Electronic structure and lattice dynamics in kesterite-type ${\text{Cu}}_2{\text{ZnSnSe}}_4$ from first-principles calculations

Electronic band structure, densities of states, and the details of chemical bonding in ${\text{Cu}}_2{\text{ZnSnSe}}_4$, a compound used in photovoltaic applications and structurally close to chalcopyrite, has been studied using the SIESTA method within the local-density approximation of the density-functional theory. Calculated zone-center phonons for ${\text{Cu}}_2{\text{ZnSnSe}}_4$ in kesterite and stannite phases reveal a similarity to those in structurally close ${\text{CuInSe}}_2$, with some additional modes which must become observable due to the reduced crystal symmetry. The prediction that the highest TO vibration mode has predominantly Zn contribution is consistent with a strong Zn concentration dependence of this particular mode earlier observed in (Zn,Cd)-mixed kesterite systems. A detailed comparison of calculated vibration spectra for kesterite and stannite phases helps to identify the features which could be useful for distinguishing these two structures in practice.

Figure 1

(Color online) Band structure of ${\text{Cu}}_2{\text{ZnSnSe}}_4$ kesterite as calculated in the LDA by SIESTA.

Figure 2

(Color online) Partial densities of states (normalized per atom) in ${\text{Cu}}_2{\text{ZnSnSe}}_4$ kesterite, broadened with the width parameter of 0.2 eV.

Figure 3

(Color online) Charge density profile (of pseudovalence states) along the lines connecting different atoms, total (dashed line) and within two energy intervals, $\left(-10:-6\right)\text{eV}$ (red line) and $\left(-6:-3\right)\text{eV}$ (green line). In the inset, the isosurfaces of two integrated densities are shown within boxes of the corresponding color. See text for details.

Figure 4

(Color online) Isosurfaces (at $\pm 0.05{\text{Å}}^{-3}$) and contours (from 0.05 to $-0.05$; linear step of $0.01{\text{Å}}^{-3}$; different colors indicate positive/negative values) of selected zone-center Kohn–Sham functions. Band indexes (number of occupied bands: 31) are shown in boxes on the left, beside the corresponding band energies. Left/right plots are views in different cutting planes of the same rectangular prism, chosen to comprise all atom types. The trace of the other cutting plane and the direction of view is shown in the upper part of each counterpart plot.

Figure 5

(Color online) $\mathbf{q}=0$ projected density of vibration modes for different atoms in ${\text{Cu}}_2{\text{ZnSnSe}}_4$-kesterite (middle panel), compared with that of ${\text{Cu}}_2{\text{ZnSnSe}}_4$-stannite (bottom panel) and ${\text{CuInSe}}_2$-chalcopyrite (top panel). The frequencies experimentally detected by Raman scattering for the latter system are indicated by vertical bars.

Figure 6

(Color online) Vibration patterns in selected modes of CZTSe-kesterite. See text for discussion.

Figure 7

(Color online) Vibration patterns in selected modes of CZTSe-stannite. See text for discussion.