Quantitative theoretical analysis of the electrostatic force between a metallic tip and semiconductor surface in Kelvin probe force microscopy

Theoretical analysis of the electrostatic force between a metallic tip and semiconductor surface in Kelvin probe force microscopy (KPFM) measurements has been challenging due to the complexity introduced by tip-induced band bending (TIBB). In this study, we present a method for numerically computing the electrostatic forces in a fully three-dimensional (3D) configuration. Our calculations on a system composed of a metallic tip and GaAs(110) surface revealed deviations from parabolic behavior in the bias dependence of the electrostatic force, which is consistent with previously reported experimental results. In addition, we show that the tip radii estimated from curve fitting of the theory to experimental data provide reasonable values, consistent with the shapes of tip apex observed using scanning electron microscopy. The 3D simulation, which accounted for the influence of TIBB, enables a detailed analysis of the physics involved in KPFM measurements of semiconductor samples, thereby contributing to the development of more accurate measurement and analytical methods.