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Title: Elementary framework for cold field emission from quantum-confined, non-planar emitters

Abstract

For suitably small field emitters, the effects of quantum confinement at the emitter tip may have a significant impact on the emitter performance and total emitted current density (ECD). Since the geometry of a quantum system uniquely determines the magnitude and distribution of its energy levels, a framework for deriving ECD equations from cold field electron emitters of arbitrary geometry and dimensionality is developed. In the interest of obtaining semi-analytical ECD equations, the framework is recast in terms of plane wave solutions to the Schrödinger equation via the use of the Jeffreys-Wentzel-Kramers-Brillouin approximation. To demonstrate the framework's consistency with our previous work and its capabilities in treating emitters with non-planar geometries, ECD equations were derived for the normally unconfined cylindrical nanowire (CNW) and normally confined (NC) CNW emitter geometries. As a function of the emitter radius, the NC CNW emitter ECD profile displayed a strong dependence on the Fermi energy and had an average ECD that exceeded the Fowler-Nordheim equation for typical values of the Fermi energy due to closely spaced, singly degenerate energy levels (excluding electron spin), comparatively large electron supply values, and the lack of a transverse, zero-point energy. Such characteristics suggest that emitters with non-planar geometries maymore » be ideal for emission from both an electron supply and electrostatics perspective.« less

Authors:
;  [1]
  1. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
Publication Date:
OSTI Identifier:
22402996
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 117; Journal Issue: 17; Other Information: (c) 2015 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; CONFINEMENT; CURRENT DENSITY; CYLINDRICAL CONFIGURATION; ELECTRONS; ELECTROSTATICS; ENERGY LEVELS; FIELD EMISSION; INHOUR EQUATION; MATHEMATICAL SOLUTIONS; QUANTUM SYSTEMS; SCHROEDINGER EQUATION; SPIN; WAVE PROPAGATION; WKB APPROXIMATION

Citation Formats

Patterson, A. A., E-mail: apatters@mit.edu, and Akinwande, A. I.. Elementary framework for cold field emission from quantum-confined, non-planar emitters. United States: N. p., 2015. Web. doi:10.1063/1.4919827.
Patterson, A. A., E-mail: apatters@mit.edu, & Akinwande, A. I.. Elementary framework for cold field emission from quantum-confined, non-planar emitters. United States. doi:10.1063/1.4919827.
Patterson, A. A., E-mail: apatters@mit.edu, and Akinwande, A. I.. Thu . "Elementary framework for cold field emission from quantum-confined, non-planar emitters". United States. doi:10.1063/1.4919827.
@article{osti_22402996,
title = {Elementary framework for cold field emission from quantum-confined, non-planar emitters},
author = {Patterson, A. A., E-mail: apatters@mit.edu and Akinwande, A. I.},
abstractNote = {For suitably small field emitters, the effects of quantum confinement at the emitter tip may have a significant impact on the emitter performance and total emitted current density (ECD). Since the geometry of a quantum system uniquely determines the magnitude and distribution of its energy levels, a framework for deriving ECD equations from cold field electron emitters of arbitrary geometry and dimensionality is developed. In the interest of obtaining semi-analytical ECD equations, the framework is recast in terms of plane wave solutions to the Schrödinger equation via the use of the Jeffreys-Wentzel-Kramers-Brillouin approximation. To demonstrate the framework's consistency with our previous work and its capabilities in treating emitters with non-planar geometries, ECD equations were derived for the normally unconfined cylindrical nanowire (CNW) and normally confined (NC) CNW emitter geometries. As a function of the emitter radius, the NC CNW emitter ECD profile displayed a strong dependence on the Fermi energy and had an average ECD that exceeded the Fowler-Nordheim equation for typical values of the Fermi energy due to closely spaced, singly degenerate energy levels (excluding electron spin), comparatively large electron supply values, and the lack of a transverse, zero-point energy. Such characteristics suggest that emitters with non-planar geometries may be ideal for emission from both an electron supply and electrostatics perspective.},
doi = {10.1063/1.4919827},
journal = {Journal of Applied Physics},
number = 17,
volume = 117,
place = {United States},
year = {Thu May 07 00:00:00 EDT 2015},
month = {Thu May 07 00:00:00 EDT 2015}
}
  • 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 ofmore » 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 emitters with transverse dimensions under approximately 5 nm, and in those cases, geometry-specific ECD equations incorporating quantum-confinement effects should be employed instead.« less
  • Diamond deposition onto single Mo field emitters was accomplished by two methods: microwave plasma chemical vapor deposition and a dielectrophoresis of diamond powder. Observation by transmission electron microscopy and scanning electron microscopy revealed a significant amount of deposition at the tips. The field emission characteristics were measured before and after diamond deposition on the same emitters. Field emission from diamond coated emitters yielded significant increases in emission current and lower Fowler{endash}Nordheim slopes. We discuss a possible mechanism to explain current enhancement that depends primarily upon the Mo-diamond interface. {copyright} {ital 1996 American Vacuum Society}