Ballistic transport of long wavelength phonons and thermal conductivity accumulation in nanograined silicon-germanium alloys

Abstract

Computationally efficient modeling of the thermal conductivity of materials is crucial to thorough experimental planning and theoretical understanding of thermal properties. We present a modeling approach in this work that utilizes a frequency-dependent effective medium theory to calculate the lattice thermal conductivity of nanostructured solids. This method accurately predicts a significant reduction in the experimentally measured thermal conductivity of nanostructured Si80Ge20 systems reported in this work, along with previously reported thermal conductivities in nanowires and nanoparticles in matrix materials. We use our model to gain insights into the role of long wavelength phonons on the thermal conductivity of nanograined silicon-germanium alloys. Through thermal conductivity accumulation calculations with our modified effective medium model, we show that phonons with wavelengths much greater than the average grain size will not be impacted by grain boundary scattering, counter to the traditionally assumed notion that grain boundaries in solids will act as diffusive interfaces that will limit long wavelength phonon transport. This is further supported by using time-domain thermoreflectance at different pump modulation frequencies to measure the thermal conductivity of a series nanograined silicon-germanium alloys.