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Multiple-input single-output (MISO) ridge-optimizing quality controller for semiconductor manufacturing processes

This paper introduces an integrated run-to-run (R2R) multiple-input single-output control framework for semiconductor manufacturing processes. The controller, termed a ridge-optimizing quality controller (ROQC), can act as a recipe regulator between batches of silicon wafers during fabrication steps provided the equipment mechanism can be adequately represented by a quadratic polynomial of critical process factors, coupled with a dynamic process drifting that models equipment ageing. In each run, the process parameters in the underlying model are updated on-line using the recursive least squares method whenever the most recent controlled output is available, and subsequently a global optimization algorithm developed is employed to locate the optimum set-points inside the acceptability region of controllable factors for the execution of next run. The main components of ROQC are shown and its control performance is presented. Typical applications of R2R control to Chemical Mechanical Planarization in semiconductor manufacturing are demonstrated through simulated processes founded on the real equipment models to illustrate the proposed controller. It reveals from the experimental results that ROQC can provide suitable control actions albeit the process exhibits complicated, non-linear interaction behaviour between adjustable recipe variables. An original posterior filter termed ‘predictor corrector’ is augmented in ROQC enabling one to compensate for the disturbances of deterministic drift, first-order moving average MA(1), integrated first-order moving average IMA(1, 1) and abrupt mean shift that have frequently been found to occur in common control practice.