Phonon mode splitting

The dispersionless optical phonon mode />, splits the degenerated unperturbed electron level (j = 1,2) while the mode b2 mediates the electron transitions between the levels. This latter term represents phonon-assisted tunneling, a mechanism of the... 

Figure 1.22 Top (Vio - Vjo) Ei phonon mode splitting versus pressure. Solid lines are linear least-square fits to the experimental points. Bottom Pressure dependence of the observed optical phonons. Open (full) symbols propagation of light perpendicular (parallel) to c-axis. (Courtesy of F. Decremps [92].)...

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]. 

Infrared reflection and Raman spectroscopies have been used to derive the energies of the zone centre phonon modes in wurtzite AlxGai.xN (0 < x < 1) [1-5] (for GaN [6] and AIN [7] refer to the dedicated Datareviews). Selection rules in wurtzite allow a splitting of longitudinal and transversal modes into Ai and Ei modes and the occurrence of additional Raman active modes E2. 

Consider now the case where the energy spacing 21 is very small. Such cases are encountered in the study of relaxation between spin levels of atomic ions embedded in crystal environments, so called spin-lattice relaxation. The spin level degeneracy is lifted by the local crystal field and relaxation between the split levels, caused by coupling to crystal acoustical phonons, can be monitored. The relaxation as obtained from (12.47) and (12.48) is very slow because the density of phonon modes at the small frequency (U21 is small (recall that... 

There is only little known on both the anharmonicity of the vibrations of hydroxide ions (see, for example, Refs. [74-76]) and the TO/LO splitting of the respective phonon modes. Though investigations on overtone spectra of solid hydroxides are scarce [76,77] and, hence, only a few experimental data on the anharmonicity constants xca)e of the OH stretching modes are available in the literature [75,78] we assume that the anharmonicities of hydroxide modes do not differ from those of the vibrations of other OH groups, e.g. water molecules [40,79]. For calculation of at least crude anharmonicity constants of OH-vibrations, we recommend the procedure reported by Engstrom et al. [74] using the frequencies of the respective OH and OD modes recorded from spectra of isotopically dilute samples [79]. 

Consider an electronic transition coupled to both the relatively sharp vibron transitions and the broad spectrum of phonons. The vibrons will split the single-electron transitions characterized by the quantum number n into a series of lines characterized by the vibrational quantum number j. Each vibron level is split further into closely spaced phonon lines, which we represent by a set of quantum numbers /, representing the phonon modes. Thus, in our simple representation a state can be given by the three quantum numbers (in order of decreasing energy) (n,j, /). However, the number of phonon modes is so large that experimentally, at high temperatures, one measures only an unresolved band. 

Experimentally this effect has been found in dhcp Pr (Houmann et al. 1979) and in PrAlj (Purwins et al. 1976). The latter has cubic site symmetry and the ground and first excited states are Fj (OK) and 7 (27.4K). It orders ferromag-netically at = 33 K. At low temperatures (F T ) only three of the field-split F3-F4 magnetic excitons are seen (fig. 30) and those with 7+ polarization show a strong anti-crossing effect with a transverse acoustic phonon mode in the [001] direction. Detailed model calculations for this mixed-mode spectrum were performed by Aksenov et al. (1981) using an equation of motion approach. 

It was found that Mn " is characterized by a luminescence band peaking at 643 nm with a typical excitation spectrum and a long decay time of 29 ms. Low temperature study revealed a pure electronic transition at 615.4 nm which is the energy of the lowest split component of the " Ti(G) state above the ground state. Phonon replicas of this transition are evident showing that a particular phonon mode of 180 cm is dominantly involved (Green and Walker 1985). 

A Yamamoto, Y Yamada, Y Masumoto. Biaxial splitting of optical phonon modes in ZnSe-ZnS strained-layer superlattices. Appl Phys Lett 58 2135-2137, 1991. 

Fig. 57. The evolution of LA phonon peak position as a function of the temperature and the unnormalized phonon energy (Liu 1989b). It gives qualitatively the shape of the LA phonon dispersion curve near the mode splitting frequency. All frequencies are in units of t].

In particular, for MgBj coupling to the E2g phonon mode (in-plane stretching vibration of B-B) results in splitting of a bands (px, py electrons of B atoms in a-b plane) in F point of the first Brillouin zone (BZ) - Fig. 27.2b. Related to band topology, the analytic critical point (ACP, maximum) of o bands islocated at the... 

The inconsistency in the strain components in the a-plane QD samples reported in [57, 58] indicates a significant impact of the assumptions made in their estimation from the phonon frequencies. We note that in aU estimations of the strain components, the anisotropic phonon deformation potentials chj(to) and ce were assumed to be zero [57]. The results of the anisotropically strained GaN films presented in Sections 9.4.2 and 9.4.3 show clear splittings of the El and 2 indicating nonzero anisotropic deformation potentials for these phonon modes (Tables 9.4 and 9.5). We point out, however, that the values of the C j(xo) and c in Ref. 17 may be also affected by the assumptions made in the strain component determination by XRD (for instance the deviation from hexagonal symmetry is assumed to be small). The studies of the vibrational properties of nitride materials with nonpolar surface orientations are scarce and clearly, further experimental and theoretical investigations are needed to clarify these issues. 

GaN layers with vicinal surfaces, such as a-plane surface orientations, reveal all information on their IR active phonon modes upon application of GIRSE. Valuable information on the complete dielectric tensor anisotropy and Ai(TO) phonons in GaN, that is otherwise obscured for c-plane-oriented films, is retrieved. The capability of the GIRSE technique to detect spectrally narrow dichroism in nonpolar GaN films under anisotropic strain, thereby allowing to precisely locate the phonon mode resonances for different polarizations, has been demonstrated. As a result, splittings of the GaN i(TO) and i(LO) phonon modes under anisotropic strain have been identified, further splitting of the GaN 2 phonons measured by Raman spectroscopy has been also demonstrated. 

Fig. 77. GaAs(llO). Surface phonon dispersion predicted for the clean surface [95Fril]. The shaded area represents the projection of the bulk bands on the SBZ. The surface phonon mode above the bulk optical band splits into two modes along r - X. The uppermost mode is marked by the dashed line.

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