Temperature shift of the absorption edge and Urbach tail ofZrSxSe2−xsingle crystals

The temperature dependence of the absorption-edge energy has been determined in mixed layered transition-metal dichalcogenides of $\mathrm{Zr}{\mathrm{S}}_x\mathrm{S}{\mathrm{e}}_{2\ensuremath{-}x}$, for $x=0.5$, 1.0, 1.5, and 2.0 in the range of 32--300 K. The single crystals of $\mathrm{Zr}{\mathrm{S}}_x\mathrm{S}{\mathrm{e}}_{2\ensuremath{-}x}$ samples have been grown by the chemical vapor transport technique and characterized with the help of different methods. The absorption edge is found to shift toward lower energy with increasing the temperature. The experimental spectra and the parameters that describe the temperature dependence of the absorption edges are evaluated and described in the framework of the model proposed by Manoogian and Woolley [Can. J. Phys. 62, 285 (1984)]. The presence of the Urbach tail just below the band edge of $\mathrm{Zr}{\mathrm{S}}_x\mathrm{S}{\mathrm{e}}_{2\ensuremath{-}x}$ was observed. The steepness parameter \ensuremath{\sigma} and its functional temperature and composition dependence are discussed. Additionally, the values of the Urbach energies as well as the phonon energies are deduced. The obtained results support that the thermal phonon interactions and the structural and compositional disorders contribute to the Urbach tail in $\mathrm{Zr}{\mathrm{S}}_x\mathrm{S}{\mathrm{e}}_{2\ensuremath{-}x}$ crystals.