Equivalent circuit modeling of electron-hole recombination in semiconductor and mixed ionic-electronic conductor based devices

TL;DR

This paper develops equivalent circuit models for electron-hole recombination in semiconductors and mixed ionic-electronic conductors, enabling better understanding and optimization of solar and optoelectronic devices through analytical solutions.

Contribution

It introduces a comprehensive circuit model for electron-hole recombination that accounts for local electrostatics, especially in mixed conducting devices like halide perovskite solar cells.

Findings

Simplified models suffice for semiconductors without mobile ions.

Local electrostatics are crucial in mixed conducting devices.

Analytical solutions describe polarization effects and impedance.

Abstract

The understanding and optimization of solar energy conversion and light emitting devices can greatly benefit from equivalent circuit models describing their response. However, a general model of electron-hole recombination in semiconductors is currently missing. This study presents equivalent circuit models of radiative and non-radiative electron-hole recombination based on their linearized analytical treatment. These are integrated in a circuit model of complete devices that is equivalent to the linearized drift-diffusion equations in one dimension. The analysis of the model shows that, for most situations involving semiconductors without mobile ions, approximated models that do not account for local electrostatics are sufficient to describe the contribution of recombination to the device response. The influence of local electrostatics on non-radiative trap-mediated and Auger recombination becomes essential in mixed conducting devices, and it should be included explicitly in equivalent circuit models. Resistors used for traditional semiconductors are indeed a special case of the general model of non-radiative recombination, for which transistors gated by the local change in electrostatic potential implement a more accurate representation. For mixed conducting devices, such as halide perovskite solar cells, appropriate simplifications of the complete model provide analytical solutions describing the bulk and interfacial polarization effects that influence the small signal electrostatics, recombination currents and overall impedance. The resulting analysis is relevant to a wide range of materials and devices used for solar energy conversion as well as other optoelectronic and photo-electrochemical applications.