  The impact of boundary scattering on non-diffusive thermal relaxation of a
transient grating in thin membranes is rigorously analyzed using the
multidimensional phonon Boltzmann equation. The gray Boltzmann simulation
results indicate that approximating models derived from previously reported
one-dimensional relaxation model and Fuchs-Sondheimer model fail to describe
the thermal relaxation of membranes with thickness comparable with phonon mean
free path. Effective thermal conductivities from spectral Boltzmann simulations
completely free of any fitting parameters are shown to agree reasonably well
with experimental results. These findings are important for improving our
fundamental understanding of non-diffusive thermal transport in membranes and
other nanostructures.
