Optical Spectra Of Impurities Research Articles

Phonons and Resonances in Solids

B DiBartolo and R C Powell Chichester: J Wiley 1976 pp xvi + 515 price £15.45 The main theme of this book is the application of the methods of group theory to the properties of crystal lattice vibrations. This is used in conjunction with standard quantum mechanics in the treatment of such topics as the optical spectra of impurities in solids, the scattering of neutrons and x-rays by crystals, and the infrared and Raman scattering by phonons.

Sharp Optical Spectra of Impurities in Metals

Sharp Optical Spectra of Impurities in Metals

Effects of Dynamic Perturbations on Optical Spectra of Impurities in Insulators

Detailed expressions, derived from a phenomenological Hamiltonian, are given for optical spectra of experimental and theoretical interest for a two-level impurity complex in interaction with the quantized phonon field of lattice vibrations. These results can readily be extended to treat other quantized impurity-perturbing fields which, like the electromagnetic and lattice-vibration fields, have classical analogs (Bose-Einstein statistics). The formulas indicate how different properties of the spectral line are interrelated through the system Hamiltonian and how parameters of that Hamiltonian relate to measurable effects induced by external static stresses. The relationship of the semiclassical Franck-Condon approach (valid for strong phonon-impurity interactions) to the purely quantum treatment (necessary for an accurate analysis of weak perturbations and "motional narrowing") is discussed in detail. It is shown how the results relate to various models proposed to describe Urbach's rule and in particular how the Toyozawa-Mahr model follows from the semiclassical spectral formulas. With only minor midifications, the mathematical expressions can also be used to interpret spin-resonance spectra.

Theory of Vibrational Structure in Optical Spectra of Impurities in Solids. II. Multiplets

The results of a previous paper describing vibrational structure in the spectra of singlet-to-singlet optical transitions of impurities in solids are extended to a general class of multiplet-to-multiplet transitions. The transitions considered are those between degenerate or nondegenerate multiplets which are not interconnected by the interaction coupling the impurities to the lattice phonons. The phonon field couples impurity states within each multiplet but does not couple states in different multiplets. The results apply to systems which display strong Jahn-Teller distortions as well as to those which do not. As a specific application of our results we consider the singlet-to-doublet transitions of simple three-level systems having C3 and C3v symmetry.

Theory of Vibrational Structure in Optical Spectra of Impurities in Solids. I. Singlets

General expressions are derived describing the modifications of the optical spectra of isolated impurities induced by the subclass of interactions with host-lattice phonons which shift the energy eigen-values of the internal impurity state but which do not mix those internal states. The results apply to localized phonon modes as well as to extended modes (whose individual coupling decreases with increasing lattice volume), to anharmonic- as well as harmonic-phonon systems, and to phonon-impurity couplings which need not be linear in the dynamic local strain field. They take the form of ``linked-cluster'' expansions which, in the linear-coupling harmonic-phonon case, terminate after the second term. The relation of these expansions to moment methods is indicated. As a simple application of the linked-cluster expansions, we compute the dependence of the sharp ``no-phonon'' spectral line on impurity mass. We conclude that the no-phonon line should not exhibit isotopic-mass displacements in those impurity sites for which the lattice is inversion symmetric.

Width of the Narrow "No-Phonon" Lines in the Optical Spectra of Impurities in Solids

Phonon-impurity interactions responsible for part of the width of the no-phonon components of the sharp-line optical spectra of impurities in crystal lattices can be interpreted physically in terms of the secular-perturbation model proposed for magnetic resonance by Bloembergen, Purcell, and Pound. The low-frequency secular excursions of the impurity energy levels produced by the lattice vibrations appear as a finite linewidth to an experimenter making line-shape measurements over macroscopic time intervals. The total linewidth will of course include additional contributions from the finite impurity-state lifetime implicit in interlevel transitions induced by photons and nonsecular phonons. The theory of the no-phonon components of impurity optical spectra is closely related to the theory of line narrowing in magnetic-resonance spectra.

Intermolecular forces from optical spectra of impurities in molecular crystals

A procedure is outlined by which one can get information about the effects of electronic excitation on the interactions between molecules. The absorption and emission spectra of impurities in molecular crystals, and specifically the mean positions and widths of the lines, are required as functions of temperature. A theory of M. Lax is used to relate mean position and width to intermolecular forces. The preliminary treatment of this problem by McCarty and Robinson is evaluated and extended: their procedure is expected to be valid for very narrow lines only.