Surface charge estimation on hemispherical dielectric samples from EFM force gradient measurements

A numerical model capable of estimating the surface charge density(σ_S) and the dielectric constant(k_e) of a hemispherical sample from force gradient measurements is proposed. Force gradients are commonly detected by a biased conductive tip during electrostatic force microscopy(EFM) probing but provide limited quantitative assessment of the charge in the sample. The proposed model gives an analytical solution for the force exerted over a biased conical tip. Theoretical numerical results, presented in the form of multitraces of minimum force gradients for fixed bias voltages and tip-sample distances allow the translation of EFM force gradient measurements into functions of σ_S and k_e.