Lifetimes of Confined Optical Phonons and the Shape of a Raman Peak in Disordered Nanoparticles: II. Numerical Treatment

Disorder-induced broadening of optical vibrational eigenmodes in nanoparticles of nonpolar crystals is studied numerically. The methods previously used to treat phonons in defectless particles are adjusted for numerical evaluation of the disordered problem. Imperfections in the form of Gaussian and binary disorders as well as surface irregularities are investigated thoroughly in a wide range of impurity concentrations and disorder strengths. For dilute and weak point-like impurities the regimes of separated and overlapped phonon levels are obtained and the behavior of the linewidth predicted theoretically is confirmed, the crossover scale falls into the actual range of several nanometers. These notions survive for strong dilute impurities, as well. Regimes and crossovers predicted by theory are checked and identified, and minor discrepancies are discussed. To mention a few of them: slower than in theory increasing of the linewidth with the phonon quantum number for weak disorder and only qualitative agreement between theory and numerics for resonant broadening in strong dilute disorder. The novel phenomena discovered numerically are: "mesoscopic smearing" of distribution function in the ensemble of identical disordered particles, inflection of the linewidth dependence on the impurity concentration for light "dense" binary impurities, and position-dependent capability of strong impurity to catch the phonon. It is shown that surface irregularities contribute to the phonon linewidth less than the volume disorder, and their rate reveals faster decay with increasing of the particle size. It is argued that the results of present research are applicable also for quantum dots and short quantum wires.