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Detection of residual stress in multi-crystalline silicon wafers using swept-sne frequency response data

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Title:
Detection of residual stress in multi-crystalline silicon wafers using swept-sne frequency response data
Physical Description:
Book
Language:
English
Creator:
Best, Shawn R
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla.
Publication Date:

Subjects

Subjects / Keywords:
Audible
Modes
Resonance
Photovoltaic
Rectangular
Dissertations, Academic -- Mechanical Engineering -- Doctoral -- USF   ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: This thesis presents audible vibratory mode data obtained by mechanically exciting acoustic modes in mc-Si wafers grown by EFG technique with various levels and distributions of residual stress. Stress maps obtained using scanning infrared polariscopy are presented, illustrating the variation of residual stress.Modal analyses of the wafers are performed using the finite element method and are in remarkably good agreement with the measured frequency response data. The calculated mode shapes were further validated through classic Chladni type patterns.The vibratory data is found to correlate with the residual stress measurements. The data is fit with both linear and quadratic models with correlation coefficients of 0.8. The results reveal a dependence of wafer audible mode frequencies on residual stress level that may be useful for solar cell mechanical quality control and breakage inspection.
Thesis:
Thesis (M.S.M.E.)--University of South Florida, 2005.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Shawn R. Best.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 110 pages.

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aleph - 001681106
oclc - 62774984
usfldc doi - E14-SFE0001008
usfldc handle - e14.1008
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ABSTRACT: This thesis presents audible vibratory mode data obtained by mechanically exciting acoustic modes in mc-Si wafers grown by EFG technique with various levels and distributions of residual stress. Stress maps obtained using scanning infrared polariscopy are presented, illustrating the variation of residual stress.Modal analyses of the wafers are performed using the finite element method and are in remarkably good agreement with the measured frequency response data. The calculated mode shapes were further validated through classic Chladni type patterns.The vibratory data is found to correlate with the residual stress measurements. The data is fit with both linear and quadratic models with correlation coefficients of 0.8. The results reveal a dependence of wafer audible mode frequencies on residual stress level that may be useful for solar cell mechanical quality control and breakage inspection.
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Detection of Residual Stress in Multi-Crystalline Silicon Wafers Using Swept-Sine Frequency Response Data by Shawn R. Best A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Daniel P. Hess, Ph.D. Glen Besterfield, Ph.D. Tom Eason, Ph.D. Date of Approval: April 12, 2005 Keywords: audible, modes, resonance, photovoltaic, rectangular Copyright 2005, Shawn R. Best

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ACKNOWLEDGMENT I would like to thank Dr. Daniel P. Hess, Ph.D. for taking me as his graduate student and providing me with the tools a nd guidance to accomplish my goals as a Masters student at the University of South Fl orida. I would like to thank Sue Britten and Shirley Trevort of Mechanical Engineering fo r always being there to lend a helping hand. I would like to thank Dr. Glen Besterfield, Ph.D. for constantly reminding me that my education is priority number one and for leadi ng me into the career that I possess today. I would like to thank the professors of the Mechanical Engineering Department of the University of South Florida for giving me the to ols and skills to succeed as an engineer. I would like to thank Robert Smith and Tom Ga ge of the Engineering Machine Shop for all of their help and assistance. I would like to thank Dr. Serguei Ostapenko, Ph.D. for his support in completing this thesis. I would like to acknowledge BP Solar and RWE Schott Solar Inc. for their role in my thesis. This work was supported in part by DOE/NREL subcontract AAT-2-3160506.

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i TABLE OF CONTENTS LIST OF TABLES.............................................................................................................iii LIST OF FIGURES...........................................................................................................iv ABSTRACT......................................................................................................................x ii CHAPTER 1. INTRODUCTION.......................................................................................1 1.1 Overview...........................................................................................................1 1.2 Background.......................................................................................................1 1.3 Thesis Outline...................................................................................................2 CHAPTER 2. TEST APPARATUS AND EXPERIMENTS.............................................3 2.1 Introduction.......................................................................................................3 2.2 Test Apparatus..................................................................................................3 2.3 Test Procedure..................................................................................................6 2.4 Frequency Response and Coherence................................................................7 CHAPTER 3. EFG SOLAR CELL TEST RESULTS........................................................8 3.1 Test Specimens.................................................................................................8 3.2 Residual Stress..................................................................................................8 3.3 Frequency Response Measurements...............................................................10 3.3.1 Overview..........................................................................................10 3.3.2 Broadband Range 400-1800 Hz.......................................................11 3.3.3 Narrowband Ranges.........................................................................14 3.3.4 Narrowband Range 600-750 Hz......................................................15 3.3.5 Narrowband Range 1200-1450 Hz..................................................20 3.4 Analysis...........................................................................................................25 3.5 Discussion.......................................................................................................29 CHAPTER 4. CONCLUSIONS.......................................................................................31 REFERENCES..................................................................................................................32 APPENDICES...................................................................................................................33 APPENDIX A: M-FILES..................................................................................................34 APPENDIX B: STRESS MAPS........................................................................................41 APPENDIX C: SIGLAB VSS SETUP FILES..................................................................47

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ii APPENDIX D: RUN ORDER OF SOLAR CELL SPECIMENS OVER THE BROADBAND RANGE OF 400-1800 HZ............................................50 APPENDIX E: FREQUENCY RESPONSE PLOTS OF SOLAR CELL SPECIMENS OVER THE BROADBAND RANGE OF 400-1800 HZ.......................51 APPENDIX F: RANDOMIZATION AND RUN ORDER OF SOLAR CELL SPECIMENS OVER THE NARROWBAND RANGES.......................57 APPENDIX G: FREQUENCY RESPONSE PLOTS OF SOLAR CELL SPECIMENS OVER THE NARROWBAND RA NGE OF 600-750 HZ.....................61 APPENDIX H: FREQUENCY RESPONSE PLOTS OF SOLAR CELL SPECIMENS OVER THE NARROWBAND RA NGE OF 1200-1450 HZ.................79

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iii LIST OF TABLES Table 1 Potential descriptors for residual stress in wafers............................................10 Table 2 Response data of solar cells over the broadband range including range to zoom in for further investigation.................................................................14 Table 3 Resonance frequency of solar cell specimens 13–24 over the narrowband range of 600-750 Hz....................................................................18 Table 4 Peak amplitude at resonance of solar cell specimens 13–24 over the narrowband range of 600-750 Hz....................................................................18 Table 5 Resonance frequency of sola r cell wafers 13–24 over the narrowband range of 1200-1450 Hz....................................................................................23 Table 6 Peak amplitude at resonance of solar cell wafers 13–24 over the narrowband range of 1200-1450 Hz................................................................23 Table 7 Average dominant audibl e vibration mode test data........................................25 Table 8 Run order of specimens ove r the broad-band range of 1200-1450 Hz............50 Table 9 Solar cell specimens with asso ciated run number for narrowband range 600-750 Hz.......................................................................................................57 Table 10 Randomized ordering of speci mens for the narrowband range of 600750 Hz..............................................................................................................58 Table 11 Randomized ordering of speci mens for the narrowband range of 12001450 Hz............................................................................................................59

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iv LIST OF FIGURES Figure 1 2-Dimenional sketch of test fixture, test equi pment, and test specimen.........6 Figure 2 Representative residual stre ss maps for a 10cm x 10cm EFG wafer: a) with a relatively uniform distri bution (sample 16), and b) with a non-uniform distribution (sample 22).............................................................9 Figure 3 Frequency response of solar cell 20 symbolizing a “normal” curve over the broadband range..............................................................................11 Figure 4 Plot of the frequency response of solar cell 15 with a split in the lower resonance frequency...........................................................................12 Figure 5 Stress map of specimen 15 illustrating asymmetric distribution of residual stress................................................................................................13 Figure 6 Plot of the frequency res ponse of solar cell 16, symbolizing a “normal” plot over the narrowband range of 600 -750 Hz...........................16 Figure 7 Plot of the frequency response of solar cell 15 over the narrow-band range of 600-750 Hz with multiple sp lits in the resonance frequency.........16 Figure 8 Plot of the frequency response of solar cell 22 over the narrow-band range of 600-750 Hz with a split in the resonance frequency.......................17 Figure 9 The mean, minimum and maximu m resonance frequencies of solar cell wafers 13-24 over the narrowband range of 600-750 Hz......................19 Figure 10 The mean, minimum and maxi mum peak amplitude of solar cell wafers 13-24 over the narrowband range of 600-750 Hz.............................19 Figure 11 Plot of the frequency res ponse of solar cell 15 over the narrowband range of 1200 to 1450 Hz representing a “normal” curve over the high frequency range...............................................................................20 Figure 12 Plot of the frequency respons e of solar cell 13 over the narrowband range of 600-750 Hz with a minor sp lit in the resonance frequency............21 Figure 13 Stress map of solar cell 13 illustrating high levels of non-uniform distribution of residual stress with a profound angular distribution.............22 Figure 14 The mean, minimum and maxi mum resonance frequencies of solar cell wafers 13-24 over the narrowband range of 1200-1450 Hz..................24

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v Figure 15 The mean, minimum and maxi mum peak amplitude of solar cell wafers 13-24 over the narrowband range of 1200-1450 Hz.........................24 Figure 16 Computed audible mode shap es: a) low frequency, 668 Hz and b) high frequency, 1316 Hz...............................................................................27 Figure 17 Chladni sand patterns for a udible mode shapes: a) low frequency, 703 Hz and b) high frequency, 1380 Hz (sample 16)...................................28 Figure 18 Linear correlation of normali zed low audible mode frequency with residual stress................................................................................................30 Figure 19 Quadratic correlation of nor malized low audible mode frequency with residual stress........................................................................................30 Figure 20 Stress map of solar cell specimen 13 using scanning infrared polariscopy....................................................................................................41 Figure 21 Stress map of solar cell specimen 14 using scanning infrared polariscopy....................................................................................................41 Figure 22 Stress map of solar cell specimen 15 using scanning infrared polariscopy....................................................................................................42 Figure 23 Stress map of solar cell specimen 16 using scanning infrared polariscopy....................................................................................................42 Figure 24 Stress map of solar cell specimen 17 using scanning infrared polariscopy....................................................................................................43 Figure 25 Stress map of solar cell specimen 18 using scanning infrared polariscopy....................................................................................................43 Figure 26 Stress map of solar cell specimen 19 using scanning infrared polariscopy....................................................................................................44 Figure 27 Stress map of solar cell specimen 20 using scanning infrared polariscopy....................................................................................................44 Figure 28 Stress map of solar cell specimen 21 using scanning infrared polariscopy....................................................................................................45 Figure 29 Stress map of solar cell specimen 22 using scanning infrared polariscopy....................................................................................................45

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vi Figure 30 Stress map of solar cell specimen 23 using scanning infrared polariscopy....................................................................................................46 Figure 31 Stress map of solar cell specimen 24 using scanning infrared polariscopy....................................................................................................46 Figure 32 SigLab vss setup file for broadband range 400-1800 Hz..............................47 Figure 33 SigLab vss setup file for narrowband range 600-750 Hz.............................48 Figure 34 SigLab vss setup file for narrowband range 1200-1450 Hz.........................49 Figure 35 Frequency response plot of solar cell 13 over the broadband range of 400-1800 Hz.............................................................................................51 Figure 36 Frequency response plot of solar cell 14 over the broadband range of 400-1800 Hz.............................................................................................51 Figure 37 Frequency response plot of solar cell 15 over the broadband range of 400-1800 Hz.............................................................................................52 Figure 38 Frequency response plot of solar cell 16 over the broadband range of 400-1800 Hz.............................................................................................52 Figure 39 Frequency response plot of solar cell 17 over the broadband range of 400-1800 Hz.............................................................................................53 Figure 40 Frequency response plot of solar cell 18 over the broadband range of 400-1800 Hz.............................................................................................53 Figure 41 Frequency response plot of solar cell 19 over the broadband range of 400-1800 Hz.............................................................................................54 Figure 42 Frequency response plot of solar cell 20 over the broadband range of 400-1800 Hz.............................................................................................54 Figure 43 Frequency response plot of solar cell 21 over the broadband range of 400-1800 Hz.............................................................................................55 Figure 44 Frequency response plot of solar cell 22 over the broadband range of 400-1800 Hz.............................................................................................55 Figure 45 Frequency response plot of solar cell 23 over the broadband range of 400-1800 Hz.............................................................................................56

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vii Figure 46 Frequency response plot of solar cell 24 over the broadband range of 400-1800 Hz.............................................................................................56 Figure 47 Frequency response plot of solar cell specimen 13 over the narrowband range of 600-750 Hz; ex perimental run number 1....................61 Figure 48 Frequency response plot of solar cell specimen 13 over the narrowband range of 600-750 Hz; ex perimental run number 2....................61 Figure 49 Frequency response plot of solar cell specimen 13 over the narrowband range of 600-750 Hz; ex perimental run number 3....................62 Figure 50 Frequency response plot of solar cell specimen 14 over the narrowband range of 600-750 Hz; ex perimental run number 4....................62 Figure 51 Frequency response plot of solar cell specimen 14 over the narrowband range of 600-750 Hz; ex perimental run number 5....................63 Figure 52 Frequency response plot of solar cell specimen 14 over the narrowband range of 600-750 Hz; ex perimental run number 6....................63 Figure 53 Frequency response plot of solar cell specimen 15 over the narrowband range of 600-750 Hz; ex perimental run number 7....................64 Figure 54 Frequency response plot of solar cell specimen 15 over the narrowband range of 600-750 Hz; ex perimental run number 8....................64 Figure 55 Frequency response plot of solar cell specimen 15 over the narrowband range of 600-750 Hz; ex perimental run number 9....................65 Figure 56 Frequency response plot of solar cell specimen 16 over the narrowband range of 600-750 Hz; ex perimental run number 10..................65 Figure 57 Frequency response plot of solar cell specimen 16 over the narrowband range of 600-750 Hz; ex perimental run number 11..................66 Figure 58 Frequency response plot of solar cell specimen 16 over the narrowband range of 600-750 Hz; ex perimental run number 12..................66 Figure 59 Frequency response plot of solar cell specimen 17 over the narrowband range of 600-750 Hz; ex perimental run number 13..................67 Figure 60 Frequency response plot of solar cell specimen 17 over the narrowband range of 600-750 Hz; ex perimental run number 14..................67

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viii Figure 61 Frequency response plot of solar cell specimen 17 over the narrowband range of 600-750 Hz; ex perimental run number 15..................68 Figure 62 Frequency response plot of solar cell specimen 18 over the narrowband range of 600-750 Hz; ex perimental run number 16..................68 Figure 63 Frequency response plot of solar cell specimen 18 over the narrowband range of 600-750 Hz; ex perimental run number 17..................69 Figure 64 Frequency response plot of solar cell specimen 18 over the narrowband range of 600-750 Hz; ex perimental run number 18..................69 Figure 65 Frequency response plot of solar cell specimen 19 over the narrowband range of 600-750 Hz; ex perimental run number 19..................70 Figure 66 Frequency response plot of solar cell specimen 19 over the narrowband range of 600-750 Hz; ex perimental run number 20..................70 Figure 67 Frequency response plot of solar cell specimen 19 over the narrowband range of 600-750 Hz; ex perimental run number 21..................71 Figure 68 Frequency response plot of solar cell specimen 20 over the narrowband range of 600-750 Hz; ex perimental run number 22..................71 Figure 69 Frequency response plot of solar cell specimen 20 over the narrowband range of 600-750 Hz; ex perimental run number 23..................72 Figure 70 Frequency response plot of solar cell specimen 20 over the narrowband range of 600-750 Hz; ex perimental run number 24..................72 Figure 71 Frequency response plot of solar cell specimen 21 over the narrowband range of 600-750 Hz; ex perimental run number 25..................73 Figure 72 Frequency response plot of solar cell specimen 21 over the narrowband range of 600-750 Hz; ex perimental run number 26..................73 Figure 73 Frequency response plot of solar cell specimen 21 over the narrowband range of 600-750 Hz; ex perimental run number 27..................74 Figure 74 Frequency response plot of solar cell specimen 22 over the narrowband range of 600-750 Hz; ex perimental run number 28..................74 Figure 75 Frequency response plot of solar cell specimen 22 over the narrowband range of 600-750 Hz; ex perimental run number 29..................75

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ix Figure 76 Frequency response plot of solar cell specimen 22 over the narrowband range of 600-750 Hz; ex perimental run number 30..................75 Figure 77 Frequency response plot of solar cell specimen 23 over the narrowband range of 600-750 Hz; ex perimental run number 31..................76 Figure 78 Frequency response plot of solar cell specimen 23 over the narrowband range of 600-750 Hz; ex perimental run number 32..................76 Figure 79 Frequency response plot of solar cell specimen 23 over the narrowband range of 600-750 Hz; ex perimental run number 33..................77 Figure 80 Frequency response plot of solar cell specimen 24 over the narrowband range of 600-750 Hz; ex perimental run number 34..................77 Figure 81 Frequency response plot of solar cell specimen 24 over the narrowband range of 600-750 Hz; ex perimental run number 35..................78 Figure 82 Frequency response plot of solar cell specimen 24 over the narrowband range of 600-750 Hz; ex perimental run number 36..................78 Figure 83 Frequency response plot of solar cell specimen 13 over the narrowband range of 1200-1450 Hz; experimental run number 1................79 Figure 84 Frequency response plot of solar cell specimen 13 over the narrowband range of 1200-1450 Hz; experimental run number 2................79 Figure 85 Frequency response plot of solar cell specimen 13 over the narrowband range of 1200-1450 Hz; experimental run number 3................80 Figure 86 Frequency response plot of solar cell specimen 14 over the narrowband range of 1200-1450 Hz; experimental run number 4................80 Figure 87 Frequency response plot of solar cell specimen 14 over the narrowband range of 1200-1450 Hz; experimental run number 5................81 Figure 88 Frequency response plot of solar cell specimen 14 over the narrowband range of 1200-1450 Hz; experimental run number 6................81 Figure 89 Frequency response plot of solar cell specimen 15 over the narrowband range of 1200-1450 Hz; experimental run number 7................82 Figure 90 Frequency response plot of solar cell specimen 15 over the narrowband range of 1200-1450 Hz; experimental run number 8................82

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x Figure 91 Frequency response plot of solar cell specimen 15 over the narrowband range of 1200-1450 Hz; experimental run number 9................83 Figure 92 Frequency response plot of solar cell specimen 16 over the narrowband range of 1200-1450 Hz; experimental run number 10..............83 Figure 93 Frequency response plot of solar cell specimen 16 over the narrowband range of 1200-1450 Hz; experimental run number 11..............84 Figure 94 Frequency response plot of solar cell specimen 16 over the narrowband range of 1200-1450 Hz; experimental run number 12..............84 Figure 95 Frequency response plot of solar cell specimen 17 over the narrowband range of 1200-1450 Hz; experimental run number 13..............85 Figure 96 Frequency response plot of solar cell specimen 17 over the narrowband range of 1200-1450 Hz; experimental run number 14..............85 Figure 97 Frequency response plot of solar cell specimen 17 over the narrowband range of 1200-1450 Hz; experimental run number 15..............86 Figure 98 Frequency response plot of solar cell specimen 18 over the narrowband range of 1200-1450 Hz; experimental run number 16..............86 Figure 99 Frequency response plot of solar cell specimen 18 over the narrowband range of 1200-1450 Hz; experimental run number 17..............87 Figure 100 Frequency response plot of solar cell specimen 18 over the narrowband range of 1200-1450 Hz; experimental run number 18..............87 Figure 101 Frequency response plot of solar cell specimen 19 over the narrowband range of 1200-1450 Hz; experimental run number 19..............88 Figure 102 Frequency response plot of solar cell specimen 19 over the narrowband range of 1200-1450 Hz; experimental run number 20..............88 Figure 103 Frequency response plot of solar cell specimen 19 over the narrowband range of 1200-1450 Hz; experimental run number 21..............89 Figure 104 Frequency response plot of solar cell specimen 20 over the narrowband range of 1200-1450 Hz; experimental run number 22..............89 Figure 105 Frequency response plot of solar cell specimen 20 over the narrowband range of 1200-1450 Hz; experimental run number 23..............90

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xi Figure 106 Frequency response plot of solar cell specimen 20 over the narrowband range of 1200-1450 Hz; experimental run number 24..............90 Figure 107 Frequency response plot of solar cell specimen 21 over the narrowband range of 1200-1450 Hz; experimental run number 25..............91 Figure 108 Frequency response plot of solar cell specimen 21 over the narrowband range of 1200-1450 Hz; experimental run number 26..............91 Figure 109 Frequency response plot of solar cell specimen 21 over the narrowband range of 1200-1450 Hz; experimental run number 27..............92 Figure 110 Frequency response plot of solar cell specimen 22 over the narrowband range of 1200-1450 Hz; experimental run number 28..............92 Figure 111 Frequency response plot of solar cell specimen 22 over the narrowband range of 1200-1450 Hz; experimental run number 29..............93 Figure 112 Frequency response plot of solar cell specimen 22 over the narrowband range of 1200-1450 Hz; experimental run number 30..............93 Figure 113 Frequency response plot of solar cell specimen 23 over the narrowband range of 1200-1450 Hz; experimental run number 31..............94 Figure 114 Frequency response plot of solar cell specimen 23 over the narrowband range of 1200-1450 Hz; experimental run number 32..............94 Figure 115 Frequency response plot of solar cell specimen 23 over the narrowband range of 1200-1450 Hz; experimental run number 33..............95 Figure 116 Frequency response plot of solar cell specimen 24 over the narrowband range of 1200-1450 Hz; experimental run number 34..............95 Figure 117 Frequency response plot of solar cell specimen 24 over the narrowband range of 1200-1450 Hz; experimental run number 35..............96 Figure 118 Frequency response plot of solar cell specimen 24 over the narrowband range of 1200-1450 Hz; experimental run number 36..............96

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xii DETECTION OF RESIDUAL STRESS IN MULTI-CRYSTALLINE SILICON WAFERS USING SWEPT-SINE FREQUENCY RESPONSE DATA Shawn R. Best ABSTRACT This thesis presents audible vibrator y mode data obtained by mechanically exciting acoustic modes in mc-Si wafers gr own by EFG technique with various levels and distributions of residual stress. St ress maps obtained using scanning infrared polariscopy are presented, illustrating th e variation of residual stress. Modal analyses of the wafers are perform ed using the finite element method and are in remarkably good agreement with the measured frequency response data. The calculated mode shapes were further validat ed through classic Chla dni type patterns. The vibratory data is found to correlate with the residual stress measurements. The data is fit with both linear and quadrati c models with correlation coefficients of 0.8. The results reveal a dependence of wafer audible mode frequencies on residual stress level that may be useful for solar cell mech anical quality control and breakage inspection

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1 CHAPTER 1 INTRODUCTION 1.1 Overview The extraordinary growth of the photovol taic market over the past decade has sparked interest in the manufacturing and defect analysis of silicon wafers, the fundamental building block of solar cells. The silicon wafers of inte rest, as pertaining to this thesis, are boron doped multi-crystalline silicon (mc-Si) wafers grown by Edgedefined Film-fed Growth (EFG) technique. Th ese wafers have the possibility of meeting both requirements set forth by the photovoltaic industry of low-cost production and high efficiency. 1.2 Background In the production of multi-crystalline s ilicon (mc-Si) ribbons and tubes, applied thermo-elastic stress may exceed levels of 100 MPa. The residual stress level and its spatial distribution in wafers cut from th e ribbons depend on growth speed, thickness, and temperature gradients present during growth [1 ]. Additional stress may arise in wafers when processing into solar cells, e.g., from bulk defect precipitates, thin film deposition such as a Si3N4 anti-reflecting coating, Al-backside contact firing, and wafer handling. Such stresses create slip dislocations, whic h alter wafer stiffness, thus enhancing wafer breakage and yield reduction in solar cell production lines potentially costing millions over a years span. Specifically for wafers us ed in solar cell applications, this stress

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2 promotes various types of defect reactions, su ch as precipitation of residual impurities at dislocations, which deteriorate the electronic quality of the solar-grade mc-Si wafers [2]. There exists a need in the solar cell industry for methods of non-contact and nondestructive in-line and off-line monitoring of wafer residual stresses in as-grown as well as processed mc-Si wafers. Scanning op tical polariscopy, X-ray diffraction, TEM and micro-Raman spectroscopy have been used with some success [3] as well as scanning infrared polariscopy based on the photo-elasti c effect in stressed solids [4]. Laser measurement of the change in wafer curvatur e resulting from process steps such as thin film deposition has also been used to assess resi dual stress [5]. More recently, ultrasonics has been investigated for use in real-tim e diagnostics of defects in Cz-Si and mc-Si wafers [6, 7]. 1.3 Thesis Outline In this thesis, audible vibratory modes of mc-Si wafers arising from mechanical excitations of the wafer are used to diagnose re sidual stress. Chapter 2 describes the test apparatus and equipment used in this thesis, and explai ns the test procedure for performing the tests. Chapter 2 also give s general background information on frequency response and coherence. The test specimens used in this thes is are described in Chapter 3 and illustrates representative st ress maps and frequency respons e plots of the wafers. The data extracted from the frequenc y response plots is analyzed a nd discussed in Chapter 3. The conclusions are found in Chapter 4 a nd the references and appendices follow.

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3 CHAPTER 2 TEST APPARATUS AND EXPERIMENTS 2.1 Introduction This chapter describes the test apparatus wh ich consists of the test fixture and test equipment. Following those descriptions is the test procedure used for this thesis. Frequency response and coherence are also ex plained to help the reader understand the data presented. The residual stress associated with the mc-Si wafers is thought to have a direct effect on the stiffness of the wafer. If this hypothesis is true, and knowing that stiffness directly affects the frequency re sponse of an object, the stress would also have an effect on the frequency response and mode shapes of the wafers. To test this hypothesis, the residual stress of each wafer was measured using Scanning Infrared Polariscopy. Next, the frequency response and coherence of each wafer was measured and then compared to the residual stress data. 2.2 Test Apparatus The vibration measurement test setup is il lustrated in Figure 1. The test fixture is a custom part machined out of aluminum 6061-T6 with a Danco Company #74 o-ring (Stock #35719B) attached with super glue at the fixture and test wafer interface. The rubber o-ring between the aluminum fixture a nd the test specimen is needed due to the lack of flatness inherent to the wafers. Without the o-ring, the wafers would move bilaterally atop the fixture causi ng chatter, thus leading to unu sable data. The o-ring adds

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4 damping to the system, but its effect on the frequency response of the wafers was found to be constant. The aluminum fixture is fi tted with a 3/8” x ” I.D. hose barb to MIP adapter. The adapter and o-ring combination ar e used to secure the test specimen to the fixture using a one phase induction moto r vacuum pump (SaveVac 85) and Tygon Laboratory and Vacuum Tubing Formulati on R-3603 (Part Number AAC00029). This allows us to secure the test specimen to the fixture without constraining th e edges of the specimen. The aluminum fixture is mounted onto an electrodynamic vibration generator, (Vibration Test Systems model number VG 100M-4 vibrator with trunion). The electromagnetic vibration genera tor, also referred to as a shaker, is fitted with a Low Noise B-1 Blower which is used to keep the sh aker coil cool. The bl ower is incorporated with a sound absorption system to reduce its noise level. A piezoelectric accelerometer (PCB Pi ezotronics Model #333B32) is mounted onto the fixture for shaker control. Its ra nge of operation is between 0.5-3000 Hz and its sensitivity is 94.5 mV/g. The se nsitivity of the accelerometer is entered into the SigLab software so that the signal can be converte d to useful measurements. The accelerometer is connected to input channel 1 and is used as the reference value when calculating frequency response. A sound level meter (Quest Technologies Model 2900) is mounted to a tripod and positioned 2cm +/0.2cm above the test specime n to record the audible modes. The sound level meter has a full output range of +/5 Vpk (3.16 Vrms). The sound level meter is limited in its function as it can only be set to read sound pressure for a 60 dB range. Since we are interested in the peak amplit udes, the microphone is set to read 60-120 dB.

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5 With this being said, the sensitivity of the sound level meter is 5V/120 dB. This sensitivity is used in the SigLab software to convert the sound level meter signal to decibels. A 6ft shielded, 1/8” mono mi niplug to RCA phono plug, fitted with a goldplated RF adapter ( accepts phono plug, fits BNC jack) is plugged into the sound level meter AC output and runs to input channel 3 of the SigLab hardware. The measurement from the sound level meter is the output of our test specimens and is referred to as the Response Channel. A SigLab dynamic signal analyzer (D SP/MTS Technology Inc. Model 20-42) used in conjunction with SigLab and MatL ab R12 software (DSP/MTS Technology Inc.) is used to apply a swept-sine input to the test specimen a nd to record the fixture input acceleration and the resulting sound pressure resp onse. The analyzer consists of 4 input channels and 2 output channels. All the cha nnels are fitted with BNC connections. The analyzer calculates the frequency response w ith the fixture acceleration defined as the input (reference channel) and the sound pre ssure as the output (response channel). The output of the dynamic signal analyzer mu st be amplified in order to apply the correct amount of voltage to the shaker. A Techron Power Supply Amplifier (Model #7541) is connected to the output channel 1 of the dynamic signal analyzer and is used to drive the shaker. The amplifie r settings were adjusted to supply a significant amount of power to the shaker without causing the wafer to be forced into its nonlinear region. The amplifier is set to constant voltage and the level control set to 475 (0-1000 range).

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6 2.3 Test Procedure Prior to any testing, the SigLab hardwa re must first be powered up. After powering up the SigLab hardwa re, the vss software of SigL ab can be initiated. The SigLab vss setup files used in this thesis can be found in Appendix C. Then the amplifier can be powered up and the B-1 Blower set to low. The mc-Si wafer is centered on the cylindric al test fixture, u tilizing a centering fixture to ensure a consistent location +/-0.2cm from test to te st. The solar cell is held in place with application of a weak vacuum at its center utilizing the SaveVac85 pump. No visible wafer bending was observed after a pplication of this negative pressure. Figure 1. 2-Dimenional sketch of test fixt ure, test equipment, and test specimen. 2 cm test specimen shaker microphone test fixture to vacuum pump control accelerometer

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7 2.4 Frequency Response and Coherence The frequency response function, also known as the transfer function, is a complex function of frequency that contains both magnitude and phase information and is presented graphically using magnitude and phase versus frequency plots. Swept-sine is a method of measuring the frequency response function of a dynamic system. Swept-sine frequency response utilizes a sine wave as the system excitation and is stepped through the frequency range of interest. The refe rence channel (always channel 1 in vss) measures the excitation signal while the res ponse channels measure the output of the system(s) under test. All input channels are measured using a narrow-band tracking filter whose pass-band is centered on the excitation fre quency of each step. The tracking filter helps reduce the effects of system noise. The ratio of the sine wave amplitudes (Response Channel/ Reference Channel) is disp layed as the transfer function magnitude. The computation is actually the ratio of the cross-spectrum and the reference autospectrum which is complex and contains both magnitude and phase information. The coherence is a function of frequency. It provides a measurement of the power in the sound pressure that is caused by th e power in the fixture acceleration. A coherence of 1 means that all of the m easured sound pressure is caus ed by the acceleration input; whereas a coherence of 0 means that none of th e sound pressure is caused by the input. The excellent (i.e., near unity) coherence shown in Figure 3 was found in all tests.

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8 CHAPTER 3 EFG SOLAR CELL TEST RESULTS 3.1 Test Specimens A set of 10cm x 10cm as-grown mc-Si wafers produced by the Edge-defined Film-fed Growth (EFG) method [8] with a nom inal thickness of 340 micron was used in this study. All wafers were ini tially screened for de fects such as microcracks at the wafer edge, which could affect the excited vibr atory modes, using high resolution Scanning Acoustic Microscopy (SAM). A threshold cr ack length of 10 microns at the wafer periphery was used to exclude samples from th is study [7]. The acoustic microscopy also was used to measure wafer thickness requi red for both the optical polariscopy and vibration measurements and analyses. 3.2 Residual Stress Following SAM inspection, the wafers were measured with scanning infrared polariscopy to assess the level and distri bution of in-plane stress using a method described elsewhere [4]. Stress maps of the twelve test wafers were obtained from this infrared polariscopy. They can be found in A ppendix B. Representative stress maps are presented in Figure 2. Each of the stress maps in Figure 2 uses a grid of 100x100 data points to cover the 10 cm square wafer. Fi gure 2a shows an exampl e of a wafer with a fairly uniform stress distribution over most of the wafer (sample 16). In contrast, significant non-uniform variati on in the residual stress dist ribution is observed within wafer sample 22 as illustrated in Figure 2b.

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9 Figure 2. Representative residual stress ma ps for a 10cm x 10cm EFG wafer: a) with a relatively uniform distribution (sam ple 16), and b) with a non-uniform distribution (sample 22). (b) (a)

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10 Potential single number descriptors have been identified to quantify the stress maps. These include average stress, peak st ress, average of lowest ten percent stress, average of highest ten percent stress, average of highest five percent stress, and average of highest one percent stress. Table 1 summarizes the computed values of these descriptors for the twelve test wafers. The m-file, new_percent.m, used to extract these descriptors from the raw stress data can be found in Appendix A along with other m-files used for data analysis in this thesis. Table 1. Potential descriptors fo r residual stress in wafers. Sample Number Thickness [microns] Average Stress [MPa] Peak Stress [MPa] High Stress (1%) [MPa] High Stress (5%) [MPa] High Stress (10%) [MPa] Low Stress (10%) [MPa] 13 348 5.06 28.58 21.47 17.20 15.17 1.39 14 341 4.37 31.37 19.47 15.43 13.38 1.45 15 340 4.10 29.46 20.29 14.03 11.32 1.27 16 366 2.81 25.01 8.46 6.03 5.28 1.48 17 369 3.33 30.57 16.83 11.27 8.87 1.41 18 356 4.58 37.78 18.54 14.66 12.64 1.28 19 343 4.11 29.56 20.85 16.42 13.62 1.19 20 349 4.93 28.66 20.72 17.11 15.00 1.55 21 344 5.38 44.77 25.58 18.61 15.46 1.60 22 346 5.65 29.17 23.45 18.82 16.60 1.35 23 347 4.36 29.84 21.55 17.08 14.44 1.32 24 344 4.10 29.54 22.37 17.56 13.93 1.28 3.3 Frequency Response Measurements 3.3.1 Overview The shaker was used to excite the twel ve solar cell wafers, numbered 13 thru 24, and the frequency response of each wafer wa s recorded. The wafers were tested over

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11 three various ranges explained la ter in detail. The order in which they were tested was randomized to minimize any type of creep or bias measurements. The randomization tables and run order for the broadband ra nge tested can be found in Appendix D. 3.3.2 Broadband Range 400-1800 Hz Initially, the 12 specimens were swept-sine tested once each from 400 Hz to 1800 Hz with a tracking bandwidth of 10 Hz. The broadband range produced similar curves for all of the wafers, with the exception of specimens 15 and 22. The curves that are similar to the norm will be referred to as “normal” curves. The plots of these “normal” curves are similar in shape but vary in resonance frequency and peak amplitude. Figure 3 is the broadband frequency response of specime n 20 and is representative of a “normal” curve. The “normal” plot is well defi ned by two separated resonance frequencies, smooth lines, and a phase change of 180 degrees at resonance. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 3. Frequency response of solar cell 20 symbolizing a “normal” curve over the broadband range.

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12 Figure 4 is a plot of th e frequency response of so lar cell 15. At the lower resonance frequency, there appears to be tw o audible modes in the 650-750 Hz range. This split may be attributed to asymmetric distribution of residual stress within the wafer illustrated in figure 5. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 4. Plot of the frequency response of solar cell 15 with a split in the lower resonance frequency. The frequency response plot and stress map of solar cell 22 have similar characteristics as that of solar cell 15 a nd therefore the same assumption of asymmetric distribution of residual stress also applies. Frequency re sponse plots over the 400-1800 Hz broadband range of all the specimens used in this thesis can be found in Appendix E.

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13 Figure 5. Stress map of specimen 15 illu strating asymmetric distribution of residual stress. The main purpose of analyzing the fre quency response of the wafers over the broadband range was to obtain a global view of the dynamics, and to identify narrowband ranges to zoom in on for be tter resolution. Table 2 summarizes the frequency response data obtained over the broadband range. It contains frequency response data for the twelve specimens and the range to zoom-in on for more precise data at resonance.

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14 Table 2. Response data of solar cells ove r the broadband range including range to zoom-in for further investigation. Specimen Number Low Resonance Frequency Peak Amplitude High Resonance Frequency Peak Amplitude Low Frequency Range High Frequency Range 13 700 4.84 1340 4.40 640-740 1230-1400 14 660 4.77 1290 4.90 600-720 1200-1350 15 680 2.86 1290 5.99 600-750 1200-1350 16 700 7.03 1380 4.52 650-750 1300-1450 17 700 5.32 1390 4.39 650-750 1260-1460 18 700 5.68 1360 4.45 640-740 1250-1450 19 670 5.38 1290 5.06 600-720 1200-1380 20 680 5.49 1310 5.23 600-750 1200-1400 21 670 6.29 1310 4.97 600-720 1200-1400 22 690 5.33 1320 4.75 650-750 1200-1400 23 680 7.27 1310 5.20 620-720 1200-1400 24 670 6.52 1340 4.35 600-720 1200-1400 3.3.3 Narrowband Ranges As stated earlier, the narrowband ranges were established for the purpose of zooming-in on the resonance frequencies to be tter distinguish the di fferences between the solar cell wafers. The information obtai ned over the broadband range led to the determination of the narrow-band frequency ranges of 600-750 Hz for the first resonance frequencies and 1200-1450 Hz for the second res onance frequencies. These ranges were chosen because they capture all of the wafe rs first and second resonance frequencies, respectively. The capturing of all wafers in one range is beneficial to the experimenter in that it allows for no necessary changes in th e parameters of the SigLab software from wafer to wafer during the experiment. The tr acking bandwidth for bot h ranges was set at 2-Hertz so that better accuracy could be obt ained. The wafers were randomly run three times over each narrowband range in order to account for the induced variability caused

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15 by the experimenter when positioning the solar cell wafers on the fixture. The randomization tables and run order for each narrowband range can be found in Appendix F. The SigLab parameters for each range can be found in Appendix C of this thesis. 3.3.4 Narrowband Range 600-750 Hz The 600-750 Hz narrowband range produced similar results to that of the broadband range in the sense that all solar ce ll specimens appear to be normal with the exception of solar cells 15 and 22. It shoul d be noted that solar cell 14, although not as significant as 15 and 22, also displayed some “abnormal” attributes. Figure 6 shows a representative “normal” curve for the 600-750 Hz range. Again, it differs from other “normal” curves with respect to amplitude and frequency. Figure 7 and 8 are frequency response plots of solar cell wafers 15 and 22, respectively. It is noted that with the narrow-band, there are three peaks about th e resonance frequency. Referring back to Figure 2, there are only two peaks at the lower resonance frequency. This alone justifies the use of narrowband ranges to produce more precise plots around the areas of interest.

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16 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 6. Plot of the frequency response of solar cell 16, symbolizing a “normal” plot over the narrowband range of 600 -750 Hz. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 7. Plot of the frequency response of solar cell 15 over the narrowband range of 600-750 Hz with multiple splits in the resonance frequency.

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17 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 8. Plot of the frequency response of solar cell 22 over the narrowband range of 600-750 Hz with a split in the resonance frequency. Figures 6 thru 8 can be found in Appendi x G along with the other solar cells coherence and frequency response plots fo r the narrowband range of 600-750 Hz. The resonance frequencies and peak amplitudes were extracted from these graphs and are summarized in Table 3 and Table 4, respectiv ely. In addition to Table 3 and Table 4, Figures 9 and 10 are graphical summarie s of the mean, minimum, and maximum resonance frequencies and peak amplitudes for all 12 wafers in the specified range of 600-750 Hz. The mean value is used as a label for each wafer.

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18 Table 3. Resonance frequency of solar cell specimens 13–24 over the narrowband range of 600-750 Hz. Specimen Resonance Frequency Mean Number [Hz] [Hz] Test 1 Test 2 Test 3 13 698 702 702 701 14 662 664 660 662 15 674 674 674 674 16 702 702 704 703 17 706 706 706 706 18 696 698 696 697 19 672 672 674 673 20 678 678 678 678 21 672 672 674 673 22 688 688 688 688 23 680 678 678 679 24 672 672 672 672 Table 4. Peak amplitude at resonance of solar cell specimens 13–24 over the narrowband range of 600-750 Hz. Specimen Peak Amplitude Mean Number [dB/g] [dB/g] Test 1 Test 2 Test 3 13 6.62 6.75 6.80 6.73 14 5.53 5.61 4.48 5.21 15 4.62 4.73 4.68 4.68 16 7.64 7.76 7.52 7.64 17 6.43 6.34 6.29 6.35 18 6.21 6.41 6.32 6.31 19 5.48 5.77 5.52 5.59 20 7.32 7.14 7.01 7.16 21 6.30 6.41 6.14 6.28 22 4.93 4.75 5.28 4.99 23 7.37 7.47 7.38 7.41 24 7.24 7.02 7.30 7.19

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19 662 674 703 706 697 673 678 673 688 701 672 679 650 660 670 680 690 700 710 131415161718192021222324 SpecimenResonace Frequency [Hz] Figure 9. The mean, minimum and maximum resonance frequencies of solar cell wafers 13-24 over the narrowband range of 600-750 Hz. 6.73 5.21 4.68 6.31 7.16 6.28 5.59 7.64 6.35 7.41 7.19 4.99 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 131415161718192021222324 SpecimenPeak Amplitude[dB/g] Figure 10. The mean, minimum and maximum peak amplitude of solar cell wafers 13-24 over the narrowband range of 600-750 Hz.

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20 3.3.5 Narrowband Range 1200-1450 Hz The narrowband range of 1200 to 1450 Hz produced “normal” graphs for all eleven of the twelve wafers. Figure 11 is a plot of solar cell 15 over the 1200-1450 Hz range. Remember that solar cell wafers 15 and 22 were considered to be abnormal in the 600-750 Hz range discussed earlier. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 11. Plot of the frequency response of sola r cell 15 over the narrowband range of 1200 to 1450 Hz representing a “normal” curve over the high frequency range. Solar cell specimen 13 was the only wafer that graphically displayed a split about the resonance frequency over the narrow band range of 1200-1450 Hz. During testing, solar cell 13 made an “abnormal” whistle when resonating. Unlike the other specimens that gradually climbed a pitch scale while approaching resonance and then steadily declined, specimen thirteen disp layed a fluctuating pitch about resonance. Figures 12 and

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21 13 are the frequency response plot and stress map of so lar cell 13, respectively. The stress map, Figure 13, displays a profound angul ar distribution of residual stress in addition to the vertical distribut ion existing in other specimens. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 12. Plot of the frequency response of sola r cell 13 over the narrowband range of 600-750 Hz with a minor split in the resonance frequency.

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22 Figure 13. Stress map of solar ce ll 13 illustrating high levels of non-uniform distribution of residual stress with a profound angular distribution. The frequency response plots over the narrowband range of 1200-1450 Hz for all solar cell specimens can be found in Appe ndix H. Table 5 and Table 6 summarize the data obtained from the frequency response pl ots found in Appendix H. In addition to Table 5 and Table 6, Figures 14 and 15 are gr aphical summaries of the mean, minimum, and maximum resonance frequencies and peak amplitudes for all 12 wafers in the specified range of 1200-1450 Hz.

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23 Table 5. Resonance frequency of solar cell wafers 13–24 over the narrowband range of 1200-1450 Hz. Specimen Resonance Frequency Mean Number [Hz] [Hz] Test 1 Test 2 Test 3 13 1336 1340 1334 1337 14 1284 1290 1284 1286 15 1294 1294 1294 1294 16 1380 1380 1380 1380 17 1388 1388 1384 1387 18 1364 1364 1364 1364 19 1296 1298 1300 1298 20 1312 1312 1310 1311 21 1312 1314 1316 1314 22 1324 1316 1316 1319 23 1310 1310 1314 1311 24 1342 1346 1346 1345 Table 6. Peak amplitude at resonan ce of solar cell wafers 13–24 over the narrowband range of 1200-1450 Hz. Specimen Peak Amplitude Mean Number [dB/g] [dB/g] Test 1 Test 2 Test 3 13 4.34 4.64 4.46 4.48 14 5.38 5.50 5.16 5.35 15 6.59 5.91 5.90 6.13 16 4.48 5.19 5.01 4.89 17 4.89 4.78 4.66 4.78 18 4.62 4.92 4.92 4.82 19 5.72 5.88 5.87 5.83 20 5.43 5.38 5.58 5.46 21 5.22 5.23 5.28 5.25 22 5.03 5.20 5.19 5.14 23 5.53 5.21 5.41 5.38 24 4.66 4.89 4.55 4.70

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24 1294 1387 1364 1311 1345 1319 1314 1311 1286 1298 1380 1337 1260 1280 1300 1320 1340 1360 1380 1400 131415161718192021222324 SpecimenResonance Frequency [Hz] Figure 14. The mean, minimu m and maximum resonance fr equencies of solar cell wafers 13-24 over the narrowband range of 1200-1450 Hz. 5.83 5.14 5.38 4.82 6.13 5.35 4.78 4.89 5.46 5.25 4.70 4.48 4.00 4.50 5.00 5.50 6.00 6.50 7.00 131415161718192021222324 SpecimenPeak Amplitude [dB/g] Figure 15. The mean, minimum and maximum peak amplitude of solar cell wafers 13-24 over the narrowband range of 1200-1450 Hz.

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25 3.4 Analysis Frequency response data were obtained for all of the twelve 10cm x 10cm wafers. Two dominant audible vibratory mode s where found over the 400-1800 Hz range explored. A summary of the dominant audi ble natural frequenc ies and corresponding amplitudes for all twelve test samples is provi ded in Table 7. The low-frequency mode is in the 662 to 706 Hz range and the high-freque ncy mode is in the 1286 to 1387 Hz range. These frequencies and amplitudes are found to vary from wafer to wafer, but remain repeatable from test to test In addition, mode splitting was observed for the low frequency mode in the frequency response data for wafers 15 and 22 as illustrated in Figure 7. This characteristic may be attri buted to non-uniform re sidual stress or other defects in the wafer. Table 7. Average dominant audibl e vibration mode test data. Low Mode High Mode Specimen Natural Peak Natural Peak Number Frequency Amplitude Frequency Amplitude [Hz] [dB/g] [Hz] [dB/g] 13 701 6.73 1337 4.48 14 662 5.21 1286 5.35 15 674 4.68 1294 6.13 16 703 7.64 1380 4.89 17 706 6.35 1387 4.78 18 697 6.31 1364 4.82 19 673 5.59 1298 5.83 20 678 7.16 1311 5.46 21 673 6.28 1314 5.25 22 688 4.99 1319 5.14 23 679 7.41 1311 5.38 24 672 7.19 1345 4.70

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26 Modal analyses of the wafers are perform ed using the finite element method. The wafer is modeled with shell elements with the center 12.7mm (0.5”) diameter fixed. The material is modeled as isotropic with a m odulus of 170 GPa, a Poisson’s ratio of 0.27 and a density of 2.329 kg/m3. The analysis predicts nineteen vibrat ory modes over the 0 to 2,000 Hz range. However, most of these mode shapes e xhibit asymmetry and are not efficient sound radiators. Two symmetric mode shapes are found at 668Hz and 1316Hz. These mode shapes are illustrated in Figures 16. The inherent symmetry in these two modes makes them the dominant audible modes in the frequency range considered. The calculated modal frequencies of 668Hz and 1316Hz are in remarkably good agreement with the measured data summarized in Table 7, especially considering the simple isotropic material model assumed in the finite element analysis. The calculated mode shapes were furthe r validated through classic Chladni type patterns presented in Figure 17. These were obtained by sprinkling fine sand on the wafer while exciting the sample at each audi ble mode frequency. The sand collects at the nodal lines of the mode shapes. A compar ison of the nodal lines from the calculated mode shapes in Figure 16 with the nodal sa nd lines in Figure 17 show s there is excellent agreement.

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27 Figure 16. Computed audible mode shapes : a) low frequency, 668 Hz and b) high frequency, 1316 Hz. (a) (b)

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28 Figure 17. Chladni sand patterns for a udible mode shapes: a) low frequency, 703 Hz and b) high frequency, 1380 Hz (sample 16). (b) (a)

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29 3.5 Discussion The measured low audible mode frequency data is plotted against the average of the highest ten percent residual stress descri ptor in Figures 18 and 19. To factor out wafer thickness variation on natural freque ncy, the frequency data are normalized by thickness to the three-halves power [9] in th e plots in Figures 18 and 19. Wafer thickness data for all specimens is included in Table 1. This normalized frequency and residual stress data is fitted to a linear model in Fi gure 18 and to a quadratic model in Figure 19. The plot shows that the vibra tion data correlates reasonably we ll with the stress data with correlation coefficients of 0.8. Note that data from sample 15 is not included in these fits because it appears as an outlier ; with sample 15 data included the correlation coefficients drop to 0.6. The data and models show a notable depe ndency of the audible mode frequencies on the residual stress. The audible frequenc ies increase with incr easing stress suggesting that increasing residual stress increases wafer s tiffness. Similar analyses with the high audible mode frequency data showed this tre nd but with lower correlation coefficients of 0.5.

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30 16 17 18 13 14 19 20 21 22 23 24 R2 = 0.8 0.098 0.099 0.100 0.101 0.102 0.103 0.104 0.105 0.106 0.107 0.108 0.109 4.006.008.0010.0012.0014.0016.0018.00 Average of the Highest 10% Residual Stress (MPa)Normalized Natural Frequency,f/h3/2 (Hz/m3/2) Figure 18. Linear correlation of normali zed low audible mode frequency with residual stress. 16 17 13 14 18 19 20 21 22 23 24 R2 = 0.8 0.099 0.100 0.101 0.102 0.103 0.104 0.105 0.106 0.107 0.108 0.109 4.006.008.0010.0012.0014.0016.0018.00 Average of the Highest 10% Residual Stress (MPa)Normalized Natura l Frequency, f/h3/2(Hz / m3/2) Figure 19. Quadratic correlation of normali zed low audible mode frequency with residual stress.

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31 CHAPTER 4 CONCLUSIONS Audible vibratory mode data from a set of EFG mc-Si wafers with various levels and distributions of residual stress has been presented. The audible modes have been found to exhibit symmetry compared to non-audi ble vibratory modes. Mode splitting has been found in frequency response measuremen ts of wafers with non-uniform residual stress distributions. Analysis of this vibratory data and the wafer residual stress measurements has shown reasonably good co rrelation for both linear and quadratic models. The audible natural frequencies of th e wafers have been found to increase with increasing stress. Currently, further research into the rela tionship between residual stress of silicon wafers and frequency response data is being conducted at the Un iversity of South Florida. The investigations include othe r types of silicon wafers rangi ng in thickness, shape, size, and growth technique. Impact testing is also being explored as a quicker alternative to swept-sine testing. Stress diagnostics utilizing frequency re sponse data has the ability of meeting both requirements of low-cost production a nd high efficiency in the manufacturing of silicon wafers. The results show promise for a fast and reliable metrological tool for inline diagnostics of wafers with less than optimum properties due to as-grown and process-induced defects.

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32 REFERENCES 1. Y. Kwon, S. Danyluk, L. Bucciar elli and J. P. Kalejs 1987 J. Crystal Growth 82, 221227. Residual stress measurement in silicon sheet by Shadow Moire interferometry. 2. S. Ostapenko, I Tarasov, J. P. Kalejs, C. Haessler and E. U. Reisner 2000 Semicond. Sci. Technol. 15, 840-848. Defect monitoring using scanning photoluuminescence spectroscopy in mc-Si wafers. 3. Y. Gogotsi, C. Baek and F. Kirscht 1999 Semiconductor Science and Technology 14, 936. Raman micro-spectroscopy study of processing-induced phase transformations and resi dual stress in silicon. 4. M. Yamada 1985 Appl. Phys. Lett. 47, 365-367. Quantitative photoelastic measurement of residual strains in undoped semi-insulating GaAs. 5. R. W. Hoffman 1966 in Physics of Thin Films (G. Hass and T. E. Thun, editors) 211. New York: Academic Press. 6. S. Ostapenko and I. Tarasov 2000 Appl.Phys.Lett 76, 2217. Non-linear resonance acoustic vibrations in Cz-Si wafers. 7. A. Belyaev, S. Lulu, I. Tarasov, S. Ostapenko and J. P. Kalejs 2002 IEEE Proceedings 332-335. Stress diagnostics in mc-S i wafers using an acoustic technique. 8. J. P. Kalejs 2004 Diffusion and Defect Data Part B (Solid State Phenomena) 95-96 159-174. Silicon ribbons for solar cells. 9. R. D. Blevins 2001 Formulas for Natural Frequency and Mode Shape Florida: Krieger Publishing. 10. S. R. Best, D. P. Hess, A. Belyaev, S. Ostapenko and J. P. Kalejs et al. Submitted to Applied Acoustics Audible Vibration Diagnostics of Thermo-Elastic Residual Stress in Multi-Crystalline Silicon Wafers.

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33 APPENDICES

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34 APPENDIX A: M-FILES dataplot_bb.m % Dataplot_bb.m Rev. 8/15/03 % Retrieves and plots freq response data and coherence over broadband range 400-1800 Hz from Siglab swept-sine test data files (.vss) % Type “dataplot_bb”; press enter % Type “load 13bb.vss –mat” (replace 13 with sp ecimen number of inte rest) ; press enter % Type “return” ; press enter keyboard % Coherence vs Frequency Plot subplot(311) plot(Fvec,CohDat,'k') set(gca,'fontname','Arial') ylabel('Coherence') axis([400 1800 0 1]) % xlabel('Frequency [Hz]') % Magnitude vs Frequency Plot subplot(312) plot(Fvec,(24/10.582)*a bs(XferDat),'k') %set(gca,'fontname','Arial') ylabel('Magnitude (dB/g)') axis([400 1800 0 7]) % xlabel('Frequency [Hz]') % Phase vs Frequency Plot subplot(313) plot(Fvec,(unwrap(angle(XferDat))).*(180/pi),'k') %set(gca,'fontname','Arial','fontsize','12') ylabel('Phase (deg)') xlabel('Frequency (Hz)') % End

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35 APPENDIX A (Continued) dataplot_low.m % Dataplot_low.m 8/15/03 % Retrieves and plots freq response data and coherence over narrowband range 600-750 Hz from Siglab swept-sine test data files (.vss) % Type “dataplot_low”; press enter % Type “load 13low_1.vss –mat” (replace 13 with specimen number of interest and 1 with experimental run number) ; press enter % Type “return” ; press enter keyboard % Coh vs plot subplot(311) plot(Fvec,CohDat,'k') ylabel('Coherence') axis([600 750 0 1]) % xlabel('Frequency [Hz]') % Mag vs freq plot subplot(312) plot(Fvec,(24/10.582)*a bs(XferDat),'k') ylabel('Magnitude (dB/g)') axis([600 750 0 8]) % xlabel('Frequency [Hz]') % Phase vs freq plot subplot(313) plot(Fvec,(unwrap(angle(XferDat))).*(180/pi),'k') ylabel('Phase (deg)') xlabel('Frequency (Hz)') % End

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36 APPENDIX A (Continued) dataplot_high.m % Dataplot_high.m 8/15/03 % Retrieves and plots freq response data and coherence over narrowband range 12001450 Hz from Siglab swept-sine test data files (.vss) % Type “dataplot_high”; press enter % Type “load 13high_1.vss –mat” (replace 13 with specimen number of interest and 1 with experimental run number) ; press enter % Type “return” ; press enter keyboard % Coh vs plot subplot(311) plot(Fvec,CohDat,'k') ylabel('Coherence') axis([1200 1450 0 1]) % xlabel('Frequency [Hz]') % Mag vs freq plot subplot(312) plot(Fvec,(24/10.582)*a bs(XferDat),'k') ylabel('Magnitude (dB/g)') axis([1200 1450 0 7]) % xlabel('Frequency [Hz]') % Phase vs freq plot subplot(313) plot(Fvec,(unwrap(angle(XferDat))).*(180/pi),'k') ylabel('Phase (deg)') xlabel('Frequency (Hz)') % End

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37 APPENDIX A (Continued) new_percent.m %name of file : new_percent %retrieves desired percent of stress %Procedure %Type “new_percent13” (change 13 to desired specimen num ber) ; press enter %Type “load stress13” (change 13 to de sired specimen number) ; press enter %Type “return” ; press enter keyboard xmin = 11; xmax = 103; ymin = 3; ymax = 101; %must change stress13 to desire d wafer prior to running program x=stress13(ymin:ymax, xmin:xmax); %The size of x is an A by B matrix [a b]=size (x); c=a*b; d=9206; %Now we reshape the original matrix to a matrix with only one row and 'c' columns r=reshape(x,1,c); %Sort the matrix in ascending order s=sort (r); y=s(1:d); %This value can be checked with given values to check validity of program peak_stress=(max (y))/2 % Average of largest (n umeric) percent of x %p is defined as the amount of data points to be taken into account based on a percentage

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38 APPENDIX A (Continued) new_percent.m (Continued) %1 percent p=round(0.01*d); high1=0; for i=1:p high1=y(d-i+1)+high1; end high1=high1/(2*p) %5 percent p=round(0.05*d); high5=0; for i=1:p high5=y(d-i+1)+high5; end high5=high5/(2*p) %10 percent p=round(0.10*d); high10=0; for i=1:p high10=y(d-i+1)+high10; end high10=high10/(2*p) %Average of smallest 10 percent of x p=round(0.10*d);

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39 APPENDIX A (Continued) new_percent.m (Continued) low = 0; for i = 1:p low=y(i)+low; end low = low/(2*p) % Average of stresses avg = 0; for i = 1:d avg = y(i) + avg; end avg = avg/(2*d) %end

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40 APPENDIX A (Continued) efg_usf.m %name of file: efg_usf.m %plots stress map of specimens %Procedure %Type “efg_usf” ; press enter %Type “load stress13” (change 13 to de sired specimen number) ; press enter %Type “return” ; press enter keyboard xmin = 11; xmax = 103; ymin = 3; ymax = 101; %change stress13 to wafer of interest set(surface(stress13/2), 'edgecolor', 'none'); caxis([0 30]);colorbar; axis([xmin xmax ymin ymax]);

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41 APPENDIX B: STRESS MAPS Figure 20. Stress map of solar cell specimen 13 using scanning infrared polariscopy. Figure 21. Stress map of solar cell specimen 14 using scanning infrared polariscopy.

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42 APPENDIX B (Continued) Figure 22. Stress map of solar cell specimen 15 using scanning infrared polariscopy. Figure 23. Stress map of solar cell specimen 16 using scanning infrared polariscopy.

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43 APPENDIX B (Continued) Figure 24. Stress map of solar cell specimen 17 using scanning infrared polariscopy. Figure 25. Stress map of solar cell specimen 18 using scanning infrared polariscopy.

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44 APPENDIX B (Continued) Figure 26. Stress map of solar cell specimen 19 using scanning infrared polariscopy. Figure 27. Stress map of solar cell specimen 20 using scanning infrared polariscopy.

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45 APPENDIX B (Continued) Figure 28. Stress map of solar cell specimen 21 using scanning infrared polariscopy. Figure 29. Stress map of solar cell specimen 22 using scanning infrared polariscopy.

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46 APPENDIX B (Continued) Figure 30. Stress map of solar cell specimen 23 using scanning infrared polariscopy. Figure 31. Stress map of solar cell specimen 24 using scanning infrared polariscopy.

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47 APPENDIX C: SIGLAB VSS SETUP FILES Figure 32. SigLab vss setup file for broadband range 400-1800 Hz.

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48 APPENDIX C (Continued) Figure 33. SigLab vss setup file for narrowband range 600-750 Hz.

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49 APPENDIX C (Continued) Figure 34. SigLab vss setup file for narrowband range 1200-1450 Hz.

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50 APPENDIX D: RUN ORDER OF SO LAR CELL SPECIMENS OVER THE BROADBAND RANGE OF 1200-1450 HZ Table 8. Run order of specimens over the broadband range of 1200-1450 Hz. Specimen Number Run Order 13 5 14 4 15 12 16 8 17 6 18 10 19 3 20 1 21 11 22 7 23 9 24 2

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51 APPENDIX E: FREQUENCY RESP ONSE PLOTS OF SOLAR CELL SPECIMENS OVER THE BRO ADBAND RANGE OF 400-1800 HZ 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -500 0 Phase (deg)Frequency (Hz) Figure 35. Frequency response plot of solar cell 13 over the broadband range of 1200-1450 Hz. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 36. Frequency response plot of solar cell 14 over the broadband range of 1200-1450 Hz.

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52 APPENDIX E (Continued) 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 37. Frequency response plot of solar cell 15 over the broadband range of 1200-1450 Hz. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 38. Frequency response plot of solar cell 16 over the broadband range of 1200-1450 Hz.

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53 APPENDIX E (Continued) 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 39. Frequency response plot of solar cell 17 over the broadband range of 1200-1450 Hz. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 40. Frequency response plot of solar cell 18 over the broadband range of 1200-1450 Hz.

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54 APPENDIX E (Continued) 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 41. Frequency response plot of solar cell 19 over the broadband range of 1200-1450 Hz. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 42. Frequency response plot of solar cell 20 over the broadband range of 1200-1450 Hz.

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55 APPENDIX E (Continued) 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 43. Frequency response plot of solar cell 21 over the broadband range of 1200-1450 Hz. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 44. Frequency response plot of solar cell 22 over the broadband range of 1200-1450 Hz.

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56 APPENDIX E (Continued) 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -200 0 200 Phase (deg)Frequency (Hz) Figure 45. Frequency response plot of solar cell 23 over the broadband range of 1200-1450 Hz. 400 600 800 1000 1200 1400 1600 1800 0 0.5 1 Coherence 400 600 800 1000 1200 1400 1600 1800 0 5 10 Magnitude (dB/g) 400 600 800 1000 1200 1400 1600 1800 -600 -300 0 Phase (deg)Frequency (Hz) Figure 46. Frequency response plot of solar cell 24 over the broadband range of 1200-1450 Hz.

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57 APPENDIX F: RANDOMIZATION AND RUN ORDER OF SOLAR CELL SPECIMENS OVER THE NARROWBAND RANGES Table 9. Solar cell specimens w ith associated run number for narrowband range 600-750 Hz. Specimen Experimental Run Number 13 1 2 3 14 4 5 6 15 7 8 9 16 10 11 12 17 13 14 15 18 16 17 18 19 19 20 21 20 22 23 24 21 25 26 27 22 28 29 30 23 31 32 33 24 34 35 36

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58 APPENDIX F (Continued) Table 10. Randomized ordering of specimens for the narrowband range of 600-750 Hz. Experimental Random Number Run Specimen Run Number in Ascending Order Order Number 31 268 1 23 19 285 2 19 5 297 3 14 18 323 4 18 23 466 5 20 12 668 6 16 10 718 7 16 8 746 8 15 13 796 9 17 32 820 10 23 7 829 11 15 16 885 12 18 11 1016 13 16 15 1063 14 17 2 1075 15 13 24 1102 16 20 17 1125 17 18 29 1161 18 22 35 1171 19 24 3 1257 20 13 1 1273 21 13 9 1299 22 15 6 1348 23 14 26 1372 24 21 33 1409 25 23 27 1418 26 21 21 1449 27 19 34 1502 28 24 14 1531 29 17 36 1644 30 24 25 1649 31 21 20 1670 32 19 28 1708 33 22

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59 APPENDIX F (Continued) Table 10. (Continued) Experimental Random Number Run Specimen Run Number in Ascending Order Order Number 4 1826 34 14 22 1898 35 20 30 1903 36 22 Table 11. Randomized ordering of speci mens for the narrowband range of 1200-1450 Hz. Experimental Random Number Run Specimen Run Number in Ascending Order Order Number 10 1 1 16 36 202 2 24 32 418 3 23 31 455 4 23 20 471 5 19 25 475 6 21 19 649 7 19 7 1016 8 15 29 1023 9 22 21 1115 10 19 30 1193 11 22 26 1321 12 21 24 1412 13 20 2 1416 14 13 12 1711 15 16 28 1722 16 22 34 1796 17 24 15 2180 18 17 18 2228 19 18 16 2395 20 18 5 2508 21 14 17 2734 22 18 11 3122 23 16 27 3572 24 21 8 3663 25 15

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60 APPENDIX F (Continued) Table 11. (Continued) Experimental Random Number Run Specimen Run Number in Ascending Order Order Number 9 3743 26 15 4 3805 27 14 3 3822 28 13 1 4199 29 13 13 4213 30 17 23 4979 31 20 14 5260 32 17 35 5525 33 24 22 5713 34 20 33 5743 35 23 6 5984 36 14

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61 APPENDIX G: FREQUENCY RESP ONSE PLOTS OF SOLAR CELL SPECIMENS OVER THE NARROW BAND RANGE OF 600-750 HZ 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 47. Frequency response pl ot of solar cell specimen 13 over the narrowband range of 600-750 Hz; experimental run number 1. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 48. Frequency response pl ot of solar cell specimen 13 over the narrowband range of 600-750 Hz; experimental run number 2.

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62 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 49. Frequency response pl ot of solar cell specimen 13 over the narrowband range of 600-750 Hz; experimental run number 3. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 50. Frequency response pl ot of solar cell specimen 14 over the narrowband range of 600-750 Hz; experimental run number 4.

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63 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 51. Frequency response plot of solar cell specimen 14 over the narrowband range of 600-750 Hz; experimental run number 5. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 52. Frequency response plot of solar cell specimen 14 over the narrowband range of 600-750 Hz; experimental run number 6.

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64 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 53. Frequency response pl ot of solar cell specimen 15 over the narrowband range of 600-750 Hz; experimental run number 7. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 54. Frequency response pl ot of solar cell specimen 15 over the narrowband range of 600-750 Hz; experimental run number 8.

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65 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 55. Frequency response pl ot of solar cell specimen 15 over the narrowband range of 600-750 Hz; experimental run number 9. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 56. Frequency response pl ot of solar cell specimen 16 over the narrowband range of 600-750 Hz; experimental run number 10.

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66 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 57. Frequency response pl ot of solar cell specimen 16 over the narrowband range of 600-750 Hz; experimental run number 11. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 58. Frequency response pl ot of solar cell specimen 16 over the narrowband range of 600-750 Hz; experimental run number 12.

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67 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 59. Frequency response pl ot of solar cell specimen 17 over the narrowband range of 600-750 Hz; experimental run number 13. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 60. Frequency response pl ot of solar cell specimen 17 over the narrowband range of 600-750 Hz; experimental run number 14.

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68 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 61. Frequency response pl ot of solar cell specimen 17 over the narrowband range of 600-750 Hz; experimental run number 15. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 62. Frequency response pl ot of solar cell specimen 18 over the narrowband range of 600-750 Hz; experimental run number 16.

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69 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 63. Frequency response pl ot of solar cell specimen 18 over the narrowband range of 600-750 Hz; experimental run number 17. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 64. Frequency response pl ot of solar cell specimen 18 over the narrowband range of 600-750 Hz; experimental run number 18.

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70 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 65. Frequency response pl ot of solar cell specimen 19 over the narrowband range of 600-750 Hz; experimental run number 19. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 66. Frequency response pl ot of solar cell specimen 19 over the narrowband range of 600-750 Hz; experimental run number 20.

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71 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 67. Frequency response pl ot of solar cell specimen 19 over the narrowband range of 600-750 Hz; experimental run number 21. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 68. Frequency response pl ot of solar cell specimen 20 over the narrowband range of 600-750 Hz; experimental run number 22.

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72 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 69. Frequency response pl ot of solar cell specimen 20 over the narrowband range of 600-750 Hz; experimental run number 23. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 70. Frequency response pl ot of solar cell specimen 20 over the narrowband range of 600-750 Hz; experimental run number 24.

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73 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 71. Frequency response pl ot of solar cell specimen 21 over the narrowband range of 600-750 Hz; experimental run number 25. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 72. Frequency response pl ot of solar cell specimen 21 over the narrowband range of 600-750 Hz; experimental run number 26.

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74 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 73. Frequency response pl ot of solar cell specimen 21 over the narrowband range of 600-750 Hz; experimental run number 27. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 74. Frequency response pl ot of solar cell specimen 22 over the narrowband range of 600-750 Hz; experimental run number 28.

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75 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 75. Frequency response pl ot of solar cell specimen 22 over the narrowband range of 600-750 Hz; experimental run number 29. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 76. Frequency response pl ot of solar cell specimen 22 over the narrowband range of 600-750 Hz; experimental run number 30.

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76 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 77. Frequency response pl ot of solar cell specimen 23 over the narrowband range of 600-750 Hz; experimental run number 31. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 78. Frequency response pl ot of solar cell specimen 23 over the narrowband range of 600-750 Hz; experimental run number 32.

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77 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 79. Frequency response pl ot of solar cell specimen 23 over the narrowband range of 600-750 Hz; experimental run number 33. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 80. Frequency response pl ot of solar cell specimen 24 over the narrowband range of 600-750 Hz; experimental run number 34.

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78 APPENDIX G (Continued) 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 81. Frequency response pl ot of solar cell specimen 24 over the narrowband range of 600-750 Hz; experimental run number 35. 600 650 700 750 0 0.5 1 Coherence 600 650 700 750 0 5 Magnitude (dB/g) 600 650 700 750 -200 0 200 Phase (deg)Frequency (Hz) Figure 82. Frequency response pl ot of solar cell specimen 24 over the narrowband range of 600-750 Hz; experimental run number 36.

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79 APPENDIX H: FREQUENCY RESP ONSE PLOTS OF SOLAR CELL SPECIMENS OVER THE NARROW BAND RANGE OF 1200-1450 HZ 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 83. Frequency response pl ot of solar cell specimen 13 over the narrowband range of 1200-1450 Hz; experimental run number 1. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 84. Frequency response pl ot of solar cell specimen 13 over the narrowband range of 1200-1450 Hz; experimental run number 2.

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80 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 85. Frequency response pl ot of solar cell specimen 13 over the narrowband range of 1200-1450 Hz; experimental run number 3. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 86. Frequency response pl ot of solar cell specimen 14 over the narrowband range of 1200-1450 Hz; experimental run number 4.

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81 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 87. Frequency response pl ot of solar cell specimen 14 over the narrowband range of 1200-1450 Hz; experimental run number 5. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 88. Frequency response pl ot of solar cell specimen 14 over the narrowband range of 1200-1450 Hz; experimental run number 6.

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82 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 89. Frequency response pl ot of solar cell specimen 15 over the narrowband range of 1200-1450 Hz; experimental run number 7. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 90. Frequency response pl ot of solar cell specimen 15 over the narrowband range of 1200-1450 Hz; experimental run number 8.

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83 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 91. Frequency response pl ot of solar cell specimen 15 over the narrowband range of 1200-1450 Hz; experimental run number 9. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 92. Frequency response pl ot of solar cell specimen 16 over the narrowband range of 1200-1450 Hz; experimental run number 10.

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84 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 93. Frequency response pl ot of solar cell specimen 16 over the narrowband range of 1200-1450 Hz; experimental run number 11. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 94. Frequency response pl ot of solar cell specimen 16 over the narrowband range of 1200-1450 Hz; experimental run number 12.

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85 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 95. Frequency response pl ot of solar cell specimen 17 over the narrowband range of 1200-1450 Hz; experimental run number 13. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 96. Frequency response pl ot of solar cell specimen 17 over the narrow-band range of 1200-1450 Hz; experimental run number 14.

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86 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 97. Frequency response pl ot of solar cell specimen 17 over the narrowband range of 1200-1450 Hz; experimental run number 15. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 98. Frequency response pl ot of solar cell specimen 18 over the narrowband range of 1200-1450 Hz; experimental run number 16.

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87 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 99. Frequency response pl ot of solar cell specimen 18 over the narrowband range of 1200-1450 Hz; experimental run number 17. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 100. Frequency response pl ot of solar cell specimen 18 over the narrowband range of 1200-1450 Hz; experimental run number 18.

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88 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 101. Frequency response pl ot of solar cell specimen 19 over the narrowband range of 1200-1450 Hz; experimental run number 19. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 102. Frequency response pl ot of solar cell specimen 19 over the narrowband range of 1200-1450 Hz; experimental run number 20.

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89 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 103. Frequency response pl ot of solar cell specimen 19 over the narrowband range of 1200-1450 Hz; experimental run number 21. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 104. Frequency response pl ot of solar cell specimen 20 over the narrowband range of 1200-1450 Hz; experimental run number 22.

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90 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 105. Frequency response pl ot of solar cell specimen 20 over the narrowband range of 1200-1450 Hz; experimental run number 23. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 106. Frequency response pl ot of solar cell specimen 20 over the narrowband range of 1200-1450 Hz; experimental run number 24.

PAGE 105

91 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 107. Frequency response pl ot of solar cell specimen 21 over the narrowband range of 1200-1450 Hz; experimental run number 25. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 108. Frequency response pl ot of solar cell specimen 21 over the narrowband range of 1200-1450 Hz; experimental run number 26.

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92 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 109. Frequency response pl ot of solar cell specimen 21 over the narrowband range of 1200-1450 Hz; experimental run number 27. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 110. Frequency response pl ot of solar cell specimen 22 over the narrowband range of 1200-1450 Hz; experimental run number 28.

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93 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 111. Frequency response pl ot of solar cell specimen 22 over the narrowband range of 1200-1450 Hz; experimental run number 29. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 112. Frequency response pl ot of solar cell specimen 22 over the narrowband range of 1200-1450 Hz; experimental run number 30.

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94 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 113. Frequency response pl ot of solar cell specimen 23 over the narrowband range of 1200-1450 Hz; experimental run number 31. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 114. Frequency response pl ot of solar cell specimen 23 over the narrowband range of 1200-1450 Hz; experimental run number 32.

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95 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 115. Frequency response pl ot of solar cell specimen 23 over the narrowband range of 1200-1450 Hz; experimental run number 33. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 116. Frequency response pl ot of solar cell specimen 24 over the narrowband range of 1200-1450 Hz; experimental run number 34.

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96 APPENDIX H (Continued) 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 117. Frequency response pl ot of solar cell specimen 24 over the narrowband range of 1200-1450 Hz; experimental run number 35. 1200 1250 1300 1350 1400 1450 0 0.5 1 Coherence 1200 1250 1300 1350 1400 1450 0 5 Magnitude (dB/g) 1200 1250 1300 1350 1400 1450 -200 -100 0 Phase (deg)Frequency (Hz) Figure 118. Frequency response pl ot of solar cell specimen 24 over the narrowband range of 1200-1450 Hz; experimental run number 36.