Finite element analysis and equivalent parallel-resistance model for conductive multilayer thin films

The standard collinear four-point probe method is an indispensable tool and has been extensively used for characterizing conductive thin films with homogeneous and isotropic electrical properties. In this paper, we conduct three-dimensional (3D) finite element simulations on conductive multilayer films to study the relationship between the reading of the four-point probe and the conductivity of the individual layers. We find that a multilayer film may be modeled as a simple equivalent circuit with multiple resistances, connected in parallel for a wide range of resistivity and thickness ratios, as long as its total thickness is smaller than approximately half of the probe spacing. As a result, we may determine the resistivity of each layer sequentially by applying the four-point probe, with the original correction factor π /ln(2), after deposition of each layer. (paper)