Transverse Optical Phonon Research Articles

Anisotropy, phonon modes, and lattice anharmonicity from dielectric function tensor analysis of monoclinic cadmium tungstate

We determine the frequency dependence of four independent CdWO$_4$ Cartesian dielectric function tensor elements by generalized spectroscopic ellipsometry within mid-infrared and far-infrared spectral regions. Single crystal surfaces cut under different angles from a bulk crystal, (010) and (001), are investigated. From the spectral dependencies of the dielectric function tensor and its inverse we determine all long wavelength active transverse and longitudinal optic phonon modes with $A_u$ and $B_u$ symmetry as well as their eigenvectors within the monoclinic lattice. We thereby demonstrate that such information can be obtained completely without physical model line shape analysis in materials with monoclinic symmetry. We then augment the effect of lattice anharmonicity onto our recently described dielectric function tensor model approach for materials with monoclinic and triclinic crystal symmetries [Phys. Rev. B, 125209 (2016)], and we obtain excellent match between all measured and modeled dielectric function tensor elements. All phonon mode frequency and broadening parameters are determined in our model approach. We also perform density functional theory phonon mode calculations, and we compare our results obtained from theory, from direct dielectric function tensor analysis, and from model lineshape analysis, and we find excellent agreement between all approaches. We also discuss and present static and above reststrahlen spectral range dielectric constants. Our data for CdWO$_4$ are in excellent agreement with a recently proposed generalization of the Lyddane-Sachs-Teller relation for materials with low crystal symmetry [Phys. Rev. Lett. 117, 215502 (2016)].

Raman Mapping and Delineation of III-V Semiconductor Band Bending Characteristics

Raman spectroscopy has previously been used to ascertain the nature and extent of band bending at III-V semiconductor interfaces. Many previous investigations have focused on samples cleaved in vacuum and subsequently exposed to oxygen gas or a thin metal deposition; generally, specific polarizations of incident and scattered light are applied and collected in order to specify and isolate the desired phonon peaks under investigation1,2. We demonstrate herein a more general and easily applied method to investigate III-V interfaces by Raman spectroscopy using analysis of the longitudinal optical (LO) and transverse optical (TO) phonons; furthermore, we provide a means by which the ratios resulting from such experimentation may be normalized. Interfaces can be deeply buried under tens or hundreds of nm of material and still be investigated, unlike the case with photoelectron spectroscopy; furthermore, this technique can provide electronic mapping of such interfaces with micron sensitivity.

Inelastic x-ray investigation of the ferroelectric transition in SnTe

We report that the lowest energy transverse-optic phonon in metallic SnTe softens to near zero energy at the structural transition at $T_C=75 \text{~K}$ and importantly show that the energy of this mode below $T_C$ increases as the temperature decreases. Since the mode is a polar displacement this proves unambiguously that SnTe undergoes a ferroelectric displacement below $T_C$. Concentration gradients and imperfect stoichiometry in large crystals may explain why this was not seen in previous inelastic neutron scattering studies. Despite SnTe being metallic we find that the ferroelectric transition is similar to that in ferroelectric insulators, unmodified by the presence of conduction electrons: we find that (i) the damping of the polar mode is dominated by coupling to acoustic phonons rather than electron-phonon coupling (ii) the transition is almost an ideal continuous transition (iii) comparison with density functional calculations identifies the importance of dipolar-dipolar screening for understanding this behaviour.

Pressure dependence of refractive index, dielectric constants and optical phonon frequencies of indium arsenide

A pseudopotential approach has been employed so as to investigate the pressure dependence of refractive index, dielectric constants and optical phonon frequencies for InAs. At zero pressure our findings are compared to those reported in the literature and found to be generally in reasonably good agreement. The pressure dependence of all features of interest showed a monotonic behavior. The linear pressure coefficient of the refractive index and dielectric constants are calculated and reported. The transverse and longitudinal optical phonon frequencies are found to shift towards high frequencies when pressure is applied.

Anisotropic distortion and Lifshitz transition inα-Hf under pressure

In this work we report a theoretical investigation on behavior of the elastic constant ${\mathrm{C}}_{44}$ and the transverse optical phonon mode ${\mathrm{E}}_{2g}$ of $\ensuremath{\alpha}$-Hf under pressure within the density functional theory. In contrast to many other reported transition metals, the above two quantities do not show a synchronous relation as pressure increases. Below 13 GPa, an opposite shifting tendency has been observed. However, once the pressure is raised above 13 GPa, the trend is pulled back to be consistent. This anomalous behavior is figured out to be caused by the large lattice anisotropy of the $c/a$ ratio along with the elastic anisotropy. The synchronous behavior is found to be in accordance with the behavior of $c/a$ ratio with increased pressure. In our band-structure investigations the electronic topological transition has been discovered at 10 GPa, which relates to the change of $c/a$ ratio suggested by recent literature. The presence of the Van Hove singularity shown in the densities of states has been identified and regarded as the origin of the variation of ${\mathrm{C}}_{44}$ and ${\mathrm{E}}_{2g}$.

ZA-derived phonons in the Raman spectra of single-walled carbon nanotubes

We report the observation of four Raman modes in individual, aligned single-walled carbon nanotubes, with frequencies between the RBM and D modes, and above the G± modes. By studying the diameter and excitation-energy dependence, we find that these strongly dispersive and comparatively intense modes share the lowest-frequency helical phonon branch as the origin, which can be derived from the out-of-plane acoustic (ZA) phonon branch of graphene. This ZA phonon is observed due to a defect-assisted, double-resonant process, similar to the D mode; its two-phonon overtones and combinations with transverse optical (TO) phonons do not require defects. Our assignment is supported by a theoretical model based on sixth-nearest neighbour tight-binding and a force-constant approach. We present a complete theoretical evaluation of the diameter and excitation-energy dependence of the ZA, 2ZA, and TO±ZA modes, which fits very well to our experimental results and previous studies of the so-called region of intermediate frequency modes.

Phononic Origins of Friction in Carbon Nanotube Oscillators.

Phononic coupling can have a significant role in friction between nanoscale surfaces. We find frictional dissipation per atom in carbon nanotube (CNT) oscillators to depend significantly on interface features such as contact area, commensurability, and by end-capping of the inner core. We perform large-scale phonon wavepacket MD simulations to study phonon coupling between a 250 nm long (10,10) outer tube and inner cores of four different geometries. Five different phonon polarizations known to have dominant roles in thermal transport are selected, and transmission coefficient plots for a range of phonon energies along with phonon scattering dynamics at specific energies are obtained. We find that the length of interface affects friction only through LA phonon scattering and has a significant nonlinear effect on total frictional force. Incommensurate contact does not always give rise to superlubricity: the net effect of two competing interaction mechanisms shown by longitudinal and transverse phonons decides the role of commensurability. Capping of the core has no effect on acoustic phonons but destroys the coherence of transverse optical phonons and creates diffusive scattering. In contrast, the twisting and radial breathing phonon modes have perfect transmission at all energies and can be deemed as the enablers of ultralow friction in CNT oscillators. Our work suggests that tuning of interface geometries can give rise to desirable friction properties in nanoscale devices.

Surface effects on the photoconducting properties of SrTiO3 thin films

We report a study of the photoconducting properties of semiconducting SrTiO3 thin films. The photoconducting spectrum shows a pronounced rise around 3.2 eV with a typical indirect gap dependence, involving a transversal optical phonon of 25 meV. While these features remain unaltered under the influence of an applied electric field in ambient conditions, in a vacuum the rest of the spectrum does not, shifting to lower energies for higher electric fields. Time dependent photoconductivity response while illumination is applied confirms the loss of efficiency of the 3.7 eV transition. At low-temperatures, the photoconducting spectrum at low-electric fields has striking similarities to the ones at room-temperature for high-electric fields. This ability to control the photoconducting response through external parameters is explained considering a model of a downward band bending generated by oxygen vacancies at the surface in concomitant with recent findings at the surface of SrTiO3.

Effects of optical phonon interaction on dynamical valley polarization in graphene

The present report is concerned with the dynamical behavior of [Formula: see text]-electronic valley states, under the interaction with transverse zone-boundary optical phonons, in graphene. It is assumed that the phonons are thermal and obey the Bose–Einstein distribution, while the [Formula: see text]-electrons are initially prepared in an experimentally realizable particular valley state. In our study, we take the view that such a mixture is completely described by a time-dependent density operator which is then determined, to the second-order of perturbation, from the governing Schrödinger equation. Employing the density operator so calculated, an analytical expression for the valley polarization, as a function of time, phonon frequency and temperature, is obtained. The results, accompanying with illustrative figures, reveal that the [Formula: see text]-electrons, through the elastic exchange of energy with phonons, change the valley states periodically with characteristics that strongly depend upon the temperature. It is in particular shown that as the temperature is raised, the time-averaged valley polarization approaches zero, as expected. Our calculations also show that the amplitude of valley oscillations is solely determined by the temperature and phonon frequency: an increase in the temperature enlarges the amplitudes in contrast to the phonon frequency which does the reverse. Along these lines, moreover, we demonstrate that the frequency of valley oscillations is determined by the electronic momentum deviation from the valley states, along with the phonon frequency.

Effects of two-mode transverse optical phonons in bulk wurtzite AlGaN on electronic mobility in AlGaN/GaN quantum wells

The two-mode property of bulk transverse optical (TO) phonons in ternary mixed crystals of wurtzite AlxGa1-xN has been investigated by introducing impurity modes in a modified random-element isodisplacement model. Based on the dielectric continuous model, the uniaxial model, and the Lei-Ting balance equation, the effects of the two-mode property on electrostatic potentials of interface optical and confined optical phonons in AlGaN/GaN quantum wells, as well as their influences on the electronic mobility (EM), are discussed by a component-dependent weight model. Our results indicate that the total EM decreases to a minimum at first and then increases slowly with x under the influences of the competitions from the eight branches of phonons. The further calculation shows that the total EM decreases with the increment of temperature in the range of 200 K < T < 400 K and reduction of well width d. As a comparison, the EM is calculated for an Al0.58Ga0.42N/GaN quantum well at room temperature, and our result is 1263.0 cm2/Vs, which is 1.44 times of the experiment value. Our result is expected since the difference between our theory and the experiment is mainly due to the neglect of interface-roughness and other secondary scattering mechanisms. Consequently, the two-mode property of bulk TO phonons in ternary mixed crystals does affect obviously on the electron transport in the quantum wells. And our component-dependent weight model could be extended to study the electric properties influenced by optical phonons in other related heterostructures.

Magnetic, optical, and electron transport properties ofn-type CeO2: Small polarons versus Anderson localization

We report magnetic susceptibility, electrical conductivity and optical absorption of ${\mathrm{Ce}}_{1\ensuremath{-}x}{M}_{x}{\mathrm{O}}_{2}$ where $M$ = Nb,Ta and $0\ensuremath{\le}x\ensuremath{\le}0.03$. The dc conductivity follows a simple thermally activated Arrhenius-type behavior in the $T=70$--700 K range with a change in slope at ${T}^{*}\ensuremath{\approx}155$ K. The high-temperature activation energy shows gradual increase from $\ensuremath{\approx}170$ to 220 meV as the dopant concentration increases. The activation energy of the low-temperature conductivity shows a broad minimum of $\ensuremath{\approx}77$ meV at $x\ensuremath{\approx}0.01$. Electron transport and localization mechanisms are analyzed in the framework of the Holstein small polaron, Anderson localization, and Jahn-Teller distortion models. The fit to the small polaron mobility is dramatically improved when, instead of the longitudinal phonons, the transverse optical phonons are considered in the phonon-assisted electron transport. This serves as an indirect evidence of a strong $4{f}^{1}$ orbital interaction with the oxygen ligands, similar to the case of ${\mathrm{PrO}}_{2}$. Based on comparison of the experimental data to the models, it is proposed that the defect-induced random electric fields make the dominant contribution to the electron localization in donor-doped ceria.

Raman scattering from GaAs/AlGaAs multiple quantum well structures grown by two-step molecular beam epitaxy

We report polarized and spatially resolved Raman scattering from GaAs/Al0.3Ga0.7As multiple quantum well (MQW) structures grown by a two-temperature step molecular beam epitaxy method, in which an initial GaAs buffer layer is deposited at low temperature and a subsequent GaAs layer is deposited at high temperature. Polarized Raman spectra revealed several transverse optical (TO) and longitudinal optical (LO) phonons, i.e., GaAs, GaAs-like, and AlAs-like TO and LO phonons. The Raman peaks related to the AlGaAs barriers were significantly enhanced under resonant excitation near the band gap energy of AlGaAs, In addition, resonant Raman scattering from the side edges of the samples exhibited symmetry-forbidden GaAs-like and AlAs-like LO phonons. To investigate stress and strain evolutions in the GaAs buffer layers, spatially resolved Raman measurements were performed along the growth direction, obtained via the side edges of the samples. Interestingly, Raman maps across the GaAs layers showed that the usually doubly degenerate GaAs TO phonons were split into two distinct phonons. Depending on the two-step growth temperatures, the peak energies of the TO phonons evolved differently along the growth direction. The built-in stress and strain depth-profiles in the GaAs buffer layers were estimated using a biaxial assumption.

氧化镁单晶在太赫兹波段的介电特性

The dielectric properties of single-crystal MgO were studied by terahertz time-domain spectroscopy in the frequency range extending from 0.5 to 9.5 THz. The refractive index, power absorption, and the complex dielectric function were extracted from experimental data. At low terahertz frequencies band (2 THz), the absorption coefficient was extremely low and increased with increasing frequency. Meanwhile the corresponding refractive index had low dispersion, increasing from 3.12 to 3.15. Two prominent resonances were observed at 3.16 THz and 8.11 THz and were well-described by a multiple-oscillator model through theoretical fitting. The interaction of incident photons and the transverse optical (TO) phonons in the crystal were studied and it gives good evidence to further applications in developing broadband terahertz components and terahertz spectroscopy.

Nonlinear optical coefficients of wurtzite-typeα-GaN determined by Raman spectroscopy

Raman scattering on phonons in GaN with wurtzite structure ($\ensuremath{\alpha}$-GaN) is used to determine the coefficients of second-harmonic generation (SHG) and the linear electro-optic effect (LEO) in the region of optical transparency for excitations below the band gap. For wurtzite-type crystals, the symmetry requires that three SHG coefficients ${d}_{31}, {d}_{33}$, and ${d}_{24}$ and three LEO coefficients ${r}_{31}, {r}_{33}$, and ${r}_{42}$ be considered. In this work, the dependence of these SHG and LEO coefficients on the Raman scattering intensities of the polar transverse optical (TO) and longitudinal optical (LO) phonon modes in wurtzite-type crystals and their corresponding Faust-Henry coefficients is derived. In the case of GaN, the obtained SHG coefficients are $\left|{d}_{31}\right|$ = 2.46 pm/V, $\left|{d}_{33}\right|$ = 3.97 pm/V, and $\left|{d}_{24}\right|$ = 2.48 pm/V, which agree well with results measured by other methods. Also, all three LEO coefficients of GaN have been determined: $\left|{r}_{13}^{S}\right|$ = 0.72 pm/V, $\left|{r}_{33}^{S}\right|$ = 1.31 pm/V, and $\left|{r}_{42}^{S}\right|$ = 0.38 pm/V. Contrary to previous reports, our results indicate an important contribution of the ionic lattice displacements to the linear electro-optic effect. The ratios of the three SHG coefficients or the three LEO coefficients, which correspond to different nonlinear susceptibility tensor elements, depend on the relative intensities of the polar TO and LO phonon modes connected with different Raman tensor elements.

Effects of crystal anisotropy on optical phonon resonances in midinfrared second harmonic response of SiC

We study the effects of crystal anisotropy on optical phonon resonances in the second harmonic generation (SHG) from silicon carbide (SiC) in its Reststrahl region. By comparing experiments and simulations for isotropic 3C-SiC and anisotropic 4H-SiC in two crystal cuts, we identify several pronounced effects in the nonlinear response which arise solely from the crystal anisotropy. Specifically, we demonstrate that the axial and planar transverse optical phonon resonances selectively and exclusively appear in the corresponding tensor elements of the nonlinear susceptibility, enabling observation of an intense SHG peak originating from a weak phonon mode due to zone-folding along the c-axis of 4H-SiC. Similarly, we identify an anisotropy factor $\zeta \equiv \epsilon_\perp/\epsilon_\parallel$ responsible for a steep enhancement of the transmitted fundamental fields at the axial longitudinal optical phonon frequency, resulting in strongly enhanced SHG. We develop a general recipe to extract all these features that is directly applicable to all wurtzite-structure polar dielectrics, where a very similar behavior is expected. Our model study illustrates the opportunities for utilizing the crystal anisotropy for selectively enhancing nonlinear-optical effects in polar dielectrics, which could potentially be extended to built-in anisotropy in artificially designed hybrid materials.

Resonant bonding driven giant phonon anharmonicity and low thermal conductivity of phosphorene

Two-dimensional (2D) phosphorene, which possesses fascinating physical and chemical properties distinctively different from other 2D materials, calls for a fundamental understanding of thermal transport properties for its rapidly growing applications in nano- and optoelectronics and thermoelectrics. However, even the basic phonon property, for example, the exact value of the lattice thermal conductivity ($\ensuremath{\kappa}$) of phosphorene reported in the literature, can differ unacceptably by one order of magnitude. More importantly, the fundamental physics underlying its unique properties such as strong phonon anharmonicity and unusual anisotropy remains largely unknown. In this paper, based on the analysis of electronic structure and lattice dynamics from first principles, we report that the giant phonon anharmonicity in phosphorene is associated with the soft transverse optical (TO) phonon modes and arises from the long-range interactions driven by the orbital governed resonant bonding. We also provide a microscopic picture connecting the anisotropic and low $\ensuremath{\kappa}$ of phosphorene to the giant directional phonon anharmonicity and long-range interactions, which are further traced back to the asymmetric resonant orbital occupations of electrons and characteristics of the hinge-like structure. The unambiguously low $\ensuremath{\kappa}$ of phosphorene obtained consistently by three independent ab initio methods confirms the phonon anharmonicity to a large extent and is expected to end the confusing huge deviations in previous studies. This work further pinpoints the necessity of including van der Waals interactions to accurately describe the interatomic interactions in phosphorene. We propose in 2D material that resonant bonding leads to low thermal conductivity, despite that it is originally found in three-dimensional (3D) thermoelectric and phase-change materials. Our study offers insights into phonon transport from the view of orbital states, which would be of great significance to the design of emerging phosphorene-based nanodevices.

Laser Structuring for Control of Coupling Between THz Light and Phonon Modes

Modification of surface and volume of sapphire is shown to affect reflected and transmitted light at THz spectral range. Structural modifications were made using ultra-short 230 fs laser pulses at 1030 nm and 257.5 nm wavelengths forming surface ripples of ~250 nm and 60 nm period, respectively. Softening of the transverse optical phonon TO1 mode due to disorder was the most pronounced in reflection from laser ablated surface. It is shown that sub-surface periodic patterns of laser damage sites have also modified reflection spectrum due to coupling of THz radiation with phonons. Application potential of laser structuring and disordering for phononic engineering is discussed.

Strained HgTe plates grown on SrTiO3 investigated by micro-Raman mapping

HgTe plates have been grown by vapor phase epitaxy on (111) SrTiO3 substrates with a preferred orientation in the (111) crystalline direction, as indicated by x-ray diffraction. Examination of the plates using the micro-Raman mapping shows that the HgTe plates exhibit unusual strain patterns: the Raman peaks from the transverse-optical and longitudinal-optical phonons for the thicker (central) parts of the HgTe plates are at the same frequency as that of the bulk HgTe, while the Raman peaks for the thinner parts of the HgTe plates, which surround the thicker parts and can hardly be seen in a scanning electron microscope, are significantly larger in frequency. The full width at half maximum is smaller in the thinner areas than in the thicker parts. Theoretical analysis shows that the HgTe plates on SrTiO3 substrates suffer from compressive stress, and this may be sufficient to induce the three-dimensional topological insulator behavior in HgTe.

(Al, Er) co-doped ZnO nanoparticles for photodegradation of rhodamine blue

Pure and co-doped (Al, Er) ZnO nanoparticles (NPs) have been synthesized by hydrothermal method using (Zn, Er and Al) nitrates. X-ray diffraction patterns reveal the formation of single phase of ZnO wurtzite-type structure. The crystallite size for pure ZnO is in the order of 26.5 nm which decreases up to the range 14.2–22.0 nm after (Al, Er) co-doping. SEM micrographs show that the specimen is composed of regular spherical particles in the nanoscale regime with homogeneous size distribution and high tendency to agglomeration. FTIR spectra exhibit absorption lines located at wavenumbers corresponding to vibration modes between the constituent atoms. Raman spectra recorded under excitation (λ exc = 632.8 nm) reveal peaks related to modes of transverse and longitudinal optical phonons of the wurtzite ZnO structure. The energy band gap E g of ZnO:(Al, Er) NPs ranges in 3.264–3.251 eV. The photocatalytic activity of pure and co-doped (Al, Er) ZnO NPs was evaluated by the photodegradation of rhodamine blue under an irradiation of wavelength 554 nm. It is found that a photodegradation rate above 90 % could be achieved for a period of time of 40 min for pure ZnO and 120 min for (Al, Er) co-doped ZnO. A photodegradation mechanism is proposed.

Optical and morphological characteristics of zinc selenide-zinc sulfide solid solution crystals

Experiments were performed to study the effect of point defects on the optical and morphological characteristics of zinc selenide-zinc sulfide ZnSe-ZnS (ZnSexS(1-x)) solid solution crystals grown under terrestrial (1-g) condition. We used the composition ZnSe0.91S0.09 and ZnSe0.73S0.27 for the detailed studies. Crystals of 8 mm and 12 mm diameter were grown using physical vapor transport methods. These crystals did not exhibit gross defects such as voids, bubbles or precipitates. The photoluminescence spectra indicated strong red emission for the 610–630-nm wavelength region in both crystals. This emission could be explained on the basis of high energy irradiation of Zn selenide. For the ZnSe0.73S0.27 crystal, absorption starts at a lower wavelength range (300 nm) when compared to the ZnSe0.91S0.09 crystal presumably due to the much higher bandgap of ZnS than that of ZnSe. Sharp peaks at 451 and 455 nm were observed for both samples corresponding to the band edge transitions, followed by a strong peak at 632 nm. These results were consistent with the observations based on Raman spectroscopy studies. Under 532-nm laser illumination both transverse optical (TO) and longitudinal optical (LO) phonon peaks appeared at Raman shifts of 220 and 280 Δcm−1, respectively. These peaks are similar to those observed for pure ZnSe Raman spectra for which TO and LO occur at 200 and 250 Δcm−1 for the x-axis (first order) polarization.