Using LDA with on-line experiment methods for coping with changes in MIMO dynamic model

Many semiconductor processes have the major problem that die-level signature profiles often look completely different on different devices. During ‘in-parallel’ and ‘in-series’ manufacturing control procedures, equipment frequently suffer ageing and tool-wearing effects that induce control model changes and generate unstable control. Therefore, if a control system does not compensate for this variation, the next device will not carry out the required follow-up process control. To solve this problem, we propose a novel control framework that integrates the concepts of self-tuning control, on-line experiments, and linear discriminant analysis (LDA). In this paper, LDA with self-tuning control is used to evaluate process changes and adjust the process recipe. When the system determines that the process has generated a large change, the system applies the design-of-experiment concept continuously to collect process data over an expanded experimental range and uses these data with the least squares error (LSE) method to estimate new model parameters. The proposed control strategy then uses the minimized-total-cost principle and applies a trust-region algorithm to obtain a recipe for the next period. Simulation studies show that the proposed system is able to satisfy the control requirement precisely. Finally, a relevant semiconductor multiple-input multiple-output (MIMO) model is used to illustrate the necessary control procedure for verifying the practicability of the proposed system in a MIMO dynamic process.