A new analytical model for cathodoluminescence emission as a function of the beam energy in GaAs and InP materials

Starting from an analytical expression of the energy loss as a function of the depth, a complete analytical calculation has been done for the cathodoluminescence (CL) intensity in GaAs and InP materials. For the case of a bulk substrate, the analytical expression of the CL intensity depends on the parameters of the bulk semiconductor (diffusion length of the minority carriers, absorption coefficient of the emitted light) and of the surface recombination velocity. By varying the electron beam energy, the generation of carriers is changed in depth and the variation of the CL intensity allows the determination of the semiconductor and surface parameters. For the case of a substrate with a top layer of the same material, but with a different diffusion length and a different quantum yield, a complete analytical expression of the CL intensity can be obtained. The variation of the CL intensity as a function of the beam energy allows the determination of the parameters of the substrate and of the top layer, as well as the quantum yield ratio between the top layer and the substrate. Application examples are shown for both cases.