Scaling for quantum tunneling current in nano- and subnano-scale plasmonic junctions

When two conductors are separated by a sufficiently thin insulator, electrical current can flow between them by quantum tunneling. This paper presents a self-consistent model of tunneling current in a nano- and subnano-meter metal-insulator-metal plasmonic junction, by including the effects of space charge and exchange correlation potential. It is found that the J-V curve of the junction may be divided into three regimes: direct tunneling, field emission, and space-charge-limited regime. In general, the space charge inside the insulator reduces current transfer across the junction, whereas the exchange-correlation potential promotes current transfer. It is shown that these effects may modify the current density by orders of magnitude from the widely used Simmons' formula, which is only accurate for a limited parameter space (insulator thickness > 1 nm and barrier height > 3 eV) in the direct tunneling regime. The proposed self-consistent model may provide a more accurate evaluation of the tunneling current in the other regimes. The effects of anode emission and material properties (i.e. work function of the electrodes, electron affinity and permittivity of the insulator) are examined in detail in various regimes. Our simple model and the general scaling for tunneling current may provide insights to new regimes of quantum plasmonics.