{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T01:05:33Z","timestamp":1781658333734,"version":"3.54.5"},"reference-count":26,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T00:00:00Z","timestamp":1696896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The semiconductor industry is one of the most technology-evolving and capital-intensive market sectors. Effective inspection and metrology are necessary to improve product yield, increase product quality and reduce costs. In recent years, many types of semiconductor manufacturing equipments have been equipped with sensors to facilitate real-time monitoring of the production processes. These production-state and equipment-state sensor data provide an opportunity to practice machine-learning technologies in various domains, such as anomaly\/fault detection, maintenance scheduling, quality prediction, etc. In this work, we focus on the soft-sensing regression problem in metrology systems, which uses sensor data collected during wafer processing steps to predict impending inspection measurements that used to be measured in wafer inspection and metrology systems. We proposed a regressor based on Long Short-term Memory network and devised two distinct loss functions for the purpose of the training model. Although the assessment of our prediction errors by engineers is subjective, a novel piece-wise evaluation metric was introduced to evaluate model accuracy in a mathematical way. Our experimental results showcased that the proposed model is capable of achieving both accurate and early prediction across various types of inspections in complicated manufacturing processes.<\/jats:p>","DOI":"10.3390\/s23208363","type":"journal-article","created":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T10:23:42Z","timestamp":1696933422000},"page":"8363","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Soft-Sensing Regression Model: From Sensor to Wafer Metrology Forecasting"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6918-8214","authenticated-orcid":false,"given":"Angzhi","family":"Fan","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Chicago, Chicago, IL 60637, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6182-3153","authenticated-orcid":false,"given":"Yu","family":"Huang","sequence":"additional","affiliation":[{"name":"Seagate Technology, Fremont, CA 94538, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fei","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sthitie","family":"Bom","sequence":"additional","affiliation":[{"name":"Seagate Technology, Bloomington, MN 55435, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cho, K., van Merrienboer, B., Bahdanau, D., and Bengio, Y. (2014). On the Properties of Neural Machine Translation: Encoder\u2013Decoder Approaches. arXiv.","DOI":"10.3115\/v1\/W14-4012"},{"key":"ref_3","first-page":"6000","article-title":"Attention Is All You Need","volume":"30","author":"Vaswani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kowsari, K., Jafari Meimandi, K., Heidarysafa, M., Mendu, S., Barnes, L., and Brown, D. (2019). Text classification algorithms: A survey. Information, 10.","DOI":"10.3390\/info10040150"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15919","DOI":"10.1007\/s00521-021-06268-0","article-title":"Neural machine translation: Past, present, and future","volume":"33","author":"Mohamed","year":"2021","journal-title":"Neural Comput. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"19143","DOI":"10.1109\/ACCESS.2019.2896880","article-title":"Speech recognition using deep neural networks: A systematic review","volume":"7","author":"Nassif","year":"2019","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3168","DOI":"10.1109\/TII.2019.2902129","article-title":"Nonlinear Dynamic Soft Sensor Modeling With Supervised Long Short-Term Memory Network","volume":"16","author":"Yuan","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2022.3152856","article-title":"A Supervised Bidirectional Long Short-Term Memory Network for Data-Driven Dynamic Soft Sensor Modeling","volume":"71","author":"Lui","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2955","DOI":"10.1109\/TII.2021.3110507","article-title":"A Novel Soft Sensor Modeling Approach Based on Difference-LSTM for Complex Industrial Process","volume":"18","author":"Zhou","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMECH.2013.2273435","article-title":"Regression methods for virtual metrology of layer thickness in chemical vapor deposition","volume":"19","author":"Purwins","year":"2013","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","article-title":"A tutorial on support vector regression","volume":"14","author":"Smola","year":"2004","journal-title":"Stat. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5853","DOI":"10.1109\/TII.2021.3053128","article-title":"A Survey on Deep Learning for Data-Driven Soft Sensors","volume":"17","author":"Sun","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1002\/aic.690370209","article-title":"Nonlinear principal component analysis using autoassociative neural networks","volume":"37","author":"Kramer","year":"1991","journal-title":"AIChE J."},{"key":"ref_14","unstructured":"Kingma, D.P., and Welling, M. (2013). Auto-Encoding Variational Bayes. arXiv."},{"key":"ref_15","unstructured":"Smolensky, P. (1986). Information Processing in Dynamical Systems: Foundations of Harmony Theory, Colorado Univ at Boulder Dept of Computer Science. Technical report."},{"key":"ref_16","unstructured":"Hinton, G.E. (2012). Neural Networks: Tricks of the Trade, Springer."},{"key":"ref_17","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep learning, MIT Press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1109\/ACCESS.2017.2779939","article-title":"LSTM Fully Convolutional Networks for Time Series Classification","volume":"6","author":"Karim","year":"2018","journal-title":"IEEE Access"},{"key":"ref_20","first-page":"1929","article-title":"Dropout: A simple way to prevent neural networks from overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhang, C., Yella, J., Huang, Y., Qian, X., Petrov, S., Rzhetsky, A., and Bom, S. (2021, January 15\u201318). Soft Sensing Transformer: Hundreds of Sensors are Worth a Single Word. Proceedings of the 2021 IEEE International Conference on Big Data (Big Data), Orlando, FL, USA.","DOI":"10.1109\/BigData52589.2021.9671925"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yella, J., Zhang, C., Petrov, S., Huang, Y., Qian, X., Minai, A.A., and Bom, S. (2021, January 15\u201318). Soft-Sensing ConFormer: A Curriculum Learning-based Convolutional Transformer. Proceedings of the 2021 IEEE International Conference on Big Data (Big Data), Orlando, FL, USA.","DOI":"10.1109\/BigData52589.2021.9671991"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Qian, X., Zhang, C., Yella, J., Huang, Y., Huang, M.C., and Bom, S. (2021, January 15\u201318). Soft Sensing Model Visualization: Fine-tuning Neural Network from What Model Learned. Proceedings of the 2021 IEEE International Conference on Big Data (Big Data), Orlando, FL, USA.","DOI":"10.1109\/BigData52589.2021.9671850"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Huang, Y., Zhang, C., Yella, J., Petrov, S., Qian, X., Tang, Y., Zhu, X., and Bom, S. (2021, January 15\u201318). GraSSNet: Graph Soft Sensing Neural Networks. Proceedings of the 2021 IEEE International Conference on Big Data (Big Data), Orlando, FL, USA.","DOI":"10.1109\/BigData52589.2021.9671903"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TNN.2008.2005605","article-title":"The Graph Neural Network Model","volume":"20","author":"Scarselli","year":"2009","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_26","unstructured":"Kipf, T.N., and Welling, M. (2016). Semi-Supervised Classification with Graph Convolutional Networks. arXiv."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/20\/8363\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:04:17Z","timestamp":1760130257000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/20\/8363"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,10]]},"references-count":26,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["s23208363"],"URL":"https:\/\/doi.org\/10.3390\/s23208363","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,10]]}}}