Elementary framework for cold field emission from quantumconfined, nonplanar 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 semianalytical ECD equations, the framework is recast in terms of plane wave solutions to the Schrödinger equation via the use of the JeffreysWentzelKramersBrillouin approximation. To demonstrate the framework's consistency with our previous work and its capabilities in treating emitters with nonplanar 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 FowlerNordheim 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, zeropoint energy. Such characteristics suggest that emitters with nonplanar geometries maymore »
 Authors:
 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., Email: apatters@mit.edu, and Akinwande, A. I.. Elementary framework for cold field emission from quantumconfined, nonplanar emitters. United States: N. p., 2015.
Web. doi:10.1063/1.4919827.
Patterson, A. A., Email: apatters@mit.edu, & Akinwande, A. I.. Elementary framework for cold field emission from quantumconfined, nonplanar emitters. United States. doi:10.1063/1.4919827.
Patterson, A. A., Email: apatters@mit.edu, and Akinwande, A. I.. Thu .
"Elementary framework for cold field emission from quantumconfined, nonplanar emitters". United States.
doi:10.1063/1.4919827.
@article{osti_22402996,
title = {Elementary framework for cold field emission from quantumconfined, nonplanar emitters},
author = {Patterson, A. A., Email: 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 semianalytical ECD equations, the framework is recast in terms of plane wave solutions to the Schrödinger equation via the use of the JeffreysWentzelKramersBrillouin approximation. To demonstrate the framework's consistency with our previous work and its capabilities in treating emitters with nonplanar 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 FowlerNordheim 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, zeropoint energy. Such characteristics suggest that emitters with nonplanar 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 FowlerNordheim (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 quantumconfined electron supply. This work presents an analytical framework for treating cold field emission from metals that includes the effects of a quantumconfined 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 »

Field emission from diamond coated molybdenum field emitters
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 Modiamond interface. {copyright} {ital 1996 American Vacuum Society}