Sheet resistance determination of electrically symmetric planar four-terminal devices with extended contacts

Abstract

This paper reports an analytic method to determine the sheet resistance Rsq of symmetric planar four-terminal devices based on resistance measurements. Using the technique of conformal mapping it is first shown that any such device is electrically equivalent to a corresponding symmetric unit disk with the same Rsq and invariant under rotations by 90°. Two independent resistances measurable on these devices are expressed analytically as a function of Rsq and of the contact opening angle α. These two resistances fully characterize the electrical properties of such planar conductive devices. A simple procedure to extract both α and Rsq from the resistance values is then presented. These findings are corroborated by the experimental characterization of four-contact devices of ten different geometries fabricated using a commercial complementary metal oxide semiconductor process. From these widely different devices, the sheet resistance of a n-well is extracted to be 1042Ω with a relative uncertainty of only 0.45%.