Model dielectric function phonons

In the IR spectral region, DFs i(ui) are sensitive to phonon and plasmon contributions. Hence, IR model dielectric functions (MDFs) are written as the sum of lattice and free-charge-carrier fcc(u ) contributions [73]... 

In the infrared spectral region, the dielectric function ej(o)) is sensitive to phonon and plasmon contribution. Therefore, the infrared model dielectric function can be written as a sum of lattice, sj (co) and free-charge carrier. 

The temperature-dependent Purcell factor has been determined to explain the PL data. By taking into account the dependence of electron-electron and phonon-electron scatterings on temperature, Drude model is used fcff calculating the temperature-dependent dielectric functions of Al and the results are shown in Fig. 13.6(a) indicating the functions are rather insensitive to temperature [22]. On the other hand, for ZnO, reflectivity measurements have been performed and the reflectance spectra are shown in Fig. 13.6(b) for different temperatures. To extract... 

In our case of semiconductor nanocrystals, the real part of the dielectric function becomes negative in the vicinity of the transverse-longitudinal splitting, i. e. in the frequency range between the transverse, Qt, and longitudinal, Ql, frequencies of an optical phonon, Qt < < Ql. In this frequency range, the dielectric function is well modeled by the expression ... 

As an example, we estimate the resonance enhancement of an intraband optical transition in silicon carbide (SiC) nanociystals. The dielectric function of SiC is well modeled by the expressions (7) with = 6.52, Qt = 793.9 cm" (and the wavelength At = 12.6 pm), = 970.1 cm (Al = 10.3 pm), and y = 4.763 cm. Note that the relaxation parameter y is much less than the optical phonon frequencies, y/Qi = 0.006 and y/ L = 0.005. The solution of the resonance condition (6) results in Q w 902cm and the corresponding resonance wavelength A 11 pm. Here and hereafter, in all onr numerical estimates we accept the permittivity of a host matrix Shost = 2.25, because this value is typical for many solvents, glasses, and polymers. Then, the gain factor G(Q) is estimated to be approximately 3.6 x 10. ... 

Free-charge carriers in semiconductors form collective excitation modes, the so-called plasma mode (plasmon). The plasma modes will couple to the LO lattice modes and form the so-called coupled LO plasmon-phonon (LPP) modes. Depending on the strength of the coupling, the free carriers thereby influence the dielectric function. A possible contribution from free carriers to the dielectric functions is also accounted for by virtue of the classical Drude model [38] ... 

In particular, the phonon dispersion relations and polarization vectors can be calculated with reasonable accuracy using force-constant models [59] or the embedded atom method [60-62], In recent calculations of Fe-ph and X for surface states, wave functions obtained from the one-electron model potential [63, 64] have been used. For the description of the deformation potential, the screened electron-ion potential as determined by the static dielectric function and the bare pseudopotential is used, Vq z) = f dz e (z,2/ gy)qy), where (jy is the modulus of the phonon momentum wave vector parallel to the surface, and bare Fourier transform parallel to the surface of the bare electron-ion... 

In its basic expression, the Drude model does not predict that the absorption bandwidth is affected by particle size. Experimentally, colloidal systems having a weak cluster-matrix interaction show a well-established inverse correlation with respect to the plasmon bandwidth with particle size. In order to describe the bandwidth dependency on particle size. Hovel et al. [47] proposed a classical view of free-electron metals here, the scattering of electrons with other electrons, phonons, lattice defects and impurities leads to a damping of the Mie resonance. Briefly, in realistic metals, the dielectric function is composed of contributions from both interband transitions and the free-electron portion [48]. The free-electron dielectric function can be modified by the Dmde model to account for this dependency, giving [47-50]... 

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