New Scaling of Child-Langmuir Law in the Quantum Regime

摘要: 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 the CL law is increased by larger factor due to tunneling through space-charge potential, interaction becomes important when applied gap voltage ${V}_{g}$ spacing $D$ are, respectively, on order Hartree energy level, nanometer scale. It found that scaling ${V}_{g}^{3/2}$ ${D}^{\ensuremath{-}2}$ no longer valid in regime, new ${V}_{g}^{1/2}$ ${D}^{\ensuremath{-}4}$ established. smooth transition from regime also demonstrated.