Ball Grid Array Solder Joints Thermal Profile Prediction and Recipe Optimization with Physics-Informed Neural Network

Ball Grid Array Solder Joints Thermal Profile Prediction and Recipe Optimization with Physics-Informed Neural Network | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Ball Grid Array Solder Joints Thermal Profile Prediction and Recipe Optimization with Physics-Informed Neural Network Zhenxuan Zhang, Yuanyuan Li, Sangwon Yoon, Seungbae Park, Daehan Won This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4765110/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Based on comparable research studies, the reflow process has been iden- tified as the most critical process to ensure the quality of solder joints on printed circuit boards (PCBs) manufactured using surface mounting technology (SMT). An example of this is the ball grid array (BGA), which is a package that has one face partially covered by pins in a grid pattern that is connected to the pads on the PCB. It is important to note that the solder joints for BGAs are located at the bottom of the package, as opposed to passive components. Because the cover case of the BGA blocks the convection heat from the air, the BGA joints require a greater amount of parasite conduction heat from the boards and pack- age cover. During the manufacturing process, solder paste manufacturers provide specifications, along with temperature curves (i.e., thermal pro- files), to ensure the quality of the solder joints. In the context of the BGA thermal study, one of the significant challenges will be measuring the temperature under the package and predicting the temperature. Thus, a non-contact profile prediction model would help with predicting the BGA joint thermal profile. As part of this study, (1) a physics-informed artificial neural network (PINN) was proposed for temperature predic- tion for the BGA solder joints, and (2) an experiment was conducted 1 2 Thermal Profile Prediction and Recipe Optimization for BGAs to measure the solder joint temperature underneath the BGAs for con- firmation. The study also proposed (3) an optimization model based on mixed integer programming (MILP) to obtain the reflow recipe for the product that contains passive components and BGA packages, which have different heat capacities, by minimizing the difference of the ther- mal profiles. The prediction accuracy is higher than 96% in terms of the R 2 fitness to the actual thermal profile. In the optimized recipe, there was a 50% reduction in the gap between the peak temperatures of the hottest (passive components) and the coldest (BGA center) joints. surface mounting technology (SMT) ball grid array (BGA) thermal profile prediction physics-informed artificial neural network (PINN) mixed-integer linear programming (MILP) Full Text Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4765110","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":330323116,"identity":"ecea0e8c-4c9e-4436-b4ad-f48ffc31f756","order_by":0,"name":"Zhenxuan Zhang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zhenxuan","middleName":"","lastName":"Zhang","suffix":""},{"id":330323117,"identity":"ae5df70b-597b-4af2-ac20-0667cd559acb","order_by":1,"name":"Yuanyuan Li","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yuanyuan","middleName":"","lastName":"Li","suffix":""},{"id":330323118,"identity":"4bdc7d85-5965-4513-98e0-7d6a946459c5","order_by":2,"name":"Sangwon Yoon","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Sangwon","middleName":"","lastName":"Yoon","suffix":""},{"id":330323119,"identity":"c2140757-356c-4d9b-a3d8-c64ba087c20c","order_by":3,"name":"Seungbae Park","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Seungbae","middleName":"","lastName":"Park","suffix":""},{"id":330323120,"identity":"328c8a69-1a6f-4cfe-8113-98d65a21b5e2","order_by":4,"name":"Daehan Won","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYDCCGyCi4gAPAwMPXMyACC1nYFoSiNXC2HaAgXgtfLd7DB8XzrsjY86/9uCnmz9s8hjYm7dJ4NMieeeMsfHMbc94LGe8S5bOSUgrZuA5VoZXi8GN3G3SvNsO8xjcOGMA1HI4sUEix4wILXPAWox/g7XIvyFGSwNQy/keM6gtPPi1SN7I/2zMc+wZ0BYeM+uctLTENp60Ygt8WvhupCU+5qm5Y29w/ozx7Rwbm8R+9sMbb+DTggASCRCajTjlIMB/gHi1o2AUjIJRMLIAAF+NToDx84SnAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-2566-8061","institution":"Binghamton University","correspondingAuthor":true,"prefix":"","firstName":"Daehan","middleName":"","lastName":"Won","suffix":""}],"badges":[],"createdAt":"2024-07-18 21:51:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4765110/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4765110/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90260305,"identity":"6616b871-8758-4ef7-8cd7-23b7cef0059d","added_by":"auto","created_at":"2025-08-31 13:56:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":746803,"visible":true,"origin":"","legend":"","description":"","filename":"IJAMTFAIM2023.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4765110/v1_covered_02ed1976-52fa-4230-9b97-f54beb2195cd.pdf"}],"financialInterests":"","formattedTitle":"Ball Grid Array Solder Joints Thermal Profile Prediction and Recipe Optimization with Physics-Informed Neural Network","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"surface mounting technology (SMT), ball grid array (BGA), thermal profile prediction, physics-informed artificial neural network (PINN), mixed-integer linear programming (MILP)","lastPublishedDoi":"10.21203/rs.3.rs-4765110/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4765110/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBased on comparable research studies, the reflow process has been iden- tified as the most critical process to ensure the quality of solder joints on printed circuit boards (PCBs) manufactured using surface mounting technology (SMT). An example of this is the ball grid array (BGA), which is a package that has one face partially covered by pins in a grid pattern that is connected to the pads on the PCB. It is important to note that the solder joints for BGAs are located at the bottom of the package, as opposed to passive components. Because the cover case of the BGA blocks the convection heat from the air, the BGA joints require a greater amount of parasite conduction heat from the boards and pack- age cover. During the manufacturing process, solder paste manufacturers provide specifications, along with temperature curves (i.e., thermal pro- files), to ensure the quality of the solder joints. In the context of the BGA thermal study, one of the significant challenges will be measuring the temperature under the package and predicting the temperature. Thus, a non-contact profile prediction model would help with predicting the BGA joint thermal profile. As part of this study, (1) a physics-informed artificial neural network (PINN) was proposed for temperature predic- tion for the BGA solder joints, and (2) an experiment was conducted\u003c/p\u003e \u003cp\u003e1\u003c/p\u003e \u003cp\u003e2 \u003cem\u003eThermal Profile Prediction and Recipe Optimization for BGAs\u003c/em\u003e\u003c/p\u003e \u003cp\u003eto measure the solder joint temperature underneath the BGAs for con- firmation. The study also proposed (3) an optimization model based on mixed integer programming (MILP) to obtain the reflow recipe for the product that contains passive components and BGA packages, which have different heat capacities, by minimizing the difference of the ther- mal profiles. The prediction accuracy is higher than 96% in terms of the \u003cb\u003eR\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e fitness to the actual thermal profile. In the optimized recipe, there was a 50% reduction in the gap between the peak temperatures of the hottest (passive components) and the coldest (BGA center) joints.\u003c/p\u003e","manuscriptTitle":"Ball Grid Array Solder Joints Thermal Profile Prediction and Recipe Optimization with Physics-Informed Neural Network","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-16 19:15:23","doi":"10.21203/rs.3.rs-4765110/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f3da7689-78b7-4292-ae58-93c951f6fb8c","owner":[],"postedDate":"August 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-31T13:48:19+00:00","versionOfRecord":[],"versionCreatedAt":"2024-08-16 19:15:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4765110","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4765110","identity":"rs-4765110","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}