An evaluation of model predictive control in run to run processing in semiconductor manufacturing

Many steps in the manufacturing of semiconductors offer no opportunity for real-time measurement of the wafer state, necessitating the use of pre-and post-process measurements of the wafer state in a run-to-run; control algorithm. The predominant algorithm in the industry is an extended form of SPC using an EWMA filter(1) to adjust a model parameter vector using the available measurements. This paper evaluates the merits of using an optimal discrete controller relying on a discrete-time constrained state-space process model that incorporates feedforward action using the pre-process measurement and feedback using the post-process measurement, accounts for the process statistics using a noise model and optimal filtering theory, and ensures integral action in the controller by estimating unmeasured disturbances. Comparisons to the EWMA algorithm are presented using simulations based on actual plant data from a chemical-mechanical polishing application. The polish process is particularly suitable for the application of such a controller because of the natural method the controller provides for incorporating unmeasured disturbances, like pad and slurry changes, in the control action.