Electric Field Modeling in Anisotropic Dielectrics

Abstract

We model the electric field distribution below a conductive tip positioned above an anisotropic dielectric sample, as used in scanning probe investigations. The electric field is calculated for a realistic tip shape (radius 50 nm) and tip-sample distance (2 nm). The calculations are performed for a ferroelectric BaTiO₃ sample. It is shown that the lower dielectric constant ε _c along the crystallographic c-axis has a decisive influence on the electric field distribution. The field is concentrated below the conductive tip, approaching a maximal field strength of up to 10⁶ V/m and 10⁵ V/m for c- and a-oriented domains, respectively, at a tip bias of 1 V. Furthermore, in c-oriented domains the field decays very rapidly into the sample being concentrated to the near-surface region only. The results have implications for various scanning probe microscopy methods utilizing the response of the sample to an electric field, such as piezoresponse force microscopy, Kelvin probe force microscopy, and electro-optic scanning probe microscopy.

Keywords:

• Scanning probe microscopy
• electric field
• finite element modeling
• anisotropic dielectrics

Acknowledgement

This work is financially supported by the German Federal Research Society (DFG) in the Graduate College “Sensorics,” Dresden.