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. The samples were obtained through a hydrothermal route and a subsequent thermal treatment of solids at 550°C for 1 hour under nitrogen flow (50 mL min-1). The characterization was done by X-ray diffraction (XRD), 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 impedance spectroscopy results at room temperature with a probability of 95%, confirm the reliability of data in relation with the Kramers-Kronig equations, which allow to relate the values of real and imaginary impedance. The mathematical modelling and the Nyquist plots allowed to obtain information of the conductance, reactance and inductance, achieving conductivity values around 10-5 and 10-3 Ω-1. m-1.