Cluster expansion and optimization of thermal conductivity in SiGe nanowires

Abstract

We investigate the parametrization and optimization of thermal conductivity in silicon-germanium alloy nanowires by the cluster-expansion technique. ${\text{Si}}_{1\ensuremath{-}x}{\text{Ge}}_{x}$ nanowires are of interest for thermoelectric applications and the reduction in lattice thermal conductivity $({\ensuremath{\kappa}}_{L})$ is desired for enhancing the thermoelectric figure of merit. We seek the minimization of ${\ensuremath{\kappa}}_{L}$ with respect to arrangements of Si and Ge atoms in 1.5 nm diameter [111] ${\text{Si}}_{1\ensuremath{-}x}{\text{Ge}}_{x}$ nanowires, by obtaining ${\ensuremath{\kappa}}_{L}$ from equilibrium classical molecular-dynamics (MD) simulations via the Green-Kubo formalism, and parametrizing the results with a coarse-grained cluster expansion. Using genetic algorithm optimization with the coarse-grained cluster expansion, we are able to predict configurations that significantly decrease ${\ensuremath{\kappa}}_{L}$ as verified by subsequent MD simulations. Our results indicate that superlatticelike configurations with planes of Ge show drastically lowered ${\ensuremath{\kappa}}_{L}$.