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Development of a Novel Micro-Electrochemical Solid State Sensor Array (MES3A) Suitable for Flow Visualization of Liquid ...

Permanent Link: http://ufdc.ufl.edu/UFE0024185/00001

Material Information

Title: Development of a Novel Micro-Electrochemical Solid State Sensor Array (MES3A) Suitable for Flow Visualization of Liquid Metal Melts
Physical Description: 1 online resource (312 p.)
Language: english
Creator: June, Michael
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: array, coefficient, diffusion, film, microsensor, oxygen, thin, ysz
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A micro-scale solid-state electrochemical sensor array based on yttria-stabilized zirconia (YSZ) was designed, fabricated, and tested. The motivation for developing this sensor array was for flow visualization of low Prandtl number fluids at small scale such as solder bumps. The sensor array consisted of 40 sensors and each cell is schematically represented as: Au|Cr|Cu|Cu/Cu2O||YSZ||OM where OM is oxygen dissolved in liquid metal. The array of 200x200 nm^2 sensors was fabricated on Si(100) wafers using lithography and deposition of sputtered YSZ, Ta/Ta3N5 Cu barriers, PETEOS-based SiO2 dielectric isolation, Cu interconnects, and Au/Cr contacts. An in-plane conductivity analysis of sputtered-YSZ revealed 25 nm grains of YSZ having very good texture and oriented in the (111) direction that showed high ionic conductivity. XRD patterns of arrays after annealing at 850 degreeC showed only formation of TaSix at the SiO2/Ta3N5 interface, which served to increase the barrier quality. Further testing of the array with liquid Sn confined in a cylinder showed only a fraction of the devices operated and had a short life-time. A failure analysis revealed difficulties with cracking of the thin film YSZ. Simulations were performed to guide the sensor array design and validation. The Chebyshev spectral method was used to solve the equations describing tracer oxygen 2-D transport at high-temperature in tin melts confined in a right cylindrical geometry. Simulation of oxygen variations produced during titration resulted in significant buoyancy driven flow. Further numerical analysis illustrated a method by which flow can be electrochemically detected and the minimum fluid velocities that can be experimentally measured. The implementation of a periodic boundary condition was simulated to minimize fluid flow to allow mass transfer data to be quickly extracted from the system response. The use of a periodic boundary condition was also used in specific conditions to induce fluid flow having a specific periodicity.
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 Michael June.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Anderson, Timothy J.
Local: Co-adviser: Narayanan, Ranganathan.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024185:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024185/00001

Material Information

Title: Development of a Novel Micro-Electrochemical Solid State Sensor Array (MES3A) Suitable for Flow Visualization of Liquid Metal Melts
Physical Description: 1 online resource (312 p.)
Language: english
Creator: June, Michael
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: array, coefficient, diffusion, film, microsensor, oxygen, thin, ysz
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A micro-scale solid-state electrochemical sensor array based on yttria-stabilized zirconia (YSZ) was designed, fabricated, and tested. The motivation for developing this sensor array was for flow visualization of low Prandtl number fluids at small scale such as solder bumps. The sensor array consisted of 40 sensors and each cell is schematically represented as: Au|Cr|Cu|Cu/Cu2O||YSZ||OM where OM is oxygen dissolved in liquid metal. The array of 200x200 nm^2 sensors was fabricated on Si(100) wafers using lithography and deposition of sputtered YSZ, Ta/Ta3N5 Cu barriers, PETEOS-based SiO2 dielectric isolation, Cu interconnects, and Au/Cr contacts. An in-plane conductivity analysis of sputtered-YSZ revealed 25 nm grains of YSZ having very good texture and oriented in the (111) direction that showed high ionic conductivity. XRD patterns of arrays after annealing at 850 degreeC showed only formation of TaSix at the SiO2/Ta3N5 interface, which served to increase the barrier quality. Further testing of the array with liquid Sn confined in a cylinder showed only a fraction of the devices operated and had a short life-time. A failure analysis revealed difficulties with cracking of the thin film YSZ. Simulations were performed to guide the sensor array design and validation. The Chebyshev spectral method was used to solve the equations describing tracer oxygen 2-D transport at high-temperature in tin melts confined in a right cylindrical geometry. Simulation of oxygen variations produced during titration resulted in significant buoyancy driven flow. Further numerical analysis illustrated a method by which flow can be electrochemically detected and the minimum fluid velocities that can be experimentally measured. The implementation of a periodic boundary condition was simulated to minimize fluid flow to allow mass transfer data to be quickly extracted from the system response. The use of a periodic boundary condition was also used in specific conditions to induce fluid flow having a specific periodicity.
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 Michael June.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Anderson, Timothy J.
Local: Co-adviser: Narayanan, Ranganathan.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024185:00001


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1 DEVELOPMENT OF A NOVEL MICRO -ELECTROCHEMICAL SOLID STATE SENSOR ARRAY (MES3A) SUITABLE FOR FLOW VISUALIZATION OF LIQUID METAL MELTS By MICHAEL P. JUNE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF F LORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Michael P. June

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3 To my wonderful family, who so patiently waited.

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4 ACKNOWLEDGM ENTS I would like to express my thanks and gratitude to the many people that guided, assisted, and influenced me over the course of my studies. Special thanks go to Dr s Tim Anderson and Ranga Narayanan for their advice, encouragement, and technical expert ise. I would also like to thank Dr. Jae Jeong Kim of Seoul National University and his lab group, specifically Dr. Mincheol Kang, for their expertise and wonderful hospitality. I would also like to thank the many others at the University of Florida who w ere a great help to me. Thanks t o Dr. Tim Andersons lab group ( specifically Dr. Matt Monroe, Oh Hyun Kim, Dojun Kim, and Jooyoung Lee ) for their techn ical support and friendship. S pecial appreciation is also given to Weidong Guo for his assistance with th e numerical code I would like to thank Dr. Valentin Craciun, Ionana Craciun, Andrew Gerger, and the MAIC staff for their material characterization assistance. My gratitude is also extended to Dennis Vince and Jim Hinnant for always being ready and able to assist. Finally, I thank my wonderful family for their unending patience and support. I thank m y p arents, Carl and Jennifer, for their guidance and encouragement; and my sister, Rachel, and brother, Jason, for their innate ability to proliferate ambienc e through humor. Most importantly, I thank my wonderful wife, Kristin, for her steadfast understanding and unending support. I also express my appreciation for the research grants from NSF (OISE 0610744) and NASA (NNG05GL58H) that monetarily supported this work.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 9 LIST OF FIGURES ............................................................................................................................ 10 NOMENCLATURE ........................................................................................................................... 19 Standard Conventions ................................................................................................................. 19 Roman Symbols .......................................................................................................................... 19 Greek Symbols ............................................................................................................................ 20 Standard Abbreviations ............................................................................................................... 21 ABSTRACT ........................................................................................................................................ 23 CHAPTER 1 INTRODUCTION AND REVIEW OF LITERATURE .......................................................... 25 Motivation and Overview ........................................................................................................... 25 Bulk Crys tal Growth ................................................................................................................... 27 Bridgman Growth ................................................................................................................ 28 Float Zone Growth ............................................................................................................... 29 Czochralsk i Growth ............................................................................................................. 30 Convective Effects in Crystal Growth Methods ........................................................................ 30 Mass Transfer Effects .......................................................................................................... 32 Gravitational Effects ............................................................................................................ 34 Convective Effects in Solder Bumps ......................................................................................... 34 Presence of Voids ................................................................................................................ 35 Need for In Situ Detection Method..................................................................................... 37 Flow Visualization Techniques .................................................................................................. 38 Electrochemically Based Oxygen Sensors ................................................................................ 40 Functionality ........................................................................................................................ 42 Connection to MEMS .......................................................................................................... 42 Integrated Circuit Fabrication Techniques ................................................................................ 44 Photolithography and Patterning ........................................................................................ 45 Material Deposition ............................................................................................................. 48 Material Removal ................................................................................................................ 51 Experimental Approach .............................................................................................................. 53

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6 2 FUNDAMENTALS OF SOLID STATE ELECTROCHEMI STRY AND TRANSPORT PHENOMENA ............................................................................................................................ 64 Introduction ................................................................................................................................. 64 Principles of MES3A Operation ................................................................................................. 64 Solid State Electrochemistry Basics .......................................................................................... 65 Thermodynamic Principles ................................................................................................. 69 Yttria Stabilized Zirconia .................................................................................................... 77 Electrolytic Reaction Mechanisms ..................................................................................... 83 Solid -State Electrochemical Measurements .............................................................................. 85 Potentiometric Measurements ............................................................................................. 85 Coulometric Measurements ................................................................................................ 87 Periodic Boundary Conditions ............................................................................................ 88 Flow Visualization Measurements ..................................................................................... 90 Impedance Measurements ................................................................................................... 91 Sources of Measurement Errors .......................................................................................... 95 Transport Phenomena Basics ..................................................................................................... 97 Overview of Convection ..................................................................................................... 98 Governing Equ ations ......................................................................................................... 101 Exploration of Dimensionless Parameters ....................................................................... 103 Summary .................................................................................................................................... 109 3 USING THE SPECTRAL CHEBYSHEV METHOD TO PREDICT MASS TRANSFER EFFECTS ............................................................................................................ 122 Introduction ............................................................................................................................... 122 Basis for Spectral Chebyshev ................................................................................................... 122 Discretizing the Equations of Change ...................................................................................... 124 Mass Balance ..................................................................................................................... 129 Specie s Balance ................................................................................................................. 129 Momentum Balance ........................................................................................................... 131 Combining the Equations of Change ................................................................................ 132 Boundary Conditions ......................................................................................................... 134 Operation of the Spectral Code ................................................................................................ 134 Sizing the Mesh ................................................................................................................. 135 Stepping in Time ................................................................................................................ 135 Benchmarking the Spectral Code ............................................................................................. 136 Numerical Analysis of Mass Transfer ..................................................................................... 138 Case 1: Bottom Depletion Configuration ......................................................................... 139 Case 2: Top Depletion Configuration............................................................................... 141 Case 3: Periodic Concentration Boundary Condition Configuration ............................. 148 Summary ............................................................................................................................ 157 Visualization of Fluid Flow ...................................................................................................... 157 Experimental Setup and Justification of the Numerical Code ........................................ 158 Numerical Analysis ........................................................................................................... 159 Summary ............................................................................................................................ 160 Conclusions ............................................................................................................................... 160

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7 4 DESIGN, FABRICATION, AND CHARACTERIZATION OF THE MES3A DEVICE ... 184 Introduction ............................................................................................................................... 184 Design of the Device ................................................................................................................. 184 Material Selection .............................................................................................................. 185 Structural Integrity ............................................................................................................. 186 Fabrication of the Device.......................................................................................................... 188 Lithography and Mask De signs ........................................................................................ 188 Thermal Oxidation and Oxide Etch .................................................................................. 190 PVD and CMP of Copper .................................................................................................. 191 CVD of PETEOS ............................................................................................................... 192 TEOS Etch and PVD of Gold ........................................................................................... 192 TEOS Etch and PVD of YSZ ............................................................................................ 193 Planarization and Cutting .................................................................................................. 193 Characterization of the Device ................................................................................................. 194 Cross -Sectional View of MES3A ...................................................................................... 194 Overall XRD of MES3A .................................................................................................... 195 Surface Analysis of the MES3A Device ........................................................................... 196 XRD Analysis of YSZ ....................................................................................................... 197 XPS Analysis of YSZ ........................................................................................................ 198 Surface Analysis of YSZ ................................................................................................... 1 99 XRD Analysis of Gold Contact Pad ................................................................................. 200 Summary ............................................................................................................................ 201 Conclusions ............................................................................................................................... 201 5 VALIDATION AND ENHANCEMENT OF THE MES3A DEVICE .................................. 215 Introduction ............................................................................................................................... 215 Validation Experiments ............................................................................................................ 215 Measuring Open Cell Potential ......................................................................................... 215 Mass Transfer Measurements ........................................................................................... 217 Summary ............................................................................................................................ 219 Examination of Device Breakdown ......................................................................................... 219 Physical Experimental Results .......................................................................................... 219 Devi ce Characterization .................................................................................................... 220 Summary ............................................................................................................................ 221 Investigation of the YSZ Sensor Fabrication Process ............................................................. 221 Sample Preparation ............................................................................................................ 222 XPS Analysis of Underlying Copper ............................................................................... 223 XRD Analysis of YSZ ....................................................................................................... 223 Impedance Spectroscopy of YSZ ..................................................................................... 224 Summary ............................................................................................................................ 225 Suggested Modifications to the ME S3A Fabrication Process ................................................ 226 Sputtering YSZ .................................................................................................................. 226 Copper Interconnects ......................................................................................................... 227 Substrate Material .............................................................................................................. 227 Conclusions ............................................................................................................................... 227

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8 APPENDIX A EXTRANEOUS NUMERICAL OUTPUT ............................................................................. 237 B NUMERICAL ANALYSIS SOURCE CODE ........................................................................ 284 C VOLUME EXPANSION OF THE UNDERLYING COPPER INTERCONNECT ............ 298 LIST OF REFERENCES ................................................................................................................. 303 BIOGRAPHICAL SKETCH ........................................................................................................... 312

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9 LIST OF TABLES Table page 3 1 Non -dimensional values for the crystal growth geometry ................................................. 125 3 2 Excluded radial distance, r for a specific set of grid points ........................................... 127 3 3 Terms for the discretized equations of change ................................................................... 128 3 4 Physical parameters of liquid tin at 750oC ......................................................................... 139 3 5 Experime ntal parameters for bottom depletion experiment .............................................. 141 3 6 Geometric parameters and results for top depletion numerical analysis .......................... 146 3 7 Geometric parameters and results for a periodic boundary condition .............................. 150 4 1 Melting temperature and CTE of device materials ............................................................ 187 4 2 Radial distances of YSZ sensors for three experimental dimensions ............................... 189 5 1 Prepared YSZ samples for impedance and XRD analysis ................................................. 223 5 2 Summary of XRD and impedance study of YSZ samples ................................................ 226 C1 Physical parameters of copper and copper Oxide ............................................................. 298

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10 LIST OF FIGURES Figure page 1 1 Vertical Bridgman crystal growth ......................................................................................... 54 1 2 Float zone crystal growth ....................................................................................................... 55 1 3 Czochralski crystal growth method ....................................................................................... 56 1 5 Characteristic axial composition of binary solutions grown under diffusion controlled and well mixed conditions (for a distribution coefficient of 0.7 and an initial melt composition of Co) ................................................................................................................. 58 1 6 Final bubble configuration for top to bottom melting and bottom to top melting of a solder bump ............................................................................................................................ 59 1 7 Rudimentary oxygen sensor .................................................................................................. 60 1 8 Common positive photoresist usage ..................................................................................... 61 1 9 Common negati ve photoresist usage ..................................................................................... 62 2 1 Galv anic and electrolytic cell .............................................................................................. 110 2 2 Component view of the electrochemical potential at steady-sta te equilibrium ................ 110 2 3 Ellingham diagram of potential oxidation r eactions .......................................................... 111 2 4 Oxygen saturation concentration and electrical potential .................................................. 112 2 5 Phase diagram of ZrO2-Y2O3............................................................................................... 113 2 6 Various zirconia -base d crystal structures ........................................................................... 114 2 7 Elect rolytic domain of 9 mol% YSZ ................................................................................... 115 2 8 Electrolytic domain of 9 mol% YSZ with material oxides ............................................... 116 2 9 Possible electrolyti c reaction mechanisms ......................................................................... 117 2 10 Time dependent current response to an applied pote ntial ................................................. 118 2 11 Typical flow visualization measurement ............................................................................ 119 2 13 Natura l and Marangoni convection ..................................................................................... 121 2 14 Lateral and horizontal stacking o f convective streamlines ................................................ 121

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11 3 1 Converting the physical domain into a computational domain for a right cylinder of physical domain (0, H) and (0, R) ....................................................................................... 161 3 2 Flow chart of the Chebyshev spectral method used in this work ...................................... 162 3 3 Benchmark geometry with analytical solution ................................................................... 163 3 4 Surface plot of the radial velocity component .................................................................... 164 3 5 Surface plot of the axial velocity component ..................................................................... 165 3 6 Surface plot of the pressure ................................................................................................. 165 3 7 Surface plot of the concentration ........................................................................................ 166 3 8 System configuration for numerical Cases 1, 2, and 3 ...................................................... 167 3 9 Time evolution of the concentration profile for Case 1 ..................................................... 168 3 10 Time evolution of the axial velocity profile for Case 1 ..................................................... 169 3 11 Time evolution of the pressure profile for Case 1 .............................................................. 169 3 12 Analytical, numerical, and experimen tal bottom deple tion results .................................. 170 3 13 Time evolution of the concentration profile for Case 2 .................................................... 171 3 14 Time evolution of the axial velocity pro file for Case 2 .................................................... 172 3 15 Time evolution of the pressure profile for Case 2 ............................................................. 172 3 16 Comparison between top and bottom depletion numerical results .................................. 173 3 17 Axial velocity and concentration profile at onset of fluid flow ....................................... 173 3 18 Velocity and concentrati on profile at maximum fluid velocity ....................................... 174 3 19 Onset time of fluid flow vs. the RaS ( =R/H) ................................................................... 174 3 20 Maximum fluid velocity vs. the RaS .................................................................................. 175 3 21 Qualitative analysis of flow regimes for periodic concentration ..................................... 176 3 22 Maximum fluid velocity vs. frequency .............................................................................. 177 3 23 Onset time vs. frequency .................................................................................................... 178 3 24 Time dependent current density vs. time (variable Do) .................................................... 179 3 25 Time dependent current density vs. time (variable frequencies) ..................................... 180

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12 3 26 Pseudo steady state current density vs. time (variable Do) ............................................... 1 81 3 27 Pseudo-steady state current density vs. time (variable C) .............................................. 182 3 28 System configuration for flow visualization ..................................................................... 183 4 1 Cross -sectional schematic of the MES3A design .............................................................. 202 4 2 Cracks in the TEOS layer with a curvilinear shape and in the shape of spider -cracks and ridges .............................................................................................................................. 202 4 3 Cu via has completely br oke through the TEOS layer and is beco ming exposed with noticeable stress marks on the TEOS surface ..................................................................... 203 4 4 Oxidized c opper delaminating the YSZ at 6000x and 2700x ........................................... 203 4 5 Chip layout for the YSZ 1 mm sensor array design and 3 mm sensor array design ....... 204 4 6 Copper and gold component design for the 3mm MES3A design ................................... 204 4 7 Copper shadow mask .......................................................................................................... 205 4 8 SE M image of BOE etch revealing 3:1 etch ratio and the feature size spacing .............. 205 4 9 SEM image of copper overdeposited on a thermally oxidized wafer and a magnified image to discern the thickness ............................................................................................. 206 4 10 Surface of copper and thermal oxide after CMP ............................................................. 206 4 11 Gold contact pad viewed through an optical microscope and SEM .............................. 206 4 12 Top view of fabricated wafer by an optical micr oscope and SEM ................................ 207 4 13 Cross -sectional view of sputtered YSZ showing uniformity and columnar structures ............................................................................................................................... 207 4 14 Cross -sec tional TEM image of the MES3A device ........................................................... 208 4 15 XRD scan of the MES3A device ........................................................................................ 209 4 16 Surface scan of devices surface over 500 m x 500 m and surface scan of copper interconnect over 200 m x 200 m ................................................................................... 209 4 17 XRD analysis of YSZ on thermal oxide ............................................................................ 210 4 1 8 XPS analysis of YSZ on thermal oxide ............................................................................. 211 4 19 SEM image of YSZ sensor pad .......................................................................................... 212

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13 4 20 AFM image of the YSZ sensor pad ................................................................................... 212 4 21 Surface scan of YSZ sensor over 5 m x 5 m and 1 m x 1 m ................................. 213 4 22 AFM image of porous YSZ pad ......................................................................................... 213 4 23 XRD of gold contact pad .................................................................................................... 214 5 1 Schematic of experimental vessel ...................................................................................... 229 5 2 Process flow diagram of experimental setup ..................................................................... 230 5 3 Experimental setup for mass transfer measurements ........................................................ 230 5 4 Open circuit potential vs. temperature ............................................................................... 231 5 5 Open cell p otential vs. time ................................................................................................ 232 5 6 XPS analysis of copper/copper oxide substrate mixture .................................................. 233 5 7 XRD analysis of YSZ sputtered samples at 200 W .......................................................... 234 5 8 XRD analysis of YSZ sputtered samples at 300 W .......................................................... 235 5 9 Log of conductivity vs. temperature .................................................................................. 236 A 1 Experiment #3 1A Radial and axial velocity .................................................................. 238 A 2 Experiment #3 1A Contour plot of the concentration ...................................................... 238 A 3 Experiment #3 2A Radial and axial velocity .................................................................. 239 A 4 Experiment #3 2A Contour plot of the concentration ...................................................... 239 A 5 Experiment #3 3A Radial and axial velocity .................................................................. 240 A 6 Experiment #3 3A Contour plot of the concentration ...................................................... 240 A 7 Experiment #3 4A Radial and axial velocity .................................................................. 241 A 8 Experiment #3 4A Contour plot of the concentration ...................................................... 241 A 9 E xperiment #3 4B Radial and axial velocity .................................................................. 242 A 10 Experiment #3 4B Contour plot of the concentration....................................................... 242 A 11 Experiment #3 4C Radial and axial velocity .................................................................. 243 A 12 Experiment #3 4C Contour plot of the concentration....................................................... 243

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14 A 13 Experiment #3 4D Radial and axial velocity .................................................................. 244 A 14 Experiment #3 4D Contour plot of the concentration ...................................................... 244 A 15 Experiment #3 4E Radial and axial v elocity ................................................................... 245 A 16 Experiment #3 4E Contour plot of the concentration ....................................................... 245 A 17 Experiment #3 5A Radial and axial velocity .................................................................. 246 A 18 Experiment #3 5A Contour plot of the concentration ...................................................... 246 A 19 Experiment #3 5B Radial and axial velocity .................................................................. 247 A 20 Experiment #3 5B Contour plot of the concentration....................................................... 247 A 21 Experiment #3 5C Radial and axial velocity .................................................................. 248 A 22 Experiment #3 5C Contour plot of the concentration....................................................... 248 A 23 Experiment #3 5D Radial and axial velocity .................................................................. 249 A 24 Experiment #3 5D Contour plot of the concentration ...................................................... 249 A 25 Experiment #3 5E Radial and axial velocity ................................................................... 250 A 26 Experiment #3 5E Contour plot of the concentration ....................................................... 250 A 27 Experiment #3 6A Radial and axial velocity .................................................................. 251 A 28 Experiment #3 6A Contour plot of the concentration ...................................................... 251 A 29 Experiment #3 6B Radial and axial velocity .................................................................. 252 A 30 Ex periment #3 6B Contour plot of the concentration....................................................... 252 A 31 Experiment #3 6C Radial and axial velocity .................................................................. 253 A 32 Experiment #3 6C Contour plot of the concentration....................................................... 253 A 33 Experiment #3 6D Radial and axial velocity .................................................................. 254 A 34 Experiment #3 6D Contour plot of the concentration ...................................................... 254 A 35 Experiment #3 6E Radial and axial velocity ................................................................... 255 A 36 Experiment #3 6E Contour plot of the c oncentration ....................................................... 255 A 37 Experiment #3 7A Radial and axial velocity .................................................................. 256

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15 A 38 Experiment #3 7A Concentration profile .......................................................................... 256 A 39 Experiment #3 7A Amperometric response ...................................................................... 256 A 40 Experiment #3 7B Radial and axial velocity .................................................................. 257 A 41 Experiment #3 7B Concentration profile .......................................................................... 257 A 42 Experiment #3 7B Amperometric response ...................................................................... 257 A 43 Experiment #3 7C Radial and axial velocity .................................................................. 258 A 44 Experiment #3 7C Concentration profile .......................................................................... 258 A 45 Experiment #3 7 C Amperometric response ...................................................................... 258 A 46 Experiment #3 7D Radial and axial velocity .................................................................. 259 A 47 Experiment #3 7D Concentration profile .......................................................................... 259 A 48 Experiment #3 7D Amperometric response ...................................................................... 259 A 49 Experiment #3 7E Radial and axial velocity ................................................................... 260 A 50 Experiment #3 7E Concentration profile ........................................................................... 260 A 51 Experiment #3 7E Amperometric response ...................................................................... 260 A 52 Experiment #3 7F Radial and axial velocity ................................................................... 261 A 53 Experiment #3 7F Concentration profile ........................................................................... 261 A 54 Expe riment #3 7F Amperometric response ....................................................................... 261 A 55 Experiment #3 7G Radial and axial velocity .................................................................. 262 A 56 Experiment #3 7G Concentrati on profile .......................................................................... 262 A 57 Experiment #3 7G Amperometric response ...................................................................... 262 A 58 Experiment #3 7H Radial and axial velocity .................................................................. 263 A 59 Experiment #3 7H Concentration profile .......................................................................... 263 A 60 Experiment #3 7H Amperometric response ...................................................................... 263 A 61 Experiment #3 7I Radial and axial velocity .................................................................... 264 A 62 Experiment #3 7I Concentration profile ............................................................................ 264

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16 A 63 Experiment #3 7I Amperometric response ........................................................................ 264 A 64 Experiment #3 7J Radial and axial velocity .................................................................... 265 A 65 Experiment #3 7J Concentration profile ........................................................................... 265 A 66 Experiment #3 7J Amperometric response ....................................................................... 265 A 67 Experiment #3 7J Radial and axial velocity .................................................................... 266 A 68 Experiment #3 7J Concentration profile ........................................................................... 266 A 69 Experiment #3 7J Amperometric response ....................................................................... 266 A 70 Experiment #3 8A Radial and axial velocity .................................................................. 267 A 71 Experiment #3 8A Concentration profile .......................................................................... 267 A 72 Experiment #3 8A Amperometric response ...................................................................... 267 A 73 Experiment #3 8B Radial and axial velocity .................................................................. 268 A 74 Experi ment #3 8B Concentration profile .......................................................................... 268 A 75 Experiment #3 8B Amperometric response ...................................................................... 268 A 76 Experiment #3 8C Radial and axial velocity .................................................................. 269 A 77 Experiment #3 8C Concentration profile .......................................................................... 269 A 78 Experiment #3 8C Amperometric response ...................................................................... 269 A 79 Experiment #3 8D Radial and axial velocity .................................................................. 270 A 80 Experiment #3 8D Concentration profile .......................................................................... 270 A 81 Experiment #3 8D Amperometric response ...................................................................... 270 A 82 Experiment #3 8E Radial and axial velocity ................................................................... 271 A 83 Experiment #3 8E Concentration profile ........................................................................... 271 A 84 Experiment #3 8E Amperometric response ...................................................................... 271 A 85 Experiment #3 8F Radial and axial velocity ................................................................... 272 A 86 Experiment #3 8F Concentration profile ........................................................................... 272 A 87 Experiment #3 8F Amperometric response ....................................................................... 272

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17 A 88 Experiment #3 8G Radial and axial velocity .................................................................. 273 A 89 Experiment #3 8G Concentration profile .......................................................................... 273 A 90 Experiment #3 8G Amperometric response ...................................................................... 273 A 91 Experiment #3 8H Radial and axial velocity .................................................................. 274 A 92 Experiment #3 8H Concentration profile .......................................................................... 274 A 93 Experiment #3 8H Amperometric response ...................................................................... 274 A 94 Experiment #3 8I Radial and axial velocity .................................................................... 275 A 95 Experiment #3 8I Concentration profile ............................................................................ 275 A 96 Exp eriment #3 8I Amperometric response ........................................................................ 275 A 97 Experiment #3 8J Radial and axial velocity .................................................................... 276 A 98 Experiment #3 8J Concentration profile ........................................................................... 276 A 99 Experiment #3 8J Amperometric response ....................................................................... 276 A 100 Experiment #3 9A Radial and axial velocity .................................................................. 277 A 101 Experiment #3 9A Concentration profile .......................................................................... 277 A 102 Experiment #3 9A Amperometric response ...................................................................... 277 A 103 Experiment #3 9B Radial and axial velocity .................................................................. 278 A 104 Experiment #3 9B Concentration profile .......................................................................... 278 A 105 Experiment #3 9B Ampe rometric response ...................................................................... 278 A 106 Experiment #3 9C Radial and axial velocity .................................................................. 279 A 107 Experiment #3 9C Concentration profile .......................................................................... 279 A 108 Experiment #3 9C Amperometric response ...................................................................... 279 A 109 Experiment #3 9D Radial and axial velocity .................................................................. 280 A 110 Experiment #3 9D Concentration profile .......................................................................... 280 A 111 Experiment #3 9D Amperometric response ...................................................................... 280 A 112 Experiment #3 9E Radial and axial velocity ................................................................... 281

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18 A 113 Experiment #3 9E Concentration profile ........................................................................... 281 A 114 E xperiment #3 9E Amperometric response ...................................................................... 281 A 115 Experiment #3 9F Radial and axial velocity ................................................................... 282 A 116 Experiment #3 9F Concen tration profile ........................................................................... 282 A 117 Experiment #3 9F Amperometric response ....................................................................... 282 A 118 Experiment #3 9G Radial and axial velocity ................................................................... 283 A 119 Experiment #3 9G Concentration profile .......................................................................... 283 A 120 Experiment #3 9G Amperometric response ...................................................................... 283 C1 Oxygen concentration vs. electrical potential (750 oC) .................................................... 300 C2 Schematic of volume expansion in a copper node ............................................................ 302

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19 NOM ENCLATURE The following nomenclature is used throughout the dissertation with an effort to abide by the SI units and IUPAC conventions A few exceptions have been made, resulting from dissimilar local denotations and simplifications, which ar e clarified below. Standard Conventions o Initial Ox Oxidized Species Dimensionless Gradient e Electron Red Reduced Species Standard State h Hole d Derivative of j Subscript Pertaining to Species j Rxn Reaction Change in Su perscript Pertaining to Phase Roman Symbols Symbol Description Typical Units A Area cm 2 a j Activity of Species j None B Interface Temperature Gradient K cm 1 C Capacitance F C Dimensionless Concentration None C j Concentratio n of Species j M, mol cm 3 D j Diffusivity of Species j cm 2 s 1 E Electrical Potential V f Solidified Fraction of the Original Melt None F Faraday s Constant C (mol e ) 1 F Dimensionless Body Force None G Mola r Gibbs Energy J/mol G Gibbs Energy J g Acceleration Due to Gravity m s 2 H Height m m H Molar Enthalpy J/mol, cal/mol I Current A j Imaginary Unit None k Boltzmann Constant J K 1 eV K 1 L Inductance H m j Mobility of Species j cm 2 V 1 s 1 n Concentration of Electrons M, mol cm 3 n Moles of Electrons per Mole of Reduced Species mol e (mol Red) 1 n Moles of Electrons m ol NA Numerical Apertures None

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20 Roman Symbols Symbol Description Typical Units O Moles of Oxygen on an Anion Lattice Site Mol P Dimensionless Pressure None p Pressure Pa p Concentration of Holes M, mol cm 3 Q Rate of Solidification cm s1 q j Electric Charge of Species j C R Gas Constant J mol 1 K 1 R Res istance R Radius cm r Non Dimensional Radius None r Computational Radius cm r Radial Position cm S Molar Entropy J mol 1 K 1 S Entropy J K 1 T Temperature K T Dimensionless Temperature None t Time s t j Transference Number of Species j None U Internal Energy J, cal V Volume m 3 V Dimensionless Velocity None V OC Open Circuit Voltage V 2 OV Moles of Oxygen Vacancies Mol W Work Done by the System J, c al W Non pV Work Done by the System J, cal Z Impedance z Axial Position c m z Non Dimensional Axial Position None z Computational Axial Position c m z j Charge Number None G reek Symbols Symbol Description Typical Units Nodal Region of an Electrochemical System None Thermal Diff usivity cm 2 s 1 Nodal Region of an Electrochemical System None S Solutal Volume Expansion Coefficient mol 1 T Thermal Volume Expansion Coefficient K 1

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21 Greek Symbols Symbol Description Typical Units Slope of Liquidus Line K Aspect Ratio Non e Electrostatic Potential of Phase V Mole Fraction None Electrolytic Region of an Electrochemical System None o Solutal Distribution Coefficient None Wavelength nm Minimum Resolution nm j Chemical Potential of Species j in Phase kJ mol 1 o j Standard State Chemical Potential of Species j kJ mol1 j~ Electrochemical Potential of Species j in Phase kJ mol1 Density g cm 3 j Conductivity of Species j S cm 1 S Solutal Surface Tension Gra dient ergs cm 2 K 1 T Thermal Surface Tension Gradient ergs cm 2 mol 1 Time Constant /Dimensionless Time None Reaction Quotient None Angular Frequency s 1 Seebeck Coefficient mV o C 1 Standard Abbreviations Abbreviation Description AFM Atomi c Force Microscopy ALD Atomic Layer Deposition BOE Buffered Oxide Etchant CE Counter Electrode CMP Chemical Mechanical Polishing CPE Constant Phase Element CTE Coefficient of Thermal Expansion CVD Chemical Vapor Deposition CZ Czochralski Crystal Gr owth EBD Electron Beam Deposition ECD Electrochemical Deposition EDS Electron Dispersive Spectroscopy EMF Electromotive Force FCC Face Centered Cubic FIB Focused Ion Beam FWHM Forward Width Half Maximum FZ Float Zone Crystal Growth

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22 Standard Abbre viations Abbreviation Description IC Integrated Circuit ICE Internal Combustion Engine Le Lewis Number Ma Marangoni Number MEMS Micro Electromechanical Systems MES 3 A Micro Electrochemical Solid State Sensor Array OCP Open Cell Potential PECVD Plasm a Enhance Chemical Vapor Deposition PLD Pulsed Layer Deposition PR Photoresist Pr Prandtl Number PVD Physical Vapor Deposition Ra S Solutal Rayleigh Number Ra T Thermal Rayleigh Number RE Reference Electrode RF Radio Frequency RIE Reactive Ion Etchi ng Sc Schmidt Number SEM Scanning Electron Microscopy SOFC Solid Oxide Fuel Cells STM Scanning Tunneling Microscopy TEOS Tetra Ethoxy Silane TPB Triple Phase Boundary UV Ultraviolet Light WE Working Electrode XRD X Ray Diffraction YSZ Yttria Sta bilized Zirconia

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23 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMENT OF A NOVEL MICRO -ELECTROCHEMICAL SO LID -STATE SENSOR ARRAY (MES3A) SUITABLE FOR FLOW VISUALIZATION OF LIQUID TIN MELTS By Michael P. June May 2009 Chair: Tim Anderson Major: Chemical Engineering A micro -scale solid -state electrochemical sensor array based on yttria -stabilized zirconia (YS Z) was designed, fabricated, and tested. The motivation for developing this sensor array was for flow visualization of low Prandtl number fluids at small scale such as solder bumps. The sensor array consisted of 40 sensors and each cell is schematically represented as: Au|Cr|Cu|Cu/Cu2O||YSZ||[O]M where [O]M 2 sensors was fabricated on Si(100) wafers using lithography and deposition of sputtered YSZ, Ta/Ta3N5 Cu barriers, PETEOS -based SiO2 dielect ric isolation, Cu interconnects, and Au/Cr contacts. An in-plane conductivity analysis of sputteredYSZ revealed 25 nm grains of YSZ having very good texture and oriented in the (111) direction that showed high ionic conductivity. XRD patterns of arrays a fter annealing at 850 C showed only formation of TaSix at the SiO2/ Ta3N5 interface, which served to increase the barrier quality. Further testing of the array with liquid Sn confined in a cylinder showed only a fraction of the devices operated and had a short life time. A failure analysis revealed difficulties with cracking of the thin film YSZ. Simulations were performed to guide the sensor array design and validation. The Chebyshev spectral method was used to solve the equations describing tracer oxyge n 2 D

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24 transport at high temperature in tin melts confined in a right cylindrical geometry. Simulation of oxygen variations produced during titration resulted in significant buoyancy driven flow. Further numerical analysis illustrated a method by which flow can be electrochemically detected and the minimum fluid velocities that can be experimentally measured. The implementation of a periodic boundary condition was simulated to minimize fluid flow to allow mass transfer data to be quickly extracted from the s ystem response. The use of a periodic boundary condition was also used in specific conditions to induce fluid flow having a specific periodicity.

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25 CHAPTER 1 INTRODUCTION AND REVIEW OF LITERATURE Motivation and Overview Recent liquid Sn flow visualizatio n experiments have successfully employed macro -sized electrochemical cells to detect fluid flow in high temperature liquid metal systems. These macro electrochemical cells acc urately monitored oxygen tracer species in constrained right cylindrical and rect angular geometries. Additional experimentation demonstrated a sensor response time on the order of 103 s and the capability to monitor flow velocities as low as 104 cm s1 [1, 2]. The expe rimental results using the macro -sensors inspired the development of an array of sensor s with feature sizes on the order of microns These micro electrochemical cells will be used to monitor fluid flow profiles in small geometries and give higher resolution of fluid flow in the macro -geometries The focus of this dissert ation is to fabricate, validate, and implement a novel electrochemical technique intended to study flow profiles and characteristics of liquid metals in micro -scale geometries (on the order of a few centimeters to a few microns ) As in the macro scale syst em t his technique uses solid -oxide electrochemical cells in electrolytic mode to establish known oxygen tracer boundary conditions and to sense the system response using cells operating in galvanic mode A program of research is described in the following chapters to develop such a measuring device, MES3A ( Micro Electrochemical Solid State Sensor Array ) and to demonstrate its potential in a liquid tin system of geometric interest. Fabrication is accomplished through the use of numerous microelectronic man ufacturing methods such as lithography, sputtering, and chem ical mechanical polishing While these methods are well understood and widely practiced, the proposed fabrication of these microscaled oxygen sensor arrays has not previously been attempted.

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26 Th e appeal of this measuring technique is the sensors ability in any gravitational field to monitor, measure, and confirm predicted flow profiles, phases and characteristics of opaque, liquid metals at high temperature The small feature size of the propose d sensor array will allow it to monitor small systems These electrochemical sensors require only a heat source and conductive contacts for electrical input and output signals. This setup a llows for easy data storage and transmission coupled with low powe r consumption. Simple, reliable, and widely applicable sensors are a necessity for detecting oxygen tracers in the model liquid tin system Potential applications of MES3A include determination of two -phase flows, measurement of oxygen partial pressures, a nd the removal or addition of oxygen through titration. Future applications of the micro -sensor arrays could be extended to flow measurements in small length scale processes such as micro -fluidics and micro -mixing Other aspects include micro fuel cells, c hemical clean up systems, and materials processing (e.g., welding, crystal growth, casting, dendrite formation, interface demarcation). Developing a methodology to measure the dynamic state in a real system holds the promise of improving the connection be tween experimental and numerical modeling work. On one hand, researchers performing flow visualization experiments involving liquid metals cannot accurately measure the dynamic state in the melt, and do not quantitatively understand the effect of specific processing conditions on the dynamic state. On the other hand, researchers simulating processes cannot easily validate the ir results experimentally since direct measurements are often difficult to obtain. This sensor array could provide a methodology for pr obing the influence of certain experimental v ariables, experimental data model validation, and a g eneral contribution to the basic unde rstanding of the fluid physics pertaining to low Prandtl number liquids.

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27 The original motivation for this dissertatio n was to better understand the fluid dynamics in a liquid solder bump commonly used in the IC industry. It is believed the dynamic state of the solder bump b efore and during solidification, can greatly affect the resulting quality of the bump. The conce pt of fabricating these micro -scale sensors was b ased on previous experime nts directed at understanding fluid dynamics of bulk crystal growth using macro -sensors to establish known oxygen tr acer boundary conditions and sense the system response at the boun dary. The remainder of this chapter reviews the results of using a macro -sensor array to understand the applied geometry followed by a review of fluid flow in solder bumps. An overview of a solid oxide electrolyte and electrochemical cells is also presente d with a short discussion of the fabrication techniques used in this work. Bulk Crystal Growth The existence of an escalating electronics industry relies heavily on the economical, efficient and superior production of boules (ingots) comprised of semiconducting materials suitable for integrated circuits (ICs). These manufactured boules (typically single crystalline with a minute impurity concentration) can be thinly sliced into wafers that serve as the foundation of integrated circuits Applications of semi conducting materials range from digital logic circuits to micro electromechanical system (MEMS) devices. To sufficiently support such devices, the boules and resulting wafers must have a high crystalline order with minimal defects and impurities. Unfortuna tely the boule production process contains a number of operational conditions that can negatively affect the finished product. Nonideal outcomes include crystalline structure degradation, buildup of contaminants and in compound semiconductor alloys poor mixing. Natural and/or Marangoni (thermocapillary) convection is a main contributor to the quality degradation of boules during the manufacturing process. These types of convection result

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28 from instabilities in the buoyant or surface tension forces as a byp roduct of (often unavoidable ) temperature and/or solutal gradients. Despite past efforts to minimize fluid movement using magnetic or low gravitational fields, b oule production still includes substantial fluid flow [3, 4]. The growth of bulk single c rystal semiconductors is critical to the success of the IC and related industries. The process most often involves the directional solidification of a melt that is typically a metal in the molten state. The process is accompanied by significant convection in the melt driven by applied forces (e.g., crucible rotation, crystal rotation), buoyancy forces (thermal or solutal produced density variations), or other factors such as surface tension variations. The control of the dynamic state in the melt has been s hown to directly influence the quality of a subsequently grown crystal. A short review of the three most common growth techniques is given next and followed by a discussion of convective effects. Bridgman Growth Bridgman growth, also referred to as direct ional solidification, is a popular bulk crystal growt h method that employs and imposes a temperature gradient. A smal l seed or single crystalline form of the charge is place d at one end of the container to nucleate the single crystal upon solidificati o n After melting the charge (and a small portion of the seed ) the growth process is commenced by either moving the crucible along the growth axis toward the colder end or moving the furnace in the opposite direction. Although the arrangement places the hot less dense material above the cooler region, radial thermal gradients (and potentially solutal variations for multi -comp onent systems ) can produce natural convection. Temperature and solutal gradients are the underlying source of fluid flow during Bridgm an growth. Bridgman growth is a relatively simple process that does not require much attention from an operator. This method has been used to grow III -V ( e.g., GaAs, InP ) and II-VI ( e.g., CdTe) compounds comprised of volatile constituents [5]. Despit e the simplicity of Bridgman growt h, a

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29 numbe r of drawbacks remain; low th roughput, poor process monitoring, residual stress and impurities derived from the container wall. Flow dynamics in the melt can change dramatically during re -solidification as the am ount of liquid decreases in an enclosed geometry. Although Bridgman growth is often used for boule development the potential drawbacks translate into using another process for commercial growth. Float Zone Growth The float zone (FZ) crystal growth method is similar to Bridgman growth except a small liquid zone is melted instead of the entire charge. FZ growth, unlike Bridgman growth, employs two cool regions and one hot region resulting in two solid -liquid interfaces noted in Figure 1 2. Interestingly, the liquid region between the two solid regions of the forming boule will not pull apart as long as its surface tension forces of the liquid region can overcome the gravitational forces acting on the melt. A surface tension gradient along the materials surfa ce can (and typically does) induce thermocapillary flows [6]. The FZ crystal growth methodology is usually reserved for Group IV materials with silicon and germanium crystals commercially produced by this approach The durability of the FZ process is ill ustrated by its simple setup, necessity for modest operational attention, and the ability to either constrain a charge (in the case of volatile components) or allow the charge to be exposed to vacuum or inert ambient [7]. The ability of an impurity to diff use ahead of the solid liquid interface (determined by thermodynamic solubility properties), combined with multiple solidification passes from a heat source, can result in an ultra high purity boule [8]. The most sig nificant advantage of FZ is the ability to grow single crystalline materials without a container reducing residual stress and impurity levels.

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30 Czochralski Growth The third and most popular crystal growth method is Czochralski (CZ) growth. This growth method can induce forced convection when the seed and subsequent solidified single crystalline structure are rotated and pulled from a m olten pool of the charge. Additional instabilities such as centripetal forces and axial temperature and solutal gradients can produce forced, natural, and thermoca pillary convective flows [9]. The se convective flows can be beneficial when desiring a well mixed molten pool of material, but can also be a drawback when the fluid velocity affects the solute concentration at the solidification interface. CZ growth enjoys widespread popularity because of its capab ility to grow di slocation free 16 in. diamet er silicon wafers and is a reliable method for producing 8 and 12 in. diameter silicon boules [10]. Other advantages of the CZ process include high throughput, ease of monit oring the crystal growth process and the potential to produce even larger diameter boules. Some shortcomings of the method include difficulties in th e seeding process, determining proper rotational speeds, and the need to closely monitor the growth process. Despite the se drawbacks CZ growth is often the method of choice for manufacturing boules comprising of non-volatile constituents. The method can even be extended to volatile materials such as III -V compound semiconductors when an immiscible encaps ulant (e.g. B2O3) is used to contain the vapor s Convective Effects in Crystal Growth Methods The previous description of various crystal growth methods illustrated the presence and incorporation of convective flows during boule production It was also con strued that the se convective flows are often the result of thermal and solutal instabilities in the bulk (or along the boule surfaces ), which can negatively affect the growth properties of crystals. Generally c ompositional homogeneity (radially and axially ) of the boule is desired and necessary when fabricating materials whose physical properties are dependent upon composition ( e.g. electronic

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31 properties of semiconductors) For growths performed within typical earth gravitational fields forced convection is used in CZ growth to provide a more controlled and quantified fluid flow that overrides fluid flow resulting from natural Marangoni and other sources of convective flow For the remaining two methods convection in the melt can disrupt the uniformity of a dopant and degrade the physical quality of the single crystalline material. In the CZ methodology forced convection can be introduced into the liquid mel t by either rotating the seed, melt container, or applying a magnetic field. A number of studies have dealt with the numerical analysis of forced convecti on that mask the e ffects of natural and thermocapillary fluid movement and allow for the growth of high quality boules [12, 13]. Kim et al. were able to show experimentally the use of forced convection i ncreases the removal rate of an excess solute at the interface and redistribute s surplus back i nto the melt [11]. Furthermore, redistribution of the solute via forced convection linearizes the solid liquid growth interface and reduces segregation, constitu tional super -cooling, and dendritic growth, resulting in high axial homogeneity in the boule [11]. For Bridgman growth, the key to growing a homogenous crystal boule is to prevent convection. For congruently melting materials this translates into control o f thermal gradients to minimize convection. For incongruent melting materials including solutes, the composition gradients will naturally develop since the growth interface is at or near equilibrium. These composition gradients will eventually lead to compositional variations that can induce flow After a period of time a diffusion profile is established in the melt adjacent to the interface resulting in a non uniform composition across the bulk. For these reasons, there has been interest in growing these m at erials in space under microgravity conditions.

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32 Mass Transfer Effects An excellent example of an incongruent melting system is the pseudo -binary phase diagram of PbxSn1 xTe (see phase diagram in Figure 1 4 ). This simple isomorphous phase diagram is bound by the melting temperature of PbTe (~924 oC) and that of SnTe (~806 oC). Illustrated by the dashed line in the figure, a t a particular temperature there is a concentration difference between the amount of Sn in the solid and liquid phase As the solid fre ezes, the Sn concentration in the solid is less than that in the liquid and thus Sn is rejected into the melt. The Sn rejected at the mov ing solid liquid interface is re -introduced into the bulk liquid by mass transport. If the solutal gradient becomes la rge enough this driving force can lead to a curved solid liquid growth interface, segregation, constitutional super -cooling, and even dendritic growth upon solidification of the melt [11]. Tiller et al. w ere able to relate the ratio of the temperature gra dient at the interface, B, to the growth rate, Q to determine if constitutional supercooling would occur This ratio is expressed in Equation (1 1) where is the slope of the liquidus line Ds is the diffusion coefficien t of the solute in the solution o is the distribution coefficient and Co is the initial solute concentration [17]. s o o oD C Q B 1 (1 1) The distribution coefficient is a m easure of the gap size between the solidus and liquidus lines given in Equation ( 1 2 ) where CS is the concentration of the solute in the solid and CL is the concentration of the solute in the liquid at the interface. L S oC C (1 2)

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33 When there is sufficient convective flow in the melt to assume it is well -mixed the axial composition can be modeled by Equation (1 3) where C is the solute (SnTe) concentration and f is the fraction of the original melt that has solid ified [16]. 1) 1 ( of C Co o (1 3) If the concentration gradient cannot create a solidification instability and there are no resulting convective flows in the melt the solute is distribu ted into the melt solely by diffusion. In a diffusion limited growth the axial composition is given in Equation (1 4) o S o o oD Qz C z C exp 1 1 (1 4) A schematic comparison of the composition profiles between the diffusion-dominated and the convection dominated Bridgman growth is shown in Figure 1 5. The diffusion -controlled condition exhibits a homogeneous concentration profile except for the concentration at the beginning and end of the profi le where the steady diffusion is limited by the end wall s The fully mixed condition has an ever increasing concentration (for o>1) across the length of the boule. Since the goal of the solidification process is to produce a homogeneous boule, the superio r method is diffusion -dominated Bridgman growth. While diffusion limited growth is preferred, since most of the boule is of constant composition, achieving this mode in earths gravit ational field is very difficult The large solutal gradient diffusion pr ofile near the interface can result in buoyant convection due to the presence of grav ity (resulting in a body force ). There have been efforts to reduce buoyancy driven flows through the use of magnets on susceptible materials [14, 15]. Although these metho ds have resisted the onset of convection in liquid metal melts by maintaining a diffusion dominated

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34 system these schemes are often difficult to control, tune, and serve as a universal solution to controlling solute distribution in solidification processes Gravitational Effects As previously mentioned, gravitational forces do not make Earth a good candidate for diffusion -dominated growth, thus suggesting crystal growth in a micro -gravity environment such as space Witt et al. w ere able to successfully grow InSb boules in a microgravity environment during the Skylab project [18] which initiated a large push to perform solidification experiments in space. Unfortunately, the microgravity solidification results have not been as promising as originally hoped. It was discovered that g jitter and residual acceleration (even on the order of 105 g) induce s convective flows [19]. Also, the effects of Marangoni convection were not expected and unfortunately contributed to the onset of convective flow [20, 21]. It is noted however, that Kinoshita claims to offset the convection by starting with a graded concentration profile in microgravity fields on the order of 103 to 104 [19]. Regardless, the future of microgravity crystal growth remains unclear due to the sim pl e fact that even if diffusion dominated flows are achiev ed in these microgravity environments, the operational cost of placing the essential hardware in orbit remains quite large. Convective Effects in Solder Bumps Systems containing transitive solid liqu id interfaces leading to bulk fluid flow are not limited to semiconductor solidification processes and can easily be extended to solder bumps. Solder bumps are the bonding material that link electrical semiconductor contacts to external connections. Solder bumps generally consist of metal powder dispersed in a continuous phase known as the vehicle [22]. The metal powder can have varying compositions but is typically tin based with small percentages of lead, silver, and a number of other metals with a recen t shift to

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35 lead -free solders [23 26]. The bond is made when the solder bump undergoes a reflow process that melts the solder paste followed by a cooling stage that allows the material s to solidify. This heating and cooling process can be performed in a top to bottom or a bottom to top fashion; that is to say the heat is applied to the top or bottom of the material first and then distributed, mainly through conduction, towards the opposite region. This distribution of heat give s at least temporarily, a t emperature gradient across the bulk of the solder bump and across the free or interfacial surface s ( that creates surface tension gradients) that can result in buoyancy generated flows. An examination of the literature reveals most bulk flow in quiescent so lder bumps is induced via surface tension gradients [27 31]. A numerical analysis of solder bumps in flip-chip geometries performed by Panton et al (built upon previous numerical models of Goenka and Achari and Bailey et al. ) revealed the surface tensio n gradient between the molten solder bump and air drives fluid flow on the surface of the bump [29 31]. Then, by means of the viscous properties the motion of the free surface is conveyed to the bulk [27]. A nondimensional analysis of the mathematical mod el revealed low Marangoni, capillary, and Reynolds numbers indicating, respectively, the flow does not affect the temperature field, the free surfaces are undistorted due to the flow, and the inertial effects are negligible, thus simplifying the calculatio ns [27]. The interest in mathematically modeling the re circulating bulk flow within molten solder bumps was to determine the motion and final location (upon solidification of the melt) of voids that can occur in the solder bump. Presence of Voids Voids ar e mainly formed during the reflow process when gases from the vehicle, or flux, become trapped in the coalescing metal particles [28 32]. Voids can have a range of harmful effects such as the reduction of joint strength, reduction of electrical and thermal conductivity, instigation of electromigration due to local peaks of current density, and an incongruence of the

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36 local resistances [25, 3 2, 33]. Chan et al concluded pores (a primitive name for voids) cannot be limited by increasing the reflow time, and t he only means by which pores could escape the bump was if their sizes exceeded the base width [32]. A n increasing interest in the formation, motion, and final location of voids has been initiated d ue to their multitude of negative effects This attention i s a direct result of solder bump applications calling for a reduced amount of solder that magnifies the se negative effects Since there are no current or past experimental in situ methods of monitoring the motion of voids, the analysis of void motion has for many years relied heavily on numerical and post reflow sample analysis. Panton et al. was able to build upon previous numerical models to determine the final location of voids in cylindrical solder bump flip -chip geometries under two melting conditions : top to bottom and bottom to top. Their calculations were based on a number of assumptions, including a cylindrical solder bump geometry, bubbles (voids) ranging in size, and the immediate coalescence of two voids into a larger void upon contact, as propo sed by Goenka and Achari [27, 29]. Results of the numerical analysis claimed voids should be found at the top of the melt in both cases due to the stronger buoyant forces of voids overcoming any downward forces of the resulting weak bulk flow. The top to bottom melting process resulted in many smaller voids found in a ring shape on the outward upper edges of the melt as shown in Figure 1 6 A [27]. In bottom to top melting, the voids coalesced into a very large void at the center of the melt as shown in Fig ure 1 6 B [27]. The differing results are a consequence of the dissimilar thermal profiles resulting in opposite bulk fl ow directions. Recognizing the higher surface tension regions (lower temperature) pull on the lower surface tension regions (higher temperature) it is easy to visualize the direction of flow on the surface and therefore what the resulting direction of flow must be throughout the bulk to

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37 maintain an axis -symmetric, re -circulating flow profile. The top to bottom melting results in voids at the edges of the melt since they were pushed apart from the resulting flow profile and the bottom to top melting results in a large void since the voids have been pushed together by the resulting bulk flow. It is expected that the proposed MES3A device may be used to experimentally confirm the numerical results of Panton et al. Additionally the MES3A device could be used to monitor fluid velocities that occur during the reflow process. Since voids consist mainly of trapped oxygen i t may even be possible to use the MES3A device in titration mode to remove the voids. Need for In Situ Detection Method As previously mentioned there have not been significant in situ experimental analyses of void formation and movement in solder bumps. Post reflow experimental ana lyses however, have been carried out on many occasions by cutting samples at varying heights and examining the sizes and quantities of voids found. While post -experimental analysis does not divulge the entire story, it does provide insight to the final position of voids. Experimentally recreating the ir own numerical analysis, Panton et al were able to confirm that melting directions do indeed have an effect on the movement and final distribution of voids This was done by experimentally observing a large void forming at the top of the melt, in the case of bottom to top melting, and many smaller voids forming on the outer edges, in the case of top to bottom melting [28]. It should be noted, however, that there were some discrepancies between the experiment al and numerical results. Most notably, experimental cross -sections revealed extraneous voids in both melting cases outside of their expected and numerically predicted regions. L arge voids were also found in the case of top to bottom melting when the numer ical forecasts predicted only small voids. These discrepancies most likely arise from the breakdown of numerical assumptions, particularly those barring r adial temperature gradients, constraining the driving

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38 forces of fluid flow to that of thermocapillary forces, and the assumption that voids coalesce instantaneously on contact. Many of the complexities pertinent to solder bump solidification are similar to those faced with solidification of s emiconductor materials. An in situ device has been proposed t o help resolve the differences between model predictions and post solidification analyses. The next section reviews the literature on methods pertinent to visualizing fluid flow in liquid metal systems. Flow Visualization Techniques The typical method used t o probe convective profiles i nvolves tracer and dye materials. Tracers and dyes are commonly used to determine the fluid streamlines via a prolonged photographical exposure and/or a series of photographs to determine the respective tracer or dye positions in the fluid as a function of time This is a straightforward method that has proven effective in transparent systems. Stewart and Weinberg attempted to circumvent the opacity issue faced with metallic samples by monitoring injecte d radioactive tracers int o liqui d tin and lead samples to determine an average fluid velocity [74, 75]. There was not a significant amount of success with this method, as the radioactive tracers were difficult to introduce, required a detection system (with obvious safety issues), and encountered radioactive contamination issues. The common problem with practically all tracers or dyes is their inherent disruption of the system. Additional methods based on regional temperature differences have been experimentally exercised to varyi ng degrees of success. For example interferometry, a method based on the temperature dependence of a materials refractive index, can be used to chart isothermal regions to deduce flow profiles in a convecting sample [76]. Oertel and Buhler used such a met hod and were able to determine flow patterns in low Prandtl number materials [77]. Unfortunately

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39 interferometry is only suitable for transparent and at the very least relatively translucent materials. To side -step the opacity issue, Hurle et al. used a series of thermocouples to determine the isothermal regions of a gallium metal melt [78]. They were partially successful in determining the development of oscillatory convective flows in gallium using only thermocouples. L ow Prandtl number materials however, have a small er thermal boundary layer compared to the momentum boundary layer (due to its high material thermal conductivity), indicating a quick equilibration of temperature throughout the sample. Thus local and regional temperature gradients are qui ckly minimized, making the measured temperature less sensitive. Furthermore, the thermocouple can disrupt the flow and also locally conduct heat along the wires to further corrupt the data Magnetic probing methods have been adapted in an attempt to monit or flow patterns and velocities This is an intriguing solution to determine fluid velocities of molten metals by implementing elementary electromagnetic physics. Remembering that a current and electric field are induced when a metal moves through a perman ent magnetic field, a relationship can be resolved between the resulting current and fluid velocity. Ricou and Vives were able to determine fluid velocities in a number of metallic samples; however, difficulties were encountered when adapting the system to smaller geometries [79]. X ray radiography is another interesting method utiliz ed to monitor flow profiles in opaque materials. A majority of the reported studies focus ed on in situ measurements of interfacial crystal growth characteristics. Studies by Ba rber et al. and Simchick et al. used x -ray radiography to monitor Bridgman crystal growth at the solid -liquid interface of germanium and lead tin telluride crystals [8082]. Additional studies by Kakimoto et al in CZ growth

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40 geometries and Nakamura et al. in FZ growth geometries employed x-ray radiography to further understand dendritic growth and flow effects at the crystallization interface [8384]. While these studies were able to extract interfacial information across the spectrum of crystal growth meth odologies, x ray radiography unfortunately require d tracers and an expensive setup. The flow visualization techniques summarized above have a number promis ing aspects, but also have drawbacks ranging from sample contamination to the inability of measuring quantitative parameters across a broad spectr um of low Prandtl number materials Another methodology inv olves titrating oxygen atoms in t o metallic melts and electrochemically sensing their concentrations along the container boundaries to determine flow dynamics [1, 2, 16, 72, 73]. The abilit y of the electrochemical sensor to detect oxygen concentrations on the order of ppm (and concent ration perturbations) result s in tracers that 1) do not affect the flow profiles to be measured, 2) do not contaminate the sample, 3) can be employed in any geometry, and 4) can be easily removed at the conclusion of an experiment. The challenge for this particular method is to relate the measured oxygen surface concentration to the bulk concentration, which requires a suitab le model and sufficient data. Further reducing the size of an individual sensor and employing more sensors per area will increase the spatial resolution of the detection method Electrochemically Based Oxygen Sensors In the late 1970s, oxygen sensors deve loped by Bosch gained widespread use and public notoriety as an excellent tool for controlling the air -to -fuel ratio in automobile engines [34]. The electrochemically -based oxygen sensors created by Bosch proved useful and upon further research (assisted by stricter emission standards from the government), led to the development of oxygen sensors capable of monitoring ICE emissions. These oxygen emission sensors were capable of observing combustive side reactions and various by -products of incomplete hydro carbon combustion. Recent developments now allow these oxygen sensors to monitor

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41 several different gases such as CO, NOx, H2, SO2, and a number of hydrocarbons with reasonable selectivity [35 39]. Researchers, however, were using this approach well before the development of Boschs ICE specific oxygen sensors. As early as 1933, Wagner was able to derive a relationship between the chemical potential gradient present in a solid state electrochemical system and its resultant steady state open circuit EMF [40] This derivation, and a later understanding of transport mechanisms across doped zirconia materials, opened the field to a number of systematic studies focused on thermodynamic and kinetic measurements [41]. Ramanaryanan claims much of the current focus o n thermodynamic measurements is a result of the innovative studies by Kiukkola and Wagner and Peters et al [42]. These researchers used solid state oxygen ion conductivity of zirconia and thoria based solid electrolytes to determine the Gibbs energy of fo rmation for various oxides [43 46]. Some areas of interest utilizing solid state electrochemical thermodynamic measurements are as follows: an expansion of Gibbs energy measurements, component activity measurements in liquid and solid solutions, solubility o f oxygen in metals, a determination of transference numbers across solid state electrolytes, and stability analyses of electrode materials [1, 2, 16, 42, 47 49]. Two main areas of study exist in regards to kinetic measurements: transport phenomena in th e solid state electrolyte, and kinetics of reaction(s) occurring at the electrolyte interface [42]. The polarization technique, pioneered by Hebb and Wagner, is typically employed to study the aforementioned systems [50 51]. This method produces valuable kinetic information by measuring the polarization or non -ohmic response at the electrode -electrolyte junction, a result of the rate limiting step in the kinetic processes occurring in the bulk electrolyte or at the electrolyte /electrode interface [42]. A brief review of literature will demonstrate the widespread

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42 use of solid state electrolytes as effective tools in determining not only electrode and electrolyte reaction kinetics, but mass transport data as well [1, 2, 16, 37, 51 53]. Functionality Oxygen s ensors based on solid -state electrochemistry use an electrolyte that can conduct only oxygen ions while blocking the transport of electrons, holes, or any other types of ions. Because ion ic transport is thermally activated and the mobilities are low, these solid -state electrolytes are operated at elevated temperature to ensure operation is with in the electrolytic domain ( i.e. the ionic transference number is 0.99). When a solid electrolyte separates two regions of varying oxygen chemic al potential (thermodynamically equivalent to a difference in the oxygen partial pressure) in open circuit an EMF develops across the electrochemical cell It is important to note an electrochemical cell consists of two nodes on either side of the electro lyte capable of conducting electrons. The nodes must be in the proximity of the electrolyte so that if an oxygen atom adsorb s to the surface of a node, e lectrons can be supplied to create an oxygen ion and then the captured ion can be easily transported across the electrolyte. The reverse is true when an oxygen ion reaches the nodal interface on the opposite side of the electrolyte. The area where the node, oxygen atom, and electrolyte are in contact is commonly called the triple region or triple phase bo undary (TPB). A more complex discussion of the solid state electrochemistry is given in Chapter 2. An overview, however, is given here to understand the context of this dissertation. A schematic depicting the basic operation of an oxygen sensor is given i n Figure 1 7 Connection to MEMS Recent advances in solid state oxygen sensors have focused on the miniaturization and micromachining of these devices. La Roy et al were the first to thin the transition thicknesses of the electrolyte to micro thicknesses by evaporating LaF3, an oxygen ion conductive electrolyte

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43 material, onto alumina substrates accompanied by suitable electrodes [54]. Further work by Velasco et al used a thin layer of Yttria -Stabilized Zir c onia (YSZ) instead of LaF3 [55]. Since this time numerous researchers have employed thin layers of YSZ for oxygen sensors with excellent results [34 39, 56 63]. It should be noted that thin layers is a non -standardized term reported in literature as thickness varying from tens of microns to well below the submicron level on the order of nanometers [5758]. One device of note constructed by Radhakrishnan co nsisted of multiple micro oxygen sensors in an electrical series to increase the selectivity of his detector [39]. The ability to construct thin elect rolyte and nodal layers using various fabrication processes similar to IC fabrication processes have allowed these types of oxygen sensors to join a growing class of micro electromechanical systems devices simply known as MEMS. Melding oxygen sensors with electronic devices allows for the simple integration of solid state electrochemistry into microelectronics. This combination proves advantageous because the resulting signal from an electrochemical sensor is electronic. Use of integrated circuit fabricatio n processes also allows the designer to easily employ further innovative, intricate, and elegant sensor designs. Considerable effort has been put into micromachining and miniaturizing oxygen sensors, mainly due to the numerous advantages of scaling down th e electrolyte and nodal material thicknesses. These advantages include lower operating temperature, lower power consumption, easy integration into electronic systems, and reduced size and weight [59 61]. The return gained by fabricating oxygen sensors thro ugh IC fabrication processes proves to be a valuable tool in transforming macro -sized oxygen sensors into simple, reliable, and versatile sensors.

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44 The reduction of sensor size and thicknesses has two major drawbacks. First, the coefficient of thermal expa nsion, CTE, mismatch between the materials used in a cell can cause mechanical failure [38]. The CTE mismatch leads to cracking, delamination, and an inevitable short -circuiting of oxygen through the electrolyte. The second issue of thinning the electrol yte is deterioration of its ionic conductivity. Miyauchi claims the ionic conductivity of thin electrolytes decreases due to high grain boundary resistances and columnar or porous microstructures within the electrolyte material [62]. Gopel unsuccessfully t ried to determine the absolute oxygen sensor limitation, but concluded the feasibility of YSZ to maintain its resistive properties to all charge carriers, save oxygen ions, in an ever decreasing thickness (on the order of a few monolayers) is based on main taining a stable TPB [63]. While there are a few issues to decreasing the size of oxygen sensors that need to be resolved the promise of oxygen sensors as micro electrochemical devices inclu de lower operational temperature easy integration into electroni c systems, and the ability to develop intricate sensor designs. To overcome the issues with reducing oxygen sensor device sizes, a different fabrication process from that of macro oxygen sensors must be applied. A distinct methodology for constructing such micro oxygen sensors has been created by adapting the production techniques used in IC fabrication. Integrated Circuit Fabrication Techniques Integrated circuits are miniaturized adaptations of electrical circuits, generally consisting of networked transistors and conductive contacts manufactured on thin semiconducting substrates (e.g. Si Ge GaAs InP ). Depending on the desired physical characteristics semiconducting materials can be used in a number of applications including transistors, lasers, and photo detectors. The most widespread employment of a s emiconducting material is manifested in microprocessors having a dense integration of transistors.

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45 The feature sizes of transistors and conductive contacts have been significantly reduced over the past half century to maintain low production costs and increase performance and computing power. The advancement of microprocessors to the micron scale was made possible through a series of micro -fabrication techniques. These techniques involve patterning a wa fer (or substrate) with a particular microcircuit design, then depositing specific materials on to those defined regions and removing the excess material. Recently, extending microelectronic construction to feature sizes on the order of nanometers has been made possible through improvements in implementing these basic patterning, deposition, and etching/material removal processes Photolithography and Patterning To successfully fabricate integrated circuit patterns of the required length scales (formerly mi crometers and presently nanometers), effective techniques were developed and subsequently enhanced to achieve these dimensions. The most common means of defining and patterning miniaturized features is photolithography. Photolithography employs a material known as photoresist (PR) that develops by changing its chemical structure relative to the amount of light it is exposed to Use of a mask design overlaying a substrate spin-coated with photoresist allows the user to define specific areas where li ght can a nd cannot pass through. The PR material is then defined by these explicit regions The two types of photoresist, positive and negative, are both light -sensitive organic polymers that can be used. The region of positive PR material illuminated will have it s polymer chains broken. T he unexposed photoresist will be hardened and highly resistant to etchants a fter a heat treatment while the developed region will be susceptible and easily removed by etchants Negative PR works in the opposite fashion to that of positive PR Figures 1 -8 and 1 9 summarize the employment of positive and negative photoresist as a masking agent.

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46 If the mask is in contact or close proximity to the photoresist, the process is referred to as contact lithography, and the mask design cove rs the entire wafer. In projection lithography, the entire wafer is developed by exposing an individual region of the wafer to a pattern that is repeated by a stepper tool [64]. The se small areas are defined by a reticle. The design contained in a reticle or a series of reticles is a comprehensive grouping of transistors that compose a microchip. The microchip or grouping of transistors cut from the wafer with a dice saw is known as a die. Over the years projection lithography has become the most commonly utilized industrial technique due to the decreased frequency of wafer damage. Improvement in the field of photolithography has occurred in the tools and methodology used to develop the PR. The employment of optical lithography has allowed the semiconductor industry to maintain its pace of doubling the number of transistors on a chip approximately every two year s (commonly known as Moores Law) and decreasing the feature size [64]. One method of reducing feature size is to decrease the wavelength of light us ed in PR exposures. Although the wavelength of light has a physical limitation around 400 nm, innovative tactics were used to improve the minimum resolution. Currently, the photoresist spin coated onto the wafers is developed by a number of light sources ranging from visible light to the much shorter wavelengths of deep ultra violet light. The Rayleigh criterion where is the minimum resolution, is the wavelength, and, NA is the numerical aperture illustrates the importance of wavelength through its direct proportionality to resolution [64]. NA (1 5) This proportional correlation has spurned recent efforts to explore new light sources with smaller wavelengths. As smaller wavelengths are employed, the minimum resolution achievable

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47 will undoubtedly improve. However, new concerns about PR and substrate damage due to the increased energy that accompanies smaller wavelengths must be addressed. One popular solution to the wavelengt h limitation of visible light was the development of immersion lithography. Immersion lithography allows for a fluid, typically water, to be placed between the photoresist and lens that projects the mask design. The addition of a fluid with a higher index of refraction than air increase s the NA, or numerical aperture, giving a much smaller minimum resolution. In the early developmental stages of immersion lithography, defects could occur due to the occurrence of microbubbles and bubble related defects. Thes e shortcomings were later eliminated with engineered nozzle designs and fluid management strategies [65]. Solutions to these early difficulties permitted the success of immersion lithography that allowe d current studies by Owa et al., Prabhu and Lin, and S witkes and Rothschild to develop feature sizes ranging from 50 150 nm [6567]. In addition to using the visible light spectrum, some scientists have begun experimenting with ultraviolet radiation to develop smaller feature sizes. Bjorkholm was able to s uccessfully develop lines with features sizes of 80 nm using the naturally smaller wavelengths of extreme ultraviolet radiation [68]. Deep UV light for such applications is typically supplied by excimer lasers that operate through the combination of an ine rt (argon, nitrogen, etc.) and reactive (chlorine or fluorine) gas. Additional research has been conducted with other radiation sources with even smaller wavelengths, such as ele ctron beam, ion beam and x rays. U nfortunately, these methods are more costly to develop and operate [64, 68]. As the desired feature sizes become smaller, it is expected that the lithography methods of today will no longer be viable, necessitating a transformation into the field of nanolithography. Currently there are a number of methods being investigated, including that proposed by

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48 Anderson et al combining current photolithography steps with chemical self assembly techniques [69]. Other proposed methods are the use of atomic force microscopy (AFM) and scanning tunneling microsc opy (STM), which allow in some cases for the manipulation of individual atoms [70 71]. Studies performed by Austin et al using nano imprint lithography processes were able to achieve line widths of 5 nm having a pitch of 14 nm. Surveying the literatu re, it appears there are a number of candidates that will prove capable of maintaining Moores Law, despite the future feature size requirements. Considerable research is being conducted in the development of masks, photoresist material, and the methods in which the photoresist is developed. Not long ago, it was proposed optical lithography would be obsolete and unable to achieve the features sizes presently required, but a steady stream of advances have allowed optical lithography to remain the industry st andard. Drawing on this knowledge, researchers are confident they will be able to make the necessary advances to remain in stride with Moores Law. Material Deposition After a wafer has been prepared for the addition of supplemental materials, the focus o f the fabrication process turns to the techniques used to deposit a thin film of these materials. Deciding which tool or apparatus to employ primarily depends on the inherent qualities of the material to be deposited, the physical restrictions of the subst rate, and the required thin film quality. The most common materials deposited are either those of the conductive nature (to serve as electrical interconnects) or materials that exhibit dielectric behavior (to effectively insulate the conductive interconnec t materials). A number of the methodologies utilized in semiconductor fabrication will be summarized in the subsequent paragraphs. D ue to its ability to produce high purity materials chemical v ap or d eposition (CVD) has emerged as a robust semiconductor fa brication deposition tool. A full range of crystalline

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49 structures (single crystalline, poly -crystalline, and amorphous) are achievable, with the potential for epitaxial growth in some cases. CVD operates through the mixture of precursors that chemically react with each other to result in a specifically deposited material on a substrate. Most CVD applications in the semiconductor process contend with the application of tetra -ethoxysilane (TEOS), an excellent dielectric material that becomes a form of SiO2 o nce deposited on a substrate. Through the use of plasma e nhanced CVD (PECVD), Chang et al. was able to successfully deposit thick and impermeable SiO2 in high aspect ratio trenches [85]. Additionally Fujino et al. was able to grow a higher quality SiO2 film at high ozone concentrations that are more suitable for etching processes [86]. Another pro cess that is similar to CVD is atomic l ayer d eposition (ALD). ALD also uses precursors that are introduced to the substrate in gaseous form; however in ALD the precursors are introduced into to the system sequentially to result in a thin film deposited in monolayer increments. Films grown in this fashion are often highly conformal, pinhole -free and chemically bonded to the substrate [87]. The most applicable stud ies completed involve the development of diffusion barrier material delivery methods. ALD exhibits advantageous thin film qualities that allow tantatlum/tantalum nitride layers to serve as excellent copper diffusion barriers. Experiments performed by Black et al. and Van der Straten et al. have further demonstrated the successful application of a copper diffusion barrier material (tantalum/tantalum nitride) via atomic layer deposition [88, 89]. Another popular methodology is physical vapor deposition (PVD) which includes a variety of processes that deposit a thin film through the condensation of a vaporized material. Electron beam deposition (EBD) uses an electron beam powerful enough to sublimate the target material. Atoms ejected from the target materia l are scattered throughout the vessel housing and

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50 substrate where the ejected material adsorbs to the substrate surface [90]. Similar to EBD, pulsed laser deposition (PLD) uses cyclic laser pulses to vaporize the target material and, in some cases, can epi taxial ly grow oxides on dissimilar substrates for semiconductor and solid state electrochemical applications [91]. The most popular PVD technique, commonly referred to as sputtering, involves the acceleration of atmospherically inert (typically argon) ato ms into a target. The target consists of the material to be deposited and during the deposition process momentum from the inert atmospheric ions (created from the plasma environment sustained on the target surface via a magnetron) is transferred to the tar get ejecting target material atoms. Typically copper is sputtered onto patterned wafers to create interconnects in semiconductor applications. Multiple studies have shown sputtering is an efficient method for depositing metal contacts [92 93]. Additionally Tsai and Barnett and Will et al. have successfully sputtered thin films of YSZ onto various substrate materials. [94 95]. Electrochemical deposition (ECD) differs greatly from the above mentioned methods, but can also be used to deposit thin material la yers onto a conductive substrate. This type of deposition occurs in a liquid environment instead of a gaseous atmosphere where the material to be deposited has been dissolved into the liquid. ECD is an extremely popular process for depositing electrical vi as for semiconductor devices due its excellent gap -filling capability [96]. While the electroplating process, a form of ECD, must use a charged substrate, electroless deposition uses the reductive properties of an aqueous solution to deposit a material wit hout the need for an electrically biased substrate. Recent studies by Shacham Diamand et al. have extended the electroless copper deposition methods from critical dimensions larger than 10 m to sub -micron length scales [97].

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51 In summary a large number of material deposition methods are used in the semiconductor fabrication process. Often due to the intended outcome certain methodologies are chosen over another to produce better results respective to the materia l being deposited. The success of these various deposition schemes have allowed for the development and f abrication of systems outside the semiconductor realm. Material Removal The remaining major step of any microfabrication process involves the successful removal of extraneous material. The two key circumstances that require the attention of material removal are the etching of vias for subsequent material deposition and a successive step to a material deposition procedure where excess material is removed and occasionally planarized. Material is ofte n removed through either a chemical etching process conducted in a wet environment or through material bombardment in a dry environment. The etchants utilized in the etching process are chosen due to their selectivity for a particular material and the degr ee of isotropy (equal etching in all directions) that the etching process exhibits. The selectivity and isotropy for an etchant can vary over a range of materials and even different crystalline faces of a similar material. Figure 1 10 presents the basics o f an etchants material selectivity and isotropy. The most common form of etching is the wet etch process, in which samples are immersed in a chemically reactive fluid for a specific period of time. To ensure the etching process is not mass transfer limit ed the fluid or etching sample may be agitated in the solution. The etching process may also be performed at higher temperatures to accelerate the kinetics of the etchant to an appropriate rate. The most common wet etchant used to remove SiO2 is a buffered oxide etchant (BOE), created from a mixture of ammonium fluoride (NH4F) and hydrofluoric acid (HF) [98, 99].

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52 Due to the nature of the wet etching process, the resulting etch profile is typically isotropic. Often a more anisotropic profile is desired and can be achieved through a dry etch process. Dry etching uses the momentum of ions to dislodge the material to be removed. Ions (typically nitrogen or chlorine) assail the surface of the sample, removing material and can u nfortunately (and often) cause sur face damage. Because the ions are specified in a direction towards a particular sample, this process of material removal encourages anisotropic etching. Reactive ion etching (RIE) is a popular dry etch methodology that combines the physical material remova l via energy transfer from the bombarded ions with chemically reactive components to result in a dry etch process that minimizes the physical damage [100]. Despite the increased cost of dry etching, the process has become an integral part of the semiconduc tor fabrication process due to its anisotropic and small feature size capabilities [101, 102]. The wet and dry etch processes are the methods of choice when trying to etch vias into a material A fter a material is deposited however, another means of remov ing excess material must be employed. This is often achieved by a technique known as chemical mechanical polishing (CMP). The CMP process combines a physical (polishing pad) and chemical (abrasive chemically reactive slurry) process to remove the unwanted material. The slurry weakens the material, allowing the polishing pad to remove it and in effect planarize the surface. Numerous studies continue to improve upon the CMP process and its current drawbacks such as end -point detection, erosion (the removal of all materials below a line of planarization), and dishing (the removal of one particular material below a line of planarization) [103104]. Despite its drawbacks, this particular technique has found its niche in the semiconductor fabrication process remov ing excess copper material deposited into the interconnect trenches [104].

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53 Each method has unique characteristics that may be chosen depending on the desired application: wet etching is inexpensive, dry etching allows for anisotropy, and CMP results in pl anarization Each of these methods is well understood and available for a number of microfabrication applications. The combination of wafer patterning methods, material deposition techniques, and material removal practices results in a highly efficient mic ro -fabrication methodology. Experimental Approach The focus of this dissertation is the construction, validation, and implementation of a M icro -Electrochemical S olid S tate S ensor A rray MES3A, into an opaque liquid metal system to determine flo w profiles with high spatial resolution in constrained geometries. Sensors were operated by tracking packets of oxygen atoms traveling through a liquid metal m elt from one sensor to the next. M iniaturization and development of a sensor array based on the previously constructed macro scale systems by Hurst, Sears, Kao, Gupta, and Crunkleton was achieved [1, 2, 16, 72, 73]. An initial numerical analysis of a constrained geometry was performed and the results are presented in Chapter 3 with accompanying benchmark prob lems to validate the numerical method. Following the justification of the numerical method, a description of the expected concentration profiles subject to a number of boundary conditions to be used for diffusion coefficient measurements is also summarized in Chapter 3. Construction of the micro sensor array was achieved through a sequence of IC fabrication techniques The full process included the deposition of YSZ, Cu, Au, and TEOS proceeded by photolithography and followed by material removal methods. T hree different sensor spacing designs were fabricated to evaluate the importance of the geometric aspect ratio in a constrained

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54 system. A comprehensive review and discussion of the fabrication process is outlined in Chapter 4 The constructed sensor array was subsequently tested and evaluated through a number of experiments measuring the open cell potential in liquid tin melts. These results were determi ned over a range of temperature and operational conditions to determine the robustness of the newly assem bled device. Chapter 5 discusses the attempted experiments and their results and concludes with suggested modifications to the MES3A design. Figure 1 1 V ertical Bridgman c rystal g rowth Charge Adiabatic Zone Heat Zone Cool Zone Adiabatic Zone Heat Zone Cool Zo ne Seed

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55 Figure 1 2 Float zone crystal growth Single Crystalline Material Polycrystalline Material Seed Molten Material Heat Source Heat Source

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56 Figure 1 3. Czochralsk i crystal growth method Molten Charge Single Crystalline Mat erial Heated Crucible Seed Rotating Head

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57 Mole Fraction of PbTe 0.0 0.2 0.4 0.6 0.8 1.0 Temperature ( oC ) 800 820 840 860 880 900 920 940 CLCSLIQUID SOLID Figure 1 4. Phase diagram of the pseudobinary mixture PbxSn1xTe [1]

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58 Normalized Crystal Length, f 0.0 0.2 0.4 0.6 0.8 1.0 C/C o 0.0 0.5 1.0 1.5 2.0 Well Mixed Melt Condition Diffusion Controlled Mass Transfer Condition Figure 1 5 Characteristic axial composition of binary solutions grown under diffusion controlled and well mixed conditions (for a distribution coefficient of 0.7 and an initial melt composition of Co) [1]

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59 Figure 1 6 Final bubble configuration for A) top to bo ttom melting and B) bottom to top melting of a solder bump

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60 Figure 1 7. Rudimentary oxygen s ensor Electrolyte Porous Cathode Porous Anode 2O 2 + 4e O 2 O 2 2O 2 + 4e O 2 O 2 O 2 V OC + Region of higher oxygen chemical potential Region of lower oxygen chemical potential Porous Cath ode e e O O O Triple Phase Boundary Region O 2 Electrolyte Diatomic Oxygen Atomic Oxygen

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61 Figure 1 8. C ommon p ositive p hotoresist u sage Photoresist Mask Light Source Photoresist 1) Coat with photoresist 2) Exposure (bonds broken) 3) Remove exposed photoresist 4) Etc h silicon wafer 5) Remove remaining resist Silicon Wafer Silicon Wafer Silicon Wafer Silicon Wafer Silicon Wafer

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62 Figure 1 9. C ommon n egativ e p hotoresist u sage Photoresist Mask Light Source Photoresist 1) Coat with photoresist 5) Remove remaining resist 2) Exposure (bonds cross linked) 3) Remove exposed photoresist 4) Etch silicon wafer Silicon Wafer Silicon Wafer Silicon Wafer Silicon Wafer Silicon Wafer

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63 Figure 1 10. Etchants material s el ectivity and i sotropy Material 2 Photoresist Material 1 Material 1 Material 1 Material 1 ETCHANT SELECTIVITY 1) Excellent etchant selectivity 2) Poor etchant s electivity ETCHANT ISOTROPY 1) Isotropic Etch 2) Anisotropic Etch

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64 CHAPTER 2 FUNDAMENTALS OF SOLID STATE ELECTROCHEMISTRY AND TRANSPORT PHENOMENA Introduction T he utilization of a solid state electrolyte at the mic ron -scale for supplying, sensing, and removing oxygen from a liquid metal system is the essence of the proposed flow visualization technique presented in this dissertation Specifically, the solid st ate electrolyte material yttria stabilized zirconia (YSZ), which exhibits (at elevated temperatures) high oxygen ion conductivity over a wide range of oxygen partial pressures is used in this study Fortunately YSZ is rigid and does not react with the material of interest, liquid tin. These characteristics make YSZ an excellent electrolyte candidate and the backbone of the MES3A device This chapter outlines the fundamentals of electrochemical measurements and the basis of the anticipated fluid mechanics for the designed experiments. A discussion of the general theory and governing equations of electrochemical measurements is accompanied by a description of potential sources of measurement error. In regards to the various types of convective flows (e.g. natural and thermocapillary) to be associated with experimen ts are incorporated into the equations of change. Thus, a fundamental basis of electrochemical measurements and fluid mechanics is formulated Principles of MES3A Operation The constructed device will operate in two different modes: titration (electrolyti c) and detection (galvanic) In the titration mode the micro -sensors will effectively transport oxygen into or out of a system via an applied voltage or current. The titration (electrolytic) mode will allow the operator to control the initial concentratio n of oxygen and impose boundary conditions on the system. Operating the micro -sensors in the detection (galvanic) mode allows for in situ monitoring of the oxygen concentration at the surface of the electrolyte via a measured voltage

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65 The two different mod es can easily be switched In one mode, titration supplies a plug of oxygen that is used as a tracer T he detection mode tracks the movements of the oxygen plug, and a second use of the titration mode will remove the plug of oxygen from the system up on completion of the experiment allowing the liquid metal system to return to its initial condition. Maintaining a low concentration of oxygen in the system is accomplished by long time applications of an electrical potential to the electrochemical cells. A low level of oxygen ensures the tracer concentration does not interfere with the fluid and prevents formation of oxide phases. Due to the locally high oxygen concentration gradient between the plug of oxygen and the oxygen deficient metal melt a signif icant diffusive driving force will effectively disperse the plug Thus, the numerical analysis of a traversing plug of oxygen over a range of fluid velocities must include mass diffusivity. Needless to state, when the convective velocity is less than t he diffusion velocity the flow visualization experiments cannot be performed. Solid State Electrochemistry Basics In any typical electrochemical system there are two nodes (an anode and cathode) separated by an electrolyte. Ideally these nodes conduct el ectrons and serve as a source or sink for electrons generated or consumed via electrochemical reactions at the nodal interface. The electrolyte material is preferably resis tive to electron and hole transport (to avoid short circuiting of the system ) and pr eferentially conductive to ion transport shared amongst both nodal electrochemical reactions. E lectrochemistry can then be defined as the exchange of electrical and chemical energy in a system where an electrochemical reaction occurs. There are two types of electrochemical reactions used in electrochemistry: oxidation and reduction. These two reactions are respectively summarized in Equation (2 -1) and Equation (2 2) where, Red is the reduced material, Ox is the oxidized material, and, n*, is the stoich iometric moles of electrons.

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66 Red Ox + n*e(2 1) Ox + n*eRed (2 2) The location of the oxidation reaction determines the anode and the reduction reaction specifies the cathode. Nodes are described in this manner so that the respective reaction locations can be referred to universally and regardless of the operating cell mode (i.e. galvanic and electrolytic). Figure 2 1 depicts the two main types (or operational modes) of electrochemical cells that are traditionally employed in electrochemistry, as well as in this study, and illustrates the importance of the nodal nomenclature. A galvanic cell is an electrochemical cell that effectively converts chemical energy into electrical energy. The cathodic (or reduction ) reaction at the cathode of a galvanic cell consumes electrons and thus tak es on a more positive potential than the anode. This increase in positive potential is due to the inability for a sufficient number of electrons to be transferred from the anode to the cathode as a result of the large impedance between the nodes Similarly the anode becomes more negative because a sufficient amount of the generated electrons are unable to cross the resistive threshold, resulting in an accumulation of charge. Often an infinite resistance (open circuit) is placed across the two nodes of a galvanic cell for thermodynamic measurements. These measurements often include an open cell potential that correlate s to the maximum amount of potential energy in the system. The electrolytic cell, on the other hand, has a power source placed between the electrical connections of the two nodes providing a source of electrical energy to drive nodal electrochemical reactions. Thus, an electrolytic cell is the opposite of a galvanic cell because it transforms electrical energy into chemical energy. Due to the application of a specific potential source there can be an increase or decrease in the charge at a particular node controlled by the

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67 power source. For instance, at the cathode in Figure 2 1, there are a sufficient number of electrons supplied by the power source to maintain the cathodes more negative potential than the anode despite the cathodic reactions consumption of electrons. The same argument can be made for the positive potential obtained in the anode of an electrolytic cell. Figure 2 2 further depicts the exchange of ions and the ir effects on the electrical and chemical potential of the electrochemical system to be used in the subsequent experiments. The reactions occurring at each node have a corresponding oxygen chemical potential, j, eff ective ly separated by the electrolyte. A brief overview of the operational basis is given with a review of the thermodynamic derivations in the next section. In this particular setup, the chemical potential is greater in the reference electrode than the wo rking electrode. As a side note electrodes can have additional monikers (e.g. CE, WE, RE) supplementing the anode or cathode with a supplementary description CE signifies a counter electrode, in which a current is passed or voltage is applied instead of the WE ( working electrode ) to preserve the integrity of the electrochemical system. The significance of the WE and RE (reference electrode) will be covered in subsequent paragraphs. In galvanic mode the chemical potential gradient between the reference and working electrode drives oxygen from one node to th e other via the YSZ in an attempt to equilibrate the oxygen chemical potentials of each node To accomplish this, oxygen ions are liberated from the RE electrode and captured at the WE where there is respectively, the consumption and production of electrons. The transfer of electrons establishes an electrical potential difference E across the electrolyte. Since oxygen ions are charged, this electrical potential difference counteracts the chemical p otential At equilibrium the chemical potential is just balanced by the electrostatic potential to yield a constant electrochemical potential across the electrolyte. The

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68 increase of a negative electrical charge at a node impedes transport of oxygen ions to ward th e node of similar charge. The reverse is true for a node with increasing positive electrical charge At steady -state equilibrium the time -independent electrical potential difference is defined as an electrostatic potential difference, The measure of equilibrium between the chemical and electrical potential is observed through the electrochemical potential ( F z a RTj j j jln ~ ) for each component of the nodal reactions. Intuitively, the cell is said to be in equilibrium when the nodal electrochemical reactions are in equilibrium and the electrochemical potential of the charged species transferred across the electrolyte is constant across the cell. At equilibrium the electrostatic potential difference of oxygen between the two elec trodes is proportional to the measured electrostatic potential difference. The activity of oxygen in the working electrode can then be computed from the known activity of oxygen in the reference electrode. T he chemical potential of oxygen in the reference electrode is constant and presumably known since the cell is in equilibrium. For example, the two phase Cu/Cu2O reference mixture, at constant temperature will maintain a constant oxygen chemical potential at the electrode electrolyte interface as long as the mixture remains two -phased and the rate of equilibration is faster than the oxidation or reduction rate The assumption that the potential is constant at the RE is the basis for a constant or reference electrical potential. F or a given temperature the reference electrode serves as a basis for measuring electrical potentials in the WE by maintaining a constant electrical potential. Unless the oxygen chemical potential at an electrode is invariant (e.g., two -phase Cu/Cu2O reference mixture at constant te mperature) the chemical potential will change with perturbations of the oxygen content. As previously stated, for a particular oxygen activity there is an explicit

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69 chemical potential at the electrode -electrolyte surface corresponding to a specific electric al potential at a constant t emperature. This new potential and oxygen activity is computed by measuring the new WE electrical potential relative to the known RE electrical potential. In this work, a reference electrode and an applied or measured voltage is used to establish an oxygen boundary condition or sense oxygen activity. It is assumed that the rate of local equilibration at both electrodes is fast relative to the transport rates caused by convection and diffusion. Thus, a more detailed description of the thermodynamics is given in the next section. Thermodynamic Principles The previous description of the relationship between chemical and electrical potential is captured by the Nernst equation. There are a number of methods that can be used to deri ve the Nernst equation and important concepts can be realized through these various methodologies. A formal representation of the electrochemical system used in this work is given in Equation ( 2 3 ) where define different regions of the electrochemical cell where [O]Sn denotes a liquid alloy of oxygen dissolved in tin. ) ( ), ( || ) ( || ) ( ), (2l Sn l O s YSZ s O Cu s CuSn (2 3) The nodal electrochemical react ion that takes place at the electrode electrolyte interface and the electrode electrolyte interface, respectively, are summarized below and yield the overall reaction given in Equation (2 6) 2 22 2 O Cu e O Cu (2 4) e O O SnSn22 (2 5) SnO Cu Sn O Cu 22 (2 6)

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70 Again t he [O]Sn term represents oxygen dissolved in liquid tin Of course, when the concentration reaches the temperature dependent saturation limit, a second phase, SnO2, forms. At this point the [O]Sn becomes constant at a fixed temperature and results in an open circuit potential. Beginning with basic thermodynamic fundamentals, a physical conception of the reversible system can be achieved by relating the internal energy, U to the work, W done by the system via a combination of the first two laws of thermodynamics. dU = d(S) dW (2 7) The dW term is equivalent to the work done by the change in pressure, p or volume, V as well as any additional work done by the system, W*, that is not related to the pV work. dW = d(pV) + dW* (2 8) Additionally the thermodynamic relationship between the Gibbs energy, G a nd the internal ene rgy has been given in Equation ( 2 9 ). dG = dU + d(pV) d(TS) (2 9) Combining Equations {2 7} {2 9} and assuming the system is operating und er constant temperature and pressure conditions the Gibbs energy can be related to the maximum amount of non -expansion related work performed by the specified system. For the Gibbs energy difference there is a resulting maximum amount of work, furt her cla rified in Equation (2 11) dG = -dW* max (2 10) RxnG = W* max (2 11) Remembering that electrolytic electrochemical cells operate on the basis of moving charged particles (oxygen ions) in the system through an applied electrical potential, it is clear that the work, W*, done by the system is the amount of electrical work it takes to move the

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71 charged particles across the electrolyte and to drive the respective nodal reactions to their respective extents. Conversely in a galvanic cell the maximum work done by the system is the work done by the chem ical reactions to transport oxygen ions across the electrolyte to result in a specific electrical potential. The relationship between work and the electrical energy is realized through a potential difference, often referred to as an EMF (or electromotive force ) that moves the charged particle. From a historical standpoint, an electrical potential difference that creates a driving force (resulting from a particular process in this case a galvanic reaction that separates charge ) is referred to as the electromotive force, EMF; while an applied electrical potential is referred to simply as an electrical potential. Understanding that the electrical charge of a particle, q can be represented by nF the work, W*, can be related to the electrical potential. W* = n*F (2 12) Inserting Equation (212) into Equation (2 11) gives a relationship between the change in the molar Gibbs energy and the electrical work done by the system. nF GRxn (2 13) Previous discussions illustrate the relationship of energy conversion between electrical and chemical energy The relationship encompassing the chemical e nergy in the electrochemical system can be established through the molar Gibbs energy of the reaction containing the standard state molar Gibbs energy of the reaction, RxnG and the reaction quotient, ln RT G GRxn Rxn (2 14) F urther examination of Equation (2 14) reveals the Gibbs energy change of the reaction is equal to the standard state Gibbs energ y change of the reaction when the react ion is in equilibrium (that is = 1 ). The reaction quotient is the relationship between the activities of the

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72 products divided by the activity of the reactants and serves as a quantitative measure for the extent of the reaction. Sn O Cu O Cua a a aSn 22 (2 15) Assuming the activity of any pure substance is unity; the reaction quotient is quickly simplified and is seen only to depend upon the activity of the diluted oxygen in the liquid tin. For low concentrations a further simplification of the activity can be made through the use of Henrys and Raoults law that approximates the activity of a species to be equal to the concentration of that diluted spec ies. These assumptions will be used later in Equation (2 18). Approaching the Gibbs energy from a different perspective a thermodynamic relationship between the Gibbs free energy of the reaction, the molar enthalpy, H the molar entrop y, S and temperature can be written Rxn Rxn RxnS T H G (2 16) Likewise, a similar relationship can be made between the standard state G ibbs energy change of the reaction and the standard state enthalpy and entropy change of the reaction. Rxn Rxn RxnS T H G (2 17) These reference states can b e based on the temperature and pressure of interest and the pure components of the reactions. An Ellingham diagram is a convenient tool to use when comparing the stability of materials in a common oxidizing/reducing ambient condition. For this application, t he Ellingham diagram can be quite useful for determining the thermodynamic direction of oxygen transport, oxygen partial pressures at a specific temperature, and the potential reactions between the materials used to construct MES3A. The Ellingham diagram in Figure 2 3 summarizes the potential oxidation reactions that include the specific materials of

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73 constructing the sensor array. This diagram also includes lines of constant 2OP at equilibrium. The stoichiometry of the given oxidation re actions are based on 1 mol O2 so that all reactions have the same basis. The dashed lines in this figure are lines of constant 2OP and thus the equilibrium 2OP for a particular oxidation reaction at a specific temperatur e is given by their interaction. Using Henrys law the molar Gibbs energy can now be defined as a function of the chemical reaction taking place in the system where the saturation concentration of oxygen in tin is used as the reference concentration sat O Rxn RxnC C RT G GSnln (2 18) The following electrochemical equation can be derived by considering the relationship between the Gibbs energy and the respective electrical energy of the sy stem as shown in Equation (2 13) Sat OC C RT nF nFsn] [ln (2 19) Rearranging Equation ( 2 19) gives the most common form of the Nernst equation that accurately relates the electrical energy in the system to that of the chemical energy. Sat OC C nF RTSnln (2 20) The chemical potential energy of each reaction component can be ca lculated using Equation (2 21) and the overall reaction can be summarized by Equation (2 -22) employing the same simplification and standard states used in the above derivations. j j ja RT ln (2 21)

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74 SnO Rxn Rxna RT ln (2 22) Noting the standard state molar Gibbs energy change is equal to the standard sta te chemical potential of the overall reaction, Rxn, a correlation between the chemical and electrical energy can be made. Following the realization of the standard state chemical potentials thermodynamic equality ; the de rived relationship in Equation (2 23) is rather straightforward. RxnnF (2 23) The evolution of Equation ( 2 23) indirectly explains the equivalence of the electrochemical potential across the body of the ce ll. This is realized by noting the respective nodal electrochemical reactions taking place must be in electrochemical equilibrium as show n in Equations (2 24) and (2 25) 2 2~ ~ 2 ~ 2 ~O Cu e O Cu (2 24) e O O SnSn~ 2 ~ ~ ~2 (2 25) The electrochemical potential for each species, j~ is defined by Equation (2 26) where zj is the charge number of species j. F z a RTj j j jln ~ (2 26) Additional simplifications and assumptions conveniently outlined by Bard and Faulkner are ne cessary for complete definition of the system [105]. 1. For an uncharged species j j ~ 2. For any pure phase with unit activity j j ~ 3. For electrons in a metal 1 z the activity coefficient 1 since the electron concentration is large relative to the change from the electrochemical reactions;

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75 thus Fe e~ 4. For equilibrium of species j between the phases (regions) of the cell j j~ ~ The electr ochemical potential of the oxygen ions in the specific electrochemical systems of interest (Equations (2 27) and (2 28)) can be determined at each electrode according to: e O Cu Cu O~ 2 ~ ~ 2 ~2 2 (RE) (2 27) Sn e O OSn~ ~ 2 ~ ~2 (WE) (2 28) Since oxygen ions are free to transport across the YSZ and Equation (2 29) can now be derived assuming the oxygen electrochemical potential is equivalent across the cell 2 2 2 2~ ~ ~ ~O O O O (2 29) Then combining Equations (2 27) through (2 39) the following relations hip can be derived. Sn e O e O Cu CuSn~ ~ 2 ~ ~ 2 ~ ~ 22 (2 30) Employing Equation ( 2 26) and grouping the charged terms on the left hand side of the equation with the thermodynamic terms on the right hand sided one arrives as the following equation. Sn O Cu O Cu Sn O Cu O Cua a a a RT FSn Sn 2 22ln 2 2 (2 31) The standard state of oxygen dissolved in liquid tin does not have a value unless it has been replaced by SnO2 in the chemical reaction. The inclusion of the st andard states represents the chemical potential of the pure components for a chosen temperature and pressure of interest. The same assumption used in the previous discussion of the activities are used again in this case where the pure substances are assume d to be unity and the solubility of oxygen in liquid tin is

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76 small enough to follow Henrys law. The saturation concentration for the temperature and pressure of interest is used as a reference concentration. *E is used as the measured e lectrical potential for a corresponding concentration ] [SnOC Sat O RxnC C RT F E FSn* *ln 2 2 (2 32) A reference concentration has been employed through the derivations as a basis for all concentrat ions. The reaction product SnO2 forms as a pure second phase at saturation and the solubility of oxygen in Sn is a function of only temperature. Ramanarayanan and Rapp experimentally determined the saturation oxygen mol fraction, sat O in liquid tin from 750 to 950 oC where R has units of cal mol1 K1 [136]. RTsat O000 30 exp 10 3.13 (2 3 3) Figure 2 4 shows the temperature dependence of the saturation concentra tion noting that Equation (2 33) was extrapolated to lower temperatures using an average tin density of 6.7 g/cm3 [1]. Figure 2 4 is coupled with the saturation potentials calculated from the Gibbs energies derived from Figure 2 3. At this point of the discussion an assumption that is often overlooked in the thermodynamic derivations of the Nernst equation must be addressed. The derivation assumes the electrolyte effectively transports the oxygen ions from one node to another. Electrolyte effectiveness can be measured through the ionic transference number, tion that is the ratio of the ionic conductivity to the conductivity of ions, holes, and electrons. h e ion ion iont (2 34)

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77 When th is value is equal to or greater than 0.99 the electrolyte is considered to be suitable for transferring only ions. The Wagner equation incorporates the ionic transference number into the chemical and electrical energy relationship [106]. 2 2 2 O OO iond t zF RT (2 3 5) A simple integration of the Wagner equation will result in a variation of the Nernst e quation that incorporat es the ionic transference number. Taking the ionic transference number to be unity reduce s to Equation (2 35) to Equation (222) The Wagner equation is significant because it accounts for conductivity (e.g., hole or electron) from charged species other than ionic conduction. Yttria Stabilized Zirconia It is apparent from the Wagner equation that selection of an electrolyte with 99 0 iont is important. In this particular system yttria stabilized zirconia was chosen due to its high oxygen cond uctivity, low conductivity of electrons and holes, low solid state mass diffusivity of natural atomic species and good material stability in oxidizing and reducing environments. High ionic conductivity is made possible by doping a sufficient amount of ytt ria (Y2O3) into zirconia (ZrO2). This process stabilizes the cubic zirconia crystal structure and generates oxygen vacancies within the lattice structure subsequently affecting the conductivity of oxygen ions Numerous studies have concluded a doping level of 8 mol% Y2O3 exhibits the best overall characteristics, particularly in regards to the ionic conductivity [107 109]. Previous studies have shown that oxides having a cubic fluorite structure exhibit high ionic conductivity [ 110, 111, 116]. P ure zirconi a however, has a monoclinic structure at room temperature and converts to a stable cubic fluorite structure at approximately 2300 oC, well outside of the operational temperature range. Thus a dopant is added to lower the thermal energy

PAGE 78

78 necessary to stabi lize the cubic fluorite structure of zirconia. In 1951 Duwez et al experimented with yttrium as a dopant and developed a phase diagram for the system [112]. In the following years there was disagreement on the reported structures and phase changes at low dopant levels (< 20 mol% Y2O3) below 2500 oC, resulting in the publishing of dissimilar phase diagrams among many researchers. The c onflicting reports in the literatur e are likely due to the presence of meta -stable structures. Yashima et al attributes th e confusion to slow cation -diffusion mechanism that lead to invalid conclusions when examining these meta -stable structures [113]. A number of papers have concluded there indeed a formation and transformation of meta -stable structures within the phase diagram region [113116]. Combining the analysis by Yashima et al and Fevre et al (recognizing YO1.5 is stoichiometrically equivalent to Y2O3 as follows: x [YO1.5] = 2x/(1+x) [Y2O3]) a reasonable phase diagram (containing the meta -stable tetragonal phases) can be constructed in Figure 2 5. The phase diagram of the ZrO2Y2O3 system reveals a number of phases and compounds that can form depending on the Y2O3 content and temperature. The phase diagram in F igure 2 5 shows the transformation zirconium undertakes as Y2O3 is introduced at room temperature. The material begins in the monoclinic phase with no dopant, proceeds through the tetragonal region, and arrives in the cubic section at approximately 12 mol% Y2O3. In the cubic stabilized region the material tak es on a cation face centered cubic (FCC) sublattice consisting mainly of zirconium with some yttrium atoms replacing the zirconium atoms in the sublattice; w hile the anion sublattice takes on a simple cubic lattice structure made up of oxygen atoms [116]. The main region of interest is that surrounding 8 mol% Y2O3, where the cubic structure of the yttria zirconia material is often reported as stabilized. Interestingly 8 mol% YSZ falls in the meta -

PAGE 79

79 stable tetragonal region and requires an increase in temper ature to gain the desired cubic structure. Yashimas notation (m -monoclinic, t and t -meta -stable tetragonal, and cubic) used in Figure 2 5 is further described by Figure 2 6 where the dark circles are the cations and the light circles are anions The c rystal structure of the t meta -stable tetragonal phase maintains the same geometry as the cubic structure except for displacement of oxygen atoms as shown in the figure This t meta -stable phase begins at approximately 8 mol% YSZ (at room temperature) and is often claimed or confused in other works as the onset of the cubic crystal structure. It is noted that the t phase exhibits a stabilized FCC fluorite crystal structure on the cation sub lattice with the anion sub lattice maintaining a simple cub ic structure that undergoes slight restructuring (through movement of the oxygen atoms) with the further addition of yttria. Besides stabilizing zirconia, the addition of yttria also increases the concentration of oxygen vacancies by doping an aliovalent cation yttrium (Y3+) into a zirconium (Zr4+) based structure. For every two yttrium atoms injected into the cation sub lattice one oxygen vacancy in the anion sub lattice is created in order for the compound to retain charge neutrality The ambient pres sure of oxygen can also affect the number of oxygen vacancies. The reaction s governing the defect chemistry interaction are illustrated in Equation { 2 3 6} and {2 37}, where O* is oxygen sitting in an anion lattice site, 2 OV is an oxygen vacancy, h is an electronic hole, and eis a free electron. High oxygen partial pressure leads to hole conduction via the reaction in Equation (2 36) h O V g OO2 ) ( 2 1* 2 2 (2 3 6) In the case of low oxygen ambient pressure additional oxygen vacancies can be formed to produce electron conductivity ( 2 3 7)

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80 e V g O OO2 ) ( 2 12 2 (2 3 7) Oxygen ion transport in the YSZ material can occur not only through oxygen vacancies but along grain boundaries as well Unfortunately, it has been well documented that ionic conductivity along grain boundaries in thin films re duce the ionic conductance by a factor of 100 compared to the bulk conductivity, effectively reducing the total ionic conductivity of the material [117]. This drastic reduction of the ionic conductivity is attributed to space charge regions and/or dopant s egregation along the grain boundary that traps mobile oxygen vacancies and encourage s the buildup of yttrium along the grain boundary [118]. Fisher and Matsubara found through simulations tilt grain boundaries typically reduce the ionic conductivity by t rapping oxygen vacancies while twist grain boundaries encourage rapid diffusion of oxygen vacancies [118]. For thin film s of YS Z obtaining a high order of crystallinity while minimizing tilt grain boundaries will be crucial to acquiring suitable ionic con ductivity. The total conductivity of the YSZ material can be expressed as a function of the electrical carrier concentration where, is the conductivity, q is the charge, m is the mobility, n is concentration of the conduction band electrons, p is the concentration of valence band holes, and, CD, is the concentration of the ionic defects. j h h e e D D D j j j totm pq m nq m q C m q C (2 38) Generally the mobility of electrons and holes is much greater than that of ionic defects so a substantial number of defects must be present in order for the material to be dominated by ionic conductivity [16]. The relative importance of ionic conductivity to the total conductivity is represented through the ionic transference number tot ion iont (2 39)

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81 As previously stated, when the ionic transference number is 0.99, the electrolyte is operating within the electrolytic domain defined by a temperature and oxygen partial pressure The electron, hole, and ionic condu ctivity values must be determined over a range of temperature and oxygen pressure to determine the electrolytic region. A study by Kleitz et al reported the electron and hole conductivities in 9 mol% YSZ depend on temperature and oxygen partial pressure g iven below where, k is the Boltzmann constant in eV K1 [119]. kT pO e72 3 exp 10 5 54 1 52 (2 4 0) kT pO h5 1 exp 144 12 (2 4 1) The ionic conductivity of YSZ has also been studied by Strickler and Carlson and Schouler et al both reporting similar results [120121]. Strickler and Carlson define the ionic conductivity in terms of the temperature as follows (notably the ionic conductivity is not pressure dependent within the electrolytic domain) [120]. kTion78 0 exp 115 (2 4 2) Revisiti ng the defect chemistry shown in Equations (2 38) and (2 39) for low partial oxygen pressures electron conductivity dominates over hole conductivity due to the production of electrons. With the continual decrease of pressure it is clear the YSZ material w ill become increasingly n type At a very low oxygen partial pressure the contribution of hole conduction is so small it can be negated from the overall conductivity calculation. The opposite case is true for a high oxygen partial pressure where the condu ctivity of the electrons is negligible and the YSZ becomes an increasingly p type material with increasing oxygen partial pressure. T o find the upper and lower limit s of the oxygen partial pressure that will allow for electrons or holes to

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82 reduce the ionic transference number below the operational value of 0.99, Equations ( 2 4 0) (2 4 2) mus t be substituted into Equation ( 2 39) while setting the ionic transference number to 0.99. Simplification of the substitution yields the following equations that give the respective high and low partial pressure of oxygen where the ionic transference number remains greater than or equal to 0.99. 956 9 88 2 ln2 kT ph O (2 4 3 ) kT pe O76 11 27 52 ln2 (2 4 4) Examining Equations ( 2 4 3) and ( 2 4 4), it is clear the ionic conductivity will be greater than or equal to 99% of the total conductivity as long as the partial pressure of oxygen does not exceed the pressure defined in Equation ( 2 4 3) and does not fall below the lower pres sure limit defined in Equation ( 2 4 4) The r egion between these two lines is known as the electrolytic domain as shown below in Figure 2 7 The ionic conductivity increases with temperature due to the necessi ty of thermal energy to move vacancies across the electrolyte, and thus oxygen ions Examination of Figure 2 8 however, reveals that as the temperature in creases the 2OP range of the examined electro lytic region decreases due to the higher activation energy for creating holes or electrons relative to an oxygen vacancy. On the lower end of the temperature scale the electrolytic region is l arge, but oxygen ion mobility decreases rendering this range impractical. For bulk YSZ a temperature of approximately 600 oC is needed to supply sufficient thermal energy to the system. Interestingly it has been proposed and confirmed by many researchers t hat using a thin film of YSZ the transport length can be lowered and in turn the required operational temperature reduced [122124]. It is

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83 expected that a thin film will increase the effectiveness of an electrolyte material employed as a sensor. Following the determination of a suitable electrolytic domain, it is important to ensure the oxygen partial pressure at the electr odes is within the electrolytic domain Figure 2 8 pl ots the oxygen partial pressure for all the metal oxides of the materials employed in the experiments explained in these studies Fortunately the ele ctrolytic domain of 9 mol% YSZ, which likely extend s to 8 mol% YSZ is large and encompas ses the oxygen partial pressure range of the metal oxide electrodes. The partial pressure of oxygen in the silicon dioxide, however, is only within the electrolytic range below approximately 800 oC. This is not considered an issue because the silicon dioxide is considered stable and saturated with oxygen. Thus oxygen traveling form high to low oxygen pa rtial pressure will not be affected by the silicon dioxide, transporting oxygen between the copper/copper oxide and tin/tin oxide mixtures because the silicon dioxide has already reached its solubility limit. Additionally it is assumed the effect of the pa rtial pressure of oxygen from the silicon dioxide does not affect the bulk of the YSZ which is also exposed to those partial pressures in the tin/tin oxide and copper/copper oxide compounds. The equilibrium partial pressures of oxygen in the material oxide s were used as a reference because they represent the maximum solubility of oxygen in the oxides. SnO2 was used as the reference oxide (for determination of CSat) because it was more stable than SnO. Electrolytic Reaction Mechanisms Now that the method of oxygen transport across the electrolyte has been established it is important to understand the mechanisms by whic h oxygen ions enter and exit the electrolyte. As schematically shown in Figure 29, O2 and eare transported to the surface, where three diff erent events can take place across the YSZ. Two o xygen atoms can either 1) immediately incorporate

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84 into the electrolyte at the TPB (triple phase boundary), 2) adsorb on the nodal surface and diffuse along the surface of the node until they r each the TPB, o r 3) adsorb on the nodal surface and diffuse through the nodal bulk material directly to the electrode/electrolyte interface. The first two cases typically occur in any electrochemical system where the species to be transported across the electrolyte does not have to diffuse through the bulk nodal material to reach the electrode/electrolyte interface. For the work completed in this dissertation it is expected that the third case relating to an internal diffusion mechanism is the dominant electrolytic reacti on mechanism for the working electrode (Sn(l)/[O]Sn(l)) and possibly the reference electrode (Cu(s)/Cu2O(s)). This is due to the kinetics of the nodal reactions occurring much faster than the oxygen diffuses through the liquid tin melt. The three reaction mechanisms outlined by Kleitz and Petitbon have been illustrated by Horita et al. and shown in Figure 2 9 [125126]. A n overpotential associated with the required energy to drive the TPB reaction mechanisms is shown in this figure. Donaghey and Pong sugges t additional reaction mechanisms, but reason for their metal -metal oxide system (where a dense node completely covers the electrolyte) the only feasible mechanism is ionic diffusion through the electrode [135]. A review of literature will reveal numerous e xperimental and theoretical numerical analyses of the reaction mechanisms at the TPB. [125-130]. Multiple authors have recognized the third reaction mechanism involve s diffusi on through the nodal bulk material which Kleitz later coined an Internal Diffu sion (ID) node [125, 131132]. Kleitz and Petitibon examined all three reaction mechanisms illustrated in Figure 2 9 and concluded that while ionic diffusion through the electrode can be quite slow the electrode/electrolyte reaction occurs faster in the internal diffusion node than it does for the other two mechanisms [125]. Many researchers have observed the ID node through its typical

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85 impedance response that results in a space limited diffusion curve denoted by a Warburg impedance curve [125, 127, 1331 34]. The question still remains in the scientific community, however, whether the ID reaction mechanism is a sub -case of the TPB reaction mechanism or not Past work using the Cu/Cu2O liquid tin system operated successfully assuming the rate limiting step of the ID node reaction is the diffusion of ions through the electrode due to the low mass diffusivity of oxygen in liquid tin [1, 2] Solid State Electrochemical Measurements Voltage, current, and impedance measurements can be measured with an electroch emical system and then analyzed to better understand the system behavior. Equilibrium voltage measurements correspond to electrochemical potential differences (and under certain circumstances concentrations of specific species ), while current measurements can be related to the movement of that species. These types of measurements are often employed in the thermodynamic and kinetic measurements discussed in the previous section. Impedan ce measurements often assist in understanding the limitations of a system by either revealing an electronic or ionic resistance of a material or illuminating the rate limiting step of a species tran s port or reaction mechanism. All of these types of measurements were employed in this dissertation Potentiometric Measurements T he most common type of measurements w as time -dependent potentiometric values that could be related to the diffusivity of oxygen. Bri e fly, the oxygen concentration in liquid tin contained in a cylindrical geometry with solid electrolytes capping the top and bottom was first equilibrated to give a uniform concentration across the melt The oxygen was then depleted from the top of the liquid tin by applying a large potential (~1 to 1.2 V) across the upper electrochemical cell. The measured EMF of the oxygen se nsor (i.e., bottom of the

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86 electrochemical cell) w as used to determine the oxygen diffusi on coefficient in liquid tin Assuming equilibration of the electrodes was rapid relative to oxygen diffusion in Sn, the voltage applied or measured corresponds to a sp ecific oxygen concentration in the liquid t in at the melt/electrolyte interface Measuring the open circuit potential of the bottom cell and having an oxygen concentration allowed for the time dependent voltage measurements to be related to the diffusion coefficient by first solving F ick s second law It was assumed that transport of dissolved oxygen was one -dimensional diffusion limited (i.e., excludes radial diffusive dependence and convective/buoyant forces and the diffusion coefficient was concentratio n independent ). 2 2z C D t C (2 46) The boundary and intended conditions given below can be achieved by applying a large voltage (~1 to 1.2 V ) at top of the cell to create an oxygen concentration on the order of 1 part per trillion effectively quantified as zero The concentration can be assumed as zero because the concentration of the liquid tin is on the order of 1 ppm 0 0 0 0 0 0 0 z t z C H z t C H z C t Co (2 47) Solving Ficks law with the above boundary and intended conditions gives the analytical solution, where H, is the height of the cell, z is the axia l direction, D is th e diffusion coefficient, and, C is the oxygen concentration. H z n t n H D n C t z Cn n o2 1 2 cos 2 1 2 exp 1 2 1 4 ,2 2 0 (2 48)

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87 The oxygen concentration was monitored at z = 0 It is important to note that for long time ( D H t2178 0 ), only the fi rst term of the series is important as the second term of the Fourier series is reduced to less than 1% of the first term. This simplifies the solution to the more manageable relation. t H D C tCo4 exp 4 02 2 (2 49) Combining Equations, (2 35) and ( 2 49) a relationship can be derived between the electrical potential and the diffusion coefficient as follows. 4 ln 4 0 22 2t H D E t E RT Fo (2 5 0) This relationship shows that the slope of the electrical potential difference [E (0,t) Eo] versus time is directly proportional to the diffusivity while the intercept value depends only on the measurement temperatures and is used to evaluate the quality of the experimental data. Co ulo metric Measurements Co ulo metric measurements offer a different perspective than voltage measurements as current indicates the rate of ion transport The measured current in the previous pump -out transit experiment is related to the flux of oxygen ions across the top-cell electrolyte. Application of Fick s first law where, I, is the current and A is the surface area of the electrolyte gives the following expression nFA I z C D (2 5 1) Again it is clear that a relationship exists between the diffus i on coefficient and measured current. Differentiating the expression for concen tration (Equation ( 2 48)) with respect to z and evaluated at z = H with the long time approximation gives:

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88 tH D H DFA C Io Ionic 2 24 4 ln (2 5 2) This equation can be used to solve for the diffusivity coeffi ci ent by plotting the ln(IIonic) vs. time then equating the slope and yintercept to their respective values. As an aside, special care must be taken when measuring the current in an electrochemical system W hen voltage is applied to the system there are two components to the measured current : an ionic current (the flow of ions) and an electrical current (the flow of electrons) across the electrochemical cell. At the onset of an applied voltage the ionic current will be much larger than the electronic current because oxygen ions are being transported across the electrolyte medium to equilibrate the system. If the potential is maintained the ionic current will exponentially decrease and the measured current will approach a finite value corresponding to the electronic current. The ionic current will effectively decrease to zero because the electrochemical cell will become equilibrated at the new oxygen concentration level set by the applied voltage The depiction of a typical curren t response to an initially applied then held constant electrical potential is shown below in Figure 2 1 0 When determining the diffusion coefficient (that deals strictly with the movement of oxygen ions) from current measurements it is important to use o nly the ionic current in the calculations by subtracting the electronic current from the total current measured. Of course, if the transference number of the solid electrolyte is unity, ielectronic = 0. Periodic Boundary Conditions Diffusion coefficients can also be measured through the use of periodic boundary conditions. It is anticipated that the use of a periodic boundary condition can minimize fluid motion generated from solutal gradients in the liquid melt. By using Equation (2 46) in a semi infinite geometry with the boundary and intended conditions given below, an analytical solution

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89 can be derived for the diffusion coefficient where Camp is the amplitude of the time dependent concentration and w is the frequency that concentration. This derivation will be used as a basis some of the numerical work contained in Chapter 3. t i ampe R C t z C 0 (2 53) oC t z C (2 54) The boundary condition of note is expressed in Equation (2 53), where the real part of eit is applied. The simplest way to solve this problem analytically is to use a trial equation that follows the form given in Equation (255). t ie z C R C (2 55) Note that the concentration in Equation (2 60) has been re -scaled as oC C C to give the new boundary conditions: ampC t z C 0 0 (2 56) 0 t z C (2 57) Inserting Equation (255) into (2 46) results in Equation (2 58), that can be simplified into Equation (2 59) t i t ie C R z D e C R t 2 2 (2 58) t i t ie z C D R e i C R 2 2 (2 59) Taking the spatial derivative of Equation (2 59) and canceling the exponential terms present on both sides results in Equation (2 60)

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90 0 2 2 C D i z C (2 60) The solution of the second order differential equation is well known and expressed as Equation (2 61). z D i s z D ie c e c C 1 (2 61) 2 1 ii (2 62) Implementing the boundary conditions and recognizing the equality, the concentration solved for can be inserted into Equation (2 55) to result in the solution below. t i z D ampe R e C C 2 (2 63) Through a trigonometric identity, Equation (2 63) can be put into a much more manageable form shown in Equation (2 64). o z D ampC z D t e C C 2 cos2 (2 64) At this point further numerical derivations could be made to relate the concentration to potentiostatic or coulometric measurements. This solution, however, is only val id for a semi infinite volume and does not directly correspond to the geometries used in the numerical analysis in Chapter 3. Nonetheless this solution gives an excellent basis for the expected concentration profiles in similar geometries. Flow Visualization Measurements The movement of oxygen in liquid tin can is electrochemically visualized in a number of ways One method requires an EMF measurement to obtain the oxygen diffusion coefficient in a non -convective system then measuring the oxygen diffusivi ty again in the same system under

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91 convective conditions. Under the convective conditions an effective diffusivity is measured (combination of convection and diffusion), and a comparison of the two will reveal the increased transport of oxygen. Detecting a change in the transport of oxygen can lead to quantitative observations of the fluid velocity (if there is prior numerical knowledge of the system that can be used for comparison) and a qualitative assessment of the fluid flow profile. The second type of measurement involves tracking a packet of oxygen through the liquid tin melt via time dependent potentiometric measurements. F irst an electrical potential is applied to the electrochemical cell for a substantial period of time to equilibrate the oxygen concentration in the melt. Next the electrical potential is briefly changed to introduce oxygen into the system. The pulse of oxygen introduced into the system will then transport as a packet of oxygen that can be detected as it passes an individual s ensor via an electrical response. Measurement of fluid velocities and observ ation of the respective fluid flow profiles must be performed over a relatively short period of time since the packet disperses by diffusion. The diffusive effect of the oxygen tracer and the typical method of visualizing fluid flow are summarized in Figure 2 1 1, with the understanding multiple sensors can b e employed. A numerical analysis of this particular type of flow detection was attempted and can be further reviewed in Chap ter 3. Impedance Measurements An impedance measurement is tool that can characterize processes in an electrochemical system. Measuring the impedance of an electrochemical cell not only reveals the electrical impedance of the system, but can also give valua ble information about electrolytic reaction kinetics and diffusive effects of reactants in a node or in the electrolyte To use impedance the resistance term in Ohms law must be rewritten as, Z the impedance covering all forms of resistance instead of, R the simple resistance.

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92 I V Z (2 65) Z can consist of simple resistance, capacitance, C, inductance, L and a const ant phase element (CPE) as summarized below. Resistance R Z Capacitance C j Z1 Inductance L j Z CPE C j Z Typically, a sinusoidal electrical signal (voltage or current) is applied t o a system over a range of frequenc y resulting in a sinusoidal electrical response (current or voltage respectively). Equation ( 2 66) shows for small frequencies (having similar capacitive and inductive values), the capacitance and CPE impedance will be the dominant feature, while the indu ctance will take precedence at higher frequencies as long as the elements are in series. If the elements are in combinations of parallel and series the location of these circuit elements can vary. What makes these circuit elements detectable is the electr ical response will be out of phase with the applied electrical signal giving an impedance measurement component in the imaginary domain, j For each possible circuit element (resistor, capacitor, inductor, CPE) and combination thereof there is a specifi c electrical response. A grouping of equivalent circuits can be deduced revealing the rate processes of an electrochemical system from these known impedance results. Typical impedance results for electrochemical systems reveal a blocking of charge carrier s (i.e. grain boundaries, pores, and multiple phases), degradation of electrical contact, and space -charge layers [141]. A resistive element represent s an electrical barrier to conduction which is often the (2 66)

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93 case for the nodal contacts. A capacitive circui t element represents the storage of energy in an electric field and is often coupled with a resistive element to effectively describe the diffuse double layer of an electrochemical system [142]. The inductive circuit element is an interesting observation in electrochemical impedance measurements requiring further electrochemical research for a complete understanding of its equivalent circuit element and corresponding physical or chemical process. An inductive circuit element represents another form of energy storage through the use of a magnetic field. The impedance response from an electrochemical system that results in an inductive circuit element is rare and there is still some confusion about its physical process. While few proposed theories have been universally accepted a number of authors have concluded the induction element is produced by adsorption of ions on the nodal surface [143144]. Another equivalent circuit component under some scientific scrutiny is a constant phase element (CPE) These operate similarly to capacitive elements, except the phase angle remains a constant value between 0o and 90o over a range of frequencies while the phase angle of a capacitive element changes with frequency. Many attribute the CPE to current density gradi ents along the electrode surface as a result of heterogeneous surfaces [143, 145]. A particular type of impedance is the Warburg impedance (observed when = 0.5 giving a constant phase angle of 45o) that is related to the diffusion of ions to the electrode -electrolyte interface [125, 127, 133134]. Warburg impedance plays a large role in the reconstruction of an equivalent circuit that is typically obser ved in electrochemical systems having an internal node. Careful analysis of the impedance results, however, should be employed as the results can often be misinterpreted. Some curves that appear as a straight line (appearing as a Warburg tail) can actually be part of a

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94 large semicircle, but due to difficulties at low frequency, adequate data may not be available to complete the curve. L arge semicircle curves representing an RC circuit can actually be a combination of multiple RC curves unseen due to the se nsitivity of the impedance tool. Special care in data analysis should be taken when observing impedance measurements at low frequency Below is an example of an electrochemical system with an ID node that assumes all circuit elements operate ideally. The e quivalent circuit has an ohmic drop (from nodal contacts) in series with a typical equivalent circuit for the double layer charging (capacitance in parallel with a resistance) coupled with a diffusion limited node exhibited by a specified CPE known as War burg impedance. The Nyquist (or Cole Cole) plot relates the real and negative imaginary components of the impedance where the low -frequency response is on the far right and the high -frequency response is on the left. There is one semicircle representing the single resistance element in series with the double layer charging element. Where the curves intersect the real axis the respective resistances can be calculated The higher -frequency intercept is related to the first resistance and the lower frequen cy intercept is an additive combination of both resistances. The peak of the semicircle gives the respective time constant with which the capacitive circuit element can be calculated. Unfortunately there is some information that can be lost in a Nyquist plot so the addition of the Bode plot (also shown in Figure 2 1 2) is an excellent supplement. In the Bode plot, frequency increases in the typical left to right direction opposite that of the Nyquist plot. This means the CPE (Warburg impedance) response is on the left side of the Bode plot and not the right side as it is shown in the Nyquist plot. The phase angle becomes a constant value of 45o at low frequencies which leads to the deduction of a Warburg impedance constant phase element.

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95 The phase angle becomes zero when the resistive elements are realized and 90o for the capacitive element. Impedance spectroscopy is an excellent tool for characterizing electrochemical systems due to the substantial amount of information it provides Areas of active r esearch include advancements in CPE theory and the physical processes surrounding induction. The ability to measure kinetic and mass transfer effects in addition to the various resistive effects in electrode and electrolyte materials will allow continual advancement of efficient and well understood electrochemical systems. Impedance spectroscopy was used in this study to measure the ionic conductivity of thin film YSZ. Sources of Measurement Errors Although great precautions are taken to minimize experimen tal error in electrochemical measurements, the potential for error still exists Several sources of error are attributed to temperature gradients within the experimental setup These gradients are often the result of non uniform heat zones inside the furna ce and close proximity materials of varying thermal conductivity values For instance a temperature gradient across the electrochemical cell will alter the EMF response by encouraging a redistribution of the charge carriers. Goto and Pluschkell examined t his particular phenomenon and observed the following relationship for an electrochemical cell under such conditions [138]. ' ~ ~ 12 2 2 2T T p T p T nF EO O O O (2 67) the Seebeck coefficient relat es the change in temperature to an electronic response over two dissimilar materials. Th e Seebeck coefficient is not constant and changes as a function of the partial pressure of oxygen in YSZ. An experimental study by Fischer determine d the Seebeck coefficient relation ship over an intermediate temperature range (600oC 1000oC) as it applie d to

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96 9 mol% YSZ where the units of is in mV/oC and the units of the operational oxygen partial pressure is in mmHg [1]. 2 2159 ln 0220 0 492 0O Op p (2 68) Inserting operational oxygen pressures into Equation ( 2 68) reveal s a Seebeck coefficient on the order of 0.5 mV/oC. This small value requires a large temperature gradient over a very small region for the Seebeck coefficient to affect measurements on the order of 1 V but can affect the sensitivity of the detector b y distorting slight changes in the liquid tins oxygen concentration. The Seebeck effect can also occur within the cell when two dissimilar metals are joined together. For the experiments carried out in this dissertation a rhenium wire was used to make co ntact to the liquid ti n anode and then a copper wire wa s connected to the rhenium wir e When there is a temperature difference between two dissimilar metals an EMF was produced between the two materials. Although a voltage drop wa s expected over the two ma terials the Seebeck effect wa s not time dependent. Therefore, if an electrical potential difference is used to measure particular values during an experiment to determine the diffusion coefficien t, the Seebeck effect will be constant over both measurement s and the error will cancel. However if a potential difference is not used to calculate a value, and only one electrical potential value is measured (for instance in open cell potentials) the Seebeck effect can modify the measured values. These errors ca n sometimes be corrected by calibrating the electrochemical cell using identical electrodes where the EMF should equal zero and operating in an isothermal region. Additional sources of error can occur when a large voltage is applied to an electrochemical c ell Large applied potentials and insulating circuit elements can result in a significant ohmic

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97 drop across the electrochemical cell At high current density significant electrode polarization can occur and drive irreversible nodal reactions. Polarization can also occur at the electrode/electrolyte interface, with a large buildup of oxygen. This can oxidize the nodal material at the electrode -electrolyte interface hampering the effective transfer of oxygen to the remaining nodal material. Another area of concern is the ohmic drop that can occur across the electrolyte material as a result of inefficient oxygen transport across the electrolyte. Much of the resistance in thin film YSZ originates from the lack of sufficient thermal energy, crystalline defects and/or excessive grain boundaries [139]. When a thin film of YSZ is deposited pinholes can be created. Pinholes can occur as a direct result of the deposition process or indirectly during a liftoff or etching process [140]. The resulting pinholes or vias allow oxygen to move through the nodes without an electrochemical reaction effectively short circuiting the system. Sputtering YSZ can result in poor contact at the electrode electrolyte interface creating another source for ohmic drop [123]. Transp ort Phenomena Basics The transport of mass, energy, and momentum were present in the conducted experiments In mass transfer, oxygen ions are transported across the electrolyte from one node to the other. Once the oxygen atoms are present in the nodes oxy gen diffuses throughout the nodal regions in the metal melt from the high to low regions of concentration. Thermal energy is transmitted from the heating coils of the furnace through various materials to the electrochemical cell components. Just as mass di ffuses from a high to low concentration, thermal energy diffuses (mainly through conduction or convection) from high to low regions of temperature. The most interesting form of transport is momentum transfer where there can be sustained convection or moti on of the liquid metal melt. The onset of this convective nature is often a result of a mass or thermal imbalance overcoming the dissipative effects of the fluids viscosity. The inclusion of mass and thermal

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98 driving forces stress the importance of taking into consideration the species and energy balance when analyzing fluid flow. Since mass transfer has been discussed, and it is well understood that energy transfer can be thought of as an analogous transport phenomena to mass transport, a review of these t opics are not necessary. This work involves the formulation of a micro sensor array to visualize flow in liquid metal systems over small length scales. This general problem was inspired by the solder bump problem. The aim of this work is to initiate a nume rical study of fluid flow in low Pr fluids and to design a device capable of measuring the fluid flow. The following paragraphs will discuss the basic framework for modeling convective flow. Overview of Convection Convection can be classified into differ ent types each named to reflect the driving force. Forced convection, for instance, arises when there is a non -zero velocity boundary condition employed, often by mechanically moving a surface or another fluid over the fluid of interest. The boundary adja cent to the moving fluid also moves w ith some velocity due to viscous effects. Another type of convection is buoyant natural convection, which arises from gravity acting on density gradients in the fluid. Liquid metal density is mainly a function of temp erature and composition inconsistencies. For density gradients perpendicular to the direction of gravity, the system is always unstable [147148]. This stresses the importance of operating all experiments as close to isothermal conditions as possible. Of c ourse, experimentally this is never possible and the goal is then to minimize the convective velocity relative to the diffusive velocity. The axial direction of the melt should be parallel to the direction of gravity to minimize any horizontal temperature and solutal gradients that would arise due to the tilt of the melt. Stability in systems for which the density gradient parallel is to the direction of gravity is different If a denser fluid is located below a less dense fluid, convection will not occur b ecause there is no gravity induced potential difference between the heavier and lighter regions of the

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99 fluid. D enser fluid located above a less dense fluid will result in a potential for fluid flow. For small potentials, the fluid will be unable to convect because inertial dissipation (due to viscosity) will dominate. At a threshold potential naturally convective flow is sustained (as the viscosity is no longer capable of dispersing sufficient energy) These fluid density gradients can be created by the p resence of thermal and solutal gradients. For most fluids, the density decreases with increasing temperature, as atoms and molecules gain energy and expand the volume of the fluid. For a thermally induced density inversion ( a less dense fluid be low a more dense fluid), the temperature at the bottom of the fluid must be higher than the temperature at the top of the fluid. When the composition of the fluid is changed, the density of the fluid is also affected. When oxygen is introduced into a liquid tin syste m the regions of tin with a higher concentration of oxygen are lower density than regions with lower concentrations of oxygen. Thus, when oxygen is introduced into the bottom or removed from the top of the liquid tin melt there is a potential for naturall y convective flow. Multiple studies have addressed natural convection and the first were stability analyses by Thomson and Bernard [149 150]. Bernard described convection driven by a thermal gradient occurring within a particular type of system and obs erved a series of flow patterns. Rayleigh then mathematically describe d the convecting system to determine the onset of observed convective patterns [151]. Although Rayleigh s model incorporated faulty assumptions they did not significantly affect his res ults. F ollow up studies by a number of authors were able to correct Rayleighs analysis by considering free surface driving forces and expand the study of natural convection over numerous geometries and boundary conditions [152155]. Another type of conve ction that occur s only if the fluid has a free surface is Marangoni convection. Marangoni flow results from surface tension gradients and is not related to

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100 gravitational force Surface tension is inversely proportional to temperature and thus an increase in temperature will decrease the surface tension. The presence of warmer and cooler regions along the surface will give rise to surface tension gradients R egions of higher surface tension will pull on lower surface tension regions inducing fluid flow. W armer and cooler regions of the free surface are often caused by minute perturbations of a perfectly flat surface, which creates regions of varying surface tension. Concentration can also have the same effect by perturbing local surface tension values along the free surface. Marangoni convection is an interesting type of convection that has been indirectly observed in a number of natural convection experiments by Bernard [156]. The onset of Marangoni convection usually occurs when the viscous and thermal/ solutal forces are unable to damp out perturbations amongst the interfacial surface tension. Numerous studies have explored flow patterns o f specific Marangoni flows occurring in shallow pool geometries [157158]. Studies by Koschmeider and Biggerstaff and Koschmeider and Prahl review ed the studies by Rayleigh and Bernard to determine the onset of Marangoni convection in shallow pool cylindrical geometries [159 160]. Additionally an excellent review of Marangoni convection wa s supplied by Johnson and Naraya nan [156]. Buoyant natural convection is dominant in crystal growth geometries that do not involve a moving boundary, and is constrained by a rigid geometry synonymous with the diffusion experiments employed in this work. The solder bump problem involve s natural and Marangoni convection. Natural convection can only occur in the presence of a gravitational force and Marangoni convection can only occur when there is a free surface. Figure 2 -14 further illustrates the differences between thermally driven natural and Marangoni convection.

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101 Governing Equations The transport phenomena physically described in the previous section can also be mathematically stated for a specific system of interest. Diffusion and flow visualization experiments corresponding to B ridgman crystal growth are reviewed below. For buoyant effects, the following mathematical expressions can be manipulated to incorporate the transport of mass, momentum, energy, and a particular species respectively. These equations, written in non dimens ional form, reflect the motion of the liquid tin and the respective motion of the oxygen species in the liquid tin, constrained by rigid boundaries on all sides. 0 V (2 69) F T Pr Ra F C Sc Ra V P V V VT s 2 (2 70) T T V T Pr2 (2 71) C C V C Sc2 (2 72) The momentum equation shows for thermal and solutal contributions sufficient to generate a density gradient, the momentum, energy, and species equations become inseparable. This greatly increases the difficulty of determining a solution, and means the three equations, in theory, must be solved simultaneously. If the contribution of the species or thermal gradient can be determined ins ufficient, the equations can be de -coupled, simplifying the calculations. A simplification of the system observed in the momentum balance given in Equation (2 75) was first proposed by Boussinesq, who approximated the inertial effects from a density gradi ent as negligible, while the change in density made a marked difference to any resulting flow. This means the density gradient needs only to be recognized in the density term when

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102 coupled with a gravitational force, and all other occurrences of the density term can be replaced with an average density. The Boussinesq approximation is highlighted below, where and S, is the coefficients of volume expansion relative to temperature and concentration, accordingly, and, o, is the density at temperature, To [161]. o S o T oC C T T 1 (2 73) This approximation also simplifies the density term to an average density that can be used in all other density terms not coupled with a gravitational term. In the case of the solder bump geometry, different transport equations must be employed to examine systems likely to be dominated by Marangoni convection instead of buoyant natural convection. For flip chip bonding Marangoni convection is modeled in system with rigid boundaries only at the top and bottom of the melt, allowing the melt to be u nconstrained on its sides. A convective driving force can be created through application of a solutal and/or temperature gradient across the free surfaces. For this system, four non -dimensional transport equations describe the physical nature of the solder bump system when there is considerable contribution of surface tension driven convection. 0 V (2 74) V P V V T Re C Re VT S 2 (2 75) T T V T Ma C Ma Le T PrT S 2 (2 76) C C V T Le Ma C Ma C ScT S 2 (2 77) An e xamination of the transport equations governing the solder bump geometry reveals the momentum, energy, and species equations are again coupled, complicating solution

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103 strategies. A minimization of the solutal or temperature gradient can effectively decoupl e some of the transport equations and simplify calculations. These continuity equations differ from those for Bridgman growth geometry, notably in the exclusion of the body force in the solder bump geometry and the evolution of dissimilar dimensionless groups originating from unrelated velocity scales. Exploration of Dimensionless Parameters An advantage of reducing the continuity equations to a non -dimensional form is the production of dimensionless groups. Exploring these dimensionless groups can give an excellent assessment of the system and the effect of various physical parameters. Each dimensionless group signifies a ratio between two competing processes. Assessing the value of a dimensionless group will reveal the dominant process present. The magnitu de and importance of each equations individual terms can then be evaluated by the value of its preceding dimensionless number. This often allows for the exclusion of terms, and greatly simplifies calculations through a determination of negligible terms. M uch can be accurately theorized about a particular system through the analysis of dimensionless groups. The first dimensionless group of interest is the Prandtl number, Pr that arises in both the Bridgman and solder bump geometries. The Prandtl number is the ratio of momentum diffusivity to thermal diffusivity: Pr (2 78) The Prandtl number relates the relative thickn esses of the corresponding momentum and thermal boundary layers. For Prandtl numbers greater than one, the diffusivity of momentum is much larger than the thermal diffusivity, indicating the momentum boundary layer is larger than the thermal boundary layer The opposite case is true for Prandtl numbers less than one. Thus, in

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104 a fluid flow system with a low Prandtl number (indicating a small momentum boundary layer), the fluids viscosity will not retard the flow as much as a higher fluid viscosity represent ed through a larger Prandtl number. The larger the effect of viscosity, the greater the effect of momentum diffusivity, and the larger the Prandtl number. It should be noted that while there is less diffusion of momentum for a low Prandtl number fluid, inc reasing the thermal diffusivity value in order to lower the Prandtl number does not necessarily sustain fluid flow. Systems with large thermal diffusivity values will diffuse thermal energy very quickly, leaving very small thermal gradients across small ge ometries. This is due to the large thermal boundary layer decreasing the temperature gradient across the fluid, a key driving force of buoyant natural convection. As a reference the Prandtl numbers of water, air, and the liquid tin employed in the experime nt are approximately 7, 0.7, and 0.008, respectively [1]. For a low Prandtl number material, the impedance to the flow will most likely come from the equilibration of temperature for systems with nonDirichlet boundary conditions and not necessarily from the viscosity. For systems with low Prandtl number materials exposed to multiple Dirichlet boundary conditions and able to sustain specific temperature boundary conditions, there will be little resistance to the momentum of the flow. The second dimensionle ss number that can be realized in the first set of continuity equations is the Schmidt number, Sc The Schmidt number represents the ratio between the momentum and mass diffusivities. D Sc (2 79) The Schmidt number is often thought of as the mass analog to the Prandtl number, so the analysis made in the previous paragraphs can be restated with the diffusivity of mass r eplacing the thermal diffusivity. For small Schmidt numbers, the fluid has a large diffusive boundary layer

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105 compared to the momentum boundary layer. In systems that have concentration set at only one boundary, and no mass flux across the remaining boundari es, the concentration will relatively quickly equilibrate. This reduces fluid flow resulting from a concentration gradient across the fluid. The opposite case is true for larger Schmidt numbers, where the momentum will diffuse much faster than a particular species in the fluid. As a point of reference the Schmidt number of oxygen in water is ~500, while oxygen in air is 0.7, and oxygen in liquid tin is ~30 [1]. In some cases it is important to compare the thermal and mass diffusivity terms to determine t he relative boundary layer thicknesses. This is accomplished by dividing the Schmidt number by the Prandtl number to derive the Lewis number, Le D Pr Sc Le (2 80) A similar analysis to that made with the Prandtl and Schmidt number can again be made with the Lewis number. From the comparison of the Schmidt and Prandtl numbers given previously, it is clear the thermal boundary layer in tin is much larger than the mass transfer boundary layer. Additionally, the statements made previously concerning systems with one or multiple Dirichlet boundary conditions with respect to concentration or temperature are applicable to the analysis of the Lewis Number. The dimensionless groups discussed to this point are for determining dominant physical processes, but are unable to relate those physical properties to inertial effects corresponding to the fluids velocity. The Reynolds number, Re provides a comparison between inertial and viscous forces. H ReT S T S ,v (2 81)

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106 Often the velocity term, vS,T, appearing in the Reynolds number i s also scaled by a number of physical parameters for various types of flows (solutal or temperature -driven fluid flow), always resulting in the appropriate units for velocity. The different scaling used for velocity will be reviewed later. The Rayleigh nu mber, Ra relates the forces that encourage flow to those that discourage fluid motion. This can be seen in the thermal and solutal Rayleigh numbers given below. 3TH g RaT T (2 82) D CH g RaS S 3 (2 83) The thermal Rayleigh number relates the buoyant forces generated by a temperat ure gradient to the thermal and momentum diffusivity of the fluid. The same comparison can be made for the solutal Rayleigh number, where the buoyant force is generated from a concentration gradient. The numerator represents the potential energy in the sys tem, while the denominator represents an avenue for this energy to be dissipated. If the Rayleigh number increases to a particular threshold, the total potential energy can no longer be sufficiently dissipated by the diffusive parameters represented in the denominator, and the extraneous energy is transformed into convection. Considerable work has been conducted in determining the critical Rayleigh number of various systems to predict the onset of convection. The characterization of one specific system gen erally involves three critical Rayleigh numbers. The first critical Rayleigh number denotes the onset of convection, the second signals a change in the flow to a time dependent oscillatory flow, and the third critical Rayleigh number indicates the onset of turbulent flow. The first critical Rayleigh number has been found to be 1708.8 for a laterally unbounded fluid that is

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107 bounded on the top and bottom by rigid walls maintained at constant and different temperatures [1]. For a system with an upper free surf ace the first critical Rayleigh number was found to be 1100.7 [1]. The importance of the first critical Rayleigh number stems from its applicability to all fluids regardless of their physical parameters. The same cannot be said about the second critical R ayleigh number. Koschmeider and Busse determined that the onset of the second critical Rayleigh number was a function of Pr and aspect ratio of the geometry constraining the fluid [162163]. This was also found true for the third critical Rayleigh number. The inclusion of Pr and aspect ratio in the second and third critical Rayleigh number unfortunately does not allow for a universal assessment. A brief comment should be made about the effects of the aspect ratio and the observations made by those authors exploring various flow regimes over a range of Rayleigh numbers. The aspect ratio relating the height of the fluid to the radial width is given below. R H (2 84) At a constant height, the importance of an aspect ratio becomes more significant since the width of the fluid decreases the effects of a sidewall. The wall is not moving, and is therefore imposing a zero vel ocity boundary condition (no slip) on the moving fluid. Through the diffusivity of momentum, the wall will serve as a brake for the fluid. An aspect ratio gives an excellent perspective of the fluid geometry, and as the aspect ratio changes, so do the convective flow patterns. For small aspect ratios, the rolls affiliated with the circular nature of the streamlines associated with convection occur next to each other laterally. In large aspect ratios, the rolls are stacked on top of each other. Multiple studies have determined the shape of these rolls and their correspondence to the fluids constraining geometry with regards to lateral or horizontal stacking depicted below in Figure 2 15 [164165].

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108 Synonymous to the dimensionless Rayleigh number, the Marangoni number relates the potential energy from the surface tension to the sources of energy dissipation. The dimensionless thermal and solutal Marangoni numbers given below relate the potential energy from a surface tension gradient to the diffusivity of momentum and thermal or mass diffusivity respectively. TH MaT T (2 85) D CH MaS S (2 86) The same analysis given of the Rayleigh number can also be stated for the Marangoni number in regards to the onset of a flow. Numerical analyses by Davis resolved the critical thermal Marangoni number to be 80, and Stelian claims the critical solutal Marangoni number is 50 [166167]. Further examinations by Savino and Monti showed time -dependent oscillatory regimes in liquid bridges. These were also observed in liquid tin bridges depen dent upon Pr explored by Yang and Kou [168 169]. It is important to recognize in Bridgman growth geometry, the velocity is scaled by different parameters than that of the solder bump geometry. The velocity in the Bridgman growth geometry is scaled by /L, so that there is no dimensionless group in front of the non-linear velocity term. Other scaling options exist, but /L is often chosen as the most convenient velocity due to the inclusion of the dissipative momentum term. The maximum expected velocity for the system can also be calculated from V = (2 g TH)0.5, where only the buoyant terms are used [161]. In the solder bump geometry, the velocity can either be scaled by the solutal surface tension gradient or the thermal surface tension gradient. H CS sv (2 87)

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109 H TT Tv (2 88) It should be noted that the scaling of velocity must remain constant throughout the entirety of the governing equations. Summary This chapter provides a foundation necessary for executing and interpreting electrochemical measurements of m ultiple transport phenomena systems. The operation of sensors through galvanic and electrolytic operational modes was outlined, with an emphasis on the boundary conditions that can be applied. Further discussion clarified how the sensors will be employed over a range of physical experiments and specific boundary conditions. A review of underlying thermodynamic principles and the mechanism of oxygen ion transport in an electrochemical system clarified how the electrochemical sensors operate. The transport ph enomena associated with the range of experiments discussed was reviewed, with a focus on fluid motion. A description of fluid motion was then described with a summary of its multiple driving forces. The flow regimes subject to these driving forces and the importance of the aspect ratio were also discussed. A review of the necessary electrochemical sensor measurement fundamentals was supplied as a precursor to the implementation of MES3A into systems of interest. The transport phenomena and electrochemical f undamentals will be used in the numerical analysis of the MES3A validation experiments reviewed in Chapter 3.

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110 Figure 2 1. G alvanic and electrolytic cell [105] Figure 2 2 Component view of the elec trochemical potential at steady -state equilibrium Cu/Cu 2 O Sn (Dissolved Oxygen) YSZ Cu 2 O + 2e 2 Cu + O 2 O 2 [O] Sn + 2e O 2 Sn ref Sn O Sn Oa RT ln ref Chemical Potential Electrical Potential Reference Electrode Working Electrode nF ref Sn ref O Sn ORT nF a a exp e e e e Sn + 2O 2 SnO 2 + 4e SnO 2 + 4e Sn + O2 4Cu + 2O 2 2Cu 2 O + 4e 2 Cu 2 O + 4e 4Cu +2O 2 Anode Anode Cathode Cathode Power Source Sn, SnO 2 || YSZ || Cu, Cu 2 O Sn, SnO 2 || YSZ || Cu, Cu 2 O GALVANIC CELL ELECTROLYTIC CELL Electrolyte

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111 Temperature ( K ) 700 800 900 1000 1100 1200 Gibbs Energy of Formation ( kcal/mol O2 ) -250 -200 -150 -100 -50 PO 2 (atm)10-2510-1010-1510-2010-510-3010-3510-4010-4510-5510-5010-6010-65) ( 2 ) ( ) ( 22s CuO g O s Cu ) ( 2 ) ( ) ( 42 2s O Cu g O s Cu ) ( 2 ) ( ) ( 22s SnO g O l Sn ) ( ) ( ) (2 2s SnO g O l Sn ) ( ) ( ) ( 5 45 2 2s O Ta g O s Ta ) ( ) ( ) (2 2s SiO g O s Si ) ( ) ( ) (2 2s ZrO g O s Zr ) ( 3 2 ) ( ) ( 3 43 2 2s O Y g O s Y Figure 2 3. Ellingham diagram of potential o xidation reactions [137]

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112 Temperature ( K ) 700 800 900 1000 1100 1200 Saturation mole fraction ( mol O/mol Sn ) 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 Saturation Concentration ( mol O/cm3 ) 1e-8 1e-7 1e-6 1e-5 1e-4 Temperature ( K ) 700 800 900 1000 1100 1200 Saturation Potential ( mV ) 460 470 480 490 500 510 520 530 540 Figure 2 4 Oxygen saturation c oncentration and e lectrical p ote ntial [136, 137]

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113 Figure 2 5. Phase d iagram of ZrO2Y2O3 [113, 115]

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114 Figure 2 6 Various zirconia based crystal structures [113] b b a c m phase MONOCLINIC SYSTEM b 99 o a a t phase TETRAGONAL SYSTEM c > a = b, =90o Oxygen displacement exists a a t phase TETRAGONAL SYSTEM c = a = b, =90o Oxygen displacement exists a a a a c phase CUBIC SYSTEM c = a = b, =90o Oxygen displacement does not exist

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115 Figure 2 7. Electrolytic d omain of 9 mol% YSZ [1]

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116 Temperature-1 x 1000 ( K-1 ) 0.8 0.9 1.0 1.1 1.2 1.3ln PO2 ( atm ) -140 -120 -100 -80 -60 -40 -20 0 20 40 60 Temperature ( oC ) 500 600 700 800 900tion < 0.99 tion < 0.99) ( 2 ) ( ) ( 22s SnO g O l Sn ) ( ) ( ) (2 2s SnO g O l Sn ) ( ) ( ) (2 2s SiO g O sSi ) ( 2 ) ( ) ( 22s CuO g O s Cu ) ( 2 ) ( ) ( 42 2s O Cu g O s Cu Figure 2 8. Electrolytic domain of 9 mol% YSZ with material o xides

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117 Figure 2 9. P ossible electrolytic reaction mechanisms [125, 126] Oxygen ion diffuse s through bulk electrolyte 1 2 Oxygen ion adsorbs on the electrode surface O 2 2e 1 3 O 2 4 Oxygen ion diffuses through bulk electrolyte O 2 Oxygen is transported to the electrode Oxygen ion adsorbs to the electrolyte surface O 2 O 2 2 Oxygen ion diffuses through bulk el ectrode 1 2 Oxygen ion adsorbs on the electrode surface O 2 2e 1 3 O 2 4 O 2 Oxygen ion adsorbs to the electrolyte surface Oxygen is transported to the electrode O 2 O 2 2 Oxygen ion diffuses along the electrode f Nodal Surface Diffusion/TPB 1 O 2 O 2 2e 1 3 4 Oxygen ion diffuses through bulk electrolyte O 2 Oxygen ion adsorbs on the electrolyte surface Oxygen is transported to the electrode TPB Mechanism Intern al Diffusion O 2 O 2 O 2 ad O 2 O 2 O 2 O 2 ELECTROLYTE NOD OVERPOTENTIAL, TPB O 2 O 2

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118 Figure 2 10. Time dependent current response to an applied potential [146] CELL CURRENT ( mA ) TIME ionic electronic totali i i i total (measured) i electronic i ionic (calculated) Cu, Cu 2 O | YSZ | Sn, SnO 2

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119 Figure 2 11. Typical flow visualization m easurement Fully Developed Fluid Flow of a Liquid Tin Sensor 2 Sensor 1 MES 3 A 2 1 2 1 2 1 2 1 2 1 2 1 Oxygen Atoms = 0 = 1 =2 = 3 = 4 = 5 = 6 = 7 = 8 E (V) 1.2 0.5 0 4 8 Sensor 1 Sensor 2 Sensor 1 Galvanic Mode Sensor 2 Galvanic Mode Sensor 2 Electrolytic Mode

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120 Figure 2 12. Impedance s pectra of an ID electrochemical s ystem [146] R 1 R 2 Warburg Impedance C 1 R 1 R 2 CPE C 1 R 1 Z j Z r R 1 + R 2 R2C1 Warburg Tail |Z| BODE PLOT NYQUIST PLOT PROPOSED W ARBURG IMPEDANCE CIRCUIT EQUIVALENT CIRCUIT FOR AN INTERNAL DIFFUSION NODE

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121 Figure 2 13. Natural and Marangoni c onvection [156] Figure 2 14. Lateral and horizontal stacking of convective streamlines HOT COLD HOT COLD HOT COLD >> 1 = 1 < <1 COLD HOT COLD HOT COLDER COLDER WARMER GAS GAS LIQUID LIQUID INTERFACIAL TENSION DRIVEN CONVECTION BUOYANCY DRIVEN CONVECTION

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122 CHAPTER 3 USING THE SPECTRAL CHEBYSHEV METHOD TO PREDICT MASS TRANSFER EFFECTS Introduction Before using the fabricated micro -sensor array to examine the solder bump problem the device must first be validated by studying convective flow in a constrained cylinder. Numerical simulations of tin melt systems were performed to postulate the physical experimental results that will be used to validate the dev ice. The spectral Chebyshev collocation method was used to perform computational fluid dynamics and achieve this goal. This chapter reviews the use, implementation, and results of the spectral method pertaining to various mass transfer boundary conditions imposed upon a right cylindrical geometry. Basis for Spectral Chebyshev The spectral technique is an effective methodology for solving various differential equations lacking analytical solutions. This method is similar to the finite element method, as linear combinations of Nth degree polynomials are used to determine a solution over a domain divided into several intervals. While the finite element technique uses linear combinations to solve local collocation points the spectral method resolves the linea r combinations globally [172]. Although the two methods are similar, each has certain advantages depending on the circumstances. For instance, the spectral method is excellent for examining simple geometries and in some circumstances can be employed in complex non -orthogonal geometries. The spectral method also has a clear advantage over finite element approach when resolving computations involving a time -stepping scheme. The benefit results from the spectral method converging to a solution exponentially in time while the finite elements method does so linearly [173]. Additionally, the error (difference between the actual and computationally computed value) in a

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123 spectral calculation quickly becomes so small (on the order of 1012), the error associated wit h the calculation is a result of rounding errors linked to the computer and not the methodology [173]. A drawback of the spectral method is an increase in the required computational time compared to that of finite elements. The spectral methodology, howeve r, is becoming more practical due to the ever -increasing speed and processing power of computers. The spectral Chebyshev technique was chosen since this work is focused on simple cylindrical geometries and the results can be quickly obtained with high acc uracy. The Chebyshev methodology was also chosen because the Chebyshev polynomials sufficiently subdue Runges phenomenon. Runges phenomenon describes the error that results when using high -ordered polynomials to fit a particular function. Interpolating h igher -ordered polynomials over a range of evenly spaced collocation points does result in an excellent fit to a bulk of the function. The use of evenly-spaced collocation points, however, creates increasingly large oscillations of the fitting function at t he nodes. These large oscillations result in a significant amount of error at the boundaries of the functions domain and can greatly affect the convergence of the solution. It was discovered that Runges phenomenon can be quelled using collocation points that are not evenly spaced and, thus, have a higher density at the edges of the domain. Fortunately, Chebyshev nodes are generated in this fashion. The node can be generated in two different ways depending on the type of the differential equation to be so lved [174]. For differential equations that do not have a spatial variable in the denominator Gauss Lobatto nodes are used. These nodes are generated from Equation (3 1) resulting in unevenly spaced nodes across a domain of [1 1], but symmetric around the midpoint of the domain. N j N j xj, 0 cos (3 1)

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124 If the differential equation to be solved has a spatial variable in the denominator, severe numerical issues arise a s this variable approaches zero. This issue can be resolved by generating Gauss -Radau nodes by using Equation (3 2). N j N j xj, 0 1 2 2 cos (3 2) The GaussRadau nodes are ge nerated over a domain of [ 1] where, is a value very close to 1. Again, generating the nodes in this fashion alleviates any issues that may result from the spatial variable equaling zero in the denominator. Discretizing the Equations of Change Sin ce the domain of the generated Chebyshev nodes is always [ 1 1], it is vital the system of differential equations to be solved is transformed into the same domain. Quite often differential equations governing a particular geometry will be defined physicall y over a domain other than [ 1 1]. For these cases, the physical domain must then be linearly transformed into a computational domain corresponding to the physical domain. When the domain is transformed, the differential equations and their respective boundary conditions must also have their spatial variables changed accordingly. For example, in the case of the right cylinder shown below in Figure 3 1, the physical domain of the dimensional height in the axial direction is from [0 H] and the radius in the r adial direction is also from [0 R]. Normalizing both the z and r directions will give a physical domain of [0 1]. The dimensional physical domain does not necessarily have to be converted into a nondimensional physical domain, but scaling the geometry can ease future implementation and increase the scope of potential calculations. As a note, all numerical output in this chapter (such

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125 as length, velocity, pressure, and concentration fields ) will be reported in their nondimensional form. Table 3 1 summarize s the non-dimensional values used to scale the cylindrical geometry and the corresponding equations of change relating to the crystal growth geometry discussed in Chapter 2. Table 3 1. Nondimensional values for the crystal growth geometry Non -Dimensional Term Non -Dimensional Symbol Scaled Value Radius r R r r Height z H z z Time 2R t Aspect Ratio H R Radial Velocity rv Rr rv v Axial Velocity zv Hz zv v Pressure P H g P R P 2 2 Concentration C o S oC C C where C C C C *, Schmidt Number Sc D Sc Solutal Rayleigh Number Ras D H R C g Ras 2* Following the scaling of the necessary equations, the nondimensional physical z -spatial direction and r -spatial direction must now be transformed into a computational domain of [ 1 1]. This transformation relates nodes of the physical space, 0, and, 1, to the nodes of the computational space, 1, and, 1. In the case of converting the axial spatial direction, the

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126 following equation converts the non-dimensional physical s patial variable z to z the computational spatial variable [174]. 1 2 z z (3 3) Due to numerical calculation issues, conversion of the physical radial spatial variable is done in a slightly different manner. A number of computational difficulties are faced when a spatial variable in the denominator becomes equal to zero and this is the case when employ ing the cylindrical equations of change. The problem is avoided in the computations by defining the computational domain only over part of the total non -dimensional physical domain (from 1+ to 1, where is a value very close to 1). Since never equals 1, there is never the inclusion of the physical radial point of 0. This geometric adjustment allows for the computation to proceed without inhibition from the radial value equaling 0 in the physical domain. The linear transformation for exchanging the non dimensional physical radial spatial variable, r to the computational spatial variable, r, is highlighted in the following equation where the domain now lies between [ 1] [174]. 1 1 r r (3 4) Using this linear transformation, concern exists over the small portion of the physical domain that was excluded. The excluded portion for this particular case is equal to 2 1 where is the last node generated in Equation (32). The radial distance that was excluded is a function of N and is summarized below in Table 3 2.

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127 Table 3 2 Excluded radial distance, r for a specific set of grid points N Excluded Distance, r 5 2.0 x 10 2 10 5.6 x 10 3 15 2.6 x 10 3 20 1.5 x 10 3 25 9.5 x 10 4 30 6.6 x 10 4 The radial distance excluded in the computationa l domain decreases for an increasing N value (corresponding to N+1 nodes). For 31 nodes, the excluded radial distance is ~0.07% of the non -dimensional radius. This small area of exclusion should not be troubling, save for a situation when the scale of the excluded region approaches that to which a phenomenon is expected to be observed. Careful selection of the radius, R and the number of nodes ( N+1 ) can prevent many of these troubling situations from occurring. Fortunately, excluding a portion of the phys ical domain comes with the consolation of not requiring a second boundary condition. When the computational space ends at there is only one radial boundary, located at r= 1, that requires a boundary condition. As previously mentioned, the Chebyshev spectral method operates by estimating the parameters of polynomials to the solution. These coefficients can be resolved fro m linear equations. Further discussion of this matter can be explored in works by Boyd, Trefethen and Guo, Labrosse and Narayanan [172174]. The following subsections explore the equations of change used to model various configurations of time -dependent d iffusion in right cylindrical geometries. These cylindrical geometries are similar to the crystal growth geometry and solder bump length scales discussed in Chapter 2. The equations of change used to describe mass transfer are first given in their non-

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128 dime nsional form, then transposed into computational space, and finally discretized into matrix form. Table 3 3 is useful in translating the discretization terminology that is used in the following section. For example, Dr and Dz are the differentiation matric es that are generated from the Chebyshev nodes highlighted in Equations (3 3) and (3 4). Combining the discretized equations of change into one large system of equations allows for the numerical computation to be made. Table 3 3 Terms for the d iscretiz ed equations of c hange Discretization Term Discretization Symbol Discretization Value Identity Matrix I (N+1 Rows and Columns) 1 0 0 1 I Kronecker Product d c b a d c b a d c b a 0 0 0 0 0 0 0 0 1 0 0 1 Inverse Radial Term Dg 1 1 r Dg Radial Coefficient drp 1 drp First Radial Derivative Dr r Dr First Axial Derivative Dz z Dz The code will be va lidated by examining axial diffusion of oxygen under non-convective conditions in a cylindrical geometry. This was followed by another cylindrical geometry numerical analysis of 2 D (axial and radial) mass transport (via diffusion and convection) to determine fluid velocities generated by solutal gradients. A secondary study of the 2 D transport was performed with the intent of introducing transient solutal gradients that did not generate

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129 flow. All studies culminated into an attempt to model the pathway of an oxygen tracer introduced over a radius smaller than the radius of the tin melt. Before these studies could be initiated a validation of the equations of change used in the numerical code was carried out. The discussion below reviews how the equations of change were numerically implemented. Mass Balance The mass balance can be written in its non -dimensional form as noted below. 0 z v v 1z 2 r r r r (3 5) Equ ation (3 5) assumes that density does not change with time or position and velocity has only z and r dependence. Equation (3 5) can be transformed from the physical domain to the computational domain using Equations (3 3) and (3 4) to obtain the following equation. 0 z v 2 r v 1 r v 1z 2 r r (3 6) Now that Equation (3 5) is transformed into computational space, Equation (3 6) is discretized into matrix form through the use of the Kronecker p roduct (highlighted in Table 3 3) to give the following equation. 0 v 2 v1 n z 2 1 n r r zI Dz Dr Dg drp I (3 7) Equation (3 7) now represents the discretized form of Equation (3 5) where the differentiation matrices Dr and Dz are generated from the Chebyshev nodes. Species Balance A species balance can be written for the cylindrical system as shown in Equation (3 8). 2 2 2 z 2 r1 v v z C r C r r r z C r C C Sc (3 8)

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130 The non linear portion of this equation is preserved due to the relative magnitude of the Schmidt number. While this means the calculation is slightly complicated by the obvious coupling of the species and momentum balance, the equations can be solved simultaneously when using the spectral meth od explicitly. For completion, the terms are removed from Equation (3 8) because there is no movement of the species in the -direction. Following the same procedure as that for the mass balance, Equation (3 8) is converted into the computational domain with the following result. 2 2 2 2 2 2 z 2 r4 1 1 1 v 2 v 1 z C r C r C r z C r C C Sc (3 9) Following the transformation to the computational domain, the species balance is discretized into the following equations. z r 3 1 2 2 2 2v v 2 3 4 C f C I I Dz Sc Dr Dr Dg Sc drp In r z (3 10) n n z n nC Ir Dz C Dr I drp C C C f n z 2 n r 1 z r 3v 2 v 2 2 1 2 v v, 1 1 n z 2 1 1 n rv 2 v n n zC Ir Dz C Dr I drp (3 11) As in the mass balance, the linear portion of the differential equation is placed on the left side and the nonlinear terms on the right side. The time derivatives present in the equations of change were approximated by a secondord er time scheme referred to as the leap frog method proposed by Trefethen [173]. This time scheme, Equation (3 12), was used primarily because it guarantees convergence for

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1 31 25 6 N [173]. Decreasing the value reduces the possibility of in stabilities that can quickly amplify and disrupt the convergence of a computational solution. 1 12 1 2 2 3n n nC C C C (3 12) The term, nC in Equation (3 1 2) correlates to the concentration solved at the nth time step. This means that the 1 nC and 1 nC terms are the concentration solved at the nth+1 and nth1 time step, respectively. The spectral method as a whole operates by calculating the 1 nC concentration from the nC and 1 nC elements. Momentum Balance A balance of the momentum is also needed so that an unstable concentration gradient (denser fluid above a less dense fluid) can be considered. The inertial terms have been removed, as they do not significantly affect the results of the calculation (save for an increase of the computational time). The coupling of the species and momentum balances is clearly seen wit h the inclusion of the concentration in the momentum balance. In the case of generated fluid flow, the velocity in the direction was removed because the geometric arrangement of the imposed boundary conditions limits fluid flow to the axial and radial di rections. The Rayleigh number used is the modified Rayleigh number given in Table 3 1. This number can be converted to its typical form by multiplying the modified Rayleigh number by 2. The non-dimensional momentum balances for the axial and radial compo nents are as follows. C Sc Ra r r r z PS 2 z 2 2 z zz v r v 1 v (3 13) 2 r 2 2 r rz v v 1 v r r r r r P (3 14)

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132 These equations are transformed into the computational domain following the procedures used in the previous sections to obtain the following equations. C Sc Ra z r r r z PS 2 z 2 2 z 2 z 2 zv 4 v v 1 1 1 2 v (3 15) 2 r 2 2 2 r 2 r 2 r 2 rz v 4 v r v 1 1 1 r v 1 1 v r r r P (3 16) The respective axial and radial momentum balances are then discretized using the ti me scheme addressed in the previous section and separated into the linear and non -linear terms. The following equations reflect the discretized versions of the axial and radial momentum balances. z 2 1 n z 2 2 2 2 1v v 2 3 4 2 C f I I Dz DgDr Dr drp I P I Dzr z n r (3 17) 1 1 n z n z z 22 v 2 1 v 2 v n n sC C Sc Ra C f {3 18) r 1 1 n r 2 2 2 2 2 1v v 2 3 4 C f I I Dz Dg DgDr Dr drp I P Dr drp Ir z n z (3 19) 1 n r n r r 1v 2 1 v 2 v f (3 20) The axial and radial comp onents of the momentum balance are now effectively discretized and can be implemented into the code. Combining the Equations of Change The discretized equations of change can be combined into one large linear equation represented in matrix form. Equation (3 21) given below illustrates the various linear equations,

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133 where the first row corresponds to the momentum balance for the r -velocity component, the second row the z -velocity component, the third row the mass balance, and the last row the species balance The previously discretized values resolved in the previous sections are now inserted into the matrix. z r 3 z 2 r 1 1 1 1 n z 1 n r 2 2 2v v 0 v v v v 2 3 0 0 0 0 0 0 2 3 0 0 0 2 3 C f C f f C P I I In n z r z r (3 21) Equation (3 21) can be represented by Equation (3 22) where the respective r and z velocity components, pressure, and the concentration profile can be solved using Equation (323). b x A (3 22) b A x 1 (3 23) Notably, Equation (3 21) represents all of the governing equations, and solving this system of equations for a given time step results in an explici t solution for the velocity, pressure, and concentration for that particular time step. In some situations, it may be prudent to solve the concentration profile separately from the momentum balance via an implicit method. When the implicit method is used, the momentum balance is solved first and then inserted into the calculation of the concentration profile. The concentration profile is then solved and reinserted into the momentum calculation. This process repeats for a given time step until the two soluti ons converge. The explicit method, capable of solving both the concentration and momentum simultaneously, was used due to the simplicity of implementation and negligible cost of

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134 computational time. The use of the explicit method in this work resulted in an explicit solution for a single time step that did not require an iterative (implicit) process. Boundary Conditions A final step involving the implementation of boundary conditions is required before the velocity, pressure, and concentration profiles are resolved. The boundary conditions must be appropriately implemented into the A matrix and b column vector represented in Equation (3 22). This was first done by discretizing the boundary conditions in the same fashion as the equations of change. The second step comes from understanding the Chebyshev collocation points are generated from 1 to in the radial direction and from 1 to 1 in the axial direction. Following these steps allow for the discretized boundary conditions to be implemented into the appropriate rows and columns of the A matrix and b column vector. An excellent review of this process is given by Guo, Labrosse, and Narayanan [174]. Operation of the Spectral Code The Chebyshev spectral method can be properly understood and implemented given the previous discussion and a review of implementing boundary conditions. The code is then solved for the first time step explicitly, so there is no need for convergence criteria. The code is then solved for subsequent time steps until there is no differe nce in the velocity, pressure, and concentration profiles. The code is said to have converged to the steady state solution when the following convergence criteria is achieved. 12 n z n r 1 1 1 n z 1 n r10 v v v v abs max n n n nC P C P (3 24)

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135 To further illustrate the simplicity of the Chebyshev spectral method, a flow chart is supplied in Figure 3 2. Sizing the Mesh For the spectral method to work properly, the cylindrical geometry must be discretized into se veral collocation points in both the axial and radial directions. The combination of all the collocation points is referred to collectively as the mesh. The size of the mesh depends on the total number of grid points generated in the radial and axial posit ions. Increasing the number of grid points reduces the space between the collocation points, and effectively increases the resolution of the solution. In this work a mesh of 25x25 was used to resolve all of the resulting computations. This resolution was used because the available DELL computer had insufficient memory to invert a larger matrix. To give a sense of scale a grid size of 25x25 generated an A matrix of 2704x2704 mesh elements. To determine if the computational results were affected by mesh size a smaller number of grid points (20x20) were used after obtaining computational results from the 25x25 mesh grid. The lower resolution mesh returned the same answer as the higher density mesh, but with slightly less resolution. Thus, it was surmised that the 25x25 mesh was sufficient in returning a reasonable answer. Stepping in Time Another parameter that can affect the output of the numerical code is the time step. The time step, an input variable, is the increment in time for which the code steps betw een calculations. A small time step represents a very short physical period of time between the resolved species and momentum balances. The time step was kept reasonably small and below the convergence criteria of 25 6 N [173].

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136 During numer ical computations it was noticed that for an increasing solutal Rayleigh number, adherence to the time -stepping convergence criteria increased in importance. If the time steps were too large, small perturbations in the numerical model would quickly amplify over successive time steps and corrupt the simulation. The increasing likelihood of the perturbation came from the increasing probability of fluid flow (increasing the solutal Rayleigh number). Thus, a careful balance had to be made for each computation b y minimizing the calculation time (increasing the time step) and maintaining convergence of the solution (decreasing the time step). When numerically a stable solution was reached, the time increment was further reduced to ensure the time step reduction di d not affect the result. The resulting solution was deemed numerically stable if the same momentum, pressure, and concentration profiles were resolved for a smaller time step. Benchmarking the Spectral Code There are two simple methods that can be used t o validate the results of the numerical code. The first requires solving a simple problem with a known solution, and the second requires entering a guess equation into the numerical code to see if the program returns the appropriate result. In this work th e first method was chosen by exploring a specific system with a known and simple analytical solution. The examined system used the same spectral code to be used to study the mass transfer systems in the subsequent sections. The benchmark case was careful ly chosen so that it reflected mass transfer in a cylindrical geometry. This was successfully accomplished by solving for the axial and radial velocity components, pressure, and concentration of the system summarized in Figure 3 3. The physical domain of t he cylinder is [ 1 1] for the axial direction and [0 1] for the radial direction. The governing equations of the system shown in their physical domain forms can be seen in Equations (3 25) (3 28).

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137 28 3 0 v 27 3 0 v 1 z v 26 3 0 v 25 3 0 v v2 z 2 2 2 z r z r rC r r r f z P r P r 33 3 sin 32 3 cos 31 3 sin v 30 3 cos v 29 3 sin0 0 0 1 0 z r J d C z r J c P z r J b z r J a z r J fz r 410 94 9 1280 0 0244 0 02 0 d c b a The cylinder of interest has no stress boundary conditions for the momentum balance. For the species balance, a zero boundary condition for the concentration at the top and bottom is employed with a no flux condition at r = 1. The driving force, f behind the fluid flow is given by equation (3 29) where, J0, is a Bessel function and, is the first root of J1(R) = 0. In the species balance, the concentration is coupled with the fluid velocity to mimic the conditions that will be used in subsequent models. A simple analytical solution to the system exists for the proposed equations fo r the velocity, pressure, and concentration highlighted in Equations (3 30) (3 33). It is quickly seen by inserting these proposed forms into the system that the trial equations are correct. Following the analytical solution of the benchmark problem, it i s necessary to check the output of the code with the analytical solution. The result of running this benchmark case is identical to the analytical solution. The respective axial and radial velocity components, pressure, and concentration in their computati onal dimensions are highlighted in Figures 3 4 3 7. To determine if the computations results are the same as the analytical solution, a careful comparison was made between the plots and the functions used in the analytical solution. A qualitative analysi s reveals the shapes of the graphs correspond to the expected graphical shapes of Equations (3 30) (3 33). On a more specific and quantitative evaluation basis the maximum and minimum values were taken of the resulting plots. These values corresponded dire ctly to the

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138 maximum and minimum of the analytically solved equations. As a more extensive test, the analytical equations were graphed and compared to the numerical output and found to be exactly the same. Thus, the written Chebyshev spectral code used in t his study is capable of numerically analyzing coupled differential equations in a right cylindrical geometry. Numerical Analysis of Mass Transfer This section examines mass transfer effects of oxygen in an isothermal liquid tin system. The system consists of the right cylindrical geometry that allows for oxygen to be removed from either the top or bottom of the geometry via a constant electrical potential. The numerical analysis explores both top and bottom depletion scenarios that were used by previous au thors to experimentally determine the diffusion coefficient of oxygen in liquid tin [1, 2, 16, 72, 73, 161]. Notably the top depletion scenario results in fluid flow, which disrupts the pure diffusion of oxygen. This flow results from solutal instabilities in the top heavy arrangement. A third scenario substitutes a periodic concentration boundary condition in the place of a constant concentration boundary condition to minimize fluid flow within the unstable configurations. An overview of the cases and thei r respective configurations is summarized in Figure 3 8. The numerical model was configured to match the intended physical experimental conditions. Performing numerical calculations similar to the experimental work of previous authors, a liquid tin melt (t he fluid) is constrained on all sides by walls [1, 2, 16, 72, 73, 161]. These side walls will not allow oxygen transport across or along them and impose a no-slip momentum boundary condition. The top and bottom walls either comprise of a constant concentra tion, periodic concentration, or no -flux condition, depending on the examined case. The first experimental case examined is the removal of oxygen from the liquid tin melt at the bottom of the geometry. The bottom depletion configuration does not induce fl uid flow. The second case is the top depletion configuration, which can induce fluid flow if the solutal

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139 Rayleigh number is above the critical solutal Rayleigh number. The third case is a periodic boundary configuration that attempts to quell fluid flow in the unstable top depletion configuration. The physical parameters used in the computations are summarized in Table 3 4. Table 3 4. Physical parameters of liquid t in at 750oC Property Symbol Value Units Density 6.713 g cm 3 [1] Thermal Expansion Coefficient T 26 x 10 6 K 1 [1] Solutal Expansion Coefficient S 0.865 (mol fraction) 1 [16] Kinematic Viscosity 1.64 x 103 cm 2 s 1 [1] Thermal Diffusivity 0.203 cm 2 s 1 [1] Mass Diffusivity D 8.0 x 10 5 cm 2 s 1 [1] Prandtl Number Pr 0.008 -----[1] Schmidt Number Sc 25.2 -----[1] Case 1: Bottom Depletion Configuration The bott om depletion configuration was examined first to explore the diffusive effects of oxygen in the absence of fluid flow. The isothermal liquid tin cylindrical system was bound on all sides by rigid walls. At the bottom boundary, a constant sink concentration of oxygen, Cs, was used. The sink concentration was always smaller than the initial concentration of the bulk liquid tin. To simplify the analysis, the parameters were non -dimensionalized, with the initial concentration defined as unity and the sink conce ntration (at z = 0) set as zero. The constant concentration boundary condition was imposed over the entire radius, to remove any initial sources of radial solutal gradients. If there was a presence of a radial solutal gradient fluid flow would have been in duced. As expected the spectral code returned mass transfer results that showed unaided diffusion (no fluid flow) and eventual depletion of oxygen across the geometry. Figure 3 9

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140 shows the time evolution of the nondimensional concentration profile for a n aspect ratio of unity, a time scale of R2/ and non -dimensional heights The time evolution of the axial velocity and overall pressure profile are supplied in Figures 3 10 and 3 11 to confirm there was no fluid flow in the melt. Because of the redundanc y between the axial and radial velocity profiles only the axial profile was highlighted in this section. The noise at the edges of the domain in Figure 310 is most likely due to rounding errors in the numerical code. If the velocity values given in thei r scaled form are changed to their un scaled values, the actual velocity values predicted by the numerical code are on the order of 1013 cm/s. These small perturbations were regarded as noise and assumed to have no effect on the numerical results. The sam e assessment made for the previous velocity profile can also be extended to the given pressure profiles in Figure 3 11. Some slight waves in the pressure plots are attributed to the small discrepancies in the velocity profile, and were considered numerica l chatter. At each corner of the pressure profile geometry there are sharp spikes in the pressure profile representing a singularity. These singularities arise from the inability of the boundary conditions to satisfy the force balance at the corners of th e geometry in the outward and inward directions. Thus, there are two singularities per corner, resulting in 8 total singularities within the problem. Now that the numerical code has produced reasonable results, the numerical data from the bottom depletion experimental results of Sears were used as input for the written numerical code [1 ]. Sears work was used to check the reliability of the numerical code by comparing his experimental results with the computational output. The experimental parameters of Se ars system (having the same geometry as Figure 3 8) used in the computational calculations are summarized below in Table 3 5.

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141 Table 3 5. Experimental parameters for bottom depletion e xperiment [1] Radius (cm) Height (cm) T ( o C) D o (cm 2 /s) C o (mol frac) Applied Voltage (V) 0.477 0.389 723 7.54 x 10 5 2.6 x 10 4 1.5 0.477 0.467 725 7.30 x 10 5 1.6 x 10 4 1.5 0.477 0.742 730 7.72 x 10 5 2.0 x 10 4 1.5 The experimentally measured EMF by Sears was then compared to the EMF generated by the numerical code and illustrated in Figure 3 12. As a further check and comparison of the numerical data, the analytical solution (valid for D H t2178 0 ) is also represented in the plot. As expected, there is excellent agreement between the analytical and numeri cal solution. Comparing these results with the experimental data shows good agreement between the experimental and numerical results. The small difference between the experimental and numerical results could be a product of some low level convection occurr ing in the experiments, or slight discrepancies in Sears calculation of the diffusion coefficient. Sears noted that there was some experimental error tied to his calculation of the diffusion coefficients and because of these errors the analytical solution for the reported diffusion coefficients do not exactly match with his experimental results. With the increasing height of the liquid tin there is an increased potential for fluid flow. Any small perturbations to the liquid tin melt (including off axis til ting) could result in some residual flow to give the results shown in the Figure 3 -12. Case 2: Top Depletion Configuration For the top depletion configuration, a constant sink concentration of oxygen, Cs, was used at the top of the cylindrical geometry. This boundary condition effectively removes oxygen from the top of the liquid tin, creating a top heavy solutal instability. Fluid flow is expected and observed in the spectral data according to the following set of events: the fluid starts at rest, then

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142 i ncreases to a maximum velocity, followed by the slow dissipation of momentum (via a decreasing solutal driving force coupled with viscosity), and finally the fluid returns to rest with the solute equilibrated across the liquid tin. To simplify the impleme ntation of the top depletion configuration, a non-dimensional analysis was employed. Additionally, the numerical code was reconfigured for the top depletion problem by simply changing the direction of gravity rather than reconfiguring the entire code. This now means that a non-dimensional height of 1 corresponds to the bottom of the tin melt and 0 corresponds to the top of the melt. It is important to note that this geometric arrangement is maintained throughout the remainder of this chapter. The time evolu tion of the concentration profile (for an aspect ratio of 0.50 cm/1.00cm = 1/2) in the top depletion configuration is shown in Figure 3 13. The time evolution of the axial velocity and pressure profile are shown in Figures 3 14 and 3 15 with all figures ha ving non -dimensional values. The time evolution profiles of the non-dimensional concentration, pressure, and axial velocity demonstrate fluid flow in the melt and its effects on the concentration profile. For instance, the concentration profile for = 15.13 clearly shows the effect of the fluid velocity through the non linear convective part of the species balance. There is noticeable noise in the velocity profile and it is attributed to the rounding errors previously discussed. The absolute velocity is very small compared to the maximum velocity at =15.13. Additionally, the noise is considered damped and insignificant when there was reasonable fluid velocity within the melt. The numerical chatter in the pressure can also be neglected by the same rationale, as the disturbances are damped out after the pressure has been un-scaled. Due to fluid flow in the top depletion configuration, the diffusive mass transfer of oxygen is aided by convection, and the oxygen concentration is equilibrated faster than the pure

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143 diffusion case. Figure 3 16 compares th e change in concentration (measured by an EMF) between top and bottom depletion according to the numerical output. The aspect ratio of interest is 1/2 (0.50 cm/1.00 cm) and, to further understand the importance of convection, a range of solutal Rayleigh nu mbers is included in the computations of the top depletion configuration. In the bottom depletion configuration (diffusion limited), the concentration profile is linear at long times, indicating diffusive mass transfer. The top depletion configuration sta rts in the same fashion as the bottom depletion configuration, until the velocity is sufficiently large enough to affect the mass transfer of oxygen. This is shown in Figure 316, where the top depletion concentration profile diverges from the bottom deple tion profile. After the fluid velocity begins to dissipate due to the declining solutal gradient, the top depletion profile slowly returns to a diffusion -limited form of mass transfer. When the profile returns to a linear profile, having the same slope as the bottom depletion configuration, mass transfer in the system is said to be governed, again, only by diffusion. The range of Rayleigh numbers highlighted in the figure demonstrates the varying effects of adjusting the potential energy initially available to the system. In the top depletion configuration, there is a slight hump in the profile corresponding to the two highest Rayleigh numbers. This hump is attributed to a (comparatively) large fluid velocity that significantly distorts the concentration profile and drastically reduces the concentration gradient across the melt. This large reduction of the concentration gradient then quickly reduces the fluid velocity until the system slightly settles and returns to a pseudo-steady state fluid velocity. E ventually, this pseudo-steady state fluid velocity dissipates, and the mass transfer of the system is again dominated by diffusion.

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144 A practical discussion regarding the time, at which fluid flow begins is necessary. The basis will allow the onset of fluid flow in the numerical computation to be clearly defined throughout this numerical work. When operating the spectral code a qualitatively well -defined velocity profile is quickly achieved when a driving force is applied to the system. These qualitatively defined velocity profiles in the axial and radial direction represent fluid velocities on the order of 1012 cm/s. Fluid velocities on this scale are practically impossible to physically realize through measurements. The physical realization of flow veloci ties during physical experimentation comes from measuring an EMF that must differ from the EMF measured in the diffusion -dominated system. Through numerical simulation it was found that very low fluid velocities, although well defined, does not affect lin ear diffusion of a solute. As the fluid velocity increases, however, there becomes a fluid velocity (on the order of 104 cm/s for ) that disrupts the flat concentration isopleths causing them to become nonlinear. These non -linear isopleths are the result of radial solutal gradients that assist in driving fluid flow. Fortunately, these radial solutal gradients have been referenced in physical experiments via EMF measurements [1]. It is important to realize experimental EMF measurements are taken by m easuring the average EMF over the entire sensor boundary. When a radial solutal gradient encounters a sensor boundary the average EMF value can change drastically from the expected diffusion dominated EMF measurement. This abrupt change in the EMF behavior can be used to detect fluid flow. Figure 3 17 (having an aspect ratio of 0.5 cm/1.0 cm = 0.5) illustrates the smallest fluid velocity and solutal isopleths that can be experimentally recognized. Past research has also concluded the maximum sensitivity of such a large sensor (spanning a diameter of 1 cm) was on the order of 104 cm/s for experimental measurements over small heights [1, 2].

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145 The computational results show fluid flow initiates at the top of the geometry where the boundary condition is impose d and then slowly incorporates the remainder of the fluid. Since the EMF sensor is located on the opposite side of the imposed boundary condition there is some time between the flow onset (onset of non-linear isopleths) in the top part of the fluid and tha t of the fluid adjacent to the EMF sensor. For a constant RaS, the time between the onset of flow at the top and bottom of the geometry increases for taller geometries because of the increased axial distance. Because there is additional time before the flu id flow is recognized by a sensor, the bulk fluid flow can increase past the 104 cm/s value before it is sensed. Thus, for taller geometries the lowest fluid velocity measurable is larger than those fluid velocities measurable in shorter geometries. Obse rving the change in EMF is currently the only means of physically detecting fluid flow in this simple two cell arrangement. Therefore, it is necessary to determine when the EMF profile departs from the normal diffusion-dominated EMF response. For this nume rical study, a departure of 1 mV was used to indicate fluid flow had become sufficiently to affect the measured EMF. As previously mentioned fluid flow is detected because there is a radial solutal gradient generated as a byproduct of the flow. Thus during fluid flow the measured EMF at the surface is not due to any single isopleth, but due to the average adjacent concentration. This becomes more evident as the flow reaches its maximum velocity as depicted in Figure 3 18. It has been demonstrated that flui d flow develops in the top depletion configuration. An examination of the aspect ratio at which flow is generated, the velocity at which the solutal profile is affected, and the maximum velocity, is explored next. The value of RaS cannot be arbitrarily selected because there is a limitation of the maximum concentration. For a specific

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146 temperature the saturation concentration of oxygen determines the maximum concentration of oxygen in the liquid tin. Any value above the saturation concentration will simply f orm SnO2. The concentration gradient is important because it is the only variable in the RaS expression not defined by the geometry or physical parameters. The Rayleigh number contains the driving force behind fluid flow and a limitation of its value impos es a limit on the fluid flow itself. A series of numerical calculations was performed for various aspect ratios of liquid tin to observe the fluid velocity at which the profile departs from the diffusion -limited case, and the maximum fluid velocity achieva ble. Table 3 6 summarizes the aspect ratio and Rayleigh numbers ( Ras/2) that were investigated (using the physical parameters listed Table 3 4). The axial velocities close to r = 0 and r = 1 are not similar, due to the no-slip boundary condition imposed a t the wall. The maximum axial velocity occurred very close to r = 0 and is recorded in the table. Table 3 6. Geometric p arameters and results for top depletion numerical a nalysis Experiment # Height (cm) R/H) Rayleigh # Divergence Time (min) Maximum V elocity ( m/s) 3 1A 0.333 1.5 1,270* -------< 10 10 3 2A 0.400 1.25 2,190* -------< 10 10 3 3A 0.500 1.00 4,290* -------< 10 7 3 4A 1.00 0.50 34,290* 36.83 88 3 4B 1.00 0.50 30,000 46.40 62 3 4C 1.00 0.50 27,500 57.73 44 3 4D 1.00 0.50 25,000 75.13 21 3 4E 1.00 0.50 20,000 -------< 10 5 3 5A 1.25 0.40 66,690* 34.70 110 3 5B 1.25 0.40 60,000 40.60 92 3 5C 1.25 0.40 55,000 48.40 76 3 5D 1.25 0.40 47,500 65.30 48 3 5E 1.25 0.40 40,000 -------4.9

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147 Table 3 6. Continued 3 6A 1.5 0.33 115,710* 36.10 120 3 6B 1.5 0.33 100,000 44.65 93 3 6C 1.5 0.33 85,000 59.30 66 3 6D 1.5 0.33 75,000 78.50 44 3 6E 1.5 0.33 65,000 -------10 *Maximum Solutal Rayleigh Number The graphical results of these numerical c omputations are given in Appendix A. Figure 3 19 summarizes the time it takes for fluid flow to affect the measured EMF over a range of aspect ratio. For a specific aspect ratio, the larger the solutal Rayleigh number, the faster measurable fluid flow is g enerated. For a decreasing aspect ratio, the onset time for fluid flow stays low over a larger range of RaS. This means there is a greater range of RaS without fluid flow. For higher aspect ratios no flow was detected (even though the solutal Rayleigh numb er was above the critical RaS) because the concentration gradient was not maintained for a sufficient amount of time due shortened axial diffusion length scales. Simply, the solute diffused too quickly across the short height of the liquid tin to maintain a significant concentration gradient. Figure 3 20 shows the maximum achievable fluid velocity over a range of RaS and For a decreasing aspect ratio, larger solutal Rayleigh numbers were achievable, and therefore larger fluid velocities were observed. Although the maximum fluid velocities were on the order of 102 and 103 mm/s, they were significant relative to the siz e of the melt and diffusive velocity. The development of fluid flow within liquid tin in the top depletion experiments is well documented in this work as well as others [1, 2, 16, 72, 73, 161]. The generation of fluid flow in the tin melt is useful if fluid velocities are to be measured and are of interest. The original purpose of this experimental configuration, however, was to successfully measure diffusion coefficients of oxygen in the liquid tin. For the top depletion experiments to be successful, a new approach must be employed to negate the onset of fluid flow in the melt.

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148 Case 3: Periodic Concentration Boundary Condition Configuration The periodic concentration boundary condition configuration seeks to reduce the convective mass transfer effects. It has been proposed that a sinusoidal concentration boundary condition used in an unstable configuration (one that results in fluid flow) should be able to remove a solute from the system without inducing fluid flow. Moreover it is expected that a critical f requency exists where values above this frequency do not induce fluid flow This is due to the imposed periodic concentration boundary condition s ability to sustain a stable solutal gradient faster than fluid flow can be generated within the liquid tin me lt. Given the previously report ed response time of YSZ sensors on the order of milliseconds the maximum frequency at which the boundary condition can oscillate is 1 kHz. It is expected that at very low frequency the periodic boundary condition chang es so slowly the solute has time to equilibrate across the melt minimizing the solutal driving force. The task at hand is to determine the maximum and minimum frequencies and understand how the fluid reacts when exposed to frequencies between these values. The f ollowing study impose s a periodic boundary condition in the geometry used in the Case 2 : Top Depletion Configuration for which fluid flow was detected. Two sub -cases of the periodic boundary condition were explored as potential methods of removing a solut e from the top of the right cylindrical geometry without inducing fluid flow. The first sub -case examines the effects of oscillating the concentration boundary condition between the saturation concentration of the tin melt (also used as the initial conditi on) and a zero concentration boundary condition This simulate s complete removal of the solute and mimic s the top depletion numerical experiments. The periodic boundary condition is represented by a cosine function so that the initial boundary condition is the saturation concentration. Using the parameters listed in Table 3 4, the system response was computed over a range of frequency and aspect ratio to determine the frequency range for which no flow would be detected.

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149 The second sub-case examines the ef fects of starting the initial concentration of the melt at a specific value less than the saturation concentration. Unlike the previous sub -case, the periodic boundary condition will start at the initial concentration and oscillate between a concentration slightly larger and smaller than the initial bulk concentration. This does not exactly mimic the top depletion experiment, but contains elements of it through the extraction of the solute from the top of the liquid tin melt. A comparison between the two sub -cases reveals the advantages and disadvantages of the two methods. Although the geometry is not semi infinite, Equation 2 69 serve s as a guide to the structure of the ir solution s and indeed can be the actual solution if the frequency is high enough to ke ep the diffusion length small and less than the height of the melt. Equation 2 69 shows that the current response for a specific frequency has amplitude based on mass transfer (diffusion coefficient) of the solute in the melt. This study focused on the ran ge of the aspect ratio (those not having extremely large heights and examined in Case 2: Top Depletion Configuration) that have some experimental validity through direct applications to the solder bump geometry. In the first sub -case, the initial concentr ation was set as the saturation concentration using the dimensions and physical parameters employed in the Case 2: Top Depletion Configuration. The only exception is that a periodic concentration boundary condition was imposed in place of the constant conc entration at the top electrode/electrolyte interface The periodic boundary condition oscillated between the saturation concentration and a zero concentration of the solute having non -dimensional values of 1 and 0, respectively. Again the top depletion con figuration was maintained by saturating the bulk tin as an initial condition. Also it should be noted that the periodic boundary condition was a cosine function that did not impose a gradient at time t = 0. If

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150 a sine function was used the opposite case would be true and at time t = 0 the maximum solutal gradient would have been imposed. A number of spectral computations were conducted to determine the critical frequenc y that induced fluid flow over a frequency range of 1 to 105 Hz. A radius of 0.5 cm and a C of 3 x 105 mol/cm3 were maintained constant throughout all calculations Table 3 7 summarizes the geometries and parameters examined and the computational results over the frequency range of interest The numerical output for each calculation is prov ided in Appendix A. Table 3 7. Geometric parameters and results for a periodic boundary c ondition Experiment # R/H) Frequency (Hz) Maximum V elocity ( m/s) Initial Onset Time of Flow (min) 3 7A 0.33 7.50 x 10 5 1.94 -------------3 7B 0.33 1.00 x 10 4 35.0 413.3 (S. Periodic*) 3 7C 0.33 1.25 x 10 4 47.0 323.3 (S. Periodic*) 3 7D 0.33 2.50 x 10 4 65.0 175.1 (Initial Period) 3 7E 0.33 5.00 x 10 4 106 102.8 (Initial Period) 3 7F 0.33 6.25 x 10 4 109 89.1 (Initial Period) 3 7G 0.33 7.50 x 10 4 107 79.8 (Initial Period) 3 7H 0.33 1.00 x 10 3 87.0 70.6 (Initial Period) 3 7I 0.33 2.50 x 10 3 85.0 84.1 (U. Periodic*) 3 7J 0.33 5.00 x 10 3 27.3 104.1 (U. Periodic*) 3 7K 0.33 7.50 x 10 3 0.501 -------------3 8A 0. 40 1.13 x 10 4 0.20 -------------3 8B 0.40 1.25 x 10 4 18.1 397.3 (Initial Period) 3 8C 0.40 2.50 x 10 4 52.3 176.2 (Initial Period) 3 8D 0.40 5.00 x 10 4 74.4 97.6 (Initial Period) 3 8E 0.40 6.25 x 10 4 76.1 87.2 (Initial Period) 3 8 F 0.40 7.50 x 10 4 74.7 78.2 (Initial Period) 3 8G 0.40 1.00 x 10 3 61.5 68.1 (Initial Period)

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151 Table 3 7. Continued 3 8H 0.40 2.50 x 10 3 41.4 80.9 (U. Periodic*) 3 8I 0.40 5.00 x 10 3 1.98 103.5 (U. Periodic*) 3 8J 0.40 7.50 x 10 3 0.07 -------------3 9A 0.50 2.00 x 10 4 0.33 -------------3 9B 0.50 2.50 x 10 4 21.7 221.3 (Initial Period) 3 9C 0.50 5.00 x 10 4 63.4 109.8 (Initial Period) 3 9D 0.50 6.25 x 10 4 65.8 94.2 (Initial Period) 3 9E 0.50 7.50 x 10 4 47.6 91 .8 (Initial Period) 3 9F 0.50 1.00 x 10 3 11.4 80.5 (Initial Period) 3 9G 0.50 1.25 x 10 3 0.59 -------------*Flow is peri odic, but the onset time is not necessarily the period. The numerical calculations defined a critical frequency range tha t correspond s to the generation of measurable fluid flow For frequencies outside of this range no computationally measurable fluid velocities were detected. Additionally three main fluid flow behaviors were observed when exploring the region in which flow was generated. The first was fluid flow generated only in the initial period of concentration oscillation. In this case there was a sufficient concentration gradient with adequate time to develop fluid flow. The mixing effect of the fluid flow (minimizing the potential for subsequent solutal gradients large enough to generate flow) and speed of the frequency did not allow fluid flow to be generated in succeeding periods. For slightly higher frequency, fluid flow was still generated, but in an unsteady per iodic fashion denoted in Table 3 7 as (U. Periodic). An unsteady periodic flow is defined as fluid flow in which the maximum f luid velocity slightly increases after each period, reaching a maximum velocity at one particular p eriod, and then slowly decreasi ng over the remaining periods until no fluid flow was detected. Imposing s lightly lower frequenc y than those exhibiting fluid flow only

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152 in the initial period results in periodic flow and denoted in Table 3 7 as (S. Periodic). Steady periodic flow reached the same maximum fluid velocit y for each period (except for the first period due to the initial conditions) and was sustained for the length of the experiment. Thus, a periodic steady state solution was determined for all frequency ranges although only the S. Periodic fluid flows maintained a nonzero solution for long times. In summary as the time scale (1/ ) of the frequency oscillati ons approaches the diffusive time scale (H2/D) there is a region in which various types of flow developed. For frequency oscillations having a similar time scale to the diffusion time scale, no flow was generated, because the solute had time to equilibrate. For frequency oscillations with a small time scale compared the diffusion time scale, no fluid flow was detected. D ue to the lack of a significant number of data points only a qualitative picture of the flow regimes is given in Figure 3 21. It is expected future studies having a more rigorous definition of fluid flow and an increase in the number of data points will resul t in a high resolution quantitative study It is not within the scope of this study however, to determine the onset of various flow regimes, but only to determine the regions where flow is generated. Figure 3 21 gives a qualitative analysis of the various flow regimes, and when coupled with Table 3 7 clearly defines those regions where fluid flow is not detected for the aspect ratios of interest. Figure 3 21 is a qualitative representation of the experimental data summarized in Table 3 7 that shows the correspondence of the various flow regimes to the inverse of the aspect ratio (increasing height). As expected and observed in the numerical results when the height of the geometry is increased the frequency range that would generate flow is also increased. Additionally if the fluid height was sufficiently large unsteady or steady periodic fluid flow was also possible

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153 It is surmised that the unsteady periodic fluid flow is a result of the concentration oscillating slightly too fast for a significant amou nt of fluid flow to equilibrate the solute, but slow enough that there is time for some fluid flow to develop. Eventually, the concentration at the bottom of the melt is too low to maintain a concentration gradient, and fluid flow becomes impossible. In th e case of periodic fluid flow, it is suggested that the oscillating concentration boundary condition is sufficiently slow that the concentration at the bottom of the geometry can be recharged and re -initiated for each oscillation. The recharged concent ration at the bottom of the geometry is then sufficient to create a reasonable concentration gradient. There is a balance, however, where t he concentration oscillates slow enough to increase the bulk solute concentration (when the periodic concentration bo undary condition is increasing), but oscillates fast enough to create a concentration gradient across the tin melt. A graphical representation of the maximum generated fluid velocity is shown in Figure 3 22. For the larger aspect ratio ( R/H ), the maximum fluid velocity shows the expected parabolic velocity distribution over the frequency range. Interestingly the maximum fluid velocit y correspond ing to the smaller aspect ratio (taller heights at constant R ) do not behave as expected. This is due to the incr easing effect o f the unsteady periodic region, which becomes larg er for decreasing aspect ratios The onset time of flow was also observed, and is highlighted in Figure 3 23. As expected, for the smaller aspect ratios the onset time of flow at a particula r frequency is lower for the larger aspect ratios. This is b ecause the smaller aspect ratio results in a taller geometry that has a greater potential for flow. Of note, the frequency that generates fluid flow the fastest is not the same frequency that gene rates the maximum fluid velocity achievable in the melt. The most important observation made was that the most rap id onset time for fluid flow on the order of 1

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154 hour. Thus, it is possible to take coulometric data not corrupted by fluid flow for a reasonabl e period of time. Since it has been d emonstrated there is a frequenc y range over which no fluid flow is observed this range is of interest in diffusion measurements As previously mentioned, an oscillating current is measured at the top of the tin melt to result in a coulometric response. A negative current corresponds to the solute being removed from the system, and a positive current indicates solute being introduced into the system. From the sinusoidal response, mass transfer data can be extracted from the amplitude of the current. Unfortunately, the current response for frequency in the no flow regime in Figure 3 21 reflects time -dependent amplitude. This time dependent amplitude is due to an exponentially decreasing time -dependent term in the amplitu de portion of the concentration profile. The time scale for this exponential decay can be quite large, maintaining the time dependence of the amplitude for a long period of time. As previously mentioned, the typical sinusoidal response for this sub -case has a timedependent, exponentially decreasing midpoint, about which the amplitude of the current oscillates. In addition to the decreasing midpoint, while the amplitude of each sin wave appears to be equivalent they are not. A measure of the diffusion coe fficient could be taken if the periodic amplitudes were equivalent. Figure 3 24 s hows the time dependency of the current response for a constant frequency over a range of diffusion coefficients. For increasing values of the diffusion coefficient the ampl itude of frequency response also increases without a change in the phase. The offset seen in Figure 3 24 is a result of the difference in the diffusion coefficients affecting the initial response where the period is the same for all diffusion coefficients. As previously mentioned, for this sub -case the amplitude over time are not consistent. Therefore, without prior numerical knowledge of the system, it is difficult to

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155 extract quantitative information regarding the diffusion coefficient from the experimenta l measurements. The time dependent exponential decay of the amplitudal midpoint also increases the difficulty of the calculation. Further analysis of the situation revealed the exponential midpoint decay required fewer oscillations at lower frequenc y This is sensible, since more time is available at the lower frequenc y to allow for a change in the concentration. The specific role of the frequency in the exponential decay time constant is unclear because the frequency effects are most likely damped out by t he diffusion coefficient. A comparison between the decay rates of a higher and lower frequency are depicted in Figure 3 25. The decreasing sinusoidal r esponse of the current continues until the system reaches a pseudo -steady state, at which the concentrat ion at the bottom of the liquid tin melt was periodically oscillating about the same concentration. Pseudo-steady state was achieved when the specific concentration around which the entire system oscillated was half of the periodic concentration range. T he exponential decay of the sinusoidal response was negated when the system began consistently oscillating around half of the initial concentration. Unfortunately, the time necessary for the system to reach this pseudo -steady state was quite long for all fre quencies studied Thus, the idea was put forth to initiate the system at its pseudo-steady state value The second sub-case used the same geometric parameters and experimental setup as the first periodic boundary condition sub-case with only one exception in the initial concentration. Instead of using a very large initial concentration, the initial bulk concentration was reduced to half of the concentration gradient that would be spanned by the periodic boundary condition. This setup allowed for the period ic boundary condition to raise and lower the concentration of the melt by equivalent amounts. This sub -case demonstrated the importance of beginning the experiments at the ir p eriodic steady state values. When initiating the computations with these

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156 conditio ns the results clearly exhibit no time -dependence of the amperometric response (save for the initial response ). The range of frequency employed in the first sub case was again used in the second sub case. Over all frequency ranges n o fluid flow was observ ed within the liquid tin melt for all geometries explored. The lack of fluid flow was expected because of the short geometries and reduced concentration gradient. Additionally, for every concentration gradient imposed by the oscillating boundary condition (resulting from a concentration sink) that induced low level flow s there existed a counter concentration gradient when the boundary condition switched to impose a concentration source condition. This stabilizing solutal gradient counterbalanced and quickl y dissipate d any fluid flow that may have been generated. As mentioned for the previous subcase, although there were no cases of flow observed for these geometries, it is expected that with increased height there is a range of frequency that will permit f luid flow due to an increase of the potential energy. Figure 3 26 illustrates the pseudo-steady state oscillations present in the second sub-case for a range of diffusion coefficients. These results are similar to Figure 3 22, in that a larger diffusion c oefficient increases the amplitude of the response. The main difference between this and the previous sub -case is the amplitudes do not vary from one period to the next Because the amplitudes are time independent, mass transfer data can be extracted from them (specifically the diffusion coefficient). Figure 3 27 shows the effect of changing the non-dimensional concentration range around the initial bulk concentration. For example, at a non -dimensional C of 0.5 and an initial non dimensional bulk concentra tion of 0.5, the periodic concentration boundary condition ranges from 0.25 to 0.75. As Figure 327 illustrates, the only effect of changing the oscillation range is

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157 an amplification of the signal. Therefore, if the experimental amperometric response for a system is small, an increase in the concentration perturbation will increase the current signal. Summary The mass transfer effects of oxygen in an isothermal liquid tin system were analyzed for three separate cases. The first case examined the bottom dep letion of oxygen over a range of geometri c parameters and gave similar results to those obtained experimentally by other authors. The second case attempted to measure diffusion coefficients in an unstable geometry, with limited success. This case, however revealed a feasible methodology for measuring fluid velocities generated from solutal instabilities. The third case attempted to eliminate fluid flow from the unstable configurations examined in the second case through the use of periodic boundary condi tions. These efforts were successful when allowing the concentration boundary condition to oscillate evenly about its initial value. In this manner, extraction of mass transfer data was possible for the top depletion configuration. The most important condi tions for the onset of flow were a sufficient instability and an adequate amount of time for the fluid flow to gain momentum and become significant. A reduction in either of these parameters would effectively remove fluid flow from the geometry. Visualizat ion of Fluid Flow The previous sections focus on the numerical analysis of mass transfer in a right cylindrical geometry dominated by either convection or diffusion. The numerically -predicted EMF concentration profiles for the diffusion-dominated systems w ere different than those profiles corresponding to a convection dominated system. The difference in the EMF response implies that these methods can be used to detect, monitor, and extract physical properties of convective flows. Unfortunately, extracting q uantitative fluid velocity using a single macro-

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158 sensor requires prior numerical knowledge of the experimental system to which the EMF results are compared. A system of individual sensors should be used to inject and detect a packet of oxygen so that loc al spatial measurements would be available (contrary to one global measurement if using one sensor) and allow the fluid velocity to be measured without prior numerical knowledge of the system. In the previous sections, the measured concentration was an a verage of the surface concentration over the entire radius because the electrolyte boundary condition. For this reason, the implementation of a number of small independent sensors will promote higher resolution of the oxygen concentration. Experimental Se tup and Justification of the Numerical Code The geometry used in this section is the same as was previously used with one main difference. The radius over which a specific concentration is defined (located at the bottom of the liquid tin melt) has now bee n reduced to a radius smaller than the entire radius of the geometry denoted as RC. A no -flux condition was applied to the remaining radius ( r > RC) for which the concentration was not defined. A thermal driving force, rather than a solutal force, was used to generate fluid flow because the necessary boundary conditions for a solutal driving force would impede measurements of the solute as a tracer material. To generate thermally induced fluid flow, two constant temperatures were introduced at the top and bottom, with the temperature at the bottom higher than the top in order to create thermal instability. No flux heat (adiabatic) and solute conditions were enforced on the sides of the geometry. Figure 3 28 summarizes the geometry and its respective boundary conditions used in the numerical analysis. Preliminary simulations were carried out to validate the code by independently inducing a thermal and solutal gradient. Fluid flow was observed in each case corresponding to the critical Rayleigh numbers and pre vious findings. Also investigated was the potential for fluid flow

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159 (resulting from unavoidable radial solutal gradients) when introducing the solute into the melt from one sensor. Only radii 10% or less of the total radius, R, were investigated and it was found that an insignificant amount of fluid flow (<< 1 nm/s) resulted from the radial solutal gradient. Therefore, the introduction of a solute over a radius less than 10% of the total radius would not affect fluid flow within the melt, and the introductio n of a solute would serve as an excellent tracer material by not disturbing the system. Numerical Analysis Following justification of the code, the introduction of a solute within a thermal profile was investigated. First, a thermal gradient was imposed o n the system to generate fluid flow. After the fluid flow reached steady state, a constant concentration boundary condition was imposed over a radius 10% (or smaller in some cases) to introduce the solute into the convecting melt. Ideally, the solute shoul d diffuse into the melt and convect along streamlines. It should then continue to diffuse across streamlines and convect around the melt until the solute equilibrates. The expectation is that while the solute is convecting (and to a lesser degree diffusing), a tracer caught in the outer most streamline should be detected. Unfortunately, after introduction of the solute, the expected system behavior only lasted a short time before the code diverged. The code was rechecked for coding errors and was once agai n justified as functional and accurate. It was then postulated that the divergence was the result of using two very different length scales pertaining to the diffusion coefficient (~105 cm2/s) and fluid viscosity (~103 cm2/s). Because these two parameter s resulted in different in length scales, it was difficult for the code to entertain the effects of both. Attempts were made to manipulate the geometry (by shortening the height and varying the fluid velocities) to affect the length scales of these two p arameters without success. The final conclusion was that the fineness of the Chebyshev mesh was insufficient for the code to

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160 recognize both length scales. This was concluded because the simulation would operate properly in the denser part of the mesh (clos e to the edges of the geometry), then begin to diverge as the solute reached a sparser region of the mesh. It was theorized that this difficulty could be overcome by simply increasing the mesh size; however, greater computational capabilities were not avai lable. Summary An attempt was made to numerically model the introduction and movement of a solute in a thermally convective melt. It was found that a constant concentration, Csat, introduced into the melt over radii less than 10% of the total radius would not affect the overall fluid flow profile. It was also concluded that the stiff numerical problem involving the movement of a solute via diffusive and convective effects required a very fine mesh size that could effectively cover the length scales correspo nding to both diffusion and viscosity. The use of a finer mesh with an increased density of nodes should resolve the movement of a solute in a thermally convective flow. Conclusions The purpose of this chapter was the development of a numer ical method empl oyed to assist in hypothesizing future experimental results. The spectral Chebyshev method was used in this work and a review of the method was given. Special care was taken to describe the intricacies of the spectral code and how the code should be constr ucted. The spectral code was successfully benchmarked with a known analytical solution qualitative analysis of expected results, and a quantitative comparison with experimental results. Next the mass transfer effects of oxygen in a liquid tin melt were numerically explored for three configurations: bottom depletion, top depletion, and a periodic boundary condition. For the bottom depletion configuration mass transfer data were re solved for various aspect ratios that

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161 tailored well with experimental data. I n the top depletion configuration, fluid flow was detected, and efforts were made to quantify the generated fluid veloci ty A periodic boundary condition that could be used to extract mass transfer data from the top depletion configuration was also explore d. The results from these numerical experiments related the amperometric response pertinent mass transfer data. An attempt was also made to numerically model the visualization process of titrating a packet of oxygen into the tin melt and using a serie s of sensors to detect its movement. Unfortunately there was a numerical issue related to the varying length scales of the fluid and diffusive velocity. This numerical issue coupled with insufficient computer memory prevented success. Regardless, the other numerical simulations reviewed in this chapter assisted in the sensor array design and implemented MES3A validation experiments. Figure 3 1 Converting the physical domain into a computational domain for a right cylinder of ph ysical domain (0, H) and (0, R) z =H z =0 r =0 r =R PHYSICAL DOMAIN z =1 z = 1 r =1 COMPUTATIONAL DOMAIN r = NEGATED REGION 0 z 1 z 0 r 1 r r r z z

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162 Figure 3 2. Flow chart of the Chebyshev spectral method used in this w ork NO n*=n*+1 Explicitly Solve C P and v vz r for Time Step n*=n+1 Discretize the Equations of Change Input Boundary Conditions Input Physical Parameters Input Initial Conditions Steady State Convergence Criteri a: 12 1 1 *-1 n z *-1 n r n z n r10 v v v v abs max n n n nC P C P Plot C P and v vz r Steady State Solution YES

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163 Figure 3 3 Benchmark geometry with analytical solution PHYSICAL DOMAIN r = 1 r = 0 z = 1 z = 1 Line of Symmetry 0 v 0 v zr z 0 v 0 v z r z 0 v 0 v rz r C = 0 C = 0 0 r C

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164 0 0.2 0.4 0.6 0.8 1 -1 -0.5 0 0.5 1 -0.02 -0.01 0 0.01 0.02 Radius Surface Plot of Vr Velocity Height Vr Velocity Figure 3 4 Surface plot of th e radial velocity component

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165 0 0.2 0.4 0.6 0.8 1 -1 -0.5 0 0.5 1 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 Radius Surface Plot of Vz Velocity Height Vz Velocity Figure 3 5 Surface plot of the axial velocity component 0 0.2 0.4 0.6 0.8 1 -1 -0.5 0 0.5 1 -0.2 -0.1 0 0.1 0.2 Radius Surface Plot of Pressure Height Pressure Figure 3 6 Surface plot of the pressure

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166 0 0.2 0.4 0.6 0.8 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 x 10-3 Radius Surface Plot of Concentration Height Concentration Figure 3 7 Surface plot of the concentration

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167 Figure 3 8 System configuration for numerical Cases 1, 2, and 3 PHYSICAL DOMAIN r = R r = 0 z = H z = 0 Line of Symmetry Momentum: No Slip Momentum: No Slip Momentum: No Slip Species: Case 1 No Flux Species: Case 2 Constant Concentration Species: No Flux g 0 V F C Sc Ra V P Vs 2 C C V C Sc2 {3 34} {3 35} {3 36} Species: Case 3 Periodic Concentration Species: Case 1 Constant Concentration Species: Case 2 No Flux Species: Case 3 No Flux

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168 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1Concentration Surface Plot of Non-Dimensional Concentration Radius Height 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure 3 9 Time evolution of the concentration profile for Case 1

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169 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 x 10-10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 x 10-10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity Figure 3 10. Time evolution of the axial velocity profile for Case 1 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -500 0 500 Radius Surface Plot Non-Dimensional Pressure Height Pressure 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -500 0 500 Radius Surface Plot Non-Dimensional Pressure Height Pressure Figure 3 11. Time evolution of the pressure profile for Case 1

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170 Time (min) 0 10 20 30 40 50 60 E Eo (mV) -20 0 20 40 60 Numerical Solution Analytical Solution Experimental Data [1] H= 0.389 cm T= 723 oC H= 0.467 cm T= 725 oC H= 0.750 cm T= 730 oC Figure 3 12. Analytical, numerical, and e xperimental b ottom d epletion r esults [1]

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171 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1Concentration Surface Plot of Non-Dimensional Concentration Radius Height 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure 3 13. Time evolution of the concentration profile for Case 2

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172 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 x 10-10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 1.5 2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 1.5 x 10-13 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity Figure 3 14. Time evolution of the axial velocity profile for Case 2 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -150 -100 -50 0 50 100 Radius Surface Plot Non-Dimensional Pressure Height Pressure 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 Radius Surface Plot Non-Dimensional Pressure Height Pressure Figure 3 15. Time evolution of the pressure profile for Case 2

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173 Time (min) 0 20 40 60 80 E Eo (mV) 0 20 40 60 Diffusion RaS = 34,290 RaS = 30,000 RaS = 27,500 RaS = 25,000 Figure 3 16. Comparison between top and bottom depletion numerical results 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.1 0 0.1 0.2 0.3 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity 0.1 0.1 0.1 0.2 0.2 0.2 0.30.30.30.40.4 0.40.50.5 0.50.60.60.6 0.70.70.7 0.8 0.8 0.8 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 3 17. Axial velocity and concentration profile at onset of fluid f low

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174 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity 0.10.10.10.20.20.20.20.30.30.30.30.40.40.40.40.40.50.50.50.50.50.60.60.60.70.7 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 3 18. Velocity and concentration profile at maximum fluid velocity Solutal Rayleigh Number/1000 20 40 60 80 100 120 140 Onset Time (min) 30 40 50 60 70 80 90 = 0.50 = 0.40 = 0.33 Figure 3 19. Onset time of fluid flow vs. the RaS ( =R/H)

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175 Solutal Rayleigh Number/1000 20 40 60 80 100 120 Maximum Velocity ( m/s) 0 20 40 60 80 100 120 140 = 0.50 = 0.40 = 0.33 Figure 3 20. Maximum fluid veloc ity vs. the RaS

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176 Figure 3 21. Qualitative analysis of flow r egimes for periodic c oncentration

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177 Log of Frequency (Hz) -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 Maximum Velocity ( m/s) 0 20 40 60 80 100 120 = 0.33 = 0.40 = 0.50 Figure 3 22. Maximum fluid velocity vs. f requency

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178 Log of Frequency (Hz) -4.2 -4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 Initial Onset Time of Fluid Flow (min) 50 100 150 200 250 300 350 400 450 = 0.33 = 0.40 = 0.50 Figure 3 23. Onset time vs. f requency

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179 Time (s) 0 10 20 30 40 Current Density (mA/cm2) -80 -60 -40 -20 0 20 40 DO = 8 x 10-5 cm2/s DO = 4 x 10-5 cm2/s DO = 1 x 10-5 cm2/s C = CSatCo = CSatf = 1 Hz R = 0.5 H = 1.5 Figure 3 24. Time dependent current density vs. time (v ariable Do)

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180 Time (s) 0 10 20 30 40 50 60 Current Density (mA/cm2) -100 -80 -60 -40 -20 0 20 40 60 5.0 Hz 1.0 Hz 0.1 Hz C = CSatCo = CSatD = 8x10-5 cm2/s R = 0.5 H = 1.5 Figure 3 25. Time dependent current density vs. time (variable f requencies)

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181 Time (s) 0 10 20 30 40 50 60 Current Density(mA/cm2) -30 -20 -10 0 10 20 DO = 8 x 10-5 cm2/s DO = 4 x 10-5 cm2/s DO = 1 x 10-5 cm2/s C = CSat/2 Co = CSat/2 f =1 Hz R = 0.5 H = 1.5 F igure 3 26. Pseudo steady state current density vs. time (variable Do)

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182 Time (s) 0 10 20 30 40 50 60 Current Density (mA/cm2) -60 -40 -20 0 20 40 C = 1.00*CSat C = 0.50*CSat C = 0.25*CSat Co = CSat/2 f =1 Hz R = 0.5 H = 1.5 D = 8x10-5 cm2/s Figure 3 27. Pseudo -steady state current density vs. time (variable C)

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183 Figure 3 28. System configuration for flow visu alization PHYSICAL DOMAIN r = R r = 0 z = H z = 0 Line of Symmetry Momentum: No Slip Momentum: No Slip Momentum: No Slip Species: No Flux Species: No Flux g 0 V F T Pr Ra F C Sc Ra V P VT s 2 C C V C Sc2 {C 1} {C 2} {C 3} Species: C Sat /No Flux Energy: Constant Temperature Energy: Constant Temperature r = R C T Pr T21 {C 4}

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184 CHAPTER 4 DESIGN, FABRICATION, AND CHARACTERIZATION OF THE MES3A DEVICE Introduction The numerical studies presented in the previous chapter explored physical experiments pertinent to crystal growth and solder bump studies. These studies assis ted in the design of the device to accommodate the experimentally required geometry and length scales, measurement resolution, and device response. The device was also formulated to circumvent potential material limitations while maintaining essential oper ational features. Based upon the MES3A design, a fabrication process was then developed to construct the sensor array using well established IC fabrication techniques. This chapter summarizes the MES3A design and specific steps of the fabrication process u sed to assemble the device. Subsequent characterization of the fabricated sensor array focused on a quality analysis of fabricated components, device reliability, and expected performance. Design of the Device When designing the sensor array two factors w ere considered: environmental constraints and operational requirements. The environmental constraints focused on operation at high temperature (600 to 900 oC) and low oxygen partial pressure (1020 atm). These environmental constraints necessitated careful consideration of the device construction materials, particularly those susceptible to high temperature oxidation. From an operational standpoint, the device required multiple compact electrochemical cells, each having a rapid response time (~ 1 ms), and located in close proximity (~ 100 nm). The design of the sensor array included materials capable of accommodating thermal expansion, dielectric isolation, and electrochemical cell operations. Complying with the operational requirements and environmental co nstraints in the initial design allowed for construction of a

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185 structurally sound array of high temperature solid -state micro electrochemical sensors. This section gives a review of the design considerations and the subsequent section details the entire sen sor array fabrication process. Material Selection An initial step of the MES3A design was identifying materials appropriate for a solid state electrochemical cell. Chapter 2 summarized the components of a single electrochemical cell and justified use of Y SZ as the solid electrolyte. Liquid tin was chosen as the anode material, due to its high electrical conductivity, well established thermochemical and th ermophysical properties similar to silicon boules and solder bump alloys. A copper/cuprous oxide refere nce electrode was selected because of its low polarizability and well established electrochemical and thermodynamic properties. Copper is the least polarizable among common metal -metal oxide reference electrode materials, including Fe/FeO, and Ni/NiO [146] A non -polarizing electrode is desirable, since the electrode s potential represents the equilibrium value and thus serves as a known reference. Previous work using a YSZ electrolyte and liquid tin electrode established the sufficient performance of Cu/C u2O reference electrodes in powder form [1, 2, 16, 72, 73, 161]. The choice to employ Cu/Cu2O as the reference electrode material was based on the success ful studies of Sears et al. [1], and the established use of thin film copper as an electronic intercon nect material in the semiconductor industry. Thus, copper had two major roles in MES3A: a component of the reference electrode and an electrical conductor. Unfortunately, thin film copper does not readily adhere to SiO2. This was resolved by depositing a t antalum adhesion layer (15 nm) preceded by a tantalum nitride barrier (60 nm) to prevent oxygen from the silicon dioxide layer from diffusing into the copper. Fortunately, a thickness of only a few nanometers is required of each material. The combination of the Ta/TaN

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186 layer later proved useful in minimizing difficulties with the lift off process and diffusion of oxygen into the copper vias. A dielectric material was employed to electrically isolate each sensor. To electrically and ionically isolate each se nsor, various SiO2 microstructures were used to obtain the dielectric properties and to integrate the required microelectronic fabrication processes. Initially, a thin thermal oxide layer was grown on a bare silicon wafer to electrically isolate the Si waf er from the copper vias. In contrast, a TEOS layer was used to separate the copper electrodes from each other and the anode material thus isolating the electrochemical cells. TEOS was used in this case because it was the most convenient form of SiO2 to de posit as a thin film. Gold was chosen for the contact pads because of its excellent electrical conductivity properties, compatibility with copper, and resistance to oxidation. Unfortunately, gold does not adhere well to a thin film of copper, as a result o f slight oxidation of the copper surface that occurs during the fabrication process. To resolve this issue, a very thin interlayer of chromium was used to promote gold adherence to copper. Figure 4 1 gives a cross -sectional view of the MES3A design, illustrating how the materials were used in the design. Structural Integrity Silicon (100) was used as the substrate due its well established device process technology. A major concern was the temperature range in which the device would operate (~500 to 900 oC). The highest operating temperature of the device is limited by the lowest melting temperature of the device components. Additional concerns arise from thermal cycling across a large temperature range (20 to 900 oC). Different CTEs of materials create high stress regions t hat are susceptible to cracking and can lead to device failure. Table 4 1 summarizes the melting points and CTEs of the materials used.

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187 Table 4 1. Melting temperature and CTE of device m aterials Material Melting Temperature ( o C) Linear CTE (ppm o C 1 ) Silicon 1410 [137] 3 [137] Thermal Oxide 1619 [137] 0.5 [175] 8 mol% YSZ 2750 [ 113 ] 10 [176] Copper 1083 [137] 16.6 [137] Tantalum 2996 [137] 6.5 [137] Tantalum Nitride 3369 [137] 3.6 [177] Gold 1064 [137] 14 .2 [ 137] Chromium 185 7 [137] 6 [137] A slow rate of heating or cooling will reduce the impact of a CTE mismatch. Thermal management experiments revealed cracking and degradation of the TEOS layer for ramp rates greater than 1.5 oC/min. Figures 4 2 and 4 3 depict a birds eye view the typical results for large ramp rates that caused the TEOS layer to crack. Figures 4 2 A and B show only the surface TEOS layer that exhibits a range of crack formations. Figures 4 3 A and B show the TEOS layer cracked abov e a copper interconnect, likely due to the thermal mismatch between the two materials. Cracks in the TEOS layer can potentially expose the copper lines to the liquid tin, resulting in an electrical short -circuit of the electrochemical system. Further conce rns about the device structure stem from volumetric increases of the copper materials due to oxidation. Copper will be oxidized and reduced naturally during operation of each sensor. Although copper will not reduce SiO2 oxygen may transport through the TEO S layer or along the barrier layer interface. This is not expected to be an issue as transport rates are low in TEOS and the Ta/TaN barrier layer. If a crack develops, however, copper can be exposed to oxygen in the ambient atmosphere or liquid tin, oxidiz e, and result in an electrochemical short circuit.

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188 The main source of copper oxidation is oxygen in the liquid tin transported across the electrolyte to the copper interconnects. If a large amount of oxidation occurs at the top surface of the copper interc onnect the electrode surface can be completely oxidized This will reduce the electrical conductivity and block further oxidation of copper required to equilibrate the cell. Apparently this does not readily occur in bulk Cu/Cu2O, as it has been used in the past. Oxidation can increase the local volume of the copper interconnect up to 179% of its original volume [see Appendix C]. A large volume change to the physically confined Cu/Cu2O electrode can lead to cracking of the adjacent material. At elevated te mperatures, copper is ductile, but Y S Z and TEOS are brittle. It is also noted that the copper electrode is initially deposited as pure copper, and later oxidized to a two phase electrode. Most oxygen is supplied to th e copper from the ambient atmos phere or liquid tin. Figures 4 4 A and B show the unfortunate result of copper oxidation (confirmed by EDS): delamination of the YSZ and surrounding TEOS film from the device. Fabrication of the Device The following section gives a detailed description of the MES3A fabrication process, beginning with the sensor array layout. The individual fabrication steps are then fully detailed, with a discussion of the difficulties encountered, and the methodology used to resolve them. The analysis will conclude with dicing and mounting of the array to produce multiple ready to operate MES3A devices. Lithography and Mask Designs The array was designed to explore flow in small liquid metal systems using tin as the model fluid. The intended application was solder bumps with dime nsions on the order of a few mm. A plan was formulated to construct three sensor layouts to accommodate three different tin melt geometries. Three cylindrical liquid tin radii were chosen to experimentally study fluid

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189 dynamics in varying aspect ratios. The three radial lengths were coupled to a variety of container heights. Fluid flow of a liquid melt confined in a cylinder is a well -studied system, and wa s used in this work for validation. Therefore, the most beneficial geometric orientation of the YSZ sen sors is a radial spread of concentric circles, because of the expected radial direction of fluid flow. Table 4 2 summarizes the radial spacing and orientation of the YSZ sensors for the range of the selected radii. Table 4 2. Radial distances of YSZ sen sors for three experimental d imensions Quartz Tube Radius Inner YSZ Radius Middle YSZ Radius Outer YSZ Radius 1.0 0.250 0.500 0.750 2.0 0.583 1.167 1.750 3.0 0.917 1.833 2.750 *All units are millimeters Three different mask designs (drawn wi th AutoCAD) were required to accommodate the radial geometries. Example shadow masks for the deposition of YSZ corresponding to the 1 and 3 mm radii are given shown in Figures 4 5 A and B The larger outer square is the overall size of the chip, and the pa ttern inside the chip area viewed as a series of small dots (actually squares) is the sensor array. Each separate dot is a single YSZ electrochemical cell with a length and width of 20 microns. The sensors are laid out in a radial arrangement of concentric circles with the spacing indicated in Table 4 2. The mask design of each YSZ radial design required two additional masks to be prepared. One mask set specified the location of the copper lines, electrolyte, and gold contact pads. Figures 4 6 A and B illustrate the copper and gold masks used for the 3 mm sensor design. The copper mask design in Figure 4 6 A shows the electronic vias (20 microns wide) from the YSZ sensor to the gold contact pads (200 microns square) seen in Figure 4 6 B Arrows were

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190 added to the gold sensor mask design for alignment of the quartz tubing during experimental preparations. Using the three masks (copper, YSZ, and gold) for the three different radial dimensions, each material was deposited on the silicon wafer using lithographic methods. The mask designs summarized above were then combined into one large mask spanning the entire 4 wafer that included the three different radial designs. Figure 4 7 shows the copper mask used in the fabrication process. To use the shadow mask properly, the wafer was coated with Clariant AZ1512 positive photoresist and then soft bake d to set the resist. The shadow masks (whether copper, YSZ, or gold), produced by the Sanjin company, was centered using a Karl Suss MA 6 aligner and exposed on a CNF EV 620 contact aligner. Following exposure, a hard bake of the resist was carried out to solidify the exposed mask design into the photoresist. Etching followed the hard bake, and the wafer was then placed in an acetone bath agitated by an ultrasonicator to remove the remaining photoresist. Thermal Oxidation and Oxide Etch The MES3A fabrication process was initiated by oxidizing a 4 in. (100) silicon wafer via wet oxidation. The (100) silicon wafer was chosen as a substrate because of its cleavage, etching c haracteristics, and widespread use in the semiconductor industry. The silicon wafer was first cleaned by dipping it into an ammonium based cleaning solution (NH4OH + H2O2 + H2O). Following the cleaning process, approximately 1 m of SiO2 was grown on the silicon wafer using the wet oxidation method and an Integrator Circuit Technology MT 800 at 1000 oC. The grown oxide layer served as the dielectric between the semiconducting silicon substrate and copper vias.

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191 The copper mask w as next used to etch trenches to be filled with copper. There trenched areas were defined by depositing the resist and implementing a soft bake. After the copper trench was photolithographically defined, the copper trenches were etched using a BOE (LAL500) solution obtained from Samsung. Previous etching experiments determined a BOE etch rate of the thermal oxide to be 5.6 /s at room temperature. The thermal oxide was etched to a depth of 0.50 m. During the etch test, the BOE had approximately a 3:1 lateral etch rate, which was taken into consideration when designing the spacing between the device features. The 3:1 etch ratio is shown in Figures 4 8 A and B. Figure 4 8 A shows the typical boat shape that results from the etch process and Figure 4 8 B shows the importance of device feature spacing. The PR is then completely removed before the sputtering of copper onto the wafer. PVD and CMP of Copper Before depositing copper, tantalum and tan talum nitride were sputtered onto the wafer to increase copper adhesion and serve as an oxygen diffusion barrier. The TaN was deposited between the thermal oxide and copper material, while tantalum served as the glue layer between the copper and TaN. Appro ximately 60 nm of tantalum nitride and 15 nm of tantalum were DC sputtered from their targets at room temperature (manufactured by Applied Science) onto the oxidized silicon wafer. Next 900 nm of copper was DC sputtered from an Applied Science target onto the wafer resulting in a copper -coated wafer shown in Figures 4 9 A and B Following the PVD of copper, the wafer was prepared for the CMP process to remove excess copper and planarize the wafer. A G&P Technology POLI 400 polishing tool with an Al2O3 slu rry was used to planarize the wafer ensuring the copper vias were electronically isolated and located only in their wet etched trenches. A secondary SiO2 slurry (LK393C4)

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192 manufactured by Rohm & Haas was used after the Al2O3 slurry to reduce dishing effect s. The final CMP result c an be seen in Figures 4 10 A and B, where the chip surface is fully planarized. CVD of PETEOS The deposition of PETEOS was intended to electronically isolate the Cu interconnects from the liquid tin. Before deposition the wafer was cleaned by rinsing with DI water for 1 minute. DI water was used instead of an ammonium -based cleaning solution (NH4OH + H2O2 + H2O) because previous cleanings oxidized the copper, which affected the adhesion of YSZ and gold. Following the cleaning pro cess, 300 nm of plasma enhanced tetra ethoxy silane (PETEOS) was deposited on the entire wafer using an Applied Materials P5000 CVD System. Since the TEOS was applied to the entire wafer no mask was required for this step. TEOS Etch and PVD of Gold There were a few difficulties faced when depositing the gold contact pads onto the copper vias due to the amount deposited and the formation of an oxide layer on the copper surface. To resolve this issue, only 200 nm of gold was deposited, and a few precautiona ry measures were taken in the fabrication process. To reduce the oxidation of copper during the fabrication process a dry etching procedure was substituted for the original wet etch procedure. A chromium adhesion layer was also deposited to quell further o xidation and serve as a conductive adhesion layer. These procedure changes allowed the gold to securely bond to the copper. The shadow mask constructed specifically for gold was used to define the gold contact pads on the device surface. After these area s were lithographically defined, an Applied Materials P5000 tool was used to dry etch the TEOS layer to a depth of 300 nm. Following the dry etch, 20 nm of chromium and 300 nm of gold were DC sputtered from their respective targets at room temperature (man ufactured by Alpha Plus) onto the wafer. The remaining PR was then removed

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193 from the wafer with an acetone wash in an ultrasonicator. Excess gold was removed by employing the lift off process. Figure 4 11 A shows the gold contact pad on the underlying cop per via and where the copper via surfaces from the TEOS layer. Figure 4 10 B shows a SEM image of the gold contact pad and the underlying copper via where the respective grains can be observed. TEOS Etch and PVD of YSZ The wafer was again coated with PR and the YSZ shadow mask was used to photolithographically define the desired location of YSZ. The wafer was then dry etched (instead of wet etched) to minimize the amount of copper oxidation. An original thickness of 1000 nm of YSZ was reduced to 300 nm be cause of adhesion issues. The YSZ was RF sputtered from an Applied Sciences target at room temperature. The PR was then removed in an acetone bath aided by an ultrasonicator to remove the extraneous YSZ material. The devices were probed by SEM to illustrat e the success of the YSZ deposition process and the resulting sensor configuration Figure 4 1 2 A shows a plane view of the deposited YSZ pads connected to the copper vias. Figure 4 1 2 B is a SEM image taken of a different MES3A device following a thermal ramping experiment. Figure 4 1 3 A and B show a cross -sectional view of the deposited YSZ and the vertical and columnar grain orientation is noted. It is expected that the columnar nature of the grains will aid in the transport of oxygen ions across the ele ctrolyte since the grain boundaries are parallel to the direction of oxygen transport. Planarization and Cutting By design the deposited YSZ is slightly lower than the surrounding TEOS layer so a planarization step can be carried out to reduce the potenti al disruptive flow effects from an uneven surface. A very brief BOE etch planarizes the surface because of its high selectivity to the TEOS and low selectivity to the YSZ and gold pads. After the BOE etch was completed, the

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194 wafer was cleaned with a DI wate r rinse the. A Disco DAD 2H/6T Dicing saw was then used to cut each individual MES3A device from the wafer. Characterization of the Device The overall quality of the MES3A device was assessed by a series of characterization methods. The general device ar chitecture was described by microscopy images and detailed by detection methods such as XRD and XPS. A focus on individual device components led to an understanding of the microstructural occurrences in each material during the fabrication process. The rev iew revealed certain MES3A components required improvements and gave an overall functionality assessment of the device. Cross-Sectional View of MES3A A cross -sectional TEM image was taken by a JEOL TEM 2010F to gain a global assessment of the MES3A device A Strata DB 235 FIB was first used to prepare a cross sectional sample from MES3A contain in g a copper and YSZ layer. Examination of the thin film architecture showed fabrication steps used were successful in obtaining the orig inal device design. However, detection of SiO2 between the copper and YSZ films revealed the dry etch process preceding the application of YSZ was not successful. The deposited thin films can be viewed in the cross -sectional TEM image shown in Figure 4 1 4 With the exception of YSZ, the layers appear to have been perfectly applied with excellent uniformity (exampled by the Ta/TaN and Cu layers). The sputtered YSZ appears rather porous and extremely non uniform across the device surface. It is expected that the TEOS layer caused the no n uniform and porous deposition of YSZ. It is not clear whether this is a universal or local (across the entire 4 wafer) uniformity issue, but using a sensor that has a TEOS layer between the copper and YSZ will greatly impede oxygen transfer between YSZ and copper.

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195 Fortunately TEM analysis revealed regions where small areas (~100 nm) of YSZ contacted the copper layer. It is expected that if the operation of the MES3A device is successful, it will be due to these very small contact regions. However, succe ssful operation may be shortened due to these contact regions resulting in high local electronic and/or ionic currents that can further damage the sensor. A preliminary experimental analysis in the next chapter will explore this issue. Overall XRD of MES3A An XRD scan of the device was taken to further examine the crystalline structure of the MES3A components and subsequent compounds formed. For the initial XRD analysis, the fabricated device was used as a baseline. The same sample was then annealed at 850 oC for 24 hours and re -examined by XRD. XRD measurements of the samples were taken by a Philips APD 3720 using the CuK 1 wavelength of 1.54056 over a 2 range of 2565o having a power setting of 40 kV and 20 mA. The results of the XRD scans are combine d in Figure 4 1 5 The most notable signal is the sharp gold peak correlating to a high crystalline order (large grains) of the Au (111) orientation. Weaker signals come from the slight presence of Cu (111) and YSZ (220) and (200) orientations. These wea k signals were a result o f YSZ and copper being in such small quantitative proportion s to that of gold. To effectively study these materials the amount of copper and YSZ was increased by preparing new samples for XRD analysis. The most interesting result f rom the overall XRD analysis is the high crystalline order of the deposited tantalum. The high annealing temperature converted practically all of the tantalum to tantalum silicide. The typical use of the tantalum is a glue layer between the thermal oxide a nd the TaN barrier material. Figure 4 26, however, shows the tantalum interacted with the silicon

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196 (for high temperatures) in the thermal dioxide. Formation of tantalum silicide prevented the copper atoms from further diffusing into the silicon and forming copper silicide compounds. The formation of copper silicide is not desired because it would greatly decrease the electrical conductivity of the copper. The original goal of the Ta/TaN layers was to prevent oxidation of copper and according to the post anne al XRD scan this goal was accomplished. It should be mentioned; however that there may be an amorphous or very thin layer s (e.g. copper oxide formed ) that was evident in the XRD analysis. Surface Analysis of the MES3A Device Maintaining a planarized sen sor surface was key to the success of the MES3A device because a non -planarized surface can affect fluid flow profiles of the convecting liquid tin melt. A Wyko NT optical profiler was used to detect height changes on the sensor surface. Figure 41 6 A show s the results of an area scan of MES3A slightly larger than 500 m x 500 m with a root mean square surface roughness of 34 nm. Figure 4 15 B closely examines a copper line connected to a YSZ pad that was scanned over a 200 m x 200 m area that had a root mean square roughness of 97.33 nm. These results showed the pla narity of the device surface was excellent. Notably in Figure 4 1 6 B, the trenches that appear along both sides of the copper via are a result of the optics and not the physicality of a trench. The profile scan in Figure 4 15 B showed increased surface ro ughness due to the nonuniformity of the material surrounding the YSZ pad. The buildup around the YSZ pad was hypothesized to be residual PR or YSZ not originally removed by the liftoff process. Unfortunately the surface debris around the YSZ pad was not r emoved even after a one hour 70 oC acetone rinse was used. The negative result from the acetone rinse combined with an EDS examination confirmed the material was YSZ and not residual PR. A thicker PR layer will be

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197 necessary for future YSZ deposition steps to reduce the amount of material crowning the YSZ pad. During the organic wash some surface debris was removed and much of the contamination was attributed to the dicing step that can be a dirty process. More stringent sanitation efforts and a review of the dicing process are necessities for future constructions of MES3A. Despite the lack of device cleanliness, it is expected the operation of the sensors themselves are not directly affected by the debris. XRD Analysis of YSZ New YSZ samples were pre pared to examine the crystalline structure of RF -sputtered YSZ. Samples were prepared by wet oxidizing a silicon wafer, then RF sputtering YSZ onto the wafer using the same conditions and thicknesses used in the fabrication process; where the increase in d etectable material came from a larger sample surface area. XRD measurements of the samples were then taken by a Philips APD 3720 using the CuK 1 wavelength over a 2 range of 25 65o at a power setting of 40 kV and 20 mA. Three separate samples were prepared to examine the effects of thermal cycling on the crystalline structure of YSZ. Thermal cycling was used to mimic the environmental constraints placed on the device. Two of the YSZ samples were thermally cycled from room temperature to 8 5 0 oC at a heati ng rate of 1.5 oC/min, held at 8 5 0 oC for 24 hours, and then cooled back to room temperature at a cooling rate of 1.5 oC/min. One sample was annealed in air and the other in an inert argon atmosphere. The third sample was not heat treated and served as a b asis for comparison.

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198 The results of the XRD analyses for the three samples are shown in Figure 4 1 7 The most significant features of Figure 4 16 are the two reflections attributed to YSZ (111) and (200). Only very subtle changes in crystalline structure we re noticed when comparing the argon and air annealed YSZ samples to the pre anneal YSZ sample. The annealed samples peaks are slightly higher and sharper, indicating a small increase in crystallinity. This is due to the polycrystalline materials increas ing in crystalline order with the addition of thermal energy. The XRD data also reveals a slight peak shift between the annealed and pre -annealed samples. Braggs law suggests the slight peak shift to the right (a higher 2 ) indicates a decrease in the interplanar spacing. This likely signifies a small densification of the crystalline structure, possibly related to a slight phase change in the crystalline structure. Experimental error was not a factor in the observed YSZ peak shifts, as all three XRD scan s returned identical 2silicon peaks. Chapter 2 described a t -tetragonal phase, which undergoes slight restructuring to effect the lattice parameter before the crystalline transforms to the cubic phase. 8 mol% YSZ deposited at room temperature is in close proximity to the t tetragonal and cubic phase boundary. This provides further evidence that with the addition of thermal energy, the sputtered YSZ will settle into the cubic phase. It was concluded that the YSZ was in the cubic phase because the peaks of this study were s imilar to the results of Joo and Choi and Dura and Lopez where they t oo concluded YSZ was cubic [170, 171]. XPS Analysis of YSZ A compositional analysis of the prepared XRD YSZ samples was used to examine the quality of the sensors electrolyte material. Measurements were taken by a XPS/ESCA Perkin -

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199 Elmer PHI 5100 ESCA system using an aluminum xray source having an inlet angle of 45o and an intensity of 89.5 eV from 0 to 1000 eV stepping at 0.5 eV. Initial XPS results indicated the presence of oxygen, z irconia, and yttria, with their respective bonding states of 1s, 3d, and 3d. T he atomic percentages of yttri a, zirconia, oxygen, and carbon we re 4.2, 22.0, 63.1, and 10.7, respectively. The observed mole percentages indicate the desired composition of 8 m ol % YSZ, confirming the appropriate composition of YSZ was deposited to obtain the highest ionic conductivity and optimal performance of the electrolyte. After sputtering a few nm past the surface layer, only a very weak carbon signal was detected, indica ting carbon was contamination from the XPS system. Surface Analysis of YSZ The previous surface analysis raised some concern s as to the quality of deposited YSZ and a closer examination of the YSZ pad was carried out. Figure 4 1 9 shows a tilted SEM image of a YSZ pad to illustrate the presence of a crown around the pad. A number of pores are identified in the deposited YSZ material. These pores can short circuit the electrochemical system by creating alternative routes for molecular oxygen to transport across the electrolyte. A Digital Instruments Dimension 3100 AFM was used in contact mode over a 50 m x 50 m area to examine the sensor area. The crown is clearly noticeable and the extraneous noise on the surface was the result of surface debris. This particular YSZ pad sits slightly above the thermal oxide layer by approximately 200 nm. Examination of other YSZ pads revealed that the sensor pads could be located +/ 200 nm relative to the height of thermal oxide, with many senor pads within 50 nm of the thermal oxide height. It is hypothesized t hese height differences are due to non uniformity of et ch and deposition rates across the wafer. Once the wafer becomes slightly

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200 sloped, (possibly from the CMP step) the error will compound through the remaining fabrication steps resulting in some sensor pads being above and below the crown Supplementary A FM data was used to determine the surface roughness and porosity of the YSZ pad itself. Figures 4 2 1 A and B show the AFM scan used in the tapping mode over areas of 5 m x 5 m and 1 m x 1 m, respectively. The root mean square surface roughness of the s urface scans were 14.7 and 6.16 nm, respectively. Fewer perturbations and non uniformities of the smaller area resulted in decreased surface roughness. The YSZ sensor pad is relatively planar (as seen in Figure 4 20 B ) with only a few regions of additional growth. A slightly uneven (rough) surface is expected due to the high particle energies associated with sputtering. AFM measurements were employed to measure the grain size of YSZ and to further examine porosity issues. Typical YSZ grain size was on the order of 25 nm and the presence of pores is depicted in Figure 4 2 2 Height profiling many of these pores revealed their extension deep into the YSZ pad and, in some rare cases, all the way through the YSZ to the copper vias. Methods of resolving this porosity issue will be explored in Chapter 5. XRD Analysis of Gold Contact Pad An XRD analysis of the gold contact pads investigated the crystallinity of gold, chromium, and copper thin films. Samples were prepared by sputtering 200 nm of copper, 20 nm of ch romium, and 200 nm of gold onto a thermally oxidized silicon wafer following the same procedures used in the MES3A fabrication process. An XRD scan of the sample before and after an annealing process of 850 oC for 24 hours in a low oxygen partial pressure (~1020 atm) is shown in Figure 4 2 3 The same annealing temperatures and ramp rates used in the YSZ thermal cycling experiment was also employed for the gold thermal cycling experiment. The XRD

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201 measurements were taken on a Philips APD 3720 using the CuK 1 wavelength over a 2 range of 25o65o with a power setting of 40 kV and 20 mA. The XRD results shown in Figure 4 2 3 revealed a number of interesting processes that occurred during the annealing process. Notably the chromium grain size increased with temperature and various crystalline orientations of chromium oxide were formed. The formation of chromium oxide is unfortunate, because it indicates oxidation of the device. CrO3 is more stable than Cu2O, which is more stable than Au oxide, and thus oxida tion of the chromium is expected. Some metallic chromium, however, remained after the anneal. While the gold remained adhered to the sample, there was some oxidation of the underlying copper, which could have negative effects during device operation. The validation experiments carried out in the following chapter will investigate any consequences of copper oxidation. S ummary A thorough characterization of the MES3A device was accomplished through the use of multiple tools. Each tool examined various device components and their interactions within operation of MES3A. Most importantly a number of the MES3A fabrication processes were validated, with the exception of the dry etch and subsequent YSZ deposition steps. It is expected that reviewing and revising th ese two fabrication steps will improve future device performance. Conclusions Characterization of the completed MES3A device was used to perform a quality analysis of the constructed device. The characterization study showed most device components were pro perly constructed (e.g., correct location, composition). Additional analysis showed the possibility of some device elements that may be associated with failure mechanisms. The two major areas of concern is the presence of a TEOS layer between the copper an d YSZ thin film

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202 and potential oxidation of the copper via. Validation experiments were carried out in the following chapter to confirm device functionality and the numerical work of Chapter 3. Figure 4 1. Cross -sectional s chem atic of the MES3A d esign A B Figure 4 2. Cracks in the TEOS layer A) with a curvilinear shape, B) in the shape of spider cracks and ridges Silicon (100) Thermal Oxide Thermal Oxide PET EOS Ta/TaN Cu Cu 2 O Cu 2 O Au YSZ YSZ Cr TEOS TEOS

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203 A B Figure 4 3. Cu via has A) completely broke through the TEOS layer and B) is becoming expose d with noticeable stress marks on the TEOS surface A B Figure 4 4. Oxidized copper delaminating the YSZ at A) 6000x and B) 2700x TEOS TEOS Cu Cu TEOS Cu Sn Cu 2 O YSZ Cu 2 O Cu YSZ Sn

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204 A B Figure 4 5. Chip layout for the YSZ A) 1 mm sensor array design and B) 3 mm sensor arra y design A B Figure 4 6. A) Copper and B) gold component design for the 3mm MES3A design

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205 Figure 4 7. Copper shadow m ask A B Figure 4 8. SEM image of BOE etch revealing A) 3:1 etch ratio and B) the feature size spacing 498 nm 1580 nm PR PR Thermal Oxide Thermal Oxide

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206 A B Figure 4 9. SEM image of A) copper overdeposited on a thermally oxidized wafer and B) a magnified image to discern the thickness A B Figure 4 10. Surface of A) copper and B) thermal oxide after CMP A B Figure 4 1 1. Gold contact pad viewed through A) an optical microscope and B) SEM Cu Cu Thermal Oxide Thermal Oxide 900 nm Thermal Oxide Thermal Oxide Silicon Wafer Sili con Wafer Copper Copper Au Cu TEOS TEOS Cu Au

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207 A B Figure 4 1 2. Top view of fabricated wafer by A) an optical microscope and B) SEM A B Figure 4 13. Cross -sectional view of s puttered YSZ showing A) uniformity and B) columnar structures YSZ TEOS Cu YSZ YSZ TEOS TEOS

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208 Figure 4 14. Cross -sectional TEM image of the MES3A device Si SiO 2 Ta/TaN Cu YSZ SiO 2

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209 230 35 40 45 50 55 60 Intensity (a.u.) 0 500 1000 1500 2000 2500 Au (111) Ta3.28Si0.72 (200) Ta (330) Cu (111) YSZ (220)Pre-Anneal Post AnnealYSZ (200) Figure 4 15. XRD s can of the MES3A d evice A B Fig ure 4 16. A) Surface sca n of devices surface over 500 m x 500 m and B) surface scan of copper interconnect over 200 m x 200 m

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210 230 40 50 60 70 Intensity (a.u.) 0 500 1000 1500 2000 Pre-Anneal Argon Anneal Air AnnealYSZ (111) YSZ (220) YSZ (200) YSZ (311) Si (002) Si (004) K Figure 4 17. XRD analysis of YSZ on thermal oxide

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211 Binding Energy (eV) 0 200 400 600 800 1000 Relative Intensity 0 10000 20000 30000 40000 50000 60000 C KVV O KVV O 1s 63.1% Zr 3sZr 3p1 Zr 3p3Zr 3d 22.0% Y 3d 4.2%Zr 4s Zr 4p Y 3p1 Y 3p3C 1s 10.7% Figure 4 18. XPS analysis of YSZ on thermal oxide

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212 Figure 4 19. SEM image of YSZ sensor pad Figure 4 20. AFM image of the YSZ sensor pad Thermal Oxide YSZ Crown

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213 A B Figure 4 21. Surface scan of YSZ sensor over A) 5 m x 5 m and B) 1 m x 1 m Figure 4 22. AFM image of porous YSZ pad

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214 230 40 50 60 Intensity (a.u.) 0 2000 4000 6000 8000 Pre-Anneal Post AnnealAu (111) Cr (110) Cu (111) Si (004) K Cr (200) CrO2 (101) Si (002) CrO3 (211) Cu2O (211) Fi gure 4 23. XRD of gold contact pad

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215 CHAPTER 5 VALIDATION AND ENHANCEMENT OF THE MES3A DEVICE Introduction This chapter focuses on validation of the constructed MES3A device through a series of electrochemical experiments, to implement MES3A into a stud y of the solder bump problem. There were, however, difficulties in the validation experiments attributed to the fabrication process. The fabrication of the YSZ sensor pad was therefore revisited, with a closer examination of the sputtering conditions, to develop potential solution strategies. Validation Experiments The constructed MES3A device underwent two types of validation experiments. The first experiments measured the open cell potential (EMF) of the sensors in low oxygen and 21% oxygen atmospheres, to test the functionality of the device as a sensor in detection (galvanic) mode. Mass transfer measurements were then attempted, using the right cylindrical geometries highlighted in Chapter 3. These experiments tested the robustness of the sensors throug h their uses in detection and titration (electrolytic) mode. The results of both experiments are summarized in the following sections. Measuring Open Cell Potential The first experiment tested the ability of the MES3A device to accurately measure an ele ctrical potential when exposed to a particular oxygen condition. Recalling Chapter 2, the EMF is an electrical measurement of the oxygen chemical potential difference between the Cu/Cu2O reference electrode and the working electr ode (e.g., liquid tin worki ng electrode). The first condition was a low oxygen atmosphere, and the second was air ambient consisting of 21% oxygen. The electrical potentials detected by the individual sensors were then compared to the theoretical (thermodynamically -calculated) EMF v alues to confirm functionality and accuracy.

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216 The MES3A device was initially prepared by cleaning the surface, using 3 min. in warm trichloroethylene, 3 min. in warm acetone, 3 min. in warm methanol, completed by blow -drying the chip with nitrogen or argon gas. 200 nm of platinum was then sputtered onto the front -side of the device by a Kurt J. Lesker sputtering tool at 250 W. Next a copper wire contact (sheathed in an alumina tube to minimize oxidation) was made to the sputtered platinum, by attaching a c opper wire to the device surface using Ceramabond Type 571 manufactured by Aremco Products, Inc. The end of the attached wire was coated with CL115349 platinum ink manufactured by Heraeus to ensure good electrical connection to the sputtered platinum. The same process was repeated for another copper wire, which was attached to a cor responding gold contact pad The entire experimental setup was placed in an alumina tube (OD: 5.72 cm, ID: 5.08 cm, L: 50.0 cm) from Vesuvius McDaniel, and capped with a glass cell head constructed by Analytical Research Systems, Inc. The glass cell head and single-capped end of the alumina tube created an air tight chamber, allowing ambient control. Temperature was measured with a Type K the rmocouple manufactured by Omega and EMF values were collected with a Keithley 2700 Multimeter/Data Acquisition System. Figure 5 1 i llustrates the experimental setup. The assembled measurement cell required at least three repeated vacuum evacuations of the vessel (<29 mmHg vac.), followed by a purified argon purge of the system to purge oxygen from the system Following the purge process, 99.999% UHP argon (supplied by Airgas) was again introduced into the system and maintained at a slightly higher pressure than atmospheric. Before the argon entered the experimental vessel it passed through a series of purifiers starting with a Restek heated purifier, followed by a Krackeler Scientific, Inc. R&D glass moisture trap, followed by a Scott Specialty Gases indicating oxygen trap and ending with a M atheson

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217 NanoChem Minisentry for inert gases. The outgoing argon gas was bubbled into a beaker of water to minimize backflow of air into the system and maintain a positive pressure. A higher pressure in the vessel ensured any possible gas leakage that may o ccur would be in the outward direction from the experimental vessel. A simplified process gas flow diagram of the system is shown in Figure 5 2. U nfortunately, no reproducible results were obtained from the attempted measurements of the MES3A device expos ed to a reduced or atmospheric oxygen condition; in fact, the potential measured between the anode and cathode was nearly zero. An impedance measurement showed a resistance on the order of 20 ohms between the two nodes, indicative of a short circuit. Speci al care was taken for subsequent and similar oxygen atmospheric experiments, to ensure there was no direct electrical connection between the two nodes, but similar results were again obtained. This put the porosity of the YSZ sensor and its respective thin ness under suspicion. Mass Transfer Measurements The sensors were next used to detect oxygen dissolved in liquid tin, to determine if changing the YSZ sensors operating conditions would affect their measurements. In this trial the sensors were able to measure a reasonable EMF between the copper/copper oxide and tin nodes. An attempt was also made to measure the mass transfer coefficient of oxygen, following the process highlighted in the numerical depletion experiment of Chapter 3. Figure 5 3 illustrates the experimental setup used for this experiment. This setup was placed in the same alumina tube (capped by the glass cell head) used in the previous set of experiments and illustrated in Figure 5 1. The same pre -experimental atmospheric control processes and measuring methods used in the previous EMF experiment were also employed for the mass transfer measurements.

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218 The open cell potential between the liquid tin and copper electrodes was measured over a range of temperature to demonstrate the device capab ility for a particular temperature range. Figure 5 4 illustrates the measured EMF of a sensor as a function of temperature and includes the predicted equilibrium value. Although a stable open circuit voltage was measured, the deviation from the anticipate d equilibrium value supports the presence of complications. The EMF was also measured as a function of time to determine the device st ability over a period of time. The device was typically able to hold an EMF (having a voltage drift less than 5 mV) for ov er an hour before the EMF signal changed from its initial value. Figure 5 5 illustrates a typical EMF response of the device measured at 538 oC. The data was not filtered, to illustrate the significant amount of noise associated with the measurement. Despi te the noise there was an average EMF maintained throughout the measurement (denoted by the denser measurement values surrounding 0.6 V). Although relatively constant, the experimental measurements were offset by 80 mV, suggesting the higher voltage is consistent with an under -saturated Sn melt. Mass transfer measurements were next attempted through application of 1.2 V to the top of the tin melt. This reduced the oxygen concentration at the top of the liquid tin, to create the top depletion configuration discussed in Chapter 3. Ideally, mass transfer data can be extracted by measuring the EMF response at the bottom of the melt to an applied potential at the top of the melt Unfortunately, the applied potential at the top node caused the system (and the MES3A device) to short circuit. When attempting to measure the EMF at the bottom of the liquid tin melt, the potential applied to the top node was detected by the bottom nodes. This made it practically impossible to measure any mass transfer data with MES3A.

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219 Summary A series of measurements was attempted with the MES3A device, with varying success. The devices were capable of measuring an open cell potential for a period of time and a range of temperatures when exposed to liquid tin samples. The measured pote ntials, however, were different than the equilibrium values. Low EMF is a common problem for thin film electrolytes, and is not easily remedied. In addition, the device short circuited, perhaps a result of a conducting path through the YSZ electrolyte or t he TEOS layer. Thus, the EMF experiments resulted in a stable but noisy mea surement of a potential, but were not possible under an applied potential. Examination of Device Breakdown To determine the failure mechanism of the device, a post analysis of th e device data was performed. Experimental results were carefully examined, and physical examination via microscopy was also performed. A compilation of the experimental and physical results was helpful in suggesting potential device improvements. Physical Experimental Results The EMF results from the attempted mass transfer measurements showed the device was capable of measuring a potential, albeit with discrepancies in the measured results and theoretical values. This may be due to ohmic losses in the cop per / gold contacts, an overpotential created from poor contact between the YSZ and copper, or ineffective transfer of oxygen through the YSZ. A short circuit was apparent when the device measured an identical electrical potential as the potential applied to the top node. Special care w as taken to ensure liquid tin was the only metal contacting the device surface. Possible sources of the short circuit include: the dielectric

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220 layer or YSZ supported electrical conduction, or porosity in the YSZ or TEOS layer a llowing the tin sample to seep through and make direct contact to the copper vias. Device Characterization Much of the necessary device characterization analysis was discussed in Chapter 4, but a concise review is given here. The first issue is a hol e in the TEOS layer possibly allowing liquid tin to contact the copper vias and evidenced by short circuit measurements and micrographic images of a porous TEOS layer Although there were preliminary issues of cracking ( leading to copper line exposure ), ma intaining a temperature ramp rate less than 1.5 oC/min eliminated this in subsequent experiments, and was not deemed to be the source of failure. One issue r equiring further investigation wa s the TEOS layer thickness necessary to maintain its dielectric p roperties at an applied potential of up to 1.2 V. It was expected that thin film of YSZ could have a number of issues, ranging from material porosity to improper ionic conductivity. The microscopic analysis of the YSZ pads presented in Chapter 4 showed th ey contain significant pores to allow liquid tin to contact the underlying copper contacts. The TEM analysis in Chapter 4 showed the TEOS layer was not fully removed in many areas before the YSZ was sputtered onto the device. It was suspected the TEOS la yer caused the sputtered YSZ to be porous, as all preliminary expe riments with sputter deposition of YSZ onto copper resulted in dense YSZ layers. In addition to its porous deposition, only about 200 nm of the planned 300 nm of YSZ was deposited. The thin YSZ layer could have led to short circuiting by allowing sufficient electronic conduction for an applied potential because of poor dielectric strength. In this case, the YSZ material would operate with an ionic transference number well below 0.99. Another possible area for concern is the YSZ composition, but the XPS analysis in Chapter 4 showed the YSZ had the optimal composition.

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221 The presence of TEOS between the YSZ and copper presents a number of problems. A dielectric material between the electrolyte an d copper electrically insulates the nodal reaction (possibly represented by the low potentials seen in Figure 5 4). TEOS can also prevent the transport of oxygen from the liquid tin to the copper. Additionally the TEOS may serve as an oxygen source, which likely changes the partial pressure of oxygen in copper, and certainly corrupts EMF measurements. There were some areas where the TEOS layer was not present, and the YSZ contacted the copper. These small contact regions may have allowed for temporary open cell potentials to be measured for a short period of time. These very small regions where the YSZ contacted the copper may have been locally oxidized over time, thus decreasing mass transfer of oxygen to react with the Cu. Summary Further analysis of po tential sources of error and shortcomings are necessary to increase the capability of the MES3A device. A review of the dry etch process and its respective etch rates should be carried out to ensure no TEOS will be present between the copper and YSZ. The n ecessary thickness of the TEOS layer should be examined to determine if 300 nm is indeed an appropriate dielectric thickness. The same should be done to determine the necessary thickness for YSZ to maintain an ionic transference number greater than 0.99. T he optimal grain orientation of YSZ should also be determined to provide the highest ionic conductivity and improve device performance. Investigation of the YSZ Sensor Fabrication Process A study was performed to examine the effect of varying the YSZ gr ain orientation on ionic conductivity. To increase the effectiveness of the MES3A device, it was important to determine the growth conditions that produce the highest ionic conductivity since grain boundaries can dominate transport. It is expected that the grain orientation can be controlled by

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222 varying power settings on the sputtering tool and the amount of oxygen in the copper substrate. Impedance measurements examined the ionic conductivity of varying YSZ thicknesses and grain orientation over a range of temperature. These measurements were coupled with an XRD analysis of the material to relate the ionic conductivity measurements to the physical structure of the YSZ material. Sample Preparation A 4 in (100) silicon wafer was thermally oxidized via wet ox idation to obtain a 1 m dielectric layer of SiO2. The wafer was broken into smaller squares with a dimension of approximately 1.5 cm. These were then cleaned and etched using 3 min in warm trichloroethylene, 3 min in warm acetone, 3 min in warm methanol, 30 sec DI water rinse, 45 sec warm 6:1 (Ammonium Fluoride:HF) BOE etch, followed by a long DI water rinse with a N2 blow dry. The samples were then placed in a Kurt J. Lesker CMS 18 Sputter Deposition System for a series of depositions. TaN was DC sputter ed at 150 W to a thickness of 60 nm followed by 15 nm of Ta that was RF sputtered at 350 W. Next, 0.5 m of copper was DC sputtered onto the samples at 250 W. For half of the samples, 10% volume of oxygen was added to the argon flow entering the system during the DC sputter of copper This was implemented to slightly oxidize the deposited copper and thus m imic oxidation that can occur in the MES3A copper contacts during the fabrication process. Various thicknesses of YSZ were then RF sputtered onto the samples for power settings of 200 and 300 W. Table 5 1 summarizes the prepared samples, where A indicates YSZ deposited on copper, and B indicates YSZ deposited on the oxidized copper layer

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223 Table 5 1. Prepared YSZ samples for impedance and XRD a nalysis Sample Number YSZ Thickness (nm) Power Setting (W) 1A 1500 200 1B 1500 200 2A 550 200 2B 550 200 4A 845 300 4B 845 300 5A 345 300 5B 345 300 XPS Analysis of Underlying Copper It was expected that the sputtered YSZ would exhibit a different orientation if sputtered on copper versus an oxidized copper sample The copper was oxidized by adding 10% volume of oxygen to the argon supply. An XPS analysis of the oxidized samples was carried out to determine the oxygen composition of the copper surface. From the XPS analysis in Figure 5 6, it was determined the B labeled samples had a composition of 1Cu:1.3 Cu2O or 56.5% Cu2O. XRD Analysis of YSZ XRD analysis of the samples revealed two competing YSZ grain orientations of (111) and (200). The dominant grain orientation in each specific sample was dependent upon the power setting used to sputter YSZ wi th the (200) orientation dominant for the 200 W power setting and the (111) orientation dominant for the 300 W power setting. A summary of the dominant orientations (via XRD scans) are given in Figures 5 7 and 58. The oxidized sample increased the crystal linity of the sample (compared to a copper substrate sample with the same YSZ thickness see Figure 5 8 ) for the 300 W power setting. The oxidized sample substrate for the 300 W power setting, however, reduced the qualitative texture

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224 of the (111) orientat ion. For the 200 W power setting (Figure 5 7) the effects of the oxidized sample substrate were not explicit. For example, the crystallinity of samples 1A and 1B were identical, while 2B had less crystallinity than 2A. The qualitative texture of the (200) orientation also increased from sample 1A to 1B, but decreased from sample 2A to 2B giving contradicting results regarding the effects of the substrate on the texture of YSZ. As a basis, the crystallinity of each sample was gauged by its respective FWHM t o other samples with the same dominant growth orientation, and the qualitative texture of each sample as the ratio of the areas under each orientations respective XRD peak. The respective FWHMs ratios and other extracted XRD data are contained in Table 5 2. Impedance Spectroscopy of YSZ Following XRD analysis, the samples were prepared for impedance measurement by sputtering 200 nm of platinum along two opposing edges of each sample. The sputtered platinum was used as electrical contacts to allow in -pl ane impedance measurements to be taken. Platinum paste was used to connect copper wires to the platinum contacts on the samples, and the copper wires were then connected to a Gamry G300 potentiostat. The sample was housed within the experimental system previously highlighted in Figures 5 1 and 5 2. The only oxygen allowed in the system was the residual oxygen left from the purge process estimated to be on the order of 1012 atm. A low oxygen partial pressure was necessary to prevent oxidation of the copper/ copper oxide substrate sufficient to delaminate the YSZ. It should be noted however, sufficient oxidation of copper occurred (possibly from the ambient ) to make it less conductive than YSZ but insufficient for delamination An initial impedance measurem ent was taken when the sample reached 800 oC, to ensure the sample was properly configured. Next, four repeated impedance measurements were taken at 800, 750, 700, 650, 600, and 550 oC, respectively. These measurements were analyzed using the

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225 ZView softwar e suppli ed by Scribner Associates, Inc. to determine the average grain boundary resistance. The grain boundary resistance, as the dominant source of resistance in YSZ, could then be translated into a conductivity value for each sample as shown in Figure 5 9. All samples except 2A and 2B show an increase in conductivity when comparing measurements (for a specific thicknes s) between the copper and oxidized samples The oxidized samples substrate therefore may supply additional oxygen atoms to aid in conducti vity. The thickness of the YSZ layer was also found to be inversely proportional to its conductivity. Sample 5B had the highest conductivity of all samples, due to its thin YSZ layer an d copper/copper oxide substrate. The slope of the conductivity versus i nverse temperature gives an activation energy that was on the order of 0.5 eV. Summary The results of the XRD and impedance analyses are summarized into Table 5 2. These results reveal the importance of substrate material, YSZ thickness, grain orientation texture, and grain size. Generally, the oxidized sample substrate material increases the conductivity, with the exception of samples 2A and 2B. Therefore, grain size is the most dominant feature for a particular thickness, as it is proportional to conduc tivity, and explains the change in conductivity between samples 2A and 2B. A good or very good texture of the (111) or (200) orientation is also necessary for high conductivity. The analysis also shows for a particular dominant grain orientation, YSZ thick ness is inversely proportional to conductivity. It is difficult to determine the best grain orientation, due to the inability to compare the two different grain orientations at the same YSZ thickness. However, the sample exhibiting the highest conductivity had the (111) grain orientation.

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226 Table 5 2. Summary of XRD and impedance study of YSZ s amples Sample YSZ Thickness (nm) Identified Peaks Dominant Orientation FWHM (a.u.) Total Area Qualitative Analysis of Texture Conductivity at 700 oC (S/cm) 1A 1500 (111) (200) (200) 0.57 0.55 18771 69287 Good 5.79 1B 1500 (111) (200) (200) 0.53 0.55 12803 54237 Very Good 8.88 2A 550 (111) (200) (200) 0.54 0.50 9478 16129 Poor 8.68 2B 550 (111) (200) (200) 0.55 0.53 7961 7597 Very Poor 4.36 4A 845 (111) (200) (111 ) 0.71 0.36 94742 4774 Very Good 2.24 4B 845 (111) (200) (111) 0.66 0.20 72200 5800 Good 4.74 5A 345 (111) (200) (111) 0.83 0.36 36174 1599 Very Good 11.38 5B 345 (111) (200) (111) 0.75 0.51 36460 2531 Good 12.57 Suggested Modifications to the MES3A Fabrication Process The following section summarizes suggested improvements for the fabrication of the MES3A device. These suggest ions come from analysis of the preliminary validation experiments and subsequent studies. Sputtering YSZ As a result of the study in the previous section, it is clear the conductivity of the MES3A sensor can be improved by varying the sputtering conditions and material properties of the YSZ. Using the thinnest allowable YSZ layer (limited by its dielectric strength) with a gra in

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227 orientation of (111) is suggested. There is also a distinct advantage of incorporating low levels of oxygen into the copper substrate material to increase the conductivity of the YSZ. This is realized through larger YSZ grains and an additional source o f oxygen in the copper. Copper Interconnects A number of device failures were traced to the use of copper as an interconnect material. Oxidized copper can cause serious problems in regards to volume expansion (highlighted in Appendix C). It is suggested t hat a conductive oxide be used in place of the copper interconnects, so that the interconnect composition remains constant throughout the experiment. Lanthanum chromite -based materials can be doped with a range of metals such as strontium, cobalt, manganes e, iron, and ga doli ni um to affect their conductivities. The use of (RF sputtered) lanthanum chromite thin films has been widely accepted in the field of solid oxide fuel cells employing YSZ as the electrolyte material. Various forms of lanthanum chromite -b ased materials have proven to be valid as interconnect and nodal materials with sufficient conductivity to transport an electrical signal. Substrate Material One final and simple suggestion is to change the substrate material from a silicon to sapphire wa fer. Referring to Table 5 1 it is noted that the CTE of silicon differs the most from the other materials listed. A large amount of the thermal stress generated between the deposited materials comes from the slowly expanding silicon substrate. Use of a sap phire wafer with a CTE of ~8 x 106 K1 will reduce the amount of thermal mismatch between the chosen MES3A device components. Conclusions The development of MES3A as sensing device suitable for detecting oxygen tracers in liquid metal melts has progress ed through a series of physical experiments and analyses. An in -

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228 depth study to increase YSZ conductivity (originally thought to be the major cause of the devices limited functionality) was performed, resulting in a number of possible improvements for the thin film of YSZ. It is expected that the experimental results of this chapter and incorporation of the suggested changes to the device fabrication process will result in a device that is operable in both electrolytic and galvanic modes, capable of effecti vely monitoring oxygen tracers in liquid tin melts.

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229 Figu re 5 1. Schematic of experimental v essel

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230 Figure 5 2. Process flow diagram of experimental setup Figure 5 3. Experimental setup for mass transfer measurements Furnace/Reactor Beaker of Water Vacuum Pump Fume Hood Pressure Gauge Argon Cylinder Water/Oxygen Traps

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231 Temperature ( oC) 680 690 700 710 720 730 740 750 760 Open Circuit Potential (mV) 250 300 350 400 450 500 550 Experimental Measurment Equilibrium Value Cu SnO Sn O Cu 2 22 2 Figure 5 4. Open circuit potential vs. t emperature

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232 Time (min) 0 20 40 60 80 100 Open Circuit Potential (V) 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 Experimental Measurement Equilibrium Value at 538 oC Figure 5 5. Open cell potential vs. time

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233 Binding Energy (eV) 0 200 400 600 800 1000 Relative Intensity 0 1e+5 2e+5 3e+5 4e+5 Cu 2p1Cu 2p3 73.5% O KVV O 1s 26.5%Cu 3s Cu 3p Figure 5 6. XPS analysis of copper/copper oxide substrate mi xture

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234 228 30 32 34 36 Intensity (a.u.) 0 1000 2000 3000 4000 5000 6000 1A 2A 2B 1BYSZ (200) YSZ (111) F igure 5 7. XRD analysis of YSZ sputtered s amples at 200 W

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235 228 30 32 34 36 Intensity (a.u.) 0 2000 4000 6000 4A 5A 5B 4BYSZ (200) YSZ (111) Figure 5 8. XRD analysis of YSZ sputtered s amples at 300 W

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236 1000/T (K) 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 Log (Conductivity [S/cm]) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 5B 5A 1B 2A 1A 4B 2B 4A Figure 5 9. Log of conductivity vs. t emperature

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237 APPENDIX A EXTRANEOUS NUMERICAL OUTPUT The numerical output of the Chebyshev spectral code is contained in this appendix. The maximum axial and radial velocity components of the various numerical top depletion experiments carri ed out at varying solutal Rayleigh numbers are supplied for the reader to gain further understanding of the numerical results. Accompanying the velocity profiles the contour plot of the concentration at the fluids maximum velocity is also given to illustra te the lack or onset of flow within the melt. One may notice the direction of flow varies from one experiment to another. These varying directions are simply a result of perturbations generated within the numerical code making it impossible to predict the direction of fluid flow. In regards to the experimental results of the periodic boundary condition the maximum axial and radial velocities are given with the accompanying concentration profile at that point in time. Additionally the sinusoidal current response is also supplied for a clear understanding of how fluid flow affects the response and the onset of steady and unsteady periodic fluid flow. It is important to remember the plots represent the axis -symmetric geometry of a right cylinder that has solid boundaries at the top, bottom, and at r = R. At r = 0 there is a line of symmetry that bisects the right cylinder. It is also imperative that the reader recall the height represented in the figures must be inverted in the case of the top depletion and peri odic boundary condition configurations. Also for proper conversion of the non-dimensional values the proper scaling values can be calculated from Table 3 1.

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238 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 -1 0 1 2 3 x 10-11 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 x 10-11 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 1. Experiment #31A A) Radial and B) a xial v elocity 0.10.1 0.10.20.2 0.2 0.3 0.3 0.3 0.4 0.40.40.5 0.50.50.6 0.60.60.7 0.7 0.7 0.8 0.8 0.8 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 2 Exp eriment #3 1A Contour plot of the c oncentration

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239 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 -1 0 1 2 3 x 10-11 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 1.5 x 10-11 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 3 Experiment #32 A A) Radial and B) a xial v elocity 0.1 0.1 0.10.20.2 0.2 0.3 0.3 0.3 0.4 0.4 0.40.50.5 0.50.60.6 0.6 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 4 Exp eriment #3 2A Contour plot of the c oncentration

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240 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 -1 0 1 2 x 10-9 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 x 10-9 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 5 Experiment #33 A A) R adial and B) a xial v elocity 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.4 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 6. Exp eriment #3 3A Contour plot of the c oncentration

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241 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 7 Experiment #34A A) R adial and B) axial v elocity 0.10.10.10.20.20.20.20.30.30.30.30.40.40.40.40.40.50.50.50.50.50.60.60.60.70.7 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 8 Exp eriment #3 4A Contour plot of the c oncentration

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242 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 0 1 2 3 4 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 9 Experiment #34B A) R adial and B) axial v elocity 0.10.10.10.20.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.7 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 10. Exp eriment #3 4B Contour p lot of the c oncentration

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243 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 0 1 2 3 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 11. Experiment #3 4C A) R adial and B) axial v elocity 0.10.10.10.20.20.20.20.30.30.30.30.40.40.40.40.50.50.50.6 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 1 2 Exp eriment #3 4C C ontour plot of the c oncentration

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244 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 -0.1 0 0.1 0.2 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 1.5 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 1 3 Experiment #3 4D A) R adial and B) axial velocity 0.10.10.10.20.20.20.30.30.30.30.40.40.40.4 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 14. Exp eriment #3 4D Contour plot of the c oncentration

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245 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -10 -5 0 5 x 10-6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 x 10-5 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 15. Experiment #3 4E A) R adial and B) axial v elocity 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.4 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 16. Exp eriment #3 4E Contour plot of the c oncentration

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246 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -5 0 5 10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 17. Experiment #3 5A A) R adial and B) axi al velocity 0.10.10.10.20.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.50.60.60.60.60.60.70.70.70.70.80.80.80.90.9 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 18. Exp eriment #3 5A Contour plot of the c oncentration

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247 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 8 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 19. Experiment #3 5B A) R adial and B) axial velocity 0.10.10.10.20.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.60.70.70.70.70.80.80.8 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 20. Experiment #3 5B Contour plot of the c oncentration

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248 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 2 1. Experiment #3 5C A) R adi al and B) axial v elocity 0.10.10.10.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.60.70.70.7 0.80.8 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 22. Exp eriment #3 5C Contour plot of the c oncentration

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249 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 0 1 2 3 4 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 23. Experiment #3 5D A) R adial and B) axial v elocity 0.10.10.10.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.60.70.7 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 24. Exp eriment #3 5D Contour p lot of the c oncentration

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250 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.03 -0.02 -0.01 0 0.01 0.02 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 25. Expe riment #3 5E A) R adial and B) axial v elocity 0.10.1 0.1 0.20.20.20.30.30.30.40.40.40.50.50.5 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 26. Exp eriment #3 5E Contour plot of the c oncentration

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251 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -5 0 5 10 15 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 27. Experiment #3 6A A) R adial and B) axial velocity 0.10.10.10.20.20.2 0.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.6 0.70.70.70.70.80.80.80.80.90.90.90.9 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 28. Experiment #3 6A Contour plot of the c oncentration

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252 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -5 0 5 10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 29. Exp eriment #3 6B A) Radial and B) axial v elocity 0.10.10.10.20.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.60.70.70.70.70.80.80.80.80.90.90.9 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 30. Experiment #3 6B Contour plot of the c oncentration

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253 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 8 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 31. Exp eriment #3 6C A) R adial and B) axial velocity 0.10.10.10.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.60.70.70.70.70.80.80.80.80.9 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 32. Experiment #3 6C Contour plot of the concentration

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254 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 33. Experiment #3 6D A) R adial and B) axial v elocity 0.10.10.10.20.20.20.30.30.30.30.40.40.40.40.50.50.50.50.60.60.60.6 0.70.70.70.70.80.8 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 34. Exp eriment #3 6D Contour p lot of the c oncentration

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255 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.06 -0.04 -0.02 0 0.02 0.04 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 35. Experiment #3 6E A) R adial and B) axial v elocity 0.10.10.10.20.20.20.30.30.30.40.40.40.50.50.50.6 0.60.6 Contour Plot of the Non-Dimensional Concentration RadiusHeight 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure A 36. Exp eriment #3 6E Co ntour plot of the c oncentration

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256 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.015 -0.01 -0.005 0 0.005 0.01 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.05 0 0.05 0.1 0.15 0.2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 37. Ex periment #3 7A A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 38. Exp eriment #3 7A Concentration p rofile 0 500 1000 1500 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 39. Experiment #3 7A Amperometric r esponse

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257 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 -0.1 0 0.1 0.2 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 0 1 2 3 4 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 40. Exp eriment #3 7B A) Radial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 41. Experiment #3 7B Concentration profile 0 500 1000 1500 2000 2500 3000 3500 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 4 2. Exp eriment #3 7B Amperometric r esponse

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258 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 4 3. Exp eriment #3 7C A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 44. Exp eriment #3 7C Conce ntration profile 0 200 400 600 800 1000 1200 1400 1600 1800 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 45. Experiment #3 7C Amperometric r esponse

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259 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -6 -4 -2 0 2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 46. Experiment #3 7D A) R adial and B) axial velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 47. Experiment #3 7D Concentration profile 0 100 200 300 400 500 600 700 800 900 -1.5 -1 -0.5 0 0.5 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 48. Exp eriment #3 7D Amperometric r esponse

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260 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -5 0 5 10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 49. Experiment #3 7E A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 50. Exp eriment #3 7E Concentration profile 0 50 100 150 200 250 300 350 400 450 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 51. Experiment #3 7E Amperometric r esponse

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261 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -5 0 5 10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 52. Exp eriment #3 7F A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 53. Experiment #3 7F Concentration p rofile 0 50 100 150 200 250 300 350 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 54. Exp eriment #3 7F Amperometric r esponse

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262 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -5 0 5 10 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 55. Exp eriment #3 7G A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 56. Exp eriment #3 7G Concentration profile 0 50 100 150 200 250 300 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 57. Expe riment #3 7G Amperometric r esponse

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263 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -4 -2 0 2 4 6 8 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 58. Exp eriment #3 7H A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 59. Experiment #3 7H Concentration profile 0 50 100 150 200 250 -1.5 -1 -0.5 0 0.5 1 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 60. Exp eriment #3 7H Am perometric r esponse

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264 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.6 -0.4 -0.2 0 0.2 0.4 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 8 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 61. Experiment #3 7I A ) Radial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 62. Exp eriment #3 7I Concentration profile 0 20 40 60 80 100 120 140 160 180 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 63. Experiment #3 7I Amperometric r esponse

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265 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 -0.1 0 0.1 0.2 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 0 1 2 3 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 64. Exp eriment #3 7J A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 65. Experiment #3 7J C oncentration profile 0 20 40 60 80 100 120 140 160 180 200 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 66. Exp eriment #3 7J Amperometric r esponse

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266 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -4 -3 -2 -1 0 1 2 x 10-3 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.02 0 0.02 0.04 0.06 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 67. Experiment #3 7J A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 68. Experiment #3 7J Concentration profile 0 20 40 60 80 100 120 140 160 180 200 -4 -3 -2 -1 0 1 2 3 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 69. Experiment #3 7J Amperometric r espons e

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267 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 x 10-3 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -5 0 5 10 15 20 x 10-3 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 70. Experiment #3 8A A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 7 1. Exp eriment #3 8A Concentration profile 0 500 1000 1500 2000 2500 3000 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 72. Experiment #3 8A Amperometric r esponse

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268 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.1 -0.05 0 0.05 0.1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 1.5 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 7 3. Exp eriment #3 8B A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration F igure A 74. Experiment #3 8 B Concentration profile 0 200 400 600 800 1000 1200 1400 1600 1800 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 75. Exp eriment #3 8B Amperometric r esponse

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269 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -4 -3 -2 -1 0 1 2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 76. Experiment #3 8C a) Radial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 77. Exp eriment #3 8C Concentration p rofile 0 100 200 300 400 500 600 700 800 900 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 78. Experiment #3 8C Amperometric r esponse

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270 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -6 -4 -2 0 2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 79. Exp eriment #3 8D A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 80. Experiment #3 8D Concentration profile 0 50 100 150 200 250 300 350 400 450 -1.5 -1 -0.5 0 0.5 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 81. Exp eriment #3 8D Amperometric r esponse

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271 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -6 -4 -2 0 2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 82. Experiment #3 8E A) R adial a nd B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 83. Exp eriment #3 8E Concentration profile 0 50 100 150 200 250 300 350 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 84. Experiment #3 8E Amperometric r esponse 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity A

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272 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -6 -4 -2 0 2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 85. Exp eriment #3 8F A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 86. Experiment #3 8F Concentration p rofil e 0 50 100 150 200 250 300 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 87. Exp eriment #3 8F Amperometric r esponse

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273 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -6 -4 -2 0 2 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 88. Experiment #3 8G A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 89. Exp eriment #3 8G Concentration profile 0 50 100 150 200 250 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 90. Experiment #3 8G Amperometric r esponse

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274 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -4 -3 -2 -1 0 1 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 91. Exp eriment #3 8H A) R adial and B) axial velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 92. Experiment #3 8H Concentration profile 0 20 40 60 80 100 120 140 160 180 -1.5 -1 -0.5 0 0.5 1 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 93. Exp eriment #3 8H Amp erometric r esponse

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275 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.01 -0.005 0 0.005 0.01 0.015 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 -0.15 -0.1 -0.05 0 0.05 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 94. Experiment #3 8I A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 95. Experiment #3 8I Concentration profile 0 50 100 150 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 96. Exp. #38I Amperometric r esponse

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276 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -4 -2 0 2 4 6 x 10-4 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -6 -4 -2 0 2 x 10-3 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 97. Experiment #3 8J A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 98. Exp eriment #3 8J Concentration p rofile 0 20 40 60 80 100 120 140 160 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 99. Exp eriment #3 8J Amperometric r esponse

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277 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -3 -2 -1 0 1 2 x 10-3 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.01 -0.005 0 0.005 0.01 0.015 0.02 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 100. Experiment #39A A) Radial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 101. Exp eriment #39A Concentration p rofile 0 200 400 600 800 1000 1200 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 102. Exp eriment #3 9A Amperometric r esponse

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278 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 -0.1 0 0.1 0.2 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.5 0 0.5 1 1.5 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 103. Exp eriment #39B A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 1 04. Experiment #39B Concentration profile 0 100 200 300 400 500 600 700 800 900 1000 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 1 05. Exp eriment #3 9B Amperometric r esponse

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279 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 -1 0 1 2 3 4 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 1 06. Experiment #39C A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 1 07. Experiment #39C Co ncentration profile 0 50 100 150 200 250 300 350 400 450 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 1 08. Ex periment #39C Amperometric r esponse

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280 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 0.6 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -2 0 2 4 6 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 1 09. Experiment #39D A) Radial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 110. Exp eriment #3 9D Concentration p rofile 0 50 100 150 200 250 300 350 400 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 1 11. Experiment #39D Amperometric r esponse

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281 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.4 -0.2 0 0.2 0.4 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -1 0 1 2 3 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 1 12. Experiment #39E A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 113. Experiment #39E Concentration profile 0 50 100 150 200 250 300 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 114. Exp eriment #39E Amperometric response

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282 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.1 -0.05 0 0.05 0.1 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.2 0 0.2 0.4 0.6 0.8 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 1 15. Experiment #39F A) R adial and B) axial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 1 16. Exp eriment #3 9F C oncentration profile 0 50 100 150 200 250 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 1 17. Experiment #39F Amperometric r esponse

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283 A 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -4 -2 0 2 4 x 10-3 Radius Surface Plot of Non-Dimensional Vr Velocity Height Vr Velocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 -0.01 0 0.01 0.02 0.03 0.04 Radius Surface Plot of Non-Dimensional Vz Velocity Height Vz Velocity B Figure A 1 18. Experiment #39G A) Radial and B) a xial v elocity 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Radius Surface Plot of Non-Dimensional Concentration Height Concentration Figure A 1 19. Experiment #39G Concentration p rofile 0 10 20 30 40 50 60 70 80 90 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Current Density (mA/cm2) vs Time (min) Time (min)Current Density (mA/cm2) Figure A 120. Exp eriment #3 9G Amperometric r esponse

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284 APPENDIX B NUMERICAL ANALYSIS SOURCE CODE The following numerical code written for MATLAB was used for the numerical calculations in Chapter 3. A series of physical parameters could be entered and the code would internally scale the problem into a nondim ensional form. The direction of gravity could also be changed to implement stable and unstable solutal/thermal gradients. % CHEB compute D = differentiation matrix, x = Chebyshev grid function [D,x] = cheb(N) if N==0, D=0; x=1; return, end x = -co s(pi*(0:N)/N)'; c = [2; ones(N 1,1); 2].*( 1).^(0:N)'; X = repmat(x,1,N+1); dX = X-X'; D = (c*(1./c)')./(dX+(eye(N+1))); % off-diagonal entries D = D diag(sum(D')); % diagonal entries function [Dr,rp]= chebGR(Nr) C=sparse(eye(Nr,Nr)+[1,zeros(1,Nr 1);zeros(Nr 1,Nr)] -[zeros(Nr 2,2),... eye(Nr 2,Nr 2); zeros(2,Nr)]); B=sparse([]); for p=1:Nr, for j=1:Nr, B(p,j)=2*p; if p~=j 1, B(p,j)=0; end, end, end BB=sparse([zeros(Nr 1,1); 2*Nr]); A=sparse([B BB]);

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285 E=sparse([inv(C)*A; zeros(1, Nr+1)]); if Nr==0 Dr=0; r=1; return end rp=cos(2*pi*(0:Nr)/(2*Nr+1))'; for p=1:(Nr+1) for n=1:(Nr+1) t(p,n)=cos((n 1)*acos(rp(p))); end end Dr=t*E*inv(t); return end clear all; clf; clc; Nr=11; Nz =11; R=.5; H=1; Ep=R/H; Rs=.5; Temp=1023;

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286 Eo=.491; Esource=1.2; Esat=.491; Csat=3e 5; f=(8.314*Temp)/(2*96485); Cs=Csat*exp( (1/f)*(Esource Esat)); Co=Csat*exp( (1/f)*(Eo Esat)); %dcstar=(Cs -Co); %Csnd=(Cs -Co)/dcstar; %Cond=(Co Co)/dcstar; dcstar=(Co Cs); Csnd=(Co -Co)/dcstar; Cond=(Co Cs)/dcstar; D=8.0e 5; nu=1.64e 3; g= 980; Beta=.153; %Rac=0; Rac=(g*Beta*dcstar*(R^2)*H)/(nu*D); k=(g*H*R^2)/(nu^2); Sc=nu/D; vrs=nu/R; vzs=nu/H;

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287 ts=R^2/nu; tstepr=2; tnd=tstepr/ts; wreal=1e3; wnd=wreal*ts; Error = 1e 12; Ir=eye(Nr+1); Iz=eye(Nz+1); [Dr,rp] =chebGR(Nr); [Dz,z]=cheb(Nz); size1=(Nr+1)*(Nz+1);size2=2*size1; size3=3*size1; size4=4*size1; A=zeros(4*(Nr+1)*(Nz+1),4*(Nr+1)*(Nz+1)); B=zeros(4*(Nr+1)*(Nz+1),1); zz(1:Nz+1,1)=(z+1 )/2; r=(rp (1./rp((Nr+1),1)))*((rp((Nr+1),1)/(rp((Nr+1),1)1))); [Rr,Z]=meshgrid(r,zz); drp=((rp((Nr+1),1)1)/(rp((Nr+1),1))); Dg=zeros((Nr+1),(Nr+1)); for i=1:(Nr+1) Dg(i,i)=1/(rp(i,1) (1/rp((Nr+1),1))); end A(1:size1,1:size1)=kron(Iz,(((drp^2)* Dr^2)+((drp^2)*(Dg*Dr)) ((drp^2)*Dg^2)))+kron((4*(Ep^2)*Dz^2),Ir); A(1:size1,size2+1:size3)= kron(Iz,(drp*Dr));

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288 A(size1+1:size2,size1+1:size2)=kron(Iz,(((drp^2)*(Dr^2))+((drp^2)*Dg*Dr)))+kron((4*(Ep^2)* Dz^2),Ir); A(size1+1:size2,size2+1:size3)= kron((2*Dz),Ir); A(size2+1:size3,1:size1)=kron(Iz,(drp*Dg)+(drp*Dr)); A(size2+1:size3,size1+1:size2)=kron((2*(Ep^2)*Dz),Ir); A(size3+1:size4,size3+1:size4)=kron(Iz,((((drp^2)/Sc)*(Dr^2))+(((drp^2)/Sc)*Dg*Dr)))+kron((( 4/Sc)*(Ep^2)*Dz^2),Ir); for i=1:size2 A(i,i)=A(i,i) -(1.5/tnd); end for i=size3+1:size4 A(i,i)=A(i,i) -(1.5/tnd); end A(1:(Nr+1),:)=0; A(size1 (Nr+1)+1:size1,:)=0; A(1:(Nr+1),1:(Nr+1))=eye(Nr+1); A(size1 (Nr+1)+1:size1,size1 (Nr+1)+1:size1)=eye(Nr+1); for i=Nr+2:Nr+1:size1 2*(Nr+1)+1 A(i,:)=0; A(i,i)=1; end %for i=2*Nr+2:Nr+1:size1 (Nr+1) % A(i,:)=0;

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289 % A(i,i)=1; %end A(size1+1:size1+(Nr+1),:)=0; A(size2(Nr+1)+1:size2,:)=0; A(size1+1:size1+(Nr+1),size1+1:size1+(Nr+1))=eye(Nr+1); A(size2 (Nr+1)+1:size2,size2 (Nr+1 )+1:size2)=eye(Nr+1); for i=size1+Nr+2:Nr+1:size2 2*(Nr+1)+1 A(i,:)=0; A(i,i)=1; end %for i=size1+2*Nx+2:Nx+1:size2 -(Nx+1) % A(i,:)=0; % A(i,i Nx:i)=Dx(Nx+1,:); %end A(size3+1:size3+(Nr+1),:)=0; A(size3+1:size3+(Nr+1),size3+1:size4)=kron( Dz(1,:),Ir); for k=1:(Nr+1); A(size3+k,:)=0; if r(k,1)<=Rs; A(size3+k,size3+k)=1; else end end A(size4 (Nr+1)+1:size4,:)=0;

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290 A(size4 (Nr+1)+1:size4,size3+1:size4)=kron(Dz(Nz+1,:),Ir); %for i=size4 (Nr+1)+1:size4 % A(i,:)=0 ; % A(i,i)=1; %end for i=size3+Nr+2:Nr+1:size4 2*(Nr+1)+1 A(i,:)=0; A(i,i:i+Nr)=Dr(1,:); end %for i=size3+2*Nx+2:Nx+1:size4 (Nx+1) % A(i,:)=0; % A(i,i Nx:i)=Dx(Nx+1,:); %end Ai=partialinvSVD(A,size4); XX(1:size4,1)=0; XX(size 3+1:size4,1)=Cond; XXp=XX; UU=XX(1:size1); VV=XX(size1+1:size2); PP=XX(size2+1:size3); TT=XX(size3+1:size4); Uf=real(reshape(UU,Nr+1,Nz+1))'; Vf=real(reshape(VV,Nr+1,Nz+1))'; VVq=VV;

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291 VVqp=VVq; Pf=real(reshape(PP,Nr+1,Nz+1))'; Tt=real(reshape(TT,Nr+1 ,Nz+1))'; figure(1) whitebg('w'); surf(Rr,Z,Uf) title('Surface Plot of Non Dimensional Vr Velocity'); axis([0 1 0 1 1e 10 1e 10 1e 10 1e 10]); xlabel('Radius'); ylabel('Height'); zlabel('Vr Velocity'); figure(2) surf(Rr,Z,Vf) title('Surface Plot of Non Dimensional Vz Velocity'); axis([0 1 0 1 1e 10 1e 10 1e 10 1e 10]); xlabel('Radius'); ylabel('Height'); zlabel('Vz Velocity'); figure(3) surf(Rr,Z,Pf) title('Surface Plot Non -Dimensional Pressure'); axis([0 1 0 1 500 500 500 500]); xlabel('Radius');

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292 y label('Height'); zlabel('Pressure'); figure(4) surf(Rr,Z,Tt) title('Surface Plot of Non Dimensional Concentration'); axis([0 1 0 1 0 1 0 1]); xlabel('Radius'); ylabel('Height'); zlabel('Concentration'); pause Error2=1; tcounter=0; while Error < Error2 %w hile max(abs(VVqp)) (1/((1e8)*(tcounter+1))) <= max(abs(VVq)) B(1:size2,1)= ((2*XX(1:size2,1)) (0.5*XXp(1:size2,1)))/tnd; B(size3+1:size4,1)= ((2*XX(size3+1:size4,1)) (0.5*XXp(size3+1:size4,1)))/tnd; B(size1 (Nr+1)+1:size1,1)=0; B(1:(Nr+1),1)=0; B(Nr+2:Nr+1:size1 2*(Nr+1)+1,1)=0; %B(2*Nr+2:Nr+1:size1 (Nr+1),1)=0; B(size1+1:size2,1)= B(size1+1:size2,1) -((Rac/Sc)*(2*XX(size3+1:size4) XXp(size3+1:size4))); B(size1+1:size1+(Nr+1),1)=0;

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293 B(size2 (Nr+1)+1:size2,1)=0; B(si ze1+Nr+2:Nr+1:size2 2*(Nr+1)+1,1)=0; %B(size1+2*Nr+2:Nr+1:size2 (Nr+1),1)=0; B(size3+1:size4)=B(size3+1:size4)+((2*((drp*XX(1:size1,1).*(kron(Iz,Dr)*XX(size3+1:size4,1 )))+(2*(Ep^2)*XX(size1+1:size2,1).*(kron(Dz,Ir)*XX(size3+1:size4,1))))) ((drp*XXp(1: size1,1).*(kron(Iz,Dr)*XXp(size3+1:size4,1)))+(2*(Ep^2)*XXp(size1+1:size2,1). *(kron(Dz,Ir)*XXp(size3+1:size4,1))))); for i=1:(Nr+1); if r(i,1)<= Rs; %B(size3+i,1)=(1+cos(wnd*tnd*tcounter))/2; B(size3+i,1)=Csnd; else B(size3+i,1)=0; end end %B(size4 (Nr+1)+1:size4,1)=Cond; B(size4 (Nr+1)+1:size4,1)=0; B(size3+Nr+2:Nr+1:size4 2*(Nr+1)+1,1)=0; %B(size3+2*Nr+2:Nr+1:size4 (Nr+1),1)=0; XXp=XX; VVqp=VVq; XX=Ai*B; UU=XX(1:size1); VV=XX(size1+1:size2); PP=XX(size2+1:size3);

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294 TT=XX(size3+1:size4); Uf=real(reshape(UU,Nr+1,Nz+1))'; Vf=real(reshape(VV,Nr+1,Nz+1))'; VVq=VV; Pf=real(reshape(PP,Nr+1,Nz+1))'; Tt=real(reshape(TT,Nr+1,Nz+1))'; figure( 1) surf(Rr,Z,Uf) title('Surface Plot of Non Dimensional Vr Velocity'); %axis([0 1 0 1 1e 10 1e 10 1e 10 1e 10]); xlabel('Radius'); ylabel('Height'); zlabel('Vr Velocity'); figure(2) surf(Rr,Z,Vf) title('Surface Plot o f Non Dimensional Vz Velocity'); %axis([0 1 0 1 1e 10 1e 10 1e 10 1e 10]); xlabel('Radius'); ylabel('Height'); zlabel('Vz Velocity'); figure(3)

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295 surf(Rr,Z,Pf) title('Surface Plot Non Dimensional Pressure'); %axis([0 1 0 1 500 500 500 500]); xlabel('Radius'); ylabel('Height'); zlabel('Pressure'); figure(4) surf(Rr,Z,Tt) title('Surface Plot of Non Dimensional Concentration'); axis([0 1 0 1 0 1 0 1]); xlabel('Radius'); ylabel('Height'); zlabel('Concentration'); figure(5) vv=[0:.1:1]; [CC h]=contourf(Rr,Z,Tt,vv); clabel(CC,h); %contourf(Rr,Z,Tt,'Edgecolor','None'); %hold on; title('Contour Plot of the Non -Dimensional Concentration'); xlabel('Radius'); ylabel('Height'); caxis ([0 1]);

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296 %quiver(Rr,Z,Uf,Vf,max(VV)); hold off; figure(6) for pll=1:Nr+1 pr=((Nr+1)*(Nz+1)) (Nr+1); Ezt(pll,1)=Esat -f*log((TT((pr+pll),1)*(Co Cs)+Cs)/Csat); end Eto=0; for pn=1:Nr+1 Ett=Ezt(pn,1)+Eto; Eto=Ett; end Eta(tcounter+1,1)=(Ett/(Nr+1)) Eo; plot((tcounter*tnd*ts)/60,Eta(tcounter+1,1),'+','LineWidth',2); title('(Eavg(H,t) Eo) vs. Real Time (min)'); %axis([0 100 0.02 .08]); xlabel ('Real Time (min)'); ylabel('(Eavg(H,t) -Eo) (V) at z=1'); hold on; yy(tcounter+1,1)=f*(((pi^2/4)*(D/H^2)*(tcounter*tnd*ts)) -log(4/pi)); plot(tcounter*tnd*ts/60,yy(tcounter+1,1),' -'); Error2=max(abs(XX -XXp)); tcounter=tcounter+1; max(VV)*vzs

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297 min(VV)*vzs end

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298 APPENDIX C VOLUME EXPANSION OF THE UNDERLYING COPPER INTERCONNECT This appendix explores the volume expansion of copper nodes in the MES3A. The copper nodes oxidize via surface reactions and this study will show how the formation of two possible copper oxides increases the nodal volume. Another source of volume expansion to be explored is the CTE that increases the nodal volume with increasing temperature. To determine the major expansion contributor to the nodal volume a review of these two methodologies is given. The brief analysis will reiterate the importance of minimizing the amount of oxidation occurring in the copper vias. The introduction of oxygen to pure copper will first form cuprous oxide (Cu2O) and then with the addition of more oxygen form cupric oxide (CuO). Because oxygen is introduced into the copper and the copper is not removed the existing volume must expand. Using the molar volumes in Table C 1 a 67% increase in the original copper volume with the for mation of cuprous oxide and a 79% increase with the formation of cupric oxide can be calculated. A comparison of the volume change between the cuprous and cupric oxide is a 6% increase. Table C 1: Physical parameters of copper and c opper Oxide [137] Mater ial Density(g/cm 3 ) Molar Density (mol/cm 3 ) Copper (Cu) 8.9 1.40 x 10 1 Cuprous Oxide (Cu 2 O) 6.0 4.19 x 10 2 Cupric Oxide (CuO) 6.31 7.92 x 10 2 During operation of the MES3A device oxidation of the copper node must occur for an electrical potential di fference to be generated (via an electrochemical reaction). In galvanic mode the copper nodes do not have to exchange a large number of oxygen atoms with the liquid tin to achieve equilibrium. Conversely, using the MES3A device in titration mode requires a constant

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299 supply of oxygen from either the copper to the liquid tin or vise versa. The following calculation determines the necessary amount of oxygen that must be titrated from the copper node to saturate the entire tin melt. Given below in Equation ( C 1 ) is the Nernst equation corresponding to a particular electrical potential and its re spective activity. In Equation (C 2) the Nernst equation is written for the open cell equilibrium potential that also corresponds to a particular activity. Oa RT E nF ln (C 1) Sat O Sata RT E nF ln (C 2) By understandi ng how the activity changes as a function of the potential shows how the oxygen concentration changes. E RT nF E RT nF a a aSat O Sat O Oexpexp (C 3) E E RT nF a a aSat O Sat O O ln ln (C 4) The oxygen concentration is related to the activity by Henrys Law for dilute solutions and is applicable in this case. Therefore, the change in activity is converted to a change in concentration. E E RT nF C C aSat O Sat O O ln ln (C 5) E E RT nF C C aO O O (C 6) E E RT nF C CSat Sat O Oexp (C 7)

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300 E E RT nF C C C CCsat Sat O O Sat Oexp 1 (C 8) The open cell equilibrium concentration of oxygen at a temperature can be defined with its corresponding electrical potential now that the change in concentration is defined by known values. This gives a function of two variables C and E Inserting an electrical potential, E larger than the equilibrium potential, into Equation (C 8) results in a corresponding concen tration change. Figu re C 1 is the plot of Equation (C 8) depicting the change of oxygen concentration as a function of electrical potential at 700 oC. E (mV) 0 100 200 300 400 500 C (mol/cm3) 0.0 2.0e-6 4.0e-6 6.0e-6 8.0e-6 1.0e-5 1.2e-5 1.4e-5 1.6e-5 CSat Figure C 1: Oxygen concentration vs. electrical potential (750 oC) The slope is steeper for small changes in potential around the equilibrium potential and much smaller for potential changes farther away from the equilibrium potential. Simply a change

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301 in the potential around the equilibrium potential will result in a lar ge concentration change and a change further away will have a smaller concentration change. The actual amount of oxygen transported across the electrolyte can be calculated from the change in concentration multiplied by the volume of the liquid metal melt The volume of the liquid metal melt can be calculated from the surface area of the melt times an interaction distance of the melt corresponding to a diffusion length. One of the limitations is that the YSZ electrolyte is only able to sense the concentrat ion at its surface. Thus a height must be determined to which the concentration at the surface of the electrolyte is no longer affected by bulk concentration effects. This height can be defined as the diffusion length scale and for long time experiments su bstituted for the entire height of the melt. Unfortunately running a simple calculation of the number of nodes it would take to titrate out the saturated amount of oxygen in a liquid tin volume of 0.25 cm3 (a typical volume) requires over 200,000 nodes to only oxidize the nodes to cuprous oxide and over 55,000 nodes to oxidize the nodes to cupric oxide. Obviously this many nodes would be impossible to entertain into the device. Thus, the nodes at their current volume are only sufficient for open cell potent ial measurements and not titration. If attempting to use less than the number of required nodes to titrate out oxygen (at the saturation concentration) the nodes will completely oxidize and lose their applicability as an electrochemical node. The following discussion compares the full oxidation of a copper node (20 microns L x 20 microns W x 0.5 microns H) to the volume expansion due to a change in temperature. It is assumed that the TEOS walls are rigid at the operating temperature of 700 oC and that the c opper material is ductile. This means the volume expansion of the copper node can only move in the vertical direction as indicated in Figure C 2 below.

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302 Figure C 2: Schematic of volume expansion in a copper node A quick calculat ion of the volume expansion due to the CTE gives a 3.9 % volume increase over the original volume. The new heights of a copper node whether fully oxidized as cuprous or cupric oxide or expanded thermally having an original height of 500 nm is now 835 nm, 895 nm, and 5 20 nm res pectively. It is clear delamination problems are deeply rooted in oxidation of that node. Cu SiO 2 SiO 2 Cu SiO 2 SiO 2 Cu 2 O or CuO H ORIGINAL VOLUME VOLUME AFTER EXPANSION

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312 BIOGRAPHICAL SKETCH Michael June was born a Texa n in 1981, and as a child, moved between the great states of Virginia and Florida. Upon graduation from J.M. Tate High School, Michael attended Florida State University and graduated in 2003 with a B.S. in Chemical Engineering. Michael then conducted his Ph.D. research at the University of Florida under the guidance of Drs. Tim Anderson and Ranga Narayanan. Due to the nature of his research he was able to travel to Korea on two separate occasions and enjoyed the pleasure of working with research groups at Seoul National University. Additional travel opportunities allowed him to conduct fuel cell research at NASA Glenn Space Center.