Spatial batch optimal design based on self-learning gaussian process models for LPCVD processes

doi:10.1016/j.cjche.2015.11.013

Chin.J.Chem.Eng. ›› 2015, Vol. 23 ›› Issue (12): 1958-1964.DOI: 10.1016/j.cjche.2015.11.013

Previous Articles Next Articles

Spatial batch optimal design based on self-learning gaussian process models for LPCVD processes

Pei Sun, Lei Xie, Junghui Chen

State Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China

Received:2015-06-03 Revised:2015-07-19 Online:2016-01-19 Published:2015-12-28
Contact: Lei Xie, Junghui Chen
Supported by:
Supported by the National High Technology Research and Development Program of China (2014AA041803) and the National Natural Science Foundation of China (61320106009).

Spatial batch optimal design based on self-learning gaussian process models for LPCVD processes

Pei Sun, Lei Xie, Junghui Chen

State Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China

通讯作者: Lei Xie, Junghui Chen
基金资助:
Supported by the National High Technology Research and Development Program of China (2014AA041803) and the National Natural Science Foundation of China (61320106009).

Abstract

Abstract: Low pressure chemical vapor deposition (LPCVD) is one of themost important processes during semiconductor manufacturing. However, the spatial distribution of internal temperature and extremely few samples makes it hard to build a good-quality model of this batch process. Besides, due to the properties of this process, the reliability of the model must be taken into consideration when optimizing the MVs. In this work, an optimal design strategy based on the self-learning Gaussian processmodel (GPM)is proposed to control this kind of spatial batch process. The GPMis utilized as the internalmodel to predict the thicknesses of thin films on all spatial-distributed wafers using the limited data. Unlike the conventional model based design, the uncertainties of predictions provided by GPM are taken into consideration to guide the optimal design of manipulated variables so that the designing can be more prudent. Besides, the GPM is also actively enhanced using as little data as possible based on the predictive uncertainties. The effectiveness of the proposed strategy is successfully demonstrated in an LPCVD process.

Key words: Batchwise, LPCVD, Transport processes, Spatial distribution, Gaussian process model, Optimal design

摘要： Low pressure chemical vapor deposition (LPCVD) is one of themost important processes during semiconductor manufacturing. However, the spatial distribution of internal temperature and extremely few samples makes it hard to build a good-quality model of this batch process. Besides, due to the properties of this process, the reliability of the model must be taken into consideration when optimizing the MVs. In this work, an optimal design strategy based on the self-learning Gaussian processmodel (GPM)is proposed to control this kind of spatial batch process. The GPMis utilized as the internalmodel to predict the thicknesses of thin films on all spatial-distributed wafers using the limited data. Unlike the conventional model based design, the uncertainties of predictions provided by GPM are taken into consideration to guide the optimal design of manipulated variables so that the designing can be more prudent. Besides, the GPM is also actively enhanced using as little data as possible based on the predictive uncertainties. The effectiveness of the proposed strategy is successfully demonstrated in an LPCVD process.

关键词: Batchwise, LPCVD, Transport processes, Spatial distribution, Gaussian process model, Optimal design

Pei Sun, Lei Xie, Junghui Chen. Spatial batch optimal design based on self-learning gaussian process models for LPCVD processes[J]. Chin.J.Chem.Eng., 2015, 23(12): 1958-1964.

Pei Sun, Lei Xie, Junghui Chen. Spatial batch optimal design based on self-learning gaussian process models for LPCVD processes[J]. Chinese Journal of Chemical Engineering, 2015, 23(12): 1958-1964.

References

[1] T.F. Edgar, S.W. Butler,W.J. Campbell, C. Pfeiffer, C. Bode, S.B.Hwang, K. Balakrishnan, J. Hahn, Automatic control inmicroelectronicsmanufacturing: Practices, challenges, and possibilities, Automatica 36 (11) (2000) 1567-1603.

[2] J.-X. Xu, Y. Chen, T.H. Lee, S. Yamamoto, Terminal iterative learning control with an application to RTPCVD thickness control, Automatica 35 (9) (1999) 1535-1542.

[3] J.H. Lee, K.S. Lee, Iterative learning control applied to batch processes: An overview, Control. Eng. Pract. 15 (10) (2007) 1306-1318.

[4] T. Sato, Spectral emissivity of silicon, Jpn. J. Appl. Phys. 6 (3) (1967) 339.

[5] N. Cressie, C.K. Wikle, Statistics for spatio-temporal data, Wiley.com, 2011.

[6] A. Grancharova, J. Kocijan, T.A. Johansen, Explicit stochastic predictive control of combustion plants based on Gaussian process models, Automatica 44 (6) (2008) 1621-1631.

[7] T. Holsclaw, B. Sansó, H.K. Lee, K. Heitmann, S. Habib, D. Higdon, U. Alam, Gaussian process modeling of derivative curves, Technometrics 55 (1) (2013) 57-67.

[8] K. A?man, J. Kocijan, Application of Gaussian processes for black-box modelling of biosystems, ISA Trans. 46 (4) (2007) 443-457.

[9] K. A?man, J. Kocijan, Dynamical systems identification using Gaussian processmodels with incorporated local models, Eng. Appl. Artif. Intell. 24 (2) (2011) 398-408.

[10] G. Gregor?i?, G. Lightbody, Nonlinear system identification: From multiple-model networks to Gaussian processes, Eng. Appl. Artif. Intell. 21 (7) (2008) 1035-1055.

[11] G. Gregor?i?, G. Lightbody, Gaussian process approach for modelling of nonlinear systems, Eng. Appl. Artif. Intell. 22 (4) (2009) 522-533.

[12] M.P. Deisenroth, C.E. Rasmussen, J. Peters, Gaussian process dynamic programming, Neurocomputing 72 (7) (2009) 1508-1524.

[13] P. Gao, A. Honkela, M. Rattray, N.D. Lawrence, Gaussian process modelling of latent chemical species: Applications to inferring transcription factor activities, Bioinformatics 24 (16) (2008) i70-i75.

[14] T. Chen, B.Wang, Bayesian variable selection for Gaussian process regression: Application to chemometric calibration of spectrometers, Neurocomputing 73 (13) (2010) 2718-2726.

[15] A.F. Hernandez, M.A. Grover, Stochastic dynamic predictions using Gaussian process models for nanoparticle synthesis, Comput. Chem. Eng. 34 (12) (2010) 1953-1961.

[16] C. Rasmussen, C. Williams, Gaussian processes for machine learning, MIT Press, Cambridge, MA, 2006.

[17] T.A. Badgwell, T.F. Edgar, I. Trachtenberg, Modeling and scale-up of multiwafer LPCVD reactors, AIChE J. 38 (6) (1992) 926-938.

[18] K.F. Roenigk, K.F. Jensen, Analysis ofmulticomponent LPCVD processes deposition of pure and in situ doped Poly-Si, J. Electrochem. Soc. 132 (2) (1985) 448-454.

[19] C. Vinante, P. Duverneuil, J.P. Couderc, A two dimensional model for LPCVD reactors hydrodynamics and mass transfer, J. Phys. Colloq. 50 (C5) (1989) C5-35-C5-43.

[20] Q. He, S.J. Qin, A.J. Toprac, Computationally efficientmodeling ofwafer temperatures in a low-pressure chemical vapor deposition furnace, IEEE Trans. Semicond. Manuf. 16 (2) (2003) 342-350.

[21] C.K. Williams, Prediction with Gaussian processes: From linear regression to linear prediction and beyond, Learning in graphical models, Springer, Netherlands 1998, pp. 599-621.

[22] R. Murray-Smith, D. Sbarbaro, C.E. Rasmussen, A. Girard, Adaptive, cautious, predictive control with Gaussian process priors, 13th IFAC symposium on system identification, Netherlands, 2003.

[23] C.-Y. Chen, K.-C. Chang, C.-C. Lu, G.-B. Wang, Study of high-tech process furnace using inherently safer design strategies (II). Deposited film thickness model, J. Loss Prev. Process Ind. 26 (1) (2013) 225-235.

Spatial batch optimal design based on self-learning gaussian process models for LPCVD processes

Spatial batch optimal design based on self-learning gaussian process models for LPCVD processes

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 14

Recommended Articles

Metrics

Comments

[1]	Borui Liu, Tao Zhang, Yi Zheng, Kailong Li, Hui Pan, Hao Ling. A dynamic control structure of liquid-only transfer stream distillation column [J]. Chinese Journal of Chemical Engineering, 2023, 59(7): 135-145.
[2]	Danlei Chen, Yiqing Luo, Xigang Yuan. Cascade refrigeration system synthesis based on hybrid simulated annealing and particle swarm optimization algorithm [J]. Chinese Journal of Chemical Engineering, 2023, 58(6): 244-255.
[3]	Jixiang Liu, Xin Zhou, Gengfei Yang, Hui Zhao, Zhibo Zhang, Xiang Feng, Hao Yan, Yibin Liu, Xiaobo Chen, Chaohe Yang. Conceptual carbon-reduction process design and quantitative sustainable assessment for concentrating high purity ethylene from wasted refinery gas [J]. Chinese Journal of Chemical Engineering, 2023, 57(5): 290-308.
[4]	Xinqiang You, Kai Zhao, Ling Li, Ting Qiu. Ionic liquids as entrainer in extractive distillation for effectively separating 1-propanol–water azeotropic mixture [J]. Chinese Journal of Chemical Engineering, 2022, 49(9): 224-233.
[5]	Jun Zhang, Qin Wang, Weifeng Shen. Hyper-parameter optimization of multiple machine learning algorithms for molecular property prediction using hyperopt library [J]. Chinese Journal of Chemical Engineering, 2022, 52(12): 115-125.
[6]	Danlei Chen, Yiqing Luo, Xigang Yuan. Refrigeration system synthesis based on de-redundant model by particle swarm optimization algorithm [J]. Chinese Journal of Chemical Engineering, 2022, 50(10): 412-422.
[7]	Jiangyuan Qu, Nana Qi, Kai Zhang, Lifeng Li, Pengcheng Wang. Wet flue gas desulfurization performance of 330 MW coal-fired power unit based on computational fluid dynamics region identification of flow pattern and transfer process [J]. Chinese Journal of Chemical Engineering, 2021, 29(1): 13-26.
[8]	Xutao Hu, Hao Qin, Biao Hu, Hongye Cheng, Lifang Chen, Zhiwen Qi. A rate-based method for dynamic analysis and optimal design of reactive extraction: n-Hexyl acetate esterification as an example [J]. Chinese Journal of Chemical Engineering, 2020, 28(1): 76-83.
[9]	Aihong Li, Changzhan Liu, Zhiyong Liu. A heuristic design method for batch water-using networks of multiple contaminants with regeneration unit [J]. Chinese Journal of Chemical Engineering, 2019, 27(5): 1103-1112.
[10]	Tao Yang, Yiqing Luo, Yingjie Ma, Xigang Yuan. Optimal synthesis of compression refrigeration system using a novel MINLP approach [J]. Chin.J.Chem.Eng., 2018, 26(8): 1662-1669.
[11]	Lin Wang, Xianzuo Kong, Yongsheng Qi. Optimal design for split-and-recombine-type flow distributors of microreactors based on blockage detection [J]. , 2016, 24(7): 897-903.
[12]	Jimin Wang, Shen Lan, Tao Chen, Wenke Li, Huaqiang Chu. Numerical simulation and combination optimization of aluminum holding furnace linings based on simulated annealing [J]. Chin.J.Chem.Eng., 2015, 23(6): 880-889.
[13]	Binghu Li, Kuaikuai Guo, Changsheng Liu. Effect of PSA tin plating process on trace lead in tin coating [J]. Chin.J.Chem.Eng., 2015, 23(10): 1716-1720.
[14]	WU Xianli, HU Yangdong, WU Lianying, LI Hong. Model and Design of Cogeneration System for Different Demands of Desalination Water, Heat and Power Production [J]. Chin.J.Chem.Eng., 2014, 22(3): 330-338.