Phonon ballistic transport and Anderson localization in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Si</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Ge</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math>alloyed nanowires
Wei Zhang, Yangyu Guo, Shiyun Xiong, Hong-Liang Yi
Abstract
Heat transport plays a crucial role in various applications such as waste energy harvesting, thermal barrier coatings, and heat dissipation in microelectronics. In this paper, the frequency-dependent heat transport characteristics in mass disordered ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ nanowires (NWs) are investigated based on the nonequilibrium Green's function method. The results demonstrate the coexistence of phonons with ballistic transport, diffusive transport, and Anderson localization in SiGe alloyed NWs. Ballistic phonons are observed at low frequencies, with a NW length of up to 2 $\ensuremath{\mu}\mathrm{m}$ and Ge concentrations ranging from 1 to 50%. As the Ge concentration increases, the upper frequency limit for ballistic transport shifts to lower frequencies. However, the thermal conductivity contributed by these ballistic phonons increases due to enhanced scattering and localization of mid- and high-frequency phonons. Moreover, for ultralong samples, phonon localization occurs across a wide frequency range. The localization length decreases with increasing frequency, indicating that high-frequency phonons are more prone to localization in SiGe-alloyed NWs. Additionally, the localization length decreases with increasing Ge concentration, revealing a stronger localization effect in highly mass-disordered systems. Our results contribute to the understanding of heat transport in low-dimensional disordered systems and could be beneficial to guiding the design of thermoelectric materials and thermal barrier coatings.