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Title: Elementary framework for cold field emission: Incorporation of quantum-confinement effects

Although the Fowler-Nordheim (FN) equation serves as the foundation of cold field emission theory, it may not be suitable for predicting the emitted current density (ECD) from emitters with a quantum-confined electron supply. This work presents an analytical framework for treating cold field emission from metals that includes the effects of a quantum-confined electron supply. Within the framework, quantum confinement in emitters is classified into transverse and normal quantum confinement based on the orientation of the confinement relative to the emission direction. The framework is used to generate equations predicting the ECD from rectangular and cylindrical emitter geometries comprised of electron supplies of reduced dimensionality. Transverse quantum confinement of the electron supply leads to a reduction in the total ECD as transverse emitter dimensions decrease and normal quantum confinement results in an oscillatory ECD as a function of the normal quantum well width. Incorporating a geometry-dependent field enhancement factor into the model reveals an optimal transverse well width for which quantum confinement of the electron supply and field enhancement equally affect the ECD and a maximum total ECD for the emitter geometry at a given applied field is obtained. As a result, the FN equation over-predicts the ECD from emittersmore » with transverse dimensions under approximately 5 nm, and in those cases, geometry-specific ECD equations incorporating quantum-confinement effects should be employed instead.« less
Authors:
;  [1] ;  [2]
  1. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
22266199
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 114; Journal Issue: 23; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CONFINEMENT; CURRENT DENSITY; CYLINDRICAL CONFIGURATION; ELECTRONS; EQUATIONS; FIELD EMISSION; QUANTUM WELLS