Reconciliation of dipole emission with detailed balance rates for the simulation of luminescence and photon recycling in perovskite solar cells

Abstract

A theoretical description of light emission, propagation and re-absorption in semiconductor multilayer stacks is derived based on the transverse Green's function of the electromagnetic field in the presence of a complex dielectric. The canonical dipole emission model is parametrized in terms of the local optical material constants and the local quasi-Fermi level splitting using the detailed balance relation between local absorption and emission rates. The framework obtained in this way is shown to reproduce the generalized Kirchhoff relations between the luminescent emission from metal halide perovskite slabs under uniform excitation and the slab absorptance of light with arbitrary angle of incidence. Use of the proper local density of transverse photon states in the local emission rate includes cavity effects in the generalized Planck law for internal spontaneous emission, which are neglected in the conventional Van Roosbroeck-Shockley formalism and avoids spurious divergencies due to non-radiative energy transfer via longitudinal modes. Finally, a consistent treatment of re-absorption provides the local rate of secondary photogeneration required for the consideration of photon recycling in an opto-electronic device simulator that includes the effects of charge transport.