Theoretical analysis of 1D resonant tunneling behavior in ion-enhanced cold field and thermo-field emission

Abstract

In cold field and thermo-field emission, positive ions or adsorbates very close to the cathode surface can enhance emission current by both resonant and non-resonant processes. In this paper, resonant tunneling behavior is investigated by solving the one-dimensional Schrödinger equation in the presence of an ion, and the enhancement due to resonant processes is evaluated. Results shows that as the applied electric field increases, the resonant states move from higher to lower energies as the ion energy levels are shifted down. Conversely, as the ion position moves closer to the cathode, the resonant states shift up in energy. Further, through a simplified perturbation analysis, the general scaling of these trends can be predicted. These shifts of resonant states directly impact the emission current density, and they are especially relevant when the applied field is on the order of a few volts per nanometer (∼0.5–3 V/nm) and the ion is a few nanometers (∼0.5–3 nm) away from the cathode. Further, when the energy level for resonant emission coincides with the Fermi level of a metallic cathode, the current density is particularly enhanced. The results of this study suggest that it may be possible to control (augment/inhibit) the resonant emission current by manipulating the supply function of a cathode relative to the operating conditions of the emitter in either ion-enhanced or adsorbate-enhanced field emission, which can be applied to various plasma and electron emission technologies.