Phonon Splitting

The frequencies and the broadening parameters of the Fi phonons polarized in the jc-y plane parallel to the GaN [1120] and [1100] directions, extracted from 

Splitting of the E2 phonon have been also observed for anisotropically strained c-plane films on a-plane sapphire [17, 18]. A subtle difference of 0.5 cm in the E2 frequency was determined when measuring in z(xx)z and z(yx)z configurations. This is in agreement with the theoretical prediction 

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Raman optical activity can not only be measured in liquids or in solution, but also in crystals. As an example, the Raman CID spectra of both enantiomorphic forms of sodium chlorate single crystals (Lindner, 1994) together with their sum spectra are shown in Fig. 6.3-18. Here a broken line represents the (-)-form. The transitions examined belong to the triply degenerate polar F phonons split into transverse and longitudinal modes. 

Fig. 1. Simplistic view of a homogeneously broadened chromophore optical absorption spectrum at 0 K. The left-hand side shows the vibrational and phonon splitting of two electronic levels. The typical vibrational levels are split by 1000 cm", and the phonons form a quasi-continuous distribution of width approximately equal to 200 cm". The upper right-hand comer shows the absorption spectrum at 0 K with the sharp zero phonon lines of approximately 1 cm" width and the phonon wing with width approximately 200 cm". ... 

G Lermann, T Bischof, A Materny, W Kiefer, T Kiimmell, G Bacher, A Forchel, G Landwehr. Wire-width dependence of the LO-phonon splitting and photoluminescence energy in ZnSe/ Cdo.gsZnoesSe quantum wires. Phys Rev B 56 7469-7476, 1997. 

Further, the presence of anisotropic distortion of the basal plane of a-plane wurtzite layers, [s 7 Sy ), will lift-off the degeneracy of the x and e Sy. Therefore, the IR dielectric functions Sx and Sy provide access to the frequencies and broadening parameters of the TO and LO phonons with Ei symmetry polarized along the x = [1120] and y = [1100] directions. In other words, the splitting of the TO and LO with Ei symmetry that is predicted theoretically by Equation 9 [14,16] can be obtained from the IR eUipsometry data analysis. Note, that polar c-plane GaN heteroepitaxial layers that experience anisotropic distortion of the basal plane, for instance when grown on a-plane sapphire [29] will also allow assessment of the Ei phonon splitting [17, 18]. In this case, the optical measurement will depend on the orientation of the plane of incidence and incident polarization with respect to the two in-plane directions X = [1120] and y = [1100]. The standard eUipsometry measurement for non-c-plane-oriented and anisotropically strained wurtzite crystals is inapplicable and the generalized eUipsometry approach is needed. 

In this list, term 1, for example, is an operator which acts on the complete phonon state. > to give a reduction of unity in the occupation number for the mode (q,j) and an increase of unity in each of the phonons (-q J ) and (-q2J2). In other words, one phonon splits into two. The complete classification is given in Table 5.1. 

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

In order to determine the phonon dispersion of CuZn and FeaNi we made use of an expanded tight binding theory from Varma and Weber . In the framework of a second order perturbation theory the dynamical matrix splits in two parts. The short range part can be treated by a force constant model, while the T>2 arising from second order perturbation theory is given by... 

Further dehydration of boehmite at 600 0 produces y-alumina, whose spectrum is shown in Figure 3b. There is a loss in surface area in going from boehmite to y-alumina. The sample shown here has a surface area of 234 m /g (this sample was obtained from Harshaw A23945 the calcined Kaiser substrate gave an identical infrared spectrum). The y-alumina sample shows two major differences from o-alumina. First, there is a more intense broad absorption band at 3400 cm" due to adsorbed water on the y-alumina. Second, the y-alumina does not show splitting of the phonon bands between 400 and 500 cm" as was observed for o-alumina. The y-alumina is a more amorphous structure and has much smaller crystallites so the phonon band is broader. The y-alumina also shows three features at 1648, 1516 and 1392 cm" due to adsorbed water and carbonate. 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

If the Zeeman splitting is large compared to the crystal field splitting, this leads to cx B T. Usually, the direct process is important only compared to other spin-lattice processes at low temperatures, because only low-energy phonons with hojq = A contribute to the direct process. 

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]. 

At low temperatures the PLE of hydrogen-terminated PS reveals that phonons and the exciton exchange splitting contribute significantly to the observed Stokes shift [Ca6, Ku4, Ro5, Ka8, Kol3]. For oxidized PS the picture is not usually so clear, due to a recombination path that may involve surface states. 

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