Find Patterns in Your Data: Improving Robot Repeatability

Robot repeatability is the most important performance characteristic for a substrate handling robot. Placement repeatability is particularly important in wafer processing since it has a major impact on yield in light of the shrinking critical dimensions and increasing wafer size. As the requirement on wafer placement becomes tighter, it will be critical to identify opportunities to improve repeatability performance. This can be accomplished by making incremental design changes to the existing robots as well as by designing new high performance robots with tighter repeatability distributions. The main emphasis, it can be argued, will be on improving the repeatability of existing hardware without resorting to the challenge associated with designing and developing new robots.

The approach proposed in this note relies on the assumption that repeatability data is generated by a dynamic process, and can be treated as time series, with both spatial as well as temporal information embedded.   Time dependent content can be extracted using the Fast Fourier Transform; peaks in FFT correspond to the periodicities in the data. Spatial information is extracted using clustering. Clustering is a statistical technique frequently used to identify natural groupings in a data set. To illustrate the proposed method, we begin with the stated assumption that the repeatability data is generated by a dynamic iterative process expressed as r(n) = f(x(n), y(n)) + z(n); where n corresponds to the repeatability cycle number, r(n) is the radial distance at the nth repeatability cycle with x(n) and y(n) as the respective coordinates. z(n) is the random vector consisting of measurement, as well as randomness contained in the mechanics due to the numerous tolerances in the linkages. Assume that x(n) and y(n) are a nonlinear iterative function, known to possess periodic and random behavior. The spikes in the FFT spectra are a clear indication of the periodicity present in the data. The spatial patterns in the data are segregated using the clustering method. In clustering, one classifies objects (behaviors and attributes) that contain similar characteristics and groups them into subsets – thus objects belonging to one cluster have certain characteristics that separate them from objects belonging to the different cluster. The basic sequential algorithm applied here indicates presence of two clusters. The method was applied to repeatability data gathered by cycling a substrate handling robot. Using the type of analysis proposed, two distinct types of patterns were identified within the repeatability data, which were then further traced down via root cause analysis to certain mechanical aspects of the design. Minor design modifications were implemented that resulted in elimination of the patterns while improving repeatability.