Adaptive Neuro-Fuzzy Inference System Modeling of MRR and WIWNU in CMP Process With Sparse Experimental Data

Availability of only limited or sparse experimental data impedes the ability of current models of chemical mechanical planarization (CMP) to accurately capture and predict the underlying complex chemomechanical interactions. Modeling approaches that can effectively interpret such data are therefore necessary. In this paper, a new approach to predict the material removal rate (MRR) and within wafer nonuniformity (WIWNU) in CMP of silicon wafers using sparse-data sets is presented. The approach involves utilization of an adaptive neuro-fuzzy inference system (ANFIS) based on subtractive clustering (SC) of the input parameter space. Linear statistical models were used to assess the relative significance of process input parameters and their interactions. Substantial improvements in predicting CMP behaviors under sparse-data conditions can be achieved from fine-tuning membership functions of statistically less significant input parameters. The approach was also found to perform better than alternative neural network (NN) and neuro-fuzzy modeling methods for capturing the complex relationships that connect the machine and material parameters in CMP with MRR and WIWNU, as well as for predicting MRR and WIWNU in CMP.