Phonon energy width

The half width of the luminescence line by the phonon interaction mechanism, from Eq. (8.11), is 2[(2 In 2) ji This is 0.25 eV for the maximum phonon energy of 0.05 eV from the silicon network vibrations, which is a little less than the observed line width. Thus the phonon model indicates that the luminescence spectrum is dominated by the phonon interaction and that the disorder broadening contributes less. 

There is a red shift for its characteristic peaks in Raman spectrum which will induce lower phonon energy for the samples. The full widths of half-maximum of all peaks are increased and peak Intensity becomes weak when La203 was doped as an additive which means that the thermal vibration and the symmetry of the samples weaken. It is proven that the structures of samples present are in disorder and agree with the result that mentioned above. It is possible for Nd (Yi.,Lax)203 to be a new type of laser material. 

Fig.3 shows the Raman shift of (Ybo.o5Yo<)5xLax)20j ceramics. The phonon energies of (Yboo5Yo.95-xLa,)203 ceramics are between 370 and 376 cm and the FWHM (the ftill width of half-maximum) increases with the increase of LajOj content. There exists a red shift for the Raman characteristic peaks after the adding of LaaOj. 

The experiments on phycobilisomes did not give evidence for exciton-like energy transport. In particular, no specific dependence of the zero-phonon line width as a function of bum frequency could be found, a result which was considered as strong support for stochastic transport processes. 

Here Z = 8a(/ko)2(2 +7) is the width of the centre absorption band, n = where ha> is the phonon energy, sT is the energetic depth of the center, and a is the electron-phonon interaction constant Consequently, we will use this equation to explain the peculiarities of current and conductivity... 

The real part H co) is the Hilbert transform of the phonon density of states which has an approximately triangular shape with the center at ha> = 140 K and a phonon band width of = 40 K. The renormalized energies of CEF sates are then given by the solutions of... 

Fig. 32. (a) Phonon energies of CePdj versus temperature for several LA modes in the [111] direction, (b) Intrinsic phonon line widths of the corresponding modes versus temperature. The intrinsic line widths are fitted with a Lorentzian convoluted with a Gaussian for spectrometer resolution. Points without error bars are fits without a Lorentzian for phonons which are well described by spectrometer resolution alone (Severing et al. 1988). 

More recently. Green s function methods have been applied to evaluate analytic expressions of phonon frequencies and widths as well as of thermodynamic properties of the linear chain [5.7-9]. These studies have shown that the complex anharmonic self-energies, that is, the shifts and widths of the phonon energies, depend on q and on the applied frequency w. The results of such calculations for three-dimensional crystals will be discussed in Sect.5.5. 

The concept of a mobility edge has proved useful in the description of the nondegenerate gas of electrons in the conduction band of non-crystalline semiconductors. Here recent theoretical work (see Dersch and Thomas 1985, Dersch et al. 1987, Mott 1988, Overhof and Thomas 1989) has emphasized that, since even at zero temperature an electron can jump downwards with the emission of a phonon, the localized states always have a finite lifetime x and so are broadened with width AE fi/x. This allows non-activated hopping from one such state to another, the states are delocalized by phonons. In this book we discuss only degenerate electron gases here neither the Fermi energy at T=0 nor the mobility edge is broadened by interaction with phonons or by electron-electron interaction this will be shown in Chapter 2. 

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