Mathematical Model of Four-Line Probe to Determine Conductive Properties of Thin-Film Battery Electrodes

Abstract

Measurement of the electronic conductivity of porous thin-film battery electrodes poses significant challenges, particularly when the film is attached to a metallic current collector. We have developed a micro-four-line probe and testing procedure that overcomes many of these difficulties while relying on principles similar to commonly used four-point probes. This work describes a mathematical model that enables rapid inversion of the data collected by such experiments to compute two properties: bulk electronic conductivity of the film and contact resistance with the current collector. The model accounts for variable probe and sample geometry and variable resistance between the probe and the sample. Results from 2D and 3D models are presented. The full 3D model combines a Fourier series with the boundary element method to generate a solution that requires significantly less computational cost than a corresponding finite element solution for the same level of accuracy. The model confirms that the ideal probe line spacing is close to the value of the electrode film thickness.