMOS wafer with a yield of 90 %. Figure 2 12 shows the self assembly process of the microfab ricated inductors. Figure 2 12. Capillary force self assembly of microfabricated inductors ( Adapted from [25] ). Karl F. Bhringer also contributed substantially to the capillary for ce driven self assembly process. His groups approach is based on photolithographically defining and modifying the substrate surfaces into hydrophilic and hydrophobic surfaces. Capillary forces from the lubricant drive the self assembly process [16, 2628] Figure 2 13 shows the capillary force driven selective self assembly process. Assembly of s urface -mount LEDs [29] and 4 mm x 4 mm PZTs for micro pump s on a 4 substrate [30, 31] were among the first few demonstrations of this self assembly process. In [27, 32] the design and modeling of binding sites was discussed where various shapes such as circle, square, rectangle, hexagon, semicircle, C -shape d comma -shape d and ring -shaped patterns a s well as center and off -center circular cutouts were explored for assembly and alignment of components using capillary force. In [33] modeling and dependence of the of tilt angle on the volume of the adhesive and water adhesive interface tension is discussed with a model and experimental results Here, vertical vibrations were used to correct the tilt angle of the assembled parts.

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32 Part Substrate Substrate Substrate Lubricant Hydrophilic gold sites Hydrophobic sites Hydrophobic Hydrophilic Figure 2 13. Capillary force driven selective self assembly process ( Adapted from [16] ). Bhringers group also demonstrated capillary driven self assembly p rocess in dry environment using diaphragm agitation. The parts were agitated on a vibrating diaphragm and were assembled onto the inverted substrate (substrate held with its binding sites facing in the downward direction) [34] as can be seen in Figure 2 14. Using this process for assembly of a substrate wit h a 4 x 4 array and 1 mm x 1 mm x 200 m Si parts (released DRIE comb drives on SOI chips) a yield of 93 % in 30 s with 100 components was achieved. Oscilloscope Amplifier Function generator Video cpature Substrate Bouncing parts Diaphragm Figure 2 14. Capillary force driven self assembly in air assisted by diaphragm agitation (Adapted from [34] ). H. O. Jacobs group at University of Minnesota has also made considerable contributio ns to capillary force driven self assembly. This group demonstrated programmable bonding [35] which relied on selectively activating solder -coated receptor sites with embedded he aters on the backside of the substrates as shown in Figure 2 15. T hey demonstrated heterogeneous assembly

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33 of three different types of semiconductor chips (GaAs, Si, Ga P) with dimensions ranging from 200 m 500 m without any defects. Figure 2 15. Programmable bonding: Activation of solder coated receptor sites using embedded heaters on the backside of the substrate (A dapted from [35] ). Figure 2 16. 3 D self assembly using polymer adhesive for capillary force driven self assembly process ( Adapte d from [36] ).

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34 B. A. Parvizs group at University of Washington has been exploring self assembly for microscale and nanoscale packaging using shape recognition and capillary driven self assembly processes [37 39] This group has demonstrated 3 D assembly of 20 m 100 m silicon parts using cross linking polymer as adhesive liquid [36] Figure 2 16 shows the 3D self assembly silicon microparts using polymer adhesive. In [40, 41] this group addre ssed the issues related to the size limitation of the molten alloy used in capillary force driven self assembly process. Through proper selection of fluidic environment, they have achieved assembly yields of about 97 % for the 100 m size components and 85 lower limit for this process. 2 2 3 Capillary Force Driven Assembly with Shape Recognition Up to this point in this document, capillary force driven self assembly has been de scribed using some kind of adhesive or solder coated binding sites on planar substrates. Some groups have demonstrated more complexity in the self assembly process by combining capillary forces with shape recognition to achieve angular orientation and sele ctive bonding. Some of the major demonstrations using these techniques are discussed here. H. O. Jacob s group coined the combination of shape recognition and capillary force driven technique s as shape and solder directed self assembly T he parts are ca ptured into recessed receptor sites using shape recognition C apillary force s from molten solder prevent the part s from falling out of the receptor site s and also provide permanent bonding and electrical contact. Initially they demonstrated assembly and pa ckaging of 200 hundred AlGaN/GaN LEDs (chip size 380 m x 330 m) with a yield of about 95% in 2 min [42] Later they demonstrated heterogeneous assembly and packaging of functional microsystems [43 47] Here, sequential assembly of three components; 600 LEDs of 200 m size onto carri ers in 2 mins and the

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35 encapsulations units onto the device carriers was demonstrated as shown in Figure 2 17. 100% yield in 2 min for the carriers units and 97% yield for the encapsulation units was achieved. They also demonstrated assembly of 20 m size dies with angular orientation by using pedestals to guide the assembly of dies to the solder coated receptor sites [48] Figure 2 17. Shape and solder directed heterogeneous assembly and packaging of functional Microsystems [47] Copyright 2004 National Academy of Sciences, U.S.A. B. A. Parvizs group has a lso demonstrated heterogeneous self assembly of FETs and diffusion resistors [49, 50] and LED display [49, 51] onto flexible plastic substrates using shape recognition (circles, squares and triangles) and capillary, fluidic, and gravitational forces as can be seen in Figure 2 18. The assembly yield for the FETs and the diffusion resistors was about 97 % in 3 min for component sizes ranging from 100 m 300 m and for the LED display was a bout 65 % with component diameter of 320 m. The lower yield in the latter case was attributed to the variation in solder height of the LED contacts and solder degradation in acidic assembly environment [51] In a recent publication, similar technique was used to demonstrate a 3 x 3

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36 array of individually addressable fluorescence detection units through self assembly of LEDs as excitation sources and Si pn junctions as photosensors onto a common template [52] Figure 2 18. Heterogeneous self assembly using shape rec ognition and capillary force [50] Copyright 2004 National Academy of Sciences, U.S.A. Bhringers group utilized this combined technique of shape recognition and capillary for ce to demonstrate assembly and packaging with orientation uniqueness. This was achieved by fabricating 1 2 mm square parts with protruding circular (0.2 0.3 mm in diameter and 45 65 m in height) and cross (1 mm x 50 m x 35 m) pegs [53 56] Using this technique they developed a semi dry (semi DUO -SPASS) [53] and completely dry (DUO SPASS) [54] self assembly process with unique orientation. In the semi DUO -SPASS process, t he parts were fabricated with circular pegs and involved two wet steps and two dry steps. 95% 99% yield was achieved in 3 min for this process. The translational and the rotational misalignment in this case were about 0.25 mm and 18 respectively [55] In case of DUO -SPASS a two -step shape recognition process was used where along with the cir cular pegs the parts were also fabricated with the cross pegs as shown in Figure 2 19. The height of the circular peg was twice that of the cross peg. This differenc e in height allows the parts first assemble onto the receptor sites by shape recognition between the circular peg on the part and the complementary circular trench in

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37 the receptor site; in the second step the assembled parts orient themselves by shape rec ognition process between the cross peg and the cross trench. An assembly yield of 98% was achieved in 10 min with 50% redundant parts on two assembly templates having 397 and 720 receptor sites [54] The translational and the rotational misalignment in this case were about 20 m and 2 respectively [55] Figure 2 19. DUO SPASS process using shape recognition and capillary force [55] (Reprinted with permiss ion [2006] IEEE). Bhringer s group also demonstrated vertical and horizontal self assembly process in an air environment using shape recognition and capillary -driven force [57, 58] Si parts of size 790 hydrophilic. In the first step the parts are vertically mounted on a flat plate using an aperture plate that allowed only vertically standing parts to pass through it. N ext these parts were transferred onto a palletizing plate with water droplets. When transferred the parts were vertical but due to the capillary forces from water condensation these parts turn horizontally with their hydrophobic faces in upward direction. The parts were then assembled to permanent bonding plates using flip -chip bonding process. The process flow is shown in Figure 2 20. Using this process assembly of about 1000 receptor sites in about 2 min with a defect rate ~1% was

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38 achieved. S urface coverage of 31% was achieved with single batch assembly process which was doubled in 2nd batch. Figure 2 20. Capillary force driven vertical and horizontal assembly process ( Adapted from [58] ). 2 2 4 Other Self Assembly Techniques While the majority of self assembly has focused on gravitydriven and capillary -force driven processes, s ome of the other less -explored techniques for self assembly using surface tension, ele ctric an d magnetic fields are discussed here.

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39 2 2 4 1 Surface tension driven self assembly Even though capillary forces and surface tension arise from the same physical phenomenon, capillary force driven self assembly utilizes the surface tension of liquid interf aces at the binding sites. The surface tension driven assembly methods discussed here explores other uses of surface tension to enact assembly. Figure 2 21. Self assembly using surface tension of water [59] (Reprinted with permission [1996] IEEE). Isao Shimoyama demonstrated two dimensional self assembly using surfa ce tension of water as the driving force [59, 60] As seen in Figure 2 21, 100 components of 400 m size made of polyimide and polysilicon thin films were selectively bonded while floating on a water surface using two unique features of surface tension First, units located at same heights attract each other and units located at different height repel each other. Second, attractive forces exist between components with sharp ed ges. External magnets were used to magnetically stir the components in a random fashion, but the magnetic fields did not contribute significantly to the bonding process itself. Note, there were no special liquid interfaces between the parts. Richard Symss group at Imperial College London has been working on self assembly, mainly 3 D assembly of micro -devices using solder surface tension force to drive the self -

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40 assembly process [61 71] The surface tension force induced by a meltable material such as solder, glass or photoresist results in out of plane rot ation of mechanical structures made of either Si, or bonded silicon, or polysilicon or electroplated metals such as Ni and Cu. The final angle of rotation is controlled by the initial volume of the meltable material. When the meltable material is heated to its melting point, it deforms to reduce its free surface energy, resulting in out -of plane lifting of the mechanical structure. The schematic of the solder self assembly process is shown in Figure 2 22. Before Melting of solder Solder pad Hinge material Substrate Flap During melting of solder Solder After full rotation and solidification of solder Solder Flap Figure 2 22. Solder surface tension self assembly process (Adapted from [71]). This group demonstrated hinged [70] and hingeless self assembly of microstructures [61, 62] self assembly using glass as the meltable mat erial instead of solder [63] self assembly of micro -optomechanical torsion mirror scanner using photoresist as the meltable material [64, 65, 67] and self assembly of refractive collimating microlens arrays [66] Eric Yeatmans group also at Imperial College London along with Richard Syms has been working on solder surface tension driven self assembly process [61, 70 75] His efforts have mainly concentrated on post process fabrication and integration of high Q inductors [72 75] on radio and microwave frequency ICs so as to reduce losses and parasitic capacitances by separating the coil from the substrate.

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41 2 2 4 2 Electr ic field driven self -assembly In [76] Whitesides used electrostatic fields to drive the self assembly process by ionizing the surfaces of 1 0 m size gold disks and selectively pattering the Si substrate with positive and negative charges though chemical processing. When mixed together in an aqueous solution the gold disks selectively assembled on the substrate as seen in Figure 2 23. In [77] electrostatic self assembly was demonstra ted by assembly of two types of spheres made from polymethylmethacrylate (PMMA) or Teflon with diameter of 1.59 mm 3.18 mm, into an ordered lattice. Substrate Substrate Parts or Figure 2 23. Electrostatic self assembly ( Adapted from [76] ). Roger Howe along with Karl Bhringer and Al Pisano also used electric fields but without placing electrostatic charge on the parts or substrate. S urface mount capacitors and diodes were used ranging in dimensions from 0.75 mm to 2 mm [78, 79] Four surface mount capacitors were assembled in about 30 s [79] Ultrasonic vibrations were used to overcome the friction and adhesion forces and the electrostatic force was used to assemble and align the parts in spe cific locations. The setup resembled a parallel -plate capacitor with apertures in the upper electrode. The energy traps created by the fringing fields attracted the parts to the apertures thus resulting in self assembly. Figure 2 24 shows the experimental setup for the electrostatic self assembly process.

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42 Base Piezo Vf Vp Vibratory table Cr Au electrode Glass (dielectric) Part Figure 2 24. Electr ic field driven s elf assembly of surface moun t capacitors and diodes. (Adapted from [78] ). 2 2 4 3 Bridging flocculation driven self assembly Isao Shimoyamas group also demonstrated 3D self assembly of microstructures using bridging flocculation as the binding force [80] As a proof of concept, concave and convex Si microstructures with side length of 100 m were fabricated with a layer of Al2O3 deposited on the connecting surface of the concave parts. The pH of the system was controlled such that the bonding force acted only between Si and Al2O3 surfaces. Polymeric flocculant was then added to the solvent containing the microcomponents. The flocculant gets adsorbed to the microcomponents like a bridge thus flocculating the mic rocomponents and resulting in self assembly. With 300 parts of each type, concave and convex as seen in Figure 2 25, a maximum yield of 60% was achieved in 5 minutes [80] 100 mFlocculant Figure 2 25. Self assembly using bridging flocculation ( Adapted from [80] )

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43 2 2 4 4 Magnetic field driven self assembly Shimoyama s group demonstrat ed s elf assembly using external magnetic fields in two ways. The first method used multiple permanent magnets as linkage -free end effectors similar in size to the microcomponents to be manipulated [81] The magnetic field produced by solenoids arranged in a matrix controlled the magnets. The solenoids were selectively energized to manipulate the microcomponents by pushing them on the stage with the mag nets, as can be seen in Figure 2 26 [81] The second method used magnetic torque generated by the external magnetic field perpendicular to the substrate to lift hinged structures [82 84] The hinged microstructures consisted of electroplated permalloy plates with dimensions of 600 m x 800 m x 4.5 m and 200 nm nickel elastic hinges. These microstructures were sequentially lifted out of plane and assembled using external magnetic field. Also regular tetrahedrons 800 m long were sequentially assembled using this multi-step process [82 84] Figure 2 27 shows the 3D self assembly of hinged structures using an external magnetic field. Figure 2 26. Micromanipulation on microparts using external magnetic field [81] (Reprinted with permission [1995] IEEE).

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44 Figure 2 27. 3 D self assembly of hinged structures using external magnetic field [82] (Reprinted with permission [2005] IEEE). Whitesides s group also demonstrated self a ssembly using magnetic force in [85, 86] where, millimeter sized magnetic disks floating at two parallel interfaces (like two immiscible liquids) and spinning under the influence of rotating external magnetic field dynamically self assemble. 3 D self assembly was also accomplished usin g magnetic forces in [87] where flat elastomeric sheets patterned with magnetic dipoles fold ed into three dimensional objects. Figure 2 28 shows the 3D magnetic self assembly of magnetically patterned sheets into folded objects. This strategy was also used to demonstrate a basic 3D electrical circuit. Each section of the planar sheet consisted of an electr ically isolated wire which connected the two electrodes of a LED to the solder pads and magnets at the tips. The solder pads served as the electrical connection between the adjacent LEDs. The planar sheet was then suspended in water at 60C and gently agit ated. In about 1 3 min, the sheet folded into a sphere, allowing the molten solder to fuse and complete the electrical circuit, as can been seen in Figure 2 28.

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45 Figu re 2 28. 3 D magnetic self assembly [87] Copyright 2004 National Academy of Sciences, U.S.A. Fonstads group at Massachusetts Institute of Technology used micromagnets for sel fassembly of m scale devices [88, 89] They fabricated the parts and the substrates with recesses (on processed or partially processed integrated circuit wafers) having complementary shape and size to one another. A high coercivity permanent magnetic layer, such as a cobalt platinum alloy was deposited and patterned on the bottom of the recesses. The parts had a sputtered Ni layer and after they fell into recesses because of gravity they were retained in place due to the magnetic force when the snow globe assembly equipment shown in Figure 2 29 was inverted for recycling of un assembled parts

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46 Figure 2 29. Magnetic self assembly with the snow -globe set up [88, 89] (Reprinted with permission [2004] IEEE). Barbastathis et al. at Massachusetts Institute of Technology also explored the use of external magnetic field for self assembly processes [90, 91] In this approach, the membranes (100 m x 100 m x 1 m) were fabricated with a pre -patterned array of soft magnetic fil ms (10 m long and 75 nm thick) and an external magnetic field was used to align the membranes after physical fo lding. The translational alignment of about 200 nm was achieved after folding. Figure 2 30 shows the two forms of alignment methods using soft magnetic array and exte rnal magnetic field. Ravindra and Fiory at New Jers e y Institute of Technology also explored the use of magnets along with shape recognition for self assembly processes [92, 93] In this approach Co or Ni or CoPt magnetic patter ns were fabricated on the bottom of the recesses on an insulator layer. A magnetic guide layer was used to guide the parts in places. A thin layer of Co was

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47 electroplated on back side of chips and external field was applied at the bottom of the substrate u sing a rotating permanent magnet so as to cover the entire substrate area. The parts fell by gravity and were retained in place by the magnetic force. Figure 2 31 sho ws the magnetic field assisted self assembly process. Bext (i) (ii) (iii) Bext (i) (ii) (iii) Form A Form B Figure 2 30. Folding of membranes using soft -magnetic array and external magnetic field (Adapted from [91] ). IC wafer Permanent magnet Electronic filed source Nano devices Magnetic guide layer Figure 2 31. Magnetic field assisted self assembly process ( Adapted from [92] ). Qasem Ramadan et al. at Institute of Microelectronics, Singapore, explored the use of permanent magnets for self assembly [94] In this approach the substrate was patterned with physical cavities and a master array of NdFeB magnets (1 mm diameter and 3 4 mm thick) having the same pat tern as the substrate, was placed below the substrate. The target chips (1 mm

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48 x 1 mm x 0.5 mm) having electroplated CoNiP (1 m thick) with matching shape were trapped in place because of magnetic and gravitational force. Figure 2 32 shows the self assembly setup using permanent magnet array. Master array S N Host substrate Target chip Vibrator with tilting mechanism Template Fmag + Fg Magnetic film Fr Reaction zone Driving system Figure 2 32. Self assembly using permanent magnet array ( Adapted from [94] ). Table 2 1 Summary of previously demonstrated self assembly processes Driving force Group Demonstration Results Reference Gravitational A. P. Pisano Assembly of 1000 hexagons into a 2D lattice [4] Gravitational Yeh and Smith GaAs vertical emitting light emitting diodes (LEDs), GaAs/AlAs resonant tunneling diodes (RTDs), and vertical cavity surface emitting lasers (VCSELs), and optoelectronic devices 100 % yield in 2.5 min with size blocks and 90 % in 15 min with 150 x 150 x 35 3 size blocks [8 10] Bhringer 2 D & 3 D dry assembly with orientation uniqueness 100 % yield in 5 min (2X redundant parts and 18 % packing density) and 81 % yield with 1.5x redundant parts and 40 % packing density [12] 2 D & 3 D dry assembly with in plane orientation uniqueness 95 % yield with rotational orientation error of 17 and translational error of 5 m [11] Catalyst enhanced dry assembly processes parts (800 x 800 x 50 m) and catalysts (2 x 2 x 0.5 mm3) 25 50 % reduction in acceleration and up to 4 times increase in number of activated parts [13]

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49 Capillary Whitesides 3 D mm scale printed circuit boards [15] mm size polyhedra into helical aggregates with 1 4 isolated electrical circuits [ 17 ] Cylindrical display 113 GaAlAs LEDs (chip size 280 x 280 x 200 m3) Assembly of 1500 chips with 98% yield in 3 min (5000 redundant parts) [18] Howe Hexagonal micromirrors (464 m dia. and 200 m thick) onto microactuators binding site 200m dia. Fill factor of 95 % (7 binding sites) [22, 23] Si parts onto Si and quartz substrates (150 x 150 x 15 m3 400 x 400 x 50 m3) 100 % yield in 1 min (array of 98 parts), with 0.3 rotational misalignment [24] Helical and toroidal inductors (450 x 950 m2) on CMOS wafers 90 % yield [25] Bhringer Surface mount LEDs [29] PZTs (4 mm square) on pump chamber on 4 substrate [30 31] Released DRIE comb drives on SOI wafers (1 mm x 1 mm x 200 m), substrate 4 x 4 array 93 % yield in 30 s with 100 components [34] Parviz 3 D assembly of 20 m 100 m parts [39] Limitations on molten alloy size 97 % yield for 100 m size components and 80 % yield for 40 m size components and 15 % yield for 20 m size components [ 40, 41 ] Shimoyama Selective bonding 3 D sequential micro self assembly of 10 m components and microchain in two steps 1 st step 70 % yield in 60 min 2nd step 10 % yield in 720 min, max length of microchain 6 units. [19, 20, 21] Jacobs Selective bonding assembly of 300 m size LEDs (36 red, green and yellow) and Si dies with 72 interconnects [42, 43] Capillary force with shape recognition Jacobs AlGaN/GaN LEDs (380 m x 330 m) 95 % yield in 2 min [42] Heterogeneous assembly of 3 nonidentical chips GaAs, Si, GaP (200 m 500 m) [44] Sequential assembly of 3 components 600 LEDs of 200 m size onto carries and encapsulation units onto carriers 100 % yield in 2 min for LEDs and 97 % yield for encapsulation units [45 47] Angular and lateral orientation parts (500 m 2 mm) Angular orientation 3 Lateral orientation 19 m [47]

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50 Assembly of ultra small chips (20 m in length) and angular orientation using alignment pedestals [48] Bhringer Si parts (790 m x 790 m x 330 m) 99 % yield in 2 min for 1000 receptor sites [57, 58] Semi dry self assembly process (semi DUO SPASS) with orientation uniqueness (1 2 mm square parts) 95% 99 % yield in 3 min Translational & rotational misalignment 0.25 mm & 18 respectively [53, 55, 56] Completely dry self assembly process (DUO SPASS) with orientation uniqueness (1 2 mm square parts) 98 % yield in 10 min with 50 % redundant parts Translational & rotational misalignment 20 m & 2 respectively [54,55] Parviz Heterogeneous assembly of FETs, diffusion resistors (100 m 300 m) 97 % yield in 3 min for FETs and diffusion resis tors [49, 50] Micro display LEDs (320 m) 65 % yield for LED display [49, 51] Fluorescence detection units ( 3 x 3 array) [52] Surface tension (water) Shimoyama 2 D Assembly of 100 components made of polyimide and polysilicon of 400 m size [60] Surface tension (solder) Syms 3 D assembly of hinged microstructures [70] 3 D assembly of hingeless microstructures [61, 62] micro optomechanical torsion mirror scanner [64, 65, 67] refractive collimating microlens arrays [66] Yeatman integration of high Q inductors on ICs [72 75] Electric field Whitesides 10 m size gold disks on Si substrate, 2 types of spheres in an ordered lattice [76, 77] Howe, Bhringer Surface mount capacitors and diodes (0.75 mm 2 mm) 4 surface mount capacitors assembled in 30 s [78, 79] Bridging flocculation Shimoyama 3 D assembly of Si microstructures 100 m concave and convex cubes 60 % yield in 5 min with 300 parts of each kind [80] Magnetic field Shimoyama 3 D assemb ly of hinged microstructures, 3D assembly of 600 m x 800 m x 4.5 m plates and 800 m long regular tetrahedrons [82 84] Whitesides mm scale magnetic disks [85, 86] assembly of planar elastomeric sheets into 3D objects and electrical circuit with LEDs 3 min for folding of sheets into an electrical circuit sphere [87] Fonstad Integration of semiconductor devices with ICs [88, 89]

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51 Barbastathis Folding of membranes patterned with soft magnetic arrays using external magnetic field Translational alignment 200 nm [90, 91] Ravindra, Fiory Assembly of GaAs or InP devices on semi processes or processes wafers with integrated circuits [92, 93] Ramadan Parts of 1mm x 1mm x 0.5 mm size with electroplated CoNiP (1 m) [94] 2 3 Drawbacks of Previously Demonstrated Self Assembly Processes Most of these prior approaches discussed above do not match the full functionality offered by the robotic pick -n place or manual assembly. Robotic and manual assembly allows for chips to be assembled with precise latera l and angular placement, albeit in a serial fashion. To replace pick -n -place and manual assembly, self assembly techniques must be capable of similar placement functionality, but with lower cost s, higher yields and/or high er throughput To achieve this wi th self assembly, the following key features are required, which have so far been difficult with previous self assembly methods ; Orientation uniqueness assembly is restricted to one physical orientation Bonding specificity assembly restricted to only one type of component when multiple components may be present; or assembly restricted to only one type of receptor site when multiple types of receptor sites are present Interpart bonding assembly of free -floating components to one another, rather than assembly of free -floating components to a substrate Orientation uniqueness is one of the most important factors in assembly of microdevices in case of electrical and mechanical networks. To ensure proper connectivity and functioning of the final devic e, it is of utmost importance that the part orientation is maintained. In robotic pick -n place assembly the part orientation is maintained from the beginning by the manipulating arms, whereas in the case of stochastic self assembly, the start and the final positions are

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5 2 indeterminate. For correct assembly, global energy minima must be reached where the mixing forces are overcome by the binding forces. However, depending on the binding site design, there could be more than one global energy minima positions, resulting in multiple stable bonding configurations and thus incorrect assembly. To overcome this problem, techniques such as shape recognition have been explored, where either the components are fabricated with asymmetrical shapes or include additional interlocking microstructures on the components for alignment [53 56] They require fabrication of large scale asymmetrical physical microstructures, thus increa sing the fabrication complexity and also adding to the manufacturing cost. Also, asymmetrical binding sites for capillary force driven process have been implemented with little luck. Shapes such as semicircle, commas and rings have been explored for demons tration on orientation uniqueness. The assembly yield and alignment was reduced to 30 40% with use of asymmetrical bond pads [24] due to local energy minima creating misfits and more gradual slope surrou nding the minima in the bond energy curve. When considering assembly of multiple component types, bonding specificity (also known as bonding selectivity or programmability) is another key requirement. Self -assembly of multiple component types can be done from homogenous (one component type) or heterogeneous (multiple component types) mixtures of parts. Heterogeneous assembly can be further subdivided. In sequential heterogeneous assembly, multiple types of components are assembled one at a time in a serial fashion. In simultaneous heterogeneous assembly, multiple types of components are assembled in parallel. Consider an example, where part types A and B are to be assembled onto different receptor sites on substrate C. In sequential homogenous assembl y, part A is assembled,

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53 followed separately by part B. While the two assembly steps are performed separately, and parts A and B aere never mixed together, it has to be made sure that part A bonds only in the correct locations, and likewise for pa rt B. Consider heterogenous assembly where parts A and B are mixed together. In sequential heterogeneous assembly, part A is allowed to first assemble, followed by part B. Again this requires some mechanism for bonding specificity. The more desir able approach is simultaneous heterogeneous assembly where parts A and B correctly assemble completely in parallel. To enable any type of multi -part assembly (from homogenous or heterogeneous part mixtures), some type of bonding specificity is require d. In previous investigations, shape recognition approach has been explored to address this need [50, 95] Components are fabricated with mutually exclusive shapes, such as squares, triangles and ci rcles, but this adds to the fabrication complexity and also increases the cost. Also there is a limit on the number of mutually exclusive shapes possible and thus a limitation on the number of different components that could be assembled at one time. In th e case of capillary driven self assembly process, bonding selectivity has been achieved by selectively activating and deactivating the receptor sites using chemical processing [16, 19, 21, 26 28] Both of the above mentioned approaches are sequential rather than being a parallel process. Hence, the assembly time scales proportional to the different types of parts, and thus may not yield a fast and cost -effective solution. In the case of simultaneous assembly, all components types would be assembled at the same time, making it in true sense a completely parallel process. Interpart bonding is an additional feature for selfassembly techniques where at least two types of mechanically unconstrained parts could be assembled. For this to occur, the short range bonding forces have to be present between the parts, and thus the driving force cannot be an

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54 externall y applied body force such as gravity. At the same time, it is necessary that the parts do not agglomerate due to these short range bonging forces. Agglomeration can be avoided by making sure that there are no short range bonding forces acting between like parts. Also, the parts have to be able to assemble in any arbitrary direction. Interpart bonding was achieved using capillary force by Shimoyamas group [19 21] where closed link microchai n structures were formed through sequential assembly process. Whitesidess group also demonstrated bonding selectivity, where 3D electrical networks on polyhedral surfaces were formed [17] Jacobs group demonstrated assembly of LEDs on carriers and then the encapsulation units on the carrier devices [44, 47] Parvizs group showed assembly of Si parts into 3D microstructures [36] Most of these approaches, though sequential, have demonstrated successful self assembly of various functional microcomponents. 2 4 Magnetic Self Assembly (MSA) A new approach using permanent magnets as the driving force for the self assembly process is presented here. The Magnetic Self Assembly (MSA) approach is aimed at overcoming the limitations associated with the previously demonstrated self assembly approaches. The method employs integrate d micromagnets or arrays of micromagnets on the bonding surfaces of the parts and substrates C ost -effective, wafer level microfabricating technol ogies such as embedded bonded magnets [1] electrodeposition [96, 97] or sputtering [98] or can be utilized for integration of magnets onto component surfaces. C omplementary magnetic patterns on different parts can be magnetized with opposite polarities. Once these components are randomly mixed together in eit her a fluid or a dry environment the oppositely polarized parts align and assemble to one another when the intermagnetic forces between the components exceed the mixing forces. The mixing forces include all non bonding forces such as fluidic forces, colli sional forces, gravity, and inertial forces that act on the free floating parts. For a successful assembly event, the

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55 magnetic forces have to overcome these mixing forces. Permanent mechanical and/or electrical bonding can be achieved by the heating of the pre patterned solder bumps or curing of adhesive pads. Figure 2 33 shows the magnetic self assembly concept. The MSA approach offers numerous design, integration, and implementation advantages, as described below. Substrate N S N S N S N S N S N S Free floating componentsFmagnetic Receptor sites (a) (b) Part B Part A Magnets Solder pads Figure 2 33. Magnetic self assembly concept. In MSA, the strength and range (distance over which the intermagnetic forces dominate the mixing forces) of the magnetic bonding force can be controlled by the magnetic materials, the magnet geometry (shape and size) and the number of individual magnets. Thus by designing diverse asymmetric patterns, a lock and key pattern matching mechanism can be formed to achieve orientation uniqueness and bonding selectivity. Unlike self assembly processes using gravity and capillary force for orientation uniqueness and bonding selectivity, in MSA there is no need for fa bricating physically diverse shapes of components. Also by proper design of the magnets, MSA offers the potential for simultaneous heterogeneous assembly. thus making the self assembly process very cost -effective and time efficient.

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56 In MSA, the magnetic f orce is established bi -directionally between the magnets. Hence this method facilitates interpart bonding, unlike gravity -driven processes. Also, since similar components would be magnetized with the same polarity, the like components actually repel, thus agglomeration is easily avoided for interpart bonding. Additionally, since the magnetic force is independent of the environment, MSA is feasible in both wet and dry environments. MSA also allows for rejection of incorrect assemblies (reversible process), unlike capillary force driven assembly, where once a part is assembled, correctly or incorrectly, it stays assembled. MSA uses substrate vibrations, explained later in Ch 5, which are maintained at a level such that only correctly assembled components stay assembled and incorrectly bonded components are mitigated. This improves the MSA yield. Furthermore, the process of patterning and fabricating the magnets can be easily integrated with the wafer -level processing of the microfabricated devices, thus compon ents can be bulk manufactured with the pre patterned hard magnets. Also these pre -patterned magnets in MSA occupy only part of the bonding surface area, thus leaving space for mechanical contacts and electrical interconnects. Some of the potential advanta ges of magnetic self assembly over previously demonstrated self -processes are listed below; Angular and lateral alignment controlled by bonding force Small magnets leave surface area for electrical interconnects Functionality in both wet & dry environments Scalability from micro to macro -scale parts Low -cost, batch integrability Magnetic bonding forces established bi -directionally between components Bonding force controlled by magnet geometry, material and magnetization direction Polarity of the bonding forces is interchangeable Does not require actual physical contact for assembly

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57 Overall, magnetic self assembly shows promise for surpassing the performance of the previously demonstrated self assembly processes with versatile functionalit y, low -cost manufacturing, higher assembly yield, and faster assembly rates. 2 5 Conclusion The need for self assembly is emphasized with detailed description of various previously demonstrated self assembly techniques. The drawbacks of these assembly processe s are also outlined. Magnetic self assembly is presented as a viable solution to previously investigated assembly processes which suffer from fabrication complexity (high cost), low throughput low yield, and/or low functionality

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58 CHAPTER 3 3 MODELING The micromagnetic force interactions between the magnets play an important role in the practical implementation of magnetic self assembly process. Force modeling is used to study the interactions between magnets of various sizes and shap es. This chapter presents the force modeling for evaluation and quantification of micromagnetic bonding forces. A self assembly process model for characterization of magnetic self assembly process is also presented here. This statistical model is used to s tudy the effect of the various process parameters, such as the number of redundant parts and magnetic binding site design, on the progression of the assembly and the yield. 3 1 Magnetic Modeling Magnetics is a broad and complex topic, and a detailed tutorial on magnetism and magnetic materials is outside the scope of this thesis. Most of the terms used here are explained along the way. For additional information please refer to [99] or [100] A typ ical magnetization vs. magnetic field (M -H) hysteresis plot for a permanent magnet is shown Figure 3 1 The corresponding magnetic flux density vs. magnetic field (B H) relationship is governed by the material constitutive relationship 0() BHM (3 1 ) The M H plot shows how the magnetization changes with applied field for an ideal permanent magnet and a real permanent magnet. For an ideal magnet, the magnetization M is constant, i.e. M = Mr, up until an applied reversal field exceeds a critical value, denoted Hci. Above this value, the magnetization switches directions. For a real permanent magnet M is a smoothly varying, nonlinear function of the applied field, M = M (H ).

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59 T he characteristic defining properties of a permanent magnet are coercivity ( Hc), intrinsic coercivity ( Hci), remanent flux density ( Br) and maximum energy product ( BHmax), which are determined from the hysteresis curve of the magnet. Hc is the measure of the reverse magnetic field required to reduce the magnetic flux density of the sample to zero. Hc should not be confused with Hc i which is the intrinsic coercivity of the material. Hc i is the reverse field at which the magnetization M i s reduced to zero. For permanent magnets Hc i is much larger than Hc in most cases. Br 0 Mr is the residual magnetic flux density when the external magnetic field is reduced to zero after magnetizing the material. BHmax is the measure of the maximum amo unt of useful work that a permanent magnet is capable of doing outside the magnet [100] The maximum absolute value of the product of B and H (| BH |) from the second quadrant of the hysteresis curve is BHmax. All t hese magnetic properties are indicated on the hysteresis plots in Figure 3 1 and Figure 3 2 These magnetic properties are measured using a vibrating sample magnetometer (VSM), the details of which are discussed in Ch 4. L ater on in Ch 5, these properties are used to predict the bonding forces between magnets Figure 3 1 Typical hysteresis plot for a permanent magnet (M H loop)

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60 Figure 3 2 Typical B H loop for a permanent magnet 3 1 1 Force Equations One of the advantages of MSA mentioned in Ch2 was designable bonding. This feature offers versatility where magnetic patterns of various shapes and sizes facilitate smart self assembly with capabilities such as angular orientation and selective bonding. To capitalize on this feature, an understanding of the micromagnetic bonding forces and how they vary is extremely important. Analytical methods are used to estimate the magnetic bonding forces for simple shapes such as cylindrical and cuboidal magnets. For more complex geometries, finite element analysis is employed using COMSOL Multiphysics. Calculations are performed in some cases assuming idealized magnetic properties, and in other cases using the actual measured nonlinear magnetic properties. Ideal magnets with constant, uniform magnetization in the axial direction are assumed

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61 when using analytical and linear finite element analysis. More accurate calculations are performed using the actual nonlinear magnetic material properties obtained from the VSM measurements by employing nonlinear finite element analysis. The magnetic material is said to be nonlinear if the permeability, depends on H i.e. = (H) There are several common methods used to calculate forces between magnets, including Maxwells stress tensor method, virtual work method, equivalent magnetizing current method, or Kelvins formula [101105] The application of Kelvins formula requires knowledge of two quantities; the magnetization M of the material and the external magnetic field. H ere, the magnetization M of the magnet is known from the vibrating sample magnetometer (VSM) measurements, and the external field from neighboring magnets can be calculated (discussed later). With these two quantities are known, Kelvins formula offers a s traight forward approach for calculating the force on one magnet due to the field from a second magnet [105] The Kelvins formula for the force on one magnet due to the field from an external source is given as; 0dextFMH (3 2 ) where, dF is the incremental magnetic force acting on infinitesimal magnet volume d V 0 x 107 H/m is the permeability of free space, M is the magnet magnetization and extH is the external magnetic field as shown in Figure 3 3 Note, the magnetic field created by the magnet itsel f does not create a body force; only external fields from other neighboring magnets create net forces. In the case of two interacting permanent magnets, th e source of this external field is the field from the second magnet. In case of arrays of interacting magnets, the field of one magnet is the superposition of the fields from all other neighboring magnets.

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62 x z y M dV dFHext Figure 3 3 External magnetic field acting on a permanent magnet (Adapted from [105] ) The total force acting on the magnet is obtained by integrating the differential force over the magnet volume. magnet xyz VFdFdVFxFyFz (3 3 ) To simplify the calculations for analytical forc e estimates, the magnets are assumed ideal, with a constant, uniform magnetization of M = Mr = Br 0 up to the intrinsic coercivity, Hci, and r = 1 From the perspective of the M H loop, this implies a perfectly square hysteresis loop as shown in Figure 3 1 By appropriate orientation of the coordinate system, and w ith the assumption of constant magnetization in the z -direction (ideal magnetic properties) rMMz the dot product in Equation 3 2 is reduced to a simple scalar product of Mr and Hz (the external H field component in the z -direction). Thus, the force in the x, y and z -direction is given as; 0()xx rz VVFdFMH x (3 4 ) 0()yy rz VVFdFMH y (3 5 ) 0()zz rz VVFdFMH z (3 6 ) The only uknown in Equations (3 4) (3 6) is the value Hz. For calculation of the external H -field produced by the second magnet, a method employing equivalent Amperian currents is

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63 used [106] In this method, the material magnetization is represented by two equivalent currents a volume current density, mJ and surface current density, mK given by; mJM (3 7 ) mKMn (3 8 ) mJ is the volume current density inside the material, and mK is the surface current density residing on the surface of the material. Since n is the outward normal, mK is the tangential component of M Since M is assumed constant throughout the magnet volume mJ is equal to zero, and the magnitude of mK is equal to the magn etization M Next by applying Biot -Savarts law the H -field is calculated The Biot -Savarts law for the H -field generated by a current i flowing in an incremental length of conductor dl at a distance R is given as follows; 2 4 i dHdlR R (3 9 ) The H field for the cuboidal and the cylindrical magnets shown in Figure 3 -4 is given in [105] The H field in the z direction at a point P (x, y, z) for a cuboidal magnet of size 2a x 2a x 2t centered at origin; 11 222 222 11 222 222tan tan 4 tan tanpp nn pp nn o z np pn np pnxy xy zxyzzxyz M H xy xy zxyzzxyz (3 10) where ,,,pnpnxxaxxayyayya The H field in the z direction at a point for cylindrical magnet of diameter 2a and height 2t centered at origin is given as;

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64 22 2 0 2 22 22 2 03 1,;2; 0.5 20.5 121! 2! 3 1,;2; 1.5 21.5n n z n n nar a Fnn ztz zt n HM n ar a Fnn ztz zt (3 11) where F is the Gauss hypergeometric function [107] Once the H field is calculated, the force is calculated using Equations 3 4 and 3 6 The axial force between two cuboidal magnets and cylindrical magnets is derived in [105] The analytical expressions for both cases are given below. The size of the cuboidal magnets is assumed to be 2a x 2a x 2t with axial gap, da, and lateral gap, dl. The size of the cylindrical magnets is assumed to be 2a x 2t where 2a is the diameter and 2t is the height of the magnet. The schematic in Figure 3 4 shows the cuboidal and cylindrical magnets with the axial and the lateral displacements. The bonding force or the contact force is the force between the magnets when the axial and the lateral displacement is zero i.e. dl = da = 0. 2a 2t2a da dlz y x F Mr 2a 2t da dlz y x F (a) (b) Mr Mr Mr Figure 3 4 Force between cuboidal and cylindrical magnets The axial force for the cuboidal magnets is given as;

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65 22 222 2 2 0 22 222 222 22242 44 42 (8(2)8ln 16(2)ln 4 82 44 42 16842 8(4)ln 8l 16842al aal cuboidal aa a al aal aa aa aaddaa ttdddaa M F tdad atd ddaa ttdddaa ttddaa atd ad ttddaa 2 2 2 2 2 22 2 22 2 21 221 2 2 2 2 222 2n82 2 4(4)8(4)ln 8(4)168 4 2 44 16tan 4 816tan (4) 8 16(2)4448 4al a a a aal aal a aal a aa aalddaa qa tdatd tdttddda qa aa a dddaa tdq ddda tdttddaddda 2 21 1 2 1 21 14 32tan (2) 2 16(2)ln 4(4)48(2)) 2a a a al aa a tdq qa atd tdqddtdq qa (3 12) where 2222 18444aallqattddtdd and 2222 281688aallqattddtdd are terms that repeatedly appear in the above equation. The lateral force for cuboidal magnets is given as; 2 2 0 264 63 22 1 1 4 2 1 4 221 {()ln 4 ()() ( )( ) 2()ln 1 () 4tan ln ... 8tan ()(cuboidal la la la la la l la lpa M F adda papapa paddpadd at pa adda at apadd tp ad at ddapp tatd 2 1 312 6 22 2222 22 51 2 3 222 222 2 222) ()( )4tan(()) ()4 2ln ... ()() ()ln () (2) (2) 2ln (42la l l lall l l l l lll ll l lldda adpppata tp ada ddaddtaad ada papa ada pa dtaaddadtaadda t dtaadda 2 21 1 22 3) () ()4tan()8tan( )} 4a ll la ld ada ad ddaat at tp tdta (3 13)

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66 where 2 222 22 122 222 2 34 2 22 22 56224,224 22,22 22,22ll ll ll ll llllpdadatpdadat pdadatpdada pdadapdadat are terms that repeatedly appear in Equation 3 13. The axial force for the cylindrical magnets is given as; 22 22 2 2 0 22 22 55 22 22 22 6 55 22 22 2 22 9 22 2 22 2 844 2 4 4 44 3 32 168 4344 43 5 256aalaa cylindrical al a aal a al aal a aal aaltdddadtda a FM ddatda tdddagtda a ddattddda tdatdddaddd a 5 2 22 2 99 22 22 224 4a al aatda ddatda (3 14) The lateral force for cylindrical magnets is given as; 2 22 2 2 2 0 2 222 2 3 3 2 22 2 2 2 6 33 222222 22 5 5 2 22 2 2 2 6 5 2222 244 2 8 4 4 24 3 64 168 44 5 256 168ll a cylindrical la l ll ll la ll ll ll latddagtda a FM ddatda tddadtda a dadtadda tddadtda a dadt 5 22 2 7 7 2 22 2 2 2 6 77 222222 22 5 9 2 2222222 2 2 8 99 22222 22... 44 7 1024 168 434(4) 43((4)) 9 4096 (4)l ll ll la ll l llll l laalda tddadtda a dadtadda tdatddaddatda a dadtla (3 15) E quations 3 12 through 3 15 are used for analytical estimation of micromagnetic forces with axial and lateral displacements. The maximum bonding force is achieved when da = 0 and dl = 0. The results are discussed in Chapter 5.

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67 3 1 2 Finite Element Method The finite element method, though not as fast as analytical method s is used to compare with the results from the analytical methods and also to evaluate magnetic bonding forc es for magnets with complex geometries. Finite element methods are also required when the VSM measured nonlinear magnetic properties of a magnet are considered, as opposed to assuming ideal magnets with constant magnetization. COMSOL multiphysics softwar e is used to evaluate both ideal (linear) and nonideal (nonlinear) cases. In COMSOL, the constitutive relationship between magnetic flux density, B magnetic field, H, and magnetization, M is expressed 0 rrBHB (3 16) where, 0 7 H/m is the permeability of free space, r is the field -dependant relative permeability of the material, 0 rrBM is the remanent flux density, and Mr is the remanent magnetization In the ideal case, the magnetization within the magnet, M is assumed constant (independent of H ), i.e. M = Mr, and r = 1. For the nonlinear case, M is no longer constant; it is now a function of H In COMSOL, this is implemented by making r as a function of H ; i.e. r = r (H ) [108] The M H loop for the magnetic material to be analyzed is obtained experimentally using the vibrating sample magnetometer (VSM). The field-dependant relative permeability of the material, r is extracted as a function of H fro m this M -H measurement. The expression for r is derived by rearranging the terms in Equation 3 1 6 0 r rBB H (3 17)

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68 This analytic function in COMSOL is created by interpolating a look up table containing r v/s H data. An example M H loop for SmCo embedded magnet and r v/s H plots are shown in Figure 3 5 for both the ideal and the non-ideal cases. -1.5 -1 -0.5 0 0.5 1 1.5 x 106 -4 -3 -2 -1 0 1 2 3 4 x 105 H (A/m)M (A/m) Hc Mr Ms Ms = 387 kA/m Mr = 141 kA/m Hc = 88.77 kA/m (1.1 kOe) Ideal case Non-ideal case -6 -5 -4 -3 -2 -1 0 x 104 0 0.5 1 1.5 2 2.5 3 3.5 4 H (A/m)r Ideal case Non-ideal case Figure 3 5 M -H loop and r v/s H plot for SmCo magnet Since the magnet operates only in the se cond quadrant of the hysteresis loop (negative H, positive B and M) r is plotted only for negative values of H and positive values of B This extracted r is input into COMSOL Multiphysics software for FEM simulations for force estimation. FEM simulation is done using Lagrange Quadratic, triangular elements, and the number of mesh elements ranged from 2 5 million. An example plot of the FEM field solution for two cuboidal magnets is shown in Figure 3 6 This nonlinear analysis helps in understanding the difference between the ideal estimated force values and the real measured values. After the simulation of the magnet geometry, post processing tools are used to ge nerate the H field, B field plots. Following are some example force maps generated using analytical force equations. These force maps shown in Figure 3 7 and Figure 3 8 show how the axial and the lateral forces vary relative to the displacement between two magnets. The magnets were cuboidal magnets with aspect ratio (AR) of 1, where the aspect ratio is the thickness of the magnet divided by the width

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69 of the magnet. The side length of the magnets was 100 m, and the remanent flux density Br was assumed to be 1 T. The axial displacement is normalized by the thickness of the magnet, and the lateral displacement is normalized by the width of the magnet. The color in the plot indicates the magnitude of the force. Figure 3 6 Example field solution for FEM simulation of two cuboidal magnets. The color indicates the normalized magnetic flux density and arrows indicate the direction and the relative magnitude of the magnetic flux density. Such forc e maps can be used to determine the minimum force and displacement required for selfassembly. From these plots, it is clear that the magnetic force is maximized when the axial and lateral displacements are zero, i.e. the magnets are perfectly aligned. Thi s maximum force, coined the bonding force, serves as one figure of metric for comparing different

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70 magnetic patterns. The axial force rolls off very quickly with the axial and the lateral displacements The scaling goes as 1/d2 for the force between two magnetic dipoles [109] but for real magnets, this relationship can be more complex. For example, the axial force for the cuboidal magnet in Figure 3 7 reduces to about 7 % of its contact force value for an axial displacement of 1x magnet thickness. This roll -off is highly dependent on the aspect ratio (AR = thickness/w idth) of the magnets, with the roll -off being faster for magnets with AR>1 [105] From Figure 3 8 it can be seen that the lateral force is zero f or zero axial displacement. It increases to a maximum value and then decreases as the lateral displacement increases. Figure 3 7 Axial force vs. axial and lateral displacement for cuboidal magnets AR = 1 Br = 1. The axial displacement is normalized by the thickness of the magnet and the lateral displacement is normalized by the width of the magnet. The color indicates the magnitude of the force.

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71 Figure 3 8 Lateral force vs. axial and lateral displacement. The axial displacement is normalized by the thickness of the magnet and the lateral displacement is normalized by the width of the magnet. The color indicates the magnitude of the force Just knowing the magnetic forces is not sufficient to determine whether or not self assembly will occur. Each bonding event is actually a complex dynamic operation. For example, part to -substrate assembly will be later demonstrated by assembling chips onto an inverted su bstrate with receptor sites. As a randomly bouncing chip approaches a receptor site, the force between the magnets increases. At some critical displacement, the magnets are close enough where the attractive magnetic forces dominate. At this critical displa cement and force, the chip snaps on to the receptor site, and the bonding force keeps the chip from being displaced. Considering this process, t he absolute minimum force necessary for self assembly is assumed to

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72 be the weight force of the chip or component to be assembled. The actual required bonding forces are likely higher, but the chip weight serves as a reasonable lower bound and something that can be well controlled for experiments. Since Si blocks are used as the components for the experiments, the m ass for the 1 mm x 1 mm x 0.5 mm size chip is approximately 1.2 x 106 kg, corresponding to about 12 N. This weight estimate ignores the mass of any embedded magnets, which may slightly increase or decrease the weight, depending on the magnet density. Thus according to this initial assumption, for successful assembly the bonding force should exceed 12 N. Figure 3 9 shows the contour plot for the axial force with res pect to the axial and the lateral displacements for a magnet with dimensions of 850 m x 850 m x 60 m. This magnet pattern is one of the many patterns used later for self assembly demonstration. As mentioned previously the weight force of the chip is 12 N. Various contour lines for different force s are shown here. Labels in the plot indicate 1 x 50 x the weight force of the chip Ideally, if the assumption here is correct then, the two components lying within the region o f 1x contour plot will self assemble. In practice, the required force for assembly is likely higher than just the weight force of the chip since there are additional dynamic effects (collision interactions, inertial forces, etc.) during the self assembly p rocess. In most successful self assembly experiments shown later in Ch 5, the bonding force was 10100 times the weight force of the components. Similar plots can be generated using both analytical and FEM methods for understanding the inter -magnetic inte ractions. More experimental results on the critical displacements for self assembly are presented in Ch 5.

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73 1.2e-0051.2e-0056e-0056e-0056e-0050.000120.000120.000180.000180.000240.0003 Normalized lateral displacementNormalized axial displacement Force v/s axial and lateral displacement 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2 2.5 3 3.5 4 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 x 10-4 Magnet dimension 850 m x 850 m x 60 m wt. force of the chip = 12 N 1x 25x 15x 5x Figure 3 9 Comparison of force between magnets and the chip weight force 3 2 Self Assembly Process Mo deling S elf assembly is a stochastic rather than a deterministic process so any process model must be statistically based In general, a self assembly process can be described by a fixed number of receptor sites (or possible bond pairs) that are filled (b onded) using randomly mixed parts. The probability of a bonding event (a part filling a receptor site) governs the overall assembly process. The yield after time t is defined as the ratio of the correctly assembled components to the total number of receptor sites. It is assumed that the yield is initially zero, but as the receptor sites are filled, the yield asymptotes to 100 %. 3 2 1 Assembly Model Magnetic self assembly is modeled using the assembly model adapted from [44] This model is based on single -component/single receptor site capture time, T This model assumes a fixed volume with r receptor sites and p available parts. The T value is the average time for

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74 assembly when the assembly volume contains only a single part and a single receptor site. Another assumption is that the mixing and capture probabilities between individual co mponents are time invariant and independent of the available component population. This assumption is only valid whe n the unassembled parts do not hinder the assembly process i.e. the number of unassembled parts is not too large so as to impede progress In that case the assembly process will actually slow down. With the assumptions mentioned above, the assembly rate r receptor sites and p available parts is given as [44] ()()() atpara tT (3 18) where a(t) is the number of assembly events after time t T is the average time required for assembly when only a single receptor site and single part is present, ( p -a ) is the number of available parts and ( r -a ) is the num ber of empty receptor sites after a assembly events. Equation 3 17 is a first order nonlinear differential equation that depicts the assembly process and relates the assembly rate to the number of assembly events a(t) By solving Equation 3 18, a mathematical model for progression of self assembly is reached. According to the model, the number of assembly events with time is given by ()/ ()/(1) () (/)prtT prtTr e at rp e (3 19) where a (t) is the number of assembly events after time t r denotes the number of receptor sites, p denotes the number of free parts available at the beginning of the process, and T is the average single -component -single receptor site capture time. The process yield with respect to time is given by

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75 ()/ ()/()(1) () (/)prtT prtTat e yt r rp e (3 20) Note, y ( t ) = 0 for t = 0, and y (t ) = 1 for t = For p = r i.e. the case where the number of redundant parts is equal to the number of receptor sites the above equation reduces to [44] ; 1 () (1/)pryt Ttr (3 21) In the case of an abundant supply of redundant parts ( p >> r ), Equation (1 20) reduces to /()1ptT pyt e (3 22) When interpreting data, the smaller the T value, the faster is the assembly process. Also, the larger the number of available parts p the faster the assembly process. Table 3 1 shows the assembly yield as function of both time (expressed as t / T ratio) and the number of parts. Note that high assembly yields occur within only a fraction of the T -value. The information in Table 3 1 is also graphically represented in Figure 3 10. It can be seen that, at the beginning of the assembly the assembly rat e is very high and gradually reduces as more number of parts assemble. As the time progresses, the assembly yield eventually reaches 100 %. The T -value is largely determined by the bonding interface and limited by the design of the magnetic bonding interfa ce. In theory and in practice, however, the overall assembly process can be accelerated by increasing the number of redundant parts, as is evident from the plots in Figure 3 10. Table 3 1 Assembly yield as function of t / T and redundant parts t / T p = r p = 2 r p = 3 r p = 6 r 0.01 39.0 % 64.2 % 79.6 % 96.6 % 0.02 56.1 % 83.9 % 94.7 % 99.9 % 0.10 86.5 % 99.95 % 100 % 100 %

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76 Figure 3 10. Assembly yield as function of t / T and redundant parts. All the plots eventually asymptote to 100 %. This model also shows that even with increasing the number of receptor sites (i.e. assembly of massive arrays), similar yields can be achieved in the same time, i.e. the time required to achieve certain yield does not increase with the increase in the number of receptor sites, provided the number of excess parts are maintained. The T value also serves as a figureof -merit for comparison of different assembly experiments where the number of receptor sites and parts varies. The T value using the above model normalizes the assembly data, since it is independent of all the above mentioned parameters. This T -value is later used in Ch 5 to characterize part to -substrate magnetic self assembly process.

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77 3 2 2 Model Validation The appropriateness of this model to magnet ic self assembly is verified by comparing the model to experimental data. Since r and p are known, and the time progression can be measured, there is only one fitting parameter, T For magnetic self assembly, the parameter T depends on the magnet surface area, pattern symmetry, the number of magnets, bonding force and substrate vibration levels. While difficult to predict a priori the T value can be extracted from experimental assembly data (yield vs. time) by fitting the data with the model equation, us ing nonlinear least squares method in Matlab. One caveat is as follows. The model assumes that eventually the yield reaches 100%. In most of the self assembly experiments presented later in Ch 5, the yield does not reach 100%, even if the experiment were left to run for very long periods of time. This is because in a real experiments there are disassembly events and also errant assembly events. The process model does not account for disassembly or assembly errors. A much more complex theoretical model wo uld be required to account for this. As will be shown however, the simple model presented above does a reasonable job of tracking the real experiments. The data shown in Fig. 8 is for an oval 2 -fold symmetric magnetic pattern with 15 % surface area (experi ments described in detail in Ch 5). Three different data sets are shown, corresponding to different numbers of redundant parts, p = r p = 2 r and p = 3 r For each data set the data was averaged over 3 trials. The data was best fit to the model with T = 9 m in. The model shows good agreement with the experimental data, validating its applicability. Also note that while the T value is 9 min, 98.4 % yield is achieved in only 15 seconds when the number of parts is 3x the number the receptor sites.

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78 Assembly vs. Time 0 20 40 60 80 100 0 5 10 15 Time (s) % Yield Figure 3 11. Experimentally measured progression of magnetic self assembly with respect to time for different numbers of redundant parts. Data points with error bars indicate the mean a nd s tandard deviation of 3 trials. Solid curves indicate the fitted model to the experimental data with T = 9 min. This model can be applied to both part to part and part -to -substrate magnetic self assembly. However, in the case of part -to -part self assemb ly of free -floating parts it is difficult to measure the assembly vs. time data without stopping and repeating the experiment at regular intervals (difficult to observe all parts). Due to practicality, the model is used only to analyze the part to -substrat e magnetic self assembly process 3 3 Conclusion The force models described here are used for analyzing the micromagnetic bonding forces to enable the technique of magnetic self assembly. The results from using the magnetic models are described in Chapter 5 in the evaluation and quantification of bonding forces section The study of the effects of the various process parameters on the progression of the assembly using the self assembly model described in the previous section is also presented in Chapter 5. p = r p = 2 r p = 3 r

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79 CHAPTER 4 4 FABRICATION As mentioned in the previous chapters, the bonding force between the magnets is dependent on the geometry and material of the magnet. Thus, magnets of various sizes and shapes with different types of materials are fabricated to explore the use of permanent magnets for magnetic self assembly. This chapter describes the process for fabrication of the parts and the substrates with integrated micromagnets. Nowadays, the use of permanent magnets in magnetic MEMS for fab ricating magnetic sensors and actuators is a growing field of interest [110, 111] Hence, incorporating magnetic materials into micro fabrication processes is also gaining importance. Methods such as electrodeposition and sputtering have been employed for fabrication of thin film magnetic films such as CoPt [112117] FePt [118] CoNiMnP [119, 120] alloys. Neodymium iron boron (NdFeB) and samarium cobalt (SmCo), th e two most common rare earth magnetic alloys, are also finding places in microfabrication processes due to very high magnetic properties [121124] The micromagnets in this dissertation are fabricated by utilizing bonded powder magnet microfabrication techniques. The bonded powder methods described in [123] are used for fabrication of fairly large (< 100 m) NdFeB, SmCo and ferrite magnets. These magnets are later used in the demonstration of mm scale magnetic self assembly. To demonstrate magnetic self assembly at a m scale, smaller magnets fabricated using electrodeposition or sputtering processes can be used [98, 114, 125] In this chapter, fabrication of magnets utilizing bonded powders is discussed. Then the preparation of parts and substrates for magnetic self assembly demonstration is presented.

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80 4 1 Bonded Powder Magnets This section describes the fabrication process for bonded powder magnets using SmCo, NdFeB and ferrite magnetic powders. This fabrication process is similar to screen -printing, the primary difference being that the powders are packed into the substrate in a completely dry state. Two variants of the fabrica tion process are adapted from [123] 4 1 1 Polyimide -Capped Magnets The process flow for fabrication of silicon embedded polyimide capped magnets is shown in Figure 4 1 (a). In this process, a 500 m thick silicon wafer is patterned with various shapes using AZ 9260, a positive tone photoresist. Subsequently, 150 m 300 m deep trenches are etched using deep reactive ion etching (DRIE). The magnet powder (SmCo, NdFeB or ferrite) is then packed into these trenches. The average particle size of the SmCo powder is about 5 10 m, of NdFeB powder is about 50 m and that of ferrite powder is about 1 2 m After packing, a ~5 m layer of polyimide is then spun and cured at 300 C at the rate of 4 C/min, on top to retain the powder in the cavities. Other polymers such as S U 8 or Polydimethylsiloxane (PDMS) can also be used coat the magnet surfaces and lock the powder into the trenches. This method is more suitable for magnet powder with very fine particle diameter, in which case the magnet powder will not spin off during th e polymer coating. 4 1 2 Wax -Bonded Magnets A similar process flow is followed for the fabrication of wax-bonded magnets. In this case, NdFeB or ferrite powder was used. The etching of the silicon substrate is the same as before, but i nstead of using the polyim ide cap to retain the magnetic powder in the trenches, a high temperature wax powder is used to bond the magnetic powder together and lock it into the trenches. The average particle size of the wax powder is about 10 m to 15 m. The process flow is shown in Figure 4 1 (b). This dry wax powder is mixed w ith the magnetic powder and

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81 then this mixture is packed into the trenches into the Si wafer. About 3 wt % of wax powder is mixed with NdFeB powder and about 3 0 wt % is mixed with ferrite powder. When heated to a temperature of about 190 C (melting tempera ture of the wax) for 3 min, the wax melts and bonds the magnetic powder. A very small amount of this wax powder (~3 wt % in the case of NdFeB ) is enough to bind the magnetic powder. Photoresist pattern Si substrate Si substrate Si substrate with etched trenches Si substrate with packed magnet powderPolyimide capped Si embedded magnets (i) (iii) (v) (ii) (iv) Photoresist pattern Si substrate Si substrate Si substrate with etched trenches Si substrate with packed magnet + wax powderWax bonded embedded magnets (i) (iii) (v) (ii) (iv) Sample Heated at 190 C Top polyimide coat (~5 m)(a) (b) Figure 4 1 Process flo w for fabrication of Si embedded micromagnets Some of the components with integrated magnets, fabricated using above techniques are shown in Figure 4 2 The cross sect ional views of both types of embedded micromagnets are shown in Figure 4 3 Note, that the use of magnet powders and the fabrication process is interchangeable.

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82 Figure 4 2 Components fabricated using Si embedded bonded powder micromagnets. (a) Polyimide -capped bonded powder magnets, (b) Wax -bonded powder magnets Figure 4 3 Cross sectional view of Si embedded bonded pwder magnets. (a) Polyimide -capped embedded magnet, (b) Wax -bonded embedded magnet 4 2 Magnetization Once fabricated, these magnets are easily magnetized with required polarization direction using a pulse magnetizer. A schematic of the pulse magnetizer is shown in Figure 4 4 A pulse magnetizer produces a very short pulse of energy at a very high voltage and current for a fraction of a second to create an intense magnetic field that magnetizes the sample in the direction of the magnetic field It consists of a capacit or bank that discharges through a solenoid coil producing an extremely high uniform magnetic field (peak field of ~ 3 T) at the center of the solenoid, as shown in Figure 4 4 The sample to be magnetized is placed at the center of the solenoid. As a rule of thumb, the field required to magnetize a sample is about 3x Hci ( intrinsic coercivity of the sample). Po lyimide capped bonded powder magnets Wax bonded bonded powder magnets

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83 Magnetic field DC Capacitor bank Sample to be magnetized Solenoid I Figure 4 4 Pulse magnetizer 4 3 Measurement of Magnetic Properties The hysteresis loop for a magnet is measured using the vibrating sample magnetometer (VSM). The VSM works on the principle of Faradays law of induction, which states that the voltage induced in a clos ed circuit, is proportional to the time rate of change of the magnetic flux through the circuit. The basic idea is as follows. When a magnetic sample is mechanically vibrated, a time varying magnetic field is generated which can be sensed by pickup coils. The induced voltage in the pickup coils is proportional to the magnetic moment (magnetization x volume) of the sample. The system diagram of a VSM is shown in Figure 4 5 A magnetic sample is placed in a uniform magnetic field produced by an electromagnet. This field magnetizes the sample in the direction of the field, thus generating magnetic flux lines around the sample. When the sample is mechanically vibrated (75 Hz ) perpendicular to the applied field, the magnetic flux from the vibrating sample changes with respect to time. This time -varying flux induces a voltage across the terminals of pickup coils mounted on the electromagnet pole faces The applied field from th e electromagnet does not change with time (actually it changes very slowly), so the pickup coils do not sense the applied field, only the fields from the vibrating sample. This induced

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84 voltage, measured using a lock in amplifier, is proportional to the t otal magnetic moment of the sample. Function generator Audio amplifier Gaussmeter Preamplifier Lock-in amplifier Computer Vibrator Motor controller Power supply Rotating table Stepping motor Electomagnet Hall probe Pick-up coils Reference signal generator Sample Figure 4 5 System diagram of VSM Before any measurement, the VSM is calibrated using a sample similar in shape and size to the sample to be measured. This is done to determine the sensitivity (moment/volt) of the pickup coils. The calibration sample is usually a high purity nickel sphere or disk. After calibration with a reference standard, the sample to be tested is loaded into the machine, and the complete hysteresis behavior is measured by sweeping the applied field. Once the total moment is measured, the magnetization ( M ) is easily calculated as, M = moment/volume. This necessitates accurate knowledge of the volume of the magnet sample. The ideal case M -H loop and t he measured M H loop for a real hard magnet are shown in Figure 3 1

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85 The ideal hard magnets have a constant, uniform magnetization of M = Mr. The flux density ( B ) is calculated using the constitutive relationship; 0() BHM (4 1 ) where, 0 7 H/m. Figure 3 2 shows an example B -H loop for a permanent magnet The magnetic properties measured using the vibrating sample magnetometer (VSM), of the polyimide -capped SmCo magnets and the wax-bonded ferrite and NdFeB magnets are shown in Table 4 1 The NdFeB magnets possess the best magnetic properties among the three magnetic materials considered here, having an intrinsic c oercivity of 730 kA/m, a remanence of 0.36 T and a max energy product of 22 kJ/m3. Table 4 1 Magnetic properties of Si embedded micromagnets Material Particle diameter (m) Fabrication method H c i (kA/m) B r (T) BH max (kJ/m 3 ) Ferrite 2 Wax bonded 310 0.1 1.7 SmCo 10 Polyimide Capped 100 0.11 1.3 NdFeB 50 Wax Bonded 7 30 0.36 22 4 4 Part and Substrate Fabrication The magnets are integrated onto silicon substrates using the methods mentioned in the previous sections. The next step in the fabrication process is to singulate the parts and substrates. The part singulation process and substrate fabrication process is described below followed by the part and substrate preparation for experimental demonstration. 4 4 1 Pa rt and Substrate Singulation The individual parts to be assembled are created by dicing the wafer into chips of size 1 mm x 1 mm. The lateral dimensions of the Si embedded magnets vary from 150 m to 850 m, and the thickness ranges from 60 m to 150 m. M agnets covering approximately 10 % to 75 % of the 1 mm2 part surface area are fabricated. Initially simple square magnetic patterns are tested

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86 followed by pattern with increasing complexity. Different patterns with varying magnet surface area, planes of sy mmetry and number of magnets are fabricated for magnetic self assembly demonstrations. Some of the chips with different patterns of magnets are shown Figure 4 6 Fi gure 4 6 Chips with various magnet patterns A process similar to the one used for fabrication of individual parts is employed for fabrication of substrates. The only difference is that the pattering mask ha s a center to center spacing of 2.4 mm between the magnetic receptor sites. Once fabrication of magnets is complete, an n x n array of magnets is diced to form the substrate, with n ranging from 6 8. 4 4 2 Preparation of Parts and Substrates for Bonding Selec tivity Experiments In bonding selectivity experiments, two or more type of components are assembled onto the same substrate in an ordered array. As will be explained later in the Results chapter (Ch 5), the different types of components used for the bondin g selectivity experiments are similar in size (1 mm x 1 mm) and only vary in the magnetic bonding pattern. A video camera is used to capture and record the assembly data for further analysis. Since all the parts are the same size,

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87 the assembled components need to be somehow visually differentiable. This is achieved by spray -painting different types of components in different colors. The use of contrasting colors was intended to enhance computer aided image analysis of the videos taken during experiments. A process was devised to transfer the commercially diced parts to another surface to enable spray -painting of the back surfaces with paint. The diced substrates are received with the parts still attached to an underlying dicing tape. Starting from this poin t, low tack painters tape is pressed firmly against the diced parts, such that the front sides (bonding sides) of the magnets are now masked by the painters tape. The dicing tape is then carefully peeled off from the back of the diced parts as shown in Figure 4 7 The residue from the dicing tape is cleaned using a swab with acetone, making sure that the acetone does not get between the diced parts and separate the parts from the tape. Once the backsides of the parts are clean, the backsides are spray -painted with a glossy paint and set to dry for 24 hrs. The reason to follow this tedious process is to make sure that the parts do not fly off during spray painting and also so that the paint does not get on the side walls of the diced parts. Figure 4 7 Transfer of parts from the dicing tape to the painter's tape In contrast to the colored parts, the larger substrates are just cleaned with acetone, methanol and DI water, and then spray -painted with flat black paint to avoid any reflections from

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88 the polished Si surface. Figure 4 8 shows the substrate painted with flat black color and the parts painted with white glossy color. Figure 4 8 Spray painted substrate and parts in black and white 4 4 3 Part and Substrate Fabrication for Magnetic Self Assembly with Electrical Interconnects To demonstrate magnetic self assembly with electrical interconnects, a few additional steps are added to the earlier process flow where parts and substrates composed of polyimide capped bonded powder magnets are fabricated. The part magnets are fabricated using ferrite magnetic powder, and the subs trate magnets are fabricated using NdFeB magnetic powder. The reason for using different magnetic powders for parts and substrate is explained later in Ch 5 under the part to -substrate magnetic self assembly section. The process flow for the parts and sub strates with electrical interconnects is shown in Figure 4 9 Please first refer to Figure 4 1 for the process flow for fabrication of polyimide capped bonded powder magnets. After the polyimide -capped magnets are integrated into the Si substrate, the surface of the polyimide layer is roughed by doing a quick O2 reactive ion etchi ng (RIE) process. This is done to enhance the adhesion between the polyimide layer and the metal interconnects. The substrate is then patterned using a positive tone photoresist to define the electrical interconnect layout. Next, a 500 nm thick layer of Ni is sputtered on top of it followed

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89 by 200 nm thick layer of Au. Finally, a lift -off process is done to pattern the metal interconnects on the polyimide surface. The individual parts are then singulated by dicing the substrate into 1 mm x 1 mm square parts Si substrate with embedded micromagnets (i)Top polyimide coat (~5 m) Si substrate (iii) Sputtered Ni + Au layer Si substrate Photoresist pattern for electrical interconnects Si substrate Lift-off process (ii) (iv) Electrical interconnects Figure 4 9 Process flow for fabrication of parts and substrate for demonstration of magnetic self assembly with electrical interconnects For the substrate, a similar process is followed, the only difference being that the center to center spacing between the chips on the patterning mask is varied from 1.75 mm 2.4 mm. Once the substrate is diced into an n x n array, solder paste is manuall y dispensed onto the bond pad locations for both mechanical and electrical bonding. After the self assembly process, the substrate along with the assembled chips are heated so as to reflow the solder for permanent mechanical and electrical bonding (describ ed more fully in Ch 5). Figure 4 -10 shows the substrate and the parts fabricated for demonstration of magnetic self assembly with electrical interconnects.

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90 Figure 4 10. (a)Part, ( b ) Substrate with three columns of receptor sites for demonstration magnetic self assembly with electrical interconnects. Part to -substrate magnetic self assembly is a dry assembly process. T he dispensed solder bumps have to be dry to ensure that the parts assemble onto the substrate only due to magnetic interaction and not due the sticky solder paste. Also, the height of the solder bumps has to be limited to 10 15 m, so that the magnetic in teractions between the parts and the substrates are still strong enough for the parts to assemble. This is a concern since the magnetic forces roll off quickly with the spacing between the magnets, as was seen in the force maps in the Modeling chapter (Ch 3). For example, the axial force for a cuboidal magnet with an aspect ratio of 1 reduces to about 7 % of its contact force value for an axial displacement of 1x magnet thickness. To address these two issues, first a solder paste (solder particles suspended in flux) having particle size of about 15 m is selected. Once the solder paste is dispensed onto the substrate, the substrate is then heated for about 1 min @ 140 C on a hot plate to enable the solder flux to dry

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91 without causing the solder to reflow. Thi s ensures that the solder is dry during assembly and results in proper mechanical and electrical bonding later. 4 5 Conclusion Processing steps for fabrication of parts and substrates for millimeter scale assembly are discussed here. The integration of the magnets onto component surfaces and later on the measurement of their magnetic properties is also presented here. These fabricated s ilicon embedded magnets with ferrite, SmCo and NdFeB powders are intended to be used for demonstration of mm -scale self assembl y. Also fabrication and preparation of parts and substrates for demonstration of bonding selectivity and electrical interconnects is presented here.

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92 CHAPTER 5 5 RESULTS This chapter focuses on the experimental details and demonstration of magnetic self assembly at mm -scale. The initial part of this section focuses on quantification and evaluation of bonding forces between micromagnets for magnetic self assembly. Later, demonstration of part to -part and part -to -substrate magnetic self assembly is pre sented. The assembly model described in the Modeling chapter (Ch 3), is used later to analyze the part to -substrate magnetic self assembly process. Finally, magnetic self assembly is demonstrated with electrical interconnects. 5 1 Evaluation of Magnetic Bonding Forces Finite -element (FEM) and analytical methods, described in the Modeling chapter (Ch3), are used to analyze the dependence of magnetic bonding forces on the size, shape, type (soft/hard) and magnetization (x/z direction) of individual pair s of magnets as well as arrays of magnets. The analysis is performed assuming ideal magnets with a perfectly square hysteresis loop, i.e. M = Mr and r = 1. Various fabrication methods, such as electrodeposition [96] sputtering [98] bonded powder magnets [1], etc. can be adopted for integrating permanent magnets onto component surfaces. Magnetic self assembly is applicable for assembly of micro -millimeter scale components. Accordingly, the s ize of the magnets can vary from sub -micron to millimeter scale. Assuming micron scale application, the initial analysis of magnetic bonding forces is performed for magnets with the thickness of 5 m and a relatively conservative Br of 0.5 T [126] .The results from th is analysis are also applicable at millimeter scale. 5 1 1 Evaluation of Size, Shape and Type of Magnets Bonding sites are one of the most important aspects of any self assembly process. The flexibility offered in the bonding site design is one of the dominant factors for adaptability of the

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93 self assembly process. In magnetic self assembly the force between the magnets can be controlled by the size, shape, magnetic material and the magnetization of the magnet. FEA method discussed in Ch 3 was used for analysis o f size, type, and shape and magnetization direction of the magnet. For this analysis ideal magnet properties were assumed. The results based on this analysis are presented here. Figure 5 1 (a -d) shows magnets of different sizes and types, and the arrow qualitatively indicates the magnitude of the force between them. Considering different combinations of disc shaped soft and har d magnets (axially magnetized), it was found that the maximum bonding force is achieved for equally sized hard magnets. For example the force between two cylindrical hard magnets with diameter of 3 mm and height of 1.5 mm, was about 1.8 N, where as the for ce between a hard magnet and soft magnet with the same dimensions was just about 1 N. Figure 5 1 Analysis of size and type of magnet Next, various shapes were explored to determine the best shape to maxi mize the bond force. Since the goal is to maximize the surface bonding force (force per unit area), the contact force is normalized by a unit cell area, defined by a square that bounds the magnet edges (to accommodate irregular shapes). For non -square and noncircular shapes, the aspect ratio is defined as the ratio of the longest lateral dimension to the thickness of the magnet. As seen in

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94 Figure 5 2 maximum surface bonding force was achieved for square shaped magnets. Thus, for further analysis only square shaped magnets were considered. Figure 5 2 Shape analysis. To study the effects of magnetizing the sample in-pl ane (parallel to applied field) and out of -plane (perpendicular to the applied field), magnetization direction analysis was performed. The plots with both in -plane and out -of -plane magnetization for force per unit area vs. aspect ratio (AR = Thickness/Widt h) for cuboidal magnets were generated using ideal FEM analysis. Figure 5 3 shows that the peak force per unit area occurs for AR above 2. The force per unit area line arly increases for AR << 1 and rolls off to a maximum value for AR >> 1. Thus, the force per unit area for cuboidal magnets is maximized for AR > 1. For practical implementat ion using photolithographically -defined electrodeposited or sputtered magnets, hig h aspect ratios can be challenging to fabricate. Hence, further analysis considers aspect ratios of 0.5, 1, and 2.

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95 10-2 10-1 100 101 102 10-2 10-1 100 101 102 Aspect ratio [Thickness/Width]Force per unit area [N/cm2] Magnetization in z direction Magnetization in x direction Magnetization in y direction Magnetization in x direction Figure 5 3 Magnetization direction analysis. Magnetization in the y-direction is the out -of plane magnetization and the magnetization in the xdirection is the in -plane magnetization direction. A close observation of various microfabricated magnets (especially electrodeposited and embedded bonded magnets ) revealed certain geometric variations (surface irregularities) such as dishing, uneven surface, and edge effects (higher deposition at the edges compared to the center of the magnets). Again, ideal case FEM method was used to analyze the impact of these s urface effects. The schematic of the cross -sectional views of these geometrical variations are shown in Figure 5 4 The plot here shows the axial force variation with respect to the normalized axial gap (axial gap / magnet height). It is seen that the surface effects actually prove to be beneficial over short working distance s (small axial gap) presumably from local magnetic field enhancement but as the separation be tween the magnets increases, the force drops more rapidly compared to an ideal smooth, flat surface.

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96 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 102 Normalized gap (Axial gap/Magnet height)Axial force ( N) Dishing Edge effect Uneven surface Ideal case Figure 5 4 Surface effects for electroplated magnets. 5 1 2 Evaluation of Force between Arrays of Magnets To maintain the AR (0.5 2) and still get enough bonding force per unit area, arrays of micromagnets were also considered instead of a single large magnet. Contrary to ones expectation, the force between arrays of magnets is not always simply the superposition of the force between a pair of magnets, even if the physical and magnetic properties of the individual magnets are same. The force on any one magnet in an array is a resultant of the effective field from all the neighboring magnets. Also, both attra ctive and repulsive interactions exist between the magnets depending on the lateral spacing between the magnets. The potential for repulsive forces must be carefully considered. As a starting point, square -grid periodic arrays of magnets were analyzed, and the array spacing was optimized to achieve maximum force per unit area. The magnet array analysis was performed using the analytical method assuming ideal magnets, as described in the Modeling chapter (Ch 3). Figure 5 5 shows arrays of magnets on two parts indicating the magnet width, a

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97 and the center to -center array spacing, d With arrays of magnets, attractive and repulsive force interactions exist between the mag nets depending on the lateral spacing between them. Consider first just two magnets with zero axial gap, but laterally displaced. Figure 5 7 shows the plot for normalized axial force between two magnets (axial force/contact force) versus normalized lateral gap (lateral gap/magnet width) for square magnets for three different aspect ratios. The axial force is seen to change dramatically (and ev en reverse) when the magnets are laterally displaced. For lateral displacement d > 0.8 a where a is the magnet width, the force becomes negative (repulsive). As the lateral spacing d becomes greater than two to three times a the force reduces to zero; th e magnets become too far apart to have significant interaction. Part B g h i a f e c d b Part A 7 8 9 6 5 3 2 1 1 4 d d a Figure 5 5 Array of magnets on part A and part B indicating magnet width, a and array spacing, d z y x Magnet 1 Magnet 2 Lateral gap Figure 5 6 Laterally displaced magnets with zero axial gap

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98 Figure 5 7 Normalized axial force vs. normalized lateral gap for square magnets To achieve the maximum surface bonding force with optimal spacing, the total force on a substrate with regularly spaced infinite array of magnets was calculated. For example in Figure 5 5 the force acting on magnet 1 on part A, is the sum of all interactions between magnet 1 and all the magnets on part B; F1 = F1a + F1b + F1c + F1d, (5 1 ) where F1x is the axial force between magnet 1 on part A and magnet x on part B. The series sum is truncated to only include magnets within a spacing of d = 3 a The total force on part A is thus the sum of all the forces on each magnet. Ftotal = F1 + F2 + F3, (5 2 ) Figure 5 8 shows the variation of the force and force per unit area (area is the part surface area including magnets within a spacin g of d = 3 a ) with respect to the normalized array spacing for a single magnet in an array. This force increases with the spacing between the magnets and asymptotes to a maximum value where the repulsive interactions become negligible. It is also

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99 seen that the force for AR=2 is the lowest of the cases considered here. From Figure 5 8 (a), it may seem that to reduce the detrimental interactions, the array spacing has to be greater than 2.5 a ; but a closer look at Figure 5 8 (b) reveals that the force per unit area decreases with increased array spacing. It is also seen that the force per unit area increases with the aspect ratio. Thus, higher force per unit area is achieved with higher AR and lower values of d For instance, the optimal spacing for square magnets with aspect ratio of 2 occurs for d = 1.3 a (a) (b) Figure 5 8 Variation of (a) force and (b) force per unit area with respect to normalized array spacing An example to show that the higher force is achieved with an array of magnets rather than a single large magnet is presented here. Consider a chip surface area of 0.5 mm x 0.5 mm. A single large magnet (0.5 mm x 0.5 mm x 5m) covering the entire chip surfa ce would yield a force of 435 N. In contrast, if the chip surface is replaced with a 155 x 155 array of magnets (AR = 2, Br = 0.5 T, d = 1.3 a ), the force increases to approximately 7.21 mN, more than an order of magnitude improvement. Also, the total magnetic volume for a single large magnet is 1.25 x 106 cm3, whereas for an array it is 7.5 x 107 cm3. Thus, a 16x improvement in force can be achieved with almost half the magnet volume.

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100 5 2 Bonding Force Measurement Bonding force between the magnets is one of the most important parameters for characterization of magnetic self assembly process. A schematic of the set up used to measure the bonding force between the magnets is shown in Figure 5 9 As can be seen in the figure below, an analytical force balance (Ohaus) having a precision of 0.1 mg (1 N) is used to measure the force. The analytical force balance works on the force restoration principle where a mechanical beam structure is maintained in equilibrium at a reference position by electromagnetic force acting against gravity [127] When a sample is placed on the balance, the beam is displaced from its reference position. Current proportional to the mass of the sample is forced through the coil generating an electromagnetic force restoring the beam to its reference position. Ideally, the balance pan does not move during the measurement; this is important for the intended m easurement application. Ultimately, the readout on the balance is proportional to this current, and thus a very fine measurement of mass is possible with the use of analytical force balance. The readout on the balance in grams is later converted to a force unit, Newton (1 g ~9.8 mN). To measure the bonding force, the two magnets are first magnetized to exhibit mutual attraction. One magnet is fixed on the balance plate with a dead weight, and the other is fixed upside down to the 3D micropositioner, free to move in the x, y and z directions. Initially the balance read outs the weight of the fixed magnet and the dead weight. This reading is noted as the reference weight. Next, the second magnet is laterally aligned above the fixed magnet and lowered verticall y towards it. The fixed magnet experiences a pull force due to magnetic attraction between the two magnets. Thus, the balance readout starts decreasing as the upper magnet approaches the lower magnet. The balance readout, when the magnets touch is noted as the final weight. The position at which the magnets touch is detected when the readout on the

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101 balance starts increasing (instead of decreasing) due to the physical force exerted on the lower magnet by the upper magnet and the micropositioner. The differen ce between the reference weight and the final weight gives an approximation of the contact force (bonding force with zero gap) between the two magnets. Figure 5 9 Experimental set up for bonding force measurement The analytical force balance setup was first used to measure the axial magnetic force versus displacement for large, bulk -manufactured cylindrical ceramic magnets of dimension 14.2 mm (diameter) x 17.5 mm (height). These experimental results w ere compared to the axial force estimated using analytical and FEM ideal and non -ideal methods. The purpose was to validate both the experimental setup and the force calculation methods. The advantage of initially testing the bulk -manufactured magnets was that the magnetic properties were well known and the larger forces were easier to measure. Figure 5 10 shows the plot for measured axial force versus the normalized a xial gap along with the predicted forces from analytical and linear and nonlinear finite -element analysis. The

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102 axial gap is normalized by the height of the magnet. It can be seen that the expected axial force values for analytical and FEM ideal case match each other closely as expected, but the values over predict the experimental measurements and the nonlinear FEM estimations, a result of the ideal magnet assumption. The experimental force results are the lowest of all the methods considered here but follow very close to the nonlinear FEM force estimates. The purpose for non ideal FEM simulations is to closely estimate the actual force between the magnets and this plot validates the use FEM non ideal simulations for estimation of magnetic bonding forces. 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 Normalized axial gap (Axial gap/Magnet height) Axial force (N) FEM_ideal FEM_nonideal Experimental Analytical Figure 5 10. Comparison of axial force using FEM ideal, nonideal, experimental and analytical methods. The magnets used here are commercially available cylindrical ceramic magnets with dimensions of 14.2 m m (diameter) x 17.5 mm (height). The force balance setup was also used for some force measurements of microfabricated SmCo polyimide capped bonded powder magnets. The measured bond force (zero axial and lateral displacement) values for various component ty pes along with the FEM estimated force

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103 values are shown in Table 5 1 The measured force values are averaged over three trials and are reported with 95% confidence intervals. For 95% confidence level, the uncertainty is calculated by using the expression /xUtsN (5 3 ) where N (number of trails) is equal to 3, n= N 1 = 2, t = t(0.025,2)=4.303 and s is the standard deviation. First of all, it can be seen that the measured values are consistently smaller compared to the FEM estimated force values. Second, the uncertainties in the measured values are huge. It was mentioned previously that t he force value drops drastically with any axial and lateral displacements. In the analytical force balance setup, some tricks (such as using the balance readout as the guide, since the maximum force is achieved when the magnets are perfectly aligned) wer e used to align the magnets during measurement, but alignment was not guaranteed. Any misalignment may result in much lower measured forces. It is also seen that the measured forces were close to the estimated forces for magnets with large surface area. Th e larger surface area magnets offered more tolerance for any misalignments during measurement. Because of the experimental difficulties in measuring small forces requiring precise alignment, this experimental approach was abandoned. Table 5 1 Comparison of measured bonding forces with the estimated FEM forces for various component types Component type Magnet type Magnet surface area Force FEM (non linear) Force measured Square 1 SmCo 10% 80 N 24.2 7 N Square 2 SmCo 25% 120 N 91.2 43 N Square 4 SmCo 75% 200 N 135 24 N Oval SmCo 16% 50 N 25.2 4 N Stripes SmCo 12% 170 N 29 35 N Corner squares SmCo 10% 100 N 46 22 N Along with the bonding force measurement, this force measurement system was also used to determine the approximate displacement between the magnets at which the components snap

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104 together. A process similar to the one mentioned above for bonding force measur ement is used here. Previously both the magnets were fixed, one to the micropositioner and the other to the balance plate. In this case, the second magnet is free to move, so that when the inverted magnet on the 3D micropositioner is lowered towards the ma gnet on the balance plate, it jumps off the plate and assembles onto the upper magnet. The position of the micropositioner at this point is noted. The micropositioner along with the assembled chip is now lowered towards the plate. Once the chip touches the plate, the balance shows some reading; the position of the micropositioner at this point is also noted. The difference between the two positions gives the distance at which the magnets snapped together. The Square 4 pattern shown in Figure 5 13 (a), 150 m thick with the largest surface area was used for this experiment. Four trials were performed here. The average distance at which the chips snapped together for thi s pattern is about 295 93 m, about 2x the magnet thickness. The force at this displacement was then estimated using the nonlinear FEM simulation discussed in Ch 3. The estimated force at this position was about 12 N, the weight force of the chip. This test also gave further confidence in the nonlinear FEM force estimates. 5 3 Part -to -Part Magnetic Self Assembly In part to -part assembly free floating parts are assembled onto other free floating parts in a wet environment. This concept is depicted in Figure 5 11. The components to be assembled are magnetized with one polarity, and the excess redundant parts are magnetized with opposite polarity. 5 3 1 Experimental Setup A tum bler like setup shown in Figure 5 12 is used to demonstrate part to -part magnetic self assembly. The parts to be assembled and the excess parts are mixed together in a rotating conical tube with ~1 ml of methanol. The methanol enables the components to randomly mix and

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105 tumble over each other. It also prevents the components from sticking to the tube surface and mitigates air bubble formation. The tube is inclined at an angle of 35 45 and rotated at ~60 rpm. Because of the magnetization direction, like parts do not bond with each other since they have the same polarity (like poles repel), thus avoiding agglomeration. Figure 5 11. Part to -part magnetic self assembly concept. DC motor Components in methanol Conical tube Speed control Figure 5 12. Experiment set up for part to -part magnetic self assembly 5 3 2 Experiments and Results To demonstrate the part -to -part magnetic self assembly, a batch of free floating 1 mm x 1mm x 0.5 mm silicon parts were self assembled in a liquid medium (methanol). Along with inter -part bonding, 4 -fold and 2 -fold angular orientation is also demonstrated here To demonstrate angular orientation, the parts were fabricated with magnet patterns having 4 -fold

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106 and 2 -fold symmetry. Figure 5 13 shows the various parts fabrica ted using SmCo polyimide capped micromagnets with different magnetic shapes having four -fold and two -fold symmetries The square magnetic patterns shown in Figure 5 13 (a) exhibit a 4 -fold rotational symmetry resulting in four possible bonding orientations, while the corner square s stripe s and oval patterns in Figure 5 13 (b) e xhibit a 2 -fold symmetry permitting assembly in only two orientations. Analytical and FEM methods were used to estimate the bonding force between the magnets. Table 5 2 shows the estimated force values for the different magnetic patterns. Figure 5 13. Si embedded SmCo magnets with (a) 4 -fold symmetry and (b) 2-fold symmetry Table 5 2 Force estimation for Si embedded SmCo magnets for part to -part magnetic self assembly SmCo sample B r = 0.18 T Force analytical Force FEM (linear) Force FEM (non linear) Square 1 0.38 mN 0.36 mN 0.08 mN Square 2 0.67 mN 0.58 mN 0.123 mN Square 3 0.91 mN 0.83 mN 0.17 mN Square 4 1.1 mN 1 mN 0.2 mN Oval 0.212 mN 0.05 mN Stripes 0.74 mN 0.68 mN 0.173 mN Corner squares 0.44 mN 0.4 mN 0.1 mN In each of the trials, 8 parts were magnetized with one polarity and the excess (4x) parts were magnetized with opposite polarity. Figure 5 14 shows the components mixing in the conical tube and the assembled pairs. The experiment was repeated 20 times and the number of

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107 component pairs assembled after the end time of 20 s was recorded. Several trial runs in the beginning were used to estimate t he end time of the experiments, which was the time at which the assembly stopped progressing. Table 5 3 summarizes the results with 95% confidence intervals The perce ntage yield for the components with 4 -fold symmetry varies from 89% to 97%. The lower yield for the large Square 4 design is attributed to the excessive bonding force causing multiple components to stick to one another. The percentage yield for the components with 2 -fold symmetry varies from 88% to 91%, slightly lower than the 4 -fold case. In general, it was seen that higher yields were achieved with lower bonding forces, possibly because the magnets in this case were too strong. Figure 5 14. Part to -part magnetic self assembly of free floating components Table 5 3 Part -to -p art magnetic self assembly results Component T ype SA (%) NM SYM Part 1 M agnet s Part 2 M agnet s Force (mN) End Time t ( s ) End Y ield Square 1 10 1 4 fold SmCo SmCo 0. 08 20 97 2.6 % Square 2 25 1 4 fold SmCo SmCo 0.12 20 97 2.4 % Square 3 50 1 4 fold SmCo SmCo 0.1 7 20 93 4.2 % Square 4 75 1 4 fold SmCo SmCo 0.2 20 89 4.3 % Oval 16 1 2 fold SmCo SmCo 0. 05 20 90 4.4 % Stripes 12 2 2 fold SmCo SmCo 0. 17 20 89 4.8 % Corner squares 10 2 2 fold SmCo SmCo 0. 1 20 88 4.2 % Abbreviations used : SA Magnet surface area, NM No. of magnets, SYM Symmetry

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108 5 4 Part -to -Substrate Magnetic Self -assembly In part to -substrate assembly, free floating parts are assemble d onto a fixed substrate in an ordered array in a dry (air) environment, as shown in Figure 5 15. The substrate is magnetized with one polarity and the free floating parts are magnetized with opposite polarity. Substrate Free floating parts Assembled parts Receptor site magnets Figure 5 15. Part to -substrate magnetic self assembly concept 5 4 1 Experimental setup Part to -substrate m agnetic self assembly of mm -scale components is demonstrated using a shaker apparatus similar to the one in [34] The experimental setup is shown in Figure 5 16. The components are placed in a small glass container, which is rigidly mounted on an electromechanical s haker. The shaker used here is a mini shaker type 4810 with a power amplifier type 2718 from Brel and Kjaer. The substrate is attached to a rod which is glued to a vibrating piezoelectric plate. Next, the substrate along with a piezoelectric plate is atta ched, with its face down, to a 3 axis micropositioner. The micropositioner from Line Tool Co. has a total travel of 12.7 mm for each axes with a resolution of 25.4 m. The substrate is then lowered into the glass container to a distance ~10 mm above the ba se of the glass container. The vibrating piezoelectric plate aligns the components and prevents the stacking (an extra component sticking to the back of the assembled component) of components. The frequency of the vibrator is set to the resonant frequency of the piezo structure with the substrate, which is about 900 Hz. The amplitude of the vibrator is dependent on the force between the magnets on the components

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109 being assembled and is fine tuned for every pattern. For stronger magnets, higher amplitude vibr ations are required to knock off the incorrectly assembled components and self align the already assembled components. A square wave with a frequency of 3 Hz and amplitude of 2 Vpp, is fed from a signal generator through an amplifier to the shaker. Since the velocity and the 2, respectively, a high -frequency fundamental tone is required to accelerate the parts if a sine wave is used. As the square wave comprises of high frequency odd integer harmonics, a low frequen cy fundamental tone is enough to accelerate the parts for selfassembly. The shaker displacement at 3 Hz and 2 Vpp is 1.8 mm p-p causing the components to bounce up and down and self assemble onto the substrate. The function generators used in this setup are from Agilent type 33120A. A Logitech webcam (9614040403) is used to capture and record the data into a computer for further analysis. Figure 5 17 shows the actua l setup used for the demonstration of part -to -substrate magnetic self assembly. Micropositioner Power amplifier Substrate Components 3 Hz Shaker Substrate height ~ 10 mm Camera Piezoelectric vibrator Signal generators Figure 5 16. Schematic of the e xperiment set up for part to -substrate magnetic self assembly

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110 Figure 5 17. E xperiment set up for part to -substrate magnetic self assembly 5 4 2 Magnetic Self Assembly of a Homogeneous Mixture of Parts This section describes the demonstration of magnetic self assembly of a homogeneous mixture of parts. Here, only one type of component is assembled on the substrate. The parts and the substrates were fabricated using both polyimide capped and wax bonded embedded micromagnets All magnets were 150 m thick. A long with 4 -fold and 2 -fold symmetric patterns, p art to -substrate assembly is also demonstrated using 1 -fold/asymmetric patterns. The asymmetric patterns restrict the assembly to only one physical angular orientation. The various magnetic patterns used for part to -substrate magnetic self assembly demonst rations are shown in Figure 5 18. These magnetic patterns covered 10% 75 % of the chip surface area, and the number of magnets in each pattern ranged from one to fou r. Figure 5 19 shows a picture of the inverted substrate populated with parts assembled in an ordered array.

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111 Figure 5 18. Components used in part to -substrate magnetic self assembly demonstration. (a) Components with 4 -fold symmetry, (b) Components with 2 -fold symmetry, (c) Components with 1 -fold symmetry Figure 5 19. Demonstration of part to -substrate magnetic self assembly where parts have assembled onto an inverted substrate 5 4 2 1 Results for part -to -substrate assembly from a homogeneous mixture of components Two sets of experiments were conducted. In the first set of experiments, the 4 -fold symmetric patterns were studied where both the substrate and the parts were made with the same magnet type, either NdFeB or SmCo Because of stacking problems described bel ow, two improvements were made for the second round of experiments. First, strong NdFeB magnets Inverted substrate Assembled parts

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112 were used for the substrate, while weaker SmCo or ferrite magnets were used for the parts. This helped avoid stacking and agglomeration of parts. Second, active piezo vibrations were applied to the substrate during the assembly to mitigate stacking and also help in aligning the assembled parts. The results for the various magnetic patterns are tabulated in Table 5 4 All results described below were averaged over 15 trials and are reported with 95 % confidence intervals. The bonding force values for all the patterns were estimated using non-ideal FEM analysis, as discussed in the Modeling chapter (Ch 3). In the beginning, several trials for each pattern were used to determine the run time of the experiments. The run time differed for different magnetic patterns, since some patterns assembled faster than others, but the run ti me was consistent from trial to trial for a given pattern. The end time established was the time at which the assembly process essentially stopped progressing. The number of correctly assembled parts divided by the number of available receptor sites at end of this time was recorded as the end yield of the assembly process. In addition to recording the end yield value, t he video -captured assembly vs. time data was later fit with the process model (see Modeling chapter (Ch 3)) to determine a T -value. As an example the assembly versus time data for 15 trials for the Square1 pattern is shown in Figure 5 20. For these experiments, a substrate with 7 x 7 array of receptor sites was used. The figure shows the actual number of chips assembled rather than the assembly yield. It shows the exponential nature of the self assembly process where the assembly rate reduces as the receptor sites are filled. It can also be seen that th e self assembly process is a fairly repeatable process. Figure 5 21 shows time lapse images of the progression of assembly with time for the

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113 components with the Oval_1 pattern. The entire array was populated in 20 s, but more than 50% of the total receptor sites were filled in less than 4 s. Table 5 4 Part -to -substrate magnetic self assembly results Component type SA NM SYM Substrate magnet Part magnet Force (mN) End time ( s ) End y ield (%) T value (min) Experiment Set 1 Square 1 10 % 1 4 fold SmCo SmCo 0.13 58 88 .0 2.0 32.7 2.0 Square 1 10 % 1 4 fold NdFeB NdFeB 2.2 33 97.6 1.3 14.8 1.2 Square 4 75 % 1 4 fold SmCo SmCo 0.37 33 97.7 1.1 3.9 0.3 Square 4 75 % 1 4 fold NdFeB NdFeB 6.6 Stacking Experiment Set 2 Square* 20 % 1 4 fold NdFeB Ferrite 0.7 15 95.5 1.1 9.8 0.5 Square ring* 10 % 2 4 fold NdFeB Ferrite 0.72 120 98.8 0.6 60.1 5.2 Four squares* 15 % 4 4 fold NdFeB Ferrite 0.9 120 92.5 1.2 53.0 3.2 Oval_1 16 % 1 2 fold NdFeB SmCo 0.28 15 96.8 2.1 5.2 0.5 Oval_2* 15 % 1 2 fold NdFeB Ferrite 0.64 20 99.1 0.6 11.4 1.2 Stripes_1 12 % 2 2 fold NdFeB SmCo 0.86 22 94.7 2.5 12.3 1.3 Stripes_2* 20 % 2 2 fold NdFeB Ferrite 0.98 25 94.8 1.8 15.5 1.7 Corner squares 10 % 2 2 fold NdFeB SmCo 0.54 33 85.6 2.8 15.0 2.1 Line* 10 % 4 2 fold NdFeB Ferrite 0.51 180 86.1 1.3 135 10.3 Arrow head* 10 % 1 1 fold NdFeB Ferrite 0.57 180 92 1.0 277 19.4 Single triangle 10 % 1 1 fold NdFeB Ferrite 0.45 120 91.4 1.5 904 31.7 Two triangles* 15 % 2 1 fold NdFeB Ferrite 0.80 200 89.3 2.0 387 41.7 Three rectangles 13.5 % 3 1 fold NdFeB Ferrite 0.73 240 93.1 2.0 237 16.0 Four triangles* 20 % 4 1 fold NdFeB Ferrite 1.03 180 98.6 1.0 134 11.4 Components used later for ANOVA analysis Abbreviations used: SA Magnet surface area, NM No. of magnets, SYM Symmetry The extracted T parameter values are also shown in Table 5 4 The uncertainties of this parameter were calculated using Monte Carlo simulation, the program for which was developed us ing MATLAB. For each magnetic pattern, the uncertainties in the yield at five different time instances were found based on statistics from the 15 trials. As mentioned previously, the assembly rate is high in the beginning and as the parts assemble the asse mbly rate decreases. This is also seen in Figure 5 20. Hence the 5 data points were chosen appropriately. For each

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114 pattern, the time required for 50% assembly was firs t estimated. Let this point be called t50. The five data points corresponded to time t = 0, t = t50/2, t = t50, t = 2*t50 and t = end time. Assembly vs. Time 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Time (s) Number of chips assembled Figure 5 20. Assembly vs. time data for Square1 pattern for 15 t rials Figure 5 21. Snapshot views of magnetic self assembly of oval pattern from t=0 to t=20s. Monte Carlo simulation takes into account the uncertainties of each of these five data points. For each Monte Carlo trial, e ach of the five data point s was perturbed based on its

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115 individual Gaussian uncertainty distribution, and the best -fit T value was found using nonlinear least squares method The randn function in MATLAB was used to generate these random data points which are normally distributed with zero mean, variance and standard deviation of one. The simulation was run for 5000 iterations, and the probability distribution function (pdf) for the parameter T was plotted. An example histogram with superimpose d pdf plot of T for the oval_2 pattern is shown in Figure 5 22. 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 0 50 100 150 200 250 300 350 T (min) Figure 5 22. Probability distribution function of T for oval_2 pattern. The statistical moments for the different patterns were calculated and are shown in Table 5 5 The Skewness and the Kurtosis have to be equal to zero and three, respectively, for a Gaussian distribution. Since the calculated values for the Skewness and the Kurtosis in Table 5 5 are very close to the ideal values, the data is assumed to be Gaussian. Under this assumption, the 95 % confidence intervals for the T deviation. Mean 11.4 Variance 0.36 Skewness 0.15 Kurtosis 3.0

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116 Table 5 5 Statistical moments of the parameter T derived from the Monte Carlo simulation Component type Mean Variance Skewness Kurtosis Square 1 32.7 0.93 0.08 3.2 Square 1 14.8 0.36 0.05 2.9 Square 4 3.9 0.02 0.08 3.0 Square* 9.8 0.06 0.09 3.0 Square ring* 60.1 6.7 0.13 3.0 Four squares* 53.0 2.5 0.02 2.9 Oval_1 5.2 0.06 0.09 3.1 Oval_2* 11.4 0.36 0.08 3.06 Stripes_1 12.3 0.40 0.09 3.0 Stripes_2* 15.5 0.74 0.15 3.0 Corner squares 15.0 1.11 0.33 3.2 Line* 135 26.4 0.08 2.9 Arrow head* 277 94.6 0.01 3.0 Single triangle 904 251 0.02 3.0 Two triangles* 387 434 0.08 3.2 Three rectangles 237 63.20 0.01 3.1 Four triangles* 134 32.3 0.16 3.0 The part to -substrate assembly results shown in Table 5 4 are now discussed The percentage yield for the various patterns studied here varies from 85 % to 99%, and th e T values vary from about 4 900 min. In the first set of experiments, the percentage end yield varies from about 88 % to 98 % and the end time ranges from 33 s to 58 s. For the Square 1 case, higher yields and faster assembly times were achieved with Nd FeB, attributed to the higher bonding force compared to the SmCo. This trend is opposite to the one observed for part to part assembly where higher yields were achieved with lower bonding forces. The fastest assembly was seen in the Square 4 case, where bo th part and substrate magnets were SmCo, possibly due to the large magnet surface area and considerably high bonding force. The T parameter value in this case was just 4 min. For the Square 4 case, where both part and substrate magnets were NdFeB, drastically lower yields were seen, even though the bonding force was highest (about 6.6 mN). This excessive bonding force caused a considerable amount of stacking and also led to agg lomeration

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117 of the parts, thus reducing the assembly yield. Figure 5 23 shows a picture of a substrate populated with parts including some of the stacked parts. Stacki ng is defined as the assembly of an extra component on the back of an already assembled component due to excessive bonding force between components. This suggests that there is a limit for the bonding force, and that excessive bonding force may reduce the assembly yield. Note, these preliminary experiments were performed before the piezo vibrator was added to the experimental setup. Figure 5 23. Part to -substrate assembly with some stacked components In th e second set of experiments a larger variety of magnetic patterns were explored. For the 4 -fold case the end yield varies from about 92% to 99%, with T values ranging from 10 min. to 60 min. The end time varies from 15 s to 120 s. The assembly speed was hi ghest for the square pattern with 20% magnet surface area, having a T value of about 10 min. The assembly yield for the 2 -fold case varies from about 86% to 99% and T varies from 5 min 135 min. For these patterns the end time ranged from 0.25 min to 3 min. The fastest assembly was for the oval magnets, with T value of about 11 min. In contrast, the slowest assembly was for the line pattern, with the T value of about 135 min, which had the smalles t surface area and the highest number magnets of all for the 2 -fold patterns considered here. The assembly yield for the 1 -fold symmetric patterns varied from approximately 89% to 99% and T varied from about 130 min to 900 min. T he lowest value of T corre sponded to the

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118 four triangles pattern Thus the fastest assembly was observed for this pattern, but these asymmetric patterns assembled much slower than the 2 -fold or 4 -fold symmetric patterns. Figures 5 24 through 5 28 show the variation in the parameter T with respect to the magnet pattern symmetry, number of magnets, magnet surface area, bonding force and bonding force per unit area. T he variation in the parameter T with respect to the magnet pattern symmetry in Figure 5 24 shows that the T values for the 2 -fold and 4 -fold symmetric patterns are generally lower compared to the 1 -fold symmetric patterns. Since lower values of T correspond to faster assembly, this suggests that patterns with higher planes of symmetry are more desirable for faster assembly rates. Figures 5 25 through 5 28 do not show any specific trends in assembly rate with respect to number of magnets, magnet surface area, bonding force and bondin g force per unit area. Hence, to draw conclusive results for the variation in T value with respect to these parameters, more data is required. However, some i nitial observations indicate that better angular alignment can be achieved for patterns with more number of magnets. 0 1 2 3 4 5 100 101 102 103 Magnet pattern symmetryT value (min) Figure 5 24. Variation of T with respect to the magnet pattern symmetry

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119 0 1 2 3 4 5 100 101 102 103 No. of MagnetsT value (min) Figure 5 25. Variation of T with the number of magnets in the b onding pattern 0 10 20 30 40 50 60 70 80 100 101 102 103 Magnet surface areaT value (min) Figure 5 26. Variation of T with respect to the magnet surface area

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120 0 0.5 1 1.5 2 2.5 100 101 102 103 Bonding force (mN)T value (min) Figure 5 27. Variation of T with respect to the bonding force 0 0.5 1 1.5 2 2.5 x 104 100 101 102 103 Bonding force / magnet area (N/m2)T value (min) Figure 5 28. Variation of T with respect to the bonding force per unit area

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121 5 4 2 2 ANOVA analysis of magnetic self assembly experiments T o better understand the MSA process, a select number of experiments from Table 5 4 were used to characterize the dependency on various attributes of the magnetic patterns. The goal of these experiments was to study the effect of the magnet surface ar ea, symmetry of the magnetic pattern, and the number of individual magnets in a pattern on the progression of the assembly. A random Latin square design with three factors and three levels [128] was selected, as sho wn in Figure 5 29. The magnet surface was varied from 10 20%, the symmetry from 1 4, and the number of magnets from 1 4. The different magnet patterns used for this an alysis are again shown in Figure 5 30 for quick reference T he estimated bonding forces for each of these patterns and the extracted T parameter values are also shown again in Table 5 6 Figure 5 29. Latin square design with 3 levels and 3-factors for characterization of magnetic self assembly process. The effect on T due to the magnet surface area, pattern symmetry and the number of magnets was analyzed using multifactor analysis of variance (ANOVA) [128] The computation resu lts for the ANOVA are shown in Table 5 7 Once all the terms in the ANOVA table were

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122 calculated, the F test (F distribution test) was applied. Since F0.05,2,2 = 19 is greater than all the values of f in the ANOVA table, no statistical conclusion could be drawn. T he average time T statistically did not seem to depend on the magnet surface area, pattern symmetry or the number of magnets at 95% significance level. Even at 90% significance level no statistical conclusions could be made. As mentioned before, more data will be required to characterize the T parameter value. In the current design analysis, which is an incomplete layout (all combinations of input parame ters not present), interactions between various factors are assumed absent. In future work, including the combinations for the number of magnets in the design with a complete layout would allow for analysis of interactions between various control factors. Figure 5 30. Various components used in the characterization of magnetic self assembly experiments.

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123 Table 5 6 Part -to -substrate magnetic self assembly chara cterization results Component type SA SYM NM Force (mN) Yield (%) T (min) Square 20 4 fold 1 0.7 95.5 1.1 9.8 5.2 % Square ring 10 4 fold 2 0.72 98.8 0.6 60.1 8.6 % Four squares 15 4 fold 4 0.9 92.5 1.2 53.0 6.0 % Oval_2 15 2 fold 1 0.64 99.1 0.6 11.4 11 % Stripes_2 20 2 fold 2 0.98 94.8 1.8 15.5 11 % Line 10 2 fold 4 0.51 86.1 1.3 135 7.6 % Arrow head 10 1 fold 1 0.57 92 .0 1.0 277 7.0 % Two triangles 15 1 fold 2 0.80 89.3 2.0 387 11 % Four triangles 20 1 fold 4 1.03 98.6 1.0 134 8.5 % Table 5 7 ANOVA table for T analysis Source of variation df Sum of squares Mean square f (Mean square/Mean square error) A (Surface area) 2 20453.98 10226.99 1.14 B (Symmetry) 2 95665.55 47832.77 5.34 C (Number of magnets) 2 5293.44 2646.72 0.29 Error 2 17920.64 8960.32 Total 8 139333.62 5 4 3 M agnetic Self Assembly of a H etero geneous Mixture of Parts Unlike homogeneous assembly where only one type of component is assembled at a time, here parallel assembly of two different types of components from a heterogeneous mixture is demonstrated. The components are assembled in both sequential as well as simult aneous manner (explained in detail later). The components are similar in size (1 mm square Si parts) with the difference only in the magnetic pattern. Figure 5 31 sho ws the substrate patterned with two different receptor site designs and the components selectively assembling onto these receptor sites. S elective bonding is achieved by using different magnetic patterns for the different component types such that the magn etic forces between dissimilar magnetic patterns are not strong enough to enact a bond. The components used for heterogeneous assembly demonstration are shown in Figure 5 32. Sequential assembly is demonstrated using the components shown in Figure 5 32. The experimental setup used to

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124 demonstrate heterogeneous assembly is the same as the one used for homogeneous assembly. The substrate vibration proved to be the key to the success of heterog eneous assembly. Substrate Type A components Type B components Free floating components Assembled components Figure 5 31. Magnetic self assembly (MSA) of two types of parts from a heterogeneous mixture of parts Figure 5 32. Components used for sequential heterogeneous magnetic self -assembly demonstration. The general approach relied on active rejection of parts by controlling the vibration energy of the substrate. In practice, the substrate vibration level was increased to a high level such that no parts were assembling (or if they were, they were immediately being kicked out). As the vibration energy was decreased the magnetic bonding forces were sufficiently high to overcome the vibration forces, and one or more component type began to assemble Whether the parts assembled in a simultaneous or sequential fashion was found to depend largely on the magnetic bond energies, E. The nomenclature used here is EX meaning the bond energy of part Type X bonding onto receptor site Type Y. Note in genera l, EA does not necessarily equal EB since

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125 different magnetic materials may be used for the parts and substrate, even if the magnets have the same size and shape. 5 4 3 1 Sequential assembly For demonstration of sequential assembly, a square ring magnetic patt ern with 4 -fold symmetry (Type A) and an oval magnetic pattern with 2 -fold symmetry (Type B) were used, as shown in Figure 5 32 (a). In this case, the substrate used w as an 6 x 6 array of receptor sites with alternating rows of Type A and Type B components. The glass vial in the experimental set up shown in Figure 5 16 contained a m ixture of free parts of Type A and Type B. About 3x redundant parts of each type were used for the demonstration. To visually differentiate the assembled parts, both Type A and Type B parts were spray painted with green and orange color, respectively. Figure 5 33 shows the two types of parts (Type A green and Type B orange) assembled onto an inverted substrate in alte rnating rows. An assembly yield, averaged over 15 trials, of 99 % was achieved in total time of approximately 3.5 min. The assembly process is shown schematically in Figure 5 34. In the beginning high substrate vibrations prevented any assembly. However, as the vibration level was reduced, the square ring Type A parts began to assemble, but the oval Type B parts did not. If the vibration level was further reduced to the point where the Type B parts also began assembling, Type B parts also began as sembling incorrectly on to Type A receptor sites. To avoid this, the vibrations were maintained high until all of the Type A receptor sites were filled. Once all Type A sites were occupied (in about 2 min), the vibration level was lowered, and the Type B parts began correctly assembling until the array was fully populated (an additional 1.5 min). Thus, i n this demonstration, the process was sequential, although the parts were completely mixed.

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126 Figure 5 33. Demonstration of sequential magnetic self assembly of multiple component types from a heterogeneous mixture E A A E B B E B A E A B Energy to piezo vibratorTime Component Type A assemble E X Y Bond energy for component X to assemble onto receptor site Y Component Type A Component Type B No assembly Component Type B assemble tA = 2 min tB = 1.5 min Figure 5 34. Concept for sequential magnetic self assembly This sequential assembly process can be explained as follows. Since the substrate was initially populated by the square ring Type A parts, this indicates the bond energy EA was above all other bond energy levels. When the vibration energy was reduced without fully populating the Type A rec eptor sites with Type A parts, the Type B parts also preferentially assembled onto the Type A receptor sites. Only when the vibration level was lowered even

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127 further did the Type B parts begin assembling onto their correct Type B receptor sites. This indica tes the bond energy EB falls between EA and EB Moreover only at very low substrate vibration levels did the Type A parts assemble onto Type B receptors, indicating EA was the lowest bonding energy. 5 4 3 2 Simultaneous assembly Simultaneous assembly is demonstrated here through assembly of two different types of components in parallel from a heterogeneous mixture of components. For this demonstration, a large square magnetic pattern (Type A) and a small square magnetic pattern (T ype B) were used, as shown in Figure 5 35. Both magnetic patterns exhibited 4-fold rotational symmetry. The substrate used here was an 8 x 8 array of receptor sites wi th alternating rows of Type A and Type B components. In this demonstration also 3x redundant parts of each type were used. Again for visual differentiation as before the Type A and Type B components were spray painted with red and white color, respectively. Figure 5 36 shows the two types of parts (Type A red and Type B white ) assembled onto a substrate in alte rnating rows. Here, 15 trials yielded an average assem bly yield of 93% in 60 s. A schematic of the assembly process is shown in Figure 5 37. For very high substrate vibration levels, no parts assembled, as expected. Howev er, when the substrate was vibrated at an intermediate energy level, both Type A and Type B parts correctly assembled simultaneously. Figure 5 35. Components used for simultaneous heterogeneous assembly.

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128 Figure 5 36. Demonstration of simultaneous magnetic self assembly of multiple component types from a heterogeneous mixture E A A E B B E A B E B A Energy to piezo vibratorTime Components A & B assemble simultaneously E X Y Bond energy for component X to assemble onto receptor site Y t = 1 min Component Type A Component Type B No assembly Figure 5 37. Concept for simultaneous magnetic self assembly A hypothetical justification for this trend is as follows. The magnetic bond energies for parts Type A and Type B onto th eir correct receptor sites (denoted EA and EB ) are assumed much higher compared to the bond energies for incorrect assemblies (EA and EB ). During the assembly phase, the substrate vibration energy was low enough to permit correct assembling Alternate rows of Type A components Alternate rows of Type B components Substrate

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129 of Type A and Type B parts, but high enough to reject incorrect assembling of Type A parts onto Type B receptor sites and vice versa. 5 4 4 Magnetic Self Assembly Demonstration with Electrical Interconnects To demonstrate magnetic self assembly with electrical intercon nects, free floating parts are assembled onto a fixed substrate. The fabrication of parts and substrate for this demonstration were discussed in the chapter on Fabrication (Ch 4). The part and the substrate magnets are polyimide capped magnets made with fe rrite and NdFeB powders. The set up used here is similar to the one used for part to -substrate assembly in the earlier section, Figure 5 16. Since, it was observed tha t the best assembly results were achieved for the magnets with oval pattern, this pattern was chosen for demonstration of magnetic self assembly with electrical interconnects (Refer Table 5 4 Part to -substrate magnetic self assembly results.). Figure 5 38. (a) Part and (b) substrate used for demonstration of magnetic self assembly with electrical interconnects

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130 Figure 5 39. Demonstration of magnetic self assembly with electrical interconnects, substrate with assembled parts. Figure 5 38 shows a snapshot of the part and the substrate used for demonstration of magnetic self assembly with electrical interconnects. The part magnet aligns with the substrate magnet during assembly which in turn aligns the contact pads on the parts to the solder coated contact pads on the substrate receptor site. Thus, the part bridges the gap between the contact lines on either side of the patterned magnet, providing a continuous electrical connec tion between the probing pads on either side. The contact pads on both the part and the substrate are 125 m x 125 m in dimension and the contact lines are 50 m wide. For earlier demonstrations of part to -substrate assembly, the center to center spacing between the receptor sites was 2.4 mm. The substrate with electrical interconnects, shown in Figure 5 38 was patterned with three columns of receptor sites, C1 C3, with increasing density. The first column, C1 has six receptor sites with the center to center spacing of 2.4 mm. The second column, C2 has 7 receptor sites with the center to center spacing of 1.9 mm. The third Assembled parts Substrate C1 C2 C3

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131 column, C3 (most dense) has 8 receptor sites with the center to center spacing of 1.75 mm. The probing pads on the substrate were 1 mm x 1 mm in size to enable easy testing of electrical continuity between them using a multi -meter. Figure 5 39 shows the picture of the substrate with assembled parts in all the three columns, thus demonstrating assembly with more densely packed receptor sites. All three columns were assembled simultaneously. During the assembly, it was observed that the receptor sites in columns C1 and C2 assembled quickly compared to receptor sites in column C3. This is possibly because C3 has more densely packed receptor sites and any misaligned part in C3 impeded the assembly at the adjacent re ceptor site. Once the part was knocked off by the substrate vibrations, the assembly progressed in a regular fashion. The yield noted after the magnetic self assembly was 100 % (only one trial). For permanent mechanical and electrical bonding, the substrate was later subjected to pressure and heat. A flip chip bonder was used to apply the pressure and heat. No alignment was done using the flip chip bonder, since the parts were already assembled onto substrate with correct orientation. For correctly assembl ed parts, the measured average resistance between the 21 chips exhibited functional electrical connectivity, a yield of 90.5%. Two chips were found to be defect ive. The reason for these defects could be the improper dispensing of the solder. For example, if the solder bump is raised compared to the adjacent solder bumps, it would result in misalignment of the assembled chip and thus result in a defective electric al contact. In real world applications, this would not be an issue since in most cases the solder would either be sputter deposited, electrodeposited or some other advanced technology would be used.

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132 5 5 Measurement of Alignment For any viable electronic assem bly or packaging system, the alignment of the final assembled components is a very important factor for successful mechanical and electrical bonding. As the size of the components start diminishing, these alignment tolerances grow tighter. In [24] Roger Howes group used vernier scales patterned on parts and binding sites to measure the alignment of the parts assembled by capillary action. A crude method is presented here to measure the alignment of the ma gnetically assembled components. A substrate patterned with an 8 x 8 array of receptor sites was used for alignment measurement. As mentioned previously, some initial observations showed that better alignment was achieved with more number of magnets. Henc e, the pattern with four triangles, shown in Figure 5 40, with 1 -fold symmetry, was selected for alignment measurement. These parts were commercially diced into 1 mm x 1mm square parts. The center to center spacing between the receptor sites on the substrate is 2.4 mm, which is photolithographically defined. Using the part to -substrate assembly set up in Figure 5 16, the parts were assembled onto the substrate. The filled substrate, shown in Figure 5 41, was then carefully removed from the micropositioner for further measurement of alignment. The edge to edge spacing between the chips was then measured using an optical microscope. Ideally, when the alignment is perfect, this distance would be 2.4 mm. The measured average edge to edge spacing between the chips in the x-direction was 2.4 mm 6.1 m and in the y -direction was 2.4 mm 7.3 m. These results were averaged over 29 trails. The unc ertainty in this spacing also includes the uncertainty due to the variations in the sizes of the individual diced chips. The dimensions of thirteen chips were measured using the optical microscope. The average lateral dimension of the chips was about 1.16 mm 6.5 m.

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133 Due to the variations in the chip sizes, the uncertainty of the spacing between the chips is overestimated. To eliminate the variations due to the chip size, a method should be devised to directly measure the alignment between the magnets. Th is can be possible through xray or infrared imaging or by using a transparent substrate for direct visual inspection. Figure 5 40. Magnetic pattern used for alignment measurement Edge to edge spacing x Y Edge to edge spacing Substrate with arrays of receptor sites Assembled parts Figure 5 4 1 Substrate with 6 x 6 array of receptor sites used for alignment measurement 5 6 Conclusion The dependence of magnetic bonding forces on shape, size and magnetization was analyzed using analytical and FEM met hods. It was found that the magnetic forces are optimized for equally sized square shaped magnets with axial magnetization. Also, maximum bonding force was theoretically achieved with arrays of square magnets with AR (thickness/width) greater than 2 with t he center to center spacing, d of 1.3 times the magnet width, a Magnetic self assembly was demonstrated at a m illimeter scale using Si embedded bonded powder magnets. P art -to -part magnetic self assembly with angular orientation in wet environment using

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134 a tumbler like set up and Si embedded bonded powder magnets was demonstrated with a maximum yield of about 97 % in 20 s. It was seen that the assembly yield reduced with the complexity of the magnetic patterns on the components. Also, part to -substrate magn etic self assembly in dry environment using the shaker set up was demonstrated with unique angular orientation and self -directed bonding. A maximum yield of 99 % in only 20 s was achieved here. Sequential and simultaneous assembly of two different types of components from a heterogeneous mixture of components was also successfully demonstrated. Characterization of the magnetic self assembly process using the self assembly model revealed a significant dependence of the magnet pattern symmetry on the speed of assembly. It was found that patterns with more planes of symmetry are desirable for faster assembly. Finally, magnetic self assembly was also demonstrated with functional electrical interconnects. Preliminary experiments proved the feasibility of using so lder -bumps with magnetic self assembly to achieve functional electrical connections. The se initial results indicate that the magnetic self assembly method offers a highrate, high -yield approach that, with improvements, provides immense promise of utility for a variety of chip -scale assembly applications.

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135 CHAPTER 6 6 CONCLUSION AND FUTUR E WORK In this chapter, a summary of the work performed some important research contributions and conclusions are presented. Some key issues for implementation of magnetic self assembly are also discussed here. Finally, recommendations to advance this work are suggested. 6 1 Conclusion Magnetic self assembly (MSA) is proposed as a completely parallel process for assembly of homogenous and heterogeneous mixture of micro to millimeter scale components. This research work presents the versatility of MSA through various self assembly demonstrations at millimeter scale. MSA is demonstrated for both inter -part assembly and part to -substrate assembly with angular orientation. T he lateral and rotational alignment is achieved simultaneously during the assembly, unlike other approaches where alignment is one of the sequential steps in the self assembly process. MSA is also demonstrated for completely parallel part to -substrate asse mbly from a heterogeneous mixture of components. In most other previously demonstrated approaches of this programmable bonding, the assembly process was sequential where only one component was assembled at a time. Programmable bonding for MSA is demonstrat ed with simultaneous assembly of two different types of component from a heterogeneous mixture. Finally, assembly of components with functional electrical interconnects is also demonstrated. MSA appears to offer numerous advantages when compared to previously investigated self assembly methods. Previous approaches by other groups required either modifying the shape of the components or use of interlocking microstructures to achieve angular orientation and/or bonding selectivity. In either case, the fabrica tion complexity is escalated. MSA does not require any additional fabrication steps to incorporate these features. The magnet pattern is

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136 designed accordingly without changing the shape of the component. Also, most of the previous approaches do not allow for correction of incorrect assemblies. With MSA, the incorrect assemblies are rejected by substrate vibrations. Even if there are few misaligned or incorrect assemblies, it may be possible to achieve 100% yield with MSA by filling the empty receptor sites a t the end of the process using deterministic robotic assembly to correct errors. Some important observations and lessons learned in this research process are described below. The analytical and FEM analysis indicate that the force per unit area is maximiz ed for square hard magnets of equal sizes with axial magnetization. In the case of square-grid arrays, surface bonding force (force / area) is maximized for magnets with AR > 2 and center to center array spacing of about 1.3 times magnet width. Magnetic self assembly is demonstrated using 1 mm x 1mm x 0.5 mm size components with embedded bonded powder magnets. The size of the embedded micromagnets is limited by the grain size of the magnetic powders. In case of magnets with width > 850 m and height < 150 m, a considerable amount of dishing (hollow towards the center) is seen. It is observed that magnets with smaller lateral dimensions pack very well. Smaller sizes can be fabricated using electrodeposited or sputtered magnets. However these magnets are limi ted in size by the aspect ratio. Due to fabrication challenges it is difficult to fabricate high aspect ratio magnets. These aspect ratio limitations also limit the range over which the forces act. Also the magnitude of the force is limited by the volume o f the magnet, so this too sets a minimum size for the magnet. The part to -substrate assembly using the shaker set up revealed that excessive bonding force between the magnets results in stacking (component sticking to back of another component) of the com ponents. It was also found that the magnetic forces required for part -to part self assembly in liquid are lower than that required forces for part -to -substrate assembly in

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137 air. This is due to the more dynamic nature of the part -to -substrate assembly approa ch. In both types of assemblies, the assembly rate increases with the increase magnetic pattern symmetry. This indicates that symmetry, which increases the number of possible bonding orientations, directly increases the probability of an individual bonding event. In both part -to -substrate and part to -part assemblies, the surface area covered by the magnets also plays an important role. When the magnet surface area is small compared to the component surface area (< 10%) the bonding force may be enough for se lf assembly, but the assembled components lack good rotational orientation. When the surface area covered by the magnets is large, misfits occur due to excessive force and magnet area overlaps in various physical positions. Initial observations reveal that by increasing the number of magnets in the bonding pattern, finer angular alignment is achieved. In the case of heterogeneous assembly, the ability to simultaneously assemble multiple component types offers significant scaling advantages when considering complex arrangements of many different component types. For example, this may enable ultra integrated multi-chip modules comprised of microprocessors, MEMS, power supplies, memory, RF communication modules, etc. where each subsystem (chiplet) is fabricated separately and then self assembled to form smart nodes for wireless sensor networks. Some important achievements to date for MSA are listed below; Optimization and quantification of magnetic bonding forces Magnetic self assembly of homogeneous mix ture of parts into an ordered array Lateral and rotational alignment by employing induced vibrations to the substrate Magnetic self assembly of heterogeneous mixture of parts into an ordered array. Inter -part magnetic self assembly Characterization and modeling of the magnetic self assembly process Assembly of components with functional electrical interconnects

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138 6 2 Key Issues Some of the issues that might hinder the magnetic self assembly process or its adaptability for real world a pplications are discussed here. These issues could be related to the integration of magnets with components, fabrication process, experiment setups, magnet patterns and permanent bonding. The issues related to fabrication are first addressed here. In the case of the polyimide packed magnets using SmCo magnetic powder, a layer of proprietary polyimide adhesion promoter is needed to ensure proper adhesion between the Si surface and the polyimide layer. When the adhesion promoter is dispensed on the powder -p acked wafer, it tends to pull the powder out of the trenches due to surface tension. Thus, some of the magnetic powder spins off with the adhesion promoter, resulting in hollow or empty trenches. To overcome this problem, the adhesion promoter can be spun before packing the magnetic powder. Only the polyimide is spun after packing the powder. Due to the higher viscosity of the polyimide, the powder is retained in the trenches, and also the adhesion between the polyimide layer and the Si substrate is not impaired. Lack of accurate bonding force measurement is another key issue in the case of magnetic self assembly. The analytical balance used for the bonding force measurements is very sensitive; even minor air currents cause the reading to fluctuate. Hence, t he measurements should be performed in a closed chamber. However, limited access in the closed chamber may hinder in the alignment process of the magnets. Also, the force is underestimated because of the inability to exactly align the small parts; these mi salignments result in reduction of the measured force. Measurement of forces between magnets having larger surface area is more tolerant to any small misalignments. The balance readout acts as a guide for alignment since the maximum force is achieved when all the individual magnets are perfectly aligned.

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139 In this dissertation, MSA was demonstrated using SmCo, NdFeB and ferrite magnets, but MSA with electrodeposited or sputtered magnets is also promising. Ferrite powders can also be used to fabricate microsca le magnets, as the particle diameter size of this powder is about 1 2 m. The disadvantage with use of such magnets is the reduced total volume of the magnet, since the film thickness is often quite limited (few microns). One of the biggest issues with us ing thin film magnets is that the parts must come very close to one another (on the order of the magnet thickness) before the magnets interact. Using thicker magnets provides opportunities for longer range interactions and is more forgiving. Also, the ex perimental set ups for demonstration of MSA with microscale components will have to be scaled depending on the actual component sizes and the force between the magnets. The force drops off rapidly with the axial displacement. For example, in case of cuboidal magnets with AR = 1 and axial displacement equal to the height of the magnet, the force drops to about 7 % of its bondi ng force (contact force) value. Thus, for microscale magnets with a thickness of about 10 m, the interaction range is reduced compare d to the embedded magnets. This may need some modifications on how the components are mixed or agitated during the assembly process. Arrays of magnets (rather than just a few) are also an interesting possible area for further exploration. Theoretical calc ulations (see Ch5 evaluation and quantification section) show that the expected force for arrays of magnets is much higher than a single large magnet, even though the volume of the magnet is considerably reduced. Another issue with using arrays of magne ts for MSA is multiple low energy states resulting in assembly in many physical positions (including lateral and rotational). Thus, when multiple magnets are used on a single chip, it has to be made sure that the force between any one pair of individual ma gnets and the overlapped

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140 magnets in various physical positions is very small either compared to the minimum force required for self assembly or the mixing forces. In other words, the bonding force has to be greatest only in one physical orientation, in whi ch the magnetic patterns perfectly align. Substrate vibrations during assembly can be used to help knock off any parts that are misaligned or incorrectly assembled, but the selectivity of this approach is not perfect. Another issue with the current part t o -substrate assembly setup is the handling of the substrate. Currently, the substrate is attached to the micropositioner using a two sided adhesive tape. It is difficult to separate the substrate from the micropositioner without disturbing the assembled pa rts. Also very careful handling of the substrate after assembly is necessary when it has to be moved for further processing, such as permanent mechanical and electrical bonding. To overcome this problem, the micropositioner setup can be equipped with a vac uum chuck to hold the substrate in place during assembly and later easily released after the assembly. Permanent bonding is achieved using solder dots/pads that are fabricated on the surface of the components along with the magnets. These raised pads above the component surface may hinder the magnetic self assembly process. To ensure that the parts assemble even with the gap (due to the solder bond pads) between them, higher bonding forces may be required. The height of solder pads can be minimized by using electrodeposition or sputtering methods for fabrication of solder pads onto the substrate. One of the key issues facing implementation of magnetic self assembly is the effect of magnetic fields on the operation of the final assembled device. The strength of this residual magnetic field drops drastically just over a distance of few microns from the surface of the magnet. Thus, in most cases, it is expected that the magnetic field will not affect the normal operation of the device. In sensitive devices, the magnetic fields can be eliminated by

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141 demagnetization of the micromagnets. This can be achieved by heating the magnets beyond their Curie temperature or applying a monotonically decreasing ac magnetic field. Some of the results from MSA demonstrations sug gest the use of high surface area magnets for higher assembly yield and rate. This would mean less usable surface area for electrical functions and interconnects. To overcome this issue, magnets can be fabricated on the back side of the components, thus le aving plenty of component surface area for electrical interconnects. In this case now the parts assemble back to back (considering the magnet side as the front side) to the substrate. Figure 6 1 Patterned magnets on back side and electrical interconnects on the front side of the components Some preliminary experiments with large surface area NdFeB magnets were done to test this concept. The parts did assemble onto the substrate; however there was no angular alignment. The reason for this is the axial gap between the magnets on the components At this displacement the magnetic forces and torques are not enough to result in self alignment of the components. This may be solved by patterning multiple magnets on the component surfaces, perhaps a large magnet to drive rough assembly and then some s maller magnets to aid in alignment. Magnets on back side of the components Electrical interconnects on front side of the components

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142 Magnetic self assembly presents a promising and viable avenue for advancement of self assembly processes for chip -scale assembly for an exciting array of applications. 6 3 Recommended Future Work MSA was demonstrated at mil limeter scale. The next step to further this work would be to demonstrate MSA with microscale parts using electrodeposited or sputtered magnets. This would also necessitate appropriate design and scaling of the experimental setups. This work provided some characterization results on dependency of assembly rate and yield on the various process parameters. A detailed design of experiments (DOE) for studying the effect of these parameters is recommended. A first order assembly model was used here to model the self assembly process. This model did not account for the possibilities of any disassemblies or incorrect assemblies. Also, substrate vibration is a key to the successful implementation of MSA. Approach towards a comprehensive model that accounts for all these quantities is recommended to effectively model the self assembly process. Alignment measurements of the chips are currently done using edge to edge measurements of the spacing between the chips. This measurement includes the variations in the size of the individual chips. To eliminate the chip size variations, alignment of the magnets has to be measured. This can be done using X ray microscopy or infrared imaging. Currently the substrate is vibrated only in the vertical direction to knockoff the incorrectly assembled components and self align the assembled parts. An interesting aspect would be to study the effects of lateral vibrations on the alignment and assembly of incorrect components. It might provide an additional level of control for the self a ssembly process. The vibration levels could also possibly be integrated with a video analysis system to provide real -time feedback and control to maximize the assembly rate and alignment.

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143 The demonstration of MSA with electrical interconnects was done with dummy components, but it had the elements to demonstrate the concept fruitfully. Demonstration using actual components such as LEDs or functional integrated circuits would be a vital step towards displaying the adaptability of MSA in the industrial settin g. The assemblies demonstrated in this work were also two dimensional (2D). Most of the research in self assembly is focused on 2D; limited investigation has been done on self assembly of three dimensional (3D) structures. Demonstration of MSA for complex 3D structures would prove to be a very important step towards furthering this research work. Magnetic self assembly offers immense promise as a robust, cost -effective assembly processes for micro meso scale applications. The process lends itself to cus tomizable assembly configurations (front and back side assembly, part -to -part, part to -substrate), and high assembly yields and rates are achievable through prudent selection of magnetic patterns. With the potential demonstrated in this dissertation, it is hoped that MSA will emerge at the forefront of the self assembly processes and eventually gain acceptance in industrial applications.

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144 APPENDIX A MATLAB FUNCTIONS The following code is used to extract the T parameter by fitting a curve to the raw assembly data using the self assembly model described in Ch 3. clc; clear; %% load xls file [NUMERIC,TXT]=xlsread('C: \ Documents and Settings\ Valued Customer\ My Documents\ Characterization_exps \ DOE_ANOVA\ 5_pts\ charac_exps \ sq_5pt.xls '); time = NUMERIC(1:5); %% separating time and yield data yield = NUMERIC(6:10); % Set up figure to receive datasets and fits f_ = clf; figure(f_); legh_ = []; legt_ = {}; % handles and text for legend xlim_ = [Inf Inf]; % limits of x axis ax_ = subplot(1,1,1); set(ax_,'Box','on'); axes(ax_); hold on; % --Plot data originally in dataset "avg_assembly vs. time" time = time(:); yield = yield(:); h_ = line(time,yield,'Parent',ax_,'Color',[0.333333 0 0.666667],... 'LineStyle','none', 'LineWidth',1,... 'Marker','.', 'MarkerSize',12); xlim_(1) = min(xlim_(1),min(time)); xlim_(2) = max(xlim_(2),max(time)); legh_(end+1) = h_; legt_{end+1} = 'data'; % Nudge axis limits beyond data limits if all(isfinite(xlim_)) xlim_ = xlim_ + [1 1] 0.01 diff(xlim_); set(ax_,'XLim',xlim_) end % --Create fit "fit 4" fo_ = fitoptions('method','NonlinearLeastSquares','Lower',10,'Upper',100000) ; st_ = [0.2040317921465 ]; set(fo_,'Startpoint',st_); ft_ = fittype('100*(ex p(320*x/a)1)/(exp(320*x/a) 0.1667)' ,... 'dependent',{'y'},'independent',{'x'},... 'coefficients',{'a'});

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145 % Fit this model using new data cf_ = fit(time,yield,ft_ ,fo_); % Plot this fit h_ = plot(cf_,'fit',0.95); legend off; % turn off legend from plot method call set(h_(1),'Color',[1 0 0],... 'LineStyle','', 'LineWidth',2,... 'Marker','none', 'MarkerSize',6); legh_(end+1) = h_(1); legt_{end+1} = 'fit'; hold off; legend(ax_,legh_, legt_); T = coeffvalues(cf_); confidence_interval = confint(cf_); Later Monte Carlo simulation is used to numerically repeat the experiment multitude of times and the uncertainty for the T parameter is estimated. clc; clear; %% load xls file [NUMERIC,TXT]=xlsread('oval_5pts_15runs.xls'); time = NUMERIC(1:5); %% separating time and yield data avg_yield = NUMERIC(81:85); % avg yield stdev = NUMERIC(86:90); Ux = NUMERIC(91:95); n = 5000; for j=1:5 yield_1(:,j) = (randn(n,1)/1.96* Ux(j)) + avg_yield(j); end for i = 1:n time = time(:); yield_2 = yield_1(i,1:5); yield = yield_2'; % --Create fit "fit 4" fo_ = fitoptions('method','NonlinearLeastSquares','Lower',10,'Upper',100000) ; st_ = [0.2040317921465 ]; set(fo_,'Startpoint',st_); ft_ = fittype('64*(exp(320*x/a)1)/(exp(320*x/a) 0.1667)' ,... 'dependent',{'y'},'independent',{'x'},... 'coefficients',{'a'});

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146 % Fit this model using new data cf_ = fit(time,yield,ft_ ,fo_); hold off; legend(ax_,legh_, legt_); T(i) = coeffvalues(cf_); end % --Create a histogram of the results (50 bins) hist(T,50); T_min = T/60; T_avg = mean(T_min) s = std(T_min); max_T = max(T_min); min_T = min(T_min); st= (max_T min_T)/1000; PDF = normpdf(min_T:st:max_T, T_avg, s); plot (min_T:st:max_T, PDF); k = kurtosis(T_min) skew = skewness(T_min) bounds = 2*s The uncertainties in T values extracted from the Monte Carlo simulations are cross checked with T values extracted from the assembly versus time data for each experimental tra il. %% load xls file [NUMERIC,TXT]=xlsread('C: \ Documents and Settings\ Valued Customer\ My Documents\ Characterization_exps \ DOE_ANOVA\ matlab_files_15runs_5pts\ 4_c ross_sq_5pts_15runs.xls'); time = NUMERIC(1:5); %% separating time and yield data a= 6; b=10; for i=1:1:15; run(i,1:5) = NUMERIC(a:b); a = a+5; b = b+5; %end yield = run(i,:); % Set up figure to receive datasets and fits f_ = clf; figure(f_); legh_ = []; legt_ = {}; % handles and text for legend xlim_ = [Inf Inf]; % limits of x axis

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147 ax_ = subplot(1,1,1); set(ax_,'Box','on'); axes(ax_); hold on; % --Plot data originally in dataset "avg_assembly vs. time" time = time(:); yield = yield(:); h_ = line(time,yield,'Parent',ax_,'Color',[0.333333 0 0.666667],... 'LineStyle','none ', 'LineWidth',1,... 'Marker','.', 'MarkerSize',12); xlim_(1) = min(xlim_(1),min(time)); xlim_(2) = max(xlim_(2),max(time)); legh_(end+1) = h_; legt_{end+1} = 'data'; % Nudge axis limits beyond data limits if all(isfinite(xlim_)) xlim_ = xlim_ + [1 1] 0.01 diff(xlim_); set(ax_,'XLim',xlim_) end % --Create fit "fit 4" fo_ = fitoptions('method','NonlinearLeastSquares','Lower',10,'Upper',100000) ; st_ = [0.2040317921465 ]; set(fo_,'Startpoint',st_); ft_ = fittype('64*(exp (320*x/a) 1)/(exp(320*x/a)0.1667)' ,... 'dependent',{'y'},'independent',{'x'},... 'coefficients',{'a'}); % Fit this model using new data cf_ = fit(time,yield,ft_ ,fo_); % Plot this fit h_ = plot(cf_,'fit',0.95); legend off; % turn off legend from plot method call set(h_(1),'Color',[1 0 0],... 'LineStyle','', 'LineWidth',2,... 'Marker','none', 'MarkerSize',6); legh_(end+1) = h_(1); legt_{end+1} = 'fit'; hold off; legend(ax_,legh_, legt_); T(i) = coeffvalues(cf_); confidence_interval(i,:) = confint(cf_); end T_avg = mean(T) s = std(T); t= 2.145;

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148 N = 15; Ux = t*s/sqrt(N); error = Ux/T_avg*100 count = 0; for i=1:15 if T>3.3712e3 | T<2.993e3 % for 4_cross_sq, the bounds on T are form Monte Carlo simulations count = count + 1; end end count

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159 BIOGRAPHICAL SKETCH Sheetal Shetye grew up in Panvel, a small town on the outskirts of Mumbai, India, with her parents Bhalchandra and Madhuri Shetye and brother Harshal. After high school, she attended Veer Mata Jijabai Technological Institute (V.J.T.I.), Mumbai, where she received her licentiate in electrical engineering i n 1998. Later she attended K.E.S.N.N.P. College of Engineering, University of Mumbai, and graduated with a bachelors degree in electronics engineering in August 2001. In spring 2003, she began her graduate studies at University of Florida and earned her M aster of Science degree in electrical and computer engineering in December 2004. Sheetal completed her doctoral degree in electrical and computer engineering at University of Florida in August 2009. Her research interests include microelectromechanical sys tems (MEMS), Magnetics, micro electronics assembly and packaging.