Batch Sequencing for Run-to-Run Control:  Application to Chemical Mechanical Polishing

This work compliments and extends the capability of the run-to-run (R2R) control by sequencing the incomings such that improved control performance can be achieved. Unlike chemical or mechanical systems, this is important for semiconductor manufacturing processes because some prior information about the incoming wafers is generally available. First, the limitation of a R2R control type of feedback system is explained. The frequency domain explanation is as follows: a negative feedback system is effective rejecting a low-frequency type of disturbance. From the feedback property, then the answer to the feed sequencing problem becomes clear: arrange the feed (which we are capable of doing) in such a way that it gives a low-frequency characteristic. Furthermore, a scalar load strength indicator is derived, and an engineering approach is taken to sort the incomings effectively. Two policies, from thin to thick (in terms of prethickness, policy L2R) and from thick to thin (policy R2L), are proposed, and they are shown to provide a better control performance over the conventional random feed policy (R). The feed sequencing problems are tested for systems with different dimensions, e.g., single input single output, single input multiple output, and multiple input multiple output systems, which include the model of an experimental chemical mechanical polishing process, and the results show that an improved control performance can be obtained simply by arranging the feeds.