In recent years, nanostructuring has emerged as a promising strategy to tailor the properties of semiconducting materials for energy applications. In particular, recent improvements in the thermoelectric efficiency largely stem from very low thermal conductivity achieved in nanostructured materials . Atomistic simulations capable of handling large samples could greatly advance our understanding of heat transport in complex nanostructured materials, and help identify promising candidates for thermoelectric applications. Until recently, such calculations could be carried out only using molecular dynamics approaches relying on empirical interatomic potentials . In this talk, I will present an atomistic Monte Carlo method to solve the Boltzmann transport equation (BTE)  that overcomes the computational limitations of standard BTE implementations and allows for the calculation of the thermal conductivity and phonon lifetimes of large systems, using either empirical or first principles Hamiltonians. I will demonstrate how this new approach enables us to rationalize trends in the thermal conductivity of a range of SiGe based nanostructures, as a function of size and dimensionality. Work done in collaboration with Davide Donadio, Yuping He, Eamonn Murray, Francois Gygi and Giulia Galli.
 See e.g. A. J. Minnich, M. S. Dresselhaus, Z. F. Ren, and G. Chen, Energy Environ. Sci. 2, 466 (2009).
 Y. He, I. Savic, D. Donadio and G. Galli, Phys. Chem. Chem. Phys 14, 16209 (2012).
 I. Savic, D. Donadio, F. Gygi, and G. Galli, Appl. Phys. Lett. 102, 073113 (2013).
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