Methods of estimations of the band gap for kesterite Cu2ZnSnS(Se)4

Abstract

This paper presents a study related to methods of estimation of the band gap for kesterite-type Cu2ZnSnS(Se)4 based on their electronic structure and optical properties driven by the first-principles calculations within the hybrid functional. The estimations have been performed by four different methods. The first one is based on the band structure estimated as the difference of the energy corresponding to the conduction band and valence band edges. The rest three methods are based on the spectral distribution of the absorption coefficient a(ħw) driven from the first-principles calculations: (i) Tauc plot, (ii) first derivative of a(ħw) on photon energy ħw in the energy range around the fundamental absorption edge, and (iii) linear combination of the methods (i) and (ii). We show that the band gap estimated by different methods can deviate each from other drastically and the large difference is not only relayed to defects, impurities and other lattice imperfections. We show also, that the influence of lattice anisotropy on optical properties of CZTS and CZTSe is negligible. We have pointed out importance of the dependence of dielectric constant on surface texture. The equation describing dependence of dielectric constant on the experimentally observed surface texture is derived.