Density-functional tight-binding calculations of electronic states associated with grain boundaries in GaN

The electronic structure of the $\left(3\overline{7}40\right)\Sigma =37(\theta =9.3°)$, $\left(3\overline{5}20\right)\Sigma =19(\theta =13.4°)$, and $\left(1\overline{3}20\right)\Sigma =7(\theta =21.6°)$ tilt grain boundaries has been investigated by means of atomic computer simulation within the density-functional-based tight-binding approach. Among the three possible atomic configurations of these boundaries, namely, the 5/7-, the 4-, and the 8 dislocation core interfaces, it is shown that the 4 or 8 interface introduces deep states in the very center and the upper half of the band gap whereas the 5/7 interface possesses only states close to the conduction band.

Figure 1

Atomic structures of the$\left[0001\right]∕\left(1\overline{3}20\right)\Sigma =7$ $$tilt boundary. For all the figures, the full circles represent N atoms and the open circles the Ga atoms. Atomic structures of $\Sigma =37$can be found in Ref. 13 and those of $\Sigma =19$in Ref. 12.

Figure 2

Local density of states of the $\Sigma =7$ tilt boundary projected on atoms located at the $A$, $B$, $C$, $D$ and $E$ sites in Figs. 1a, 1c: (a) 5/7 and (b) 8 interface. The vertical lines show the band gap of bulk GaN.

Figure 3

Variation of atomic charges with respect to the atomic charges of the bulk crystal: (a) 5/7 and (b) 8 interface. For bulk crystal, the electron charge is $12.44e^{-}$ for Ga atoms and $5.56e^{-}$ for N atoms corresponding to a transfer of electrons from Ga to N atoms of $0.56e^{-}$.

Figure 4

Schematic diagram of energy levels in the band gap for the studied interfaces. In the notation $I_{\alpha }^{\beta }$, the symbol $\alpha$ refers to the tilt boundary and the symbol $\beta$ to the interface type. The notation $C^{\beta }$ designs the core type of the edge dislocation. The values correspond to those obtained after scaling all gap states and conduction band level energies, which give rise to a calculated gap of the bulk GaN equal to the experimental one (3.4 eV). Only values superior to 0.2 eV and inferior than or equal to 3.1 eV are mentioned.