First-principles investigation of the structural, dynamical, and dielectric properties of kesterite, stannite, and PMCA phases of ${\mathrm{Cu}}_2{\mathrm{ZnSnS}}_4$

${\mathrm{Cu}}_2{\mathrm{ZnSnS}}_4$ (CZTS) is a promising material as an absorber in photovoltaic applications. The measured efficiency, however, is far from the theoretically predicted value for the known CZTS phases. To improve the understanding of this discrepancy, we investigate the structural, dynamical, and dielectric properties of the three main phases of CZTS (kesterite, stannite, and PMCA) using density functional perturbation theory (DFPT). The effect of the exchange-correlation functional on the computed properties is analyzed. A qualitative agreement of the theoretical Raman spectrum with measurements is observed. However, none of the phases correspond to the experimental spectrum within the error bar that is usually to be expected for DFPT. This corroborates the need to consider cation disorder and other lattice defects extensively in this material.

Figure 1

Conventional unit cells of the studied CZTS crystal structures: (a) kesterite (KS), (b) stannite (ST), and (c) PMCA. The Wyckoff positions of the Cu, Zn, Sn, and S atoms (in red, blue, grey, and yellow, respectively) are also indicated.

Figure 2

Atomic decomposition of the different vibrational modes as computed from LDA. The contribution from the Cu, Zn, Sn, and S atoms are shown in red, blue, grey, and yellow, respectively. The components parallel $(\parallel )$ and perpendicular $(\perp )$ to the $c$ axis are represented using light and dark shades of the colors associated to the different atoms.

Figure 3

Transmittance calculated using LDA, PBEsol, and PBE for KS, ST, and PMCA. For comparison with experiment [42], the absorber thickness is taken to be $1\mu \mathrm{m}$ and the phonon lifetime to be 10 ps. Two series of figures are presented: (a), (b), and (c) allow for a comparison between the different functionals for KS, ST, and PMCA (red, green, and blue curves, respectively); (d), (e), and (f) permit to contrast the various phases with LDA, PBEsol, and PBE (solid, dashed, and dotted curves, respectively). The light, medium, and dark curves represent the parallel, perpendicular, and average transmittance, respectively (the directions being indicated with respect to the $c$ axis of the conventional tetragonal cell). The experimental results are shown as a black curve at the bottom of each panel. The black vertical dashed lines are drawn as a guide for the eyes at the frequencies measured experimentally.

Figure 4

Raman spectra computed using LDA, PBEsol, and PBE for KS, ST, and PMCA. For comparison with experiment [16], a temperature of 300 K is chosen for the Bose-Einstein occupation factors. Two series of figures are presented: (a), (b), and (c) allow for a comparison between the different functionals for KS, ST, and PMCA (red, green, and blue curves, respectively); (d), (e), and (f) permit to contrast the various phases with LDA, PBEsol, and PBE (solid, dashed, and dotted curves, respectively). In the lower part of the panels, the intensity is also given on a log scale in order to ease the identification of weaker peaks. The experimental results are shown as a black curve at the bottom of each panel. The vertical dashed lines are drawn as a guide for the eyes at the frequencies measured experimentally (in black and brown to distinguish TO and LO frequencies).