The electrostatic potential resulting from a metallic probe tip near a semiconductor is examined. A solution is formulated assuming circular symmetry and using prolate spheroidal coordinates in the vacuum and Cartesian coordinates in the semiconductor. The result is most directly applied to the case of a hyperbolic probe tip, but other shapes (for example, a small hemispherical protrusion on the tip apex) can also be handled. Numerical results are given for representative cases that might be encountered in scanning probe microscopy. (C) 2003 American Vacuum Society.