Lifetimes of confined optical phonons and the shape of a Raman peak in disordered nanoparticles. I. Analytical treatment

Microscopic description of Raman spectra in nanopowders of nonpolar crystals is accomplished by developing the theory of disorder-induced broadening of optical vibrational eigenmodes. Analytical treatment of this problem is performed, and line shape and width are determined as functions of phonon quantum numbers, nanoparticle shape, size, and the strength of disorder. The results are found to be strongly dependent on whether the broadened line is separated from or overlaps other lines of the spectrum. Three models of disorder, i.e., weak pointlike impurities, weak smooth random potential, and strong rare impurities, are investigated in detail. The possibility of forming the phonon-impurity bound state is also studied.