Modeling electrostatic force microscopy for conductive and dielectric samples using the boundary element method

A boundary element formulation is generalized for modeling electrostatic force microscopy (EFM) and related techniques. This formulation is able to predict measurable quantities (e.g., capacitance, force, force gradient) due to probe–sample electrostatic interactions, provided that the relevant sample (conductive or dielectric) properties (surface topography and trapped charge distributions) are prescribed. For a certain voltage bias applied between the EFM probe tip and a sample of interest, the Coulombic force and force gradient can be computed via the Maxwell stress tensor and implicit differentiation, respectively. The numerical scheme can be employed to quantify EFM images and analyze sample surfaces.