Considering the condition of ω<ωTO and the narrow frequency range, we interpret the complex phonon permittivity experimentally as ε̃phonon="Aωeiθ for amorphous carbon.
Theoretically, an increase in temperature can induce both line-width broadening and frequency downshift of phonon peaks.
In Raman scattering measurements, both the quantum confinement and defects can induce the frequency downshift of phonon peaks [45].
Changing the ratio of R and D, we can control the phonon modes in the lower frequency range.
Investigate the frequency range.
Whereas in the range of optical phonons the dielectric function is mainly governed by the phonons' frequency, strength, and damping, above this phonon range and below the optical absorption, the parameter ε inf plays a crucial role in the dielectric permittivity of the sample.
where ω is the frequency of phonons, ωm is the maximum frequency, ℏ is the reduced Planck constant, 1 exp ℏω k B T - 1 is the occupation of phonons given by the Bose-Einstein distribution, D is the phonon density of states, vg is the phonon group velocity, τ is the transmissivity of phonons, θ is the polar angle, and φ is the azimuthal angle.
Micro-Raman spectra of single-walled carbon nanotubes in the range of two-phonon 2D bands are investigated in detail.
The observed temperature dependence can be accounted for with an electron phonon scattering mechanism if there is a high frequency contribution from the intra-ball phonons and a lower frequency contribution from phonons with frequencies in the range of 10 to approximately 100 cm−100
