Phonon transversal optical

Observation of absorption bands due to LO phonons in RAIR spectra of thin, silica-like films deposited onto reflecting substrates demonstrates an important difference between RAIR and transmission spectra. Berreman has shown that absorption bands related to transverse optical (TO) phonons are observed in transmission infrared spectra of thin films obtained at normal incidence [17]. However, bands related to LO phonons are observed in transmission spectra of the same films obtained at non-normal incidence and in RAIR spectra. Thus, it is possible for RAIR and transmission spectra of thin films of some materials to appear very different for reasons that are purely optical in nature. For example, when the transmission infrared spectrum of a thin, silica-like film on a KBr disc was obtained at normal incidence, bands due to TO phonons were observed near 1060,790,and450cm [18]. 

When metals have Raman active phonons, optical pump-probe techniques can be applied to study their coherent dynamics. Hase and coworkers observed a periodic oscillation in the reflectivity of Zn and Cd due to the coherent E2g phonons (Fig. 2.17) [56]. The amplitude of the coherent phonons of Zn decreased with raising temperature, in accordance with the photo-induced quasi-particle density n.p, which is proportional to the difference in the electronic temperature before and after the photoexcitation (Fig. 2.17). The result indicated the resonant nature of the ISRS generation of coherent phonons. Under intense (mJ/cm2) photoexcitation, the coherent Eg phonons of Zn exhibited a transient frequency shift similar to that of Bi (Fig. 2.9), which can be understood as the Fano interference [57], A transient frequency shift was aslo observed for the coherent transverse optical (TO) phonon in polycrystalline Zr film, in spite of much weaker photoexcitation [58],... 

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]. 

At high temperatures above Tb 617 K PMN behaves Hke all other simple perovskites. The dynamics of the system is determined by the soft transverse optical (TO) phonon which exhibits a normal dispersion and is imderdamped at all wave vectors. Below Tb, in addition to the soft mode—which becomes overdamped—a new dielectric dispersion mechanism appears at lower frequencies which can be described by a correlation time distribution function /(t). 

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). 

This is the background for the Lyddane-Sachs-Teller relation to be treated below. For transverse optical vibrations the origin of an is field is less obvious, but it is also present and its reaction on the eigenfrequency of the TO phonon later gives rise to the polaritons. 

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

Hereby, the branches with E - and / -symmetry are twofold degenerated. Both A - and / d-modes are polar, and split into transverse optical (TO) and longitudinal optical (LO) phonons with different frequencies wto and wlo, respectively, because of the macroscopic electric fields associated with the LO phonons. The short-range interatomic forces cause anisotropy, and A - and / d-modcs possess, therefore, different frequencies. The electrostatic forces dominate the anisotropy in the short-range forces in ZnO, such that the TO-LO splitting is larger than the A -E splitting. For the lattice vibrations with Ai- and F -symmetry, the atoms move parallel and perpendicular to the c-axis, respectively (Fig. 3.2). 

Indium nitride has twelve phonon modes at the zone centre (symmetry group Cev), three acoustic and nine optical with the acoustic branches essentially zero at k = 0. The infrared active modes are Ei(LO), Ei(TO), Ai(LO) and Ai(TO). A transverse optical mode has been identified at 478 cm 1 (59.3 meV) by reflectance [6] and 460 cm 1 (57.1 meV) by transmission [24], In both reports the location of a longitudinal optical mode is inferred from the Brout sum rule, giving respective values of 694 cm 1 (86.1 meV) and 719 cm 1 (89.2 meV). Raman scattering of single crystalline wurtzite InN reveals Ai(LO) and E22 peaks at 596 cm 1 and at 495 cm 1 respectively [25],... 

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... 

For the particular case of longitudinal optical modes, we found in Eq. (9-27) the electrostatic electron-phonon interaction, which turns out to be the dominant interaction with these modes in polar crystals. Interaction with transverse optical modes is much weaker. There is also an electrostatic interaction with acoustic modes -both longitudinal and transverse which may be calculated in terms of the polarization generated through the piezoelectric effect. (The piezoelectric electron phonon interaction was first treated by Meijer and Polder, 1953, and subsequently, it was treated more completely by Harrison, 1956). Clearly this interaction potential is proportional to the strain that is due to the vibration, and it also contains a factor of l/k obtained by using the Poisson equation to go from polarizations to potentials. The piezoelectric contribution to the coupling tends to be dominated by other contributions to the electron -phonon interaction in semiconductors at ordinary temperatures but, as we shall see, these other contribu-... 

In the solid state, the polar phonons (those that are IR active) split into two components, the transverse optical mode (TO) and the longitudinal optical mode (LO). This TO/LO splitting occurs because the electric field associated with the transverse wave = 0 while that associated with the longitudinal wave is 0. The coupling of these modes with the electric fields associated with the vibration gives rise to Vlo > Vto- This factor is relevant in relation to the shape and interpretation of the IR spectra of solid materials and will be further considered below. 

This band called iTOLA because it is attributed to a combination of two intra-valley phonons the first from the in-plane transverse optical branch (iTO) and the second phonon from the longitudinal acoustic (LA) branch, iTO-t-LA, where the acoustic LA phonon is responsible for the large dispersion that is observed experimentally [69]. 

Wurtzite ZnO structure with four atoms in the unit cell has a total of 12 phonon modes (one longitudinal acoustic (LA), two transverse acoustic (TA), three longitudinal optical (LO), and six transverse optical (TO) branches). The optical phonons at the r point of the Brillouin zone in their irreducible representation belong to Ai and Ei branches that are both Raman and infrared active, the two nonpolar 2 branches are only Raman active, and the Bi branches are inactive (silent modes). Furthermore, the Ai and Ei modes are each spht into LO and TO components with different frequencies. For the Ai and Ei mode lattice vibrations, the atoms move parallel and perpendicular to the c-axis, respectively. On the other hand, 2 modes are due to the vibration of only the Zn sublattice ( 2-low) or O sublattice ( 2-high). The expected Raman peaks for bulk ZnO are at 101 cm ( 2-low), 380 cm (Ai-TO), 407 cm ( i-TO), 437 cm ( 2-high), and 583 cm ( j-LO). 

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...

TABLE 1 Principal phonon energies (meV) in six polytypes derived from the luminescence spectrum (from [26]). The notation (TA) for transverse acoustic, (LA) for longitudinal acoustic, (TO) for transverse optical, and (LO) for longitudinal optical phonons is accurate for the cubic polytype, but not for the hexagonal and rhombohedral polytypes. For details see Datareview 2.2. 

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. 

Figure 7. Bulk phonon dispersion curves for KBr and RbCl in their <100> and <111> high-symmetry directions. Both crystals have fee lattices and rocksalt structures. Note that the transverse branches, labeled TA (transverse acoustic) and TO (transverse optical), are doubly degenerate in these directions. (Adapted from Fig. 3 of Ref. 32.)...

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