Elastic scattering of acoustic phonons in Si

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Abstract
We have measured the elastic-scattering rate of high-frequency acoustic phonons in Si by combining the phonon-imaging technique, a unique sample geometry, and Monte Carlo calculations that incorporate the full elastic anisotropy of the crystal. A slotted crystal allows us to separate the purely scattered component of a heat pulse from the combined scattered and ballistic components. A series of Monte Carlo simulations is performed to predict the ratio of scattered to ballistic phonons for varying scattering strengths. Thus the experimentally measured fraction of scattered phonons can be compared with these simulations to yield a scattering rate. This procedure is necessary in order to take into account (1) the distribution of phonon frequencies, (2) the huge anisotropies in heat flux associated with phonon focusing, and (3) lifetime of the phonon source. For a high-purity Si crystal, the measured rate is found to be within experimental uncertainties of that predicted for mass-defect scattering from naturally occurring isotopes.