tions in which the limits of thermal instability and second breakdown nearly coincide.

Work has resumed on the investigation of methods for using the temperature response of a substrate diode for determining the integrity of the die attachment of integrated cir

cuits. Initial measurements on devices bonded to headers with intentionally introduced voids indicate that dc methods are not sufficiently sensitive. Pulse-heating and time-delay measurement methods are expected to provide the required sensitivity.

3.1.

Four-Probe Method

BY

For w >>s, the value of G7 (w/s) approaches 1, so that the resistivity calculated by eq (1), which is applicable for large diameter slices, should be independent of thickness; for w/s > 8, G7(w/s) differs from unity by less than 0.2 percent. At the other extreme, where w << s, the resistivity calculated by eq (3) should be independent of thickness. If the voltage-current ratio is measured on a uniform slice as a function of slice thickness, the resistivity calculated from either eq (1) or eq (3) should approach constant values at both large and small values of w/s; these values should differ by |1 - [π/(F2•1n2)]| which ranges from 1.4 percent for slice diameter D = 25s to 8 percent for D = 10s. Measurements on 1-in. (25-mm) diameter slices (NBS Spec. Publ. 400-25, fig. 1) followed this expected behavior. However, the more recent measurements on 5/8-in. (15.9-mm) diameter slices failed to approach a constant value for w/s as small as small as 0.24.

lected low-index planes of both n- and ptype silicon. Without reproducibility, a calibration curve has little meaning; if the calibration relation is nonlinear, the number of data points required to define the calibration curve is increased.

The present data were taken at probe loads of 440 mN (1 gf = 9.8 mN), which is higher than is generally used for depth profiling applications; such loads are typical of radial profiling applications. These data also provide an important background for work at lighter loads for which experience indicates a pronounced increase in measurement scatter will be seen.

For each surface preparation used, measurements were taken with five sets of probes made from four different alloys. While it is difficult to assure that the correct amount of material was removed for each preparation cycle so that the surface treatments used give results typical of the intended surface type, the following steps were taken to aid in obtaining the most representative data:

(1) specimens of like orientation and conductivity type were mounted in sets on a common block with the oriented face upward and arranged so that the resistivity was a somewhat random function of position;

(2) the order in which the probes were used for any surface preparation was randomized; and

(3) fresh surfaces were prepared each time a different set of probes was used to make the measurement.

The calibration relation was found to depend both on surface preparation and probe set used for n-type silicon; there was no probe dependence for p-type silicon. Strong nonlinearities were observed for all orientations of n-type silicon with lapped surfaces and for (111) n-type silicon with mechanically polished surfaces; smaller nonlinearities have also been observed for lapped surfaces of (111) p-type silicon. Such nonlinearities have been modeled in terms of barrier effects at the metal-semiconductor spreading resistance contact [6,7]. Results are presented below for the three major classes of silicon conductivity type and surface orientation [8].

The simplest ca case is that of p-type silicon with (111) surface orientation. As shown in figure la, nearly linear relations between

spreading resistance and resistivity are obtainable on surfaces of specimens with resistivity above 0.01 .cm either by polishing it aqueous media followed by thermal treatment (bakeout) or by polishing in nonaqueous media. The nonlinearity observed for lower resistivity specimens is believed to be due to a combination of power-supply limitations and series resistance effects.

The effect of specimen preparation on (100) n-type silicon is nearly as well defined as that described above. Results from probes with relatively low average spreading resistance, osmium or tungsten-osmium, show nearly linear responses with resistivity for all surface conditions as illustrated for tungstenosmium in figure lb. Data from the other two probe sets, tungsten carbide and tungstenruthenium, tend to show slight deviations from this linear behavior. Since these alloys have higher average spreading resistance and smaller areas of contact than the osmium and tungsten-osmium probes, the anomalous results cannot be explained in terms of alloy composition alone. Results, illustrated in figure lc, obtained with tungsten carbide probes are consistent with a residual barrier effect of a type which is more prominent on lapped surfaces of n-type specimens for all probe materials. The tungstenruthenium probe data exhibit some of the same apparent barrier effect and, on the whole, provide the most erratic results of all the probe sets in terms of local scatter about the general resistivity.

The situation for (111) n-type silicon is much more complex. For no combination of polishing preparation and probe material do the resultant data show an absence of the barrier-type nonlinearities so prominent on lapped specimens. The form of the resistivity dependence has a strong dependence on the probe set used. The higher the average spreading resistance for a given probe set, the larger are the deviations from linearity attributable to barrier effects, regardless of the polishing procedure used. Tungstenruthenium probes were in most frequent need of probe reconditioning, and the data obtained with these probe materials are the most erratic of any taken. The plots of figures ld and le exhibit surface-preparation dependence for two sets of probe materials tungsten-osmium and tungsten carbide; data from other probe materials (except for tungsten-ruthenium) generally fall within the bounds loosely defined by these plots. For chem-mechanically polished surfaces, the deviations from linear behavior are reduced

for all probes by use of the bakeout cycle. For specimens mechanically polished in an aqueous medium, barrier nonlinearities were noticeably more in evidence than for chemmechanically polished specimens and in general were centered at a somewhat higher resistivity; following a bakeout cycle, the nonlinearities attributable to barrier effects were reduced, and drastic differences in the responses of the several probe sets appeared. For specimens mechanically polished in the nonaqueous medium the results were in general agreement with those obtained on surfaces polished in an aqueous medium after bakeout, but additional changes in spreading resistance occurred when the surfaces polished in a nonaqueous medium were baked.

(J. R. Ehrstein and D. R. Ricks)

To test the validity of eq (4) on thin, nonuniform layers, spreading resistance was measured as a function of probe spacing on three thin diffused layers formed by diffusing boron into phosphorus-doped silicon. Plots of the resulting data, with s on a logarithmic scale as shown in figure 2, are linear and have a common intercept at s ≈ 2 μm. As indicated in table 1, reasonable agreement was obtained between the values of sheet resistance calculated from these plots and those measured directly with a four-probe array. These results are taken as confirmation of the validity of using this form of the correction factor in conjunction with measurements on thin, nonuniform isolated regions. The experiment also provides a useful procedure for determining the effective contact radius.

(4)

(2a/πt)ln(s/a) is the correction factor for finite slab thickness, s is the probe spacing, a is the effective contact radius of the probe tips, and t is the slab thickness. The factor p/t is the sheet resistance, R of the slab. If the spreading

S

ss

لس

1000

Figure 2. Spreading resistance, Rsp, measured as a function of probe spacing, s, for three boron-diffused wafers with different sheet resistances. (The slope of the curve, the ratio of ARsp to Alog s, is equal to 0.773 Rs, where Rs is the sheet resistance of the layer; the extrapolated intercept, Rsp = 0, occurs for s = a, the effective contact radius.)