Numerical simulation of the resonant tunneling diode using a regularized quantum hydrodynamic model

Numerical simulation of the resonant tunneling diode using a regularized quantum hydrodynamic model | 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 Numerical simulation of the resonant tunneling diode using a regularized quantum hydrodynamic model Carl Gardner This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7633374/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Time-dependent simulations of the resonant tunneling diode to steady state using the smooth quantum hydrodynamic (QHD) model are presented, which show realistic negative differential resistance (the experimental signal of quantum resonance) in the current-voltage curve. These are the first time-dependent simulations of the smooth QHD model. The simulations match fully quantum mechanical simulations of the resonant tunneling diode much better than any other QHD simulations to date. For the time-dependent simulations, a regularization of the smooth QHD model equations to prevent an unstable growing mode is implemented. The regularization involves replacing the spatial derivative of the electron density on the right-hand side of the momentum conservation equation by using a quantum generalization of the semiclassical Boltzmann distribution for electron density that captures in a simple way essential effects of quantum tunneling and resonance. Numerical methods are developed for the time-dependent smooth QHD model by using a mixture of hyperbolic, parabolic, and elliptic partial differential equation methods: (i) the underlying hyperbolic gas dynamical part of the transport equations is solved with a third-order WENO (weighted essentially non-oscillatory) method, treating the electric field, scattering, and quantum terms as source terms; (ii) the parabolic heat conduction term is incorporated with the TRBDF2 (trapezoidal rule/backward difference formula second-order) method; and (iii) the elliptic Poisson equation is solved with a standard (sparse direct or modern iterative) elliptic solver. resonant tunneling diode quantum hydrodynamic model Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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-7633374","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":556185042,"identity":"04c694ec-b525-4e6d-a2ff-4e5e2b22174b","order_by":0,"name":"Carl Gardner","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYHACxgNgCkR+gIgYENQD18I4g2QtzDzEaOFvP/vgAMMvu3y+283HPtvU1CU2sDdvk8CnReJMusEBxr5ky5l3jiXPzjl2OLGB51gZXi0GDGkMBxh7mA0MbuQYM+ewHUhskMgxw6+F/xlISz1QS/5nZot/QIfJvyGgRQJoC8OPwyBbmJkZ25iBtvDg1yJxA2hLYsNxA8kbacaMvX2Hjdt40oot8Gnh709jfPDhT7UB343kxww/vtXJ9rMf3ngDnxYwSGxD4rARVA4Gf4hTNgpGwSgYBSMUAAD080s3fpJHTQAAAABJRU5ErkJggg==","orcid":"","institution":"Arizona State University","correspondingAuthor":true,"prefix":"","firstName":"Carl","middleName":"","lastName":"Gardner","suffix":""}],"badges":[],"createdAt":"2025-09-16 19:08:15","currentVersionCode":2,"declarations":"","doi":"10.21203/rs.3.rs-7633374/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-7633374/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98245350,"identity":"706a91cc-ea1b-48e3-b4db-bbcc92a9cd91","added_by":"auto","created_at":"2025-12-15 16:17:47","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3489,"visible":true,"origin":"","legend":"","description":"","filename":"afd95b1346bf4ca6a0bd28c1ff1d746b.json","url":"https://assets-eu.researchsquare.com/files/rs-7633374/v2/0b149c7fec9fa8fc8f01b8f0.json"},{"id":100623551,"identity":"67424049-93bf-4ad3-972f-64bda6435fd7","added_by":"auto","created_at":"2026-01-19 18:50:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":476590,"visible":true,"origin":"","legend":"","description":"","filename":"JCELgardner2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7633374/v2_covered_34d40f69-2b37-4002-b22d-ead89d782703.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical simulation of the resonant tunneling diode using a\n regularized quantum hydrodynamic model","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":"resonant tunneling diode, quantum hydrodynamic model","lastPublishedDoi":"10.21203/rs.3.rs-7633374/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7633374/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" Time-dependent simulations of the resonant tunneling diode to steady\n state using the smooth quantum hydrodynamic (QHD) model are\n presented, which show realistic negative differential resistance\n (the experimental signal of quantum resonance) in the\n current-voltage curve. These are the first time-dependent\n simulations of the smooth QHD model. The simulations match fully\n quantum mechanical simulations of the resonant tunneling diode much\n better than any other QHD simulations to date.\n For the time-dependent simulations, a regularization of the smooth\n QHD model equations to prevent an unstable growing mode is\n implemented. 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