Figure of merit for thermoelectric power generation estimated from enhanced mobility in [100] oriented \textit{$\beta $}-FeSi$_{2}$ thin film

\textit{$\beta $}-FeSi$_{2}$ has been attracted to be applied to the thermoelectric device, for instance, the Seebeck coefficient shows the maximum value about 500$^{o}$C that it is good for thermoelectric power generation. However low figure of merit (Z) has been reported about 5x10$^{-4}$ K$^{-1}$. The Z is represented as $m$*$^{2/3}$(\textit{$\mu $}/\textit{$\kappa $}$_{ph})$, where $m$*, \textit{$\mu $} and \textit{$\kappa $}$_{ph}$ are effective mass, mobility and thermal conductivity, respectively. Although \textit{$\kappa $}$_{ph}$ is good for thermoelectric power, low \textit{$\mu $} has been reported as polaronic-conduction in \textit{$\beta $}-FeSi$_{2}$ crystal. In 3D electron density distribution of \textit{$\beta $}-FeSi$_{2}$ crystal, Si layer in the crystal shows covalent bonding network with Si atoms, and it suggests the new possibility for enhancement of \textit{$\mu $}. In this report, the objective is to exhibit the possibility for enhancement of Z in order to control the crystallographic orientation of \textit{$\beta $}-FeSi$_{2}$ crystal by means of film formation. \textit{$\beta $}-FeSi$_{2}$ thin film was prepared on Si(100) substrate using molecular beam epitaxy method. The crystallographic orientation of sample showed about 80{\%} of [100] direction from x-ray diffraction pattern. The transport properties were investigated using Hall measurement with van der Pauw electrode configuration. The resistivity and \textit{$\mu $} were also measured, and they were compared with \textit{$\beta $}-FeSi$_{2}$ polycrystal. In addition, enhancement of Z was estimated using above formula.