Quasidiffusive propagation of phonons in silicon: Monte Carlo calculations.

Abstract

The time-of-flight spectrum of high-frequency phonons with both anharmonic decay and mass-defect (isotope) scattering is studied numerically for silicon. For the quantitative description of the spectrum in the whole time domain (from t\ensuremath{\simeq}${\mathit{t}}_{\mathit{b}}$ to t\ensuremath{\gg}${\mathit{t}}_{\mathit{b}}$, where ${\mathit{t}}_{\mathit{b}}$ is the ballistic time of flight), we make the following substantial improvements beyond previous simulations: (1) For the anharmonic decay we consider, the multibranch decay where the energies and propagation directions of the decayed phonons are determined from the energy-momentum conservation of the process. (2) For the isotope scattering polarization-dependent anisotropic scattering is used when we discuss the phonon intensity at a time t close to ${\mathit{t}}_{\mathit{b}}$, otherwise an approximate isotropic scattering is employed. (3) The elastic anisotropy is explicitly incorporated through the group velocity of phonons to locate the positions where the scattering events occur. The simulated phonon intensity versus time of flight compares favorably with recent experiments. Specifically, the exponential decay for late arrival times observed experimentally is well reproduced. We also find the phonon focusing due to elastic anisotropy is crucial to explain the shape of the phonon intensity at t\ensuremath{\simeq}${\mathit{t}}_{\mathit{b}}$. The size of the source for the ballistic phonons is also studied.