Importance of on-site corrections to the electronic and structural properties of InN in crystalline solid, nonpolar surface, and nanowire forms

In this work, we employ first-principle calculations to predict the structural and electronic properties of InN nanowires comparing the results obtained at the local-density approximation (LDA) and at the $\text{LDA}+U$ level. Our study suggests that in the case of wurtzite InN it is important to apply an on-site Hubbard correction to both the indium $d$ states and the nitrogen $p$ states in order to recover the correct energy level symmetry and ordering at the $\Gamma$ point of the Brillouin zone and obtain a reliable description of InN band structure. We apply the methodology to predict the electronic properties of InN nanowires and find that LDA and $\text{LDA}+U$ results are in qualitative agreement both in terms of confinement and surface-passivant effects.

Figure 1

(Color online) Band structure and density of states of wurtzite InN obtained with LDA (left panel) and $\text{LDA}+U^{\left(d+p\right)}$ (right panel). The VBM is taken as energy zero.

Figure 2

Band structure of wurtzite InN bulk around the Fermi level close to the $\Gamma$ point obtained with LDA (left panel) and $\text{LDA}+U^{\left(d+p\right)}$ (right panel) approaches. The VBM is taken as energy zero.

Figure 3

(Color online) Band structure of InN $\left(1\overline{1}00\right)$ surface obtained with LDA (left panel) and $\text{LDA}+U^{\left(d+p\right)}$ (right panel) approaches. The LU state corresponds to a surface state localized on the In surface atoms and the HO state corresponds to a surface state localized on the N surface atoms. The VBM is taken as energy zero.

Figure 4

(Color online) Ball and stick representation of the investigated InN nanowires: left—1 ring NW $\left(d\approx 4.1\text{Å}\right)$, middle—2 rings NW $\left(d\approx 10.6\text{Å}\right)$, and right—3 rings NW $\left(d\approx 17.6\text{Å}\right)$. Large balls represent In atoms and small balls represent N atoms.

Figure 5

(Color online) Band structures for InN nanowires with clean surfaces: top panel—1 ring NW, middle panel—2 rings NW, and bottom panel—3 rings NW. Left column—LDA and right column—$\text{LDA}+U^{\left(d+p\right)}$. The VBM is taken as energy zero.

Figure 6

Band gap vs inverse diameter $\left(1/d\right)$ of InN nanowires with clean surface indicated by solid (LDA) and dotted $\left(\text{LDA}+U^{\left(d+p\right)}\right)$ lines, and for hydrogenated nanowires indicated by dashed (LDA) and dashed-dotted $\left(\text{LDA}+U^{\left(d+p\right)}\right)$ lines.

Figure 7

(Color online) Electronic charge-density isosurface [denoted by shaded green (gray) area] for the highest occupied state in the case of $\text{LDA}+U^{\left(d+p\right)}$: left panel—NW3 and right panel—$\text{NW}3+\text{H}$. Sketched globes represent atoms.