A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells

TL;DR

This paper introduces a fast, accurate, and robust finite difference numerical scheme with adaptive time stepping for solving complex drift-diffusion models of charge and ion transport in perovskite solar cells, addressing stiffness and parameter challenges.

Contribution

The paper presents a novel finite difference scheme with adaptive time stepping on a non-uniform grid that efficiently handles stiffness in perovskite solar cell models.

Findings

Achieves second order accuracy in space

Handles stiffness with modest computational costs

Computes transient current-voltage curves in minutes

Abstract

Drift-diffusion models that account for the motion of both electronic and ionic charges are important tools for explaining the hysteretic behaviour and guiding the development of metal halide perovskite solar cells. Furnishing numerical solutions to such models for realistic operating conditions is challenging owing to the extreme values of some of the parameters. In particular, those characterising (i) the short Debye lengths (giving rise to rapid changes in the solutions across narrow layers), (ii) the relatively large potential differences across devices and (iii) the disparity in timescales between the motion of the electronic and ionic species give rise to significant stiffness. We present a finite difference scheme with an adaptive time step that is posed on a non-uniform staggered grid that provides second order accuracy in the mesh spacing. The method is able to cope with the stiffness of the system for realistic parameters values whilst providing high accuracy and maintaining modest computational costs. For example, a transient sweep of a current-voltage curve can be computed in only a few minutes on a standard desktop computer.