A comparative analysis of run-to-run control algorithms in the semiconductor manufacturing industry

A number of algorithms have been developed that are applicable to the run-to-run control of semiconductor manufacturing processes. The algorithm implementations include the linear approximation multivariate 'Gradual Mode' (GM) controller, a time-based extended GM (GMt), the Optimizing Adaptive Quality Controller (OAQC), and the Knowledge-based Interactive Run-to-run Controller (KIRC). Research and experimentation in process control in the industry to-date has revealed that no single algorithm is sufficiently robust to cover the entire domain of process control for most tools. Indeed the optimal control solution is a multi-branch approach to control that provides for the complementary utilization of a number of control algorithms, with the various algorithms utilized in sub-domains in which they are 'best' suited to provide control advice. Unfortunately this ideal solution cannot be realized because very little information is available on the suitable sub-domains of applicability of the various algorithms. This paper addresses this issue by providing a comparative analysis of a number of run-to-run control algorithms. Each algorithm is described so as to provide insight into its potential use in run-to-run control. A comparative study of the algorithms is then presented; comparison criteria include stability and ability to control in the face of noise and drift of linear and full-quadratic processes. Although the data presented does not represent an exhaustive comparison of the alternatives, it provides information that can be utilized to realize an effective multi-branch, multi-algorithm run-to-run control strategy.