  The paper discusses the nano-diode and nano-triode structures of vacuum
electronics. Such structures may have the dielectric film with the thickness of
several nanometers wich is located on the cathode. Such film with a large
dielectric constant reduces the thickness of the potential barrier by about
film thickness and reduces the height of barrier. The grid electrode structure
may contain several periods of metallization with a thickness of tens of
nanometers, which allows one to obtain the resonant under barrier tunneling.
For all structures we obtained electrostatic Green's function, the built
profiles potential barriers, the calculated tunneling coefficients and
Volt-Ampere Characteristics (VAC) with regard to the distribution of electron
energies. The structures under consideration require to use of low voltages on
the gate (grid) electrodes. They are promising for the electron gun with a
large current controlled by low voltage on the grid, for example, in TWT with
subsequent acceleration of the electron beam. Since a major influence on the
tunneling provides the grid, the electrons emitted from the grid with
approximately the Fermi velocity, and the calculation of the electron gun with
multiple electrodes after the grid is greatly simplified.
