Simple derivation of quantum scaling in Child-Langmuir law

Author

Ang, L.K. ; Lau, Y.Y. ; Kwan, T.J.T.

Author_Institution

Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, Singapore

Volume

32

Issue

2

fYear

2004

fDate

4/1/2004 12:00:00 AM

Firstpage

410

Lastpage

412

Abstract

A simple derivation of the new scaling of Child-Langmuir law in the quantum regime is presented. Based on a dimensional argument of the Schrodinger equation and the Poisson equation, the limiting current in the deeply quantum regime is found to be proportional to the square root of the gap voltage and to the inverse fourth power of gap spacing. The importance of electron exchange-correlation interactions in the quantum regime is discussed.

Keywords

Poisson equation; Schrodinger equation; electron correlations; exchange interactions (electron); nanoelectronics; space-charge-limited conduction; Child-Langmuir law; Poisson equation; Schrodinger equation; electron exchange-correlation interactions; gap spacing; gap voltage; inverse fourth power; limiting current; quantum regime; quantum scaling; space charge; Current density; Electron emission; Laboratories; Nuclear electronics; Poisson equations; Power engineering and energy; Quantum computing; Schrodinger equation; Space charge; Voltage; Beams; cathodes; nanotechnology; space charge;

fLanguage

English

Journal_Title

Plasma Science, IEEE Transactions on

Publisher

ieee

ISSN

0093-3813

Type

jour

DOI

10.1109/TPS.2004.826366

Filename

1308484