Local Mode Frequencies Research Articles

Local-Mode Frequency Due to Light Substitutional Impurities in Alkali-Halide Crystals: Application to theUCenter

The lattice dynamics in harmonic approximation of ionic crystals with very light substitutional impurities is studied in the framework of rigid-ion and shell models. A vibrational model for the lattice defect which takes into account not only the change of mass, but also the changes of the overlap force constant, electronic polarizability and shell charge, is considered and applied for the evaluation of the local-mode frequencies of the $U$ center in NaCl, Kcl, and KI crystals. It is shown that changes of electronic polarizability and shell charge give rise to a further local change of force constant for the core motion in the shell model. A simple local change of mass is found to be quite inadequate for accounting for the influence of the $U$ center on the lattice dynamics. Instead, fairly good agreement with the experimental results on the impurity-induced infrared absorption is found if the hydrogen ion in alkali halides is considered as belonging to the halogen family with regard to the overlap potential and electronic polarizability.

Vibrational absorption of carbon in silicon

Carbon doped monocrystalline silicon has been investigated by infra-red spectroscopy in the range 1–25 μ. Local mode frequencies of 607 cm −1, 586 cm −1 and 572 cm −1 were found at room temperature for 12C, 13C, and 14C respectively. Second harmonics of the 12C and 1C frequencies were observed at 64°K. An absorption coefficient of 1 cm −1 for the carbon local mode corresponds to a carbon concentration of 1·1 × 10 17 at./ cm 3 the maximum observed carbon content was 1·2 × 10 18 at./ cm 3. In crystals containing both carbon and oxygen a band was found at 1104 cm −1 at 77°K and is tentatively assigned to a vibration of a carbon-oxygen pair. From the results it is concluded that carbon occupies substitutional sites in silicon.

Infrared Lattice Absorption of Ionic Crystals Containing Finite Impurity Concentrations

A theoretical calculation of the effect of isotopic defects on the infrared lattice absorption of ionic crystals is presented. The main concern has been to establish the relative strength of the absorption by local vibrations in such a system as compared with that of the nonlocal modes. It has been found that, when a local mode exists, it may display a vastly enhanced absorption cross section as compared with that of a charged defect in a nonpolar host. This effect arises from the fact that the uniform external field interacts directly with the zero-wave-vector components of the normal modes of the imperfect crystal. This interaction induces transitions into states which are not true eigenstates of the lattice Hamiltonian, and in which there is an effective coupling between band and local modes that results in the scattering and absorption of band-mode phonons by the local vibrations. It has been shown that if the local-mode absorption frequency is close to that of the pure crystal, a small concentration of impurity is sufficient to shift the main absorption to the local-mode frequency, as has been observed in the case of Li(H,D) mixtures containing 5% ${\mathrm{D}}^{\ensuremath{-}}$ impurity. Furthermore, application of the theory to calculating the temperature dependence of the total vibrational absorption by the local modes of $U$ centers (${\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{D}}^{\ensuremath{-}}$ ions substituted into an alkali halide) has shown that, even for single defects which produce highly localized vibrations, it is incorrect to regard the local-mode and host-lattice absorptions as independent.

Effect of Boundary Surfaces on Localized Mode Frequencies of a Crystal Containing a Mass Defect

Effect of Boundary Surfaces on Localized Mode Frequencies of a Crystal Containing a Mass Defect

H− ionic radius in alkali halide crystals from the local mode frequency of U-centres

H− ionic radius in alkali halide crystals from the local mode frequency of U-centres

Localized vibrational modes near substitutional impurities in alkali halide crystals: the U-center

Abstract The localized vibrational modes due to a substitutional, monovalent negative impurity, in an alkali halide crystal, are investigated on the basis of L ifschitz ' s theory,(1) using both point-ion(2) and polarizable-ion(3) models for the lattice dynamics. Assuming that only negative ions are polarizable, the secular equation for the frequencies of localized modes is studied taking into account the change of atomic mass, of nearest neighbor closed repulsion, of ionic polarizability and of effective electronic charge in the outer shell. The influence of these variables on the position of the frequencies of localized modes, and in particular the opportunity of using either a polarizable-ion or a point-ion model, is discussed for the case in which the localized frequency lies very near to, or very far from, the maximum frequency of the vibrational spectrum. Numerical computations using the USCC 90 Remington computer are planned for the U-center (H− substituting a halogen ion) in NaCl and KCl crystals.

Vibration of Linear Lattice Containing Impurities

By using the scattering matrix, the effects of impurities on the vibration of linear lattice are studied. It can be shown that this treatment is equivalent to that using transfer matrix. In the present treatment, however, some simple formulas are obtained for the frequencies of localized modes.