Extended antisite defects in tetrahedrally bonded semiconductors

Typically point defects are modeled by adding, removing, or exchanging at most few atoms around a given lattice site. We demonstrate the possibility of formation of extended antisite defects that involve complex, nonlocal atomic rearrangements, which cannot be captured within a simple point defect model. We illustrate the formation of extended antisite defects in ${\mathrm{Cu}}_2{\mathrm{SnS}}_3$ and ${\mathrm{Cu}}_2{\mathrm{SnZnS}}_4$ solar absorbers where they lower the formation energy by up to about 1 eV per defect. These extended antisite configurations can dramatically change the stoichiometries and doping properties of multinary semiconductors that have a propensity towards disorder.

Figure 1

First and second coordination shell of (a) Sn atom and (b) ${\mathrm{Cu}}_{\mathrm{Sn}}$ antisite defect in monoclinic ${\mathrm{Cu}}_2{\mathrm{SnS}}_3$. S-based tetrahedra: S-${\mathrm{Cu}}_2{\mathrm{Sn}}_2$ (yellow), S-${\mathrm{Cu}}_3\mathrm{Sn}$ (blue), S-${\mathrm{Cu}}_4$ (red).

Figure 2

Formation of ${\mathrm{Cu}}_{\mathrm{Sn}}$ in CTS: The smallest number of high-energy motifs after completion of simulated annealing with the motif-based model Hamiltonian as a function of the supercell size.

Figure 3

Formation energy of ${\mathrm{Cu}}_{\mathrm{Sn}}$ antisite defects calculated with $\text{DFT}+U$ as a function of the number of S-${\mathrm{Cu}}_4$ motifs. The formation energy is evaluated using a disordered supercell of CTS as reference host cell and reference chemical potentials of elemental phases in the chemical standard state ($\mathrm{\Delta }{\mu }_{\mathrm{Cu}}=\mathrm{\Delta }{\mu }_{\mathrm{Sn}}=0$).

Figure 4

Top: Mixing energies between CTS and ${\mathrm{Cu}}_3\mathrm{Sn}{\mathrm{S}}_4$ as a function of alloy compositions composition $x, {\mathrm{Cu}}_{8+x}{\mathrm{Sn}}_{4-x}{\mathrm{S}}_{12}$. Bottom: Distribution of S-${\mathrm{Cu}}_2{\mathrm{Sn}}_2$ (yellow) and S-${\mathrm{Cu}}_4$ (red) motif centers in 144 atom cells with two ${\mathrm{Cu}}_{\mathrm{Sn}}$ antisite defects; for clarity S-${\mathrm{Cu}}_3\mathrm{Sn}$ are removed.

Figure 5

Mixing energy for (a) CTS-${\mathrm{Cu}}_3\mathrm{Sn}{\mathrm{S}}_4$-ZnS and (b) CTS-CZTS-${\mathrm{Cu}}_3\mathrm{Sn}{\mathrm{S}}_4$ systems calculated within the motif-based model Hamiltonian.