Derivation of a quasi-linear second-order elliptic-parabolic model for the efficiency of silicon solar cells

In this note, we propose a mathematical model for the efficiency of a silicon solar cell. The model is rigorously derived from continuity and transport assumptions, along with the Poisson equations to describe the behavior of charge carriers in a semiconductor. The photovoltaic phenomenon was thoroughly studied to develop the model, and some parameters that play a crucial role in its efficiency have been identified. Those parameters include the diffusion, the mobility and the absorption coefficients, the permittivity, the regions width and the minority carrier lifetime. The mathematical model obtained herein is a quasi-linear second-order elliptic-parabolic partial differential equation system with strong coupling and interface. The model is defined over a spatial domain composed of three regions with different electrical properties. The fundamental physical laws of the photovoltaic effect are employed here to develop the mathematical model and its boundary conditions.