Predictive modeling of material removal rate in chemical mechanical planarization with physics-informed machine learning

Abstract Chemical mechanical planarization (CMP) is a high-precision and complex manufacturing process that removes material with chemical and mechanical forces in order to achieve highly planar surfaces. Significant research efforts have been devoted to developing physics-based and data-driven approaches to predicting the material removal rate (MRR) in the CMP process. Both physics-based and data-driven methods have advantages and disadvantages. A novel physics-informed machine learning approach is introduced to combine a physics-based model of MRR in CMP with a data-driven model of MRR in CMP. The physics-based model takes into account the contact between a polishing pad and abrasives and the contact between abrasives and a wafer. The data-driven model trained by a machine learning algorithm predicts the asperity radius and asperity density of the polishing pad using the polishing pad wear and conditioner wear estimated by the physics-based model. The predicted asperity radius and asperity density of the polishing pad are then used to estimate MRR in CMP. Experimental data collected from a CMP tool under varying operating conditions are used to train and validate the predictive model. Experimental results have shown that the physics-informed machine learning method is capable of predicting MRR in CMP with high accuracy.

[1]  J. Greenwood,et al.  Contact of nominally flat surfaces , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  Abhijit Chandra,et al.  Performance and modeling of paired polishing process , 2016 .

[3]  Ki-Hyun Park,et al.  Pad roughness variation and its effect on material removal profile in ceria-based CMP slurry , 2008 .

[4]  Jongwon Seok,et al.  An integrated material removal model for silicon dioxide layers in chemical mechanical polishing processes , 2009 .

[5]  Ki-Hyun Park,et al.  Mathematical modeling of CMP conditioning process , 2007 .

[6]  Leonard Borucki,et al.  Mathematical modeling of polish-rate decay in chemical-mechanical polishing , 2002 .

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

[8]  Yebing Tian,et al.  An analytical investigation of pad wear caused by the conditioner in fixed abrasive chemical–mechanical polishing , 2015 .

[9]  David Dornfeld,et al.  Material removal mechanism in chemical mechanical polishing: theory and modeling , 2001 .

[10]  J. Warnock,et al.  A two-dimensional process model for chemimechanical polish planarization , 1991 .

[11]  Ranga Komanduri,et al.  Process-Machine Interaction (PMI) Modeling and Monitoring of Chemical Mechanical Planarization (CMP) Process Using Wireless Vibration Sensors , 2014, IEEE Transactions on Semiconductor Manufacturing.

[12]  J. Barbera,et al.  Contact mechanics , 1999 .

[13]  Dazhong Wu,et al.  Prediction of Material Removal Rate for Chemical Mechanical Planarization Using Decision Tree-Based Ensemble Learning , 2019, Journal of Manufacturing Science and Engineering.

[14]  Seong H. Kim,et al.  A mathematical model for chemical–mechanical polishing based on formation and removal of weakly bonded molecular species , 2003 .

[15]  F. W. Preston The Theory and Design of Plate Glass Polishing Machines , 1927 .

[16]  J. Friedman Greedy function approximation: A gradient boosting machine. , 2001 .

[17]  Robert X. Gao,et al.  A deep learning-based approach to material removal rate prediction in polishing , 2017 .

[18]  P. Kramer,et al.  A theory of pad conditioning for chemical-mechanical polishing , 2004 .

[19]  Ranga Komanduri,et al.  Process Performance Prediction for Chemical Mechanical Planarization (CMP) by Integration of Nonlinear Bayesian Analysis and Statistical Modeling , 2010, IEEE Transactions on Semiconductor Manufacturing.

[20]  Bernard Zenko,et al.  Is Combining Classifiers with Stacking Better than Selecting the Best One? , 2004, Machine Learning.

[21]  Pavan Karra,et al.  Prediction of Scratch Generation in Chemical Mechanical Planarization , 2008 .

[22]  R. Komanduri,et al.  Nonlinear Sequential Bayesian Analysis-Based Decision Making for End-Point Detection of Chemical Mechanical Planarization (CMP) Processes , 2011, IEEE Transactions on Semiconductor Manufacturing.

[23]  X. H. Zhang,et al.  Diamond disc pad conditioning in chemical mechanical planarization (CMP): A surface element method to predict pad surface shape , 2012 .

[24]  Yuan Di,et al.  Adaptive virtual metrology for semiconductor chemical mechanical planarization process using GMDH-type polynomial neural networks , 2018 .