Infrared Dielectric Tensor

Before discussing this new method it is useful to recall briefly the methods which we have already discussed. Note, first of all that calculations of the dielectric tensor must be based, as is known, upon a microscopic theory Such a theory for ionic crystals was first developed by Born and Ewald (2) for the infrared spectral region. The application of this approach for the region of exciton resonances has also been demonstrated in (3). In an approach identical to that of Born and Ewald (2) the mechanical excitons (see Section 2.2) are taken as states of zeroth-approximation. In the calculation of these states the Coulomb interaction between charges has to be taken into consideration without the contribution of the long-range macroscopic part of the longitudinal electric field. If this procedure can be carried out, then the Maxwell total macroscopic fields E and H can be taken as perturbations. In the first order of perturbation theory, we find... 

In noncubic sohds, the phonon mode frequencies of the polar lattice vibrations depend, in general, on the phonon mode propagation direction. Likewise, directionally dependent free-chargescattering rates and the anisotropic inverse effective freecarrier mass tensor will produce nonscalar free-charge-carrier contributions. The infrared dielectric function is then represented by a complex-valued second-rank tensor s, which can be expressed in Cartesian coordinates (x,y,z) as ... 

The dielectric parameters are tensors, and consequently it is essential to use polarized radiation when recording the infrared absorption and reflection spectra of all but cubic crystals. Thus, with an orthorhombic crystal the reflection has to be measured with the electric vector parallel to the a, Z , and c axes. When obtaining the reflection spectra from the be plane of a monoclinic crystal, it is necessary to rotate the plane of polarization of the electric vector. The longitudinal optic (LO) frequency [see discussion of Equation (4)] can be found for q = 0 by noting that it is the frequency for which = 0. It can be measured directly in cubic crystals by a method due to Berriman [114]. 

Maradudin and coworkers [18] have demonstrated that the macroscopic low-frequency static dielectric permittivity tensor y(w) which gives the infrared spectra main contribution, is a sum of both an ionic part and a limit value of a pure electronic contribution. According to Gonze and Lee [6], one has... 

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