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Solar Cell Temperature Dependent Efficiency and Very High Temperature Efficiency Limits John Robert Wilcox Purdue University

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Solar Cell Temperature Dependent Efficiency and Very High Temperature Efficiency Limits John Robert Wilcox Purdue University Purdue University Purdue e-Pubs Open Access Dissertations Theses and Dissertations Fall 2013 Solar Cell Temperature Dependent Efficiency and Very High Temperature Efficiency Limits John Robert Wilcox Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_dissertations Part of the Electrical and Electronics Commons, Nanoscience and Nanotechnology Commons, and the Oil, Gas, and Energy Commons Recommended Citation Wilcox, John Robert, "Solar Cell Temperature Dependent Efficiency and Very High Temperature Efficiency Limits" (2013). Open Access Dissertations. 19. https://docs.lib.purdue.edu/open_access_dissertations/19 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. SOLAR CELL TEMPERATURE DEPENDENT EFFICIENCY AND VERY HIGH TEMPERATURE EFFICIENCY LIMITS A Dissertation Submitted to the Faculty of Purdue University by John R. Wilcox In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2013 Purdue University West Lafayette, Indiana ii To my loving wife Amy T. Wilcox and wonderful family. Many wonderful educators and friends that have inspired me. This great country. iii ACKNOWLEDGMENTS I would like to thank Professors Jeffery Gray and Richard Schwartz for their excellent guidance and instruction. They have been wonderful mentors. I would also like to thank Professors Mark Lundstrom, Ashraf Alam and Rakesh Agrawal for serving on my thesis committee, and Dr. Alex Haas, for his collaboration and research. Many thanks to Dr. Allen Gray, Dr. Myles Steiner, Dr. Mark Osowski, Dr. James McCambridge and JP Whitlock, their feedback and measurements have been invaluable. I appreciate the superb learning opportunities available at Purdue University. This work was supported the by the Very High Efficiency Solar Cell project, Advanced Research Projects Agency-Energy and Semiconductor Research Corporation through the Network for Photovoltaic Technology. Facilities and computer resources have been provided by Purdue’s Birck Nanotechnology Center, Network for Computational Nanotechnology, Engineering Computer Network and the School of Electrical and Computer Engineering . iv TABLE OF CONTENTS Page LIST OF TABLES .............................................................................................................. x LIST OF FIGURES .......................................................................................................... xii LIST OF SYMBOLS ..................................................................................................... xxiii NOMENCLATURE ...................................................................................................... xxxi ABSTRACT ................................................................................................................. xxxiv 1. INTRODUCTION ........................................................................................................ 1 1.1 The Value of Solar Energy ................................................................................... 1 1.2 Reducing the Cost of Solar Energy ...................................................................... 2 1.2.1 Solar Cell Research .................................................................................. 2 1.2.2 Solar Cell Modeling ................................................................................. 3 1.3 Increasing the Value of Solar Energy ................................................................... 4 1.4 Operating Temperature ......................................................................................... 6 1.5 Dissertation Synopsis ........................................................................................... 7 1.5.1 Detailed Balance Limited Very High Temperature Terminal Characteristics .......................................................................................... 9 1.5.2 Recombination Limited Very High Temperature Terminal Characteristics .......................................................................................... 9 1.5.3 Temperature Dependent Resistive Losses .............................................. 10 1.5.4 Temperature Dependent Numerical Model ............................................ 11 2. LITERATURE REVIEW ........................................................................................... 13 2.1 Solar Cell History ............................................................................................... 13 2.2 Solar Cell Fundamentals ..................................................................................... 15 2.3 Modeling Solar Cells .......................................................................................... 16 2.4 Simple Solar Cell Models ................................................................................... 17 2.4.1 Linear Temperature Dependent Curve-fits ............................................. 17 v Page 2.4.2 Ideal Diode With Resistance .................................................................. 18 2.4.3 Two or More Diode Model ..................................................................... 19 2.4.4 Other Temperature Dependent Solar Cell Models ................................. 19 2.4.5 Summary of Analytical Solar Cell Models ............................................ 20 2.5 Detailed Numerical Models of Semiconductor Devices .................................... 21 2.5.1 Detailed Modeling Programs .................................................................. 21 2.5.2 Temperature Dependent Solar Cell Modeling ........................................ 22 2.5.3 Compare Modeled and Measured Temperature Coefficients ................. 24 2.6 Related Work ...................................................................................................... 24 2.6.1 Simulating the Recombination Limited Terminal Characteristics at Very High Temperatures .................................................................... 24 2.6.2 Calculating the Series Resistance and Bias Point Losses ....................... 25 2.6.3 Detailed Numerical Modeling Temperature Dependencies ................... 26 2.7 Uncertainty in Temperature Dependent Measurements ..................................... 27 3. DETAILED BALANCE LIMITED VERY HIGH TEMPERATURE TERMINAL CHARACTERISTICS .......................................................................... 29 3.1 Terminal Characteristics ..................................................................................... 30 3.1.1 Temperature Dependent Terminal Characteristics ................................. 31 3.1.2 Temperature Dependent Terminal J-V Relationship .............................. 33 3.1.3 Bandgap Energy ..................................................................................... 34 3.1.4 Short Circuit Current .............................................................................. 38 3.1.5 Recombination Current Density ............................................................. 44 3.1.6 Open Circuit Voltage .............................................................................. 49 3.1.7 Fill Factor ............................................................................................... 54 3.1.8 Conversion Efficiency ............................................................................ 58 3.2 Real Semiconductor Materials ........................................................................... 63 3.2.1 Extrapolating the Temperature Coefficients .......................................... 63 3.2.2 Finding the Optimal Material ................................................................. 67 3.2.3 Improving the Temperature Coefficients ............................................... 70 3.2.4 3-D effects .............................................................................................. 73 3.3 Summary and Conclusions ................................................................................. 74 vi Page 3.3.1 Future Work ............................................................................................ 75 4. RECOMBINATION LIMITED VERY HIGH TEMPERATURE TERMINAL CHARACTERISTICS .......................................................................... 77 4.1 Terminal Characteristics ..................................................................................... 77 4.1.1 Multiple Diode Equation ........................................................................ 78 4.1.2 Recombination Current Density ............................................................. 79 4.1.3 Low-level Injection Limit ....................................................................... 81 4.1.4 High-level Injection Limit ...................................................................... 82 4.1.5 Theoretical Recombination Current Density .......................................... 83 4.2 Semiconductor Material Parameters ................................................................... 86 4.2.1 Intrinsic Carrier Concentration over Bandgap Fit .................................. 87 4.2.2 Recombination Coefficients ................................................................... 92 4.2.3 Shockley Hall Read Recombination ....................................................... 98 4.3 Analytical Simulations ..................................................................................... 102 4.3.1 Bandgap Optimization Over a Range of Temperatures
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