The weight function for charges - A rigorous theoretical concept for Kelvin probe force microscopy

A comprehensive discussion of the physical origins of Kelvin probe force microscopy (KPFM) signals for charged systems is given. We extend the existing descriptions by including the openloop operation mode, which is relevant when performing KPFM in electrolyte solutions. We define the contribution of charges to the KPFM signal by a weight function, which depends on the electric potential and on the capacitance of the tip-sample system. We analyze the sign as well as the lateral decay of this weight function for different sample types, namely, conductive samples as well as dielectric samples with permittivities both larger and smaller than the permittivity of the surrounding medium. Dependin…