Bias Potential for Tip-Plane Systems in Kelvin Probe Force Microscopy Imaging of Non-uniform Surface Potential Distributions

摘要

The bias potential, V_(bias) is the key quantity for the Kelvin probe force microscopy (KPFM) measurements and interpretation. Using an efficient method for electrostatic force determination, V_(bias) has been calculated for tip-plane systems, with realistic tip geometry and for non-uniform potential distributions on the plane. The considered potential distributions on the plane include a potential step, a quadratic potential island, and two quadratic potential islands with varying separation. V_(bias) has been evaluated along three different schemes, i.e., from the minimization of electrostatic force, from the force gradient, and from the integral formula. We have studied V_(bias) as a function of tip-surface distance, island size, vibration amplitude, and tip sharpness radius (the so called nanotip). We have found that there are substantial differences between the gradient and integral schemes for V_(bias) evaluation. We have determined that the nanotip presence favors an accurate potential mapping, particularly for small potential islands. The implications of the obtained results for KPFM method are also discussed.