Modeling the influence of two terminal electrode contact geometry and sample dimensions in electro‐materials. Issue 6 (17th December 2018) - Veazey, Richard A.
Abstract: Various two terminal electrode geometry configurations are commonly employed to probe the electrical properties of materials with the key consideration being how current flows through the sample. Here, finite element modeling is used to simulate the dc electrical response of an electrically homogeneous sample (based on single crystal SrTiO3 ) using two terminal electrode geometries based on full surface, top‐bottom macro‐contacts as is commonly used when characterizing bulk ceramics or large single crystals and top‐bottom and top‐top micro‐contacts that are used to characterize thin films and local intra‐ and inter‐granular regions in ceramics. Well‐known equations for macro‐ and micro‐contacts are used to calculate the conductivity of the sample and are compared to the intrinsic values to determine their accuracy. A geometric factor returns accurate bulk conductivity values when there is homogeneous current flow whereas the spreading resistance equation gives the most accurate conductivity values for heterogeneous current flow. When micro‐contacts are used, the response is dominated by a small region of high current density in the vicinity of the contact, providing local electrical properties. Interference can occur when regions of high current density overlap, providing a less resistive route for current flow, thus reducing the applicability of the spreading resistance equation. For top‐top micro‐contacts at small separations, the conductivity is overestimated. The accuracy of the spreading resistance equation increases as the contact separation increases and is within 10% error when they are separated by eight times the micro‐contact radius. Convergence of the error to values lower than 10% becomes increasingly difficult and requires excessively large (and experimentally challenging) separation distances. For example, to obtain a result with an error below 5% requires separations in excess of 28 times the micro‐contact radius. Confinement occurs when the sample size limits the ability of the current to spread out from a micro‐contact, thus increasing the resistance. As the sample shape and dimensions can limit current flow, a geometric factor can sometimes be used to determine accurate conductivity values. In some cases, interference can counter‐balance confinement to yield fortuitously accurate conductivity values.