A formation process for semiconductor quantum dots based on a surface instability induced by ion sputtering under normal incidence is presented. Crystalline dots 35 nanometers in diameter and arranged in a regular hexagonal lattice were produced on gallium antimonide surfaces. The formation mechanism relies on a natural self-organization mechanism that occurs during the erosion of surfaces, which is based on the interplay between roughening induced by ion sputtering and smoothing due to surface diffusion.