The Monte Carlo simulation method has been used to investigate the spatial distribution of deposited energy for 1-10 keV electrons incident on solid hydrogen, nitrogen, neon, silicon, aluminum, and argon. In the simulation, elastic scattering cross sections are calculated exactly using the single-atom crystalline potentials. Inelastic energy loss processes for hydrogen are based on the ionization cross section from Green and Sawada [J. Atmos. Terr. Phys. 34, 1719 (1972)] and the gas-phase stopping power from Parks et al. [Nucl. Fus. 17, 539 (1977)]. For the heavier materials a modification of Gryziński's [Phys. Rev. A 138, 305 (1965); 138, 322 (1965); 138, 336 (1965)] semiempirical expression for each core and valence electron excitation is used. The energy-deposition distribution of keV electrons and the ionization distribution of weakly bound electrons are practically equal, whereas the penetration depth distribution extends deeper into the material than the energy-deposition distribution. The energy-deposition distributions of keV electrons for light materials, except for hydrogen, can be represented quite well by a universal distribution. In addition, accurate Gaussian approximations for the different materials in the entire energy region from 1 to 10 keV have been evaluated. Parameters such as the mean penetration depth and the mean energy-deposition depth are included as well.