The lateral resolution limit for imaging periodic conducting surfaces in capacitive microscopy

The problem of the formation of capacitance images of periodic rough surfaces with a pointer as one of the electrodes of the capacitor is investigated and the lateral resolution limits are found in terms of the radius of curvature of the Gaussian-shaped pointer. The lateral resolution Limit is found to be appreciably less than the radius of curvature at the tip of the pointer. It is found that a simple 'local-height' approximation to the capacitance gives good values for image contrast even though this method does not predict the absolute capacitance values accurately It is also shown that the overall shape of the pointer does not influence the contrast of the capacitance images if the pointer is smooth and rounded. Results of a perturbative solution which includes a spectral window function are presented and compared with numerical results, and good agreement is obtained for cases when the surface is not too rough. Finally, results are presented for a fiat-topped pointer and a hole pointer.