Analytical evaluation of the capacitance of a conical sensor for micro-nano imaging techniques

The analytical modelling of a grounded truncated metallic cone is presented in this work as a contribution to the de-embedding and calibration of a scanning microwave system based on capacitance measurements for imaging and spectroscopy purposes. First, an expression for the capacitance of a uniform cylinder is derived, and successively a procedure to determine an effective uniform cylinder radius for the truncated cone is developed. The truncated cone was chosen as a suitable geometry for the calculation of the stray capacitance versus ground of a metallic tip used for scanning probe microscopy and, more specifically, microwave sensing. An accurate calculation of the aforementioned capacitance is of outmost importance for system calibration in scanning microwave microscopy (SMM) technique.