Beyond van der Pauw: Sheet resistance determination from arbitrarily shaped planar four-terminal devices with extended contacts

An extension of van der Pauw´s method to determine the sheet resistance Rsq from arbitrarily shaped devices with four peripheral contacts of any size is presented. Extracting Rsq requires the measurement of six electrical resistances on these devices and the simultaneous solution of a system of six algebraic equations. The results are obtained using the method of conformal mapping in combination with the method of images. The computational effort to extract Rsq is modest. Using finite-element analysis, our findings were verified within a relative accuracy of better than 0.1%. Experimental tests with differently shaped structures are fully consistent with the novel theory.