Electrical and optical properties of Cu$_{2}$Zn(Fe,Mn)SnS$_{4}$ films prepared by spray pyrolysis

We have analyzed the electrical and optical properties of Cu$_{2}$ZnSnS$_{4}$, Cu$_{2}$FeSnS$_{4}$, and Cu$_{2}$MnSnS$_{4}$ films with the $p$-type electrical conductivity, which were prepared by spray pyrolysis at temperature $T_S$ = 290$^{\circ}$C using 0.1 M aqueous solutions of salts CuCl$_{2}\cdot$2H$_{2}$O, ZnCl$_{2}\cdot$2H$_{2}$O, MnCl$_{2}\cdot$2H$_{2}$O, FeCl$_{3}\cdot$6H$_{2}$O, SnCl$_{4}\cdot$5H$_{2}$O, and (NH$_{2}$)CS. The energy parameters have been determined from analyzing the electrophysical properties of the films using the model of energy barriers at grain boundaries in polycrystalline materials, and the thickness of intercrystallite boundaries has been estimated. The extent of the influence of the hole concentration $p_0$ in the bulk of crystallites and height $E_b$ of the energy barriers between grains on the electrical conductivity has been determined. The optical bandgap width for thin Cu$_2$Zn(Fe,Mn)SnS$_4$ films has been calculated based on analyzing the spectral dependences of the absorption coefficient.