Atomic and electronic structure of single and multiple vacancies in GaN nanowires from first-principles

Abstract

We present a comprehensive first-principles investigation of single and multiple gallium and nitrogen vacancies in gallium nitride (GaN) nanowires. We consider nanowires in the [0001] growth direction, with diameters of 9.5 and $15.9\text{ }\text{\AA{}}$ and investigate the stability of multiple vacancies for a wide range of configurations to determine the preferred spatial distribution. The influence of saturating the dangling bonds at the edge of the nanowires is also investigated. For one, two, and three nitrogen vacancies, we find that the most favorable configuration is with the vacancies at the edge of the nanowires. We also find that for multiple (two and three) nitrogen vacancies, the vacancies prefer to cluster together rather than remain well separated. For one and two gallium vacancies, the preferred vacancy location is also at the edge of the nanowires, with clustering favored for the two vacancies. Examining the band structure of unsaturated nanowires (with and without vacancies), we observe states in the band gap that can be attributed to edge states. These edge states are removed when the dangling bonds at the edge of the nanowires are saturated with hydrogen. For unsaturated wires, the nature of the single Ga and N vacancy states is similar to in the bulk, acting as a triple acceptor and single donor, respectively. The position of the vacancy states relative to the two regions of edge-induced states is similar to their location relative to the conduction band minimum and valence band maximum in the bulk, suggesting that any conductivity arising from the vacancies will be confined to the outer region of the nanowires. The two- and three-nitrogen vacancy complexes induce additional states in the band gap, acting as double and triple donors respectively, while the two-gallium vacancy complex reconstructs to an ${\text{N}}_{3}$-like structure and induces several fully occupied and unoccupied singlet state in the band gap. Examining the defect-induced states for the gallium vacancy in the saturated wire versus in bulk GaN, we find a similar result in terms of the number, location, and occupation of the defect states, except the states in the wire are slightly deeper in the band gap. For the nitrogen vacancy in the saturated wire versus in bulk GaN, we also find similar behavior in terms of the number and occupation of the defect states. However, the higher lying singly occupied state is closer to the conduction band in the wire, and the location of the fully occupied singlet state is below the valence band maximum in bulk GaN, and above it in the saturated nanowire. Considering the formation energy of gallium and nitrogen vacancies, we find nitrogen vacancies are significantly more stable than gallium vacancies, and thus we expect them to be the major defect in GaN nanowires.