Control charts for random and fixed components of variation in the case of fixed wafer locations and measurement positions

In such processes as wafer-grinding and LPCVD, the variation within a group of measurements is traceable to various causes, and therefore, needs to be decomposed into relevant components of variation for an effective equipment monitoring and diagnosis. In this article, an LPCVD process is considered as an example, and control charting methods are developed for monitoring various fixed and random components of variation separately. For this purpose, the structure of measurement data (e.g., thickness) is described by a split-unit model in which two different sizes of experimental units (i.e., the wafer location as a whole unit and the measurement position as a split unit) are explicitly recognized. Then, control charts are developed for detecting unusual differences among fixed wafer locations within a batch and fixed measurement positions within a wafer. Control charts for the overall process average and random error variations are also developed, and the proposed method is illustrated with an example.