Longitudinal-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]. 

Barker, A. S., 1973. Infrared absorption of localized longitudinal-optical phonons, Phys. Rev., B7, 2507-2520. 

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. 

Ionic crystals also support SEW, but again no data exists where they have been used as substrates for attached molecule studies. That such studies may be feasible is illustrated in Fig. 21, which shows measured and calculated propagation distances for SrTi03 in the far infrared.— Again, these measurements were made with a molecular laser as a source. Unfortunately, for many crystals the frequency region over which SEW exist is very narrow (between the transverse and longitudinal optic phonon frequencies), and propagation distances are very short. However, ferroelectrics (and near-ferroelectrics like SrTiC ) may prove useful substrates for SEW spectroscopy. 

This scattering process is due to the interaction of electrons with the electric field induced by the lattice vibration polarization (polar longitudinal-optical phonons) occurring in polar semiconductors with partially ionic bonding. According to Devlin [55], the optical Hall mobility can be calculated by... 

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. ... 

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 . ... 

Free-carrier thermalization with lattice, emission of longitudinal optical phonons... 

M. A. Stroscio, Interaction between longitudinal-optical phonon modes of a rectangular quantum wire with charge carriers of a one-dimensional electron gas, Phys. Rev. B, 40, 6428-6432 (1989). 

Lugli P. and Goodnick S. M. (1987), Nonequilibrium longitudinal-optical phonon effects in GaAs-AlGaAs quantum wells , Phys. Rev. Lett. 59, 716-719. 

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. 

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. 

Since the excited states are electrically neutral, only the short-range, acoustic interaction is relevant in eqn (7.24). (This is also true for the exciton-polaron, as the particle and hole are closely separated.) The polaron, however, being charged also couples to the longitudinal optic phonons, so the long-range term is retained... 

G Tamulaitis, PAM Rodrigues, PY Yu. Screening of longitudinal optical phonons by carriers in quantum dots. Solid State Commun 95 227-231, 1995. 

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