Maha_Astra: A Partition-Theoretic Framework for Precision Modeling in the 1nm and 0.5nm Transistor Regimes

Maha_Astra: A Partition-Theoretic Framework for Precision Modeling in the 1nm and 0.5nm Transistor Regimes | 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 Maha_Astra: A Partition-Theoretic Framework for Precision Modeling in the 1nm and 0.5nm Transistor Regimes S. Eshwar Rao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8442680/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 the semiconductor industry pushes beyond the 3nm node towards the 1nm (Angstrom) and 0.5nm regimes, traditional continuum-based compact models such as BSIM-CMG (Berkeley Short-channel IGFET Model - Common Multi-Gate) exhibit critical divergences from experimental reality. This divergence arises fundamentally from the "smoothing" mathematical approximations used to handle the transition from subthreshold to strong inversion, which mask the discrete quantum nature of charge transport at the atomic scale. This article presents the Maha_Astra Framework, a novel theoretical approach that abandons continuum drift-diffusion physics in favor of a discrete, partition-theoretic method rooted in Srinivasa Ramanujan’s mathematics. We provide a rigorous derivation of the Maha_Astra Master Equation, contrasting it with standard industry formulations, and present a node-by-node numerical comparison from 30nm down to 0.5nm. Furthermore, we derive the quantum transport limits for Silicon, demonstrating its inevitable failure below 3nm, and provide the theoretical basis for the stability of 2D materials (MoS2 and Graphene) in the sub-1nm regime using architectural verification via Verilog. Maha_Astra Framework Ramanujan Partition Theory 1nm Transistor Scaling Discrete Transport Physics BSIM-CMG Divergence Angstrom Era Full Text Additional Declarations No competing interests reported. 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-8442680","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":565662004,"identity":"a1bbe839-a3c2-4ebc-937c-100ce7603eca","order_by":0,"name":"S. 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This divergence arises fundamentally from the \"smoothing\" mathematical approximations used to handle the transition from subthreshold to strong inversion, which mask the discrete quantum nature of charge transport at the atomic scale. This article presents the Maha_Astra Framework, a novel theoretical approach that abandons continuum drift-diffusion physics in favor of a discrete, partition-theoretic method rooted in Srinivasa Ramanujan’s mathematics. We provide a rigorous derivation of the Maha_Astra Master Equation, contrasting it with standard industry formulations, and present a node-by-node numerical comparison from 30nm down to 0.5nm. 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