Effects of Bond Disorder and Surface Amorphization on Optical Phonon Lifetimes and Raman Peak Shape in Crystalline Nanoparticles

Abstract

Optical phonons in nanoparticles with randomness of interatomic bonds are considered both analytically and numerically. For weak dilute disorder, two qualitatively different regimes of separated and overlapped levels are observed, resembling the case of random atomic masses investigated previously. At stronger and/or more dense disorder, the particles become essentially inhomogeneous, thus constituting a minimal model to describe an amorphous phase, where the picture of vibrational modes becomes more subtle. We concentrate here on the experimentally relevant case of a strong disorder located near the particle surface and formulate the core-shell model aimed to describe the ubiquitous phenomenon of particle surface amorphization. We observe a peculiar effect of volume optical phonons "repelling" from the disordered shell. It results in the Raman spectrum appearing in the form of a combination of narrow well-resolved peaks stemming from the quantized modes of a pure particle core (red-shifted due to its effective smaller size) and a wide pedestallike signal from the disordered shell, placed primarily to the right of the main Raman peak.

Bench tests for microscopic theory of Raman scattering in powders of disordered nonpolar crystals: Nanodiamonds and beyond

“…Below, we demonstrate that this method allows us not only to fit the experimental curves but also to extract from the data four parameters important for the nanopowder specification, namely, (i) the mean particle size in a powder L, (ii) the standard deviation of size distribution function δL, (iii) the disorder strength parameter S, and, with less accuracy, (iv) the particle shape parameterized by the faceting number p. It becomes possible only with the microscopic theory [34][35][36] of the phonon line broadening at hands. Indeed, this theory predicts various broadenings Γ n for various phonon modes ω n .…”

“…We formulate the disordered diagram technique for operators and Green's functions (here, is the time‐ordering operator). Upon the disorder averaging the latter obtains the form where the self‐energy part Π n ( ω ) could be calculated using different approximation schemes (see Utesov et al [ 34,36 ] for details). Here, we just present the results.…”

“…No microscopic explanation of the origin of phonon damping exists in literature, as well (see phenomenological analysis of experiments in previous studies [ 31–33 ] ). This gap has been filled in by our papers, [ 34–36 ] where the DMM‐BPM and EKFG theories have been used as starting points to calculate the optical phonon lifetimes Γ −1 in nanocrytallites and thus to broaden the Raman peak. The origin for these phonon damping has been attributed to the intrinsic (including surface) disorder always existing in nanoparticles.…”

“…This paper is aimed to demonstrate the practical applicability of the theory developed in previous works [ 19,20,34–36 ] as a regular powerful method of interpreting the Raman spectra of nanopowders of nonpolar crystals. The best way to do it is to reexamine existing experiments, extracting from the data precise and detailed information.…”

“…While the above analysis has been concentrated on weakly disordered nanocrystals, later on, it has been extended onto the Raman spectra of amorphous silicon. [37] This paper is aimed to demonstrate the practical applicability of the theory developed in previous works [19,20,[34][35][36] as a regular powerful method of interpreting the Raman spectra of nanopowders of nonpolar crystals. The best way to do it is to reexamine existing experiments, extracting from the data precise and detailed information.…”