PHONON LOCALIZATION IN MESOSCOPIC FREESTANDING FILMS

We examine the recent proposal of N Perrin concerning the possibility of observing phonon localization in mesoscopic free-standing insulatin g films with surface roughness. As our model structure, we consider a sapphire film with thickness D = 100 Angstrom, width W = 1 mu m and le ngth L = 10 mu m and surface roughness parameters Delta = 0.3D and xi = 500 Angstrom, where Delta is the rms deviation of the surface from f latness and xi the transverse correlation length. We derive an effecti ve phonon transport time tau(eff)(omega) for surface roughness scatter ing and then use this to determine the approximate frequency range ove r which the phonon localization length is less than the film length an d also obtain a rough estimate of the thermal conductivity in the temp erature range where the effect of localization is strongest.