Modeling plasma equipment using neural networks

Equipment plasma has been modeled semi-empirically using neural networks in conjunction with statistical experimental design. A 3/sup 3/ factorial design was employed to characterize the plasma, in which the variables that were varied include a source power, pressure, and Ar flow rate. As a test data for model validation, 16 experiments were additionally conducted. A total of six plasma attributes were modeled, which include electron density, electron temperature, and plasma potential as well as their spatial uniformities. A planar, inductively coupled plasma was generated in a multipole plasma etch equipment and Langmuir probe was utilized for data collection. Root mean-squared prediction errors measured on the test data are 0.323 (10/sup 11//cm/sup 3/), 0.267 (eV) and 1.141 (V) for electron density, electron temperature, and plasma potential, respectively. Comparisons with a statistical response surface model (RSM) revealed that neural network models are more accurate by an improvement of more than 25% in prediction performance. A similar level of prediction accuracy was also achieved in modeling spatial uniformity data. Consequently, neural networks demonstrated much better prediction capabilities over RSM in modeling complex equipment plasma.