COMSOL Multiphysics Software and Photovoltaics: A Unified Platform for Numerical Simulation of Solar Cells and Modules
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1 COMSOL Multiphysics Software and Photovoltaics: A Unified Platform for Numerical Simulation of Solar Cells and Modules Marco Nardone, Ph.D. Bowling Green State University Bowling Green, Ohio 1
2 Photovoltaics (PV) 2
3 Outline Fundamental Equations Key Outputs Advantages of using COMSOL Multiphysics Challenges, Tips, and Tricks 3
4 National Renewable Energy Lab 4
5 Fundamental Equations Semiconductor Physics εε ss φφ = ρρ nn tt = 1 qq JJ nn UU nn + GG nn pp tt = 1 qq JJ pp UU pp + GG pp ρρ = qq nn pp + NN AA NN DD JJ nn = qqμμ nn nn φφ + qqdd nn nn JJ pp = qqμμ pp nn φφ qqdd nn pp Dependent Variables: φ electrostatic potential n electron concentration p hole concentration 5
6 Fundamental Equations Optical Physics EE kk 0 2 εε rr EE = 0 E used to calculate power dissipation, Q Photo-generation rate given by: G = QQQQ hλλ λ = 600 nm 6
7 Fundamental Equations Optical Physics Solar Spectrum 7
8 Key Outputs Current-Voltage Characteristics (Voltage Sweep) Independent Variables 1. Light Intensity 2. Temperature 3. Voltage Bias Key Metrics 1. Efficiency 2. Open-circuit voltage 3. Short-circuit current 4. Fill factor 8
9 Key Outputs Quantum Efficiency (Light Frequency Sweep) Quantum Efficiency: 1. Efficiency of converting photons to electrons 2. Depends on light wavelength 9
10 Key Outputs Capacitance-Voltage Characteristics (Voltage Sweep Small Signal Analysis) Capacitance-Voltage: 1. Provides information on charge distribution 10
11 Unified Platform: COMSOL Multiphysics Optical (Electrodynamics) Ion Transport (reaction-diffusion) Semiconductor Thermal Customized Physics, Defect Kinetics, others Multi-physics Multi-dimensional 2D, 3D, time-dependent capabilities Multi-scale Micro-diodes to modules Customizable equations LiveLink with MatLab 11
12 Multi-dimensional 2D and 3D design features S. Jeong, M. D. McGehee, Y. Cui, Nat. Comm. 4, 2950 (2013). Z. Fan et. al. Nature Materials 8, (2009) 12
13 Multi-dimensional Grain Boundary Effects d gb /2 SnO2 CdS CdTe (N a, N t ) Grain Boundary (S gb, N gb ) Variable N a (1/cm 3 ) N t (1/cm 3 ) N gb (1/cm 2 ) S gb (cm/s) d gb (µm) Definition Bulk/grain acceptor doping concentration Bulk/grain deep gap state concentration Grain boundary surface charge density (+/-) Grain boundary surface recombination velocity Grain boundary diameter 13
14 Multi-physics Ion Migration = DDDDDD ccccee + RR Electric Field (V/cm) CdS Ion Concentration (norm.) CdTe 1-x S x CdTe 14
15 Time Dependence and Custom Physics Studying Device Degradation Degradation Physics Defect concentrations vary with time: NN tt tt = αααα NN tt ββnn tt Nardone, M., & Albin, D. S. (2015). Degradation of CdTe Solar Cells: Simulation and Experiment. Photovoltaics, IEEE Journal of, 5(3),
16 Multi-Scale Modeling Micron-Scale to Product-Scale Simulation Micron Scale Centimeter/Meter Scale 16
17 Challenges, Tips, and Tricks Ramp up dopant and defect concentrations Solve equilibrium problem first with segregated solver Sometimes helps to use coarse mesh first, then refine Ramp up light intensity Solar spectrum split into 54 chunks 17
18 COMSOL Multiphysics Software and Photovoltaics: A Unified Platform for Numerical Simulation of Solar Cells and Modules Marco Nardone, Ph.D. Bowling Green State University Bowling Green, Ohio 18
19 Bonus Slides 19
20 Semiconductor Parameters Device SnO2/CdS/CdTe baseline 1 Front CONTACTS Back φ b [ev] φ bn = 0.1 φ bp = 0.4 Se [cm/s] 1.00E E+07 Sh [cm/s] 1.00E E+07 Reflectivity Rf LAYERS SnO2 CdS CdTe W [nm] ε/ε µe [cm2/v/s] µh [cm2/v/s] NA [cm-3] E+14 ND [cm-3] 1.00E E+18 0 Eg [ev] NC [cm-3] 2.20E E E+17 NV [cm-3] 1.80E E E+19 χ [ev] Ec [ev] Ev [ev] DEFECTS (Gaussian) N DG [cm-3] 1.00E E E+14 N AG [cm-3] E+18 0 EA mid-gap ED mid-gap mid-gap WG [ev] σ e [cm2] 1.00E E E-12 σ h [cm2] 1.00E E E-15 20
21 Cell and Module Modeling σ = jj dd Cell Equivalent Circuit Monolithic Module Model j is the current from micro-diode model j 0 is the current from micro-diode model j 2 = -V 2 /(h d R TCO ), ohmic current j 1 =j 3 =0 21
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