{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T13:44:00Z","timestamp":1760708640370,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2013,12,19]],"date-time":"2013-12-19T00:00:00Z","timestamp":1387411200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A new data dimension-reduction method, called Internal Information Redundancy Reduction (IIRR), is proposed for application to Optical Emission Spectroscopy (OES) datasets obtained from industrial plasma processes. For example in a semiconductor manufacturing environment, real-time spectral emission data is potentially very useful for inferring information about critical process parameters such as wafer etch rates, however, the relationship between the spectral sensor data gathered over the duration of an etching process step and the target process output parameters is complex. OES sensor data has high dimensionality (fine wavelength resolution is required in spectral emission measurements in order to capture data on all chemical species involved in plasma reactions) and full spectrum samples are taken at frequent time points, so that dynamic process changes can be captured. To maximise the utility of the gathered dataset, it is essential that information redundancy is minimised, but with the important requirement that the resulting reduced dataset remains in a form that is amenable to direct interpretation of the physical process. To meet this requirement and to achieve a high reduction in dimension with little information loss, the IIRR method proposed in this paper operates directly in the original variable space, identifying peak wavelength emissions and the correlative relationships between them. A new statistic, Mean Determination Ratio (MDR), is proposed to quantify the information loss after dimension reduction and the effectiveness of IIRR is demonstrated using an actual semiconductor manufacturing dataset. As an example of the application of IIRR in process monitoring\/control, we also show how etch rates can be accurately predicted from IIRR dimension-reduced spectral data.<\/jats:p>","DOI":"10.3390\/s140100052","type":"journal-article","created":{"date-parts":[[2013,12,19]],"date-time":"2013-12-19T11:26:58Z","timestamp":1387452418000},"page":"52-67","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Dimension Reduction of Multivariable Optical Emission Spectrometer Datasets for Industrial Plasma Processes"],"prefix":"10.3390","volume":"14","author":[{"given":"Jie","family":"Yang","sequence":"first","affiliation":[{"name":"Energy Design Lab, Faculty of Engineering and Computing, Dublin City University, Glasnevin, Dublin 9, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Conor","family":"McArdle","sequence":"additional","affiliation":[{"name":"Energy Design Lab, Faculty of Engineering and Computing, Dublin City University, Glasnevin, Dublin 9, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Daniels","sequence":"additional","affiliation":[{"name":"Energy Design Lab, Faculty of Engineering and Computing, Dublin City University, Glasnevin, Dublin 9, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,12,19]]},"reference":[{"key":"ref_1","unstructured":"International Technology Roadmap for Semiconductors. Available online: http:\/\/www.itrs.net\/about.html."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/S0169-4332(00)00328-7","article-title":"Plasma etching: Principles, mechanisms, application to micro-and nano-technologies","volume":"164","author":"Cardinaud","year":"2000","journal-title":"Appl. Surf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1016\/S0005-1098(00)00084-4","article-title":"Automatic control in microelectronics manufacturing: Practices, challenges, and possibilities","volume":"36","author":"Edgar","year":"2000","journal-title":"Automatica"},{"key":"ref_4","unstructured":"Conde, L. An introduction to Langmuir probe diagnostics of plasmas. Available online: http:\/\/plasmalab.aero.upm.es\/\u223clcl\/PlasmaProbes\/Probes-2010-2.pdf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1063\/1.1136465","article-title":"Impedance measurement as a diagnostic for plasma reactors","volume":"52","author":"Ilic","year":"1981","journal-title":"Rev. Sci. Instrum."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5773","DOI":"10.1016\/j.tsf.2009.03.198","article-title":"Precise etch-depth control of microlens-integrated intracavity contacted vertical-cavity surface-emitting lasers by in-situ laser reflectometry and reflectivity modeling","volume":"517","author":"Song","year":"2009","journal-title":"Thin Solid Films"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/TSM.2011.2176759","article-title":"Global and local virtual metrology models for a plasma etch process","volume":"25","author":"Lynn","year":"2012","journal-title":"IEEE Trans. Semicond. Manuf."},{"key":"ref_8","unstructured":"Ocean Optics Inc. USB4000 Miniature Fiber Optic Spectrometer. Available online: http:\/\/www.oceanoptics.com\/Products\/usb4000.asp."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1109\/TSM.2009.2031750","article-title":"Virtual metrology modeling for plasma etch operations","volume":"22","author":"Zeng","year":"2009","journal-title":"IEEE Trans. Semicond. Manuf."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lynn, S., Ringwood, J., Ragnoli, E., McLoone, S., and MacGearailty, N. (2009, January 10\u201312). Virtual Metrology for Plasma Etch Using Tool Variables. Berlin, Germany.","DOI":"10.1109\/ASMC.2009.5155972"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1116\/1.1331294","article-title":"Plasma etching endpoint detection using multiple wavelengths for small open-area wafers","volume":"19","author":"Yue","year":"2001","journal-title":"J. Vac. Sci. Technol. A Vac. Surf. Films"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Westerman, R., Johnson, D., Lai, S., and Teixeira, M. (2006, January 21\u201326). Endpoint Detection Methods for Time Division Multiplex Etch Processes. San Jose, CA, USA.","DOI":"10.1117\/12.646498"},{"key":"ref_13","unstructured":"Bacelli, G., and Ringwood, J.V. (2007, January 9\u201312). Tracking Plasma Etch Process Variations Using Principal Component Analysis of OES Data. Angers, France."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1149\/1.3567696","article-title":"Endpoint detection in plasma etching using principal component analysis and expanded hidden markov model","volume":"34","author":"Kim","year":"2011","journal-title":"ECS Trans."},{"key":"ref_15","unstructured":"Yue, H.H., and Tomoyasu, M. (2004, January 14\u201317). Weighted Principal Component Analysis and Its Applications to Improve FDC Performance. Atlantis, Paradise Island, Bahanmas."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ma, B., McLoone, S., Ringwood, J., and Macgearailt, N. (2008, January 24\u201327). Selecting Signature Optical Emission Spectroscopy Variables Using Sparse Principal Component Analysis. Khulna, Bangladesh.","DOI":"10.1109\/ICCITECHN.2008.4803104"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Sharma, D., Armer, H., and Moyne, J. (2012, January 15\u201317). A Comparison of Data Mining Methods for Yield Modeling, Chamber Matching and Virtual Metrology Applications. Saratoga Springs, NY, USA.","DOI":"10.1109\/ASMC.2012.6212896"},{"key":"ref_18","unstructured":"Mardia, K.V., Kent, J.T., and Bibby, J.M. (1980). Multivariate Analysis (Probability and Mathematical Statistics), Academic Press. [1st ed.]."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s11081-008-9057-z","article-title":"Clustering and feature selection using sparse principal component analysis","volume":"11","author":"Luss","year":"2010","journal-title":"Optim. Eng."},{"key":"ref_20","unstructured":"DeMasi, O., Meza, J., and Bailey, D.H. (2011). Dimension reduction using rule ensemble machine learning methods: A numerical study of three ensemble methods. arXiv Preprint arXiv:1108.6094, code: 2011arXiv1108.6094D."},{"key":"ref_21","unstructured":"Tobias, R.D. (1995, January 2\u20135). An Introduction to Partial Least Squares Regression. Orlando, FL, USA."},{"key":"ref_22","first-page":"209","article-title":"Factor analysis as a statistical method","volume":"12","author":"Lawley","year":"1962","journal-title":"J. R. Statist. Soc. Ser. D"},{"key":"ref_23","first-page":"435","article-title":"Projection pursuit","volume":"13","author":"Huber","year":"1985","journal-title":"Ann. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Stewart, D.W. (1981). The application and misapplication of factor analysis in marketing research. J. Mark. Res., 51\u201362.","DOI":"10.1177\/002224378101800105"},{"key":"ref_25","unstructured":"Carreira-Perpinan, M.A. (1997). A Review of Dimension Reduction Techniques, Department of Computer Science, University of Sheffield. Technical Report CS-96-09."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1109\/TSM.2003.818976","article-title":"Neural network modeling of reactive ion etching using optical emission spectroscopy data","volume":"16","author":"Hong","year":"2003","journal-title":"IEEE Trans. Semicond. Manuf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1016\/S0895-4356(96)00002-9","article-title":"Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes","volume":"49","author":"Tu","year":"1996","journal-title":"J. Clin. Epidemiol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3501","DOI":"10.1002\/aic.10978","article-title":"Fault detection and diagnosis based on modified independent component analysis","volume":"52","author":"Lee","year":"2006","journal-title":"AIChE J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/1\/52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:51:31Z","timestamp":1760219491000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/1\/52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,19]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,1]]}},"alternative-id":["s140100052"],"URL":"https:\/\/doi.org\/10.3390\/s140100052","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2013,12,19]]}}}