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Photon bunching in incoherent cathodoluminescence (CL) spectroscopyoriginates from the fact that a single high-energy electron can generatemultiple photons when interacting with a material, thus revealing keyproperties of electron-matter excitation. Contrary to previous works based onMonte-Carlo modelling, here we present a fully analytical model describing theamplitude and shape of the second order autocorrelation function($g^{(2)}(\tau)$) for continuous and pulsed electron beams. Moreover, we extendthe analysis of photon bunching to ultrashort electron pulses, in which up to500 electrons per pulse excite the sample within a few picoseconds. We obtain asimple equation relating the bunching strength ($g^{(2)}(0)$ to the electronexcitation efficiency ($\gamma$), electron beam current, emitter decay lifetimeand pulse duration, in the case of pulsed electron beams. The analytical modelshows good agreement with experimental data obtained on InGaN/GaN quantum wellsusing continuous, ns-pulsed (using beam blanker) and ultrashort ps-pulsed(using photoemission) electron beams. We extract excitation efficiencies of0.13 and 0.05 for 10 and 8 keV electron beams, respectively, and we observethat non-linear effects play no compelling role even after excitation withultrashort and dense electron cascades in the quantum wells.

Photon statistics of incoherent cathodoluminescence with continuous and pulsed electron beams