The electronic and optical properties of an AgGaGeS4 crystal were studied by first-principles calculations, where the full-potential augmented plane-wave plus local orbital (APW+lo) method was used together with exchange–correlation pseudopotential described by PBE, PBE+U, and TB-mBJ+U approaches. To verify the correctness of the present theoretical calculations, we have measured for the AgGaGeS4 crystal the XPS valence-band spectrum and the X-ray emission bands representing the energy distribution of the electronic states with the biggest contributions in the valence-band region and compared them on a general energy scale with the theoretical results. Such a comparison indicates that, the calculations within the TB-mBJ+U approach reproduce the electron-band structure peculiarities (density of states – DOS) of the AgGaGeS4 crystal which are in fairly good agreement with the experimental data based on measurements of XPS and appropriate X-ray emission spectra. In particular, the DOS of the AgGaGeS4 crystal is characterized by the existence of well-separated peaks/features in the vicinity of −18.6 eV (Ga-d states) and around −12.5 eV and −7.5 eV, which are mainly composed by hybridized Ge(Ga)-s/p and S-p state. We gained good agreement between the experimental and theoretical data with respect to the main peculiarities of the energy distribution of the electronic S 3p, Ag 4d, Ga 4p and Ge 4p states, the main contributors to the valence band of AgGaGeS4. The bottom of the conduction band is mostly donated by unoccupied Ge-s states, with smaller contributions of unoccupied Ga-s, Ag-s and S-p states, too. The AgGaGeS4 crystal is almost transparent for visible light, but it strongly absorbs ultra-violet light where the significant polarization also occurs.
