Vibrational Structures Accompanying the Optic Transitions of Bound Electrons in Crystals

Abstract

A description of the phonon processes involved in the optic transitions of a bound electron in crystals is presented, with the specific properties of the electron-phonon interactions considered in detail. The set of forces that the "hole-electron pair" exerts on the surrounding lattice are used as coupling constants, and the projected density of states for the perturbed phonon field is fully explained. The orbit radii for the optic electron are assumed to be of the order of, or smaller than, the lattice parameter, and both dipole-allowed and electric-dipole phonon-forced transitions are considered. Short- and long-range forces are examined. The connection between short-range forces and the stress coefficients of the absorption (emission) band is found. The symmetry properties of the electron wave functions are further taken into account in the analysis of electrostatic types of interactions. It is shown that the electric dipole forces activate essentially the normal modes of the perfect lattice, while the short-range forces activate more easily the possible local and pseudolocal modes. An explanation is also suggested for the intraconfiguration transition of rare-earth ions not activating the pseudolocal modes. The Huang-Rhys parameter is split into local (pseudolocal) and continuum-mode terms. It is shown that the continuum-mode term prescribes how the total intensity of the band is shared among multiple-phonon lines (if present) and broad background absorption. The configuration-diagram description of the many-phonon process is subsequently considered, including the exciton absorption. An interpretation is presented of the Stokes shift between absorption and emission bands: The whole Stokes shift is split into a purely Stokes term and a stored-energy term, the latter being related to the infrared component P(r) of the polarization field. This purely Stokes term, as well as the phonon contribution to the peak position, is evaluated for the $F$ band, within the linear and quadratic approximations for the electron-phonon interaction. Finally, a qualitative explanation is suggested for the Urbach rule in Perovskite-type crystals.