Quantum extension of Child-Langmuir law

Abstract

Using a simple mean-field model of the electron-electron interaction, we have studied the effect of space charge in a planar diode. Our results show, in particular, that the classical value for the limiting current in such a diode can be exceeded by a large factor due to the effect of tunneling. The smooth transition of the solutions from the quantum to the classical (nonquantum) regime is demonstrated.