Multiplexed MPC for Multizone Thermal Processing in Semiconductor Manufacturing

It is known that a faster sampling rate allows a controller to react to unmeasurable disturbances faster. Adding feed- forward could decrease the effect of disturbance significantly, but feedback control is still required to cope with modelling errors and unknown disturbances. A variant of model predictive control (MPC), called multiplexed MPC (MMPC), has been proposed recently. The motivation for MMPC was to reduced real-time computational load and hence allow faster sampling on multivariable systems. In this brief, we report the first successful application of MMPC on a semiconductor manufacturing process. MMPC with feedforward has been demonstrated experimentally on a multizone bake plate application. While most of the temperature drop will be compensated by feedforward control, feedback provided by MMPC will cope with the errors due to warped wafers. This result is important for the semiconductor wafer baking process, because temperature nonuniformity will affect critical dimension of the wafer.