Geometric contact resistances in anisotropic conductors

For any real arrangement of contacts on an electronic device, the resistance obtained from a two-terminal measurement includes effects due to the curvature of current paths near to the contacts as well as the intrinsic bulk effects which are of primary interest and the resistance due to the interface between the contact material and the device material. Provided that the contacts are sufficiently well separated that the geometric curvature effect associated with one contact is negligible at the other then separate contact resistances can be defined for the two contacts. In this case the measured resistance can be interpreted as a series combination of two contact resistances (each including both interface and geometric effects) and a bulk resistance. The object of this paper is to show analytically that the contact resistance associated with a single contact can be obtained from an appropriate three-terminal measurement using a remote voltage probe well away from the current contacts. The limits of validity of this result are examined and are found to be relatively undemanding.