What is a deep defect? Combining Shockley-Read-Hall statistics with multiphonon recombination theory

Slow nonradiative recombination is a key factor in achieving high open-circuit voltages or high luminescence yields in any optoelectronic material. Whether a defect is contributing substantially to nonradiative recombination is often estimated by defect statistics based on the model by Shockley, Read, and Hall. However, defect statistics are agnostic to the origin of the capture coefficients and therefore conclude that essentially every defect between the two quasi-Fermi levels is equally likely to be a recombination-active defect. Here, we combine Shockley-Read-Hall statistics with microscopic models for defect-assisted recombination to study how the microscopic properties of a material affect how recombination active a defect is depending on its energy level. We then use material parameters representative of typical photovoltaic absorber materials ($\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Pb}{\mathrm{I}}_{3}$, Si, and GaAs) to illustrate the relevance, but also the limitations of our model.