Two-dimensional pheromone propagation controller applied to run-to-run control for semiconductor manufacturing

This paper presents a new perspective on process control, called the two-dimensional pheromone propagation controller (2D-PPC), which considers the spatial information about disturbances of the process within a wafer to generate new predicted intercepts of the models for the subsequent use in time–effect controller (the exponentially weighted moving average, EWMA, in this study). The 2D-PPC assumes that the disturbances have their own behavior and affect others nearby in a wafer at a run; thus, it involves the “space-effect” among disturbances of the process at measurement positions within a wafer. The framework of the space–time controller (STC), which interlaces the time–effect controller and the space–effect 2D-PPC is constructed, and the stability analysis and intrinsic characteristics of the STC are discussed. Simulations are conducted using two-dimensional anthropogenic disturbances generated from fabrication data. The results show that the STC has better performance as compared to the conventional time–effect controllers. From implementation view point, since STC does not change the original code of time–effect controller, it can be easily implemented in the current process control loop by only adding an additional space-effect controller.