Holtsmark electric field distributions and associated broadening effects due to charged defects in crystals

Abstract

Low concentrations of charged defects in crystals generate random electric fields characterized by Holtsmark distributions. In descriptions of the electric field broadening and splitting of ionic energy levels in various crystal symmetries, three distributions are frequently applicable: that for the magnitude of the local electric field, that for the planar component of the electric field perpendicular to a high-symmetry axis, and that for the component parallel to a high-symmetry axis. Expressions are derived for these distributions by generalizing earlier results for isotropic media, and series expansions and polynomial approximations are given to facilitate their use. A range of examples are described to illustrate electric field splitting of electronic levels and effects on low temperature properties.