Transverse-optical phonon

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. 

So far only one degree of freedom of the vibration has been considered, namely, in the direction of the wave vector. The removal of this restriction gives transverse optical and acoustical phonons. For these, the atoms or ions move perpendicular to the direction of wave propagation. Again, there are two possibilities. When A and B atoms vibrate in phase, there is no change of dipole moment and one speaks of a transverse acoustical phonon (TA). However, for a vibration with opposite phases in the A and B atoms, the electric dipole moment changes so that we have a transverse optical phonon (TO). 

The other solution ej - 2 =0 leads to strictly transverse optical phonons. They degenerate with the ordinary phonons given by Eq. (11.29). 

The equations of motion describing the transverse optic phonon and electromagnetic modes (modeled as oscillators with charged masses, whose displacements lie along the x direction and whose wavevectors lie mainly along the y direction in the yz plane), their coupling, and their responses... 

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... 

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. 

In compound crystals, the ujn values considered are wlo, the frequency of the longitudinal optical phonons on the high-energy (h-e) side, and wto, the frequency of the transverse optical phonons, on the low-energy side. The dielectric constant at frequencies above c lo is denoted as while that below wto is denoted as s (the index s represents static, despite the fact that s shows a small dispersion between the value just below ujto and the one at radiofrequencies1). It can be seen from expressions (3.14) and (3.15) that above ujo, the ionic contribution decreases such that qo is smaller than s. Typical values are given in Table 3.1. 

Table 8.3 The lattice constant (a), bulk modulus (B) and frequency of the transverse optic phonon at the zone centre (TO-T) for MgO from PW-LDA and LCAO-HF calculations compared to observations extrapolated to the...

Lux (lx) - The SI unit of illuminance, equal to cd sr m. [1] Lyddane-Sachs-Teller relation - A relation between the phonon frequencies and dielectric constants of an ionic crystal which states that (co., /cOj ) = e(< )/e(0), where co., is the angular frequency of transverse optical phonons, that of longitudinal optical phonons, e(0) is the static dielectric constant, and e(< ) the dielectric constant at optical frequencies. 

Raman spectra showed that the diamond phonon line broadening started to show up even at 5 seem of TMS flow rate indicating the influence of increasing P-SiC Volume% in the films with an increase in TMS flow rate. FTIR measurements illustrated that greater transverse optic phonon (TO) band intensity obtained from the samples deposited with greater TMS concentration showed qualitatively the presence of laiger volume of p-SiC in the films. As an example, FTIR speara obtained from two different diamond/p-SiC nanocomposite films deposited on W substrates are shown in Fig. 3. Additionally, quantitative compositional analysis (RBS measurements EPMA) showed that the content of p-SiC in the films corresponds almost linearly to the TMS concentration in the gas phase during the film deposition. 

Figure 3. (a) IR spectra obtained from two diamond/p-SiC nanocomposite films deposited on W substrates by using different TMS flow rates. The transverse optical phonon band around 800 cm corresponds to the presence of p-SiC. (b) Backscattered electron cross-sectional micrograph of a gradient natured diamond/p-SiC nanocomposite film deposited on BEN pre-treated (100) Si substrate. The bright spots indicate p-SiC phase. 

A qualitative, physical description of the longitudinal and transverse optical phonons is illustrated in Fig. 1.6. Kittel [22] phenomenologically explains the fact that ft)Lo > oio as follows. The local electric field induces polarization of the surrounding atoms in the opposite direction to that of the longitudinal mode but in the same direction as the transverse mode. This polarization causes an increasing resistance to the longitudinal vibration relative to the transverse one (see also Ref. [33]). 

Jensen (1971) and Vigren and Liu (1972). The theory is an extension of the static magnetostriction to the dynamic situation, and this kind of interaction failed to explain the splitting A between the MA mode and the transverse optic phonon (TO). A similar situation exists in Dy where the mixing of the optic magnon (MO) and TA mode was seen (Nicklow et al., 1972). 

T Fromherz, F Hauzenberger, W Faschinger, M Helm, P Juza, H Sitter, G Bauer. Confined transverse-optical phonons in ultrathin CdTe/ZnTe superlattices. Phys Rev B 47 1998-2002, 1993. 

Fig. 10. Schematic diagram of a transverse optical phonon in a linear polymer...

The paraelectric-ferroelectric transition is usually accompanied by small permanent relative displacements of ions or molecular groups from the symmetry positions in the paraelectric phase. Local electric dipoles result from the ion displacements and these crystals are referred to as displacive ferroelectrics. The structural instability may be associated with highly temperature-dependent low-frequency transverse optical phonons in the paraelectric phase which predominate at the Curie temperature (see, for example. Refs. 214-216 and Volume 2, Chapter 3). The nature and magnitude of the ion displacements determine many of the properties of ferroelectric crystals. 

Figure 2.17 The phonon dispersion relations for (a) GaN and (b) Si. TA, LA, LO, and TO refer to transverse acoustic, longitudinal acoustic, longitudinal optical and transverse optical phonons, respectively. Each of these represents a particular vibrational mode. Longitudinal modes run along bonds as in Figure 2.16, while for transverse modes the vibration velocity is perpendicular to the bonds. There are two transverse modes because there are two axes perpendicular to a bond direction. Figures after Levinshtein, Rumyantsev, Sergey, and Shur, Reference [5], p. 27 and 184, respectively. This material is used by permission of John Wiley Sons Inc.

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