Numerical Modeling of Photovoltaic Applications

1. Numerical Modeling of Photovoltaic Applications Assis. Prof. Antonis Papadakis

2. OUTLINE OF PRESENTATION • INTRODUCTION • MODEL DESCRIPTION • TRANSPORT PROPERTIES • CONCLUSIONS • FUTURE WORK

3. MODEL DESCRIPTION Characterisation of thin film photovoltaics by solving : • Poisson equation for the electric field • Continuity equations of charged particles: (electrons, holes) Coordinates : • 2D Cylindrical Axisymmetric • 2D Cartesian Initial Conditions: • Photovoltaic cell dimensions • Doping electron and hole densities • Material Temperature • Conformal Finite Element Mesh

4. MODEL DESCRIPTION Poisson’s Equation : Continuity Equations : Poisson and Continuity model are coupled via Ne, Nh

5. MODEL DESCRIPTION Constitutive Equations : Electric Field Electron Velocity Hole Velocity Simulation Limitations Debye Length Dielectric Relaxation

6. MODEL DESCRIPTION n TR n n r E n+1/2 n+1 r r n+1/2 n+1/2 E TR Solution Procedure Start of Time Step PO TP CON CON TP PO End of Time Step

7. TRANSPORT PROPERTIES Transport Properties of electrons and holes: • Mobilities • Velocities • Diffusion • Generation/Recombination Generation and Recombination Processes: • Auger generation and recombination or three particle transitions • Photon transition or optical generation and recombination • Impact ionization • Phonon transition or Shockley-Read-Hall generation and recombination

8. AUGER RECOMBINATION E Before After Before After - - - - Ec Dependency on Carrier Density Ev + - + + + + - + Auger Recombination Electron Capture Auger Recombination Hole Capture

9. AUGER GENERATION Before After Before After E - - - - Ec Dependency on Carrier Density Ev + + - + - + + + Auger Generation Electron Emission Auger Generation Hole Emission

10. IMPACT IONIZATION Before After Before After E - - - - Ec Dependency on Current Density and Temperature Ev + + - + - + + + Impact Ionization Electron Emission Impact Ionization Hole Emission

11. PHONON TRANSITION-RECOMBINATION Before After Before After E - Ec - - Ev + + - Phonon Transition Electron Capture Phonon Transition Hole Capture

12. PHONON TRANSITION-GENERATION Before After Before After E - Ec - - Ev + + - Phonon Transition Electron Emission Phonon Transition Hole Emission

13. PHOTON TRANSITION Before After Before After E - - Ec Ev + + - + + - Photon Recombination Photon Generation

14. GENERATION/RECOMBINATION FORMULAS Impact Ionization: Auger Recombination: Band to Band Recombination: Bulk Recombination Model: Free Carrier Absorption:

15. Electron Mobility Fig. 1. Electron mobility with respect to the donor density at a temperature of 300 K for silicon.

16. Hole Mobility Fig. 2. Hole mobility versus the acceptor density at a temperature of 300 K for silicon.

17. Electron Diffusion Fig. 3. Electron diffusion coefficient as a function of the electric field at a temperature of 300 K in silicon.

18. Hole Diffusion Fig. 4. Hole diffusion coefficient against the electric field at a temperature of 300 K in silicon.

19. Intrinsic Absorption Coefficient Fig. 5. Intrinsic absorption coefficient as a function of temperature in silicon.

20. CONCLUSIONS/FUTURE WORK • CONCLUSIONS: • Differential equations identified • Mathematical model formulation identified • Transport parameters are readily available for silicon • FUTURE WORK: • Perform thin film silicon simulations • Compare with commercial software PC1D • To simulate heating effects by solving conservation of mass, • momentum and energy for solids • Exploit adaptive mesh techniques • Expand the model in 3-Dimensions Streamer Propagation Across Gap