Wavevector and polarization resolved analysis of phonon scattering from embedded nanoparticles

Abstract

Embedded nanocrystals are capable of dramatically reducing the thermal conductivity of alloy semiconductors through increased phonon scattering, but many aspects of thermal wavelength phonon interactions with embedded nanoparticles remain understudied. Here, the wavevector- and polarization-resolved capabilities of the Frequency Domain Perfectly Matched Layer (FDPML) computational technique are exploited to study several fundamentally important phonon scattering problems across the entire Brillouin zone. We compare the atomistic predictions of FDPML against continuum mechanics approaches for spherically embedded particles. For long to mid-wavelength phonons, reasonable agreement is found with continuum theories that consider the Mie regime accurately, while commonly used “patching” theories which empirically connect the Rayleigh scattering to the geometric limit are shown to have poor agreement with more rigorous approaches. Next, the scattering cross section of optical phonons from nanoparticles is explored for the first time. We show that the scattering behavior of optical phonons is fundamentally different than their acoustic counterparts in that long wavelength optical phonons exhibit a scattering cross section nearly independent of wavelength, which we interpret as being due to zone folding of short wavelength acoustic modes from the geometric scattering regime into long wavelength optical modes. Finally, we study the scattering cross section of nanoparticles exhibiting atomic interdiffusion at the matrix-particle interface, where we find that interdiffusion both suppresses Mie oscillations and substantially increases the scattering cross section at short wavelength, compared to a solid nanoparticle with the same number of impurity atoms.