We have found that nanoholes are formed on silicon surfaces by the irradiation of electrons whose energy is above 40 keV. We have systematically investigated the size and distribution of nanoholes. In the temperature range from 300 K to 600 K, both the radii of nanohole and the distance of nearest-neighbor nanoholes increase with increasing temperature; the planar density of nanoholes decreased with increasing temperature. The data follow a simple Arrhenius law, suggesting that nanoholes are formed through the diffusion of surface vacancies. The diffusion energy is estimated to be 50 meV. Surface nanoholes are formed even at 4 K at which surface vacancies cannot diffuse thermally, presumably due to athermal diffusion of surface vacancies.