First-principles study of deformation behavior and structural defects in $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$ and $\mathrm{Cu}(\mathrm{In},\mathrm{Ga}){\mathrm{Se}}_2$

Electronic structure and total-energy calculations have been performed for $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$ and $\mathrm{Cu}(\mathrm{In},\mathrm{Ga}){\mathrm{Se}}_2$ using density-functional theory with generalized gradient corrections. To understand the fracture and deformation behavior in chalcopyrites, we calculated the cleavage and generalized stacking fault energies in $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$ and $\mathrm{Cu}(\mathrm{In},\mathrm{Ga}){\mathrm{Se}}_2$ and demonstrated a brittle character of crack propagation. Antiphase boundary and intrinsic stacking fault defects have low formation energies and are quite probable in these chalcopyrites. The main slip system and preferable cleavage plane should be $⟨\overline{1}10⟩\left(112\right)$ and (112), respectively. For the ⟨110⟩(001) and $⟨\overline{1}10⟩\left(112\right)$ dislocations in $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$, we predict a strong tendency for splitting in two partials.

Figure 1

(Color online) The structure of chalcopyrite $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$: (a) orientation along [001]; (b) orientation along [221], and (c) the structure projection on the (112) plane.

Figure 2

The GSF energies for displacement $u$ along the direction ⟨110⟩(001) for $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$ (black circle) and $\mathrm{Cu}\left(\mathrm{In}\mathrm{Ga}\right){\mathrm{Se}}_2$ (white circle).

Figure 3

The GSF energies for displacement $u$ along the direction ⟨010⟩(001) for $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$ (black circle) and $\mathrm{Cu}\left(\mathrm{In}\mathrm{Ga}\right){\mathrm{Se}}_2$ (white circle).

Figure 4

The GSF energies for displacement along the direction $⟨\overline{1}10⟩\left(112\right)$ for $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$ (black circle) and $\mathrm{Cu}\left(\mathrm{In}\mathrm{Ga}\right){\mathrm{Se}}_2$ (white circle); the shift was considered in the Cu-In layer, orientation $\left[\overline{2}\overline{2}\overline{1}\right]$.