Bypassing the Memory Wall: A Unified Quantum-Ballistic Paradigm for Sub-5nm VLSI Interconnects

Bypassing the Memory Wall: A Unified Quantum-Ballistic Paradigm for Sub-5nm VLSI Interconnects | 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 Article Bypassing the Memory Wall: A Unified Quantum-Ballistic Paradigm for Sub-5nm VLSI Interconnects S. Eshwar Rao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8604143/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 As semiconductor scaling approaches the 2nm regime, classical copper (Cu) interconnects experience a catastrophic failure known as the “Wire Wall,” characterized by Anderson Localization and exponential resistance growth. This paper presents a unified solution to the “Memory Wall” by transitioning from diffusive drift to ballistic waveguiding. We derive a unified mathematical model addressing Latency (τ ) and Energy (E) via the Bose-Ramanujan Mahalanobis (BRM) framework, demonstrating a 4080x reduction in power density and the mathematical elimination of length-dependent latency. Physical sciences/Nanoscience and technology/Graphene/Electronic properties and devices Physical sciences/Engineering/Electrical and electronic engineering Ballistic Transport QuantumConductance 2nmVLSI MemoryWall Ramanujan Graphs Mahalanobis Distance. Full Text Additional Declarations There is NO Competing Interest. 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-8604143","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":577576245,"identity":"18b38766-2c66-4afe-8715-c083ae2913ec","order_by":0,"name":"S. Eshwar Rao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIiWNgGAWjYHACZjBpAOXJgYgDD0jRYgzWkkCKlsQGEIlPi/yM3MMGP/fY2JtLJD/7XFFjkz4/7PBDoC12croN2LUY3MhLTux5lpa4c0aa8cwzx9JyN95OMwBqSTY2O4BDi0SO8QGeA4cTDG4nGDM2sB3O3Tg7AaTlQOI2HFrkZ+QYH/xz4L+9we30z4wN/w6nG85O/4BXC8ONHONkngMHGDfczjFmbGw7nCAvnYPfFoMzb4yNZQ4kJ264/6aYsbEvzXCDdE7BgQQD3H6Rb88xlnxzwM7e4MzxzYwN32zk5Wenb/7wocJODpcWLPaCVRoQUIVqbwMpqkfBKBgFo2AkAAC+1mUSTI/ergAAAABJRU5ErkJggg==","orcid":"","institution":"Sarala Birla University","correspondingAuthor":true,"prefix":"","firstName":"S.","middleName":"Eshwar","lastName":"Rao","suffix":""}],"badges":[],"createdAt":"2026-01-14 17:25:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8604143/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8604143/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104783465,"identity":"60fb1d3c-6f7d-4ed4-9522-c567fae0cafa","added_by":"auto","created_at":"2026-03-17 07:59:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":555610,"visible":true,"origin":"","legend":"Article File","description":"","filename":"rs119.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8604143/v1_covered_3a82b694-125d-436e-9fb8-0e7757067c39.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Bypassing the Memory Wall: A Unified\nQuantum-Ballistic Paradigm for Sub-5nm VLSI\nInterconnects","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Ballistic Transport, QuantumConductance, 2nmVLSI,MemoryWall, Ramanujan Graphs, Mahalanobis Distance.","lastPublishedDoi":"10.21203/rs.3.rs-8604143/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8604143/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAs semiconductor scaling approaches the 2nm regime, classical copper (Cu) interconnects experience a catastrophic failure known as the “Wire Wall,” characterized by Anderson Localization and exponential resistance growth. This paper presents a unified solution to the “Memory Wall” by transitioning from diffusive drift to ballistic waveguiding. We derive a unified mathematical model addressing Latency (τ ) and Energy (E) via the Bose-Ramanujan Mahalanobis (BRM) framework, demonstrating a 4080x reduction in power density and the mathematical elimination of length-dependent latency.\u003c/p\u003e","manuscriptTitle":"Bypassing the Memory Wall: A Unified\nQuantum-Ballistic Paradigm for Sub-5nm VLSI\nInterconnects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-17 02:42:52","doi":"10.21203/rs.3.rs-8604143/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":"43343235-5459-41c9-8f84-ee3fb8462141","owner":[],"postedDate":"March 17th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61448669,"name":"Physical sciences/Nanoscience and technology/Graphene/Electronic properties and devices"},{"id":61448670,"name":"Physical sciences/Engineering/Electrical and electronic engineering"}],"tags":[],"updatedAt":"2026-03-17T02:42:52+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-17 02:42:52","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8604143","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8604143","identity":"rs-8604143","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}