Space-Charge Limited Current From a Finite Emitter in Nano- and Microdiodes

We simulate numerically the classical charge dynamics in a microscopic, planar, vacuum diode with a finite emitter area and a finite number of electrons in the gap. We assume that electrons are emitted under space-charge limited conditions with a fixed potential applied to the diode. The Coulomb interaction between all electrons is included using the method of molecular dynamics. We compare our results to the conventional 2-D Child-Langmuir and explain how it is limited in applicability for submicrometer diameter emitters. Finally, we offer some simple relations for understanding space-charge limited flow from very small emitters.