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

TL;DR

This paper introduces a high-order, stable numerical scheme for simulating advanced solar cells, accurately capturing complex charge, exciton, and ion dynamics with verified convergence and real-device validation.

Contribution

It develops a novel high-order time-stepping method combined with structure-preserving spatial discretization for comprehensive solar cell modeling.

Findings

Achieves second-order spatial and fifth-order temporal convergence.

Accurately models exciton kinetics and ion migration in solar cells.

Reproduces J–V hysteresis without empirical parameters.

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.