Constructing a reliable neural network model for a plasma etching process using limited experimental data

Plasma etching has been widely used in the microelectronics industry to pattern submicro device geometries on silicon wafers. However, the fundamental plasma chemistry and physics in plasma etching reactors are not easy to model. Reliable empirical models for such a process are desirable for investigating the process behavior and realizing real-time control. One of the main difficulties encountered in this endeavour is that frequently very limited experimental data are available for model development for any particular apparatus. In the present work, a special artificial neural network (ANN) method is presented which shows how to develop satisfactory models even though fewer experimental data exist than there are coefficients in the ANN models. The method aims at constructing a model which can satisfy the criteria of minimum training error, maximum smoothness, and simplest network structure. Two ANN models were developed for a plasma etching reactor using CF₄/O₂ or CF₄/H₂ as a reactant that relate the manipulated and controlled variables or the manipulated and performance variables, respectively. Comparison of the predictions made by the ANN´s with those made by the second order regression models that were used as the basis of the experimental design to get the data indicated that the ANN´s predicted the process behavior more reasonably than the classical regression models when the process is operated at various operating conditions