In the Kelvin method (or vibrating capacitor method) two conductors are arranged as a parallel plate capacitor with a small spacing. In a simple model the contact potential difference (CPD) between the two materials is VCPD = 1/e(Ф2-Ф1), where Ф1 and Ф2 are the work functions of the conductors including changes due to adsorption layers on the surface. A periodic vibration of the distance between the two plates at w results in current i(t) given by
where D C is the change in capacitance. For the actual measurements of VCPD , an additional bucking voltage is applied between two plates until the space in between is field free and the current I(t) goes to zero.
High lateral resolution CPD measurements can be achieved by using a modified version of the ac SFM. The principle is similar to the Kelvin method exept that forces are measured instead of currents. An additional voltage is applied between tip and sample until the electric field in between vanishes, as determined by measuring the force caused by the applied voltage. In  the ac voltage between tip and sample was applied at the resonance frequency while the piezo-induced vibration of the cantilever was driven slightly above resonance at fres + Df. The signal change at the piezo-induced vibration amplitude was used to control the dastance between rip and sample. The second feedback loop was used to measure the CPD by minimazing the electric field between tip and sample.