LO Mode Frequencies Research Articles

Surface Plasmons and the Reflectivity ofn-Type InSb

The reflectivity of $n$-type InSb has been measured in the far infrared. The doping of the samples was such that the free-carrier plasma frequency was near the LO mode frequency. The results suggest that samples with a sufficiently thick damage layer show effects due to surface plasmons. Use of a simple model indicates that the surface-plasma excitations are coupled to the phonons.

Lattice Dynamics, Mode Grüneisen Parameters, and Coefficient of Thermal Expansion of CsCl, CsBr, and CsI

The phonon dispersion curves for CsCl, CsBr, and CsI have been obtained using a rigid-ion model with an appropriate effective ionic charge. The five model parameters for each crystal are obtained from three elastic constants and the two long-wavelength optic-mode frequencies, reliable data for which exist for all three crystals. Our results are in agreement with those of more elaborate models. The phonon density of states and the Debye characteristic temperatures are also calculated. A Born-Mayer-type potential is used to calculate long-wavelength LO and TO mode frequencies as functions of pressure from pressure dependence of bulk modulus. The result for TO of CsBr agrees well with a recent experimental determination. Next, using the values of the elastic constants and LO and TO frequencies at various pressures, $\ensuremath{\omega}\ensuremath{-}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{s}\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ curves in selected directions are generated as functions of pressure. Mode Gr\uneisen parameters are then calculated as functions of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$. Finally, the Gr\uneisen constant and the volume coefficient of thermal expansion are obtained as functions of temperature. They agree very well with available experimental data.

Effect of Particle Size and Shape on the Infrared Absorption Spectra of Barium Titanate and Strontium Titanate Powders

Effects of particle size and particle shape have been studied in the infrared absorption spectra of BaTiO3 and SrTiO3 powders to determine whether previously developed methods to treat such effects are applicable to crystals having high dielectric constant and ``soft'' lattice modes. The spectrum of both materials exhibits three absorption bands (BaTiO3: 545, 400, and 180 cm−1; SrTiO3: 605, 400, and 175 cm−1) that are considerably removed from the TO-mode frequencies computed from bulk single-crystal reflection data (BaTiO3: 510, 183, and 33.8 cm−1; SrTiO3: 546, 178, and 87.5 cm−1). These frequencies were successfully correlated with the bulk-crystal frequencies by use of classical electromagnetic scattering theory and an extension of Fröhlich's method. The low-frequency ``soft'' modes of both crystals were found to have an unusually large dependence on particle shape with the consequence that the powders absorb radiation at the corresponding LO-mode frequency.

Longitudinal-Optical-Phonon-Plasmon Coupling in GaAs

Infrared reflectivity measurements have been made at 78\ifmmode^\circ\else\textdegree\fi{}K on three samples of GaAs, doped with Te so that the plasma frequency is nearly equal to the long-wavelength LO phonon frequency. There are two prominent dips in the reflectivity spectra, but instead of occurring near the plasma frequency and LO mode frequency, they occur at the frequencies of the two normal modes of the coupled plasmon-LO-phonon system, as predicted by Varga and by Singwi and Tosi. From the reflectivity spectra at 78\ifmmode^\circ\else\textdegree\fi{}K, values of the electron effective mass of 0.067, 0.073, and $0.077{m}_{e}$ are obtained for $n$-type GaAs with 7.22\ifmmode\times\else\texttimes\fi{}${10}^{17}$, 8.75\ifmmode\times\else\texttimes\fi{}${10}^{17}$, and 14.0\ifmmode\times\else\texttimes\fi{}${10}^{17}$ carriers per ${\mathrm{cm}}^{3}$.