Surface optical phonons

Momentum conservation implies that the wave vectors of the phonons, interacting with the electrons close to the Fermi surface, are either small (forward scattering) or close to 2kp=7i/a (backward scattering). In Eq. (3.10) forward scattering is neglected, as the electron interaction with the acoustic phonons is weak. Neglecting also the weak (/-dependence of the optical phonon frequency, the lattice energy reads ... 

The continuum model with the Hamiltonian equal to the sum of Eq. (3.10) and Eq. (3.12), describing the interaction of electrons close to the Fermi surface with the optical phonons, is called the Takayama-Lin-Liu-Maki (TLM) model [5, 6], The Hamiltonian of the continuum model retains the important symmetries of the discrete Hamiltonian Eq. (3.2). In particular, the spectrum of the single-particle states of the TLM model is a symmetric function of energy. 

Bulk phonon modes are absent in wave numbers near 357 cm , the center-frequency of the second band. According to electron energy loss studies done in a vacuum [52, 53], TMA-free TiO2(110) surfaces exhibit surface optical phonons at 370-353 cm . The 357-cm band is related to the surface optical phonons. 

Chang, Y. M., Xu, L. and Tom, H. W. K. (1997) Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation. Phys. Rev. Lett., 78, 4649-4652. 

Melnikov, A. V., Radu, I., Bovensiepen, U., Krupin, O., Starke, K., Matthias, F. and Wolf M. (2003) Coherent optical phonons and parametrically coupled magnons induced by femtosecond laser excitation of the Gd(OOOl) surface. Phys. Rev. Lett., 91, 227403. 

Fig. 2.12. Left transient anisotropic reflectivity change of the (001) surface of single crystal type Ha diamond. Inset shows the FT spectrum of the oscillation, demonstrating a narrow peak of the optical phonon at 40THz. Right pump and probe polarizations to detect the optical phonon. Adapted from [50]...

We note that ionic crystals may have dielectric functions satisfying Eq. (4) for frequencies between their transverse and longitudinal optic phonon frequencies. SEW on such crystals are often called surface phonons or surface polaritons and the frequency range is the far IR. 

Fig. 1. The scattering probability P measured experimentally [13] corresponding to the excitation of the fundamental mode of the MgO surface optical phonon as a function of Eo. The fitted curve represents the theoretical expectation that P(co) a (Eqn.2).

Conventional infrared spectra of powdery materials are very often used for studying solid hydrates in terms of sample characterization (fingerprints), phase transitions, and both structural and bonding features. For the latter objects mostly deuteration experiments are included. However, it must be born in mind that the band frequencies observed (except those of isotopically dilute samples (see Sect. 2.6)) are those of surface modes rather than due to bulk vibrations, i.e., the transverse optical phonon modes, and, hence, not favorably appropriate for molecular and lattice dynamic calculations. 

Single crystal studies of solid hydrates are scarce. There are two experimental procedures possible (i) transmission spectra of thin crystal plates (see, for example. Refs. 16, 17) and (ii) reflection spectra of crystal faces . Using polarized infrared radiation, the species (symmetry) and other directional features of the water bands can be determined. In the case of reflection measurements, the true transverse and longitudinal optic phonon frequencies can be additionally computed by means of Kramers-Kronig analyses and oscillator fit methods, respectively. Both experimental techniques, however, are relatively difficult because of the lack of suitable monocrystals, the requirement of preparing sufficiently thin, i.e., <0.1 mm, crystal plates (except for studying overtone bands, see Sect. 4.2.6), and the efflorescence or absorption of water at the crystal surfaces. In favorable cases, thin sheets of orientated powdery material can be obtained . ... 

Chen Chen, Mitra Dutta, and Michael A. Stroscio, Surface-optical phonon assisted transitions in quantum dots. Journal of Applied Physics, 96, 2049-2054 (2004).31. Amit Raichura, Mitra Dutta, and Michael A. Stroscio, Acoustic Phonons and Phonon Bottleneck in Single Wall Nanotubes, J. of Computational Electronics, 4, 91-95, 2005. 

The evolution of optical phonon spectra of colloidal core/shell CdSe/ZnS nanocrystals with an increase of the shell thickness from 0.5 to 3.4 monolayers have been studied by resonant Raman spectroscopy. The results show that at a thickness of about 2ML the surface of the CdSe core is mainly defect free although the structure of the shell is not established yet. The latter occurs at the thickness more than 3.4 ML where the shell is, most likely, amorphous. It is concluded that the defect-free core/shell interface is more important for producing high-luminescence QD structures than the increase of the shell thickness. 

LO-phonon, Qlo of 206.1 cm is smaller than the corresponding bulk value of 210 cm [3] by 3.9 cm. The shift comes from two sources a red shift due to confinement of optical phonons [2], which is expected to be 4.7 cm for 4 run CdSe QDs and a blue shift from the QD lattice contraction due to an increase of the surface tension force [4]. As observed, both mechanisms contribute to the shift. A 9.2 cm" width (FWHM, T) of the LO-phonon line in our experiment coincides with that measured by a size-selective resonant Raman spectroscopy for 4.2 mn CdSe QDs [2]. 

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