Abstract
The capacitance system of a hyperboloidal tip and a rough surface is usually encountered in analyzing electrostatic force microscopy images. In this letter, a perturbation approach has been applied to solve for the electric potential of this system, in which the rough surface is treated as perturbation from a flat one. For the first-variation solution, the boundary value problem is represented in the prolate-spheroidal coordinate system and solved in terms of a generalized Fourier series involving conical functions. Based on this solution, the tip-surface Coulombic interaction can be computed. Sample calculations have been applied to sinusoidal surface profiles.
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