Theoretical estimation of tunnel currents in hetero-junctions: The special case of nitride tunnel junctions

Abstract

In tunnel junctions, an electron current is transformed into a hole current via a quantum tunnel effect through the semiconductor bandgap. We derive a complete theory for the current through tunnel junctions based on Kane's approach and extended to the general case of a nonconstant electric field and arbitrary potentials in heterostructures. The theory mixes an analytical approach based on Fermi's golden rule and the numeric calculation of wave functions in the heterostructure. The parallel component of the transport is included in the calculation and the symmetry of the conduction and valence band states are taken into account in the transition rates. The calculation is limited to the elastic case and leads to a simple and fast estimation of the tunnel current in any semiconductor junction. We applied our calculation to III-nitrides due to the importance of tunnel junctions in these materials, since they allow circumventing the problem of insufficient p-type doping in GaN and AlGaN. Our approach is also particularly relevant in III-nitride heterojunctions owing to the large band offsets and varying piezoelectric fields present in these materials. The resulting dependence of the inverse current-voltage characteristics on several parameters is studied, making it possible to optimize thickness, doping, and composition of a smaller gap semiconductor layer inserted in the junction. Among all parameters, we show the importance of the doping levels in the n and p regions, while a thin undoped interlayer with a smaller bandgap energy critically enhances the tunnel transparency.