Analysis of the correction factor in the spreading-resistance technique for monitoring epitaxial silicon

The range of applicability of the mixed-boundary-value method for calculating spreading resistance for a homogeneous slab with an effective contact-radius source and backed by a substrate of arbitrary but finite resistivity is investigated. Solutions are presented in terms of the correction factor and the source current density distributions for a slab of varying thickness and with various high-resistivity substrates. The correction factors for different schemes of calculation are correctly obtained by means of introducing an additional current source of opposite sign, but with the same absolute value, located at the drain point contact. This combination of source and drain currents gives the true value for the potential distribution along the surface of the semiconductor. This, in turn, leads to new terms in the equations obtained for the correction factors, which have been omitted in previously published works. A comparison between several schemes of calculation is presented. Within the framework of “uniform” and “variable” current distributions underneath the contact probe, there are two limits for the correction factor. A model based on a combination of these approaches is discussed, and a comparison between the proposed method and the Schumann–Gardner formulation is made.