Photon bunching in cathodoluminescence reveals fundamental properties of excitation of matter with high-energy electrons. Previous work has shown that strong bunching g⁽²⁾(0)≫1 of CL photons can occur when exciting a sample with high-energy electrons, due to the fact that a single collision cascade can generate multiple CL photons [1,2]. Until now, photon bunching in CL has been modelled using Monte-Carlo simulations, which are time-consuming and do not provide a full overview of the parameters that play a role. Moreover, CL photon bunching has been limited to the study of continuous and ns-pulsed electron beams.

In this work we develop a fully analytical model to retrieve the amplitude and shape of g⁽²⁾(τ)  upon excitation with a continuous, ns-pulsed and ultrashort (ps) pulsed electron beam [3]. The model accounts for the stochastic nature of the different processes in the sample upon excitation with high-energy electrons. We obtain a simple expression relating the amplitude of bunching g⁽²⁾(0)  with electron beam current, emitter decay lifetime, pulse duration, in the case of a pulsed electron beam, and electron excitation efficiency (γ). The latter is defined as the probability that an electron creates at least one interaction with the emitter [4].

Our model shows good agreement with experimental CL data on InGaN/GaN quantum wells (QWs) obtained with a scanning electron microscope using continuous and pulsed electron beams. We evaluate two different regimes of pulsed electron beams, either with ns pulses (6-500 ns pulse width), obtained using a beam-blanker, or ultrashort (≤ps ) pulses, performed by means of a laser-driven electron cathode. In the experiments we obtain electron excitation efficiencies of the QWs of γ=0.13  and γ=0.05  for 10 and 8 keV electrons, respectively. Moreover, the QWs exhibit a linear response despite excitation with dense ultrashort electron pulses (∼500  electrons per pulse), for which we calculate a maximum carrier efficiency of 10¹⁸cm^-3 .

Overall, this work provides an extensive analytical model to evaluate the photon statistics of incoherent cathodoluminescence using three different electron beam configurations. The simplicity of the model makes CL autocorrelation measurements more accessible, thus further enabling a quantitative analysis of electron-matter interaction inside an electron microscope.