Calculating field emission currents in nanodiodes - a multi-group formalism with space charge and exchange-correlation effects

Inclusion of electron-electron interaction is essential in nano-diodes to understand the underlying physical phenomenon and tailor devices accordingly. However, both space charge and exchange-correlation interactions involve electrons at different energies and hence a self-consistent multi-energy-group solution of the Schr\{o}dinger-Poisson system is required. It is shown here that the existence of a limiting density-dependent potential at low applied voltages allows calculation of the field emission current. Despite additional interactions, a Fowler-Nordheim behaviour is observed. It is also found that the exchange-correlation potential dominates at these voltages in nanogaps and possibly leads to a higher turn-on voltage.