[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126622-en":3,"doc-seo-126622-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},126622,549768064622,"Anda","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",8,"Research & Report","Evaluation of optical constants in oxide thin films using machine learning","An inverse optical analysis method using neural networks is developed to quantitatively evaluate optical constants from optical spectroscopy. The approach computes UV-visible measurable spectroscopic quantities from optical constants via Tomlin equations while eliminating impractical parameter combinations. A back-propagation neural network is trained on the calculated input–output relationships, then applied to measured reflectance and transmittance responses to recover the optical constants. Compared with Newton-Raphson, the method reduces reliance on expert judgment and mitigates multi-solution conversion challenges, enabling more automated, human-free data inversion.","Evaluation of optical constants in oxide thin films using machine learning  \nKyosuke Saeki1 and Takayuki Makino2,1,*  \n1 Department of Electric and Electronics Engineering, University of Fukui, Fukui 910-8507, Japan  \n2 Research Center for Development of Far-Infrared Region, University of Fukui, Fukui 910- 8507, Japan  \nE-mail: [tmakino@u-fukui.ac.jp](tmakino@u-fukui.ac.jp)  \nAbstract This paper describes an inverse analysis method using neural networks on optical spectroscopy, and its application to the quantitative optical constant evaluation. The present method consists of three subprocesses. First, measurable UV-visible spectroscopic quantities were calculated as functions of the optical constants of the solid based on the Tomlin equations [J. Phys. D 1 1667 (1968)] by carefully eliminating the unpractical combinations of optical constants. Second, the back-propagation neural network is trained using the calculated relationships between the measurable quantities and the optical constants. Finally, the trained network is utilized to determine the optical constants from measured responses. The conventional (Newton-Raphson) method tends to require the judgement of a wellexperienced analyst, while machine learning shows automatically human-free performance in data conversion.  \n1. Introduction  \nIn recent years, the importance of elucidating basic physical properties has been increasingly recognized in the development of organic and inorganic semiconductors. Efforts are being made to gain a deeper understanding of the electronic structure. The importance of optical evaluation as a characterization tool for this is well known. One of the representative techniques for such an optical characterization is UV-visible spectroscopy (UVS) . A transformation of the measured quantities into optical constants (complex refractive index) is often performed to facilitate comparison with the electronic structure properties. However, it is known that the conversion of these physical quantities may become an inverse problem depending on a semiconductor structure to be measured. Even worse, there is a multisolution problem. By setting 􀜴 is the reflectance and 􀜶 transmissivity, let us consider light of wavelength 􀟣 in air or vacuum incident normally on a film of thickness 􀝀 and complex refractive index 􀟟 − 􀝅􀟢 which is supported on a non-absorbing thick substrate of refractive index 􀝊௦ .  \nThe expressions of 􀜴 and 􀜶 are too complicated to be shown even in this case. Following Heavens [1], quantities of 􀜴 , 􀜶 are given by,  \n􀜽ଵ exp (2􀝀ଶ) + 􀜾ଵ cos (2􀝀ଵ) + 􀜿ଵ sin (2􀝀ଶ) + 􀝂ଵ exp (−2􀝀ଶ)  \n􀜴 = ~~ ~~ (1)  \n􀜽ଶ exp (2􀝀ଶ) + 􀜾ଶ cos (2􀝀ଵ) + 􀜿ଶ sin (2􀝀ଶ) + 􀝂ଶ exp (−2􀝀ଶ)  \n 32􀝊ଶ (􀟟ଶ + 􀟢ଶ )   \n􀜶 = ௦ (2)  \n􀜽ଶ exp (2􀝀ଶ) + 􀜾ଶ cos (2􀝀ଵ) + 􀜿ଶ sin (2􀝀ଶ) + 􀝂ଶ exp (−2􀝀ଶ)  \nwhere  \n􀜽ଵ = ((􀟟 − 1)ଶ + 􀟢ଶ )൫ (􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ + 􀝊ଶ௦) + 4􀟟􀝊ଶ௦൯ (3)  \n􀜽ଶ = ((􀟟 + 1)ଶ + 􀟢ଶ )൫ (􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ + 􀝊ଶ௦) + 4􀟟􀝊ଶ௦൯ (4)  \n􀜾ଵ = −2൫(􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ − 1)(􀟟ଶ + 􀟢 ଶ − 􀝊ଶ௦) + 8􀟟􀝊ଶ௦൯ (5)  \n􀜾 ଶ = −2൫(􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ − 1)(􀟟ଶ + 􀟢 ଶ − 􀝊ଶ௦) − 8􀟟􀝊ଶ௦൯ (6)  \n􀜿ଵ = 4􀟢൫−(􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ − 􀝊ଶ௦) + 2􀝊ଶ௦(􀟟ଶ + 􀟢 ଶ − 1)൯ (7)  \n􀜿ଶ = 4􀟢൫(􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ − 􀝊ଶ௦) + 2􀝊ଶ௦(􀟟ଶ + 􀟢 ଶ − 1)൯ (8)  \n􀝂ଵ = ((􀟟 + 1)ଶ + 􀟢ଶ )൫ (􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ + 􀝊ଶ௦) − 4􀟟􀝊ଶ௦൯ (9)  \n􀝂ଶ = ((􀟟 − 1)ଶ + 􀟢ଶ )൫ (􀝊ଶ௦ + 1)(􀟟ଶ + 􀟢 ଶ + 􀝊ଶ௦) − 4􀟟􀝊ଶ௦൯ (10)  \nwith  \n􀝀 ଵ = 2􀟨􀟟􀝀/􀟣 , and 􀝀 ଶ = 2􀟨􀟢􀝀/􀟣 .  \nThe measurable quantities 􀜴 and 􀜶 are usually represented as functions of complex refractive indices (􀟟 and 􀟢) . This is regarded as a direct problem. Different from the case of a substrate-free standalone wafer, the optical constants (􀟟 and 􀟢) cannot be represented by these quantities (􀜴 and 􀜶) . Because of the intimacy of the optical constants with the electronic structure of the compound, conversion of the measured quantities into these is often performed. On the other hand, this is classified into an inverse analysis.  \nTraditionally, this type of conversion has been solved numerically with e.g. Newton's method. Even worse, we suffer from the mult","cbCairp8d7LOwzQa","https://ap.wps.com/l/cbCairp8d7LOwzQa","pdf",1217628,1,13,"English","en",105,"# Introduction\n## UV-visible spectroscopy and optical constants conversion\n## Inverse analysis and the multi-solution problem\n# The proposed neural-network-based method\n## Tomlin-equation-based forward calculations\n## Back-propagation network training and inference\n## Comparison with conventional Newton-Raphson methods","[{\"question\":\"What problem does the paper address in optical evaluation of oxide thin films?\",\"answer\":\"It addresses the inverse conversion from UV-visible spectroscopic measurements (reflectance and transmittance) to optical constants, which becomes an inverse problem with a multi-solution ambiguity.\"},{\"question\":\"How does the proposed method compute measurable quantities from optical constants?\",\"answer\":\"It calculates UV-visible spectroscopic quantities as functions of the optical constants using Tomlin equations, while carefully eliminating impractical combinations of refractive index and extinction coefficient.\"},{\"question\":\"How does the machine learning approach help compared with the Newton-Raphson method?\",\"answer\":\"Newton-Raphson typically requires expert judgment and is sensitive to initial values, whereas the neural-network workflow provides automated, human-free data conversion for determining optical constants from measured responses.\"}]","Evaluation of optical constants in oxide thin films using machine learning | 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problem does the paper address in optical evaluation of oxide thin films?","Question",{"text":76,"@type":77},"It addresses the inverse conversion from UV-visible spectroscopic measurements (reflectance and transmittance) to optical constants, which becomes an inverse problem with a multi-solution ambiguity.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the proposed method compute measurable quantities from optical constants?",{"text":81,"@type":77},"It calculates UV-visible spectroscopic quantities as functions of the optical constants using Tomlin equations, while carefully eliminating impractical combinations of refractive index and extinction coefficient.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the machine learning approach help compared with the Newton-Raphson method?",{"text":85,"@type":77},"Newton-Raphson typically requires expert judgment and is sensitive to initial values, whereas the neural-network workflow provides automated, human-free data 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