Mr. Timothy L. Bittleston Profile

Timothy L. Bittleston

at Photronics Inc

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Proceedings Article | 27 December 2002 Paper

Cpk and Ppk: one capability index is not enough to measure photomask CD performance

Timothy Bittleston

Proceedings Volume 4889, (2002) https://doi.org/10.1117/12.467579

KEYWORDS: Photomasks, Critical dimension metrology, Statistical analysis, Process control, Error analysis, Photomask technology, Cadmium, Analytical research, Statistical modeling, Semiconducting wafers

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Many photomask customers require process capability reporting on a regular basis. One of their main purposes is to evaluate product quality based on process variability from period to period. The problem occurs when process improvement is based on a single reported index. There are a variety of methods used today to calculate process capability, and any one method has proven insufficient (see figure below). Process 'A' looks good with respect to the average-range divided by a constant (R-bar/d₂), but the standard deviation looks too wide. Conversely, Process 'B' looks good with respect to standard deviation, but its R-bar/d₂ is skewed too far. An explanation for this phenomenon is that the use of the standard deviation method to calculate capability (actually the performance index) ignores within-sample variation, and using the R-bar/d₂ method omits sample-to-sample variation. Therefore, both methods should be employed to better evaluate process performance and capability. This paper presents a means by which to employ the merits of both sigma estimators to achieve a better representation of continual improvement. Utilizing a method of pooling within and between-sample variation (Cvk) indicates that the two processes below actually exhibit almost identical capability.

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