A Stable, High-Order Time-Stepping Scheme for the Drift-Diffusion Model in Modern Solar Cell Simulation

arXiv:2603.09063v1 Announce Type: new
Abstract: This paper presents a one-dimensional transient drift–diffusion simulator for advanced solar cells, integrating a structure-preserving finite-volume spatial discretization with Scharfetter–Gummel–type fluxes and a high-order, L-stable implicit Runge–Kutta (Radau IIA) temporal integrator. The scheme ensures local charge conservation, handles sharp material interfaces, and achieves second-order spatial and fifth-order temporal convergence. Its accuracy is verified against the classical depletion approximation in $p$–$n$ junction and validated through excellent agreement with the established simulator for an organic photovoltaic device. The framework’s extensibility is demonstrated by incorporating exciton kinetics in organic solar cells, capturing multi-timescale dynamics, and by modeling mobile ions in perovskite solar cells, reproducing characteristic $tmem{J}$–$tmem{V}$ hysteresis without empirical parameters. This work provides a robust, high-order numerical foundation for simulating coupled charge, exciton, and ion transport in next-generation photovoltaic devices.