Published in J. Vac. Sci. Technol. B 21, 2080 (2003).

Electrostatic Potential for a Hyperbolic Probe Tip near a Semiconductor

R. M. Feenstra
Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213


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 solution 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.

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Source code for a computer program that accomplishes the solution to Poisson's equation described in this paper

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