The Relation Between the Correction Factor and the Local Slope in Spreading Resistance

Abstract

Dickey had proposed a technique, known as the local slope method, for the calculation of the correction factor which is used to obtain resistivity profiles from spreading resistance data. The technique is founded upon two asymptotic models for the conduction process involved in the spreading resistance measurement for the cases of (i) a conducting layer over an insulating substrate, and (ii) a high resistivity layer over a low resistivity or conducting substrate. The results of these two extreme cases are bridged by means of an assumed functional relation between the correction factor and the local slope of the spreading resistance data. This paper examines the two asymptotic models as well as the assumed functional relation between the correction factor and the local slope. It is shown that the asymptotic models adequately describe the behavior of the correction factor for a thin uniform layer over insulating or conducting boundaries. In addition, the single-valued relation between the correction factor and the local slope, which is assumed by the local slope methqd, is shown not to be an adequate representation of the multiple-valued relation between these two quantities found from multilayer data. For the cases considered, this distinction leads to an error in the resistivities as interpreted by the local slope method by as much as 60%. Nonetheless, the local slope res_ults qualitatively follow the multilayer results thus making the technique a usable one for the calculation of approximate correction factors. A comparison of the two correction factor vs. local slope relations provides a basis for the behavior of the interpreted resistivities when they are compared with the input resistivities.

A collection of computer programs for two-probe resistance (spreading resistance) and four-probe resistance calculations, RESPAC

“…These are discussed in detail in reference [19]. While it has been shown that the local slope equations cannot be derived from the multilayer equations [20], the speed and quality of the results make it a reasonable program to use.…”

“…0OO74348D0/ , C6/ . 00079824D0/ DATA C7/-.00029166D0/ IF (X.GT.3.0D0) GO TO 10 X2=X*X/9.D0 DBJ1=X* ( ( ( ( ( (A7*X2+A6) *X2+A5) *X2+A4) X2+A3) *X2+A2) *X2+A1) RETURN 10 X1=3.0D0/X Fl=:( ( ( ( (B7*X1+B6) *X1+B5) *X1+B4) X1+B3) *X1+B2) *X1+B1 THETA=X+ ( ( ( ( (C7*X1+C6) *X1+C5) *X1+C4) X1+C3) *X1+C2) Xl+Cl FORMAT (2X, 'CALCULATION OF THE SPREADING RESISTANCE FROM THE 1 RESISTIVITY ',/,2X, 'USING THE 33-POINT GAUSS-LAGUERRE SCHEME') GO TO (15,20,25), IBBC WRITE (6,17) SUBTH+N+DELTH , N*DELTH . C Qi^i^l^ili^l7^l]^i^l^l^l^t^l^l^liii^l^^^ilii**^l*************************** ************************** DO 100 1=1,33 90 W (I) =W (I) * (DB Jl (KA (I) THE 500 LOOP IS THE MAJOR LOOP WHICH CONTAINS THE CALCULATION OF THE C CORRECTION FACTOR INTEGRAL FOR THE N-POINT LAYERED STRUCTURE STARTING C FROM THE DEEPEST POINT TO THE TOP SURFACE.…”