Thermoelectric properties of $p$-(Bi,Sb)$_2$Te$_3$ solid solution taking into account of the energy dependence of the relaxation time

The temperature dependences of thermoelectric properties in polycrystalline layered films of $p$-Bi$_{0.5}$Sb$_{1.5}$Te$_3$ topological insulators formed on polyimide and mica substrates by discrete deposition and thermal evaporation techniques have been studied. It is shown that the increase in the figure of merit $Z$ of $p$-Bi$_{0.5}$Sb$_{1.5}$Te$_3$ depends on the value of the effective scattering parameter $r_\mathrm{eff}$, which determines the energy dependence of the relaxation time $\tau(E)$. An increase in the figure of merit, up to $Z_{max}$ = 4.5 $\cdot$ 10$^{-3}$ K$^{-1}$ at $T$ = 240 K, is observed at optimal values of the $r_\mathrm{eff}$ parameter in the annealed films formed by discrete deposition on polyimide and mica substrates. Such enhancement of $Z$ in the film on the polyimide substrate is determined by a low thermal conductivity, and on the mica one by an increase in the power factor caused by raise of the Seebeck coefficient. Deviation from the optimal values of $r_\mathrm{eff}$ in the unannealed films on polyimide during discrete evaporation results in a decrease in the figure of merit.