  We have measured the lifetimes of two zone-center longitudinal acoustic
phonon modes, at 320 GHz and 640 GHz respectively, in a 14 nm GaAs / 2 nm AlAs
superlattice structure. By comparing measurements at 296 K and 79 K we separate
the intrinsic contribution to phonon lifetime determined by phonon-phonon
scattering from the extrinsic contribution due to defects and interface
roughness. At 296 K, the 320-GHz phonon lifetime has approximately equal
contributions from intrinsic and extrinsic scattering, whilst at 640 GHz it is
dominated by extrinsic effects. These measurements are compared with
first-principles lattice dynamics calculations of intrinsic and extrinsic
scattering rates in the superlattice. The calculated room-temperature intrinsic
lifetime of longitudinal phonons at 320 GHz is in agreement with the
experimentally measured value of 0.9 ns. The model correctly predicts the
transition from predominantly intrinsic to predominantly extrinsic scattering;
however the predicted transition occurs at higher frequencies. Our analysis
indicates that the 'interfacial atomic disorder' model is not entirely adequate
and that the observed frequency dependence of the extrinsic scattering rate is
likely to be determined by a finite correlation length of interface roughness.
