Site localization of Cd impurities in sapphire

By combining first-principles electronic structure calculations and existing time-differential γ-γ perturbed-angular-correlation experiments we studied the site localization, the local environment, and the electronic structure of Cd impurities in sapphire (α-Al${}_2$O${}_3$) single crystals in different charged states. The ab initio calculations were performed with the full-potential augmented plane wave plus local orbitals method and the projector augmented wave method. Comparing the calculated electric-field-gradient tensor at the Cd nuclei in the α-Al${}_2$O${}_3$ host lattice and the corresponding available experimental values, we have seen that it is equally possible for Cd to replace an Al atom (in a negative charge state) or to be placed in an interstitial site (in a neutral charge state). To finally address the issue of the Cd impurity localization, we performed formation energy calculations. These results have shown that Cd placed in the substitutional Al site, in the negatively charged state, is the most probable configuration.

Figure 1

Corundum α-Al${}_2$O${}_3$ unit cell in (a) rhombohedral representation ($R\overline{3}c$ space group), (b) hexagonal representation, and (c) supercell with $a$′ $=$ 2$a$, $b$′ $=$ 2$b$, and $c$′ $=$ $c$, used to simulate the 1:4 (a), 1:12 (b), and 1:48 (c) cation dilution of the impurity. The gray, white, and black spheres correspond to Al, O, and Cd atoms, respectively.

Figure 2

Total density of states (DOS) of (a) pure α-Al${}_2$O${}_3$, (b) (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^0$, and (c) relaxed (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^0$. The vertical lines are at the top of the valence band (solid) and at the highest occupied state (dotted). In (a) both lines are coincident.

Figure 3

$V_{33}$ as a function of the number of steps in the atomic relaxation process, starting from the ideal experimental positions (left side) towards the final equilibrium positions, for the three (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^0$ cells shown in Fig. 1.

Figure 4

Final equilibrium positions of the Cd impurity and its oxygen nearest neighbors for (a) substitutional Cd in the Al site in (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^{1-}$ (the relaxations are magnified five times) and (b) Cd located at the interstitial site in (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^0$.

Figure 5

Partial density of states (PDOS) of (a) $d$ and $p$ contributions projected at the Cd site, (b) $p$ contribution projected at the O1 and O2 sites, for (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^0$ (on the left) and (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^{1-}$ (on the right). The vertical lines are at the top of the valence band (solid) and at the highest occupied state (dotted).

Figure 6

Partial $d$ and $p$ density of states (PDOS) projected at the Cd site for (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^0$ (left) and (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^{1-}$ (right). The vertical lines are at the top of the valence band (solid) and at the highest occupied state (dotted).

Figure 7

Total density of states (DOS) of (a) pure α-Al${}_2$O${}_3$, (b) (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^0$, and (c) (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^{2+}$. The vertical lines are at the top of the valence band (solid) and at the highest occupied state (dotted). In (a) and (c) both lines are coincident.

Figure 8

$d$ and $p$ partial density of states (PDOS) projected at the Cd site for (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^0$ (left) and (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^{2+}$ (right). The vertical lines are at the top of the valence band (solid) and at the highest occupied state (dotted). On the right, both lines are coincident.

Figure 9

$p$ partial density of state (PDOS) projected at the O1${}_{\mathrm{i}}$ and O2${}_{\mathrm{i}}$ sites for the (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^0$ (left) and (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^{2+}$ (right). The vertical lines are at the top of the valence band (solid) and at the highest occupied state (dotted). On the right, both lines are coincident.

Figure 10

Formation energies as a function of the Fermi energy level ${\varepsilon }_F$ (0 ≤ ${\varepsilon }_F$ ≤ ${\varepsilon }_g$, where ${\varepsilon }_g$ is the band-gap energy). The black solid line correspond to (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^0$, the black dashed line to (Al${}_2$O${}_3$:Cd${}_{\mathrm{s}}$)${}^{1-}$, the gray solid line to (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^0$ and the gray dashed line to (Al${}_2$O${}_3$:Cd${}_{\mathrm{i}}$)${}^{2+}$.