Performance Synthesis of Multiple Input−Multiple Output (MIMO) Exponentially Weighted Moving Average (EWMA) Run-to-Run Controllers with Metrology Delay

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The increased demand on throughput in semiconductor manufacturing often leads to a lag between the processing and metrology of wafers at a manufacturing step. This metrology lag results in a detrimental impact on the performance of a process under run-to-run control. This paper analyzes the performance of processes under exponentially weighted moving average (EWMA) run-to-run control by considering time-delayed closed-loop processes with mismatch between the process and the process model. The closed-loop performance bounds for EWMA controlled processes with delays of 0−2 runs are derived using modified stability analysis tools. Several simulations are provided to illustrate the importance of considering metrology delay and plant−model mismatch explicitly in controller performance and tuning.