Abstract
Chemical mechanical planarization (CMP) is an important operation for surface modification of wafers in semiconductor manufacturing. Productivity and quality of wafers depends strongly on the efficiency of CMP and virtual metrology (VM) is a promising tool not only to facilitate wafer-to-wafer control but also to reduce cycle time. Development of VM tools for CMP is still not a reality due to the complexity of CMP and unavailability of critical process measurements such as slurry temperature and abrasive particle size distribution in real-time. To overcome these challenges, a novel hybrid modeling framework is proposed for creating a VM solution for CMP. Physics-based models are utilized for estimating slurry temperature and mean abrasive particle size (MAPS) from sensor data. They supplement other sensor data for developing soft sensors to predict slurry temperature, MAPS, and the material removal rate (MRR). This hybrid framework is tested with about 3000 sets of published industrial sensor data. Exploratory analysis indicated two distinct regimes of operation, low and high MRR, and a strong relationship of MRR with slurry temperature and MAPS. Several machine learning (ML) algorithms such as random forest, Lasso regression and support vector machine are explored and XGBoost is found to be the best amongst them. The optimum operating conditions are determined through model-based optimization using the hybrid modeling framework and particle swarm optimization. These results suggested CMP to be carried out at the smallest MAPS to maximize MRR. This framework would be useful for building a digital twin system of CMP.
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Data availability
The raw data of the CMP process used for analysis, model development and process optimization are provided by the PHM data challenge, 2016 (PHM Society, 2016). This data is in public domain (PHM Society, 2016). The preprocessed or the clean data is available with the authors and can be made available to the requestor based on qualified request.
Abbreviations
- abs max :
-
Maximum value of particle size (µm)
- abs min :
-
Minimum value of particle size (µm)
- abs n :
-
Normalized MAPS
- AI:
-
Artificial intelligence
- AUC:
-
Area under curve
- BEOL:
-
Back end of line
- CFD:
-
Computational fluid dynamics
- CLC:
-
Closed loop control
- d j :
-
Disturbance variable
- DBN:
-
Deep belief networks
- DDMs:
-
Data driven models
- DEM:
-
Discrete element method
- E comb :
-
Combined activation energy (J/mol)
- ERT:
-
Extremely Randomized trees
- f :
-
Function of decision/disturbance variable
- FEOL:
-
Front end of line
- GBT:
-
Gradient boosting trees
- IMM:
-
Integrated metrology module
- k :
-
Thermal independent constant
- KNN:
-
K-nearest neighbors
- KPI:
-
Key performance indicators
- L2L:
-
Lot to lot
- l i :
-
Lower bounds of decision variable
- LSTM:
-
Long short-term memory
- MAE:
-
Mean absolute error
- MAPS:
-
Mean absolute particle size
- ML:
-
Machine learning
- MRR:
-
Material removal rate
- MSE:
-
Mean square error
- MTGP:
-
Multi task gaussian process
- n i :
-
Number of feature selection methods that selected ith feature
- P :
-
Pressure applied on the wafer (Pa)
- PBMs:
-
Physics based models
- PSO:
-
Particle swarm optimization
- R :
-
Universal gas constant (J/mol. K)
- R2 :
-
Coefficient of regression
- R i ,k :
-
Rank of the feature i
- RMSE:
-
Root means square error
- SAM:
-
Stand-alone metrology module
- SVM:
-
Support vector machines
- t :
-
Number of dimensional spaces
- T :
-
Slurry temperature (K)
- T max :
-
Maximum temperature (K)
- T min :
-
Minimum temperature (K)
- T n :
-
Normalized temperature
- u i :
-
Upper bounds of decision variable
- U :
-
Relative velocity (m/s)
- v j :
-
Velocity of the particle
- VM:
-
Virtual metrology
- W2W:
-
Wafer to wafer
- x i :
-
Decision variable
- x j :
-
Position of the particle
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Acknowledgements
The authors thank the management of Tata Consultancy Services for the permission to publish this paper, and Mr. K. Ananth Krishnan, Dr. Harrick Vin and Dr. Gautam Shroff for their encouragement and support.
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This study was funded by the Tata Consultancy Services Limited.
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Conceptualization: NKVN, VR; Data curation: BD; Formal Analysis and Investigation: BD, VSM; Methodology: VSM, NKVN; Supervision: VR; Validation: BD, VSM; Visualization: BD, VSM; Writing – original draft: BD; Writing – review & editing: VSM, NKVN, VR.
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Deivendran, B., Masampally, V.S., Nadimpalli, N.R.V. et al. Virtual metrology for chemical mechanical planarization of semiconductor wafers. J Intell Manuf (2024). https://doi.org/10.1007/s10845-024-02335-0
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DOI: https://doi.org/10.1007/s10845-024-02335-0