LO longitudinal optical

The vibration spectruin of GaAs, calculated by using the C, and C l values of Tabic 8-4 (TO = transverse optical LO = longitudinal optical LA = longitudinal acoustical TA = transverse acoustical). Experimental points arc from Dolling and Waugh (1965). 

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]. 

To identify c-BN, the characteristic transverse optical mode (TO) at 1065 cm-1 and longitudinal optical mode (LO) at 1340 cm-1 have been described [56]. When investigating commercial c-BN, commonly only one IR-peak between 1050 and 1100 cm-1 is observed. 

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],... 

Typical luminescence spectra of as-grown crystals show ultra-violet emission due to free excitons (including their longitudinal optical phonons-EO replicas) as well as t5 ical bands of green and yellow-orange luminescence (the temperature is 77-80 K). When the temperature is 4.2 K, the luminescence of bound excitons (including their LO - replicas) dominates. ... 

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. 

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). 

In 1997, a seminal paper of the time-resolved SHG study on a GaAs surface appeared [23], It was shown that the time-resolved SHG probes not only electronic dynamics but also lattice (phonon) dynamics. The detection scheme is as follows The pump pulse impulsively excites the longitudinal optical (LO) phonon in the GaAs... 

In the dielectric spectra therefore the IR active mode gives rise to an absorption peak near (U=tOo whose width is proportional to This is the transverse optical (TO) mode. The longitudinal optical (LO) mode appears as a peak in a plot of 1/e(cu) vs co. 

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 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. 

LA LCAO LDA LED LEED LMTO LO LPE LTLPE longitudinal acoustic linear combination of atomic orbitals local density approximation light emitting diode low energy electron diffraction linear muffin-tin orbital longitudinal optical liquid phase epitaxy low temperature liquid phase epitaxy... 

The dielectric parameters are tensors, and consequently it is essential to use polarized radiation when recording the infrared absorption and reflection spectra of all but cubic crystals. Thus, with an orthorhombic crystal the reflection has to be measured with the electric vector parallel to the a, Z , and c axes. When obtaining the reflection spectra from the be plane of a monoclinic crystal, it is necessary to rotate the plane of polarization of the electric vector. The longitudinal optic (LO) frequency [see discussion of Equation (4)] can be found for q = 0 by noting that it is the frequency for which = 0. It can be measured directly in cubic crystals by a method due to Berriman [114]. 

Here is the high-frequency dielectric constant, the static dielectric constant, and Lo the frequency of the longitudinal optical vibration mode. The values of P range from about 3 (GaP, ZnS, Csl, Nal), via 4(La202S), 5.6 (Y3AI5O12), to 7 (CaW04, YVO4). 

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