Reduction of across-wafer CDU via constrained optimization of a multichannel PEB plate controller based on in-situ measurements of thermal time constants

As line widths approach 90nm node in volume production, post exposure bake (PEB) uniformity becomes a much larger component of the across wafer critical dimension uniformity (CDU). In production, the need for PEB plate matching has led to novel solutions such as plate specific dose offsets. This type of correction does not help across wafer CDU. Due to unequal activation energies of the critical PEB processes, any thermal history difference can result in a corresponding CD variation. The rise time of the resist to the target temperature has been shown to affect CD, with the most critical time being the first 5-7 seconds. A typical PEB plate has multi-zone thermal control with one thermal sensor per zone. The current practice is to setup each plate to match the steady-state target temperature, ignoring any dynamic performance. Using an in-situ wireless RTD wafer, it is possible to characterize the dynamic performance, or time constant, of each RTD location on the sensing wafer. Constrained by the zone structure of the PEB plate, the proportional, integral and derivative (PID) settings of each controller channel could be optimized to reduce the variations in rise time across the RTD wafer, thereby reducing the PEB component of across wafer CDU.