VERIFICATION OF THE RELATION BETWEEN 2-PROBE AND 4-PROBE RESISTANCES AS MEASURED ON SILICON-WAFERS

The predicted relation between the two-probe resistance (spreading resistance) and the four-probe resistance, and the dependence of the four-probe resistance on the ratio of layer thickness to probe spacing have been experimentally verified. The verified behavior is predicted from calculations, based upon the solution of Laplace's equation, of the two- and four-probe resistance for arbitrary, vertical resistivity profiles. Arrays of lithographically fabricated, geometrically well-defined contacts on silicon wafers were utilized to make the necessary precise, reproducible resistance measurements. Additional measurements using point pressure contacts were also made. The dependence of the four-probe resistance on the ratio of layer thickness to probe spacing was verified for both the in-line and square probe configurations. Wafers that were junction isolated or back oxidized (to approximate an insulating back boundary) and p-type wafers with a back metallization (to approximate a conducting back boundary) were used. Layer thickness to probe spacing ratios were varied from 0.003 to 20. Silicon wafers with resistivities between 0.0006 and 160 Ω-cm were used. The measured resistances were found to agree with the theoretically predicted values to within the uncertainty in the resistance measurement and the expected variation of the model parameters. The accuracy with which the theory could be verified was limited by the lateral nonuniformity in resistivity of the silicon wafers. © 1990, The Electrochemical Society, Inc. All rights reserved.