An electronic model for solar cells including active interfaces and energy resolved defect densities
- Glitzky, Annegret
2010 Mathematics Subject Classification
- 35K57 35R05 35B45 78A35
- Reaction-diffusion systems, drift-diffusion processes, active interfaces, energy resolved defect densities, existence, uniqueness, a priori estimates
We introduce an electronic model for solar cells taking into account heterostructures with active interfaces and energy resolved volume and interface trap densities. The model consists of continuity equations for electrons and holes with thermionic emission transfer conditions at the interface and of ODEs for the trap densities with energy level and spatial position as parameters, where the right hand sides contain generation-recombination as well as ionization reactions. This system is coupled with a Poisson equation for the electrostatic potential. We show the thermodynamic correctness of the model and prove a priori estimates for the solutions to the evolution system. Moreover, existence and uniqueness of weak solutions of the problem are proven. For this purpose we solve a regularized problem and verify bounds of the corresponding solution not depending on the regularization level.
- SIAM J. Math. Anal., 44 (2012) pp. 3874--3900.