$\text{LDA}+U$ and tight-binding electronic structure of InN nanowires

In this paper we employ a combined ab initio and tight-binding approach to obtain the electronic and optical properties of hydrogenated Indium nitride (InN) nanowires. We first discuss InN band structure for the wurtzite structure calculated at the $\text{LDA}+U$ level and use this information to extract the parameters needed for an empirical tight-binging implementation. These parameters are then employed to calculate the electronic and optical properties of InN nanowires in a diameter range that would not be affordable by ab initio techniques. The reliability of the large nanowires results is assessed by explicitly comparing the electronic structure of a small diameter wire studied both at $\text{LDA}+U$ and tight-binding level.

Figure 1

(Color online) Band structure of InN bulk obtained with (a) $\text{LDA}+U$ and (b) TB approaches. The symmetry group labels of some relevant states are indicated in (a).

Figure 2

(Color online) Top of the InN valence band. The empty circles correspond to the $\text{LDA}+U$ bands, and the lines represent the TB bands. The component $k_z$ of the wave vector $\mathit{k}$ is normalized to $\frac{\pi }{c}$, such that $k_z=1$ correspond to A. The wave vector in the $M$ direction is expressed as $\frac{\pi }{a}\left(\xi ,\frac{1}{\sqrt{3}}\xi ,0\right)$, where $0\le \xi \le 1$. The symmetry group of the states at $\Gamma$ are indicated and the bands are denoted as A, B, and C.

Figure 3

(Color online) In the left upper part, nanowire represented with ball-and-sticks of diameter $16.2\text{Å}$. As well in the upper part, top of the valence band calculated with (a) LDAU and (b) TB method. In the lower part, we represent the square of the wave function for the valence band states $v_1$, $v_2$, $v_3$, and $v_4$ calculated with both approaches.

Figure 4

(Color online) Dependence of the confinement energy on the nanowire size. The limit of $1/r\to 0$ is the bulk band gap.

Figure 5

(Color online) Optical absorption spectra for in-plane (${\mathit{e}}_{\perp }$ multiplied by two) and on-axis $\left({\mathit{e}}_{\mathit{z}}\right)$ light polarization (see main text). The wave functions that participate in the relevant optical transitions are also represented (both spectra are displayed in the same scale).