Exploring EMWA charts to detect the quality shifts of raw materials

The incoming quality control of raw materials seeks to minimize variations and ensure consistent material quality. For example, silicon wafer flatness and thickness variation. With the current immersion lithography, the wafer flatness requirement at the exposure site has become very stringent due to the high numerical aperture of the exposure optics; wafer flatness and thickness variation were considered an important quality characteristic. In this paper, we focus on the small shift detection of raw material incoming control, such as wafer flatness and thickness, using exponentially-weighted moving average chart (EWMA) charts where possibly smooth out the “sequence-disordered effect”. The EWMA parameter optimizers are proposed to obtain realistic parameters and the average run length, ARL, is served as performance index of the optimizers. The realistic parameters is to minimize ARL1 and n-Steps-Ahead-Error based on baseline population, and to maximize ARL₀ to approach specified upper bound of false alarm rate. (Figure 1-2) The eCOA data illustrates our propose and several small shifts that are detected by EMWA do reflect assigned causes in supplier production line. (Figure 3-4) We demonstrate that a well-designed EWMA chart is also complementary to give a perspective of how small changes of the production line with sequence-disordered effects affect the incoming raw material control.