Felipe Souza Oliveira

Metallic samples of SrTiO 3 − δ with charge-carrier densities of n = 8.6 × 10 ¹⁶ cm ⁻³ and 2.0 × 10 ¹⁷ cm ⁻³ are shown to exhibit magnetic-field-induced metal–insulator transitions. Landau levels emerge in the magnetic field, and their energy spacing is comparable to the Fermi and thermal energies. A simple parallel-conduction model involving thermally-activated hopping among Landau levels is introduced to describe the data below the metal–insulator transition temperature.

The influence of the electrical contact size and shape on the electrical resistivity measurements performed with Montgomery method is evaluated by the COMSOL Multiphysics software. Results obtained with point or small size contacts ( ≤ 1% of the sample length) reproduce the expected electrical resistivity value. The simulations are compared with previous literature and experimental data obtained from copper plates. Contacts of up to 10% of the sample length are excellent choices for electrical resistivity measurements using Montgomery method, as the standard deviations are less than 1%, no matter the contact shape. When larger electrical contacts are required, triangle and concave arch contact geometries yield the lowest error and standard deviation, while square and circle should be avoided.

This work outlines the assembly of a cost-effective and straightforward apparatus designed to automate contact switching for electrical transport measurements. We report example of applications for this custom device and showcase its versatility by employing it for electrical resistivity and Hall effect measurements following the van der Pauw method on oxygen-deficient strontium titanate single crystals, measurements on compressed bismuth using the Montgomery method, and measurements on fresh cleaved Highly Oriented Pyrolytic Graphite using a multi-line electrode configuration.

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.

Numerical simulations via COMSOL Multiphysics software are used to describe the behavior of electrical resistivity of several samples with rectangular shape typically used in the Montgomery method. The simulation data obtained using four isotropic conductors allowed us to understand in detail the behavior of the electric potential and electric field of the samples. The results provide an analytical method, which can substitute the four-probe method with much more simplicity and precision.