(78b) Online Soft Sensor Adaptation of Latent Projection Growing Structure Multiple Model Systems

Online Soft Sensor Adaptation of Latent Projection Growing Structure Multiple Model Systems

Bo Lu^a, John Stuber^b, Thomas F. Edgar^a
a McKetta Department of Chemical Engineering, ^b Texas Instruments Inc.

The University of Texas at Austin, 1 University Station C0400, Austin, TX 78712
Email: edgar@che.utexas.edu

Traditional semiconductor fabrication relies on run-to-run control with external metrology measurements for controller feedback. Virtual metrology is analogous to soft sensor, which aims to predict end-of-batch quality measurements using trace data and other end-point readings from semiconductor unit operations. Based on the predictions, control engineers can then make the decision on whether to perform additional metrology sampling or apply feed-forward adjustment in subsequent processing steps (Lu et al. 2014). Divide-and-conquer based data-driven modeling have been used in virtual metrology to better approximate nonlinearities, multiple steady states, and state transitions in the underlying process. Growing structure multiple model systems (GSMMS) uses a growing self-organizing map (GSOM) to divide the input space into discrete subspaces that can then be modeled locally (Liu et al. 2009). Previous work focused on extending GSMMS to use latent projection based models using PLS or PCA. The advantages of GSMMS over alternatives such as regression trees, multimode PLS (Dunia et al. 2012) or Gaussian Mixture (Yu and Qin 2008) based approaches are the lower degrees of freedom and more efficient use of training data. Since GSMMS adapts the complexity of the GSOM during training, there are less parameters to be specified. In addition, local model training uses data from an entire “neighborhood” to improve smoothness across local model boundaries.

In this work, an online adaptive update scheme for the latent projection GSMMS has been developed. Unlike previous multiple model systems, where the online adaptation mostly focus on local model coefficient updates, the proposed update algorithm will adapt all components of the GSMMS system to potential process changes. First, the local model coefficients for each node are updated recursively. Second, the growing self-organizing map nodes are shifted to adapt changes in the clustering layer. Lastly, additional nodes can be appended to the existing model system if a previously unseen process condition occurs at run-time. The proposed online adaptation mechanism has been tested on a simulated dataset and an industrial dataset. Using the industrial dataset, potential savings and reduction in necessary measurements were calculated to demonstrate the tangible economic benefits of the proposed approach.

References

Dunia, Ricardo, Thomas F. Edgar, Terry Blevins, and Willy Wojsznis. 2012. “Multistate Analytics for Continuous Processes.” Journal of Process Control 22: 1445–56.

Liu, Jianbo, Dragan Djurdjanovic, Kenneth a. Marko, and Jun Ni. 2009. “A Divide and Conquer Approach to Anomaly Detection, Localization and Diagnosis.” Mechanical Systems and Signal Processing 23(8): 2488–99. http://linkinghub.elsevier.com/retrieve/pii/S0888327009001873 (March 8, 2012).

Lu, Bo, John Stuber, and Thomas F. Edgar. 2014. “Integrated Online Virtual Metrology and Fault Detection in Plasma Etch Tools.” Industrial & Engineering Chemistry Research 53(13): 5172–81. http://pubs.acs.org/doi/abs/10.1021/ie401448d.

Yu, Jie, and S Joe Qin. 2008. “Multimode Process Monitoring with Bayesian Inference-Based Finite Gaussian Mixture Models.” AIChE Journal 54(7): 1811–29.