# Regensburg 2013 – wissenschaftliches Programm

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# MM: Fachverband Metall- und Materialphysik

## MM 35: Computational Materials Modelling - Phonons & Phase Stability

### MM 35.3: Vortrag

### Mittwoch, 13. März 2013, 12:15–12:30, H24

**Modelling phonons in Si**_{x}**Ge**_{1−x}** alloys** — •Ankita Katre, Georg K. H. Madsen, and Ralf Drautz — ICAMS,Ruhr-Universität Bochum, 44780 Bochum, Germany

Si_{x}Ge_{1−x} alloys are important materials both for the electronics industry[1] and
for thermoelectric applications at high temperature[2]. Several
experimental and theoretical studies report the enhancement of dimensionless figure of merit (*zT*)
of Si_{x}Ge_{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_{x}Ge_{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_{x}Ge_{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).