LO Mode Frequencies Research Articles

Far infrared spectra of Si doped PbTe single crystals

The far-infrared spectroscopy was used to analyze optical properties of PbTe single crystals doped with different amounts of Si. A dielectric function that takes into account the plasmon-phonon interaction was employed in the measured data manipulation. Two frequencies of plasmon-phonon coupled modes were obtained with the best-fit method, whereas the values for LO mode and plasma frequency (ωP) were calculated. The best-fit to the experimentally obtained spectra agrees very well with the theoretical prediction.

Terahertz time-domain spectroscopy of Raman inactive phonon-polariton in strontium titanate

ABSTRACTThe Raman inactive low-frequency phonon-polariton was studied in a quantum paraelectric strontium titanate crystal. The lowest frequency IR active T1u mode was investigated by the reflectance and transmittance Terahertz Time-Domain Spectroscopy using the pulse coherent THz radiation from 0.2 to 5.0 THz. The complex dispersion relations were determined using the real and imaginary parts of a polariton wavevector calculated from the complex refractive index which reflects the T1u symmetry phonon-polariton. The remarkable change of the dispersion relation was observed in the vicinity of TO and LO mode frequencies for both real and imaginary parts of a polariton wave vector. The observed complex dispersion relation of T1u symmetry is in agreement within the experimental uncertainty with the dispersion curves fitted by the damped harmonic oscillator model.

Broadband Terahertz Time-Domain Spectroscopy of Complex Phonon-Polariton Dispersion Relation

The low-frequency phonon-polariton of a ferroelectric congruent lithium niobate crystal was studied. The lowest frequency IR active A1(z) and E(x) modes were measured by the broadband polarized Terahertz Time-Domain Spectroscopy (THz-TDS) using the pulse coherent THz radiation from 0.2 to 4.5 THz. The complex dispersion relations were determined using the real and imaginary parts of a polariton wavevector calculated from the complex extraordinary and ordinary refractive indices for the A1(z) and E(x) symmetry phonon-polaritons, respectively. The remarkable change of the dispersion relation was observed in the vicinity of TO and LO mode frequencies for both real and imaginary parts of a polariton wave vector. The observed complex dispersion relations of two symmetries are in agreement within the experimental uncertainty with the dispersion curves fitted by the damped harmonic oscillator model.

Nanostructured CdSe Films in Low Size-Quantization Regime: Temperature Dependence of the Band Gap Energy and Sub-Band Gap Absorption Tails

Temperature dependence of the band gap energy and sub-band gap absorption tails in 3D assemblies of close packed weakly quantized CdSe quantum dots deposited as thin films was studied. The range from cryogenic temperatures (∼10 K) up to 340 K was covered. Excitonic absorption peaks were not observed even at temperatures as low as 11 K, which was attributed to the finite particle size distribution and interdot electronic coupling effects. The temperature coefficient of the band gap energy of the nanostructured films of 9.4 × 10–4 eV K–1 is higher by a factor of 1.35 than the corresponding value for the bulk CdSe specimen. As compared to the case of films constituted of strongly quantized ZnSe QDs, where the factor αnanocrystal/αbulk was found to be 1.82 (Pejova, B.; Abay, B.; Bineva, I. J. Phys. Chem. C 2011, 115, 37), the present findings imply that this ratio increases upon enhancement of size quantization effects in semiconductor nanocrystals. Analysis of the temperature-dependent optical absorption data within the Bose-Einstein model implies that no phonon confinement effects influence the phonon spectrum in the presently studied material due to the very small size-quantization effects. This situation is opposite to what we have recently found in the case of 3D arrays of strongly quantized ZnSe films. The characteristic Einstein temperature of the presently studied material corresponds to phonon frequency of about 220 cm–1, in excellent agreement with the LO mode frequency of bulk CdSe (210–214 cm–1). It is demonstrated that the Urbach rule is valid in the presently studied nanostructured material in low size-quantization regime. Urbach energies are several times higher than the values characteristic for macrocrystalline materials, due to the relatively high degree of inherent structural disorder in the studied QD solids. At the same time, however, these values are approximately three times smaller than those reported for strongly quantized ZnSe films in our previous study. The dynamical (temperature-dependent) term accounts for only about 22% of the overall Urbach energy values, though this value is higher than the corresponding ratio in the case of strongly quantized ZnSe films.

Identification of longitudinal optical modes by hyper-Raman scattering in noncentrosymmetric ceramics

Hyper-Raman scattering has been applied to ceramic samples of noncentrosymmetric lead zirconate titanate (PZT5H). The intense second-harmonic signal was blocked by using a holographic notch filter. Based on comparison with conventional Raman spectra taken under the same conditions, LO mode frequencies could be derived directly from the hyper-Raman spectra. The assignment of LO mode frequencies based on hyper-Raman spectra provides the possibility to measure LO-TO splitting in noncentrosymmetric ceramics, for which conventional Raman measurements alone provide only limited information.

Infrared ellipsometric study of SiO 2 films: relationship between LO mode frequency and porosity

A method for evaluating the pore volume fraction of silica films for different pore connectivities is presented. A series of SiO 2 films, evaporated by electron gun with or without ion bombardment, have been studied using visible and infrared ellipsometry. The TO and LO mode frequencies are deduced from the dielectric function calculated from infrared ellipsometric data. The study of both TO and LO mode frequencies is shown to bring independent information on the film microstructure. The TO mode frequency (near 1075 cm −1) varies mainly with the density of the silica matrix. On the other hand, variation in the LO mode frequency (near 1245 cm −1) is mainly due to changes in porosity. In the case of films with pores largely connected, the evaluation of the pore volume fraction from the LO frequency is compared to that obtained from the analysis of the large water absorption band near 3300 cm −1 (H–OH and Si–OH stretching absorption band).

Localized optical phonons in GaAs/AlAs superlattices grown on (311)A and (311)B surfaces

A study is reported of optical vibrational modes in [311]-grown GaAs/AlAs superlattices. An analysis of the TO and LO localized modes observed in IR reflectance spectra showed that the difference between the TO and LO mode frequencies in superlattices grown on (311)A and (311)B surfaces is due to the different localization lengths of these modes. The dispersion of transverse optical phonons in GaAs derived from IR reflectance spectra is in a good agreement with Raman scattering data.

Dielectric susceptibility model for optical phonons in superlattices

The form of the long-wavelength optic-phonon modes in semiconductor superlattices is described using a dielectric susceptibility model. This model only requires knowledge of the frequencies and eigenvalues for LO and TO modes propagating along the superlattice growth direction $z.$ From these, the principal-axis dielectric susceptibilities ${\ensuremath{\varepsilon}}_{\mathrm{zz}}(\ensuremath{\omega})$ and ${\ensuremath{\varepsilon}}_{\mathrm{xx}}(\ensuremath{\omega})$ can be obtained, and so a full description of the optic phonons is possible for any phonon propagation direction. Calculations of confined LO and TO mode frequencies and displacements are made for GaAs/AlAs superlattices. The susceptibilities and mode displacements are compared using a simple continuum model and a microscopic linear-chain model. The susceptibilities are also used to model nonresonant Raman-scattering spectra, and are shown to give results that are in close agreement with published micro-Raman measurements.

Dependence of TO and LO mode frequency of thermally grown silicon dioxide films on annealing temperature

We have investigated the structural properties of oxide films using infrared spectroscopy. The TO mode frequencies depend on the annealing temperature but the LO mode frequencies are constant in the bulk region. It is considered that the TO mode frequencies represent the oxide density. In a densified vitreous silica, both the TO and LO mode frequencies decrease. In our experiment, only the TO mode frequency in the oxide bulk region depended on the annealing temperature. Since this result cannot be explained only by the oxide density, we affirm that to inspect the structural properties of oxide, not only the oxide density but also the LO mode frequencies must be taken into consideration.

Resonant Raman Scattering near E1 + Δ1 in CdxHg1−xSe

AbstractRaman scattering by phonons is measured in CdxHg1−xSe with x = 0 to 0.3 on (100), (110) and (111) surfaces near the E1 + Δ1 energy gap at room temperature. From these measurements, the composition dependence of the HgSe‐like TO and LO mode frequencies is obtained. The plasmon‐LO phonon coupled modes and a cluster mode are also observed. Effective high‐frequency dielectric constants calculated by the extended Lyddane‐Sachs‐Teller relation show a discontinuity near the semimetal‐semiconductor transition point. This discontinuity is attributed to the contribution of interband terms to the dielectric function. The results obtained from the Raman measurements are compared with those from far‐infrared measurements.

Internal-stress effects on Raman spectra of InxGa

Raman spectra of ${\mathrm{In}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As are observed over a wide range of composition. A GaAs-like mode frequency \ensuremath{\omega} is found to vary with the composition x as \ensuremath{\omega}=-32.4${x}^{2}$-18.6x+290.0 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The internal stresses due to lattice mismatch are evaluated from the deviation of the GaAs-like LO mode frequency from the above experimental equation for small lattice mismatch. An increase is found in the internal stress toward the interface from the 5000-A\r{}-thick surface layer. The stress effects on the lattice vibrations of the optical mode are discussed from a microscopic point of view.

An investigation of high temperature phonon anharmonicity of KCl by the FT-IR emission technique

P-polarized far-infrared emission spectra from KCl polycrystalline films were observed around the reststrahlen band at temperatures from 40° C up to 530° C. Based upon the virtual mode theory of thin films these were analyzed using a dielectric response function in which an empirical phonon self-energy is considered. From this analysis the empirical forms for the self-energy around the reststrahlen band were obtained at various temperatures, and also the renormalized quasiharmonic TO and LO mode frequencies and dampings were estimated at appropriate temperatures.

Infrared reflection spectra of KClO 4 single crystals

The polarized IR reflection spectra of potassium perchlorate single crystals were recorded and analysed for the frequencies of the transversal and longitudinal optical zone centre modes using classical oscillator-fit method and Kramers—Kronig analysis. For comparing the TO and LO mode frequencies obtained with the corresponding Raman data, frequencies (ω 0) unaffected by the long range electrostatic fields were calculated. These frequencies are similar to those obtained from conventional IR absorption spectra of Nujol mulls or KBr discs. From the TO/LO splittings of both the internal and external vibrations Scott and Szigeti dynamical effective ionic charges were determined and discussed in terms of ionicity and bond polarity.

The far-infrared investigation of the mode frequencies of some alkaline earth sulphides

The scarcity of spectroscopic information of the sulphides of Mg, Ca, Sr and Ba, prompted this experimental investigation for their LO and TO mode frequencies. The LO mode investigation followed a method suggested by Berreman. (1) In the present work thin films (≌μm thick) of these compounds were deposited on Si substrates under vacuum (10 −6torr). Sufficient data were obtained to facilitate a comparison of the experimental and calculated values. The results suggest that the compounds have negligible thermal expansions in the 77–295 K range and relatively high zone boundary acoustic mode frequencies.

Far infrared studies on the superionic coductor Ag 2HgI 4

Far infrared reflection and transmission properties of polycrystalline samples of Ag 2HgI 4 were measured in the region 10–200 cm − as a function of temperature between 4 K and 340 K. From a Kramers-Kronig analysis of reflectivity, TO and LO mode frequencies were found for both β and α phases. In the α phase, two have been observed in the conductivity spectrum; the band at 30 cm −1 may be associated with the attempt frequency of Ag + ions and the band around 100 cm −1 to the AgI stretching mode. In the β phase, four bending modes dominate the low frequency spectrum (25–45 cm −1) and AgI and HgI stretching modes appear between 80–120 cm −1.

Frequency‐Dependent Conductivity Studies of the Ordered and Disordered Phases of Ag2HgI4 and Cu2HgI4

AbstractFar infrared reflection and transmission properties of Cu2HgI4 are measured in the region 10 to 200 cm−1 for both, α‐ and β‐phases. The TO and LO mode frequencies are obtained from a Kramers‐Kronig analysis of the reflection spectra. Frequency‐dependent conductivity is calculated from the values of ε″ in the region 10 to 200 cm−1 for both phases. The conductivity spectra of α‐Ag2HgI4 and α‐Cu2HgI4 are analysed using the Kostadinov and Vu Thi Binh model. It is concluded that the mobile ions (Ag+ and Cu+) have two different sites ofo ccupation during their conduction process. It is suggested that other than regular tetrahedral sites, the mobile ions may occupy interstitial sites, in good agreement with the observations of Kasper and Browall and the Wiedersich and Geller model for the conduction process in these materials.

A simple method for estimating peak electron velocities in polar semiconductors

The growing interest in microwave field effect transistors points to the need for assessing rapidly the high-frequency potentiality of binary compounds and mixed crystals. Though the two relevant parameters, the breakdown field and the electron mobility, are difficult to calculate from first principles, their product is related only to the effective mass and the LO mode frequency, and this product gives a good measure of the peak electron velocity. Velocities are calculated for a number of materials, and comparisons made with experiment.

Dispersive reflection spectroscopy in the far-infrared

Techniques are described for making dispersive reflection measurements on solids between about 5 and 500cm −1 and at temperatures above 77 K using Fourier spectrometers equipped with dielectric or wire grid beam dividers and used in the asymmetric mode. Interferograms can be recorded with a positional accuracy of ±0.1 μm which is independent of the specimen temperature and the performance of the instruments is illustrated with amplitude reflection measurements on crystals of NaCl and CsI at room temperature. The ensuing dielectric response functions are also given and the TO and LO mode frequencies taken from these are in good agreement with published data. In the case of NaCl the self-energy and damping functions are also computed from the data and the results are in reasonable agreement with theoretical calculations by Hisano et al.

LO mode frequencies in III-V compounds

It is shown that, in all III-V compounds measured to date, a simple relationship connects the LO mode frequency with the atomic masses and separations, without any correction being made for the ionic contribution to the binding. Some justification is given for this surprising result.

Reststrahlen spectra of CdxSr1− xO

Measurements of the reflection spectra of polycrystalline Cd x Sr 1− x O alloys (0 ⩽ x ⩽ 0.9) at 85 and 300 K in the spectral range of lattice vibrations (200–600 cm −1) are reported. By Kramers-Kronig analysis the optical constants and the LO-mode frequencies were evaluated. The samples showed essentially one-mode behaviour with marked fine structure of the low-temperature absorption for intermediate values of x. Up to now, applying the cluster model of Verleur and Barker has not yielded a tentative explanation.