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

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.

Figures (12)

• Figure 1: Schematic of the one-dimensional sandwich-type solar-cell structure considered in this work. The device consists of an electron-transport layer (ETL), an absorber layer (perovskite or organic), and a hole-transport layer (HTL), sandwiched between left (Cathode) and right (Anode) contacts. Material parameters, generation profiles, and boundary conditions can be specified independently in each subregion.
• Figure 2: A schematic of Spatial Discretization.
• Figure 3: Schematic of LE--CT--CS state kinetics.
• Figure 4: $L^2$ error versus mesh size $h$ for $P$ (blue), $\phi$ (orange), $n$ (green), and $p$ (red), with $\mathcal{O}(h^2)$ reference line (black).
• Figure 5: $L^2$ error versus effective time stepsize $\Delta t$ for $P$ (blue), $\phi$ (orange), $n$ (green), and $p$ (red), with $\mathcal{O}(t^5)$ reference line (black).