On the physical meaning of the geometric factor and the effective thickness in the Montgomery method

Abstract

The Montgomery method is extensively employed to determine the electrical resistance tensor of anisotropic samples. This technique relies on two essential parameters describing an isotropic system: the geometric factor (H1) and the effective thickness (E). The numerical values of these parameters are intricately linked to the dimensions of an isotropic block equivalent to the studied anisotropic specimen. While these parameters hold importance, the physical interpretation of these terms still lacks clarity. In this study, we utilized the finite element method to simulate electrical transport experiments across samples of various shapes. Utilizing the Electric Currents physics interface in the COMSOL program, we were able to provide a comprehensive analysis of the physical meaning of these parameters to accurately determine the electrical properties of thin films and wafers. The presented findings related to the physical interpretation of H1 and E terms make substantial contributions to the field of electrical transport experimental techniques, which are fundamental to design advanced materials for technological applications and understand their physical properties.