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A4: Theory - bulk materials
The thermal conductivity of crystalline silicon germanium (SiGe) is a strong function of Ge content when the Ge content is less (more) than approximately 12 at% (88 at%). The thermal conductivity is approximately at its minimum value for 12-88 at% of Ge content. It is also known that the bulk nanostructuring of SiGe can further reduce the thermal conductivity by scattering of phonons at crystallite boundary interfaces. Therefore, it is expected that the thermal conductivity reaches its minimum value at the limit of fully disordered lattice, namely amorphous structure. We report the calculation results of the thermal conductivity of the amorphous SiGe versus germanium concentration and temperature employing a first-principle approach. From a computational point of view, lattice thermal conductivity is a difficult quantity to compute at microscopic level. We applied the Green-Kubo formalism within equilibrium method in molecular dynamics (MD) simulations to calculate the lattice thermal conductivity of the SiGe compound. The length of the simulation cell was ~63 Å. The effect of the cell size variation was studied as well. The thermal conductivity was calculated versus Ge content and temperature. In order to validate our results, we calculated the lattice thermal conductivity of crystallite Si and Ge as well as their amorphous phases versus temperature, which revealed good agreement with the available empirical data. We found that the lattice thermal conductivity of SiGe amorphous compound is more than an order of magnitude smaller than that of the minimum thermal conductivity of crystalline SiGe alloy. As Ge content increases the thermal conductivity drops slowly and saturates around 0.5 W/mK for Ge content of greater than 60%.