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

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Electrostatic Potential for a Hyperbolic Probe Tip near a Semiconductor

R. M. Feenstra

Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213

#### Abstract

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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