An optimal neural network plasma model: a case study

Artificial neural networks, particularly backpropagation neural network (BPNN), have recently been applied to model various plasma processes. Developing BPNN model, however, is complicated by the presence of several adjustable factors whose optimal values are initially unknown. These may include initial weight distribution, hidden neurons, gradient of neuron activation function, and training tolerance. A methodology is presented to optimize various factor effects, which was accomplished by implementing genetic algorithm (GA) on the best models. Particular emphasis was placed on a qualitative measure of initial weight distribution, whose magnitude and directionality were varied. Interactions between factors were examined by means of a 24 factorial experiment. Parametric effect analysis revealed the dissimilarity between the best and average prediction characteristics. Both gradient and initial weight distribution exerted a conflicting effect on both average and best performances. GA-optimized models exhibited about 20% improvement over the experimentally chosen best models. Further improvement of more than 30% was achieved with respect to statistical response surface models. Plasma modeled is an inductively coupled plasma, whose experimental data were collected with Langmuir probe from an etch equipment capable of processing 200-mm wafers.