and their (Sn,Ge) alloys*

The ternary materials Cu₂SnS₃ (CTS) and Cu₂GeS₃ (CGS) are currently being considered as potential candidates for absorber layers in solar cells. Their crystalline structure is close to the one of zinc-blende ZnS with two third of zinc atoms replaced by Cu atoms and one third by Ge/Sn, respectively. However, due to the symmetry breaking, the Raman spectra of CTS and CGS display a plethora of peaks.
Ab-initio modellig of these materials with standard density-functional theory (DFT) faces the difficulty that the band gap is underestimated and even inverted. We performed calculations of phonons and Raman spectra using the hybrid HSE functional which properly reproduces the electronic band structure. We model the Raman spectra of Cu₂Sn_(1-x)Ge_xS₃ alloys via interpolation of atomic masses and dynamical matrices (force constants) between the two limits of pure CTS and CGS compounds. This enables us to calculate approximately the spectra of alloyed compounds for any value of the mixing parameter x. Furthermore, we can understand the shift of the high frequency peaks of the spectra from CTS to CGS. About half of the shift is due to the difference in the masses of Ge and Sn. The other half is due to the different bond-strength of Ge-S and Sn-S covalent bonds.