Photon statistics of incoherent cathodoluminescence with continuous and pulsed electron beams

Photon bunching in incoherent cathodoluminescence (CL) spectroscopy originates from the fact that a single high-energy electron can generate multiple photons when interacting with a material, thus revealing key properties of electron-matter excitation. Contrary to previous works based on Monte-Carlo modelling, here we present a fully analytical model describing the amplitude and shape of the second order autocorrelation function ($g^{(2)}(\tau)$) for continuous and pulsed electron beams. Moreover, we extend the analysis of photon bunching to ultrashort electron pulses, in which up to 500 electrons per pulse excite the sample within a few picoseconds. We obtain a simple equation relating the bunching strength ($g^{(2)}(0)$ to the electron excitation efficiency ($\gamma$), electron beam current, emitter decay lifetime and pulse duration, in the case of pulsed electron beams. The analytical model shows good agreement with experimental data obtained on InGaN/GaN quantum wells using continuous, ns-pulsed (using beam blanker) and ultrashort ps-pulsed (using photoemission) electron beams. We extract excitation efficiencies of 0.13 and 0.05 for 10 and 8 keV electron beams, respectively, and we observe that non-linear effects play no compelling role even after excitation with ultrashort and dense electron cascades in the quantum wells.