Polarization of a semi-infinite crystal by a point defect at the surface

We consider the asymptotics of a long-range polarization in the crystal bulk and at the surface far from a point defect. Because the dielectric tensor of the crystal bulk cannot be used for ionic layers which are close to the surface, a method for calculation of ionic displacements and induced electronic dipole moments in a general case of arbitrary crystal structure has been developed. It is based only on the knowledge of the dynamical matrix of the three-dimensional crystal. The effect of the Coulomb interaction is treated by taking into account ionic vibrations and using the complete set of Maxwell's equations. Detailed expressions have been worked out for a particular case of a semiempirical model of polarizable ions interacting by means of pair interionic potentials. {} 1996 The American Physical Society.