A Monte Carlo simulation of electron scattering in the resist and substrate of a target in electron lithography was used to obtain the spatial distribution of energy deposition in the resist. Analytical approximations were subsequently obtained by a least-squares fit of Gaussian functions to the forward- and backward-scattered components of these distributions. The parameters in the analytical functions were deduced and a compendium of values are tabulated for a variety of resist thicknesses, incident electron energies, and substrates. The parameters were found to agree with other parameters that can be physically correlated with electron-scattering processes and with available experimental data. These approximations and parameters provide quantitative guidelines for understanding and compensating of electron-scattering and proximity effects in electron-beam lithography.