Tackling systematic/random variations while matching process chambers

by Debra Vogler, Senior Technical Editor, Solid State Technology

[Editor’s Note: Last week WaferNEWS highlighted several topics discussed at the recent ISMI Symposium on Manufacturing Effectiveness, including litho “hot spots,” cleaning wafer chucks, detecting/preventing ESD events, and the ongoing debate over 450mm wafers. This week we focus on another ISMI presentation: the application of multivariate analysis to manage fab processes, specifically matching chambers.]

Few fab management practices are more “in the trenches” than using mathematics and statistics to investigate and solve real-life problems. One such technique, multivariate analysis (MVA), was discussed by Bruno Michel of MKS Instruments, specifically comparing two ashing chambers that were supposed to be matched, but whose output showed differences 1.

MVA is the best tool for chamber comparison because it not only identifies the differences between chambers but also allows one to see “the hidden story” in the data, Michel said. It is specifically well suited to differentiating between the systematic and random variations in large quantities of data. He pointed out that for a specific semiconductor process in which large numbers of parameters are being monitored, only a few physical processes occur, so many of the parameters correlate — this correlation creates structure in “measurement space.” (Diane Michelson, a member of ISMI’s Technical Staff in Statistical Methods and session chair, explained the concept of measurement space to WaferNEWS as the multidimensional space of all possible measurements on all parameters.)

To illustrate the way correlated data “looks” compared to uncorrelated data, Michel presented two sample scatter plots (see Fig. 1). By evaluating the resulting scatter plot for a given process chamber, one can see if its behavior shows correlation, or if the process parameter of interest exhibits some other kind of behavior, bimodal perhaps.

Figure 1. Sample scatter plots showing a) uncorrelated data, and b) correlated data.

As with all mathematical methods, the devil is in the beginning assumptions. For chamber matching, that means starting with a known good process. Michel explained that the model of a known good process enables the evaluation of subsequent processes with just two statistics: Hotelling’s T2, an indicator of how well the wafer conforms to the model, and DModX, representing the residual error in the model. In Michel’s example of matching two ashing chambers, the scatter plot for chamber B actually showed greater correlation than the scatter plot for chamber A, but the DModX statistic for chamber B indicated a significant deviation (see Fig. 2).

Figure 2. Example of chamber matching statistics/data for a specific ashing “chamber B.”

After scatter plot evaluation, results of the two statistics (Hotelling’s T2 and DModX) are generated and outliers in the process data examined. From the scatter plot and statistics, the root causes of the anomalous behavior can be identified — which process parameter is the cause of a difference in processes between “identical” chambers (e.g., throttle speed, gas flow current, temperature current, lamp current, etc.). Once pinpointed, the process parameter(s) causing the “non-identical” performance between the two chambers can be adjusted.

The goal of chamber matching is to have two chambers output similar wafers, Jim Chalmers, paper co-author and product manager in MKS Instruments’ control and information technology division, explained to WaferNEWS. “MVA can find and identify the differences between two chambers, as well as how those differences did or did not impact the wafers,” he said. “In the event that two chambers shown by MVA to be unmatched produce similar and acceptable wafers, additional measures would be needed to further match the chambers.” Any of the tool characterization processes currently used by wafer fabs would be applicable in this case.

Commenting after the event on the efficacy of MVA, Michel told WaferNEWS that MVA offers “a tool that demonstrates the capability to identify wafer processing problems with only run time data.” Previously, wafer processing problems were found only with post-metrology data, long after the processing issue occurred, he explained. “Furthermore, MVA has also easily and quickly identified root causes of these problems.”

ISMI’s Michelson noted that MVA’s usage in wafer fabs “ranges from none at all, to outstanding examples of automation,” including advanced process control, chamber matching, and predictive and preventative maintenance (PPM), among others.

A number of speakers at the statistical methods session lamented the reluctance of many fab personnel to use more advanced statistical methods, particularly MVA. “The reasons why it [MVA] is not adopted in some fabs are varied,” Michelson told WaferNEWS, citing a lack of software integration, difficulty in interpreting multivariate control charts — or a perception that if a parameter’s measurements are within limits, the process must be running well regardless of its correlation with other parameters. “Each of these issues is currently being addressed, either through software and equipment suppliers, or through training of equipment and process engineers to the methods,” she noted.

MVA is a component of several ISMI projects, including those supporting PPM and equipment chamber matching (ECM), Michelson noted, adding that public information is available via papers presented at every AEC/APC symposium. — D.V.

1 “Multivariate Analysis in Semiconductor Chamber Matching,” B. Michel, L. Hendler,. S. Diamant, J. Chalmers; 4th ISMI Symposium on Manufacturing Effectiveness, 10/24-25/07, Austin, TX US.


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