The Monte Carlo method has been used to simulate the interaction of incident electrons of 1--10 keV with Si, Cu, Ag, and Au solids. In the simulation, the trajectories of secondary electrons inside the solids have also been included. The distributions of secondary-electron-emission sites on the surfaces of Si, Cu, Ag, and Au show multifractal behavior. For the same solids, the information dimension ${\mathit{D}}_{1}$, the correlation dimension ${\mathit{D}}_{2}$, and the minimum singularity ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{min}}$ decrease with increasing energy of the incident electrons while the maximum singularity ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{max}}$ increases. For the same primary-electron energy, ${\mathit{D}}_{1}$, ${\mathit{D}}_{2}$, and ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{min}}$ increase with increasing atomic number of the solid, while ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{max}}$ decreases. The Hausdorff dimension ${\mathit{D}}_{0}$ is almost unaltered in any case if the number of emitted secondary electrons is large enough. The results show that the higher the primary-electron energy and the lower the atomic number of the solid, the more dispersive is the distributed probability of secondary-electron-emission sites on the solid surface.