Planck's generalised radiation law and its implications for cathodoluminescence spectra

Cathodoluminescence (CL) is an important analytical technique for probing the optical properties of materials at high spatial resolution. Interpretation of CL spectra is however complicated by the fact that the spectrum depends on the carrier injection density of the incident electron beam. Here a generalised version of Planck's radiation law is used to uncover the evolution of CL spectra with injection under steady-state conditions. The importance of the quasi-Fermi level is highlighted and it is shown that steady-state luminescence is suppressed when the carrier distributions undergo a population inversion. The theory is consistent with some well-known luminescence phenomena, such as the blue shifting of donor-acceptor pair transitions with increased injection, and its predictions are experimentally verified on CdTe and GaN, which are exemplar thin-film solar cell and light emitting diode materials respectively. Furthermore, the discussion is broadened to include pulsed illumination in time resolved CL, where the carrier distribution is dynamically evolving with time.