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In the last few years, "Run-to-Run" (R2R) control techniques have been developed and used to control various semiconductor manufacturing processes. These techniques combine response surface, statistical process control, and feedback control techniques. This paper provides a literature review of R2R control methods from a statistical and control engineering point of view. It is shown that self-tuning controllers can provide a valuable control strategy for R2R applications. In this paper we address the single-inputsingle-output (SISO) case. Two proposed self-tuning controllers compensate not only for the standard case of process shifts, but also in the case a deterministic trend and/or autocorrelation is present in the observed response (i.e., in case there exist process dynamics). In order to reduce the input variance, a control chart is added to the output and acts as a deadband.
Introduction
RUN-TO-RUN (or run-by-run) process control is the name given to a collection of statistical process control (SPC) and engineering process control (EPC) techniques recently proposed for the semiconductor industry. The term run-to-run refers to the case where a control action is taken for each batch of silicon wafers produced in a process (see, e.g., Sachs, Hu, and Ingolfsson (1991), Butler and Stefani (1994), Mozumder, Saxena, and Collins (1994)). Within-run (i.e., within batch or lot) control is exercised by automatic (PID) controllers. The R2R control action consists in varying the setpoints of the automatic controllers from run to run, in a supervisory manner, as shown in Figure 1.
Batch sizes may be as small as one wafer in some semiconductor processes. This type of controller is well-suited for processes where the cost of a run far from target is very expensive and where the cost of the control action is relatively inexpensive. In addition, there are some assumptions regarding the type of stochastic processes that may be controlled with a run-to-run controller. These are discussed below. Evidently, the rationale for such an active control policy is that the process, if not controlled, will wander or drift off-target from run to run. Otherwise, a simpler process monitoring scheme will suffice (see, e.g., Box and Kramer (1992) and Montgomery, Keats, Runger, and Messina (1994) for a recent discussion of SPC versus EPC). The assumptions behind run-to-run controllers make these techniques applicable to other short-run...