Local-field effects and phonon screening in polar semiconductors

We study here the redistribution of the electronic charge associated to zone-center phonon modes in polar semiconductors, within the linear-response microscopic theory of lattice dynamics. In a polar material zone-center phonons are only well defined in the longwavelength limit. Both transverse and longitudinal phonons correspond, in the ${\overrightarrow{\mathrm{q}}}_0\to 0$ limit, to the same ionic displacements in the unit cell; owing to the presence of long-range forces, they induce a different microscopic polarization. For a TO phonon the electronic response is exactly the same as induced by a frozen-in distortion having the lattice periodicity (${\overrightarrow{\mathrm{q}}}_0=0\mathrm{}$). We develop in detail the formalism needed to describe the screening difference between LO and TO phonons, which is basically due to nonanalytic terms in the dielectric matrix. We show that this longitudinal-transverse difference is closely related to other basic local-field effects, which have recently been studied. Detailed calculations are presented for ZnSe; in order to illustrate the trends with increasing ionicity the results for Ge, which is nonpolar and isoelectronic to ZnSe, are also shown. Both calculations are based on first-principles dielectric matrices recently published. We show that the effects of the local fields are very important and essential to account for the basic trends with increasing ionicity. The same feature has recently been proved for the calculated zone-center phonon frequencies.