The Investigation of Plasmon-Longitudinal Optical Phonon Coupling and Surface Polariton Modes in Donor Doped GaAs-Al0.33Ga0.67As Multi Quantum Wells

Infrared Fourier transform spectroscopy has been used to investigate phonon, plasmon, surface polariton and plasma-longitudinal optical phonon coupling in highly donor doped multi quantum wells (GaAs/Al_0.33Ga_0.67As) and direct band gap n- type Al_XGa_1-XAs thin layer on GaAs substrate. Using different samples with different concentration of free carriers. The dispersion equation of coupling modes have been calculated by using the condition which the dielectric functions of samples are zero for longitudinal coupled modes and experimental papameters which have been obtained from the best fit p-polarized oblique incidence far infrared reflection spectra. In MQW samples, the free carriers confined to the well and carriers are quasi two dimensional. So, plasmon- LO phonon coupling occur in the well (GaAs). In n- type Al_XGa_1-XAs thin layer, the coupled modes consist of three branches of the high, intermediate and low frequency modes. Their frequencies depend on both concentration and alloy composition. To analyses the surface polariton modes we carry out attenuated total reflection (ATR) measurements. In order to support our assignment the magnetic field profiles and surface polariton dispersion curves have been calculated.     

Optical Characterization of Donor Doped Ternary Alloy Ga1-xNxAs and GaN-Ga1-xNxAs MQW by Using Infrared Fourier Transform Spectroscopy

In this work polarized infrared Fourier transform spectroscopy is employed to study the electronic and optical properties of doped Ga_1-xN_xAs ternary alloy and GaN-Ga_1-xN_xAs MQW. We have analyzed the far infrared spectra of GaN-GaNAs MQW by using a simple macroscopic theory base on effective medium approximation model. The dispersion curve of coupled LO phonon- plasmon modes were calculated from the polarized infrared reflectivity data. The GaNAs layer shows two-mode behavior in the infrared spectral range, a GaAs-like and a GaN-like sublattices. We detect the transverse optic phonon of GaN sublattice around 475 cm^-1. The origin of the sharp feature in p-polarization reflectivity about 300 cm^-1 as well as the dip at LO phonon frequency of GaAs sublattice are due to Brewster mode. The Brewster mode is couple strongly to plasmon mode. Attenuated total reflection spectroscopy has been used to excite and investigate surface plasmon and surface polariton.     

Infrared ellipsometry and Raman studies of hexagonal InN films: correlation between strain and vibrational properties

The vibrational properties of InN films with different strain have been studied using Infrared ellipsometry and Raman scattering spectroscopy. We have established a correlation between the phonon mode parameters and the strain, which allows the determination of the deformation potentials and the strain-free frequencies of the InN E₁(TO) and E₂ modes. The LO phonons and their coupling to the free-carrier plasmon excitations are also discussed in relation to the carrier concentration in the films.     

Detecting a true quantum pump effect

Reflectance measurements from p-type GaSb:Zn epitaxial films with different hole concentrations (10¹⁷–10¹⁸ cm^-3) have been investigated over the frequency region of 100–1000 cm^-1. A minimum broadening feature corresponding to the hole plasmon was observed in the reflectance spectra. The experimental infrared spectra were well fitted using a Lorentz-Drude dispersion model. The real part ε₁ of the dielectric function decreases with increasing hole concentration. However, the imaginary part ε₂ increases with hole concentration in the far-infrared region. This indicates that the acoustic- and optic-phonons mainly participate in the free carrier absorption processes. The hole mobility obtained from Hall-effect measurements is slightly larger than that derived from optical measurements and the average ratio of mobilities is estimated to be 1.33. Owing to overdamping effects, the upper branch of longitudinal-optical phonon plasmon (LPP) coupled modes was observed. The upper LPP⁺ frequency increases with hole concentration and it shows a transition from phonon-like to plasmon-like behavior. A theoretical analysis with solutions in the complex frequency plane describes these experimental results.     

Experimental studies of optical surface excitations

Experimental methods for optical excitation of nonradiative surface waves, such as surface plasmons and surface phonons, are reviewed. Results for surface plasmons in InSb obtained by using samples with line gratings in the surface and by using the technique of attenuated total reflection (ATR) are compared. Best agreement between the theoretical and experimental surface plasmon dispersion curve ω(k) of InSb is found when using excitation by ATR, since the sample surface need not be disturbed in this case. Surface phonons have been excited optically by applying ATR to alkali halide crystals and to the polar semiconductor GaP. While agreement with the theoretical dispersion curve is extremely good for GaP and also for CaF₂, there are systematic deviations to lower frequencies for NaF and other alkali halides. In polar semiconductors the free carrier plasmon couples to the LO-phonon when ω_p ≈ ω_LO. This behaviour has been investigated theoretically and experimentally for the surface modes. For an interesting application of the ATR-technique, one can use the fact that dispersion and linewidth are a direct measure of the complex dielectric function ε(ω) in the frequency range of the optical surface waves.     

Lo phonon-plasmon coupling in non-stoichiometric rutile TiO2

The analysis of the infrared reflectivity spectrum of partially reduced rutile TiO_1.96 reveals a plasmon-LO phonon coupling. Pure-phonon and plasmon frequencies and life times are determined by fit with an appropriate model using the factorized form of the dielectric function for the phonon modes added to a plasmon contribution also derived from the factorized form. Results are compared with data obtained in the insulating stoichiometric rutile.     

On the mixed nature of the 740 cm band in wurtzite GaN films: A polarized Raman scattering investigation

A detailed study of the polarized Raman scattering of wurtzite GaN films is presented, focusing on the nature of the band centered at 740 cm⁻¹ observed in the X(Z, Z)X configuration. The origin of this band is ascribed to the mixed contribution of the A₁ and E₁ longitudinal phonon modes coupled with the free carrier excitation. The spectral profile of the 740 cm⁻¹ Raman band has been successfully reconstructed through a linear combination of the A₁-E₁ longitudinal phonon plasmon-coupled modes, leading to a free carrier concentration in good agreement with Hall effect measurements.     

Phonon dispersion curves and densities of lithium-intercalated iron phosphorus trisulfide

Summary The lattice dynamics of Li-intercalated FePS₃ has been studied by means of a force constant model generated by a set of short-range two-body potentials. The intercalated phases have been investigated for the three stoichiometric compositions: Li_0.5FePS₃, LiFePS₃, Li_1.5FePS₃, with the aim of analysing the evolution of the host lattice normal modes as a function of the concentration, and of finding the dispersion of the new phonon branches induced by lithium. The above special values of lithium concentration have been chosen because the size of the unit cell keeps the same as in the host material. The force constants are fitted to the infrared data and the phonon dispersion curves and the phonon energy densities have been calculated. A spectroscopic method for monitoring lithium migration in the host material is proposed.     

GaN载流子浓度和迁移率的光谱研究

用红外反射光谱的方法对生长在蓝宝石衬底上的α-GaN外延薄膜的载流子浓度和迁移率进行了研究.通过测量蓝宝石衬底和不同Si掺杂浓度的一系列GaN外延膜的远红外反射谱并进行理论计算和拟合,得到GaN中的声子振动参量和等离子振荡的频率及阻尼常量,并由此计算得到其载流子浓度和迁移率.计算结果,红外方法得到的载流子浓度与Hall测量相一致,但迁移率比Hall迁移率要低约二分之一.同时红外谱与喇曼谱上明显观察到LO声子与等离子体激元耦合模,(LPP)随掺杂浓度的变化. 关键词： α-GaN外延薄膜 红外反射光谱 载流子浓度 迁移率 LO声子与等离子体激元耦合模 Raman光谱     

Impact of anisotropy on polar optical vibration in a wurtzite cylindrical nanowire with ring geometry

The quasi-confined (QC) phonon modes, surface optical (SO) phonon modes and corresponding Fröhlich-like Hamiltonian in a wurtzite cylindrical nanowire with ring geometry are investigated in the framework of the dielectric continuum model and Loudon’s uniaxial crystal model. Numerical calculations are focused on the dispersion relations of the SO phonons and the electron–SO phonon coupling strength. Results show that there are only two branches of SO phonon modes. The dispersions of the two branches of SO phonon modes are obvious when the phonon wave-number k_z or the azimuthal quantum number m is small. Typical degenerating behavior of the SO modes is evidenced due to the anisotropic effect of wurtzite crystal. Moreover, when k_z or m are large enough, the frequencies of the two branches of SO modes converge to a definite limiting frequency in single planar heterostructure. The calculations of the electron–SO phonon coupling strength reveal that the high-frequency SO modes (SO₊) play a more important role in the coupling strength than the low-frequency ones (SO₋). Furthermore, the long-wavelength SO phonons with small m are the main factor contributing to the electron–phonon interaction.     

Experimental measurement of acoustic plasmons in polycrystalline palladium

An experimental study of collective oscillations in Pd covering the region of very low energy and momentum transfers is reported. Through Dynamic Electron Scattering spectroscopy, structure factor spectra were measured from 80?K to 298?K on a bulk polycrystalline Pd sample. Here we report the first experimental evidence of damped acoustic plasmons and their evolution to the single-particle excitation continuum. The acoustic plasmons follow a linear dispersion and are experimentally shown to be a separate and distinct resonance mode from acoustic surface plasmons. Calculations of the dielectric function employed a model that incorporates complete mixing of two conduction bands with contributions from both interband and intraband transitions. The model was used in computational studies that focused on specific experimental results to aid the characterization and understanding of the plasmon behavior. We found that the Pd acoustic plasmon energy matched the longitudinal phonon anomaly that has sparked numerous theoretical reports on the possible energetic coupling of these modes. Further experimental evidence of plasmon and phonon dynamical processes are found in the linewidth analysis of the data. The primary decay mechanism of the plasmons is interpreted to be strong phonon-assisted interband transitions. Further spectral features and the plasmon velocity are also reported.     

Elementary excitations at doped polar semiconductor surfaces with carrier-depletion layers

We make a comparative analysis of coupled carrier plasmon–polar phonon modes at doped polar semiconductor surfaces in the absence and the presence of a carrier-depletion layer. Our analysis shows how the effect of the depletion layer appears in the spatial structure of each excitation mode visualized in a contour map of the induced charge-density, the coupling character elucidated by the phase relation and the amplitude ratio of the carrier component and the polar-phonon component in the induced charge-density distribution, and the energy-loss intensity due to the surface excitation.     

Plasmon modes of double-layer graphene at finite temperature

We calculate the dynamical dielectric function of doped double-layer graphene (DLG), made of two parallel graphene monolayers with carrier densities n₁ and n₂, and an interlayer separation of d at finite temperature. The results are used to find the dispersion of plasmon modes and loss functions of DLG for several interlayer separations and layer densities. We show that in the case of n₂=0, the finite-temperature plasmon modes are dramatically different from the zero-temperature ones.     

Renormalization of phonon frequencies by conduction electrons in layer systems with application to YBa2Cu3O7

It is generally assumed that there are free electronic carriers associated with the CuO₂ planes in high-temperature superconductors. Regarding these carriers as confined to these planes their influence on phonon frequencies is studied within the framework of a shell model of lattice dynamics taking into account the long-range part of the electron-phonon coupling. We find a complete suppression of the LO-TO splitting for modes polarized along the planes by metallic screening and a strong coupling of electronic plasmon and particle-hole excitations especially to some To-phonon branches polarized perpendicular to the conducting planes, particularly pronounced in systems with at least two CuO₂ planes per unit cell. Numerical results are presented for YBa₂Cu₃O₇.     

Infrared spectroscopy of solids

For materials like small gap semiconductors or intercalated layered compounds the general form of the complex dielectric function is: ϵ(ω) = ϵ_x + Δϵ_inter + Δϵ_intra + Δϵ_ph, where ϵ_∞is the high frequency dielectric constant due to all interband transitions except the uppermost valence band and the lowest conduction band, Δϵ_inter is the contribution to the dielectric constant due to this two bands in particular, Δϵ_intra is the contribution due to intraband free carrier transitions and Δϵ_ph is the contribution due to lattice vibrations. The contribution from transitions between valence and conduction bands to the imaginary part of the dielectric function Δϵ_inter(ω,T) for a narrow gap material can be readily calculated in the random phase approximation (RPA) formalism. The real part Δϵ_inter is obtained by performing the Kramers-Kronig inversion on the expression Δϵ_inter. Dielectric function of HgTe between 8 and 300 K is discussed. The interband contribution to the complex dielectric function in a layered intercalation compound is also examined. Pure graphite, first and second stage compounds are treated as an example. Reflectivity and magnetoreflectivity spectra simultaneously determining the plasma and the cyclotron frequencies, allow one to measure the free carrier density, hence the Fermi level, and the effective mass of the carriers. The variation of the effective mass as a function of the position of the Fermi level traces the energy bands dispersion relation. An example of such investigations is given for PbSe layered materials like Bi₂Se₃ are also studied by infrared reflectivity spectroscopy. Intercalation of such materials increases the free carrier population which consequently moves the Fermi level up in the conduction band. Analysis of reflectivity spectra allows an accurate determination of the free carrier concentration and gives a useful tool for the investigation of atom insertion in layered materials. Recent experiments on the intercalation of Li in a certain number of layered materials will be presented. In the frame of the classical theory of independent harmonic oscillators, the phonon contribution to the dielectric function is given by the sum of transverse modes for each oscillator with the corresponding damping parameters and oscillator strength. The complex dielectric function can then be written as a set of separate equations for the real and imaginary parts of the wave-number-dependent dielectric function. In the spectral region when phonon and plasmon frequencies may coincide a strong plasmon-phonon coupling will be experienced. In a simple model with one LO and one TO frequency, one expects two singularities at the two maxima of the function 1m −ϵ⁻¹; representing longitudinal modes. The frequencies generally labeled ω₊ and ω_- correspond to longitudinal oscillations with the lattice and electron plasma vibrating, respectively, in phase and 180° out of phase. In small gap materials the situation is more complex. Because of the particular band structure, the contribution Δϵ_inter(ω) must be included. In some cases it also becomes necessary to include additional oscillators with strong polar character corresponding to a particular defect or to additional vibrations. The implications of all these fundamental concepts in the investigation of high Tc materials is discussed and examples given.     

Electron-phonon coupling in intrinsic trans-polyacetylene

We consider a valence force field model for the phonon spectrum of (CH)_x and find that phonon coupling to extended π electron states must be included to describe the observed Raman active modes of the polymer. The calculated phonon spectra are shown to possess the zone center dispersion anomalies characteristic of a condensed Peierls ground state.     

Specific heat and lattice dynamics of layered TiS2 crystal

The specific heatC of the layered 1T-CdI₂ type TiS₂ crystal has been measured over the temperature range 20–300 K using a thermal relaxation method. Based on the available information about lattice dynamics for acoustic and optical phonon modes in TiS₂, the dispersion curve and the density of states for each mode are evaluated using a simplified phonon Brillouin zone of a cylindrical form. The calculatedC-T curve is in good agreement with the observation.     

Far-infrared spectroscopy of CdTe1−xSex(In): Phonon properties

The far-infrared reflectivity spectra of CdTe_0.97Se_0.03 and CdTe_0.97Se_0.03(In) single crystals were measured at different temperatures. The analysis of the far-infrared spectra was carried out by a fitting procedure based on the dielectric function which includes spatial distribution of free carriers as well as their influence on the plasmon–phonon interaction. We found that the long wavelength optical phonon modes of CdTe_1−xSe_x mixed crystals exhibit a two-mode behavior. The local In mode at about 160 cm⁻¹ is observed. In both sample, a surface layer with a low concentration of free carriers (depleted region) are formed.     

The quasi-confined optical phonons in wurtzite GaN/AlN multiple quantum wells

Within the framework of the dielectric-continuum model and Loudon's uniaxial crystal model, the equation of motion for p-polarization field in arbitrary wurtzite multilayer heterostructures are solved for the quasi-confined phonon (QC) modes. The polarization eigenvector, the dispersion relation, and the electron-QC interaction Fröhlich-like Hamiltonian are derived by using the transfer-matrix method. The dispersion relations and the electron-QC coupling strength are investigated for a wurtzite GaN/AlN single QW. The results show that there are infinite branches of dispersion curve with definite symmetry with respect to the center of the QW structure. The confinement of the quasi-confined phonons in the QW leads to a quantization of q_z,j characterized by an integer m that defines the order of corresponding quasi-confined modes. The QC modes are more dispersive for decreasing m. The QC modes display an interface behavior in the barrier and a confined behavior in the well. The symmetric modes have more contribution to electron-QC interaction than the antisymmetric modes. The strains have more effect on symmetry modes, and can be ignored for symmetry modes.     

Structural and phonon dynamical properties of perovskite manganites: (Tb, Dy, Ho)MnO3

A shell model has been used to study the structure, phonon dynamics and phase coexistence of perovskite manganites RMnO₃ (R=Tb, Dy, Ho). The calculated crystal structure, Raman and IR frequencies and specific heats are found to be in good agreement with the available experimental data. The phonon density of states, elastic constants, elastic stiffness, shear constants and phonon dispersion curves have been computed for these manganites. A zone center imaginary A_u mode is revealed in these phonon dispersion curves, which indicates the occurrence of the metastability of the perovskite phase. The Gibbs free energy values calculated as a function of temperature and pressure for RMnO₃ in the orthorhombic phase, when compared with those of the hexagonal phase, reveal the possibility of coexistence of these two phases in the present multiferroic manganites under ambient conditions.