Electronic band-structure and optical constants of Pb₂GeS₄: Ab initio calculations and X-ray spectroscopy experiments

The electronic band-structure of the ternary sulfide Pb₂GeS₄ was investigated by combining experimental and theoretical methods. Binding energy (BE) values of core electrons of Pb₂GeS₄ are measured employing X-ray photoelectron spectroscopy (XPS) for as-synthesized and treated with Ar⁺-ions crystal surfaces. The XPS measurements indicate that Ar⁺-ion treatment does not change the BE values of the core-level electrons of atoms constituting the Pb₂GeS₄ single crystal as well as peculiarities of the XPS valence band (VB) spectrum. The treatment does not cause changes in the crystal surface stoichiometry. The band-structure calculations based on density functional theory (DFT) reveal total density of states and partial densities of states of Pb₂GeS₄ within different exchange–correlation approximations. The best fit with the experiment is derived when the DFT calculations of Pb₂GeS₄ employ modified Becke-Johnson potential with Hubbard-corrected functional and taking into account spin–orbit (SO) interaction. The calculations indicate that top and upper portion of the VB is composed mainly by S 3p states, its central portion is formed by Ge 4p and S 3p states, while contributions of Pb 6s states dominate at its bottom with slightly smaller contributions of Ge 4s states as well. Contributions of unoccupied Pb 6p states dominate at the conduction band (CB) bottom. Regarding the occupation of the VB by Ge 4p and S 3p states, the theoretical data are confirmed experimentally by matching the XPS VB spectrum on a common energy scale with the X-ray emission spectra representing the valence S p and Ge p states. The present calculations yield that the VB maximum is positioned at the Y point, while the CB minimum at the Г point; this fact indicates that Pb₂GeS₄ sulfide is an indirect-gap material. The principal optical constants are also elucidated using the ab initio DFT calculations.