Modeling of a plasma processing machine for semiconductor wafer etching using energy-functions-based neural networks

The complex processing of plasma etching and deposition is highly nonlinear and its modeling is intractable by analytical basic-principles techniques. Neural network approaches have shown initial success for specific plasma processes in extracting implicit relations/models based on input-output measurements. The resulting modeling techniques naturally depend on the neural structure, the adopted learning algorithms, and the specific plasma process and machine. We describe a plasma processing machine designed and in operation at Michigan State University, East Lansing, which has been equipped with select sensing devices. The machine exhibits a hysteresic nonlinearity in the desirable processing modes of operation. The experimental data characterize a testbed plasma etching process using Argon gas with control inputs including incident microwave power, pressure, and cavity size. The internal states and the outputs include reflected power, electric field, and ion density. We employ several tailored networks with novel learning algorithms derived from functions that include the polynomial and the exponential energy functions. It is shown that the learning algorithms enable fast and satisfactory convergence of parameters (weights and biases) in several scenarios of modeling and generalizing the input-state-output relations of the plasma process