Optical properties and mechanisms of current flow in Cu$_{2}$ZnSnS$_{4}$ films prepared by spray pyrolysis

Thin films Cu$_{2}$ZnSnS$_{4}$ (up to 0.9 $\mu$m thick) with $p$-type conductivity and band gap $E_{g}$ = 1.54 eV have been prepared by the spray pyrolysis of 0.1 M aqueous solutions of the salts ZnCl$_{2}$ $\cdot$ 2H$_{2}$O, SnCl$_{4}$ $\cdot$ 5H$_{2}$O, and (NH$_{2}$)$_{2}$CS at a temperature $T_{S}$ = 290$^\circ$C. The electrophysical properties of the films have been analyzed using the model for polycrystalline materials with electrically active grain boundaries. The energy and geometric parameters of the grain boundaries have been determined as follows: the height of the barriers is $E_{b}\approx$ 0.045–0.048 eV, and the thickness of the depletion region is $\delta\approx$ 3.25 nm. The effective concentrations of charge carriers $p_{0}$ = 3.16 $\times$ 10$^{18}$ cm$^{-3}$ and their mobilities in crystallites $\mu_{p}$ = 85 cm$^{2}$/(V s) have been found using the technique for determining the kinetic parameters from the absorption spectra of thin films at a photon energy $h\nu\approx E_{g}$. The density of states at grain boundaries $N_{t}$ = 9.57 $\times$ 10$^{11}$ cm$^{-2}$ has been estimated.