Phonon confinement

According to Meltzer s assumption, the faster relaxation in smaller nanocrystals embedded in glass is possibly due to stronger interaction of the electronic states of lanthanide ions with the larger density of low-frequency vibrational states in the glass, which may circumvent the slowing-down tendency of the relaxation induced by phonon confinement. 

For bulk h Oj, the Raman bands are at 306, 366, 495 and 630 cm-1 [22], Raman bands of SnOj nanostructures are observed at 315, 472, 578, 632 and 773 cm-1, in agreement with the literature [23], Bulk SnOj exhibits Raman bands at 472, 632 and 773 cm-1 [24], whereas for nanostructures two extra bands are found at 315 and 578 cm-1. The Raman band positions of the nanostructures do not differ significantly from those of the bulk samples. This is not expected since phonon confinement occurs at much smaller sizes. 

In addition to structural analysis and purity evaluation, Raman spectroscopy can also be used to estimate the crystal size of nanostructured solids. In most cases size characterization using Raman spectroscopy is based on the phonon confinement model (PCM), which uses changes in Raman frequency and Raman peak shape to estimate the crystal size. Although several attempts have been made to relate confinement-induced changes in the Raman spectrum of ND to the crystal size, the agreement between calculated and experimental data and the accuracy of the fitting procedure are still unsatisfactory. A detailed discussion of the limitations of the PCM and the accuracy of previous studies on ND powders is given in Ref [86]. 

Raman spectroscopy alone is currently not able to quantitatively measure the average crystal size in ND powders [86]. However, with a better understanding of phonon confinement effects in the Raman spectrum of ND, Raman spectroscopy may be used to accurately measure the average crystal size and determine changes in the size distribution. The following section discusses the effects of crystal size, defect, and size distributions on the Raman spectra of ND and required modifications in the PCM. 

Previous studies on phonon confinement in nanocrystals did not account for possible contributions from lattice defects [100-102]. However, the parameter L in (12.3) represents the coherence length and is, therefore, a measure of the distance between dislocation, vacancies, interstitials, impurities, and other defects within the crystal lattice. The assumption that L represents the crystal size is only valid for defect-free crystals, where the surface is considered to limit the propagation of the phonons. This assumption does not hold for imperfect crystals produced by... 

Raman spectroscopy, which is also used to measure the crystal size of nano-structured solids through the phonon confinement model (PCM), provides only semi-quantitative results for size measurements in ND powders due to insufficient understanding of the Raman spectra of ND and a lack of agreement between theoretical predictions of the model and experimental Raman data. However, taking into account the broad size distribution of ND powders and the contributions of lattice defects, a significant improvement in the predictions of the model was achieved. However, a correct interpretation of Raman data and quantitative size measurements still requires additional information on sample structure and composition. Therefore, a combined use of various characterization techniques such as XRD, HRTEM, and Raman spectroscopy can be recommended for a reliable determination of the average size of ND crystals and their distribution. 

Ferrari AC, Robertson J (2004) Raman spectroscopy of amorphous, nanostructured, dia-mond-like carbon, and nanodiamond. Phil Trans Roy Soc Lond A 362 2267-2565 Osswald S, Mochalin VN, Havel M, Yushin G et al (2009) Phonon confinement effects in the Raman spectrum of nanodiamond. Phys Rev B 80(7) 075419... 

Fujii M, Kanzawa Y, Hayashi S, Yamamoto K (1996) Raman scattering from acoustic phonons confined in Si nanocrystals. Phys Rev B 54 R8373-R8376... 

A very commonly used model for the effect of phonon confinement was developed initially by Richter et al. [21] and Campbell and Fauchet [22] (RCF model), and adapted by various other researchers for their particular sample analyses. Under this model, the Raman intensity for the optical mode(s) confined to crystal domains of average diameter/) may be expressed as [23] ... 

In this chapter, we have discussed the unique interactions of electromagnetic radiation with semiconductor NWs that lead to resonant absorption and scattering, the importance of Raman selection rules and phonon confinement in determining the crystal structure of NWs, and the ways in which Raman spectroscopy can be used to measure composition, strain, and temperature quantitatively with submicron resolution. These qualities of Raman spectroscopy are already commonly employed in the characterization of semiconductor NWs, and one may anticipate Raman spectroscopy to be used even more widely as the applications to NW... 

Wang RP, Zhou GW, Liu YL, Pan SH, Zhang HZ, Yu DP, Zhang Z (2000) Raman spectral study of silicon nanowires high-order scattering and phonon confinement effects. Phys Rev B... 

Adu KW, Xiong Q, Gutierrez HR, Chen G, Eklund PC (2006) Raman scattering as a probe of phonon confinement and surface optical modes in semiconducting nanowires. Appl Phys A 85 287-297... 

Different models have been used to derive the particle size from Raman spectra As an example, we shah briefly explain the phonon confinement model (PCM). The scattering of one photon by n phonons is governed by the momentum conservation. Only vibrations from the center of the Brillouin zone (BZC) should therefore be active in one phonon process (first-order Raman spectrum) and this is actually the case in large and flawless crystals, where... 

Balandin, A., and Wang, K.L., Significant Decrease of the Lattice Thermal Conductivity due to Phonon Confinement in a Free-standing Semiconductor Quantum Well. Physical Review B, 1998. 58(3) p. 1544-1549. 

Tuinstra-Koening relation /(D)//(G) IjL where is the in-plane correlation length corresponding to phonon confinement in graphitic domains [27], The relation is often presented as /(D)//(G) = 4.4 [28],... 

Campos V. B., das Sarma S. and Stroscio M. A. (1992), Phonon-confinement effect on electron energy loss in one-dimensional quantum wires , Phys. Rev. B 46, 3849-3853. 

Highly monodisperse ZnSe nanocrystallites (NCs) were deposited on free-standing porous silieon. Optical phonons confined in nearly spherical ZnSe QDs have been studied theoretically and experimentally. Spatially quantized phonon modes are considered in the framework of the continuum model. Raman scattering and absorption of far-infrared (FIR) radiation in ZnSe quantum dots have been studied. Experimental FTIR transmittance spectra of porous silicon free layers containing nearly spherical ZnSe nanocrystals show a broad band between the bulk TO and LO phonon frequencies. 

While the electronic and optical properties of semiconductor NCs are well luiderstood, the vibrational properties (phonons confined in spherical quantum dots of several nanometers in size) of NCs received much less attention until the last few years [1-4]. An accurate description of the vibrational modes of a NC is of fundamental interest and is required to understand the coupling of vibrational modes to electronic charge. Recently, it has been shown theoretically that geometrical confinement becomes important both for infrared and Raman-active phonons in the limit of a small size of QDs [5]. In this paper, we report the observation of coupled phonon modes in ZnSe spherical quantum dots. 

Macedo AG, Ferreira RAS, Ananias D, Reis MS, Amaral VS, Carlos LD, Rocha J (2010) The effects of phonon confinement on anomalous thermalization, energy transfer, and upconversion in Ln -doped Gd203 nanotubes. Adv Func Mater 20 624—634... 

Contrary to the case of bulk crystalline Si, the temperature dependence of porous Si is monotonic and does not present any maximum in the investigated temperature range 35-350 K. It is generally governed by phonon confinement in the Si nanostructures composing the silicon skeleton. 

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