Spreading Resistance Probe‐Spacing Experiment Simulations: Effects of Probe‐Current Density and Layer Thickness

Abstract

Model spreading resistance data were calculated using three forms of the probe‐current density: the original Schumann and Gardner version, the Choo uniform current density, and the ring delta function current density in order to determine whether probe‐spacing experiment simulations are sensitive to the specific form of the probe‐current density. Further, since the probes of the spreading resistance and of the four‐probe sheet resistance apparatus view the material as a continuum, the dependence of the results of the probe‐spacing simulation on the number of layers used in the calculation was also investigated. From the analysis, it is possible to conclude, aside from the differences in the interpreted radii, that the results of the probe‐spacing simulations in the surface region are not particularly sensitive to the choice of either the current density or the number of layers used in the simulation (provided, of course, that the number of layers is of reasonable size to be representative of the continuous nature of the underlying resistivity). The failure of the probe‐spacing experiment simulation to obtain the correct surface sheet resistance for the case of a lightly to moderately doped layer over a substrate of the same conductivity type is not changed by either the probe‐current density or the discrete layer nature of the calculations used to generate the data. The variable that has the strongest influence on the outcome of the probe‐spacing experiment is the substrate resistivity. Hence, for junction‐isolated layers and for heavily doped layers over substrates of the same conductivity type, probe‐spacing experiments will yield the correct sheet resistance in the surface region.