Perturbation theory for surface-profile imaging with a capacitive probe

We derive a perturbative series solution to the capacitance between two par allel electrodes with irregular profiles. The coefficients in the series ar e calculated using fast Fourier transform algorithms resulting in a very fa st method. The applicability of the perturbative series solution is extende d by introducing a spectral window function which can make the series conve rge in cases where the standard series does not converge. We show that the filtered perturbative solution is applicable to surface profiles with surpr isingly large features. However, limitations on its applicability to surfac es with high spatial frequencies remain. Perturbation theory could be a pow erful tool for simulating surface-profile images obtained by scanning a cap acitive probe. (C) 2000 American Institute of Physics. [S0003-6951(00)02539 -0].