Shape dependence of the capacitance of scanning capacitance microscope probes

The capacitance of approximately conical scanning capacitance microscope probes placed perpendicularly over a conducting plane has been modelled using the finite element method. The dependence on tip/surface distance, radius of curvature of the tip apex, cone angle and height has been analysed. Both shielded and unshielded probes have been considered. The fits of obtained dependences have been combined into an analytic approximation of the capacitance as a function of tip/surface distance, radius of curvature, cone angle and height. The results can be used to estimation of stray capacitance, achievable lateral resolution and contrast.