Performance assessment of run-to-run control in semiconductor manufacturing based on IMC framework

Abstract

The objective of this paper is to propose a universal methodology for performance assessment of run-to-run control in semiconductor manufacturing. The slope of the linear semiconductor process model is assumed to be known or subjected to mild plant/model mismatch. Based on an internal model control framework, analytical expressions of minimum variance performance (MVP) and best achievable performance (BAP) for a series of run-to-run control schemes are derived. In the methodology, closed-loop identification is utilised as the first step to estimate the noise dynamics via routine operating data, and numerical optimisation is employed as a second step to calculate the best achievable performance bounds of the run-to-run control loops. The validity of the methodology is justified by examples of performance assessment for EWMA control, double EWMA control and RLS-LT control, even under circumstances where the processes encounter model mismatch, metrology delay and more sophisticated noises. Several essential characteristics of run-to-run control are discovered by performance assessment, and valuable advice is offered to process engineers for improving the run-to-run control performance. Furthermore, a useful application example for online performance monitoring and optimal tuning of run-to-run controller demonstrates the advantage of the methodology.

Keywords:

• performance assessment
• run-to-run control
• minimum variance performance
• best achievable performance
• IMC