Dynamic Support Vector Regression Control System for Overlay Error Compensation With Stochastic Metrology Delay

摘要

This study aims to develop a robust monitoring system for advanced control and compensation of the overlay errors based on $oldsymbol {epsilon }$ -insensitive support vector regression (SVR), considering metrology delay. The proposed $oldsymbol {epsilon }$ -insensitive SVR control system has the ability to solve quadratic optimization problems in real settings. To investigate the consistency and reliability of the proposed algorithm, a simulation study based on empirical data was conducted to validate the solution quality enhancement by the proposed approach. The stability of the system under metrology delay was investigated when Lyapunov stability function takes place as the kernel function of the $oldsymbol {epsilon }$ -insensitive SVR optimization system. For sensitivity analysis, we compared and analyzed the effect of noise and time-varying metrology delay, within an online process with a simulation study based on empirical data. This approach can effectively reduce the misalignment of the overlay errors through the self-tuning process of $oldsymbol {epsilon }$ -insensitive SVR and provide real-time decision aid for process engineers. Note to Practitioners-In practice, there are dynamic metrology delays that have not been adequately addressed. This study developed a robust monitoring system that can consider metrology delay for advanced control and effective compensation of the overlay errors. A study based on empirical data has validated the practical viability of the proposed approach. Indeed, the proposed algorithm can obtain a high degree of reliability for the measurement data in the complicated semiconductor fabrication process. Indeed, the developed solution is implemented in real practice.