Modelling and Optimising Gaas/Al (X) Ga (1-X) As Multiple Quantum Well
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University of London Imperial College of Science, Technology and Medicine Department of Physics Modelling and Optimising GaAs/AlxGa1 xAs − Multiple Quantum Well Solar Cells James P. Connolly arXiv:1006.1053v1 [cond-mat.mes-hall] 5 Jun 2010 Submitted in part fulfilment of the requirements for the degree of Doctor of Philosophy in Science of the University of London and the Diploma of Imperial College, January 1997 2 Abstract The quantum well solar cell (QWSC) is a p - i - n solar cell with quantum wells in the intrinsic region. Previous work has shown that QWSCs have a greater open circuit voltage (Voc) than would be provided by a cell with the quantum well effective bandgap. This suggests that the fundamental efficiency limits of QWSCs are greater than those of single bandgap solar cells. The following work investigates QWSCs in the GaAs/AlxGa1−xAs materials system. The design and optimisation of a QWSC in this system requires studies of the voltage and current dependencies on the aluminium fraction. QWSCs with different aluminium fractions have been studied and show an increasing Voc with increasing barrier aluminium composition. The QE however decreases with increasing aluminium composition. We de- velop a model of the QE to test novel QWSC designs with a view to minimising this problem. This work concentrates on two design changes. The first deals with com- positionally graded structures in which the bandgap varies with position. This bandgap variation introduces an quasi electric field which can be used to increase minority carrier collection in the low efficiency p and n layers. This technique also increases the light flux reaching the highly efficient depletion regions. The second design change consists of coating the back of the cell with a mirror to exploit the portion of light which is not absorbed on the first pass. A model of the QE of compositionally graded QWSC solar cells with back surface mirrors is developed in order to analyse the effect of these design changes. These changes are implemented separately in a number of QWSC designs and the resulting experimental data compared with the model. An optimised design is then presented. 3 Acknowledgements The work in this thesis would not have happened without the support of a multitude of people. Keith Barnham has been a tireless source of encouragement and ideas over the years. Endless thanks to Jenny Nelson for always knowing what was wrong with models, for her encyclopaedic knowledge, and being there to recommend films, or have them recommended. Then there are all those who have passed through here, or are still here, including Jenny Barnes, Ian Ballard, Alex Zachariou, Paul Griffin, Ernest Tsui and Ned. Next come the people who actually produced the solar cells in this thesis. Christine Roberts was always ready to answer constant questions about MBE machines and AlGaAs. John Roberts’ produced the grade which worked first time, and was full of suggestions for new material tests. Malcolm Pate produced innumerable devices over the years, including the wafer squashed by the Royal Mail. Then there are collaborators overseas. Antonio Marti Vega helped me take some measurements which can’t be fitted in. Two hundred pages is quite enough! And Rosa Maria Fernandez Reyna in Madrid, who explained them to me and showed me around Madrid, including some very nice cafes and cinemas. Enrique Gr¨unbaum took TEM measurements which helped explain one of the more mystifying samples in this project, along with SIMS measurements by Federico Caccavale. The latter were enabled by Massimo Mazzer who arranged the SIMS measurements in Padua, and always had ideas for everything, including jazz concerts. And thanks to all the people who have made daily life about the department more interesting, such as Jean Leveratt for chats on level 8 at lunchtimes and solutions to all sorts of problems, Lydia, also of Level 8, and Betty Moynihan for help with the technicalities of writing up on level 3. As for finance, I thank the Greenpeace Trust who made the project possible, and who enabled me to go to the Solar World Congress. Finally, there all the people I have known, or got to know over the years. 4 There are those who are overseas - Chris and Olenka, Marc and Malar and the Smiths, Claire and the Granjon Clan. All the Tuckmans and associates in North London apart from Jo in Guatemala, Kerry and Alberta, Karen in the East, (big) Phil, (other) Phil, Hiroe, Bruce who used to be in the West, Paul and Catherine in the centre, Vince in Cambridge, the Marchants (Pete and Jo) and Kul. Then theres Tanveer (I won, I think?), Tristan, Dorothy, Dave, Wing, thanks for the coffee Steve, and Rosa in Madrid. Thanks to everyone ... ! Finally, thanks to the family: Jim, Eva, Marie Pascal, Anne Catherine, Jeanne Chantal, Isabel and Oona for the support over the years, and for coming over now and then to visit. This thesis is dedicated to my parents. Contents 1 Introduction 17 1.1 CurrentEnergyUseandAlternatives . 17 1.2 ReducingtheCostofPhotovoltaicPower . 18 1.3 IntroductiontotheOptimisationProgram . 19 2 Introduction to Solar Cells 21 2.1 Physics of Solar Cells . 21 2.1.1 Intrinsic Semiconductors in Equilibrium . 22 2.1.2 DopedSemiconductors . 24 2.2 ThePhotovoltaicEffect ....................... 26 2.2.1 Light Absorption and Pair Generation . 27 2.2.2 ChargeSeparation ...................... 29 2.2.3 Current-Voltage Characteristic of a p-n Junction in the Dark 32 2.2.4 The p-n Junction in the Light . 35 2.3 Thep-i-nSolarCell.......................... 37 2.3.1 Space Charge Region of a p-i-n Diode . 37 2.3.2 The Background Doping Problem in p-i-n Structures . 40 2.4 Limiting Efficiency of Solar Cells . 42 2.4.1 Higher Efficiency Designs . 44 2.5 Quantum Well Solar Cells . 45 2.6 TheQWSCintheAlGaAsSystem . 46 2.7 Conclusions .............................. 48 5 Contents 6 3 Quantum efficiency and short circuit current models 49 3.1 Introduction.............................. 49 3.1.1 ReviewofPreviousWork. 49 3.2 Preliminary definitions . 51 3.3 Calculation of light intensity in a QSWC . 52 3.3.1 Definitions........................... 52 3.3.2 Phaseandreflectance. 55 3.3.3 GenerationRate ....................... 55 3.4 Photocurrent ............................. 57 3.5 Intrinsicregionphotocurrent. 58 3.6 pandnRegionContributions . 59 3.6.1 Drift and Diffusion Currents . 59 3.6.2 CurrentandContinuity . 60 3.6.3 TransportEquationsfornLayers . 61 3.6.4 General Analytical Solution . 62 3.6.5 BoundaryConditions .................... 63 3.7 ConstantTransportParameters . 64 3.7.1 ZeroField........................... 64 3.7.2 Non Zero Effective Fields . 65 3.8 GradedQWSCsandNumericalSolutions . 67 3.8.1 Surface Boundary Condition in Compositionally Graded Cells.............................. 68 3.8.2 NumericalAccuracy .. .. 68 3.8.3 Comparisons of Analytical and Numerical Solutions . 70 3.9 Conclusion............................... 72 4 Model Parameters and Program Design 74 4.1 Programdesign ............................ 74 4.2 DesignandGrowthParameters . 76 4.3 OpticalParameters .......................... 78 4.3.1 IncidentFlux ......................... 78 Contents 7 4.3.2 AbsorptionCoefficient . 78 4.3.3 Reflectivity .......................... 79 4.3.4 Refractiveindex........................ 80 4.4 Transportparameters. 80 4.4.1 Band gap Parametrisations and the Quasi-Electric Field . 81 4.4.2 Minority carrier lifetime . 82 4.4.3 Mobility and Diffusion Coefficient . 83 4.4.4 Diffusion length . 83 4.4.5 Recombination velocity . 84 4.4.6 Discussion........................... 86 5 QE Modelling and Optimisation 87 5.1 UngradedCells ............................ 88 5.1.1 PreviousWork ........................ 88 5.2 Further QE Enhancements Above the Barrier Bandgap . 92 5.2.1 Light Absorption and Minority Carrier Generation . 92 5.2.2 Minority Carrier Transport . 98 5.2.3 Minority Carrier Concentration . 103 5.2.4 QEandShortCircuitCurrent . 107 5.2.5 Windows............................ 110 5.3 Further QE Enhancement Below the Barrier Bandgap . 112 5.3.1 Generation, Flux and QE in Mirrored Cells . 115 5.4 Conclusions .............................. 122 6 Device fabrication and characterisation 123 6.1 SampleGrowth ............................ 123 6.1.1 Metalorganic Vapour Phase Epitaxy (MOVPE) . 123 6.1.2 Molecular Beam Epitaxy (MBE) . 124 6.2 Processing............................... 125 6.2.1 DeviceGeometry ....................... 126 6.2.2 MirrorBackedDevices . 127 6.2.3 EffectsofProcessing . 127 Contents 8 6.3 Characterisation............................ 128 6.3.1 Photoconductivity Experiment . 128 6.3.2 Monochromatic current-voltage characteristics . 129 6.3.3 Quantum efficiency measurements . 132 6.3.4 Reflectivitymeasurement. 132 6.3.5 Externalcharacterisation. 133 6.4 Conclusion............................... 134 7 Preliminary Characterisation 136 7.1 MonochromaticIVMeasurements . 136 7.1.1 TrendsinQWSCandp-i-nDeviceMIVData. 138 7.1.2 Growth Optimisation Studies . 144 7.1.3 Passivationeffects. 146 7.1.4 Conclusions .......................... 149 7.1.5 ReflectivityMeasurements . 150 7.1.6 Conclusions .......................... 152 8 Experimental and Modelled QE Spectra 154 8.1 Principles of Data Fitting . 154 8.1.1 Samplegeometry ....................... 155 8.1.2 Samples with efficient minority carrier transport . 155 8.1.3 Samples with simplified modelling . 156 8.1.4 Samples with high surface recombination parameters . 157 8.1.5 Gradedsamples........................ 158 8.1.6 Modelling of the quantum well QE ............. 160 8.1.7 Mirrorbackedsamples . 160 8.2 GradediRegionSamples.