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 subdomains 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.