High thermoelectric performance in metastable phase of silicon: a first-principles study

In this work, both thermal and electrical transport properties of diamond$-$cubic Si (Si$-$I) and metastable R8 phase of Si (Si$-$XII) are comparatively studied by using first$-$principles calculations combined with Boltzmann transport theory. The metastable Si$-$XII shows one magnitude lower lattice thermal conductivity than stable Si$-$I from 300 to 500~K, attributed from the stronger phonon scattering in three$-$phonon scattering processes of Si$-$XII. For the electronic transport properties, although Si$-$XII with smaller band gap (0.22 eV) shows lower Seebeck coefficient, the electrical conductivities of anisotropic $n$$-$type Si$-$XII show considerable values along $x$ axis due to the small effective masses of electron along this direction. The peaks of thermoelectric figure of merit ($ZT$) in $n$$-$type Si$-$XII are higher than that of $p$$-$type ones along the same direction. Owing to the lower lattice thermal conductivity and optimistic electrical conductivity, Si$-$XII exhibits larger optimal $ZT$ compared with Si$-$I in both $p$$-$ and $n$$-$type doping. For $n$$-$type Si$-$XII, the optimal $ZT$ values at 300, 400, and 500 K can reach 0.24, 0.43, and 0.63 along $x$ axis at carrier concentration of $2.6\times10^{19}$, $4.1\times10^{19}$, and $4.8\times10^{19}$~cm$^{-3}$, respectively. The reported results elucidate that the metastable Si could be integrated to the thermoelectric power generator.