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

Physical Review B: Condensed Matter and Materials Physics. 2020. Vol. 102. No. 20. P. 205422.

Koniakhin S., Oleg I. Utesov, Yashenkin A.

Disorder-induced broadening of optical vibrational eigenmodes in nanoparticles of nonpolar crystals is studied
numerically. The methods previously used to treat the phonons in defectless particles are adjusted for numerical
evaluation of the disordered problem. Imperfections in the forms 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 pointlike impurities the regimes of separated and overlapped phonon levels are
obtained and the behavior of the linewidth predicted analytically 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 the analytical approach are checked and identified, and the minor discrepancies
are discussed. We mention a few of them: slower than in analytics increasing of the linewidth with the phonon
quantum number for weak disorder and only a qualitative agreement between analytics and numerics for the
resonant broadening in strong dilute disorder. The novel phenomena discovered numerically are the “mesoscopic
smearing” of the distribution function in the ensemble of identical disordered particles, an inflection of the
linewidth dependence on the impurity concentration for light “dense” binary impurities, and a position-dependent
capability of a strong impurity to catch the phonon. It is shown that surface irregularities contribute to the phonon
linewidth less than the volume disorder, and their rates reveal faster decay with increasing of the particle size.
It is argued that the results of the present research are applicable also for quantum dots and short quantum wires.

Keywords: Lifetime, время жизни, беспорядок, Disorder, Raman spectroscopy, Рамановская спектроскопия, nanoparticles, наночастицы