TY - JOUR

T1 - Lifetimes of confined optical phonons and the shape of a Raman peak in disordered nanoparticles. II. Numerical treatment

AU - Koniakhin, Sergei

AU - Utesov, Oleg

AU - Yashenkin, Andrey G.

N1 - Publisher Copyright: © 2020 American Physical Society.

PY - 2020/11/16

Y1 - 2020/11/16

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85097156457&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/509406bd-7628-3589-9922-bd885281fc53/

U2 - 10.1103/PhysRevB.102.205422

DO - 10.1103/PhysRevB.102.205422

M3 - Article

VL - 102

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 20

M1 - 205422

ER -