Analytical Solutions of the Frequency Shifts of Several Modes in Dynamic Force Microscopy Subjected to AC Electrostatic Force

Kelvin probe force microscopy is currently used to measure contact potential difference and topography of sample on a nanometer scale, based on the behaviors of the first two resonant frequencies. In this study, an analytical method to determine the frequency shifts of several modes in dynamic force microscopy subjected to AC electrostatic force is proposed. The numerical results determined by the proposed method are close to the experimental ones. If the amplitude and the frequency of the AC voltage are suitable, a large frequency shift and a linear relation between the frequency shift and the tip-sample distance will be obtained. In other words, properly controlling the AC voltage will increase the accuracy of measuring the sample's topography. Moreover, it is found that even without an optimized compensation dc voltage, increasing the first frequency shift and decreasing the tip radius and the half open angle of the tip can increase the accuracy of measuring a step height. Finally, it is found that when the oscillation amplitude and the tip-sample distance are constant, increasing the negative dc voltage will increase the accuracy of the measurement of contact potential by using the frequency shift. In addition, an assessment of the conventional perturbation method is presented and the two methods are compared.