not exposed to the same set of probe conditions, it is not possible to draw firm conclusions regarding the relative sensitivity of wafer types to various measurement conditions.

For the matrix experiment, a set of specimens representative of various layer characteristics Imethod of fabrication, thickness, and sheet resistance was selected from available stock; the properties of the specimens used are listed in table 2. In each case the substrates were of opposite type with roomtemperature resistivity in the range 0.5 to 50.cm. Because the initial screening showed that the several available wafers of any one layer type, thickness, and sheet resistance combination were not in general good enough replicates (2 percent or less variation in sheet resistance), it was decided to use only one wafer of each type to generate the comparison of the various measurement conditions.

The principal intent of the study was to identify as wide a range of measurement conditions as possible for which valid results could be obtained in order to make any resulting recommended procedures applicable to as wide a variety of commercial resistivity test sets as possible, as well as to identify a safe guard band to allow for degradation of equipment as commonly experienced in a production environment. A secondary purpose was to provide a basis for unifying, where possible, the several differing sets of conditions recommended for use in making sheet resistance and resistivity measurements by the four-probe method [1,2].

Table 3 lists the characteristics of the probes used in the study. Some probes were used exactly as bought, with a hemispherical tip at the end of the stylus as shown on the left in figure 1. For this case, the size given is the radius of the tip. Other probes started with a hemispherical tip, but were lapped flat prior to use as shown on the right in figure 1. For these probes the size given is the radius of the flatted probe tip. Blunted probes were included in the study because they were expected to minimize stress concentration in the silicon under the probe. Such stresses appear to be responsible for junction leakage to the substrate, particularly in thin epitaxial wafers. The risk entailed with blunted probes is that the contact resistance to the specimen may become undesirably large, due, for example, to stray dirt accumulating under a probe tip or to a surface oxide film. Such contamination appears, in general, to be less easily pene

trated with a flatted than with a rounded probe tip. Except for the bottom three sets in the table, all four probes in a given set were identical. Probe loads used in the study are also listed in the table.

To establish a baseline, measurements were made for each measurement condition using a value of current which provided a voltage of 10 to 15 mV between the inner probes of the four-probe array; this is a somewhat more restrictive condition than that recommended in the standard method [1]. In general, measurements made at currents one-tenth of this nominal value yielded sheet resistance values which were the same as those made with the baseline current within the estimated measurement error of 1 percent. Except in a few cases, measurements made at currents five times this nominal value also yielded the same sheet resistance value.

To compare measurements made under various conditions, six measurements were made for each case using the nominal value of current. For each specimen, the correct sheet resistance value was taken as the highest stable reading. Excessive leakage to the substrate, which occurred when sharp points or large loads were used, caused the measured sheet resistance to be smaller than the correct value. Use of lightly loaded, blunt tips fre- . quently resulted in erratic contacts which caused an increase in the variability of a six-measurement data set. Typically a good set of data had a relative sample standard deviation less than 1 percent.

The results of these experiments suggest that one should use hemispherical or flatted probes with a radius of at least 0.004 in. (0.1 mm) with a load in the range 30 to 80 gf (0.29 to 0.78 N). Although current levels to provide a voltage of 10 to 20 mV between the inner probes are preferred, the current levels specified in the standard method [1] are also satisfactory. An interlaboratory test to verify these conclusions is now being conducted in cooperation with Committee F-1. (J. R. Ehrstein and D. R. Ricks)

3.2. Spreading Resistance

Experiments to determine the effect of specimen surface preparation and probe material on the empirical relation between silicon re

sistivity, p, and spreading resistance, R Rsp'

(NBS Spec. Publ. 400-25, pp. 8-12) were continued with the study of surfaces mechani

cally polished with 0.3-um alumina in an aqueous slurry. Measurements were made both immediately after polishing and after a subsequent bakeout in room air at 160°C for 20 min.

Results obtained on the specimen block with (111) p-type surfaces were very similar to those obtained previously on either of the types of chem-mechanically polished surfaces [3], silica sol [4] or zirconium silicate [5]. The spreading resistance response was very erratic for freshly prepared surfaces of specimens with resistivity greater than 0.2 cm, but a very stable, nearly linear relationship between resistivity and spreading resistance was obtained after bakeout.

On the specimen block with (111) n-type surfaces, the data obtained on the mechanically polished surfaces were unlike those obtained on either lapped or chem-mechanically polished surfaces. Prior to bakeout, data taken with all five probes exhibited very nonlinear p-R relationships as shown in figure sp

2a. After bakeout, both sets of osmiumtungsten tips, one relatively sharp, one relatively blunted with use, showed a noticeably more constant ratio between spreading resistance and resistivity than did the other three probes shown in figure 2b. This probe material dependence was not seen for any other surface orientation or finish.

cm

As previously described (NBS Spec. Publ. 40019, p. 10), the diffused layers had a boron surface density slightly less than 1019 n-3 and nominal junction depths of 1 and 2 um. The incremental sheet resistance measurements were made by repetitively anodically oxidizing the specimen surface, stripping the oxide, and measuring the sheet resistance by the four-probe method [1]. The specimens measured were 1-in. (25-mm) diameter disks, ultrasonically machined from the center of each wafer. Prior to anodization, the disks were cleaned first in a mixture of approximately 5 parts (by volume) deionized water, 1 part hydrogen peroxide, and 1 part ammonium hydroxide; then in a mixture of approximately 6 parts deionized water, 1 part hydrogen peroxide, and 1 part concentrated hydrochloric acid; rinsed in deionized water; and dried in air [9].

The anodizing solution was made up by dissolving 3.86 g of potassium nitrate in 19.5 ml of deionized water and adding 946 ml of reagentgrade ethylene glycol which yields a 0.04 molal solution of potassium nitrate with 2 percent water. During anodization the back side of the disk is held against a carbon block electrode by means of a vacuum through a tube which surrounds the electrode. The disk was lowered face down into the anodizing solution which was contained in a glass beaker; a second tube around the electrode supplied a downdraft of nitrogen to keep the dielectric solution from creeping over the lip and oxidizing the back side of the disk.

A constant current, about 10 mA/cm2, was passed through the disk; the positive electrode was a platinum wire spiral at the bottom of the beaker. To reduce forward resistance, the junction was illuminated by a 500W projection lamp aimed through the side of the beaker. To offset the heating effect of the projection lamp, the anodizing solution was continually pumped through tubing resting in an ice bath. Upon returning to the main beaker, the solution was directed at the center of the wafer front surface through a nozzle about 1/8 in. (3.2 mm) in diameter about 1 in. (25 mm) away from the surface. The purpose of the jet was to clear the surface of bubbles and to provide refreshed solution at the wafer surface.

Current was supplied until the current supply was forced to provide about 270 V more than the turn-on voltage. The oxide thickness was determined from the measured voltage difference using a calibration curve established empirically with the use of ellip

Following each oxide growth step, the wafer was agitated in hydrofluoric acid for about 5 min to remove the oxide, rinsed in a flowing deionized water bath for about 10 min, and blown dry with nitrogen. Sheet resistance was measured with a collinear fourprobe array with equally spaced probes, with 62-mil (1.59-mm) separation and tungsten carbide tips lapped flat (see sec. 3.1.) to give a contact radius of about 2 mils (50 μm). The probes were loaded with a force of 30 gf (0.29 N) each. Sheet resistance was measured over 20 to 25 increments, converted to sheet conductance, plotted as a function of position, and smoothed graphically. The local slope of the smoothed sheet conductance curve was calculated at 40-nm intervals to yield the bulk conductivity as a function of position. Bulk conductivity was converted to net acceptor density on the basis of Wagner's empirical relation [12].

Spreading resistance measurements were race with a commercial two-probe instrument (E5 Spec. Publ. 400-25, p. 9) on wafers diffuse: at the same time as the replicate wafer seasured by the incremental sheet resistance method. Chips cut from the wafer were beveled at an angle of 0.50 deg with a silica sol solution [4] on a methyl methacrylate plate. Measurements were made at lateral tervals of 5 um with well conditioned estim tungsten alloy probes loaded with a force : 20 gf (0.2 N) and spaced 50 um apart.

The results of these comparisons are shown in figure 4. The relatively close agreement suggests that the parallel superposition approach is quite accurate on this type of structure. One reason for some of the discrepancy near the surface on both specimens may be a bevel-rounding effect. It was assumed for the calculations that each successive point was a constant distance further below the original surface, but slight rounding of the bevel at its apex makes this a poor assumption for the first few points on the profile. Extensive additional comparisons will be required before conclusions can be drawn regarding the range of validity of this approach for determining correction factors. (J. R. Ehrstein, F. H. Brewer, and D. H. Dickey†)

Photovoltaic Method 5

Interest in a rapid, nondestructive method for measuring resistivity uniformity of silicon slices has been rekindled because of the importance of this parameter in determining the characteristics and the performance of high-power semiconductor devices. Variations in the resistivity of a slice of starting material not only cause variations in the characteristics of devices fabricated from that slice, but can also contribute to poor yields in the manufacturing process and adversely affect the reliability of finished devices. For instance, poor junction geometry and nonuniform current distributions are frequent in devices fabricated from inhomogeneous material. Also, localized regions of low resistivity limit the ultimate device operating voltage to a value below that possible from the remainder of the device.

The feasibility of utilizing the bulk photovoltaic effect [13] for measuring resistivity variations along the diameter of a circular silicon slice has been demonstrated [14]. The technique was shown to be nondestructive in that no contact is required with the surface area on which devices are to be fabricated and to have better spatial resolution than the widely used four-probe method [15, 16]. However, to take advantage of the potential speed of this scanning technique it is necessary to automate the data collection and analysis procedures. Further, improvements in slice mounting and contacting are necessary to facilitate rapid exchange of specimens, and comparison of the spatial resolution with that of the spreading resistance method [6,7] is desirable.