Theory of shot noise in high-current space-charge-limited field emission

Abstract

This paper studies the electron shot noise of high current space-charge limited (SCL) field emission, including the effects of both quantum partitioning and Coulomb correlation of the emitted tunneling electrons inside a gap. The Fano factor $(\ensuremath{\gamma})$ is calculated over a wide range of applied voltages, gap spacings, and electron pulse lengths in classical, quantum and relativistic regimes. It is found that the effect of space charge smoothing (observed in thermionic emission) is no longer valid for high current field emission, as the space charge field will increase the potential barrier and thus decrease the degree of quantum partitioning (larger $\ensuremath{\gamma}$). However, the shot noise of SCL field emission in a nanogap may be suppressed due to the combination of Coulomb repulsion and exchange-correlation potential among the tunneling electrons, where the dynamics of the electrons inside the gap are treated by using a quantum mean field model. Coulomb correlation can be ignored when the pulse length of the electron beam is much smaller than the gap transit time. Possible experimental settings are discussed in order to observe the shot noise suppression of field emission with and without the space charge effects.