Quantum extension of Child-Langmuir law

摘要

Using a simple mean field model of the electron-electron interaction, study has been done of the effect of space charge in a planar diode. 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 (non-quantum) regime is demonstrated.