A Second Look at 2D Simulation of FIB Milling: Accounting for Mean-Free Path Effects in Redeposition and Sputtering

A Second Look at 2D Simulation of FIB Milling: Accounting for Mean-Free Path Effects in Redeposition and Sputtering | 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 A Second Look at 2D Simulation of FIB Milling: Accounting for Mean-Free Path Effects in Redeposition and Sputtering Ta-Shun Chou, Mathias Rommel This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7338867/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 This work presents a predictive 2D mathematical model for focused ion beam (FIB) milling that incorporates primary sputtering, redeposition, and secondary sputtering effects. Model validity is evaluated through comparison with experimental data and simulation results. Findings show that micro-trench geometry is strongly influenced by redeposition and ion reflection, particularly in high-aspect-ratio structures. Secondary sputtering from backscattered or reflected ions becomes significant for aspect ratios above 1, while sputtering from sputtered atoms is negligible due to their low energy. The model applies the cosine law to approximate the angular distribution of sputtered atoms and reflected ions, validated using Monte Carlo simulations (TRIM). Mean free path effects, especially under long dwell times, are shown to influence local pressure and particle distribution in deep trenches. Using a string-segment method, the 2D model efficiently handles sputtering and redeposition with reduced computational cost. Simulations across varying trench aspect ratios and dwell times demonstrate good agreement with literature, confirming the model’s predictive capability for surface topography evolution. Focus ion beam milling Topography simulation Sputtering Mean free path Full Text Additional Declarations The authors declare no competing interests. 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-7338867","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":498290750,"identity":"84419620-aa6f-4aa4-9a2d-9e2c3ea95222","order_by":0,"name":"Ta-Shun Chou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABA0lEQVRIie2QsWrDMBCG/yJwlmu8KqjkGQ4KoYWCX0Vg8CRIupSMhYCnQleHvkyKwVlCZw2GGgqZDYbSIUPVmKQdVJqxgz6QEIc+7v4DAoF/itjf0p2Wdf9o2F0r/3f6qZwVB0WfqgjCQcHvSjJYie42rxE/LSp1M8sSqEXV6lmN4fre34V0pJb5FrKuMmXYCFxUaaF5i9HG34YwfRfneQmWZuKUeZRYc+myuIrVfiVuRHdUrnhOkNOuV14bvyI11FEBGwnphuu7+OOTbSJFLyVJm6XXD5yxy7IfjEYb/2CDRy06uivHcZE+249d+rWxN7S7cjxc++N/r+HvSiAQCARO5hOpvlJVeHrz/gAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-3897-6573","institution":"Leibniz Insitute for Crystal Growth","correspondingAuthor":true,"prefix":"","firstName":"Ta-Shun","middleName":"","lastName":"Chou","suffix":""},{"id":498290751,"identity":"45037497-4233-4bf8-8864-ef805e1b9e12","order_by":1,"name":"Mathias Rommel","email":"","orcid":"","institution":"2Fraunhofer Institute for Integrated Systems and Device Technology IISB","correspondingAuthor":false,"prefix":"","firstName":"Mathias","middleName":"","lastName":"Rommel","suffix":""}],"badges":[],"createdAt":"2025-08-10 12:48:17","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7338867/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7338867/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88867346,"identity":"d6e4d5fb-748b-4dbb-b623-1cb37afb7b15","added_by":"auto","created_at":"2025-08-12 08:39:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":562142,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptFIBModellingV7.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7338867/v1_covered_cbd170e4-ff7e-4553-9b2a-b699095e0d2a.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eA Second Look at 2D Simulation of FIB Milling: Accounting for Mean-Free Path Effects in Redeposition and Sputtering\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Fraunhofer Institute for Integrated Systems and Device Technology","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":"Focus ion beam milling, Topography simulation, Sputtering, Mean free path","lastPublishedDoi":"10.21203/rs.3.rs-7338867/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7338867/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work presents a predictive 2D mathematical model for focused ion beam (FIB) milling that incorporates primary sputtering, redeposition, and secondary sputtering effects. Model validity is evaluated through comparison with experimental data and simulation results. Findings show that micro-trench geometry is strongly influenced by redeposition and ion reflection, particularly in high-aspect-ratio structures. Secondary sputtering from backscattered or reflected ions becomes significant for aspect ratios above 1, while sputtering from sputtered atoms is negligible due to their low energy. The model applies the cosine law to approximate the angular distribution of sputtered atoms and reflected ions, validated using Monte Carlo simulations (TRIM). Mean free path effects, especially under long dwell times, are shown to influence local pressure and particle distribution in deep trenches. Using a string-segment method, the 2D model efficiently handles sputtering and redeposition with reduced computational cost. Simulations across varying trench aspect ratios and dwell times demonstrate good agreement with literature, confirming the model\u0026rsquo;s predictive capability for surface topography evolution.\u003c/p\u003e","manuscriptTitle":"A Second Look at 2D Simulation of FIB Milling: Accounting for Mean-Free Path Effects in Redeposition and Sputtering","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-12 08:23:48","doi":"10.21203/rs.3.rs-7338867/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":"a13301de-7128-44cc-beff-db16eeaa5631","owner":[],"postedDate":"August 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-12T08:23:48+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-12 08:23:48","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7338867","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7338867","identity":"rs-7338867","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}