Use of Phonon Confinement Model in Simulation οf Raman Spectra of Nanostructured Materials

Abstract

The simulation of the Raman spectra of nanostructured materials, where the effects of frequency shift and asymmetric broadening of the Raman modes play an important role, can be very useful in systematic characterization of these materials. Use of phonon confinement model for calculating Raman spectra of different nanomaterials is considered both from the viewpoint of different confinement function and the confinement strength, as well as the dimensionality of the confinement model. The phonon dispersion relations and the choice of their approximation are also studied. The influence of particle size distribution on the shape of the calculated spectra is discussed and contributions of Gaussian and asymmetric Gaussian distribution are compared. The effects of average and inhomogeneous strain on the behavior of simulated Raman spectra are also discussed. The results of the phonon confinement model are compared to the experimental spectra of CeO2 and anatase TiO2 nanopowders.

Raman study of structural disorder in ZnO nanopowders

“…This implies that some other parameters must be included in the simulation of E 2 high by PCM, such as lattice strain effects and anisotropy of Brillouin zone. [34] In a further simulation of the E 2 high Raman mode, its high sensitivity to lattice strain is taken into account. The tensile strain along the c-axis, followed by an increase of the lattice parameter Relative Raman shift / cm -1 Figure 3.…”

Raman scattering on nanomaterials and nanostructures

“…One of the examples is the phonon dispersions for E g mode of anatase TiO 2 used by different authors [9] and presented in Fig. 4(a).…”

“…4(d)). Although polynomial function fits calculated phonon dispersion more precisely, both linewidth and shape of the Raman spectra, suggests use of cosine dispersion as more proper one [9]. Raman mode asymmetry is the result not only of phonon confinement in whole BZ, but also the particle size distribution (PSD).…”

Probing the phonon confinement in ultrasmall silicon nanocrystals reveals a size-dependent surface energy

“…Indeed, this interpretation was eluded to already by a number of investigators 30,31 in what is typically referred to as "soft confinement," whereby the phonon effectively "leaks" out into the surrounding matrix. However, most workers 2,3,6,16,17,32,33 report better agreement with their measured data, either by increasing a or by defining the confinement envelope to be a sinc function, 18,34 analogous to the ground state electronic wave-function in an infinite potential well, both of which yield a boundary value of zero for the phonon wave-function. The difference being that the latter ensures that the value of the phonon wave-function goes to zero only at the nanocrystal boundary, which, with the exception of the shape of the wave-function inside the nanocluster amounts to a similar result as that we have obtained in this work, where a ¼ 3.…”