Plasma etching process plays a critical role in semiconductor manufacturing. Becausephysical and chemical mechanisms involved in plasma etching are extremely complicated,models supporting process control are difficult to construct. This paper uses a 35-runD-optimal design to efficiently collect data under well planned conditions for importantcontrollable variables such as power, pressure, electrode gap and gas flows ofCl2 and He andthe response, etching rate, for building an empirical underlying model. Since therelationship between the control and response variables could be highly nonlinear, ageneralized regression neural network is used to select important model variables andtheir combination effects and to fit the model. Compared with the response surfacemethodology, the proposed method has better prediction performance in training and testingsamples. A success application of the model to control the plasma etching processdemonstrates the effectiveness of the methods.

The polynomial chaos expansion (PCE) is an efficient numerical method for performing a reliability analysis. It relates the output of a nonlinear system with the uncertainty in its input parameters using a multidimensional polynomial approximation (the so-called PCE). Numerically, such an approximation can be obtained by using a regression method with a suitable design of experiments. The cost of this approximation depends on the size of the design of experiments. If the design of experiments is large and the system is modeled with a computationally expensive FEA (Finite Element Analysis) model, the PCE approximation becomes unfeasible. The aim of this work is to propose an algorithm that generates efficiently a design of experiments of a size defined by the user, in order to make the PCE approximation computationally feasible. It is an optimization algorithm that seeks to find the best design of experiments in the D-optimal sense for the PCE. This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm. The efficiency of our approach in terms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.