[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122599-en":3,"doc-seo-122599-105":30,"detail-sidebar-cat-0-en-105":91},{"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},122599,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Machine learning reconstruction of depth-dependent thermal conductivity profile from frequency-domain thermoreflectance signals","Depth-dependent thermal conductivity characterization is crucial for revealing structure–property relationships in functional materials, yet remains difficult with conventional thermoreflectance. A machine-learning reconstruction method extracts depth-dependent thermal conductivity directly from frequency-domain phase signals, using kernel ridge regression to avoid assuming any predefined functional form. The approach accurately recovers typical exponential and Gaussian profiles and can reconstruct complex synthetic distributions. It further demonstrates strong performance for ion-irradiated semiconductors using Fourier-transformed TDTR signals.","Machine learning reconstruction of depth-dependent thermal conductivity profile from frequency-domain thermoreflectance signals  \nZeyu Xiang 1, Yu Pang 1, Xin Qian 1*, Ronggui Yang 1,2*  \n1Department of Engineering Thermophysics, School of Energy and Power Engineering,  \nHuazhong University of Science and Technology, Wuhan, Hubei 430074, China  \n2State Key Laboratory of Coal Combustion, School of Energy and Power Engineering,  \nHuazhong University of Science and Technology, Wuhan, Hubei 430074, China  \n*[Corresponding authors: xinqian21@hust.edu.cn](Corresponding authors: xinqian21@hust.edu.cn); [ronggui@hust.edu.cn](ronggui@hust.edu.cn);  \nABSTRACT  \nCharacterizing materials with spatially varying thermal conductivities is significant to unveil the structure-property relationship for a wide range of functional materials, such as chemical-vapor-deposited diamonds, ion-irradiated materials, nuclear materials under radiation, and battery electrode materials. Although the development of thermal conductivity microscopy based on time/frequency-domain thermoreflectance (TDTR/FDTR) enabled inplane scanning of thermal conductivity profile, measuring depth-dependent thermal conductivity remains challenging. This work proposed a machine-learning-based reconstruction method for extracting depth-dependent thermal conductivity 􀜭 (􀝖) directly from frequency-domain phase signals. We demonstrated that the simple supervised-learning algorithm kernel ridge regression (KRR) can reconstruct 􀜭 (􀝖) without requiring preknowledge about the functional form of the profile. The reconstruction method can not only accurately reproduce typical 􀜭 (􀝖) distributions such as the pre-assumed exponential profile of chemical-vapor-deposited (CVD) diamonds and Gaussian profile of ion-irradiated materials, but also complex profiles artificially constructed by superimposing Gaussian, exponential, polynomial, and logarithmic functions. In addition, the method also shows excellent performances of reconstructing 􀜭 (􀝖) of ion-irradiated semiconductors from Fouriertransformed TDTR signals. This work demonstrates that combining machine learning with pump-probe thermoreflectance is an effective way for depth-dependent thermal property mapping.  \nKeywords: depth-dependent thermal conductivity, machine-learning reconstruction, frequency-domain thermoreflectance (FDTR)  \nCharacterizing spatially varying thermal conductivities has been increasingly significant in unveiling the structure-property relationship and the applications of functional materials 1–4. The in-plane scanning of the thermal conductivity profile has been enabled by scanning the sample surface with local measurements, such as time-or frequency-domain thermoreflectance (TDTR/FDTR)2,5,6 and scanning thermal microscopy (SThM)7,8 . Mapping depth-dependent thermal conductivity profile 􀜭 (􀝖) of inhomogeneous materials, however, remains an unsolved challenge, such as chemical-vapor-deposited (CVD) diamonds9–11, ion-irradiated semiconductors near the doped or damaged sites12–14, and electrode materials15–17, just to name a few. Although scanning measurements could be performed by exposing and polishing the cross-section along the depth direction, preventing unwanted fractures becomes difficult when dealing with thin and fragile samples. Recently, non-intrusive characterization of 􀜭 (􀝖) is achieved using thermoreflectance measurements11,18, leveraging the frequency dependence of  \n1  \nthermal penetration depth 􀝀􀯣 = 􁉂􀰗􀯄􀮼􀯙􁉃 2 , with 􀜭 , 􀜥 and 􀝂 being the thermal conductivity, volumetric heat capacity, and modulation frequency of the pump (heating) laser, respectively. Such characterization technique requires developing thermal models that can handle nonuniform thermal conductivity by discretizing the sample into many layers, and the thermal conductivity in each layer is assumed to be uniform. To reconstruct thermal conductivity distribution from experimental data, a functional form of 􀜭 (􀝖) needs to be assumed with fit","cbCait7y2kZJ07SQ","https://ap.wps.com/l/cbCait7y2kZJ07SQ","pdf",1780289,1,22,"English","en",105,"# Abstract\n## Background and challenge\n## Method: machine learning with frequency-domain thermoreflectance\n## Demonstrations and reconstruction performance","[{\"question\":\"Why is measuring depth-dependent thermal conductivity important?\",\"answer\":\"It helps reveal structure–property relationships in functional materials such as CVD diamonds, ion-irradiated materials, nuclear materials under radiation, and battery electrode materials.\"},{\"question\":\"What signals does the proposed method use to reconstruct the depth-dependent profile?\",\"answer\":\"It uses frequency-domain phase signals from pump-probe thermoreflectance (FDTR) to extract the depth-dependent thermal conductivity profile.\"},{\"question\":\"Does the reconstruction require pre-assuming the functional form of the thermal conductivity profile?\",\"answer\":\"No. The kernel ridge regression model is trained so it can reconstruct the profile without needing pre-knowledge of the functional form.\"}]","Machine learning reconstruction of depth-dependent thermal conductivity profile from frequency-domain thermoreflectance signals | 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is measuring depth-dependent thermal conductivity important?","Question",{"text":75,"@type":76},"It helps reveal structure–property relationships in functional materials such as CVD diamonds, ion-irradiated materials, nuclear materials under radiation, and battery electrode materials.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What signals does the proposed method use to reconstruct the depth-dependent profile?",{"text":80,"@type":76},"It uses frequency-domain phase signals from pump-probe thermoreflectance (FDTR) to extract the depth-dependent thermal conductivity profile.",{"name":82,"@type":73,"acceptedAnswer":83},"Does the reconstruction require pre-assuming the functional form of the thermal conductivity profile?",{"text":84,"@type":76},"No. The kernel ridge regression model is trained so it can reconstruct the profile without needing pre-knowledge of the functional 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