A robust metric for measuring within-wafer uniformity

Within-wafer uniformity is traditionally measured by the signal-to-noise ratio (SNR), defined as the estimated standard-deviation of within-wafer measurements over the mean of those measurements, Unfortunately, in the presence of deterministic variations of the response over the wafer (such as the bull's eye effect of some processes), the SNR is sensitive to both the location and the number of the measurements taken, A robust metric for describing within-wafer uniformity is developed and compared with the SNR method. The new metric, termed the integration statistic (I) is shown to be robust to both the location and number of measurements taken on the wafer and has lower variance than the SNR metric. The implications of this robust behavior are that fewer measurements can be taken to achieve a given accuracy in the uniformity estimate and that uniformity estimates are consistent with respect to variations in the orientation of the uniformity pattern to the measurement pattern.