Mathematical modelling of the conductivity in CZTiS-CZSnS as a function of synthesis temperature

The electrical behavior of photovoltaic materials related with Cu₂ZnTiS₄ and Cu₂ZnSnS₄ materials were analyzed as function of synthesis temperature in accordance with a new mathematical model based on the Kramers–Kronig equations with a high reliability. The samples were obtained through a hydrothermal route and a subsequent thermal treatment of solids at 550 °C for 1 h under nitrogen flow (50 ml min⁻¹). The characterization was done by x-ray diffraction, ultraviolet spectroscopy (UV), Raman spectroscopy, atomic force microscopy (AFM) and solid state impedance spectroscopy (IS) techniques. The structural characterization, confirm the obtention of a tetragonal material with spatial group I-42m, oriented along (1 1 2) facet, with nanometric crystal sizes (5–6 nm). The AFM and Raman analysis confirm a high level of chemical homogeneity and correlation with the synthesis temperature, associated with the roughness of the samples. The UV spectroscopy confirm a band gap around 1.4–1.5 eV, evidencing the effectiveness of the synthesis process. The IS results at room temperature with a probability of 95%, confirm a high consistency of data with respect to values of real and imaginary impedance, allowing to obtain information of the conductance, reactance and inductance, achieving conductivity values around 10⁻⁵ and 10⁻³ Ω⁻¹ m⁻¹ in comparison with traditional mathematical models used for this purpose. (paper)