Study of Phonon Brillouin Spectrum of Crystal Films

On the basis of the theory of phonon Green’s function, the lineshape formula of phonon Brillouin spectrum is deduced, and the numerical results are reported. It is found that the energy band of phonon splits into a series of energy levels in terms of quantum size effect. It is also found that short-wavelength phonons participate in Brillouin scattering as well as long-wavelength phonons so that blue-shift and split occur for the phonon Brillouin spectrum, which are inversely proportional to the size of nanometer crystal particles. The results can be used to measure the size of nanometer crystal particles.