Low-frequency Raman scattering |
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Experimentally, Raman scattering from confined acoustic
phonons in a nucleated glasses has been reported by Duval et. al. [Phys. Rev. Lett.
56, 2052 (1986)], in metals by Mariotto et al. [Europhys.
Lett. 6, 239 (1988)] and in semiconductor nanocrystals by Ovsyuk et al. [JETP Lett. 47, 298 (1988)]. After these publications, the low-frequency Raman
scattering from acoustic vibrations of the nanoparticles has become an
effective method to determine the size of particles. The size of
nanoparticles, was deduced from the energy of the peak, since the
frequency of all modes, scales as the inverse of linear dimension of the
particle, in accordance with the expression, w = kv /d , where v is the
sound velosity, d is the size of the particle.
In semiconductor quantum dots (QDs) not only the
electronic but also the lattice vibrational modes become discrete
due to three- dimensional confinement. As the size of QDs decreases,
phonons with a larger wave vector are involved in the electron-phonon
interaction. Hence, the electron-phonon interaction with acoustic phonon
modes becomes more pronounced as compared to the scattering of electrons
by optical phonons. It turned out that size-quantized acoustic phonon
modes in QDs can be observed with help of low-frequency Raman scattering
in the range of the spectrum ~ 10 cm -1 [NN Ovsyuk et al. JETP Letters 47, 298 (1988)].
We investigated of the influence of the matrix on the frequencies of acoustic phonons confined in the QDs. At the present time it is assumed that this influence is very small and negligible. We have analyzed heterophase systems with different relations between elastic constants and densities and showed that the influence of the matrix on the frequencies of the acoustic
phonons confined in the QDs is significant even if Lame's constants and mass densities of a nanocrystals and a matrix
are quite different from each other [NN Ovsyuk and VN Novikov. Phys. Rev. B 53, 3113 (1996)]. What is more important, the new torsional surface vibrations arise as nanocrystals are embedded in a matrix. Just these vibrations take part in the low-frequency Raman scattering described in most experiments despite the fact that only spheroidal modes can be seen in the Raman spectrum due to selection rules for Raman scattering on spherical nanoparticles. However, in practice the form of the nanocrystals in a glass matrix may have deviations from a perfect spherical one. In this case, the selection rules can be relaxed and not only spheroidal
modes, but torsional vibrational modes can be seen in the Raman scattering spectra.
The low-frequency Raman scattering appears to be a sensitive method for the investigation of the initial stage of
nucleation in multi- and monocomponent
systems [NN Ovsyuk. Europhys. Lett. 89, 26001 (2010)]. In the case of the mono-component systems, when the crystalline nuclei
do not have an acoustic mismatch as compared to the amorphous matrix, we cannot observe
their surface vibrations, but we can make use of the fact that in nucleation there is a jump in
a structure correlation length. This results in a sharp decrease in contribution to the density of
the acoustic vibration states because of decreasing the concentration of structural correlations
on which acoustic phonons are localized. In addition, low-frequency Raman spectroscopy may be
useful in the research into the phase transformation in materials for phase-change memories.
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