Band structure calculation of field emission from AlxGa1−xN as a function of stoichiometry

Abstract

The field emission current density j from the ternary alloys AlxGa1−xN is theoretically calculated as a function of stoichiometry. The material parameters of AlxGa1−xN are obtained as weighted averages of those of AlN and GaN. Using the method of W. W. Lui and M. Fukuma [J. Appl. Phys. 60, 1555(1986)], the transmission coefficients are numerically calculated using Airy functions that are solutions of the Schrödinger equation in a piecewise linear potential region. Band structure effects in the calculation of j are included using the projection of the energy ellipsoids on the emission surfaces. The results for j show a strong dependence of the field emission on the stoichiometric composition, which reflects the composition dependence of the electron affinity. The Fowler–Nordheim plots and calculated field electron energy distribution curves both exhibit structures which suggest different field-dependent transmission probabilities in the low and high field regimes.