A method is described for studying thermal phonon scattering in thin f
ilms on dielectric substrates below a few Kelvin. It is used to study
silica films on silicon substrates. Using Monte Carlo simulations with
no free parameters, we find that thermally grown silica films 0.1 to
1.0 mu m thick scatter the phonons as strongly as bulk silica, and hen
ce, have the same thermal conductivity as bulk silica,,while a 0.1 mu
m thick e-beam evaporated silica film has a thermal conductivity five
times smaller than bulk silica, indicative of additional defects.