Yield Assessment for Dynamic Etching Processes With Variance Change

In manufacturing industries, yield is the essential quality for any mass production process. Particularly, in advanced and complex semiconductor processes, the yield requirements are becoming more stringent. Process capability index $C_{pk} $ has been widely employed to measure yield for processes with a very low fraction defective. However, unobserved slight and temporary process variations due to dynamic environments occur frequently, even when conventional control charts are applied. Reliance on control charts may cause inaccurate capability evaluation and overestimation of the production yield. Thus, a procedure for precisely assessing yield is necessary. In this article, three conventional control charts for monitoring process variation are investigated and the corresponding magnitudes for dynamic $C_{pk} $ calculation and accurate yield assessment are provided. The probability density function and the cumulative distribution function of the proposed dynamic $C_{pk} $ are explicitly derived. For yield assessment, a procedure to solve the lower confidence bound of $C_{pk}^{D} $ is provided. Based on the proposed method and the tabulated numerical tables, we can avoid overestimating the true production yield and make more trustworthy decisions. Finally, for demonstration purposes, an application of etching process yield measurement is provided.