Shape-based optimal estimation and design of curve evolution processes with application to plasma etching

Considers the problem of determining a finite number of discrete parameters appearing in a nonlinear partial differential equation describing a curve evolution process. The method is applied to the plasma etching of thin films for semiconductor manufacturing. Results are obtained within the mathematical framework of level set methods. Here, the evolution of the curve under study is captured through the evolution of a level set function. The underlying physics of the process are completely contained in a scalar function called the speed function. The degree of difficulty of treating the evolution equation depends on the functional dependencies of the speed function. The paper presents optimal estimation and design techniques based on analytical gradient computations for a class of position and orientation dependent speed functions. The technique is demonstrated on a plasma etching model taken from the literature. Only simulation results are presented, but the model under study has been shown to reproduce experimental data with reasonable accuracy. In the estimation problem, parameters in the model are fit to best match the feature shape measured in experiments. In the optimal design problem, parameter values are selected to most closely attain a desired feature shape.