On the limiting density of field emission current from metals

The present work considers the problem of the field emission characteristics of metals for the range of external electric fields 10⁸-10⁹ V/cm. It has been shown that, as far as the field emission is considered, ultrahigh fields are the electric fields at which the decrease of the height of the potential barrier due to the Schottky effect is greater than the work function of the emitter. In this case, the penetration of the external electric field into the metal emitter results in a substantial increase in electron density near the emission boundary. It has also been shown that the Fowler-Nordheim relation that describes the electric field dependence of the current density does not hold at ultrahigh fields. Analytical expressions for this dependence have been obtained taking into account the perturbation of the electronic structure of the emitter by the external electric field both in the WKB and in the Miller-Good approximation in the low-temperature limit. Based on the results obtained, it has been shown that the saturation of the FE current density does not happen, as supposed earlier, and the current density practically linearly increases with electric field.