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

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The bias potential, $V_{\text{bias}}$, is the key quantity for the Kelvin probe force microscopy (KPFM) measurements and interpretation. Using an efficient method for electrostatic force determination, $V_{\text{bias}}$ 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. $V_{\text{bias}}$ 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 $V_{\text{bias}}$ 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 $V_{\text{bias}}$ 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.
2010-02-25