Features of vacuum resonant tunneling at one-and two-well barrier potentials

The features of one-dimensional vacuum tunneling and calculation of the tunneling current in barrier quantum structures with one and two wells are considered. The structures are formed by several electrodes: the cathode, the anode and two grids. The potential profiles are constructed by the method of multiple images. Equations for eigenvalues and metastable levels of a structure with an arbitrary potential profile are found. For full resonant tunneling, the metastable levels must fall into the region of the electron kinetic energy distribution at the cathode, which occurs in single-well structures in the absence of an anode voltage or at a low anode voltage compared to the voltage on the grids. A significant voltage at the anode leads to an asymmetric structure and incomplete resonant tunneling. In this case, a two-well structure with a double grid allows obtaining full resonant tunneling for a number of energies and increasing the tunneling current by orders of magnitude.