Screened-exchange density functional theory description of the electronic structure and phase stability of the chalcopyrite materials ${\text{AgInSe}}_2$ and ${\text{AuInSe}}_2$

We present a systematic assessment of the structural properties, the electronic density of states, the charge densities, and the phase stabilities of ${\mathrm{AgInSe}}_2$ and ${\mathrm{AuInSe}}_2$ using screened-exchange hybrid density functional theory, and compare their properties to those of ${\mathrm{CuInSe}}_2$. For ${\mathrm{AgInSe}}_2$, hybrid density functional theory properly captures several experimentally measured properties, including the increase in the band gap and the change in the direction of the lattice distortion parameter $u$ in comparison to ${\mathrm{CuInSe}}_2$. While the electronic properties of ${\mathrm{AuInSe}}_2$ have not yet been experimentally characterized, we predict it to be a small gap ($\approx 0.15$ eV) semiconductor. We also present the phase stability of ${\mathrm{AgInSe}}_2$ and ${\mathrm{AuInSe}}_2$ according to screened-exchange density functional theory, and compare the results to predictions from conventional density functional theory, results tabulated from several online materials data repositories, and experiment (when available). In comparison to conventional density functional theory, the hybrid functional predicts phase stabilities of ${\mathrm{AgInSe}}_2$ in better agreement with experiment: discrepancies in the calculated formation enthalpies are reduced by approximately a factor of 3, from $\approx 0.20$ eV/atom to $\approx 0.07$ eV/atom, similar to the improvement observed for ${\mathrm{CuInSe}}_2$. We further predict that ${\mathrm{AuInSe}}_2$ is not a stable phase, and can only be present under nonequilibrium conditions.

Figure 1

Electronic band structure of ${\mathrm{CuInSe}}_2$ according to DFT-PBE (left) and DFT-HSE06 (right), in comparison to recent ARPES measurements (middle). Adapted with permission from Ref. [33]. Copyrighted by the American Physical Society.

Figure 2

Density of states (DOS) for ${\mathrm{CuInSe}}_2$ (left), ${\mathrm{AgInSe}}_2$ (middle), ${\mathrm{AuInSe}}_2$ (right) calculated by DFT-PBE (upper) and DFT-HSE06 (lower). The black lines are total DOS, and red, blue, and green lines are projected DOS of Cu/Ag/Au, In, and Se respectively. The Fermi level is shown by the dashed grey line.

Figure 3

Electronic charge density distribution of ${\mathrm{CuInSe}}_2$ (left), ${\mathrm{AgInSe}}_2$ (middle), ${\mathrm{AuInSe}}_2$ (right), across a plane that contains Cu/Ag/Au, In, and Se atoms according to DFT-HSE06. The contour lines of isosurfaces are spaced logarithmically and the arrows are marked corresponding to the same isosurface value for all three materials.

Figure 4

Comparisons of formation enthalpies of the chalcopyrites and the binaries calculated by DFT-PBE and DFT-HSE06 with experimental data for $X{\mathrm{InSe}}_2$ [40], Cu-Se and In-Se binaries [43], and Ag-Se binary [44]. (a) Absolute values of formation enthalpies in eV per atom. (b) Absolute deviations from the experimental values in eV/atom.

Figure 5

Phase stability diagrams of ${\mathrm{CuInSe}}_2$ according to DFT-PBE (left), DFT-HSE06 (middle), and experimental data (right). The area below the blue lines or above the red lines indicate where ${\mathrm{CuInSe}}_2$ is unstable with respect to formation of Cu-Se or In-Se binaries, respectively. The shaded area shows the chemical potential range for which ${\mathrm{CuInSe}}_2$ is stable.

Figure 6

Phase stability diagrams of ${\mathrm{AgInSe}}_2$ according to DFT-PBE (left), DFT-HSE06 (middle), and experimental data (right). The area below the blue line or above the red lines indicate where ${\mathrm{AgInSe}}_2$ is unstable with respect to formation of Ag-Se or In-Se binaries. The shaded area shows the chemical potential range for which ${\mathrm{AgInSe}}_2$ is stable.

Figure 7

Phase stability diagrams of ${\mathrm{AuInSe}}_2$ from DFT-PBE (left), DFT-HSE06 (right). The area below the blue lines or above the red lines indicate where ${\mathrm{AuInSe}}_2$ is unstable with respect to decomposition to Au-Se and In-Se binaries. ${\mathrm{AuInSe}}_2$ is not stable in either DFT functional for any value of chemical potentials.

Figure 8

Density of states (DOS) for binary compounds calculated by DFT-HSE06. The black lines are total DOS, and red, blue, and green lines are projected DOS of Cu/Ag/Au, In, and Se respectively. The Fermi level is shown by the dashed grey line.