Transverse Optical Phonon Research Articles

Phonon-assisted indirect transitions in angle-resolved photoemission spectra of graphite and graphene

Indirect transitions of electrons in graphene and graphite are investigated by means of angle-resolved photoemission spectroscopy (ARPES) with several different incident photon energies and light polarizations. The theoretical calculations of the indirect transition for graphene and graphite are compared with the experimental measurements for highly-oriented pyrolytic graphite and a single-crystal of graphite. The dispersion relations for the transverse optical (TO) and the out-of-plane longitudinal acoustic (ZA) phonon modes of graphite and the TO phonon mode of graphene can be extracted from the inelastic ARPES intensity. We find that the TO phonon mode for $k$ points along the $\Gamma$-$K$ and $K$-$M$-$K'$ directions in the Brillouin zone can be observed in the ARPES spectra of graphite and graphene by using a photon energy of about 11.1 eV. The relevant mechanism in the ARPES process for this case is the resonant indirect transition. On the other hand, the ZA phonon mode of graphite can be observed by using a photon energy of about 6.3 eV through a nonresonant indirect transition, while the ZA phonon mode of graphene within the same mechanism should not be observed.

Biaxial stress evaluation in GeSn film epitaxially grown on Ge substrate by oil-immersion Raman spectroscopy

GeSn is being paid much attention as a next-generation channel material. In this work, we performed the excitation of forbidden transverse optical (TO) phonons from strained GeSn, as well as longitudinal optical (LO) phonons, under the backscattering geometry from the (001) surface by oil-immersion Raman spectroscopy. Using the obtained LO/TO phonons, we derived the phonon deformation potentials (PDPs), which play an important role in the stress evaluation, of the strained Ge1−xSnx for the first time. The results suggest that PDPs are almost constant for the Ge1−xSnx (x < 0.032). Biaxial stress calculated using the derived PDPs reasonably indicated the isotropic states.

Uniaxial strain-induced Kohn anomaly and electron-phonon coupling in acoustic phonons of graphene

Recent advances in strain engineering at the nanoscale have shown the feasibility to modulate the properties of graphene. Although the electron-phonon (e-ph) coupling and Kohn anomalies in graphene define the phonon branches contributing to the resonance Raman scattering, and is relevant to the electronic and thermal transport as a scattering source, the evolution of the e-ph coupling as a function of strain has been less studied. In this work, the Kohn anomalies and the e-ph coupling in uniaxially strained graphene along armchair (AC) and zigzag (ZZ) directions were studied by means of density functional perturbation theory calculations. In addition to the phonon anomaly at the transversal optical (TO) phonon branch in the K point for pristine graphene, we found that uniaxial strain induces a discontinuity in the frequency derivative of the longitudinal acoustic (LA) phonon branch. This behavior corresponds to the emergence of a Kohn anomaly, as a consequence of a strain-enhanced e-ph coupling. Thus, the present results for uniaxially strained graphene contrast with the commonly assumed view that the e-ph coupling around the K point is only present in the TO phonon branch.

Two-prism crystal structures for far-field imaging of subwavelength features at terahertz frequencies

We investigate how a system of two single crystals can be used for far field imaging of subwavelength features. We make use of the phonon response to induce canalization of narrow collimated beams in crystals with suitably high anisotropy at the appropriate transverse optical phonon frequency. By cutting the crystals into suitably designed prisms, we show that an magnified image can be obtained and projected into the far field by a two-prism structure, noting that a single prism does not give a faithful reproduction of the object and will usually result in total internal reflection of most of the radiation. We show simulations using triglycine sulphate, which is both highly anisotropic and has very low absorption, at low temperature.

Characterization of Thermal Oxides on 4H-SiC Epitaxial Substrates Using Fourier-Transform Infrared Spectroscopy.

Fourier transform infrared (FT-IR) spectra were measured for thermal oxides with different electrical properties grown on 4H-SiC substrates. The peak frequency of the transverse optical (TO) phonon mode was blue-shifted by 5 cm-1 as the oxide-layer thickness decreased to 3 nm. The blue shift of the TO mode indicates interfacial compressive stress in the oxide. Comparison of data for the oxide on a SiC substrate with that for similar oxides on a Si substrate implies that the peak shift of the TO mode at the SiO2/SiC interface is larger than that of SiO2/Si, which suggests that the interfacial stress for the oxide on the SiC substrate is larger than that on the Si substrate. For the SiO2/SiC interfacial region (<3 nm oxide thickness), despite the fact that the blue shift of the TO modes becomes larger while approaching the oxide/SiC interface, the peak frequency of the TO modes red-shifts at the oxide/SiC interface. The peak-frequency shift of the TO mode for the sample without post-oxidation annealing was larger than that for the samples post-annealed in a nitric oxide atmosphere. The channel mobilities are correlated with the degree of shift of the TO mode when the oxide thickness is <3 nm. It appears that the compressive stress at the SiO2/SiC interface generates silicon suboxide components and weakens the Si-O bonds. As the result, the TO mode was red-shifted and the oxygen deficiency increased to relax the compressive stress in the oxide with <3 nm thickness. Fourier transform infrared spectroscopy measurements provide unique and useful information about stress and inhomogeneity at the oxide/SiC interface.

FTIR Ellipsometry Study on RF sputtered Permalloy-Oxide Thin Films

The optical properties of RF sputtered polycrystalline permalloy oxide (PyO) thin films were studied in the infrared by variable angle ellipsometry. The dispersion of PyO shows a Lorentzian dispersion peak at 381.5 cm-1. We attribute this peak to the transverse optical phonon of PyO. This peak is consistent with a rocksalt crystal structure for the Ni0.81Fe0.19O1-d thin films.

Fano resonance of Li-doped KTa(1-x)NbxO3 single crystals studied by Raman scattering.

The enhancement of functionality of perovskite ferroelectrics by local structure is one of current interests. By the Li-doping to KTa1−xNbxO3 (KTN), the large piezoelectric and electro-optic effects were reported. In order to give new insights into the mechanism of doping, the microscopic origin of the Fano resonance induced by the local structure was investigated in 5%Li-doped KTN single crystals by Raman scattering. The coupling between the continuum states and the transverse optical phonon near 196 cm−1 (Slater mode) caused a Fano resonance. In the vicinity of the cubic-tetragonal phase transition temperature, TC-T = 31 °C, the almost disappearance of the Fano resonance and the remarkable change of the central peak (CP) intensity were observed upon heating. The local symmetry of the polar nanoregions (PNRs), which was responsible for the symmetry breaking in the cubic phase, was determined to E(x, y) symmetry by the angular dependence of Raman scattering. The electric field induced the significant change in the intensity of both CP and Fano resonance. From these experimental results, it is concluded that the origin of the Fano resonance in Li-doped KTN crystals is the coupling between polarization fluctuations of PNRs and the Slater mode, both belong to the E(x, y) symmetry.

Thermal behavior of high-frequency optical phonons in tetragonal BaTiO3 single crystal

The temperature dependence of the optical phonon modes in the tetragonal BaTiO3 single crystal was investigated by means of polarized Raman spectroscopy measurements. A special attention was devoted to the Raman spectra deconvolution to separate between first- and second-order bands, which can be discriminated from the difference in the temperature behavior of scattered intensity. Both A1 mode motions along the polar c axis and E vibrations (except the well-known soft mode) normal to c were studied and discussed. The temperature dependences of frequency and damping of each optical phonon were achieved and then interpreted in terms of third- and fourth-order anharmonic potential. It was derived from this analysis that the A1 transverse optical phonon arising from the hardening of the soft phonon of the cubic phase possesses large anharmonic motion of Ti versus O ions. A significant anharmonicity was as well found for phonons associated with O octahedral distortion.

Anisotropy, phonon modes, and free charge carrier parameters in monoclinicβ-gallium oxide single crystals

We derive a dielectric function tensor model approach to render the optical response of monoclinic and triclinic symmetry materials with multiple uncoupled infrared and farinfrared active modes. We apply our model approach to monoclinic $\beta$-Ga$_2$O$_3$ single crystal samples. Surfaces cut under different angles from a bulk crystal, (010) and ($\bar{2}$01), are investigated by generalized spectroscopic ellipsometry within infrared and farinfrared spectral regions. We determine the frequency dependence of 4 independent $\beta$-Ga$_2$O$_3$ Cartesian dielectric function tensor elements by matching large sets of experimental data using a point by point data inversion approach. From matching our monoclinic model to the obtained 4 dielectric function tensor components, we determine all infared and farinfrared active transverse optic phonon modes with $A_u$ and $B_u$ symmetry, and their eigenvectors within the monoclinic lattice. We find excellent agreement between our model results and results of density functional theory calculations. We derive and discuss the frequencies of longitudinal optical phonons in $\beta$-Ga$_2$O$_3$. We derive and report density and anisotropic mobility parameters of the free charge carriers within the tin doped crystals. We discuss the occurrence of longitudinal phonon plasmon coupled modes in $\beta$-Ga$_2$O$_3$ and provide their frequencies and eigenvectors. We also discuss and present monoclinic dielectric constants for static electric fields and frequencies above the reststrahlen range, and we provide a generalization of the Lyddane-Sachs-Teller relation for monoclinic lattices with infrared and farinfrared active modes. We find that the generalized Lyddane-Sachs-Teller relation is fulfilled excellently for $\beta$-Ga$_2$O$_3$.

Structural characterization of AlGaAs:Si/GaAs (631) heterostructures as a function of As pressure

AlGaAs:Si/GaAs heterostructures were grown on (631) and (100) GaAs substrates and studied as a function of the As cell beam equivalent pressure. High-resolution x-ray diffraction patterns showed that the highest quality AlGaAs epitaxial layers were grown at PAs = 1.9 × 10−5 for (100)- and PAs = 4 × 10−5 mbar for (631)-oriented substrates. Raman spectroscopy revealed higher crystalline quality for films grown on (631) oriented substrates. The GaAs- and AlAs-like modes of the AlGaAs(631) films exhibited increased intensity ratios between the transverse optical phonons and longitudinal optical phonons with increasing PAs, whereas the ratios were decreased for the (100) plane. This is in agreement with the selection rules for (631) and high-resolution x-ray diffraction observations. Anisotropy and surface corrugation of the AlGaAs(631) films also were characterized using atomic force microscopy and Raman spectroscopy.

Engineering the Reststrahlen band with hybrid plasmon/ phonon excitations

Abstract

Phenomenology of ripples in graphene

A recent experimental study has shown that the flat geometry of graphene is unstable, leading to the formation of a corrugated structure: topological defects and ripples [1]. Graphene can be viewed as a crystalline membrane. An ideal flat 2D-crystal could not exist at a finite temperature [1], and the long range order in graphene’s structure occurs because of ripples and topological defects. Both of these factors facilitate the achievement of thermodynamic stability in grapheme [2] and they could be induced to relieve the membrane’s strain. As far as we know, no widely accepted model for ripples in monolayer graphene exists. The crumpled membrane theory does not work for graphene at relevant temperatures. Some authors try to obtain a ripplelike solution from the renormalization group approach, but the only result is the appearance of some characteristic length of a correct magnitude. The phenomenon under consideration looks too simple to be described with a use of the sophisticated fluctuation theory: we assume that the ripple theory has to be the mean field one. The somewhat similar problem of undulations in biological membranes was solved by taking into account the internal degrees of freedom [3]. One such fluctuating degree of freedom was the membrane thickness. In the case of graphene, a natural candidate on this position is the in-plane transverse optical phonon. The spatial period of the ripple is determined by the ratio of the coefficients in the thermodynamic potential derivative expansion. The out-of-plane subsystem acquires periodicity due to the interaction between the subsystems. Two interaction mechanisms: bilinear and biquadratic were considered. Only solutions with vanishing Gaussian curvature are admissible. The suggested phenomenological description needs to be justified by future microscopic theory.

Far-Field Spectroscopy and Near-Field Optical Imaging of Coupled Plasmon-Phonon Polaritons in 2D van der Waals Heterostructures.

A new hybridized plasmon-phonon polariton mode in graphene/h-BN van der Waals heterostructures is presented, featuring the ultrahigh field confinement characteristic of the graphene plasmon and the long lifetime property of the h-BN transverse optical phonon. This enables an ultralong hybrid plasmon lifetime of up to 1.6 ps (with ultrahigh mode confinement up to >l0(2)/7000 and ultrasmall group velocity down to 0.001c, where c is the speed of light in vacuum), superior to any localized plasmon ever demonstrated.

Identification of Cobalt Oxides with Raman Scattering and Fourier Transform Infrared Spectroscopy

Although Raman spectral fingerprints of Co3O4 have been well established, the infrared spectrum of Co3O4 is less understood due to its dependence on sample morphologies and experimental configurations. The same is true for both Raman and infrared spectra of CoO. In this study, we present a comprehensive optical characterization of Co3O4 and CoO with Raman scattering and Fourier transform infrared spectroscopy (FTIR). Two of the transverse optical (TO) phonons and their corresponding longitudinal optical (LO) phonons of Co3O4 above 500 cm–1 are observed in both transmission and diffuse reflectance with LO/TO intensity ratios depending on particle size and the incident angle of FTIR beam. CoO is featured by a broad infrared band around 510 cm–1. In contrast to many previous reports, no Raman-active phonon line is observed, which is in agreement with the selection rule for rock-salt CoO. Nevertheless, CoO can still be characterized by Raman scattering from magnetic excitations in its antiferromagnetic phase ...

Study ofAandBsites order in lanthanide-doped lead titanate ferroelectric system

Pb0.88Ln0.08TiO3ferroelectric system, whereLn= La, Sm, Eu, and Dy, has been characterized using Scanning Electron Microscopy, Raman spectroscopy, and X-ray diffraction experiments. Softening of the lowest transverse optical phonon modeE(1TO) was evaluated as a function of the rare earths’ ionic radius suggesting partial occupation of lanthanide ions at theAandBsites of the perovskite structure. Using Rietveld refinements, it has been established a higher incorporation of Ln3+ions into theAsites of the perovskite structure than that of theBsites for the studied ceramics. The occupation atBsites increases slightly with the decreases of the ionic radii of the lanthanides.

Structural and optical properties of CdTe thin film: A detailed investigation using optical absorption, XRD, and Raman spectroscopies

Physical vapor deposition (PVD) is used to grow CdTe thin films of different thicknesses on glass substrates. The characterization of the samples is then investigated optically and structurally. Three experimental techniques were used in this study; optical absorption (ABS), Raman, and X‐ray diffraction (XRD) spectroscopies. In optical ABS spectroscopy, the Urbach energy related to the width of long‐wavelength tail decreases from 827 to 585 meV as the thickness increases from 100 to 500 nm, respectively. The thickness‐dependent particle size was calculated using the value of the size‐dependent optical absorption edge energy. A shift of 710 meV in the ABS edge energy takes place as the thickness increases from 100 to 500 nm. Thickness‐dependent shifting and widening of XRD line is presumably due to the size effect and strain. Relative to the phonon frequency of bulk CdTe crystal, a thickness‐dependent blueshift was observed in Raman spectra for the Longitudinal Optical (LO) phonon frequency, while a redshift for the longitudinal acoustic (LA) and transverse optical (TO) phonon frequencies is observed. In the present work, the results of optical absorption, XRD, and Raman analyses are combined in order to study the effect of particle‐size evolution, thickness‐dependent strain, and structural disorder.

Controlling the thermal conductance ofgraphene/h−BNlateral interface with strain and structure engineering

Although phonon-mediated thermal conduction in pristine graphene and hexagonal boron nitride is well understood, less is known about phonon transport in single-sheet graphene-hexagonal boron nitride ($\mathrm{Gr}/h\ensuremath{-}\mathrm{BN}$) lateral heterostructures, where the thermal resistance of the interfaces plays an important role in the overall thermal conductivity. We apply the newly developed extended atomistic Green's function method to analyze with detail the effect of strain and structure engineering on the thermal conductance ${G}_{\mathrm{int}}$ of the $\mathrm{Gr}/h\ensuremath{-}\mathrm{BN}$ interface. Our calculations show that longitudinal tensile strain leads to significant ${G}_{\mathrm{int}}$ enhancement (up to $25%$ at 300 K) primarily through the improved alignment of the flexural acoustic phonon bands, despite the reduction in the longitudinal acoustic (LA) and transverse acoustic phonon velocities. In addition, we find that alternating C-N zigzag bonds along the zigzag interface lead to a greater ${G}_{\mathrm{int}}$ than C-B bonds through more effective transmission of high-frequency LA and transverse optical phonons, especially at high strain levels. We also demonstrate how the interfacial structure dramatically affects the orientation of the transmitted optical phonons, a phenomenon that is neither seen for acoustic phonons nor predictable from conventional acoustic wave scattering theory. Insights from our paper can provide the basis for manipulating the interfacial thermal conductance in other two-dimensional heterostructures.

Many-electron effects on the dielectric function of cubicIn2O3: Effective electron mass, band nonparabolicity, band gap renormalization, and Burstein-Moss shift

We systematically investigate the influence of free-electron concentrations from $1.5\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ up to $1.6\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ on the optical properties of single-crystalline ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ in the cubic bixbyite structure. Dielectric functions of bulk crystals and epitaxial films on various substrates are determined by spectroscopic ellipsometry from the mid-infrared $(37\phantom{\rule{4pt}{0ex}}\mathrm{meV}\ensuremath{\approx}300\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1})$ into the ultraviolet $(6.5\phantom{\rule{4pt}{0ex}}\mathrm{eV})$ spectral region. Eight transverse optical phonon modes are resolvable for low carrier-density material. The analysis of the plasma frequencies yields effective electron masses which increase from a zero-density mass of ${m}^{*}=0.18{m}_{0}$ to $0.4{m}_{0}$ at $n={10}^{21}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. This mirrors the nonparabolicity of the conduction band being described by an analytical expression. The onset of absorption due to dipole-allowed interband transitions is found at $3.8\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ for $n\ensuremath{\le}{10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. It undergoes a blue-shift (effective Burstein-Moss shift) for higher electron densities as a result of the dominating phase-space filling compared to band gap renormalization. A comprehensive model describing the absorption onset is developed, taking nonparabolicity into account, yielding an accurate description and explanation of the observations. The agreement of modeled and measured absorption onset independently supports the effective electron masses derived from infrared data. The high-frequency dielectric constant of undoped ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ is found to be ${\ensuremath{\varepsilon}}_{\ensuremath{\infty}}=(4.08\ifmmode\pm\else\textpm\fi{}0.02)$.

Phonon coupling to dynamic short-range polar order in a relaxor ferroelectric near the morphotropic phase boundary

We report neutron inelastic scattering experiments on single crystal PbMg$_{1/3}$Nb$_{2/3}$O$_{3}$ doped with 32\% PbTiO$_{3}$, a relaxor ferroelectric that lies close to the morphotropic phase boundary. When cooled under an electric field $\mathbf{E} \parallel$ [001] into tetragonal and monoclinic phases, the scattering cross section from transverse acoustic (TA) phonons polarized parallel to $\mathbf{E}$ weakens and shifts to higher energy relative to that under zero-field-cooled conditions. Likewise, the scattering cross section from transverse optic (TO) phonons polarized parallel to $\mathbf{E}$ weakens for energy transfers $4 \leq \hbar \omega \leq 9$ meV. However, TA and TO phonons polarized perpendicular to $\mathbf{E}$ show no change. This anisotropic field response is similar to that of the diffuse scattering cross section, which, as previously reported, is suppressed when polarized parallel to $\mathbf{E}$, but not when polarized perpendicular to $\mathbf{E}$. Our findings suggest that the lattice dynamics and dynamic short-range polar correlations that give rise to the diffuse scattering are coupled.

Infrared spectroscopy of silicon carbide layers synthesized by the substitution of atoms on the surface of single-crystal silicon

This paper presents the results of the infrared spectroscopic study of silicon carbide epitaxial layers grown by the substitution of atoms on the surface of single-crystal silicon. It has been found that, in the infrared spectra, there is a band at 798 cm–1, which corresponds to a transverse optical (TO) phonon in the lattice of silicon carbide. The parameters of disordered silicon carbide on the surface of pores between the epitaxial layer of silicon carbide and the silicon substrate have been determined. It has been revealed that, in the infrared spectra of silicon carbide, there is a band in the wavenumber range of 960 cm–1. A hypothesis has been proposed, according to which this band corresponds to the energy of the previously theoretically predicted elastic dipole consisting of an elastically interacting carbon atom located in an interstitial position and a silicon vacancy.