Phonon dispersion in GaAs

The dispersion of eigenvectors shown in Fig. 7.3.1 is similar to that found in Ge (Fig. 5.7.1) - the effect of the lowered crystal symmetry is apparent, namely in making the amplitudes of displacements generally unpredictable from symmetry alone. The end-points of the eigenvector dispersion are in excellent agreement with values calculated by the frozen phonon method (or, whenever possible, predicted by symmetry). Note that in Ge the L0(X) and LA(X) modes are degenerate, so that different combinations of those displayed in Fig. 5.7.1 are equivalent the two corresponding to a 

So far we have been dealing with various forms of the response to displacements of atoms. In Section 6 also certain electric fields have been studied, we benefited from the fact that displacing atoms in GaAs generates dipoles and therefore electric fields all the reasonings of Section 6 were, however, limited to polar crystals and e.g. determination of static dielectric constant e as in Section 6.2 would be impossible in Ge or other homopolar substances. From the point of view of studying dielectric properties, the main drawback of Section 6 was our dependence upon the various displacement patterns the electric fields could not be varied at will, as an independent variable. The present Section summarizes the most recent applications of the DF which tend to fill this blank and to open the way to direct treatment of dielectric properties of semiconductors, within the framework of the Density Functional. They are the treatment of constant macroscopic electric field imposed from outside (Section 8.1) and direct evaluation. of the individual elements of the inverse dielectric matrix s ( q + + g ) (Section 8.2). 

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