The space‐charge region that is induced in a semiconductor half‐space by an external point charge is analyzed. The mathematical model gives rise to a free‐boundary problem, since the edge of the space‐charge region [a surfacez=z(d) in cylindrical coordinates] is unknown. From the formal solution of Poisson’s equation, an integral equation forz(d) is derived and approximately solved. The solution describes the depletion region in dependence of the magnitude of the point charge, the charge‐semiconductor distance, and the doping and dielectric constant of the semiconductor. Approximate expressions are derived for the force acting on the point charge and are used to estimate the electrostatic force between the tip and a silicon sample in a scanning force microscope. The limitations of the model are discussed and its generalization to the case of a semiconductor coated by a dielectric film is outlined. ©1995 American Institute of Physics.