  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 shows that, for most situations
involving semiconductors without mobile ions, approximated models that do not
account for local electrostatics are sufficient to describe non-radiative
recombination. The influence of local electrostatics becomes essential in mixed
conducting devices, and it should be included explicitly in equivalent circuit
models. Recombination resistors used for traditional semiconductors are indeed
a special case of the general model, for which transistors implement a more
accurate representation. For mixed conducting devices, such as hybrid
metal-halide perovskite solar cells, appropriate simplifications of the
complete model provide analytical solutions describing the bulk and interfacial
polarization effects that influence local electrostatics, recombination
currents and overall impedance. The resulting analysis is relevant for a wide
range of materials and devices used for solar energy conversion as well as
other optoelectronic and photo-electrochemical applications.
