The spontaneous emission spectrum in n-type GaAs of donor concentration 6 × 1017 cm−3 excited by a 40 kV electron beam at different ambient temperatures above 100°K is theoretically determined. The procedure of determination is justified through reasonable agreement of the temperature dependence of the peak emission energy and the half-width of spontaneous emission as obtained from the computed cathodo-luminescence spectra with that observed experimentally. It is also concluded that the procedure will be equally valid for temperatures below 100°K and for arbitrary values of the donor concentration provided that the diffusion lengths of the minority carriers and the absorption coefficients as appropriate to such temperatures and donor concentrations are known. © 1973 Taylor and Francis Group, LLC.