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 ~ 1 nm) and planar surfaces (WIWNU ~ 1%, thickness standard deviation (SD) ~ 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.

[1]  Scott G. Meikle,et al.  Modeling of Chemical Mechanical Polishing Processes Using a Discretized Geometry Approach , 2000 .

[2]  Margaret A. Nemeth,et al.  Applied Multivariate Methods for Data Analysis , 1998, Technometrics.

[3]  Wolfram Burgard,et al.  Robust Monte Carlo localization for mobile robots , 2001, Artif. Intell..

[4]  Fredrik Gustafsson,et al.  Particle filters for positioning, navigation, and tracking , 2002, IEEE Trans. Signal Process..

[5]  A. Doucet.  On sequential Monte Carlo methods for Bayesian filtering , 1998 .

[6]  Nando de Freitas,et al.  An Introduction to MCMC for Machine Learning , 2004, Machine Learning.

[7]  Darren B. Ward,et al.  Particle filtering algorithms for tracking an acoustic source in a reverberant environment , 2003, IEEE Trans. Speech Audio Process..

[8]  Tetsuya Homma,et al.  Low dielectric constant materials and methods for interlayer dielectric films in ultralarge-scale integrated circuit multilevel interconnections , 1998 .

[9]  Ronald J. Gutmann,et al.  Pad porosity, compressibility and slurry delivery effects in chemical- mechanical planarization: modeling and experiments , 2000 .

[10]  Joost J. Vlassak,et al.  A model for chemical–mechanical polishing of a material surface based on contact mechanics , 2004 .

[11]  Michael A. West,et al.  Combined Parameter and State Estimation in Simulation-Based Filtering , 2001, Sequential Monte Carlo Methods in Practice.

[12]  Nando de Freitas,et al.  Sequential Monte Carlo in Practice , 2001 .

[13]  Ping Hsun Chen,et al.  A chemical kinetics model to explain the abrasive size effect on chemical mechanical polishing , 2005 .

[14]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[15]  Satish T. S. Bukkapatnam,et al.  Sensor-based modeling of slurry chemistry effects on the material removal rate (MRR) in copper-CMP process , 2009 .

[16]  Frank Dellaert,et al.  A Rao-Blackwellized particle filter for EigenTracking , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[17]  Ronald J. Gutmann,et al.  Chemical processes in the chemical mechanical polishing of copper , 1995 .

[18]  Hong Hocheng,et al.  Modeling and Experimental Analysis of the Material Removal Rate in the Chemical Mechanical Planarization of Dielectric Films and Bare Silicon Wafers , 2001 .

[19]  Gottlieb S. Oehrlein,et al.  Chemical Mechanical Planarization of Copper Damascene Structures , 2000 .

[20]  Arun K. Sikder,et al.  Chemical mechanical planarization for microelectronics applications , 2004 .

[21]  Ben J. A. Kröse,et al.  Auxiliary particle filter robot localization from high-dimensional sensor observations , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[22]  Jingang Yi,et al.  On the wafer/pad friction of chemical-mechanical planarization (CMP) processes- Part II: experiments and applications , 2005 .

[23]  William Whittaker,et al.  Conditional particle filters for simultaneous mobile robot localization and people-tracking , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[24]  G. Bahar Basim,et al.  Fundamentals of Slurry Design for CMP of Metal and Dielectric Materials , 2002 .

[25]  Yongwu Zhao,et al.  A micro-contact and wear model for chemical-mechanical polishing of silicon wafers , 2002 .

[26]  I. Ali,et al.  Chemical-mechanical polishing of interlayer dielectric: a review , 1994 .

[27]  P. Fearnhead,et al.  Improved particle filter for nonlinear problems , 1999 .

[28]  Shu-Kai S. Fan.  Quality improvement of chemical-mechanical wafer planarization process in semiconductor manufacturing using a combined generalized linear modelling - non-linear programming approach , 2000 .

[29]  John A. Tichy,et al.  Material removal model for chemical–mechanical polishing considering wafer flexibility and edge effects , 2004 .

[30]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[31]  David Dornfeld,et al.  Monitoring of Ultraprecision Machining Processes , 2003 .

[32]  Craig B. Borkowf,et al.  Random Number Generation and Monte Carlo Methods , 2000, Technometrics.

[33]  Arnaud Doucet,et al.  Sequential Monte Carlo Methods to Train Neural Network Models , 2000, Neural Computation.

[34]  Sebastian Thrun,et al.  FastSLAM 2.0: An Improved Particle Filtering Algorithm for Simultaneous Localization and Mapping that Provably Converges , 2003, IJCAI.

[35]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[36]  Arun K. Sikder,et al.  Optimization of tribological properties of silicon dioxide during the chemical mechanical planarization process , 2001 .

[37]  David Dornfeld,et al.  Material removal regions in chemical mechanical planarization for submicron integrated circuit fabrication: coupling effects of slurry chemicals, abrasive size distribution,and wafer-pad contact area , 2003 .

[38]  A. Doucet,et al.  Parameter estimation in general state-space models using particle methods , 2003 .

[39]  Ronald J. Gutmann,et al.  Chemical Mechanical Planarization of Microelectronic Materials , 1997 .

[40]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

[41]  Ronald J. Gutmann,et al.  Inverse analysis of material removal data using a multiscale CMP model , 2003 .

[42]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[43]  R. Bucy,et al.  Digital synthesis of non-linear filters , 1971 .

[44]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[45]  W. Tseng,et al.  A Comparative Study on the Roles of Velocity in the Material Removal Rate during Chemical Mechanical Polishing , 1999 .

[46]  Dieter Fox,et al.  Adaptive real-time particle filters for robot localization , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[47]  Sudipta Seal,et al.  Effect of glycine and hydrogen peroxide on chemical–mechanical planarization of copper , 2003 .