Field emission in diode and triode vacuum nanostructures

This paper explores nanodiode and nanotriode structures with incorporated dielectric films in vacuum electronics. Such emission structures allow for very high (on the order of 10 12 A / m 2 and more) current densities and differ greatly from conventional field emitters. For all structures considered, we derive the electrostatic Green’s function, construct potential barrier profiles, calculate tunneling coefficients, and determine the volt-ampere (VAC) characteristics, taking into account the distribution of electron energies. This work presents novel results, including a precise formula for the potential distribution in a structure with a dielectric film. This formula accounts for the finite conductivity of the semiconductor film and incorporates the reverse tunnel current within the structure. Considering this effect in nanostructures is crucial, particularly at low anodic voltages. © 2025 Author(s).