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Abstract

Si_xGe_1−x alloys are important materials both for the electronics industry [1] and for thermoelectric applications at high temperatur e[2]. Several experimental and theoretical studies report the enhancement of dimensionless figure of merit (zT) of Si_xGe_1−x random alloys by reducing thermal conductivity[3,4]. The phonon calculations required to determine the thermal conductivity of random alloys are computationally expensive using DFT. We have therefore developed a model for obtaining phonon spectra of Si_xGe_1−x random alloys. The model parameters are extracted from DFT-calculated force constant matrices for pure Si and pure Ge. We include the contributions upto second nearest neighbour as we find that the phonon frequencies obtained by considering only the onsite and first nearest neighbour force constant matrices are not sufficient for approximating the acoustic phonon modes. The model allows us to determine the phonon frequencies for Si_xGe_1−x alloys accurately and efficiently without performing ab initio calculations. [1] J. Ouellette, The Industrial Physicist 8, 22 (2002). [2] G. A. Slack and M. A. Hussain, J. Appl. Phys. 70, 2694 (1991). [3] H. Lee, D. Vashaee, D. Z. Wang, M. S. Dresselhaus, Z. F. Ren, and G. Chen, J. Appl. Phys. 107, 094308 (2010). [4] C. Bera, N. Mingo, and S. Volz, Phys. Rev. Lett. 104, 115502 (2010).