Process Performance Prediction for Chemical Mechanical Planarization (CMP) by Integration of Nonlinear Bayesian Analysis and Statistical Modeling

Chemical mechanical planarization (CMP) process has been widely used in the semiconductor manufacturing industry for realizing highly finished (Ra $\sim 1$ nm) and planar surfaces (WIWNU $\sim 1\hbox{\%}$, thickness standard deviation (SD) $\sim 3$ nm) of in-process wafer polishing. The CMP process is rather complex with nonlinear and non-Gaussian process dynamics, which brings significant challenges for process monitoring and control. As an attempt to address this issue, a method is presented in this paper that integrates nonlinear Bayesian analysis and statistical modeling to estimate and predict process state variables, and therewith to predict the performance measures, such as material removal rate (MRR), surface finish, surface defects, etc. As an example of performance measure, MRR is chosen to demonstrate the performance prediction. A sequential Monte Carlo (SMC) method, namely, particle filtering (PF) method is utilized for nonlinear Bayesian analysis to predict the CMP process-state and for tackling the process nonlinearity. Vibration signals from both wired and wireless vibration sensors are adopted in the experimental study conducted using the CMP apparatus. The process states captured by the sensor signals are related to MRR using design of experiments and statistical regression analysis. A case study was conducted using actual CMP processing data by comparing the PF method with other widely used prediction approaches. This comparison demonstrates the effectiveness of the proposed approach, especially for nonlinear dynamic processes.