Analysis of stray capacitance in the Kelvin method

Abstract

We present a theoretical analysis of the Kelvin probe circuit taking into account both the parallel capacity induced by the connecting cables and fringing fields. We demonstrate a simple explicit solution for low modulation index ε and suggest an optimized detection method for ε close to unity. We extend the analysis to include stray capacitance terms for both the static- and vibrating-plate earthed (spe, vpe) configurations and examine the variation in apparent contact potential difference Vapp as a function of the Kelvin probe mean spacing. This analysis is primarily intended for UHV applications where shielding problems, due either to connecting cables within the system or nonideal system configurations, e.g., imposed by sample mounting constraints, are nontrivial. Using a specially developed computer-steered Kelvin probe and shield potential Vs coupled to a data acquisition system (DAS) we have tested the above model. We find Vapp to be linear with Vs and varies quadratically with mean spacing in both spe and vpe configurations. In the latter case the effect was much smaller; however, it must be taken into account for sub-meV operation.