Dielectric functions of Cu2ZnSn(SxSe1-x)4 thin film absorbers with varied x were determined by spectroscopic ellipsometry and ab initio calculations. From the combination of experimental and theoretical studies, the fundamental interband transition energy E0 (∼1–1.5 eV) and the next following transition energy E1 (∼2–3 eV) were identified and found to blue-shift with increasing sulfur anion content, while keeping the energy separation E1−E0 almost constant, ∼1.4 eV from experiments, and 1 eV from theory. In addition, the average dielectric responses were found to decrease with sulfur anion content from both theoretical and experimental results. The Tauc optical bandgap value Eg determined on samples prepared on Mo and soda lime glass substrate showed a positive linear relationship between x and bandgap Eg. The bandgap bowing factor determined from the theoretical data is 0.09 eV.

The crystalline structural, electronic and optical properties of the alloys Cu2ZnSn1−xGexS4, Cu2ZnSn1−xSixS4, Cu2ZnSn1−xGexSe4 and Cu2ZnSn1−xSixSe4 are calculated by first‐principles using both the generalized gradient approximation and a hybrid functional approach. We find that the electronic band structures are qualitatively very similar for these alloys. The band‐gap energy Eg(x) (for x = 0, 0.125, 0.25, 0.5, 0.75, 0.875 and 1) increases almost linearly with Ge and Si substitution. However, for very Si rich Cu2ZnSn1−xSixS4 alloys (but not for Cu2ZnSn1−xSixSe4) there is an abrupt increase of Eg(x) for x > 0.96. We therefore analyse this effect by calculating the electronic structures for x = 0.93, 0.96 and 1. We find that the Sn‐like states form localised density‐of‐states below the conduction band edge in Cu2ZnSn1−xSixS4, while corresponding states resonate more with the conduction bands in Cu2ZnSn1−xSixSe4. The effect in S‐based alloys is a direct consequence of the energetically high conduction band edge for Cu2ZnSiS4 in combination with energetically low Sn‐like states. Furthermore, the calculated dielectric constants are relatively similar for all alloy configurations. Overall however, our results suggest that it is possible to use Si and Ge as alloying element in quaternary Cu2ZnSnS4 to improve the photovoltaic properties.

The vacancy formation Gibbs free energy, enthalpy and entropy in fcc Al, Ag, Pd, Cu, and bcc Mo are determined by first-principles calculations using the quasi-harmonic approximation to account for vibrational contributions. We show that the Gibbs free energy can be determined with sufficient accuracy in a single-volume approach using the fixed equilibrium volume of the defect-free supercell. Although the partial contributions to the Gibbs free energy, namely, the formation enthalpy and entropy exhibit substantial errors when obtained directly in this approach, they can be computed from the Gibbs free energy using the proper thermodynamic relations. Compared to experimental data, the temperature dependence of the vacancy formation Gibbs free energy is accounted for at low temperatures, while it overestimates the measurements at high temperature, which is attributed to the neglect of anharmonic effects.

Structural, electronic, and optical properties of Cu 2 ZnSn(S x Se 1-x ) 4 semiconductors are studied theoretically for different concentration of S and Se anions. The optical properties are calculated at three levels of theory, in the generalized gradient approximation (GGA), meta-GGA, and with a hybrid functional. The GGA and meta-GGA calculations are corrected with an onsite Coulomb U d term. Lattice constants, dielectric constants, and band-gaps are found to vary almost linearly with the concentration of S. The authors also show that a dense sampling of the Brillouin zone is required to accurately account for the shape of the dielectric function, which is hard to attain with hybrid functionals. This issue is resolved with a recently developed k Áp based interpolation scheme, which allows us to compare results of the hybrid functional calculations on an equal footing with the GGA and meta-GGA results. We find that the hybrid functionals provide the overall best agreement with the experimental dielectric function.