WIAS Preprint No. 1524, (2010)

Analysis of electronic models for solar cells including energy resolved defect densities



Authors

  • Glitzky, Annegret

2010 Mathematics Subject Classification

  • 35K57 35R05 35B45 78A35

Keywords

  • Reaction-diffusion systems, drift-diffusion processes, energy resolved defect densities, motion of charged particles, existence, uniqueness, a priori estimates

DOI

10.20347/WIAS.PREPRINT.1524

Abstract

We introduce an electronic model for solar cells including energy resolved defect densities. The resulting drift-diffusion model corresponds to a generalized van Roosbroeck system with additional source terms coupled with ODEs containing space and energy as parameters for all defect densities. The system has to be considered in heterostructures and with mixed boundary conditions from device simulation. We give a weak formulation of the problem. If the boundary data and the sources are compatible with thermodynamic equilibrium the free energy along solutions decays monotonously. In other cases it may be increasing, but we estimate its growth. We establish boundedness and uniqueness results and prove the existence of a weak solution. This is done by considering a regularized problem, showing its solvability and the boundedness of its solutions independent of the regularization level.

Appeared in

  • Math. Methods Appl. Sci., 34 (2011) pp. 1980--1998.

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