The influence of an emitter accumulation layer on field emission from a multilayer cathode

A numerical model has been developed to investigate resonant electron field emission from Si–SiO2–Si–SiO2 multilayer cathodes incorporating Si quantum well (QW). The positions of the energy levels in the Si QW were calculated by numerical solution of the time-independent Schrödinger equation, taking into account the boundary conditions on the electron wave function and its derivative, and a difference in effective mass in adjacent layers. Emission currents from 3D electron states of the Si emitter conduction band, and from 2D states of its accumulation layer energy sub-bands, were taken into account. A triangular-well model has been used for accumulation layer, with Airy functions as envelope electron wave functions. Analysis of the field emission current–voltage dependencies showed the following. For a highly doped emitter, there is only one resonant current maximum, which corresponds to resonant tunneling of 3D electrons of emitter through a resonant level in the Si QW in the cathode coating. When, as emitter doping level is decreased the first occupied energy sub-band occurs in the accumulation layer QW, there is increase of emission from it and the current resonance maximum divides into two, and so a second current maximum appears at higher electric field than first one. It corresponds to resonant tunneling of electrons from accumulation layer 2D states through the same resonant level in the Si QW of cathode coating. The enhancement characteristics of a resonance peak depend on emitter doping considerably more for a 2D electron emission than for 3D electron emission.