Nitrogen vacancies in InN: Vacancy clustering and metallic bonding from first principles

We perform first-principles density-functional theory calculations to investigate the structural and electronic properties and the formation energies of nitrogen vacancies in wurtzite InN. We report an extensive and systematic study of the favorable atomic and electronic configurations of up to six vacancies in large supercells. The isolated vacancy acts as a donor in a p-type material where there is very little interaction between the singly positive charged vacancies. Their spatial distribution is therefore predicted to be random arrangements of single defects. However, in more n-type materials, the neutral charge state becomes favored and we find that the vacancies then prefer to be situated close to one another on the nearest-neighbor (like species) sites, forming ``vacancy complexes or clusters.'' In the highest positive charge state of the complexes, the clustering is unstable with respect to isolated single positive charged vacancies. However, the negatively charged and lower positively charged (e.g., $1+$ and $2+$ charge states for three nitrogen vacancies) complexes also exhibit an attractive interaction between the vacancies, thus also favoring clustering. The formation of such nitrogen vacancy clusters gives rise to local indium-rich regions with metallic-like bonding. We discuss the effect that these defect structures have on the nature of the electronic states in the region of the band gap, in relation to recent experimental results (as measured by, e.g., infrared photoluminescence, x-ray diffraction, and transmission electron microscopy).