The Relation Between Two-Probe and Four-Probe Resistances on Nonuniform Structures

A general relation between the two-probe resistance (spreading resistance) and the four-probe resistance on nonuniform resistivity structures i derived. Numerical techniques are presented and discussed for the evaluation of these equations for nonuniform structures. The r lation between the four-probe resistance, Z(x, S), and the incremental sheet resistance, ~t(x), is shown to arise in the limit as the probe spacing becomes large compared to the distance to an insulating boundary. Specific examples are drawn from calculations on implant-type structures into substrates having insulating boundaries near the end of the implanted region (junction isolation), as well as those where the insulating boundary is far from the implanted region (emulating the back surface of a same conductivity-type substrate). Also presented is a method for the self-consistent calibration of spreading resistance profiles utilizing Z(x,S). Recently, Dickey (1) has proposed that the two-probe spreading resistance measured on the surface of a thin, nonuniform resistivity, junction- isolate