Comparison of direct tunneling in Metal-GaN Schottky junctions using different k⃗ · p⃗ models for the complex bandstructure

In this work, we study the phenomenon of Direct Tunneling(DT) in Metal-nGaN Schottky junctions. We first compare tunneling current densities computed using quantum (NEGF) and the semi-classical (WKB) transport formulations, based on a single band parabolic approximation to the complex GaN bandstructure. We then estimate current densities using the WKB transport formulation, with complex bandstructures extracted from the two band k⃗ · p⃗ and four band k⃗ · p⃗ theories of the wurtzite GaN. We find that a WKB transport formulation is quite reliable for low bias values. We also find that the use of multi-band k⃗ · p⃗ models for calculating tunneling effective mass is necessary to estimate tunneling current densities accurately.