(76a) A Novel Mixed Product Run-to-Run Control Algorithm – Dynamic Ancova Approach

Run-to-run control techniques have been widely used in semiconductor manufacturing industry. This paper presents a novel run-to-run control algorithm based on dynamic ANCOVA approach to deal with high mixed problems, i.e., many different products are manufactured in many different tools. Analysis of variance (ANOVA) is a standard statistical tool in the area of linear modeling of multi-factor systems (Montgomery, 1997). ANOVA has also been applied to semiconductor industries in many different areas such as control chart build-up (Runger, 1998) and feedback variable selections (Patterson, 2003). Analysis of covariance (ANCOVA) is a combination of regression and ANOVA. Wise (1997) implement the scheme of ANCOVA in benchmarking of multivariate statistical process control tools. The model used for control is based on the ANCOCA analysis of the system output. Specially, a dynamic term, an ARIMA model is included in the process model to characterize the unexpected disturbance such as drift, shift and/or some other unknown disturbances. It is shown from the study below that process variations can be reduced drastically by introducing the dynamic term. One important feature of the proposed method is that it has comparable performance for the products which are produced only occasionally. This makes it highly suitable for mixed product control system. A simulation example shows that this novel approach is superior to existed mixed product run-to-run control approach especially in case of low frequency products.

Keywords: dynamic ANCOVA, run-to-run control, mixed product system, semi-conductor manufacturing