Finite Conductivity Effects in Electrostatic Force Microscopy on Thin Dielectric Films: A Theoretical Model

Abstract

A study of the electrostatic force between an Electrostatic Force Microscope tip and a dielectric thin film with finite conductivity is presented. By using the Thomas-Fermi approximation and the method of image charges, we calculate the electrostatic potential and force as a function of the thin film screening length, which is a magnitude related to the amount of free charge in the thin film and is defined as the maximum length that the electric field is able to penetrate in the sample. We show the microscope’s signal on dielectric films can change significantly in the presence of a finite conductivity even in the limit of large screening lengths. This is particularly relevant in determining the effective dielectric constant of thin films from Electrostatic Force Microscopy measurements. According to our model, for example, a small conductivity can induce an error of more than two orders of magnitude in the determination of the dielectric constant of a material. Finally, we suggest a method to discriminate between permittivity and conductivity effects by analyzing the dependence of the signal with the tip-sample distance.