Simple derivation of quantum scaling in Child-Langmuir law

被引：73

作者：

Ang, LK ^{[1
]}

Lau, YY

Kwan, TJT

机构：

[1] Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore

[2] Univ Michigan, Dept Nucl Engn & Radiol Sci, Ann Arbor, MI 48109 USA

[3] Los Alamos Natl Lab, Div Appl Phys, Los Alamos, NM 87545 USA

来源：

IEEE TRANSACTIONS ON PLASMA SCIENCE | 2004年 / 32卷 / 02期

关键词：

beams; cathodes; nanotechnology; space charge;

D O I：

10.1109/TPS.2004.826366

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

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.

引用

页码：410 / 412

页数：3