Longitudinal Optical Phonon Frequency Research Articles

Anomalous first-order Raman scattering in III-V quantum dots: Optical deformation potential interaction

In contrast to the most commonly studied nanocrystals of II-VI materials, resonant Raman spectra of colloidal III-V quantum dots (QDs) show two almost equally intense peaks centered approximately at the longitudinal and transverse optical (TO) bulk phonon frequencies. The ``anomalous'' spectra of III-V QDs are explained in the framework of a microscopic theory for the first-order resonant Raman scattering, which takes into account the optical deformation potential (ODP) and Fr\ohlich exciton-phonon interactions---valid for spherical nanoparticles. It is obtained that: (i) the ``anomalous'' TO peak is mostly due to confined phonon modes with the angular momentum ${l}_{p}=3$; (ii) Raman intensity depends on the QD radius $(R)$ as ${R}^{\ensuremath{-}3}$ for the ODP mechanism, while for the Fr\ohlich one it is proportional to ${R}^{\ensuremath{-}1}$; and (iii) the relative intensity ${I}_{\text{TO}}/{I}_{\text{LO}}$ ratio value is higher in backscattering configuration for cross polarization than for parallel one. Raman spectra calculated within the Luttinger-Kohn Hamiltonian for the electronic states and a phenomenological theory of optical vibrations including rigorously both the mechanical and electrostatic matching boundary conditions explain the experimental data for InP QDs using bulk phonon parameters and ODP constant.

Pressure-induced metallization and resonant Raman scattering in Zn1−xMnxTe

Pressure-induced resonant Raman scattering is adopted to analyze the zone-center optical phonon modes and crystal characteristics of Zn1−xMnxTe (0≦x≦0.26) thin films. The pressure (Pt) at which the semiconducting undergoes a transition to the metallic phase declines as a function of Mn concentration (x) according to the formula Pt(x)=15.7−25.4x+19.0x2 (GPa). Pressure-dependent longitudinal and transverse optical phonon frequencies and the calculated mode Grüneisen parameters were adopted to investigate the influence of Mn2+ ions on the iconicity. The experimental results indicate that the manganese ions tend to increase the iconicity of ZnTe under ambient conditions, whereas an external hydrostatic pressure tends to reduce the iconicity and the bond length of Zn1−xMnxTe.

On the surface relaxation of transition metals

First principles band structure calculations are presented for the layer relaxation of the close-packed surfaces of 5d transition metals. Anomalously large relaxations are found for group IVA and VIIA hcp metals. For these elements, the size of the layer relaxation exhibits an unusually slow decay with the distance from the surface. We argue that this phenomenon can be attributed to the peculiar flat and degenerate d-bands located close to the Fermi level in the L-A-H top-plane of the hcp Brillouin zone, and which are also responsible for the anomalously low [001] longitudinal optical phonon frequencies observed in these hcp metals.

Infrared spectra of semiconducting silicides nanolayers

The infrared absorption is studied of samples consisting of a Si matrix with unburied nanolayers of the semiconducting silicides β-FeSi2 and Mg2Si. Features additional to those due to the transversal optical phonons of the compounds are observed. The features are interpreted in the framework of the appearance of surface and interface phonon polaritons, which absorb the light. Insofar as the frequencies of the longitudinal optical (LO) phonon-polariton modes are close to those of the LO phonon frequencies, the infrared transmittance of nanolayers can be regarded as a method for direct determination of these frequencies.

Reflectance studies of candidate THz emitters

Semiconductors are efficient emitters of terahertz (THz, 1012 Hz) radiation. Non-contact means of accurately measuring the physical parameters of these materials are of great value. The reflectance of polar crystals yields important information. A dramatic change in reflectance occurs in the frequency range between the transverse-optical (TO) and the longitudinal-optical (LO) phonons. For many materials these frequencies are of the order of a few THz. Analysis of the reflectance in and near this region yields (a) the TO phonon frequency ωT, (b) the LO phonon frequency ωL, (c) the low-frequency or DC reflectance R(0), and thence the DC refractive index, n(0), and dielectric constant, ɛ(0); (d) the high-frequency or optical reflectance R(∞), and thence n(∞) and ɛ(∞) and (e) the phonon damping factor Γ. These constants depend on the lattice itself and may be described within the Lorentz model. If, in addition, the crystal possesses free carriers, reflectance measurements further yield (f) the plasma frequency ωP, and thence the carrier concentration ne/h and (g) the plasma damping factor γ which may be understood in terms of the Drude model. Samples in the form of a parallel plate give rise to interference fringes that yield (h) the sample thickness t. We have examined many polar crystals with a view to understanding THz emission from them with the overall goal of improving the emission efficiency. Measurements have been made in the region 1.5–21 THz (50–700 cm−1) of single and multilayer samples. We use the sum rule to check the internal consistency of the experimental measurements. We have re-examined the relationship between the phonon frequencies and the reduced ion mass. We find the effective spring constant is very similar in all I–VII materials studied and likewise within the II–VI and III–V classes. We use shell theory to account for these results.

Effects of alloying and localized electronic states on the resonant Raman spectra of Zn1−xMgxO nanocrystals

Using resonant Raman spectroscopy, the authors report on the alloying effect and localization of electronic states in Zn1−xMgxO (x<0.15) nanostructures with average sizes in the range of 20–150nm. Anomalous intensity enhancement of the second-order longitudinal optical phonon has been observed, which is due to Fröhlich interaction via the localized exciton as the resonant intermediate electronic states. The alloying-induced disorder due to Mg incorporation led to the enhancement of exciton localization as well as the asymmetric broadening of longitudinal optical phonon line shape. The composition in ZnMgO could be determined by the first-order longitudinal optical phonon frequency via a bowinglike quadratic fit. This simple relationship is in perfect match to the modified random-element-isodisplacement model and provides a nondestructive approach to probe the quantitative composition distributions in wurtzite ZnMgO alloy system.

Magnetized Plasma in Polar Semiconductors

Plasma excitations in solids have been intensively studied already at the time of the 1960’s. A significant interest was focused on doped polar semiconductors. In these systems, the nowadays text-book effect of coupling between plasmons and optical phonon modes can be clearly observed as demonstrated, for example, by the pioneering work of Mooradian and Wright [1] on inelastic light scattering in n-type GaAs samples. The properties of a plasma subjected to a static magnetic field are significantly modified. A magnetic field B applied to a metallic system introduces a characteristic frequency, namely the cyclotron frequency ωc =eB/m of motion of the carriers (with an effective mass m) in the plane perpendicular to the field direction. In polar-semiconductor plasmas, by changing the magnetic field the cyclotron frequency ωc can be made comparable to all important frequencies of the system, namely the plasma frequency ωp and the frequencies of longitudinal (LO) and transverse (TO) optical phonons. The physics of coupled plasmon phonon modes under these particular and interesting conditions has never been fully explored in Raman scattering experiments in 3D systems. On the other hand, there exist a number of works, concerning both Raman scattering and far-infrared magneto-spectroscopy which address the issue of coupling between the electronic and phonon excitations in twodimensional semiconductor structures. The physics of low energy excitations in these structures is far more complex because of the modification of the energy spectrum due to effects of spatial confinement. The results of high-magmetic-field (up to 28T) inelastic light scattering studies on coupled plasmon-LO-phonon modes in bulk, degenerate n-type GaAs will be presented. [2] The data analysis implies the use of a standard dielectric function approach. Results obtained for samples with high electron concentration are well understood. A strong interaction of coupled LO-phonon-plasmon modes with the collective cyclotron resonance excitations (Bernstein modes) is observed. In samples with lower electron concentration, an unexpected Raman scattering signal in the vicinity of the undressed optical phonon is observed at high magnetic fields. A field induced metal-insulator transition is shown to be observable in Raman scattering experiments in samples with lowest electron concentration. The plasmon-phonon modes which are characteristic of the metallic state are replaced by intradonor excitations in the case of the insulating state. It is very interesting, that the resonant magnetopolaron effect reflecting the interaction between the LO phonon and the 1s-2p intradonor excitation is observed in the insulating state but no coupling between LO-phonon and cyclotron resonance excitations is seen in the metallic state. This result allows us to discuss some aspects of an apparent controversy existing in two-dimensional systems regarding the fundamental problem of Frohlich interaction: whether it manifests itself as a resonant repulsion between the cyclotron resonance and LO-phononlike modes for a two-dimensional electron gas, or not.

Stimulated Raman Scattering in a Weakly Polar III-VSemiconductor: Effect of dc Magnetic Field and Free CarrierConcentration

Using the hydrodynamic model of semiconductor plasmas, we perform ananalytical investigation of stimulated Raman scattering (SRS) of anelectromagnetic pump wave in a transversely magnetized weakly polarsemiconductor arising from electron-density perturbations and molecularvibrations of the medium both produced at the longitudinal opticalphonon frequency. Assuming that the origin of SRS lies in thethird-order susceptibility of the medium, we investigate the growthrate of Stokes mode. The dependence of stimulated Raman gain on theexternal dc magnetic field strength and free carrier concentration isreported. The possibility of the occurrence of optical phaseconjugation via SRS is also studied. The steady-state Raman gain isfound to be greatly enhanced by the presence of the strong external dcmagnetic field.

Polarized far infrared magnetoplasmon reflectivity of doped CdxMn1–xTe semimagnetic semiconductor in the Voigt configuration

AbstractCalculations of the p‐polarized far infrared magnetoplasmon reflectivity of semimagnetic semiconductor Cdx Mn1–x Te doped ternary alloy in the presence of a magnetic field parallel to the surface of the sample (the Voigt geometry) are used to investigate magnetoplasmon and zone center optical phonon frequencies. It is assumed that the sample is characterized by a dielectric tensor in which the optical phonon contribution and free carriers (plasmon and cyclotron response) are included. The results show that the transverse optical phonon mode is sensitive to the alloy composition, x, and can be used to determine the value of x. The longitudinal optical phonon frequencies are shifted due to phonon‐plasmon coupling in doped samples. Also, the influence of composition on the vibrational modes in zinc blende Cdx Mn1–x Te is described within a modified random element isodisplacement (MREI) approach. By indicating the plasmon and cyclotron frequencies from p‐polarized reflectivity spectra and the Voigt permittivity, we calculated the carrier concentration and the effective masses of the carriers. Furthermore, we indicate the frequencies of the phonons at the Γ, K, X and L high symmetry points of the Brillouin zone based on a microscopic second‐neighbor rigid ion model (RIM). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Infrared optical anisotropy of diluted magneticGa1−xMnxN∕c-sapphire epilayers grown with a GaN buffer layer by metalorganic chemical vapor deposition

Optical anisotropy of hexagonal ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{N}$ ($x$ from 0.0% to 1.5%) epitaxial films grown on $c$-plane sapphire substrates has been investigated using far- and mid-infrared $s$- and $p$-polarized reflectance spectra at oblique incidence (at 10\ifmmode^\circ\else\textdegree\fi{}, 22\ifmmode^\circ\else\textdegree\fi{}, and 32\ifmmode^\circ\else\textdegree\fi{}, respectively). The experimental data at room temperature can be well reproduced simultaneously in the measured frequency region of $200--2000\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ $(5--50\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})$, which was based on a four-phase layered system using a $4\ifmmode\times\else\texttimes\fi{}4$ matrix method [M. Schubert, Phys. Rev. B 53, 4265 (1996)]. The lattice vibrations perpendicular and parallel to the optic $c$ axis (${E}_{1}$ and ${A}_{1}$ modes) were expressed by Lorentz oscillator dielectric function model. There was a striking absorption dip at the ${A}_{1}$ phonon frequency in $p$-polarized reflectance spectra due to the optical anisotropy. These infrared-active phonon parameters were obtained with uniaxial dielectric tensor. It was found that the ${A}_{1}$ longitudinal-optical phonon frequency linearly increases with the Mn composition for the diluted magnetic semiconductor epilayers. The broadening values of the ${A}_{1}$ phonon changed from 3.6 $(\ifmmode\pm\else\textpm\fi{}1.3)$ to 9.0 $(\ifmmode\pm\else\textpm\fi{}1.6)\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, showing the high film crystal quality. Moreover, the ordinary and extraordinary dielectric functions ${\ensuremath{\epsilon}}_{\ensuremath{\perp}}$ and ${\ensuremath{\epsilon}}_{\ensuremath{\Vert}}$ of the epilayers were determined. It indicated that ${\ensuremath{\epsilon}}_{\ensuremath{\Vert}}$ was larger than ${\ensuremath{\epsilon}}_{\ensuremath{\perp}}$ for the ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{N}$ films in the reststrahlen region, which can be ascribed to slight structural degradation of the wurtzite lattice.

Pressure-dependent Raman scattering and photoluminescence of Zn1−xCdxSe epilayers

Raman and photoluminescence spectra of cubic Zn1−xCdxSe (0≦x≦0.32) epilayers were obtained at high pressure. The impurity mode I observed in the phonon Raman spectra at low temperature confirms the intermediate phonon mode behavior. A split transverse optical phonon mode was found in the down-stroke high-pressure Raman scattering. Additionally, the pressure-dependent longitudinal optical (LO) phonon frequencies and the Grüneisen parameter (γLO) were obtained by quadratic polynomial fitting. Pressure-driven resonant Raman scattering effect was observed in samples with a high Cd concentration (x≧0.18). The critical pressure of semiconductor-to-metal phase transition (Pt) decreases as the Cd content increases. As the Cd concentration increases from 0 to 0.32, Pt falls from 13.6to9.4GPa, according to Pt (GPa)=13.6−6.8x−20.3x2.

Residual strain measurements in InGaAs metamorphic buffer layers on GaAs

This work deals with the strain relaxation mechanism in InGaAs metamorphic buffers (MBs) grown on GaAs substrates and overgrown by InAs quantum dots (QD). The residual strain is measured by using Raman scattering and X-ray diffraction, both in Reciprocal Space Map and in single ω-2θ scan modes (ω and θ being the incidence angles on the sample surface and on the scattering planes, respectively). By relating the GaAs-like longitudinal optical phonon frequency ωLO of InGaAs MBs to the in-plane residual strain e measured by means of photoreflectance (PR), the linear e-vs.-ωLO working curve is obtained. The results of Raman and XRD measurements, as well as those obtained by PR, are in a very satisfactory agreement. The respective advantages of the techniques are discussed. The measurements confirm that strain relaxation depends on the thickness t of the buffer layer following a ~t-1/2 power law, that can be explained by an energy-balance model.

Experimental Evidence of the Vacancy-Mediated Silicon Self-Diffusion in Single-Crystalline Silicon

We have determined silicon self-diffusivity at temperatures 735-875 degrees C based on the Raman shift of longitudinal optical phonon frequencies of diffusion annealed 28Si/30Si isotope superlattices. The activation enthalpy of 3.6 eV is obtained in such low temperature diffusion annealing. This value is significantly smaller than the previously reported 4.95 eV of the self-interstitial mechanism dominating the high temperature region T>>855 degrees C and is in good agreement with the theoretical prediction for the vacancy-mediated diffusion. We present a model, containing both the self-interstitial and the vacancy terms, that quantitatively describes the experimentally obtained self-diffusivity between 735 and 1388 degrees C, with the clear crossover of the two diffusion mechanisms occurring around 900 degrees C.

Energy gaps and lattice dynamic properties of InAs xSb 1− x

The results of pseudopotential within the virtual crystal approximation (VCA) combined with the Harrison bond-orbital model calculations of the electronic and lattice dynamic properties of InAs x Sb 1− x are presented. The results include energy band-gaps, elastic constants, sound wave velocities, longitudinal optical (LO) and transversal optical (TO) phonon frequencies. The effect of compositional disorder on the fundamental energy band-gap has been examined and found to be important. Thus, this effect is included in all the calculations of the quantities being studied here. The agreement between our numerically calculated results and the available experimental data is found to be satisfactory. The information derived from the present study shows that InAs x Sb 1− x properties might be useful in optoelectronic applications as regards infrared and mid-infrared spectral regions.

Polar optical phonons in semiconducting CdS nanocrystals

We have experimentally and theoretically studied IR-active optical phonons, which are spatially confined in the volume of semiconducting CdS nanocrystals of various shapes synthesized in a dielectric matrix (porous aluminum oxide). Within an approach admitting the mixing of all expected types of vibrations, the complete sets of phonon modes are determined for a spherical quantum dot (QD) and a cylindrical quantum wire (QW) in this matrix. Based on these results, the polarizability spectra of QDs and QWs, as well as the effective dielectric function of a composite material containing such nanoparticles, are calculated for the far-IR wavelength range. It is established that the spectrum of the dielectric function exhibits specific features in the region between the transverse and longitudinal optical phonon frequencies of the massive semiconductor material. These features explain the rather unusual structure of the IR spectra of the composite samples studied.

Phonon frequencies and related parameters in Ga xIn 1−xSb and InAs xP 1−x

For the anionic GaxIn 1− x Sb and cationic InAs x P 1− x mixed crystals, the longitudinal and transversal optical phonon frequencies, Fröhlich coupling parameter, Debye temperature of the longitudinal phonon frequency and effective polar field are obtained from band-structure calculations based on the pseudopotential scheme. The results regarding optical phonon frequencies of the hosts InP, InAs, InSb and GaSb crystals are compared with experiment and showed generally satisfactory agreement. For the remaining studied quantities, the present results are predictions.

Ultrafast hole burning in intersubband absorption lines of GaN∕AlN superlattices

The authors present evidence for a distinct optical phonon progression in the nonlinear intersubband absorption spectra of electrons in a GaN∕AlN superlattice. Femtosecond two-color pump-probe experiments in the near infrared show spectral holes separated by the longitudinal optical (LO) phonon frequency and a homogeneous line broadening of approximately 50meV. The nonlinear bleaching signal decays with a time constant of 160fs due to intersubband scattering of delocalized electrons, followed by a weak picosecond component attributed to the relaxation of electrons from longer-lived localized states.

Preparation of ternary Cd 1–x Zn x S alloy by photochemical deposition (PCD) and its application to photovoltaic devices

p-SnS/n-Cd1–xZnxS heterojunctions were fabricated by using pulsed electrochemical deposition (P-ECD) and photochemical deposition (PCD) methods. CdSO4, ZnSO4 and Na2S2O3 were used for the deposition of Cd1–xZnxS alloys by PCD method on the indium-tin-oxide (ITO) coated glass substrates. The x values in the Cd1–xZnxS were varied by changing the Na2S2O3 concentration in the deposition bath. SnS layer was deposited by P-ECD using SnSO4 and Na2S2O3. The composition details of the n-Cd1–xZnxS window layer were estimated from LO (longitudinal optical) phonon frequency observed from the Raman studies. The photovoltaic properties of the fabricated solar cell structure glass/ITO/Cd1–xZnxS /SnS/In are characterised under the photon intensity 100 mW/cm2 and we observed the short circuit current density as 4.8 mA/cm2, open circuit voltage as 280 mV and fill factor as 0.34. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Interfacial operator approach to computing band structures for photonic crystals of polar materials

In this study, we propose an interfacial operator approach to compute surface phonon modes for one- and two-dimensional periodic arrays of polar materials in a finite-difference formulation. The key aspect of the approach is to introduce an interfacial variable along the interface between the polar material and the surrounding dielectric material, which represents the local strength of the surface phonon modes along the interface. In this approach, the apparently nonlinear eigenvalue problem can be reformulated as a quadratic eigensystem, and thus further reduced to a standard linear eigenvalue problem. Band structures can be computed directly without the need of examining transmission spectra as in the finite-difference time-domain method, or locating the mode frequency by testing an auxiliary function in other methods. Applying the method to four different types of photonic crystals of polar materials, we are able to uncover several interesting results by studying the effect of dimension, the size (filling ratio) effect, the effects of the transverse optical phonon frequency $({\ensuremath{\omega}}_{T})$, and longitudinal optical phonon frequency $({\ensuremath{\omega}}_{L})$ as well as the effect of shape or geometry of the polar material.

Infrared reflectance measurement for InN thin film characterization

AbstractInfrared reflectance measurements of a series of InN thin films have been performed and attempt to derive carrier concentration and other physical constants for InN thin film characterization. Fitting calculations are performed by use of the dielectric function equation based on phonon‐plasmon coupling model. Longitudinal and transverse optical phonon frequencies, plasma frequency and their damping parameters can be derived from fitting. From those results, electrical and phonon properties of InN and characterization of films are discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)