Structures and electronic states of Mg incorporated into InN surfaces: First-principles pseudopotential calculations

Structures and electronic states of Mg incorporated into InN surfaces in various orientations including nonpolar $\left(10\overline{1}0\right)$ and $\left(11\overline{2}0\right)$ as well as polar (0001) and $\left(000\overline{1}\right)$ surfaces are systematically investigated by performing first-principles pseudopotential calculations. Employing a thermodynamic approach, the calculated surface energies demonstrate characteristic features in the stability of Mg-incorporated surfaces depending on the growth condition. The calculated density of states also predict that regardless of surface orientation, Mg acceptors at the surface are compensated by the extra electrons originating from the surface states of In layers in bare surfaces.

Figure 1

(Color online) Calculated formation energies of Mg-incorporated (a) InN(0001) and (b) $\text{InN}\left(000\overline{1}\right)$ surfaces (solid lines) using Eq. (1) as a function of ${\mu }_{\text{In}}$, along with those for bare surfaces (dashed lines). The value of ${\mu }_{\text{Mg}}$ are $E_{\text{Mg}}-2.5$ and $E_{\text{Mg}}-2.7\text{eV}$, which correspond to Mg-rich conditions $\left(p=1.0\times {10}^{-7}\text{Torr}\right)$ at $T=725$ and 825 K for InN(0001) and $\text{InN}\left(000\overline{1}\right)$ surfaces, respectively.

Figure 2

(Color online) DOS for (a) laterally contracted In-bilayer structure $\left({\text{In}}_{\text{bilayer}}\right)$ and the $2\times 2$ surface with three substitutional Mg atoms $\left({\text{Mg}}_{\text{In}}\left(3/4\right)\right)$ by Mg incorporation on InN(0001) surface, and for (b) In-adlayer reconstruction $\left({\text{In}}_{\text{adlayer}}\right)$ and In-adlayer structure with substitutional Mg $\left({\text{In}}_{\text{adlayer}}+{\text{Mg}}_{\text{In}}\right)$ on InN(0001) surface. The local DOS of N atom near the surface for ${\text{Mg}}_{\text{In}}\left(3/4\right)$ and ${\text{In}}_{\text{adlayer}}+{\text{Mg}}_{\text{In}}$ is also shown by blue (dotted) lines. The energy gap obtained from bulk VBM and CBM in the band structure of Mg-incorporated InN surfaces is shown by shaded region. The zero of energy is set at the VBM. The vertical solid and dashed lines denote the Fermi energies of Mg-incorporated and bare surfaces, respectively.

Figure 3

(Color online) Calculated formation energies of Mg-incorporated (a) $\text{InN}\left(10\overline{1}0\right)$ and (b) $\text{InN}\left(11\overline{2}0\right)$ surfaces (solid lines) using Eq. (1) as a function of ${\mu }_{\text{In}}$, along with those for bare surfaces (dashed lines). The value of ${\mu }_{\text{Mg}}$ is $E_{\text{Mg}}-2.5\text{eV}$, which corresponds to Mg-rich conditions $\left(p=1.0\times {10}^{-7}\text{Torr}\right)$ at $T=725\text{K}$.

Figure 4

(Color online) Schematic top views of (a) $\text{InN}\left(10\overline{1}0\right)$ with In bilayer $\left({\text{In}}_{\text{bilayer}}\right)$, (b) Mg-incorporated $\text{InN}\left(10\overline{1}0\right)$ with In adlayer $\left({\text{In}}_{\text{adlayer}}+2{\text{Mg}}_{\text{In}}\right)$, (c) $\text{InN}\left(11\overline{2}0\right)$ with In adlayer $\left({\text{In}}_{\text{adlayer}}\right)$, and (d) Mg-incorporated $\text{InN}\left(11\overline{2}0\right)$ with In adlayer. Large and small gray circles represent In and N atoms, respectively. Red (black) circles denote Mg atoms and blue (light-gray) circles top-layer In atoms. The unit cell used in this study is shown by dashed rectangle.

Figure 5

(Color online) DOS for (a) laterally contracted In-bilayer structure $\left({\text{In}}_{\text{bilayer}}\right)$ and In-monolayer surface with two substitutional Mg atoms $\left({\text{In}}_{\text{adlayer}}+2{\text{Mg}}_{\text{In}}\right)$ by Mg incorporation on $\text{InN}\left(10\overline{1}0\right)$ surfaces, and for (b) $\text{InN}\left(11\overline{2}0\right)$ surface with In adlayer $\left({\text{In}}_{\text{adlayer}}\right)$ and In-adlayer surface with two substitutional Mg atoms $\left({\text{In}}_{\text{adlayer}}+2{\text{Mg}}_{\text{In}}\right)$. Note that the gap energies obtained by the calculations of $\text{InN}\left(10\overline{1}0\right)$ and $\left(11\overline{2}0\right)$ surfaces are larger than that in the bulk case by 0.4 and 0.5 eV, respectively. The same notation as in Fig. 2.