Longitudinal optical mode

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. 

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],... 

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. 

Transverse and Longitudinal Optic Modes in the alpha and beta Phases of Quartz. 

Since the jp-polarized radiation at cpi 0° has tangential and normal electric field components (1.4.4°), these components will interact with those dipoles within the film that are oriented parallel and perpendicnlar to the snrface, respectively, according to the selection mle (1.27). Fmthermore, under action of the external electric field normal to the surface, the dipoles experience an additional electric field induced by the polarized chemical bonds within the layer. It follows that in the jp-polarized spectra, the band near the longitudinal optical mode vlo will be observed, in addition to the band near vro resulting from the dipoles parallel to the film. In light of the discussion in Section 1.8.2, it is evident that because the dipole oscillations responsible for the vro band are directed along the surface, these oscillations will be quenched by a metal surface and, hence, be absent in p-polarized spectra of films on mefal substrates, as demonstrated in Fig. 3.2. 

This dispersion relation shovm in Figure 24.17 is similar to the upper or longitudinal branch of Figure 24.5. No wave can propagate if ta < cap and above tap, only the longitudinal mode can be excited. Recall that we defined o>l as the frequency at which the dielectric constant became positive again. So we see that for conductive media, the plasma frequency corresponds to the frequency of the longitudinal optical mode. 

It is evident Irom Fig. 10 that there are six distinct phonon modes in the monolayer graphite. The LO branch is a longitudinal optical mode. The LA branch is a longitudinal acousticlike mode. The ZO branch is a vertically vibrating transverse optical mode. The ZA branch is a vertically vibrating acoustic-like mode. The SHO branch is a shear horizontal optical mode. The SHA is a shear horizontal acoustic-like mode. The last two SH modes appear because of the lack of mirror symmetry in these experiments (39). 

Improvements Further improvements have been introduced, as experimental data have become more reliable. For example, neutron scattering experiments have proved that the longitudinal optic mode frequencies at the zone centre are systematically lower than predicted. Various models result from the idea that this discrepancy may be assigned to the neglect of ionic polarization. 

The relation (4.110) for e(w) applies for optically isotropic diatomic crystals with one LO-mode and two degenerate TOrWodes at q 0. Crystals of the same symmetry containing n ions in the unit cell possess n - 1 longitudinal optical modes with frequencies w.(LO) and n - 1 doubly degenerate trans-... 

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