A theory in terms of the Boltzman transport equation is presented for the spectral distribution of excited (hot) electrons in solids. Solutions of the steady-state, field-free equations are obtained by a Green's function technique, which offers the advantage of separating the excitation mechanism from the scattering processes. For purposes of application the question of an electron beam normally striking the planar surfaces of copper and silicon is investigated. Scattering functions representing electron–electron and, most importantly, electron–plasmon interactions are developed from which the necessary Green's functions are derived. Secondary emission spectra are then predicted, using an excitation function based on a perturbation calculation and using an appropriate emission probability formulation. Inclusion of the plasmon scattering contribution leads to agreement with experiment within 10%–20%. Approximate closed-form solutions to the necessary integrals are also offered as well as a more empirical approach to obtaining the electron energy distributions.