Thermal conductivity of Si1−xGex/Si1−yGeysuperlattices: Competition between interfacial and internal scattering

Abstract

We investigate thermal transport in Si/Ge and Si${}_{1\ensuremath{-}x}$Ge${}_{x}$/Si${}_{1\ensuremath{-}y}$Ge${}_{y}$ alloy superlattices based on solving the single-mode phonon Boltzmann transport equation in the relaxation-time approximation and with full phonon dispersions. We derive an effective interface scattering rate that depends both on the interface roughness (captured by a wave-vector-dependent specularity parameter) and on the efficiency of internal scattering mechanisms (mass-difference and phonon-phonon scattering). We provide compact expressions for the calculations of in-plane and cross-plane thermal conductivities in superlattices. Our numerical results accurately capture both the observed increase in thermal conductivity as the superlattice period increases and the in-plane vs cross-plane anisotropy of thermal conductivity. Owing to the combined effect of interface and internal scattering, an alloy/alloy superlattice has a lower thermal conductivity than bulk SiGe with the same alloy composition. Thermal conductivity can be minimized by growing short-period alloy/alloy superlattices or Si/Si${}_{1\ensuremath{-}x}$Ge${}_{x}$ superlattices with the SiGe layer thicker than the Si one.