The Physics of Spreading Resistance Measurements

The spreading resistance method is uniquely suitable for the determination of electrical resistivities in a number of situations. However the technique does not simply measure the resistivity beneath the contacts. Considering the two probe configuration, what is actually measured is the ratio ΔV/I. Here ΔV is the difference between the Fermi levels of the probes necessary to maintain the sampling current I. This difference in the Fermi levels of the probes depends on the zero bias resistance of the probe - semiconductor contacts, the effective resistivity of the layers in a multilayer structure, and the configuration of the structure. The zero bias resistance depends on temperature and details of the metal-semiconductor contact including surface history. Effective resistivities enter into the measurement - and not the actual resistivities - because of the fact that the use of pressure probes creates a stress field under the contacts. This field falls off with a characteristic length of the order of the contact radius. Thus piezoresistivity effects - well known for Si - can be operative under the contacts. As a consequence of these various effects the interpretation of what ΔV/I is actually measuring is not straightforward. Practical application of the spreading resistance technique necessitates making certain simplifying assumptions. In light of the various phenomena involved in a spreading resistance measurement it is imperative that the implications of these assumptions to the accuracy of the measurement be understood.