{"title":"Mathematical Modeling of Field Emission From a Microscale-Size Cathode to a Vacuum","authors":"V. G. Danilov;V. D. Borisov","doi":"10.1109/TED.2025.3535843","DOIUrl":null,"url":null,"abstract":"In this article, we propose a numerical method for calculating solutions of the PDE (the heat equation for the cathode temperature and the continuity equation for the current density inside and outside the cathode) with discontinuous flux at the emission surface of a cathode placed in a vacuum. The discontinuity of the flux appears because of the Nottingham effect and tunneling of emitting electrons. In the present article, this approach is applied to mathematical modeling of field emission from a conic silicon cathode of small size (about ten micrometers) to a vacuum, but can be used in other problems with similar types of flux jumps.","PeriodicalId":13092,"journal":{"name":"IEEE Transactions on Electron Devices","volume":"72 3","pages":"1462-1468"},"PeriodicalIF":3.2000,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Electron Devices","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10891157/","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
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Abstract
In this article, we propose a numerical method for calculating solutions of the PDE (the heat equation for the cathode temperature and the continuity equation for the current density inside and outside the cathode) with discontinuous flux at the emission surface of a cathode placed in a vacuum. The discontinuity of the flux appears because of the Nottingham effect and tunneling of emitting electrons. In the present article, this approach is applied to mathematical modeling of field emission from a conic silicon cathode of small size (about ten micrometers) to a vacuum, but can be used in other problems with similar types of flux jumps.
期刊介绍：
IEEE Transactions on Electron Devices publishes original and significant contributions relating to the theory, modeling, design, performance and reliability of electron and ion integrated circuit devices and interconnects, involving insulators, metals, organic materials, micro-plasmas, semiconductors, quantum-effect structures, vacuum devices, and emerging materials with applications in bioelectronics, biomedical electronics, computation, communications, displays, microelectromechanics, imaging, micro-actuators, nanoelectronics, optoelectronics, photovoltaics, power ICs and micro-sensors. Tutorial and review papers on these subjects are also published and occasional special issues appear to present a collection of papers which treat particular areas in more depth and breadth.
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