Characterization of vibrational and mechanical properties of quaternary compounds Cu${}_2$ZnSn$S_4$ and Cu${}_2$ZnSnSe${}_4$ in kesterite and stannite structures

In this paper, structural, elastic, and dynamical properties of Cu${}_2$ZnSnS${}_4$ and Cu${}_2$ZnSnSe${}_4$ are calculated for kesterite and stannite structures using the density functional and density functional perturbation theories. The stability of these two materials, either in a kesterite or stannite crystal structure, is verified by using both elastic constants and phonon dispersions results. No significant difference is observed between the calculated energetic, mechanical, and dynamical properties of the kesterite and stannite phases of either compound. Using extensively rich sampled first Brillouin-zone phonon data, relaxation time-dependent lattice thermal conductivities are predicted through the solution of the phonon Boltzmann transport equation. For both compounds, the relaxation time-dependent lattice thermal conductivity of the stannite structure along the $x$ or $y$ directions is found to be $\sim$25$\%$ larger than its value in the $z$ direction; in contrast, the predicted difference in the kesterite structure is only $\sim$5$\%$.

Figure 1

Schematical representation of eigendisplacement patterns of (a) kesterite and (b) stannite structures.

Figure 2

Calculated phonon dispersions and densities of states for Cu${}_2$ZnSnS${}_4$.

Figure 3

Calculated phonon dispersions and densities of states for Cu${}_2$ZnSnSe${}_4$.

Figure 4

Calculated lattice thermal conductivity within constant relaxation time approximation in $x$ (or $y$) and $z$ directions (a) for CZTS and (b) for CZTSe.