Numerical study of the lateral resolution in electrostatic force microscopy for dielectric samples.

We present a study of the lateral resolution in electrostatic force microscopy for dielectric samples in both force and gradient modes. Whereas previous studies have reported expressions for metallic surfaces having potential heterogeneities (Kelvin probe force microscopy), in this work we take into account the presence of a dielectric medium. We introduce a definition of the lateral resolution based on the force due to a test particle being either a point charge or a polarizable particle on the dielectric surface. The behaviour has been studied over a wide range of typical experimental parameters: tip-sample distance (1-20) nm, sample thickness (0-5) µm and dielectric constant (1-20), using the numerical simulation of the equivalent charge method. For potential heterogeneities on metallic surfaces expressions are in agreement with the bibliography. The lateral resolution of samples having a dielectric constant of more than 10 tends to metallic behaviour. We found a characteristic thickness of 100 nm, above which the lateral resolution measured on the dielectric surface is close to that of an infinite medium. As previously reported, the lateral resolution is better in the gradient mode than in the force mode. Finally, we showed that for the same experimental conditions, the lateral resolution is better for a polarizable particle than for a charge, i.e. dielectric heterogeneities should always look 'sharper' (better resolved) than inhomogeneous charge distributions. This fact should be taken into account when interpreting images of heterogeneous samples.