Mathematical Modelling of the Electric Field in Anisotropic Semiconductors during Hall Measurements

In modern discrete functional semiconductor devices and structural elements of micro- and nanoelectronics, use is made of materials with anisotropy of electrical properties. In particular, such materials are crystalline thermoelectrics, layered graphite structures, and strained silicon. In the practical application of these semiconductors, it becomes necessary to measure their kinetic coefficients. However, the electrodynamics of these media differs from that of isotropic ones, which requires the correction of existing methods for measuring the conductivity and concentration of the majority charge carriers. The paper presents a technique for solving the Neumann problem with inhomogeneous boundary conditions for the electric field potential in a rectangular region in a relatively weak magnetic field in a linear approximation. The boundary value problem considered in the paper is encountered in the analysis of measurements of the Hall effect by probe methods. Using the perturbation theory and the Fourier method, an expression for the Hall field potential is obtained and presented in rectangular coordinates as a series of harmonic functions, which is convenient for further application. Practically important expressions for analyzing the results of Hall measurements by probe methods have been obtained for anisotropic samples with flat boundaries. Analysis of the obtained solution and computer simulation of the electric potential in anisotropic semiconductor wafers with flat boundaries are performed. An experimental verification of the obtained distributions of potentials and practical recommendations on the application of the obtained theoretical expressions are presented.