Phonon mean free path spectrum and thermal conductivity for Si1−xGex nanowires

Abstract

We reformulate the linearized phonon Boltzmann transport equation by incorporating the direction-dependent phonon-boundary scattering, and based on this equation, we study the thermal conductivity of Si1−xGex nanowires and derive their phonon mean free path spectrum. Due to the severe suppression of high-frequency phonons by alloy scattering, the low frequency phonons in Si1−xGex nanowires have a much higher contribution to the thermal conductivity than pure silicon nanowires. We also find that Si1−xGex nanowires possess a stronger length-dependent, weaker diameter-dependent, and weaker surface roughness-dependent thermal conductivity than silicon nanowires. These findings are potentially useful for engineering Si1−xGex nanowires for thermoelectric applications.