Mathematical modeling of the cathodoluminescence of excitons generated by a narrow electron beam in a semiconductor material

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A mathematical model of the cathodeluminescence of free excitons excited by a narrow electron beam in a semiconductor material is described and investigated. The model is based on an analytical solution to equations of the three-dimensional diffusion of excitons. It is shown that the model can be used to estimate the diffusivity of excitons from experimental time-of-flight measurements of samples coated with a lightproof mask with round apertures. The parameters of gallium nitride were used in the modeling.