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.
To accurately control critical dimension (CD) metrology in a standard real-time solution across a multi-site operation there is a need to collect measure-to-measure and day-to-day variation across all sites. Each individual site's needs, technologies, and resources can affect the final solution. A preferred statistical process control (SPC) solution for testing measure-to-measure and day-to-day variation is the traditional Mean and Range chart. However, replicating the full measurement process needed for the Mean and Range chart in real-time can strain resources. To solve this problem, an initially proposed measurement methodology was to isolate a point of interest, measure the CD feature n number of times, and continue to the next feature; however, the interdependencies in measure-to-measure variation caused by this methodology resulted in exceedingly narrow control limits.
This paper explains how traditional solutions to narrow control limits are statistically problematic and explores the approach of computing control limits for the Mean chart utilizing the moving range of sample means to estimate sigma instead of the traditional range method. Tool monitoring data from multiple CD metrology tools are reported and compared against control limits calculated by the traditional approach, engineering limits, and the suggested approach. The data indicate that the suggested approach is the most accurate of the three solutions.
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