Calculations of field emission from AlxGa1−xN as a function of stoichiometry

The field emission current densities from ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N}$ are theoretically calculated as a function of stoichiometry. The material parameters of ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N}$ are obtained as weighted averages of those of AlN and GaN. The Poisson equation is first solved to obtain the energy band diagrams as a function of the composition x. The transmission coefficient through the tunneling barrier is numerically calculated using the fact that the Airy function is the exact solution of Schrödinger’s equation for a linear potential. By evaluating the energy-dependent integral on the band structure-dependent surface that is given by projecting the energy ellipsoid on the emission surface, we obtained the field electron energy distribution $\mathrm{j(E).}$ The calculated emission current j shows a strong dependence of the field emission on the stoichiometric composition x. The obtained Fowler–Nordheim plots exhibit different field dependent structures in the low and high field regimes. It is also found that the carrier concentration dependence of j is not pronounced for low fields but becomes significant for high fields.