Transverse Optical Phonon Research Articles

Study of the band-gap energy of radiation-damaged silicon

The transmission of silicon crystals irradiated by 24 GeV/c protons and reactor neutrons has been measured for photon energies, E γ , between 0.95 and 1.3 eV. From the transmission data the absorption coefficient α is calculated, and from α(E γ ) the fluence dependence of the band-gap energy, E gap, and the energy of transverse optical phonons, E ph, determined. It is found that within the experimental uncertainties of about 1 meV neither E gap nor E ph depend on fluence up to the maximum fluence of 1 × 1017 cm−2 of the measurements. The value of E gap agrees within about 1 meV with the generally accepted value, if an exciton-binding energy of 15 meV is assumed. A similar agreement is found for E ph. For the extraction of E gap and E ph the second derivative of smoothed with a Gaussian kernel has been used.

Theory of superconductivity in doped quantum paraelectrics

Recent experiments on Nb-doped SrTiO3 have shown that the superconducting energy gap to the transition temperature ratio maintains the Bardeen–Cooper–Schrieffer (BCS) value throughout its superconducting dome. Motivated by these and related studies, we show that the Cooper pairing mediated by a single soft transverse-optical phonon is the most natural mechanism for such a superconducting dome given experimental constraints, and present the microscopic theory for this pairing mechanism. Furthermore, we show that this mechanism is consistent with the T2 resistivity in the normal state. Lastly, we discuss what physical insights SrTiO3 provides for superconductivity in other quantum paraelectrics such as KTaO3.

Formation of epitaxial 3C-SiC layers on Si by rapid vacuum thermal processing

The results of a study of the structure and phase composition of epitaxial layers of silicon carbide (SiC) formed on silicon substrate with orientation (100) under rapid vacuum thermal processing are presented. Planar-view transmission electron microscopy investigation revealed the formation of epitaxial layers of cubic polytype SiC (3C-SiC) on silicon in the process of carbidisation at 1100 °C during 30 s, using a gas mixture of propane (10 %) and argon (90 %) as a carbon source. The formation of a monocrystalline 3C-SiC with polycrystalline inclusions and twins on all possible planes {111} was found. A rather narrow band of 793 cm–1 transverse optical phonon mode SiC on Raman spectra confirms the formation of a cubic polytype SiC. It is noted that the presence of a 180 cm–1 spectral line and a 793 cm–1 half-width band on Raman spectra indicate the presence of deformation defects in SiC.

Anharmonic phonon coupling and decay of optical phonons in polycrystalline CdSe thin films

The lifetime of longitudinal optical (LO) phonon is a key parameter that significantly affects the performance of semiconductor optoelectronic devices. Herein, in situ temperature-dependent resonance Raman scattering experiment has been performed to study the phonon anharmonicity in sputter-deposited CdSe thin films. Strong multiphonon scattering processes involving 1LO + TO, 2LO-TO, 2LO + TO, 2LO+ E2low and TO-E2low are well resolved and allow us to investigate the anharmonic decay of 1LO, 2LO, and 1LO + TO phonon modes. Fundamental 1LO and its overtone 2LO phonon modes asymmetrically decay into a pair of transverse optical (TO) and transverse acoustical (TA) phonon at the ‘A’ point of the Brillouin zone along Γ−A direction. With increasing temperature, enhanced anharmonic phonon coupling and phonon decay led to an almost linear decrease in the wavenumber of both modes and a nearly linear increase in their full-width half maxima. The composite 1LO + TO mode exhibited a ∼ 30% faster decay rate compared to the decay rate of the fundamental 1LO phonon mode.

Characterisation of optical phonons within epitaxial Ge2Sb2Te5/InAs(111) structures

Femto-second pump-probe and micro-Raman spectroscopy (RS) measurements have been made to identify optical phonons in Ge2Sb2Te5/InAs(111) and an InAs(111) substrate. A theory of transient stimulated Raman scattering (TSRS) incorporating the Raman tensor predicts which phonon modes may be observed in transient reflectance (R) and anisotropic reflectance (AR) pump-probe measurements, and how their amplitudes depend upon angles φ and θ that describe the orientation of the pump and probe beam electric fields within the sample plane. AR measurements of an InAs(111) substrate revealed the 6.5 THz T2 transverse optical phonon with amplitude proportional to sin(2(θ−φ)), as expected for both TSRS and the specular optical Kerr effect (SOKE), confirming that TSRS and SOKE are equivalent descriptions of the same phenomenon. The AR responses of Ge2Sb2Te5/InAs(111) revealed a single coherent optical phonon (COP) mode at about 3.4 THz with sin(2(θ−φ)) amplitude variation that confirms the T2-like character of the mode and hence the underlying cubic structure of the epilayer. This mode was also observed in the R measurement for one sample, with amplitude independent of φ and θ as predicted by TSRS theory. Both R and AR signals were heavily damped, which is attributed to dephasing of T2x, T2y and T2z modes that become non-degenerate due to structural distortions. RS measurements revealed three modes for Ge2Sb2Te5/InAs(111) and three modes for InAs(111). Taken together the TSRS and RS measurements provide rich information about optical phonons in the phase change material Ge2Sb2Te5 and the InAs(111) surface.

Large-area long-wave infrared broadband all-dielectric metasurface absorber based on markless laser direct writing lithography.

Scalable and low-cost manufacturing of broadband absorbers for use in the long-wave infrared region are of enormous importance in various applications, such as infrared thermal imaging, radiative cooling, thermal photovoltaics and infrared sensor. In recent years, a plethora of broadband absorption metasurfaces made of metal nano-resonators with plasmon resonance have been synthesized. Still, their disadvantages in terms of complex structure, production equipment, and fabrication throughput, limit their future commercial applications. Here, we propose and experimentally demonstrate a broadband large-area all-dielectric metasurface absorber comprised of silicon (Si) arrys of square resonators and a silicon nitride (Si3N4) film in the long-wave infrared region. The multiple Mie resonance modes generated in a single-size Si resonator are utilized to enhance the absorption of the Si3N4 film to achieve broadband absorption. At the same time, the transversal optical (TO) phonon resonance of Si3N4 and the Si resonator's magnetic dipole resonance are coupled to achieve a resonator size-insensitive absorption peak. The metasurface absorber prepared by using maskless laser direct writing technology displays an average absorption of 90.36% and a peak absorption of 97.55% in the infrared region of 8 to 14 µm, and still maintains an average absorption of 88.27% at a inciedent angle of 40°. The experimentally prepared 2 cm × 3 cm patterned metasurface absorber by markless laser direct writing lithography (MLDWL) exhibits spatially selective absorption and the thermal imaging of the sample shows that the maximum temperature difference of 17.3 °C can exist at the boundary.

STRUCTURAL AND OPTICAL PROPERTIES OF SiC/Si HETEROSTRUCTURES OBTAINED USING RAPID VACCUM-THERMAL CARBIDIZATION OF SILICON

TEM investigation revealed that the rapid vacuum-thermal carbidization of silicon at 1100C leads to the formation of cubic silicon carbide (SiC) layers. The band of the IR transmission spectrum at 798 cm–1 corresponding to the stretching vibration of Si-C and the maximum of Raman spectrum at 793 cm–1 relating to transverse optical phonon mode of SiC confirm the formation of a layer of the cubic SiC politype. The absorption
 band of Si-O-Si (1100 cm–1) was found using the IR-spectroscopy. The dependence of the transmission coefficient on the wavenumber was determined.

Hyper‐Raman scattering study of the soft mode in relaxor ferroelectric (Ba0.8Sr0.2)0.925Bi0.05Ti0.95(Zn1/3Nb2/3)0.05O3

AbstractWe report hyper‐Raman scattering measurements of the lowest transverse optic (TO) phonon branch in the relaxor Bi0.05‐BSTZN in the paraelectric phase from 300 to 973 K. The results evidence a displacive‐like behavior from a highly damped soft mode at high temperature to an overdamped (quasi‐elastic‐like) component on cooling close to Tc. A fit with a mean field law gives a temperature T0 = 102 K significantly lower than T0 = 188 K found by dielectric measurements. Reconciling the two experiments likely deserves considering a coupled modes analysis involving a second mode at slightly higher wavenumber. This behavior is very similar to that previously observed in PMN. Considering the rather complex chemical composition of the present compound as compared with PMN, these results emphasize a universal low‐wavenumber dynamics of ferroelectric relaxors.

Infrared-active phonon modes and static dielectric constants in α-(AlxGa1−x)2O3 (0.18 ≤ x ≤ 0.54) alloys

We determine the composition dependence of the transverse and longitudinal optical infrared-active phonon modes in rhombohedral α-(AlxGa1−x)2O3 alloys by far-infrared and infrared generalized spectroscopic ellipsometry. Single-crystalline high quality undoped thin-films grown on m-plane oriented α-Al2O3 substrates with x = 0.18, 0.37, and 0.54 were investigated. A single mode behavior is observed for all phonon modes, i.e., their frequencies shift gradually between the equivalent phonon modes of the isostructural binary parent compounds. We also provide physical model line shape functions for the anisotropic dielectric functions. We use the anisotropic high-frequency dielectric constants for polarizations parallel and perpendicular to the lattice c axis measured recently by Hilfiker et al. [Appl. Phys. Lett. 119, 092103 (2021)], and we determine the anisotropic static dielectric constants using the Lyddane–Sachs–Teller relation. The static dielectric constants can be approximated by linear relationships between those of α-Ga2O3 and α-Al2O3. The optical phonon modes and static dielectric constants will become useful for device design and free charge carrier characterization using optical techniques.

Rotational g factors and Lorentz forces of molecules and solids from density functional perturbation theory

Applied magnetic fields can couple to atomic displacements via generalized Lorentz forces, which are commonly expressed as gyromagnetic $g$ factors. We develop an efficient first-principles methodology based on density-functional perturbation theory to calculate this effect in both molecules and solids to linear order in the applied field. Our methodology is based on two linear-response quantities: the macroscopic polarization response to an atomic displacement (i.e., Born effective charge tensor), and the antisymmetric part of its first real-space moment (the symmetric part corresponding to the dynamical quadrupole tensor). The latter quantity is calculated via an analytical expansion of the current induced by a long-wavelength phonon perturbation, and compared to numerical derivatives of finite-wavevector calculations. We validate our methodology in finite systems by computing the gyromagnetic $g$ factor of several simple molecules, demonstrating excellent agreement with experiment and previous density-functional theory and quantum chemistry calculations. In addition, we demonstrate the utility of our method in extended systems by computing the energy splitting of the low-frequency transverse-optical phonon mode of cubic SrTiO$_3$ in the presence of a magnetic field.

Underdamped longitudinal soft modes in ionic crystallites-lattice and charge motions observed by ultrafast x-ray diffraction.

Soft modes in crystals are lattice vibrations with frequencies that decrease and eventually vanish as the temperature approaches a critical point, e.g., a structural change due to a phase transition. In ionic para- or ferroelectric materials, the frequency decrease is connected with a diverging electric susceptibility and, for infrared active modes, a strong increase in oscillator strength. The traditional picture describes soft modes as overdamped transverse optical phonons of a hybrid vibrational-electronic character. In this context, potassium dihydrogen phosphate (KH2PO4, KDP) has been studied for decades as a prototypical material with, however, inconclusive results regarding the soft modes in its para- and ferroelectric phase. There are conflicting assignments of soft-mode frequencies and damping parameters. We report the first observation of a longitudinal underdamped soft mode in paraelectric KDP. Upon impulsive femtosecond Raman excitation of coherent low-frequency phonons in the electronic ground state of KDP crystallites, transient powder diffraction patterns are recorded with femtosecond hard x-ray pulses. Electron density maps derived from the x-ray data reveal oscillatory charge relocations over interatomic distances, much larger than the sub-picometer nuclear displacements, a direct hallmark of soft-mode behavior. The strongly underdamped character of the soft mode manifests in charge oscillations persisting for more than 10 ps. The soft-mode frequency decreases from 0.55 THz at T = 295 K to 0.39 THz at T = 175 K. An analysis of the Raman excitation conditions in crystallites and the weak damping demonstrate a longitudinal character. Our results extend soft-mode physics well beyond the traditional picture and pave the way for an atomic-level characterization of soft modes.

Magnetic Control of Soft Chiral Phonons in PbTe.

PbTe crystals have a soft transverse optical phonon mode in the terahertz frequency range, which is known to efficiently decay into heat-carrying acoustic phonons, resulting in anomalously low thermal conductivity. Here, we studied this phonon via polarization-dependent terahertz spectroscopy. We observed softening of this mode with decreasing temperature, indicative of incipient ferroelectricity, which we explain through a model including strong anharmonicity with a quartic displacement term. In magnetic fields up to 25T, the phonon mode splits into two modes with opposite handedness, exhibiting circular dichroism. Their frequencies display Zeeman splitting together with an overall diamagnetic shift with increasing magnetic field. Using a group-theoretical approach, we demonstrate that these observations are the result of magnetic field-induced morphic changes in the crystal symmetries through the Lorentz force exerted on the lattice ions. Thus, our Letter reveals a novel process of controlling phonon properties in a soft ionic lattice by a strong magnetic field.

Anomalous transverse optical phonons in SnTe and PbTe

We present a study of the soft transverse optic phonon mode in SnTe in comparison to the corresponding mode in PbTe using inelastic neutron scattering and ab-initio lattice dynamical calculations. In contrast to previous reports our calculations predict that the soft mode in SnTe features a strongly asymmetric spectral weight distribution qualitatively similar to that found in PbTe. Experimentally, we find that the overall width in energy of the phonon peaks is comparable in our neutron scattering spectra for SnTe and PbTe. We observe the well-known double-peak-like signature of the TO mode in PbTe even down to $T$ = 5 K questioning its proposed origin purely based on phonon-phonon scattering. The proximity to the incipient ferroelectric transition in PbTe likely plays an important role not included in current models.

Infrared dielectric functions and Brillouin zone center phonons of α−Ga2O3 compared to α - Al2O3

We determine the anisotropic dielectric functions of rhombohedral $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ by far-infrared and infrared generalized spectroscopic ellipsometry and derive all transverse optical and longitudinal optical phonon mode frequencies and broadening parameters. We also determine the high-frequency and static dielectric constants. We perform density functional theory computations and determine the phonon dispersion for all branches in the Brillouin zone, and we derive all phonon mode parameters at the Brillouin zone center including Raman-active, infrared-active, and silent modes. Excellent agreement is obtained between our experimental and computation results as well as among all previously reported partial information from experiment and theory. We also compute the same information for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, the binary parent compound for the emerging alloy of $\ensuremath{\alpha}$-(${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{)}_{2}{\mathrm{O}}_{3}$, and use results from previous investigations [Schubert, Tiwald, and Herzinger, Phys. Rev. B 61, 8187 (2000)] to compare all properties among the two isostructural compounds. From both experimental and theoretical investigations, we compute the frequency shifts of all modes between the two compounds. Additionally, we calculate overlap parameters between phonon mode eigenvectors and discuss the possible evolution of all phonon modes into the ternary alloy system and whether modes may form single-mode or more complex mode behaviors.

Investigation of Be doped GaSb with varying hole concentrations using single magnetic field Hall measurement and Raman spectroscopy

Raman scattering results on Beryllium doped Gallium antimonide (GaSb) epi-layers with varying hole concentrations (3 × 1017 cm−3 to 5 × 1019 cm−3) are presented in this study. The hole concentrations are determined from single magnetic field Hall measurements and corrected taking into consideration two band conduction. The Raman spectra show four distinct features: Longitudinal optical (LO) phonon mode from the surface accumulation/depletion region, disorder activated forbidden transverse optical (TO) phonon mode, LO phonon coupled Plasmon (LOPC) mode and the uncoupled LO phonon mode from the bulk region. A detailed Raman line-shape analysis using deformation potential and electro-optic contribution has been carried out to reproduce the experimental results. The effect of plasmon damping on the LO phonon coupled Plasmon (LOPC) mode is discussed. Free hole concentrations are derived from the Raman line-shape analysis and compared with that from the Hall measurements.

Effects of electron-phonon intervalley scattering and band non-parabolicity on electron transport properties of high-temperature phase SnSe: An ab initio study

High-temperature phase tin selenide (β-SnSe) possesses a large power factor owing to its innately complex band structure. A detailed analysis of the electron-phonon (e-ph) intervalley scattering between the different non-parabolic valleys in β-SnSe remains to be disclosed. Using ab initio approach, the phonon-limited carrier mobility, Seebeck coefficient, and power factor in the range from 800 to 950 K were calculated. The e-ph intervalley scattering was shown to drastically increase the electron scattering rates, particularly in the processes involving acoustic or transverse-optical phonons. This scattering suppresses the mean free path of holes and electrons to less than 2 nm, which is detrimental to the power factor. As the temperature increases, the hole and electron mobilities decrease with the relations from T−2.38 to T−3.47 in different crystallographic directions, the values which drop much faster than the predictions given by the typical T−1.5 dependence, partly because of the high non-parabolicity of the band structure. This study highlights the necessity of explicitly considering the synergetic effect from the e-ph intervalley scattering and band non-parabolicity when modeling the electron transport of β-SnSe.

Theory of superconductivity due to Ngai's mechanism in lightly doped SrTiO3

We develop a theory of superconducting pairing in low-density strontium titanate due to the quadratic coupling of electron density to soft transverse optical phonons first proposed by Ngai [Phys. Rev. Lett. 32, 215 (1974)]. This leads to a static attractive potential between electrons with decay length ${l}_{\mathrm{eff}}$ that scales inversely with soft optical gap ${\ensuremath{\omega}}_{T}$. For low electron densities $n\ensuremath{\le}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, attraction between electrons is static and local in space; thus the transition temperature ${T}_{c}$ was found using known results for low-density electron gas. The ${T}_{c}(n)$ dependence for low doping was calculated and found to be in agreement with experimental data. In addition, we show that suppression of ${T}_{c}$ by hydrostatic pressure and strong increase in ${T}_{c}$ due to isotope substitution $^{16}\mathrm{O}{\ensuremath{\rightarrow}}^{18}\mathrm{O}$ observed experimentally also can be explained within our theory.

Mapping propagation of collective modes in Bi2Se3 and Bi2Te2.2Se0.8 topological insulators by near-field terahertz nanoscopy

Near-field microscopy discloses a peculiar potential to explore novel quantum state of matter at the nanoscale, providing an intriguing playground to investigate, locally, carrier dynamics or propagation of photoexcited modes as plasmons, phonons, plasmon-polaritons or phonon-polaritons. Here, we exploit a combination of hyperspectral time domain spectroscopy nano-imaging and detectorless scattering near-field optical microscopy, at multiple terahertz frequencies, to explore the rich physics of layered topological insulators as Bi2Se3 and Bi2Te2.2Se0.8, hyperbolic materials with topologically protected surface states. By mapping the near-field scattering signal from a set of thin flakes of Bi2Se3 and Bi2Te2.2Se0.8 of various thicknesses, we shed light on the nature of the collective modes dominating their optical response in the 2-3 THz range. We capture snapshots of the activation of transverse and longitudinal optical phonons and reveal the propagation of sub-diffractional hyperbolic phonon-polariton modes influenced by the Dirac plasmons arising from the topological surface states and of bulk plasmons, prospecting new research directions in plasmonics, tailored nanophotonics, spintronics and quantum technologies.

On the role of the energy loss function in the image force on a charge moving over supported graphene

We use a dielectric response theory to describe electrodynamic forces on a charged particle moving parallel to a supported two-dimensional layer. Using a Kramers–Kronig relation, we show that the image force on the particle can be expressed in terms of the energy loss function of the target materials. This enables us to analyze the stopping and the image forces on the particle on equal footing in the frequency–momentum domain encompassing all the energy loss channels in the target. Using the example of a graphene layer on a silicon carbide substrate, we show that both the image and stopping forces can be decomposed into contributions coming from two modes arising from hybridization of the sheet plasmon in doped graphene and a transverse optical phonon in the substrate.

Correlation between Contact Angle and Surface Roughness of Silicon Carbide Wafers

Two-inch diameter 6H-SiC wafers were sliced from a SiC ingot and the wafers were ground and polished using different diamond slurries (1 μm and 0.1 μm in particles size) to investigate their dependence on wetting on surface roughness (Ra) and polarity using precisely dispensed de-ionized (DI) water drops. The Ra of the Si-face (0001) SiC wafer, after grinding and polishing, was 5.6 and 1.6 nm, respectively, as measured by atomic force microscopy (AFM). For C-face (000–1) SiC wafers, the Ra was 7.2 nm after grinding and 3.3 nm after polishing. The average contact angle measurement of the SiC wafers after final polishing showed clear differences between surface polarity; the contact angle for the Si-face (0001) was ~7o greater than that for the C-face (000–1). The difference in contact angles between the Si-face (0001) and the C-face (000–1) tends to increase as the reduction of surface roughness approaches the final stage of polishing. The uniformity of Raman peak intensity in the folded transverse optical phonon band at ~780 cm−1 in scanned areas correlated well with the surface roughness measured by AFM. The contact angle measurement can be used as a convenient surface polarity and surface roughness testing technique for SiC wafers.