Practical issues in run by run process control

Several works have described the implementation of systems for the run by run (RbR) control of semiconductor fabrication processes. In this paper, we consider algorithmic issues not often discussed arising out of our experience in the RbR control of chemical mechanical polishing (CMP). These issues include, first, limits on multiple input variables (machine settings). Such constraints must be implemented efficiently, and we compare a fast heuristic-based constraint method against a full optimization approach. Second, an input weight method enables the process engineer to manage which input parameters should be more readily modified and which should be changed less. Third, we have found that rounding off of suggested recipes before use on equipment (because of limited granularity in machine settings) can degrade the operational results compared to those ideally expected. We describe a heuristic that handles the quantization of input variables so as to improve the model based recipes suggested by the controller. This heuristic avoids the computational implication of a full integer optimization problem. Finally, we discuss methods for the selection of key controller parameters (e.g. the "forgetting factor" in an exponentially weighted moving average controller). Together, these and similar practical barriers must be understood and solved in order to have a usable run by run control strategy. These extensions to the MIT RbR algorithms have been implemented and successfully demonstrated in the control of CMP processes.