Statistical Engineering Division, CAML
Semiconductor Devices Division, EEEL
The purpose of this project is to produce five issues of SRMs with certified resistivities at 200, 100, 10, 1, 0.1 and 0.01 ohm.cm levels. The SRMs come from a crystal that has been grown from liquid silicon doped with boron. Resistivity decreases with slicing position down the crystal.
The SRMs are intended for on-line calibration of instruments used in semiconductor fabrication. The project began several years ago with the validation of a more precise method (relative to the existing ASTM standard method) for measuring resistivity (or sheet resistance) of silicon wafers with probing instruments.
This is a classic situation of a quantity that is defined solely by a method (instrumention and procedures) and certified artifacts disseminated by a national laboratory. The research phase for this project studied failure modes, wafer stability, instrument geometries, effects of wear on probes, effects of repeated probing on wafer surfaces, and photo-electric effects (exposure to light). These experiments uncovered some mechanisms which are not yet fully understood, although physical arguments can be made by way of explanation, and suggested sources of uncertainty to be examined during the certification process.
For the certifications, the same experimental design was applied to all five issues. A check wafer, chosen at random from the batch of approximately150 SRMs from a single crystal, was measured daily to estimate components of variance. A pre-certification experiment on five wafers was conducted to: identify the probe with the best precision, test the difference between two geometries for that probe, estimate systematic differences among the five NIST probes, and estimate temporal components of variance. This phase was followed by the certification where all wafers from the crystal were measured with a single probe. This, in turn, was followed by a post- certification experiment, identical to the pre-certification experiment, that checked for change or drift in the process.
Sources of type A uncertainties for the 200 ohm.cm level wafers are: 1) probe precision; 2) run-to-run variability; 3) long-term variability in the measurement process; 4) a correction to certified values for bias in the certification probe; and 5) a one-sided effect to account for initial probe/wafer damage.
Type B uncertainties are yet to be evaluated. Significant photo-
electric effects make one issue unsaleable and, for another, the
photo-electric effect is treated as a component of uncertainty in the
Figure 1: Differences from the wafer mean (ohm.cm) for 5 probes (coded 1-5) for each of 5 wafers and confirm that there are systematic differences among the 5 NIST probes.
Date created: 7/20/2001