LO-phonon

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]. 

In addition to the photoluminescence red shifts, broadening of photoluminescence spectra and decrease in the photoluminescence quantum efficiency are reported with increasing temperature. The spectral broadening is due to scattering by coupling of excitons with acoustic and LO phonons [22]. The decrease in the photoluminescence quantum efficiency is due to non-radiative relaxation from the thermally activated state. The Stark effect also produces photoluminescence spectral shifts in CdSe quantum dots [23]. Large red shifts up to 75 meV are reported in the photoluminescence spectra of CdSe quantum dots under an applied electric field of 350 kVcm . Here, the applied electric field decreases or cancels a component in the excited state dipole that is parallel to the applied field the excited state dipole is contributed by the charge carriers present on the surface of the quantum dots. 

Fig. 2.1. Double-pump and probe reflectivity signal of coherent LO phonons of GaAs (left) and coherent A g phonons of Bi (right). The horizontal axis gives the time delay of the probe pulse with respect to the first pump pulse in both panels. Ati2 (At) in the left (right) panel is the time delay between the two pump pulses in units of the LO phonon period i/ [q=114 fs (A g phonon period T = 341 fs). From [5] and [6]...

One of the applications of TRXRD is to study complex systems where electric fields couple to multiple degrees of freedom. Though femtosecond laser pulses can generate THz radiation from ferroelectric LiTa03, the corresponding lattice motion remained undetected by optical measurements. Cavalleri and coworkers demonstrated the coherent modulation of the X-ray intensity at 1.5 THz [10], and assigned it as phonon-polariton mode of A symmetry (Fig. 3.3). Nakamura and coworkers detected the coherent LO phonon of CdTe... 

In photoexcited polar semiconductors, the coherent LO phonons couple with photocarriers to form coherent LO phonon-plasmon coupled (LOPC) modes, which exhibit fundamentally different properties from those of bare phonons. Huber and coworkers revealed the ultrafast transition of an optical... 

If the dephasing time of the coherent phonons depend critically on the carrier density, photo-injection of carriers with the second pump pulse can annihilate them partially or completely, depending on its fluence but not on its relative timing. Such incoherent control was demonstrated for the LO phonons of GaAs [37],... 

Therefore LO phonons exist with the frequencies u>L independent of k. 

The coupling of plasmons with LO phonons leads to coupled plasmon-pho-non states. For a cubic crystal with 2 atoms in the elementary cell and one infrared-active eigen frequency cop, the frequency-dependent dielectric constant is according to Eq. (11.17)... 

According to the general rule, LO phonons are obtained when e = 0. With (11.38) it follows from (11.40)... 

The phonon branch that is suspected to interact strongly with the charge by the ARPES measurement, namely the zone-boundary Cu-0 bondstretching LO phonon branch (Fig. 1), was found by inelastic neutron scattering to show unusual temperature dependence [8],... 

Figure 11 1 1 Schematics of the Cu-O hond-stretching zone-houndary LO phonon (halfbreathing) mode...

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). 

Figure 5. Pressure dependence of parameter C in the dispersion law for the LA-LO phonon branch (a) and pressure dependence of parameters A and B in the dispersion law for the TA phonon branch (b).

The first investigation of the phonon modes in binary InN was an extrapolation of the Gai-xInxN (0 < x < 1) alloy modes in reflection towards the binary compound [1], A typically high free carrier concentration in the mid 1020 cm 3 range controls the absorption (Drude absorption) in the infrared and must also account for the broadened Reststrahlen band in pure InN films (e.g. in [1]). In this case infrared active phonons couple to the plasma of the free electrons forming phonon-plasmon coupled modes [10,11], However, layers of low carrier concentration have been achieved and pure LO phonon energies have been derived in Raman spectroscopy. Resonant Raman spectroscopy at 514 nm has been performed, assigning five of the six Raman allowed zone centre phonon modes [8,9] (TABLE 1). 

The free carrier concentration at room temperature was determined by Raman experiments using the Ai(LO) phonon-plasmon coupled mode and by the reflectance in the mid-infrared and the optical absorption in the near-infrared range. Each experiment for the GaN layer of 60 pm thickness showed a free carrier concentration in the order of 1017 cm 3. 

Figure 1. The q dependence of the effective charge of oxygen in the 1 -d Hubbard model due to the LO phonon monde, calculated for the ring o( /V— 12 sites with doping level. v = 0, 1/3 and for N — 16 with x — 0, 1/4. The dashed line indicates the ionic value (static charge)1. ...

Fig. 15.8 Confocal Raman microscopy and SNOM images of a locally stressed SiC crystal (a) Rayleigh intensity map. (b), (c) Spectral position maps of fitted TO and LO phonon lines obtained by fitting a Lorentzian peak, (d) Topography of the indent, (e) SNOM amplitude for cOiR = 924 cm. (f) SNOM amplitude for (0 = 944 cm (Reprinted from [68])...

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