Spreading resistance modeling for rapid extraction of contact resistivity with a four-point probe

Abstract

Extraction of contact resistivity (ρc) with the four-point probe (4PP) method requires considerably fewer fabrication and measurement steps compared to conventional alternatives (e.g. the transfer length method, TLM). Yet, the method is rarely used, mainly due to the requirement of 3D simulations used in the data fitting procedure. Moreover, a work analyzing the details of the method, which can provide a quantitative guideline to the users, is lacking in the literature. In this work, we show that the 3D simulations can be replaced with a spreading resistance model (SRM) implemented in a numerical calculation platform (e.g. MATLAB). Using the SRM, we achieve drastically short calculation durations (<1 s) compared to durations of 3D simulations based on the finite element method. We show that the resolution and reliability of the extracted ρc depends critically on geometrical and electrical parameters of the system, such as the probe tip spacing and sheet resistances of the layers. We also present an alternative measurement procedure that is fully based on 4PP measurements of only one substrate, which eliminates the need for an eddy-current measurement or an additional set of dedicated samples. We demonstrate the viability of the 4PP method in experiments by comparing the results with those obtained by the TLM, for ρc between 5 × 10−3 to 1 × 100 Ω cm2. Lastly, we provide a free software that can execute the calculations discussed herein.