The stability and performance of the EWMA and double-EWMA run-to-run controllers with metrology delay
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Because of the ever-increasing demands on product quality, feedback con- trol has become a necessary enabling component in the manufacture of modern semiconductor devices. The nature of semiconductor manufacturing is such that measurements of device quality characteristics are not available during the processing of the product. Measurements are not made until after the product is processed and necessary changes to tool setting can only be made to subsequent production runs. This control scheme, termed run-to-run control, has become the cornerstone of process control in the semiconductor manufacturing industry. In addition to the ever-increasing demands on product quality, the semi- conductor manufacturing industry continues to see stringent growth in throughput requirements. Because of the demands on production throughput, it is rarely possi- ble to perform quality measurements on a batch of wafers before processing begins on the following batch of wafers. The delay between product manufacturing and product metrology coupled with inaccurate process models can lead to process in- stabilities and deterioration in controller performance. This dissertation investigates the robust stability requirements of processes controlled with EWMA and double- EWMA run-to-run controllers with delays between processing and metrology. In addition, the effects of model mismatch and metrology delay on the closed-loop performance of the EWMA and double-EWMA run-to-run controllers are derived by extending the robust stability methodology. Finally, these robust performance requirements are used to find the optimal tuning parameters for the double-EWMA controller. These tuning parameters allow for the largest model uncertainty while guaranteeing a predetermined minimum closed-loop transient performance.