Critical-point Phonon Frequencies Research Articles

Critical-point phonon frequencies of diamond.

The phonon-dispersion curves derived from neutron-scattering experiments performed on diamond [J. Warren et al., Phys. Rev. 158, 805 (1967)] are not accurate enough to yield the exact frequencies of critical-point (CP) phonons and, thus, to provide a satisfactory interpretation of second-order optical spectra. A self-consistent analysis of such spectra [S. Solin and A. Ramdas, Phys. Rev. B 1, 1687 (1970)] was not fully successful because of ambiguities that arise in assigning second-order infrared absorptions and features in the Raman spectra to specific two-phonon summations. A more effective method for obtaining accurate CP phonon frequencies involves investigating defect-activated one-phonon absorptions; in this paper, we take advantage of the availability of chemically vapor-deposited (CVD) diamond for the purpose of locating and assigning infrared (ir) absorption features in the one-phonon region to CP phonons at the Brillouin-zone boundary. Fourier-transform ir absorbance spectra of CVD diamond exhibit a complex structure at wave numbers below the 1332.5-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ lattice-mode cutoff, which is induced by impurity-associated defect centers and yields the exact positions of 16 zone-edge CP phonons. In conjunction with the triply degenerate zone-center mode, this set of phonons then provides the basis for predicting the positions of second-order optical features through simple summations. When the selection rules are taken into account, the procedure yields excellent results, not only in terms of CVD-diamond ir spectra, but also in regard to earlier measurements of the intrinsic two-phonon absorption coefficient of type-IIa natural diamond [J. Hardy and S. Smith, Philos. Mag. 6, 1163 (1961)] and the second-order polarization-dependent Raman spectra recorded by Solin and Ramdas.

Pressure dependence of zone-boundary phonons in AlSb

Abstract We have investigated the effect of hydrostatic pressure on zone-boundary and other critical-point phonon frequencies of AlSb by second-order Raman scattering. A softening of the TA(X), TA(L) and (L/T)A([Sgrave]) modes has been observed for pressures up to the first phase transition at 7.7 GPa. The LA(L) as well as the optical TO at X-, L-, and LO at [Sgrave]-, X-points harden with increasing pressure. Mode Griineisen parameters of all the resolved modes were calculated. Reflectivity measurements indicate that the high pressure phase above 7.7 GPa is metallic.

A critical point analysis of two phonon structure in the far infrared dielectric response of GaAs

The technique of asymmetric Fourier transform spectroscopy has been used to determine the complex relative permittivities of undoped GaAs at frequencies near the transverse optic mode. It is demonstrated that the anharmonic damping function calculated from these results is sensitive to two phonon processes excited by the anharmonic decay of the q≃O transverse optic phonon. Critical-point phonon frequencies are assigned from the structure revealed in damping function.

Lattice dynamics of sodium and rubidium halides

The lattice-dynamical properties of NaBr, NaI, RbCl, RbBr and RbI have been investigated by utilizing a 7-parameter bond-bending force model (BBFM) recently proposed for NaCl structure. The model basically incorporates i) noncentral nearest-neighbour and central next-nearest-neighbour interactions, ii) bond-bending forces due to the deformations in the interbond angles and iii) long-range Coulombic interactions. The seven disposable parameters employed in the present treatment were determined by making use of the experimental values of three elastic constants, four critical-point phonon frequencies and the lattice equilibrium condition. The model thus has been used to study the phonon dispersion relations, phonon density of states and temperature variation of the Debye characteristic temperatures of the afore-said compounds. Theoretical results have been compared with the available experimental data and reveal good agreement.

Lattice dynamics of alkali halides, (LiF and NaCl)

A new 7-parameter bond-bending force model (BBFM) has been proposed to investigate the lattice dynamics of I–VII compounds having NaCl structure. The total potential energy of the system incorporates three types of interactions: i) central ion-ion forces, ii) bond-bending forces and iii) long-range Coulombic interactions. The model parameters have been determined by making use of three elastic constants, four critical-point phonon frequencies and the lattice equilibrium condition. The application of the model has been made to calculate the phonon dispersion relations, phonon density of states and the temperature dependence of the Debye characteristic temperature of lithium fluoride (LiF) and sodium chloride (NaCl) Theoretical results have been compared with the available experimental data and the possible source of improvement is suggested. The overall agreement seems to be quite encouraging and gives confidence in this approach. The noteworthy features, mentioned in the last section, also lend support to the success of the model calculations.

Lattice dynamics of ZnTe, CdTe, GaP, and InP

An eight-parameter bond-bending force model (BBFM), recently developed by us for zinc-blende (ZB) structure, has been used to study the lattice dynamics of other compounds of the II–VI and III–V groups. The model parameters were calculated using six critical point phonon frequencies, two elastic constants, and the lattice equilibrium condition. Phonon dispersion curves, phonon density of states, and Debye-characteristic temperatures have been calculated. The comparison of theoretical and the available experimental results reveals a fairly good agreement. The merits and demerits of the present model have been discussed in full.

Lattice Dynamics of Potassium Halides (KCl, KBr and KI)

To investigate the lattice dynamics of potassium halides a newly proposed 7-parameter bond-bending force model (BBFM) is used. The total potential energy of the system incorporates the short-range forces (radial+-bond-bending) as well as the long range Coulombic interactions. The 7 parameters employed in the present treatment are determined by making use of the experimental values of three elastic constants, four critical point phonon frequencies and the lattice equilibrium condition. The model has been applied to calculate the phonon dispersion relations, phonon density of states and the Debye-characteristic termperatures (θ D ) of KCl, KBr, and KI. Theoretical results have been compared with the available experimental data. It is observed that the agreement between theory and experiment is very good and thus gives a confidence in this approach. The remarkable features pertaining to the physical significance of the model have been discussed.

Lattice dynamics of II–VI and III–V compounds

To study the lattice dynamics of II–VI and III–V compounds having zinc-blende structure in a model which incorporates three types of interactions: (i) central ion-ion forces (ii) bond-bending forces and (iii) long range Coulombic forces, has been developed. The model involves in total eight disposable parameters. The use of six critical point phonon frequencies, two elastic constants and the lattice equilibrium condition has been made to evaluate the consistent values of the parameters. The application of the present model has been made to calculate the phonon dispersion relations of ZnSe and InSb compounds. The comparison of theoretical results with the available experimental data has been made along the three symmetry directions [100], [110] and [111]. A reasonably good agreement is observed between theory and experiments.

Lattice Dynamics of ZnTe: Phonon Dispersion, Multiphonon Infrared Spectrum, Mode Grüneisen Parameters, and Thermal Expansion

A four-parameter rigid-ion model utilizing an effective ionic charge is used for the determination of phonon dispersion, phonon density of states, and the Debye characteristic temperature of ZnTe. Structures in the infrared spectrum of ZnTe are assigned to multiphonon combinations of various critical-point phonon frequencies. Using the long-wavelength optic-mode phonon frequencies as well as the elastic constants and their respective pressure derivatives as input data, the mode Gr\"uneisen parameters, the Gr\"uneisen constant, and the coefficient of thermal expansion of ZnTe are calculated.

Infrared Combination Mode Absorption in Lithium-Boron-Doped Silicon

Infrared absorption bands due to double-quantum transitions of local lattice-mode vibrations in boron-lithium-doped silicon have been observed. The transitions are found near twice the frequency of all local modes and at the sum frequency of the two strongest local-mode vibrations, which are those associated with boron-lithium pairs. The relative strengths of the pair modes, the displacement of the modes from the mode due to isolated substitutional boron, and the relative strengths of the overtone absorption bands are consistent with the assumption of a predominantly Coulomb interaction between the boron and lithium ions. Five additional absorption bands, with frequency depending upon boron isotope, are found at frequencies not corresponding to sums of local-mode frequencies. Four of these bands occur at sum frequencies of the two strongest local-mode frequencies and of silicon critical-point phonon frequencies. The dependence of the frequency of all absorption peaks on lithium and boron isotopes is used to assist in the assignment of the absorption bands.