title: New scaling of child-langmuir law in the quantum regime.
abstract: This paper presents a consistent quantum mechanical model of Child-Langmuir (CL) law, including electron exchange-correlation interaction, electrode's surface curvature, and finite emitter area. The classical value of the CL law is increased by a larger factor due to the electron tunneling through the space-charge potential, and the electron exchange-correlation interaction becomes important when the applied gap voltage Vg and the gap spacing D are, respectively, on the order of Hartree energy level, and nanometer scale. It is found that the classical scaling of Vg(3/2) and D(-2) is no longer valid in the quantum regime, and a new scaling of Vg(1/2) and D(-4) is established. The smooth transition from the classical regime to the quantum regime is also demonstrated.
authors.affiliation: School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore. elkang@ntu.edu.sg
authors.forename: L K
authors.initials: LK
authors.lastname: Ang
authors.forename: T J T
authors.initials: TJ
authors.lastname: Kwan
authors.forename: Y Y
authors.initials: YY
authors.lastname: Lau