[en] The ion irradiation-induced intermixing of thin elemental marker layers buried in vapor-deposited amorphous silicon is interpreted by an analytical model based on the theory of random flights and elementary range theory. The general features of ion beam mixing are faithfully described and quantitative predictions of the magnitude of the observed effects are in good agreement with experimental data. The model predicts that the mixing is analogous to thermal diffusion with an effective diffusion coefficient that is proportional to the ion flux and the linear energy deposition density (Fsub(D)). The diffusion coefficient is shown to depend on the marker and matrix materials through their atomic masses, atomic numbers and the effective displacement energy of the marker atoms. The model is derived for dilute impurities in a host matrix, but an approximate method for extension to higher concentrations is suggested. The model is shown to be applicable in situations in which the energy deposited per atom is not a large fraction of the heat of fusion of the solid. (orig.)