Plasmon-phonon Modes Research Articles

Multivalued dispersion equation for coupling between plasmons and surface optical phonons in a graphene/polar-substrate system

Dispersion equations are a common paradigm of collective excitation physics. However, in some systems, dispersion equations contain multivalued functions and their solutions are ambiguous. As an example, we consider graphene on a polar substrate where Dirac plasmons are coupled with surface optical phonons. The dispersion equation for this system contains square-root singularity. Using the initial value problem resolves this uncertainty and gives a unique solution. Particularly, we found that the lower plasmon-phonon mode, which in terms of dispersion can have a good quality factor, is almost absent in excitation spectra. The physical reason and experimental evidence of the mode collapse are discussed. Published by the American Physical Society 2024

Thermally tunable phonon–plasmon polariton modes at hexagonal boron nitride (hBN) and indium antimonide (InSb) interfaces

Abstract This work examines the propagation of thermally tunable phonon–plasmon modes at the interfaces of hexagonal boron nitride (hBN) and isotropic indium antimonide (InSb). Both theoretical modeling and numerical simulations are carried out to analyze the effect of temperature on surface wave behavior. hBN is realized as a polar material via the Lorentzian model, while InSb ismodeled as a temperature-sensitive material (TSM) in the framework of Drude’s model. The possible plasmon–phonon polaritonic interactionsarestudied for the TSM–elliptic type interface and TSM– hyperbolic type interface. It is reported that by varying the temperature, the surface modes can be tuned for the lower and upper Reststrahlen (RS) bands of hBN. The dispersion curve, effective mode index, propagation length, and phase speed are computed for each case under different temperatures. It is concluded that the hBN–InSb-based phonon–plasmon polariton modes are actively tuned by changing the external temperature in the lower and upper RS bands. Surface waves propagating across the interface can be modulated from the terahertz (THz) region to the infrared (IR)region by changing the temperature of InSb. This study will help researchers to design innovative thermo-optical sensors, plasmonic platforms, detectors, and surface waveguides in the THz and IR regions.

Detection of an unintentional Si doping gradient in site-controlled GaN nanowires grown using a Si3N4 mask by spatially resolved cathodoluminescence and Raman spectroscopy

Highly uniform arrays of site-controlled GaN nanowires are synthesized by selective area growth using a Si3N4 mask and molecular beam epitaxy. Systematic modulation of the emission along the nanowire axis is observed in spectrally resolved cathodoluminescence linescans. We show that this intensity change is an indicator of unintentional Si incorporation during growth resulting from the interaction between the impinging Ga atoms and the mask material. The gradual reduction of the cathodoluminescence intensity along the nanowire highlights the important role of the growth geometry within the synthesis reactor, with shadowing from the elongating nanowires inhibiting the reaction with the mask. This gradient in Si doping is confirmed by the quenching of the longitudinal optical phonon line measured in Raman spectra along the nanowire axis. The corresponding carrier density is derived from the frequency of the coupled phonon–plasmon mode. The spectroscopic identification of inversion domain boundaries in the majority of the nanowires is also attributed to the Si incorporation. From temperature dependent cathodoluminescence experiments, we derive the activation energy for excitons bound to these defects.

Temperature dependence of the anisotropy of the infrared dielectric properties and phonon-plasmon coupling in n-doped 4H-SiC

Polarized infrared reflectivity spectroscopy is used to measure the temperature dependence of the anisotropy of the infrared dielectric properties and the coupling between phonon and plasmon modes in n-doped 4H-SiC. The advantage of polarized infrared spectroscopy over the commonly used Raman spectroscopy is that it enables dielectric, plasmonic, and transport properties to be probed along and perpendicular to the c-axis, which is impossible with Raman spectroscopy due to its selection rules. In addition, the infrared spectrum, comparatively rare for Raman spectroscopy, can be described at high temperatures with simple classical theory, providing more precise information on the properties of the material being measured. Analysis of the s- and p-polarized infrared reflectivity spectra of an n-doped 4H-SiC substrate shows that the strength and damping of the oscillators, the response of the bound electrons to an infrared excitation, the effective ion mass, and the transverse frequency and anharmonicity of the phonons of n-doped 4H-SiC are temperature-sensitive and strongly anisotropic. It also shows that the plasmonic properties of n-doped 4H-SiC, namely the relaxation time and the collective oscillation frequency of free electrons, are also highly anisotropic and, due to the long relaxation time of free electrons in the direction parallel to the c-axis, only the axial longitudinal phonon-plasmon modes split into low-frequency and high-frequency modes at temperatures above 700 K.

Comparison between optical and electrophysical data on hole concentration in zinc doped p-GaAs

Optical and electrophysical properties of Cz-grown zinc doped p-GaAs samples have been investigated. Middle-infrared reflection spectra of ten p-GaAs samples have been obtained. Galvanomagnetic Van der Pau measurements have been made on these samples also, and the values of resistivity and Hall coefficient have been calculated. All experiments have been carried out at room temperature.Reflection spectra have been processed by Kramers–Kronig relations. The spectral dependences of real and imaginary parts of complex dielectric permittivity have been obtained and loss function has been calculated. The value of characteristic wave number corresponding to high-frequency plasmon-phonon mode has been determined by loss function maximum position.The theoretical calculations have been made, and the dependence has been obtained which gave the possibility to determine heavy hole concentration value at T = 295K by the value of characteristic wave number. Then by comparison of optical and Hall data the values of light hole mobility to heavy hole mobility ratio have been determined. This mobility ratio has been shown to be equal to (1.9–2.8) which is considerably less, than predicted theoretical value based on assumption that both light and heavy holes are scattered by optical phonons. It has been suggested that scattering mechanisms of light and heavy holes might be quite different.

Comparison between optical and electrical data on hole concentration in zinc-doped p-GaAs

The optical and electrical properties of zinc-doped Cz p-GaAs have been studied. Reflection spectra of ten p-GaAs specimens have been taken in the mid-IR region. Van der Pau galvanomagnetic, electrical resistivity and Hall coefficient measurements have been carried out for the same specimens (all the measurements were carried out at room temperature). The reflection spectra have been processed using the Kramers–Kronig relations, spectral dependences of the real and imaginary parts of the complex dielectric permeability have been calculated and loss function curves have been plotted. The loss function maximum position has been used to calculate the characteristic wavenumber corresponding to the high-frequency plasmon-phonon mode frequency. Theoretical calculations have been conducted and a calibration curve has been built up for determining heavy hole concentration in p-GaAs at T = 295 K based on known characteristic wavenumber. Further matching of the optical and Hall data has been used for determining the light to heavy hole mobility ratio. This ratio proves to be in the 1.9–2.8 range which is far lower as compared with theoretical predictions in the assumption of the same scattering mechanism for light and heavy holes (at optical phonons). It has been hypothesized that the scattering mechanisms for light and heavy holes differ.

Influence of the quantum well dielectric permittivity on the two-dimensional plasmon-phonon

The work is devoted to a theoretical study of the effect of polarizability associated with quantum well lattice vibrations and filled electron bands on the properties of two-dimensional plasmon-phonons in InAs/AlSb and CdHgTe/CdTe single quantum well (QW) heterostructures. The spectra for the considered excitations are obtained without taking into account the spatial dispersion and with it taken into account in the framework of random phase approximation (RPA). The frequency dependence of the plasmon-phonon absorption coefficient is calculated. It is shown that taking into account the contribution of QW phonons and electrons of filled bands to the polarizability leads to the conclusion that there is a maximum frequency of plasmon-phonons and to the conclusion that the existence of plasmon-phonon modes requires that the electron mobility exceed a certain minimum value.

Определение концентрации электронов проводимости в монокриcталлических образцах n-GaSb по спектрам отражения в дальней инфракрасной области при T=295 K

A method is proposed for separately determining the concentrations of "light" and "heavy" electrons in n-GaSb. It is based on the analysis of reflection spectra in the far infrared region, taking into account the plasmon-phonon coupling. Calibration curves have been calculated that allow one to determine the concentrations of "light" and "heavy" electrons in GaSb using the frequency of high-energy coupled plasmon-phonon mode. For a series of n-GaSb samples the reflection spectra were measured and the concentrations of "light" and "heavy" electrons were determined at room temperature. Electrophysical Van der Paw measurements have been performed on the same samples at room temperature. By comparing the optical and Hall data, the ratios of the mobilities of "light" and "heavy" electrons (parameter b) were determined. This method of determining the value of the parameter b is used for the first time.

Creation of GaMnAs ferromagnetic semiconductor by combined laser method

GaMnAs layers made by pulsed laser deposition in vacuum on semi-insulating GaAs substrates have been studied. During the creation of the structures, the substrate temperature varied in the range from 200 to 350oC, and the thickness of the layers was ~ 50 nm. Samples of the manufactured structures were annealed by pulses of an excimer KrF-laser. The analysis of the Raman scattering spectra of annealed samples using their approximation by Lorentz functions showed, in addition to peaks in the LO- and TO-GaAs modes, the presence of a coupled phonon-plasmon mode. As a result of annealing, a significant increase in the hole conductivity of the layers is observed (the resistance decreases from Rs~107-109 Ω to Rs~ 900-3000 Ω). The type of magnetic field dependence of magnetization at room temperature changes significantly: there is a transition from a nonlinear characteristic with a hysteresis loop for the initial sample (appearing due to the presence of MnAs compound inclusions with a Curie temperature above room temperature) to a linear behavior for the annealed sample. The study of galvanomagnetic properties at temperatures from 10 to 150 K shows the existence of ferromagnetism in GaMnAs layers with a Curie temperature reaching 90 K. The observed effects allow us to conclude that the applied pulsed laser action leads to modification (dissolution) of MnAs inclusions, electrical activation of Mn and, as a consequence, to the formation of a single-phase ferromagnetic semiconductor GaMnAs. Keywords:: pulsed laser deposition, pulsed laser annealing, ferromagnetic semiconductor.

High-performance hyperbolic phonon-plasmon modes at mid-infrared frequencies in grounded graphene-hBN heterostructures: an analytical approach

High-performance hyperbolic phonon-plasmon modes at mid-infrared frequencies in grounded graphene-hBN heterostructures: an analytical approach

High performance mid infrared temperature sensor based on resonance excitation of hybrid Tamm surface states

Theoretical design of mid infrared temperature sensor based on the resonance excitation of hybrid Tamm surface state (HTSS) is presented. An excellent sensing performance is attained by the coupling of graphene plasmon polaritons and hexagonal boron nitride (hBN) phonon polaritons that forms hybrid polariton modes at the interface. In one dimensional ternary photonic crystal (1D TPC), terminated by hBN layer sandwiched between graphene monolayers, the coupling between Bloch surface waves and hybrid polariton modes leads to the formation of HTSS or Tamm plasmon-phonon modes. Employing Kretschmann configuration coupling mechanism, the excitation of the HTSSs at the truncated interface is manifested for transverse magnetic (TM) polarized wave. The structure supports excited HTSS between 7.14μm to 10.34μm that allows astounding control over the sensing ability by varying the number of unit cells and the resonant angles. The sensor has a high detection accuracy of 1010 at room temperature (300K). It is proved that for 50 unit cells and at 49° angle, a high quality factor of 372176, detection limit of 5K and sensitivity of 0.20pm/K is attained with operating range between 280K to 380K. The operating range is widened from 300K to 900K by changing the resonant angle from 49° to 53°. Further, for 30 unit cells and at 53° angle, the temperature sensing ability of the sensor extends from 100K to 900K with a sensitivity of 0.80pm/K and detection limit of 54.16K.

Intermediate interaction theory of the Dirac fermions with plasmon-surface LO-phonon excitations in the monolayer graphene on polar substrate

A model is suggested for the intermediate interaction of Dirac fermions with coupled plasmon-phonon modes in monolayer graphene on a polar substrate. We introduce a diagonalization procedure based on Lee-Low-Pines transformations to study the properties of both hole and electron polarons. Exact expressions are obtained for the energies of Dirac fermions taking into account their scattering by collective excitations. It is analytically shown that the Fermi velocity renormalizations for electrons and holes have the same values and depend only on the strength of the coupling between Dirac fermions and elementary excitations in the heterostructure under consideration. The obtained results can be used in order to control the electronic properties, which can provide interesting characteristics of optoelectronic devices.

Plasmon-Phonon Coupling in Electrostatically Gated β-Ga2O3 Films with Mobility Exceeding 200 cm2 V-1 s-1.

Monoclinic β-Ga2O3, an ultra-wide bandgap semiconductor, has seen enormous activity in recent years. However, the fundamental study of the plasmon-phonon coupling that dictates electron transport properties has not been possible due to the difficulty in achieving higher carrier density (without introducing chemical disorder). Here, we report a highly reversible, electrostatic doping of β-Ga2O3 films with tunable carrier densities using ion-gel-gated electric double-layer transistor configuration. Combining temperature-dependent Hall effect measurements, transport modeling, and comprehensive mobility calculations using ab initio based electron-phonon scattering rates, we demonstrate an increase in the room-temperature mobility to 201 cm2 V-1 s-1 followed by a surprising decrease with an increasing carrier density due to the plasmon-phonon coupling. The modeling and experimental data further reveal an important "antiscreening" (of electron-phonon interaction) effect arising from dynamic screening from the hybrid plasmon-phonon modes. Our calculations show that a significantly higher room-temperature mobility of 300 cm2 V-1 s-1 is possible if high electron densities (>1020 cm-3) with plasmon energies surpassing the highest energy LO mode can be realized. As Ga2O3 and other polar semiconductors play an important role in several device applications, the fundamental understanding of the plasmon-phonon coupling can lead to the enhancement of mobility by harnessing the dynamic screening of the electron-phonon interactions.

Electron heating in GaN/AlGaN quantum well in a longitudinal electric field

The heating of electrons under longitudinal optical phonon scattering in a triangular GaN/AlGaN quantum well was studied theoretically. The energy loss rate of electrons was calculated in consideration of the dynamical screening and the hot phonon effect. The dependence of the electron temperature on the longitudinal electric field was calculated. The integral terahertz emission of hot two-dimensional electrons was simulated. The role of coupled plasmon-phonon mode scattering in the GaN/AlGaN quantum well was discussed.

Scrutinizing the Debye plasma model: Rydberg excitons unravel the properties of low-density plasmas in semiconductors

For low-density plasmas, the classical limit described by the Debye-H\"uckel theory is still considered as an appropriate description even though a clear experimental proof of this paradigm is lacking due to the problems in determining the plasma-induced shift of single-particle energies in atomic systems. We show that Rydberg excitons in states with a high principal quantum number are highly sensitive probes for their surrounding making it possible to unravel accurately the basic properties of low-density nondegenerate electron-hole plasmas. To this end, we accurately measure the parameters of Rydberg excitons such as energies and linewidths in absorption spectra of bulk cuprous oxide crystals in which a tailored electron-hole plasma has been generated optically. Since from the absorption spectra exciton energies, as well as the shift of the single-particle energies given by the band edge, can be directly derived, the measurements allow us to determine the plasma density and temperature independently, which has been a notoriously hard problem in semiconductor physics. Our analysis shows unambiguously that the impact of the plasma cannot be described by the classical Debye model, but requires a quantum many-body theory, not only for the semiconductor plasma investigated here, but in general. Furthermore, it reveals an exciton scattering mechanism with coupled plasmon-phonon modes becoming important even at very low plasma densities.

Scattering of Rydberg excitons by phonon-plasmon modes

We propose a new scattering mechanism of Rydberg excitons, i.e., those with high principal quantum numbers, namely scattering by coupled LO phonon-plasmon modes, which becomes possible due to small differences in energies of the states due to different quantum defects. Already in very low-density electron–hole plasmas these provide a substantial contribution to the excitonic linewidth. This effect should allow determining plasma densities by a simple line shape analysis. Whenever one expects that low-density electron–hole plasma is present the plasmon induced broadening is of high significance and must be taken into account in the interpretation.

Exact dispersion relations for the hybrid plasmon-phonon modes in graphene on dielectric substrates with polar optical phonons.

Intrinsic optical phonons and extrinsic polar optical phonons (POPs) strongly affect the graphene surface plasmons. Specifically, extraneous POPs present on the surface of an underlying substrate change the behavior of the graphene's surface plasmons sharply due to the plasmon-phonon hybridization. Here, we report modeling of exact dispersion relations for graphene's surface plasmons affected by intrinsic optical phonons and extrinsic POPs of the surface of polar dielectric substrates with one or more vibrational frequencies. In doing so, we have employed random phase approximation with modified two-dimensional polarizability (2D-Π0). The adapted Π0 addresses limitations of the previously derived plasmons dispersion, obtained using classical two-dimensional polarizability. We show the new model overcomes the unsatisfying behavior of the plasmonic dispersion relation obtained by the classical 2D-Π0 at high-wavenumbers and its inability to indicate the starting point of the mode damping. Our new simple model eliminates the complexity of the other presented models in describing the surface plasmons' behavior, specifically at high wavenumbers. Besides, we use our dispersion model to learn about the plasmon content of the hybrid modes, which is a vital value to compute output current in plasmonic graphene-based devices. The coupled-mode lifetime due to the hybrid nature depends on both plasmon and phonon lifetimes. We capture this value here. There is an excellent agreement between our theoretical results and the experimental data reported earlier. They pave the way for the exact modeling of graphene plasmons on common polar substrates and bring in the closeness of the theoretical approaches and experimental results.

Imaging Strongly Coupled Plasmon–Phonon Modes in Mid-Infrared Double Antennas

Strong-coupling effects alter the polaritonic states of metal–dielectric nanostructures and, therefore, can be used to tailor the response of infrared (IR) photonic elements. We report on the devel...

Investigation of THz Radiation from Longitudinal Optical Phonon- Plasmon Coupling in p-i-n Diodes

Background: Terahertz radiation (THz) in infrared domain at room temperature has many applications in science and technology, especially in the technology of analyzing and processing image. This paper introduces a relatively simple method to investigate the Terahertz radiation from the coupling of Longitudinal Optical (LO) phonon and coherent plasmon in p-i-n diode structure. The frequency spectra are found from the Fast Fourier Transform (FFT) of the voltage between two neighboring points in the insulating region of this diode. Numerical calculations have been applied for GaAs semiconductor device with the photo-excited carrier density ranging from 17 1.0×10 cm-3 to 18 3.0×10 cm-3 and the insulating layer size of 500 nm. Methods: In order to study of the coupling of LO phonon in p-i-n diode based on the EMC simulations, the equation of density vibration is solved simultaneously with the simulation of carrier dynamics, this is performed with spatial resolution of 1A° and time resolution of 0.20 fs . We solve the Poisson’s equation to derive the potentials along the x-axis in both cases with and without taking into account the coupling. The frequency spectrum derived from the FFT of the voltage of two layers separated by a distance 10 nm in insulating layer (i). Results: The frequency spectrum derived from the Fourier transform of the voltage between two neighboring points with and without LO phonon–plasmon coupling is shown. We can easily observe the existence of the modes which are close to the frequency values of bulk semiconductor. It should be noted that, our calculations are reasonable agreement with experiments measured by the Ibanez et al in Phys. Rev. B 69 (7), 075314 (2004). Conclusion: In this paper, we present a relatively simple approach to investigate the THz radiation from the coupling of LO phonon-plasmon in p-i-n diode structure by taking the FFT of the voltage of two neighboring points in insulating semiconductor region. The voltage is calculated through the electric potentials which relate to the charge density via Poisson’s equation. Numerical calculations have been performed for GaAs semiconductor device with carrier density ranging from 17 1.0×10 cm-3 to 18 3.0×10 cm-3. Our simulations calculations show that with appropriate photoexcited carrier density, two strong coupling LO phonon-plasmon coherent modes are appear.

Revisiting longitudinal optical modes in materials with plasmon and plasmon-like absorptions – SrTiO3 and β-Ga2O3

We investigate exemplary the longitudinal optical (LO) mode order in compounds with a plasmon or plasmon-like phonon mode and additional phonon modes. When the oscillator strength of the plasmon or plasmon-like mode is gradually increased, a reordering of the modes takes place. Since it is not possible in crystals with orthorhombic or higher symmetry that a LO mode crosses a transverse optical (TO) mode's position, this reordering takes place via mode hybridization. During this mode hybridization, the plasmon or plasmon-like LO mode gradually becomes the originally higher situated LO mode while the latter morphs into the former. As a consequence, inner (LO-TO) and an outer (TO-LO) mode pairs are formed. These insights can be readily transferred to other semiconductors or many mode materials with reststrahlen bands, as long as their dielectric tensor can be (partly) diagonalized, and allow easily correct mode assignments.