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Improving Efficiency of Thermoelectric Devices Made of Si-Ge, Si-Sn, Ge-Sn, and Si-Ge-Sn Binary and Ternary Alloys

Thermoelectric devices with the ability to convert rejected heat into electricity are widely used in nowadays technology. Several studies have been done to improve the efficiency of these devices. However, because of the strong correlation between thermoelectric properties (electrical conductivity, Seebeck coefficient, and thermal conductivity including lattice and electron counterpart), improving ZT has always been a challenging task. In this study, thermal conductivity of group IV-based binary and ternary alloys such as SiGe, SiSn, GeSn, and SiGeSn has been studied. Phonon Boltzmann Transport Equation has been solved in the relaxation time approximation including intrinsic and extrinsic (in the presence of boundary and interfaces in the low-dimensional material) scattering mechanisms. Full phonon dispersion based on the Adiabatic Bond Charge model has been calculated for Si, Ge, and Sn. Virtual crystal approximation has been adapted to calculate the dispersion of SiGe, SiSn, GeSn, and SiGeSn. Two approaches have been introduced to reduce the lattice thermal conductivity of the materials under study. First, alloying results in a significant reduction of thermal conductivity. But, this reduction has been limited by the mass disorder scattering in the composition range of 0.2 to 0.8. Second, nanostructuring technique has been proposed to further reduce the thermal conductivity. Our study shows that, due to the atomic mass difference which gives rise to the elastic mass scattering mechanism, SiSn has the lowest thermal conductivity among the other materials under study. SiSn achieved the thermal conductivity of 1.18 W/mK at 10 nm at the Sn composition of 0.18, which is the experimentally stable state of SiSn. The results show that SiSn alloys have the lowest conductivity (3 W/mK) of all the bulk alloys, more than two times lower than SiGe, attributed to the larger difference in mass between the two constituents. In addition, this study demonstrates that thin films offer an additional reduction in thermal conductivity, reaching around 1 W/mK in 20 nm SiSn, GeSn, and ternary SiGeSn films, which is close to the conductivity of amorphous SiO$_2$. This value is lower than the thermal conductivity of SiGe at 10 nm which is 1.43 W/mK. Having lattice thermal conductivity reduced, electron transport has been studied by solving Boltzmann Transport Equation under low electric field including elastic and inelastic scattering mechanisms. Rode's iterative method has been applied to the model for obtaining perturbation of distribution function under a low electric field. This study shows that nanostructuring and alloying can reduce $\kappa_{ph}$ without significantly changing the other parameters. This is because of the phonon characteristics in solids in which MFP of phonons is much larger than those of electrons, which gives us the possibility of phonons confinement without altering electrons transport. Thermoelectric properties of SiGe in the bulk and nanostructure form have been studied to calculate ZT in a wide range of temperatures. The results demonstrate that ZT reaches the value of 1.9 and 1.58 at the temperatures of 1200 K and 1000 K respectively, with the Ge composition of 0.2 and carrier concentration of 5$\times$10$^{19}$ cm$^{-3}$ at 10 nm thickness. This model can be applied to SiSn and other binary and ternary alloys, to calculate the improved ZT. Hence, we conclude that group IV alloys containing Sn have the potential for high-efficiency TE energy conversion.
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