Nonlinear filtering for real-time sensing of patterned wafers

This thesis is concerned with nonlinear filtering for real-time in situ estimation of the evolving feature geometry of patterned semiconductor wafers undergoing plasma etching. The key difficulty of this problem is that the computational complexity of the observation model is so high that standard techniques from nonlinear estimation and filtering cannot be applied.; We propose a convex optimization based nonlinear filtering algorithm that uses a sampled version of the observation model. It is shown that the proposed algorithm generates the maximum a posteriori probability estimates in an ideal case; in general, the algorithm is shown to yield bounded error if the disturbances are small and bounded, and if the observations are redundant. Experimental results are presented to demonstrate that the algorithm is capable of accurate real-time estimation of patterned wafer parameters in a plasma etching process with optical observation.