Correlation between the electronic structures and diffusion paths of interstitial defects in semiconductors: The case of CdTe

Using first-principles calculations, we study the diffusions of interstitial defects Cd, Cu, Te, and Cl in CdTe. We find that the diffusion behavior is strongly correlated with the electronic structure of the interstitial diffuser. For Cd and Cu, because the defect state is the nondegenerated $s$-like state under the $T_d$ symmetry, the diffusions are almost along the $\langle 111\rangle$ directions between the tetrahedral sites, although the diffusion of Cu shows some deviation due to the coupling between the Cu $d$ and host $s$ orbitals. The diffusions of the neutral and charged Cd and Cu follow similar paths. However, for Te and Cl atoms, because the defect state is the degenerated $p$-like state under the $T_d$ symmetry, large distortions occur. Therefore the diffusion paths are very different from those of the interstitial Cd and Cu atoms, and depend strongly on the charge states of the interstitial atoms. For Te, we find that the distortion is mostly stabilized by the crystal-field splitting, but for Cl, the exchange splitting plays a more important role.

Figure 1

The diffusion path (a) and diffusion energy curves (b) of the interstitial Cd atom. In (a), the cyan balls represent Cd, the green balls represent Te, and the diffusion path of the interstitial Cd atom is highlighted in red. The diffusion paths are the same for neutral and charged Cd atoms. The energy of the most stable site is set to zero in (b). The black squares (Cd), red dots (${\mathrm{Cd}}^{+}$), and blue triangles (${\mathrm{Cd}}^{2+}$) represent the energies of the NEB images, and the lines are spline fittings.

Figure 2

The diffusion path (a) and diffusion energy curves (b) of the interstitial Cu atom. In (a), the cyan balls represent Cd, the green balls represent Te, and the diffusion path of the interstitial Cu atom is highlighted in red. The dashed lines indicate the [111] and [$11\overline{1}$] directions. The diffusion paths are similar for neutral and charged Cu atoms. The energy of the most stable site is set to zero in (b). The black squares (Cu) and red dots (${\mathrm{Cu}}^{+}$) represent the energies of the NEB images, and the lines are spline fittings.

Figure 3

The most stable site (a) and (c), diffusion barrier site (b), and diffusion energy curve (d) of the neutral interstitial Te. In (a)–(c), the cyan balls represent Cd, the green balls represent Te, and the interstitial Te is highlighted in red. The energy of the most stable site is set to zero in (d). The black squares represent the energies of the NEB images, and the line is a spline fitting.

Figure 4

The schematic energy positions of defect levels of Te at the $T_c$, $\mathrm{Spl}$, and $C$ sites. The filled squares represent electrons and open ones represent holes. At the $T_c$ site, the symmetry is $T_d$ and the defect levels are the triplet-degenerated $t_2$ states, which are occupied by four electrons (two holes). At the $\mathrm{Spl}$ site, the symmetry is broken so that the $t_2$ states are splitted into three nondegenerated states. For neutral Te, the first two states are fully occupied and the last one is empty. At the $C$ site, the $t_2$ states are splitted into a fully occupied nondegenerated state below the VBM and doublet-degenerated states. For ${\mathrm{Te}}^{2+}$, the doublet-degenerated states are fully empty.

Figure 5

The most stable site (a) and (c), diffusion barrier site (b), and diffusion energy curve (d) of the $2+$ charged interstitial ${\mathrm{Te}}^{2+}$. In (a)–(c), the cyan balls represent Cd, the green balls represent Te, and the interstitial Te is highlighted in red. In (a), ${\mathrm{Te}}_1$ is the interstitial atom. In (b), ${\mathrm{Te}}_1$ and ${\mathrm{Te}}_2$ share the same lattice site ($\mathrm{Spl}$ structure). In (c) ${\mathrm{Te}}_1$ enters the lattice site and kicks out ${\mathrm{Te}}_2$, which becomes the new interstitial atom. The energy of the most stable site is set to zero in (d). The black squares represent the energies of the NEB images, and the line is a spline fitting.

Figure 6

The schematic energy positions of defect levels of Cl at the $T_c$ site and $B_c$ site. The filled squares represent electrons and open ones represent holes. At the $T_c$ site, the symmetry is $T_d$ and the defect levels are the triplet-degenerated $t_2$ states. Because the defect levels of Cl are below the VBM, Cl already accepts an electron from the VBM and becomes ${\mathrm{Cl}}^{-}$. At the $B_c$ site, the symmetry is broken so that the $t_2$ states are splitted into three nondegenerated states. Two of them are still below VBM and the last one is inside the band gap. In this case, Cl becomes neutral. In this figure, the exchange splitting is not included.

Figure 7

The LDOS of Cl $p$ states at the $B_c$ site. The dashed line indicates the VBM of the host. We can clearly observe the exchange splitting ($\sim 0.5$ eV) above the VBM in the red rectangle.

Figure 8

The diffusion path and diffusion energy curve of Cl. It first diffuses from the $T_c$ site to a $B_c$ site, then diffuses from the $B_c$ to a nearby $B_c$ site, and finally diffuses from the new $B_c$ site to a new $T_c$ site. In (a), the cyan balls represent Cd, and green balls represent Te, and the diffusion path of the interstitial Cl is highlighted in red. The dashed lines indicate [111] and [$11\overline{1}$] directions. The energy of the $T_c$ site is set to zero in (b). The black squares represent the energies of the NEB images, and the line is a spline fitting. The red dots are calculated without spin polarization. Apparently, the exchange splitting plays an important role in decreasing the diffusion energy barrier.

Figure 9

The diffusion energy curve of ${\mathrm{Cl}}^{-}$. The energy of the $T_c$ site is set to zero. The black squares represent the energies of the NEB images, and the line is a spline fitting. The diffusion path of ${\mathrm{Cl}}^{-}$ is similar to that of Cd.