Utilization of EWMA-type charts for critical dimension metrology tools

Previous research suggests that the collection and testing of measure-to-measure and day-to-day variation across a multi-site operation in a standard real-time Statistical Process Control (SPC) solution can be problematic at best. Replicating the full measurement process for mean and range in real-time not only strains resources, but may not provide an adequate indicator of measure-to-measure variation, thus resulting in exceedingly narrow control limits for day-to-day variation. A proposed solution to this dilemma was to compute control limits for the Mean chart utilizing the moving range of sample means to estimate sigma instead of the traditional range method. This approach provided statistically valid control limits that solved the issue of narrow control limits. However, it did not take into account the difficulty that remained in detecting small shifts in the process mean and therefore did not allow for adequate control of critical dimension (CD) metrology tools. Two possible solutions to this problem are the utilization of an Individual (I) and Moving Range (MR) chart with sensitivity (runs) rules or an Exponentially Weighted Moving Average (EWMA) chart. This paper reviews how the method of estimating sigma satisfied the control limits issue but caused issues in implementation. It reviews the core problem of inadequate capture of measure-to-measure variation and discusses why single point measurement may be more accurate for controlling CD metrology tools. It explores the ability of the Individual chart with runs rules and EWMA methodology to detect small shifts of the process mean of a CD metrology tool. Using CD tool monitoring data, the Individual chart with runs rules chart is compared to the EWMA chart and results are discussed.