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

Akinwande, A. I.

doi:10.1063/1.4848076

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

Full Record
Other Related Research

Abstract

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 »« less

Authors:

Akinwande, A. I. ^[1]

Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

Publication Date:: Sat Dec 21 00:00:00 EST 2013

OSTI Identifier:: 22266199

Resource Type:: Journal Article

Journal Name:: Journal of Applied Physics

Additional Journal Information:: Journal Volume: 114; Journal Issue: 23; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979

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

Citation Formats


                    Patterson, A. A., E-mail: apatters@mit.edu, Akinwande, A. I., and Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Elementary framework for cold field emission: Incorporation of quantum-confinement effects.  United States: N. p., 2013. 
        Web.  doi:10.1063/1.4848076.

Copy to clipboard


                    Patterson, A. A., E-mail: apatters@mit.edu, Akinwande, A. I., & Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Elementary framework for cold field emission: Incorporation of quantum-confinement effects.  United States.  https://doi.org/10.1063/1.4848076

Copy to clipboard


                    Patterson, A. A., E-mail: apatters@mit.edu, Akinwande, A. I., and Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. 2013.  
        "Elementary framework for cold field emission: Incorporation of quantum-confinement effects".  United States.  https://doi.org/10.1063/1.4848076.

Copy to clipboard


                    
@article{osti_22266199,

  title        = {Elementary framework for cold field emission: Incorporation of quantum-confinement effects},

  author       = {Patterson, A. A., E-mail: apatters@mit.edu and Akinwande, A. I. and Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139},

  abstractNote = {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 emitters with transverse dimensions under approximately 5 nm, and in those cases, geometry-specific ECD equations incorporating quantum-confinement effects should be employed instead.},

  doi          = {10.1063/1.4848076},

  url          = {https://www.osti.gov/biblio/22266199},
  journal      = {Journal of Applied Physics},

  issn         = {0021-8979},

  number       = 23,

  volume       = 114,

  place        = {United States},

  year         = {Sat Dec 21 00:00:00 EST 2013},

  month        = {Sat Dec 21 00:00:00 EST 2013}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1063/1.4848076

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

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

Journal Article Akinwande, A. - Journal of Applied Physics

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 ourmore »« less
https://doi.org/10.1063/1.4919827
Locally Resolved Electron Emission Area and Unified View of Field Emission from Ultrananocrystalline Diamond Films

Journal Article Chubenko, Oksana; Baturin, Stanislav; Kovi, Kiran; ... - ACS Applied Materials and Interfaces

One of the common problems in case of field emission from polycrystalline diamond films, which typically have uniform surface morphology, is uncertainty in determining exact location of electron emission sites across the surface. Although several studies have suggested that grain boundaries are the main electron emission source, it is not particularly clear what makes some sites emit more than the others. It is also practically unclear how one could quantify the actual electron emission area and therefore field emission current per unit area. In this paper we study the effect of actual, locally resolved, field emission (FE) area on electronmore »« less
https://doi.org/10.1021/acsami.7b07062
Beam quality in field emitter arrays

Conference Liu, Y; Lau, Y

The emerging field of vacuum microelectronics offers exciting possibilities in miniature coherent radiation sources, flat panel displays, and ultra-fast logic circuits. The crucial component is the electron emitter, which consists of an array of sharp tips from which electrons undergo field emission according to the Fowler-Nordheim (FN) relation. In this paper, the authors present a theoretical analysis of the beam emittance and of the beam brightness expected from a field emitter array. Scaling laws for these quantities are constructed that take into account of the electric field enhancement factors that accompany the sharp tips, and they are derived in amore »« less
Theory of electron emission from atomically sharp metallic emitters in high electric fields

Miscellaneous He, Jun

A systematic theoretical investigation of the effect of tip geometry on the field emission current voltage characteristics from atomically sharp metallic field emitters is presented. A free electron model is used for the metal emitters with non-planar geometries in studying the dependence of the current density on tip geometry, local field, and temperature. The classical image interaction is derived exactly for the metal emitters modeled as cones, paraboloids, hyperboloids and sphere on cones. The classical image interaction for these non-planar emitter geometries is diminished in magnitude relative to the planar image interaction. The bias potential for the model emitter modifiesmore »« less
STUDY OF METAL SURFACES BY THE FIELD EMISSION MICROSCOPE. Technical Report No. 9

Technical Report Young, R

An investigation was initiated in order to employ the energy distribution of field-emitted electrons as a means of studying the electronic band structure in metals and semiconductors. When the energy analyzer was improved in order to carry out this study, the measured energy distribution was much narrower than that predicted by the existing normal-energy distribution theory. Further investigation reveaied that the retarding potential energy analyzer which was employed measures the total electron energy rather than the energy associated with the component of velocity normal to the surface. The Fowler-Nordheim equation was derived in a new way in order to preservemore »« less

Similar Records