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

The problem of the formation of capacitance images of periodic rough surfac es 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 curv ature 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 poin ter. It is found that a simple 'local-height' approximation to the capacita nce gives good values for image contrast even though this method does not p redict the absolute capacitance values accurately It is also shown that the overall shape of the pointer does not influence the contrast of the capaci tance images if the pointer is smooth and rounded. Results of a perturbativ e solution which includes a spectral window function are presented and comp ared with numerical results, and good agreement is obtained for cases when the surface is not too rough. Finally, results are presented for a fiat-top ped pointer and a hole pointer.