LO Phonon Energy Research Articles

Electron–phonon coupling and a resonant-like optical observation of a band inversion in topological crystal insulator Pb1−x Sn x Se

The optical reflectivity of n-type Pb0.865Sn0.135Se and Pb0.75Sn0.25Se solid solutions was measured in the THz spectral region energetically corresponding to optical phonon excitations and in the temperature range from 40 K to 280 K. The first solid solution exhibits an open energy gap with trivial band ordering at all temperatures, while for the second one the transition from trivial insulator to topological crystal insulator phase is expected. The analysis of Pb0.75Sn0.25Se data performed within the dynamic dielectric function formalism revealed an anomaly of resonance-like character in the temperature dependence of LO phonon frequency. The formula for LO phonon energy renormalization reproduced observed anomaly for energy gap equal to zero, the phase transition occurred at T 0 = (172 ± 2) K. This effect was absent for Pb0.865Sn0.135Se. Present results show that reflectivity measurements in the THz range in the vicinity of LO phonon frequency can be valuable experimental method for precise determining of band inversion temperature in narrow-gap topological materials.

Resonant Tunnelling and Intersubband Optical Properties of ZnO/ZnMgO Semiconductor Heterostructures: Impact of Doping and Layer Structure Variation.

ZnO-based heterostructures are up-and-coming candidates for terahertz (THz) optoelectronic devices, largely owing to their innate material attributes. The significant ZnO LO-phonon energy plays a pivotal role in mitigating thermally induced LO-phonon scattering, potentially significantly elevating the temperature performance of quantum cascade lasers (QCLs). In this work, we calculate the electronic structure and absorption of ZnO/ZnMgO multiple semiconductor quantum wells (MQWs) and the current density-voltage characteristics of nonpolar m-plane ZnO/ZnMgO double-barrier resonant tunnelling diodes (RTDs). Both MQWs and RTDs are considered here as two building blocks of a QCL. We show how the doping, Mg percentage and layer thickness affect the absorption of MQWs at room temperature. We confirm that in the high doping concentrations regime, a full quantum treatment that includes the depolarisation shift effect must be considered, as it shifts mid-infrared absorption peak energy for several tens of meV. Furthermore, we also focus on the performance of RTDs for various parameter changes and conclude that, to maximise the peak-to-valley ratio (PVR), the optimal doping density of the analysed ZnO/Zn88Mg12O double-barrier RTD should be approximately 1018 cm-3, whilst the optimal barrier thickness should be 1.3 nm, with a Mg mole fraction of ~9%.

Damping effect of longitudinal optical phonon—plasmon coupling on thermal radiation from surface micro-gratings on direct and indirect electronic transition type semiconductors

Thermal radiation properties of surface micro-Au-line and space structures on direct and indirect electronic transition-type semiconductors of n-type (n-) GaAs and GaP, respectively, are studied. The electron densities range from 0.62 to 1.0 × 1018 cm−3. The emission spectra of samples on n-GaAs wafers show peak energies significantly shifted from the longitudinal optical (LO) phonon energy due to the LO-phonon−plasmon coupling (LOPC) at 630 K, while partial decoupling is observed. The thermal emission from the sample on n-GaP is peaked at 395.9 cm−1, shifted only by 1.5 cm−1 from the LO-phonon energy, with a linewidth of 12.5 cm−1 at 630 K. The effect of LOPC on the emission from the sample on n-GaP is mostly suppressed because of the electron localization in the X-valley, suggesting an advantage of indirect transition-type semiconductors in LO-phonon resonant infrared emitters using the phonons generated via the electron energy relaxation.

Mid-infrared thermal radiation resonating with longitudinal-optical like phonon from n++-doped GaN–semi-insulating GaN grating structure

The mid-infrared emission mechanism of line-and-space structures of metallic plates on dielectric materials is substantiated using high conductive n-doped (n++-) GaN–semi-insulating (SI-) GaN microstripe structures on an SI-GaN epitaxial layer, which was veiled when using line-and-space structures of Au plates. The present structure exhibits a few thermal emission lines originating from electric dipoles resonating with the coherent longitudinal optical (LO) phonon-like lattice vibration, which are formed by the local depolarization electric field in the surface n++-GaN/SI-GaN/n++-GaN regions. The energies of the LO-phonon-like modes shift from the original LO-phonon energy of GaN to the lower energy region, which contrasts with the LO-phonon resonant emission from the microstructures on GaAs. These emission lines have another notable feature, i.e. the observed peak energies are independent of the polar emission angle for both s- and p-polarizations, unlike the emissions by surface phonon polaritons showing a significant directive nature of peak energies. The results show that each peak energy of the present emission lines is positioned at the zero-point of the real part of the electric permittivity comprising the components of the transverse optical phonon and other electric dipoles induced by the LO-like modes, excluding the target mode. The significant peak-energy shift of the LO-like phonons is applicable to materials with wide Reststrahlen bands, which contrasts with that of the nearly LO-phonon resonating feature of materials with narrow Reststrahlen bands, such as GaAs. The peak energy shift depending on the emission direction is observed for Au–GaN stripe structures. This property is ascribed to the imperfect Au/GaN interface with surface states through the theoretical analysis of the modified electric permittivity in the surface region, numerical simulation of the local electric field via finite-difference time-domain calculation, and experimental studies on a Ti–GaN structure and emission peaks originating from an LO-like phonon of the α-Al2O3 substrate.

Exciton states in metal halide perovskites under the effect of carrier-longitudinal optical phonon coupling

Exciton states are essential to comprehend the basal photoelectric properties in metal halide perovskites (MHPs) and provide reference for their future research, in which the exciton binding energy (EBE), determining the balance of the populations between excitons and free carriers, plays an important role in defining the optoelectronic utilization of MHPs. Thereby, we theoretically study the effects of bound potentials, due to the exciton coupling with the longitudinal optical (LO) phonon, between the electron and hole of the exciton on the EBE applying the variational method by using different effective potentials and two trail wavefunctions. We find that the EBE of this kind of materials is not only related to the chemical composition, but also remains inseparable from the space size, dielectric constant and LO-phonon energy, moreover, these correlations are better described by Barentzen potential. In addition, the results also show that the effects of carriers-LO-phonon coupling can explain the relationships between the EBE and exciton active range and effective Bohr radius to a certain extent, and can analyze their intrinsic correlation among these factors. These findings enable us to explain some experimental results and provide some help to understand optical electric dynamics in MHPs.

Carrier dynamics in quantum-dot tunnel-injection structures: Microscopic theory and experiment

Tunneling-injection structures are incorporated in semiconductor lasers in order to overcome the fundamental dynamical limitation due to hot carrier injection by providing a carrier transport path from a cold carrier reservoir. The tunneling process itself depends on band alignment between quantum-dot levels and the injector quantum well, especially as in these devices LO-phonon scattering is dominant. Quantum dots with their first excited state near the quantum well bottom profit the most from tunnel coupling. As inhomogeneous broadening is omnipresent in quantum dot structures, this implies that individual members of the ensemble couple differently to the injector quantum well. Quantum dots with higher energy profit less, as the phonon couples to higher, less occupied states. Likewise, if the energy difference between ground state and quantum well exceeds the LO-phonon energy, scattering becomes increasingly inefficient. Therefore, within 20–30 meV, we find quantum dots that benefit substantially different from the tunnel coupling. Furthermore, in quantum dots with increasing confinement depth, excited states become successively confined. Here, scattering gets more efficient again, as subsequent excited states reach the phonon resonance with the quantum well bottom. Our results provide guidelines for the optimization of tunnel-injection lasers. Theoretical results for electronic state calculations in connection with carrier–phonon and carrier–carrier scattering are compared to the experimental results of the temporal gain recovery after a short pulse perturbation.

Cyclotron-phonon resonance power absorption in free standing nanostructure of transparent conducting oxides

A theory of cyclotron-phonon resonance power absorption (CPRPA) in a free-standing nanostructure (FSNS) of transparent conducting oxides (TCO) is presented. An analytical expression for optical power absorption is obtained based on quantum mechanical perturbation technique for the case when electrons are scattered by bulk longitudinal polar optical phonons. The optical power absorption spectrum consists of a series of peaks due to electron transition between Landau levels with simultaneous absorption of photon and emission of phonon. The intensity and location of absorption peaks depends on the material parameters such as electron effective mass and LO-phonon energy. Frequency, temperature and thickness dependence of absorption power and the variation of full-width at half maximum (FWHM) of absorption peaks as a function of magnetic field, temperature, and number of Landau levels are presented. The FWHM of CPRPA peaks increases linearly with square root of magnetic field. Further, FWHM is independent of temperature and thickness of FSNS. The numerical results obtained for all TCOs confirm that CPRPA measurements would be useful in understanding optical absorption characteristics of TCOs in finite and zero magnetic fields.

Terahertz Intersubband Electroluminescence from Nonpolar m-Plane ZnO Quantum Cascade Structures

The ZnO-based heterostructures are predicted to be promising candidates for optoelectronic devices in the infrared and terahertz (THz) spectral domains owing to their intrinsic material properties. Specifically, the large ZnO LO-phonon energy reduces the thermally activated LO-phonon scattering, which is predicted to greatly improve the temperature performance of THz quantum cascade lasers. However, to date, no experimental observation of intersubband emission from ZnO optoelectronic devices has been reported. Here, we report the observation of THz intersubband electroluminescence from ZnO/MgxZn1–xO quantum cascade structures grown on a nonpolar m-plane ZnO substrate up to room temperature. The electroluminescence peak shows a line width of ∼20 meV at a center frequency of ∼8.5 THz at 110 K, which is not accessible for GaAs-based quantum cascade structures because of the reststrahlen band absorption from 8 to 9 THz. This result is an important step toward the realization of ZnO-based THz quantum cascade lasers.

Exciton emissions of CdS nanowire array fabricated on Cd foil by the solvothermal method* *Project supported by the Natural Science Foundation of Henan Province, China (Grant No. 202300410304) and Key Research Project for Science and Technology of the Education Department of Henan Province, China (Grant No. 21A140021).

Nanowires have recently attracted more attention because of their low-dimensional structure, tunable optical and electrical properties for next-generation nanoscale optoelectronic devices. CdS nanowire array, which is (002)-orientation growth and approximately perpendicular to Cd foil substrate, has been fabricated by the solvothermal method. In the temperature-dependent photoluminescence, from short wavelength to long wavelength, four peaks can be ascribed to the emissions from the bandgap, the transition from the holes being bound to the donors or the electrons being bound to the acceptors, the transition from Cd interstitials to Cd vacancies, and the transition from S vacancies to the valence band, respectively. In the photoluminescence of 10 K, the emission originated from the bandgap appears in the form of multiple peaks. Two stronger peaks and five weaker peaks can be observed. The energy differences of the adjacent peaks are close to 38 meV, which is ascribed to the LO phonon energy of CdS. For the multiple peaks of bandgap emission, from low energy to high energy, the first, second, and third peaks are contributed to the third-order, second-order, and first-order phonon replica of the free exciton A, respectively; the fourth peak is originated from the free exciton A; the fifth peak is contributed to the first-order phonon replica of the excitons bound to neutral donors; the sixth and seventh peaks are originated from the excitons bound to neutral donors and the light polarization parallel to the c axis of hexagonal CdS, respectively.

Čerenkov phonon radiation and phonon structure in electron emission, electroluminescence, and current–voltage characteristics of electroformed Al–Al2O3–Ag diodes

Electroforming of metal–insulator–metal (MIM) diodes is a non-destructive dielectric breakdown that results in a conducting filament in the insulator and changes the high resistance of the as-prepared MIM diode into a low-resistance state. It is a critical step in the development of conducting states between which switching can occur in memristors or resistive switching memories. Electroforming of Al–Al2O3–Ag diodes in vacuum results in the formation of a conducting Al2O3 filament. There are Ohmic contacts at the Al–Al2O3 and Al2O3–Ag interfaces. Electronic processes develop, such as voltage-controlled negative resistance in the current–voltage (I–V) characteristics, electron emission into vacuum (EM), and electroluminescence (EL). I–V curves, EM, and EL of three electroformed Al–Al2O3–Ag diodes with anodic Al2O3 thicknesses between 36 nm and 49 nm have been measured with 20 mV resolution between voltage steps. Periodic voltage structure occurs for the three electronic processes for applied voltages between the voltage threshold for EL, ∼2 V, and the maximum applied voltage, 11 V. The voltage peak period, 60 mV to 70 mV, is the same as the range of LO phonon energies of anodic Al2O3. The proposed mechanism is Čerenkov phonon generation by ballistic electrons whose velocity exceeds the velocity of sound in Al2O3. The phonons, in turn, modify the motion and number of electrons that are emitted into vacuum, that are responsible for EL radiation, and that contribute to conduction through the diode. The occurrence of LO phonons shows that the conducting filament is Al2O3, not Ag or Al. The phenomena may provide a new method of generating terahertz radiation.

Velocity saturation in La-doped BaSnO3 thin films

BaSnO3, a high mobility perovskite oxide, is an attractive material for oxide-based electronic devices. However, in addition to low-field mobility, high-field transport properties such as the saturation velocity of carriers play a major role in determining the device performance. We report on the experimental measurement of the electron saturation velocity in La-doped BaSnO3 thin films for a range of doping densities. The predicted saturation velocities based on a simple LO-phonon emission mode, using an effective LO phonon energy of 120 meV show good agreement with the measurements of velocity saturation in La-doped BaSnO3 films. Density-dependent saturation velocity in the range of 1.8 × 107 cm/s reducing to 2 × 106 cm/s is predicted for δ-doped BaSnO3 channels with carrier densities ranging from 1013 cm−2 to 2 × 1014 cm−2, respectively. These results are expected to aid the informed design of BaSnO3 as an active material for high-charge density electronic transistors.

Terahertz quantum cascade laser with non-resonant extraction

In order to improve the maximum operating temperature of THz quantum cascade lasers (QCLs) we propose to modify the three well resonant phonon design by increasing the energy of the separation between the bottom transition levels and the ground states, which is usually adjusted to the LO-phonon energy in GaAs. The fabricated devices based on this design with non-resonant depopulation of the bottom transition level operated in pulsed mode up to 190K, which is the best-reported performance for THz QCLs with Al0.15Ga0.85As barriers based on an Au-Au double-metal waveguide. The performed analysis showed that the achieved improvement could be explained by the proposed design modification.

Suppression of the green emission, texturing, solute-atom diffusion and increased electron-phonon coupling induced by Ni in sol-gel ZnNiO thin films

Zn1−xNixO thin films (nominal x = 0, 0.01, 0.02, 0.04, 0.1 and 0.2) were synthesized on silicon substrates through a sol-gel/dip-coating technique. Samples were studied by X-ray diffraction, scanning electron microscopy, photoluminescence spectroscopy, Rutherford backscattering spectrometry and depth-profiling X-ray photoelectron spectroscopy. The results from X-ray diffraction show growth in the wurtzite crystal structure for all samples, with cubic NiO being detected as a secondary phase for x = 0.2. While for x = 0 (pure ZnO) no texture is present, for 0 ≤ x ≤ 0.1 strong preferential crystallization along the c-axis is observed. A tendency for Ni diffusion towards the film/Si substrate interface was observed. The formation of substitutional ZnxNi1−xO solid solution for 0.01 ≤ x ≤ 0.04 is suggested by the results. Photoluminescence spectra exhibit strong near band edge UV emission and suppression of deep defect-related emission in the visible upon Ni+2 incorporation into the ZnO lattice. As in pure ZnO, the UV emission in ZnNiO at room temperature is dominated by the first two phonon replica of the excitonic emission, however the LO phonon energy (ħωLO) is reduced by up to ∼15 meV in the 0 ≤ x ≤ 0.04 range. Due to this reduction of ħωLO, the exciton-phonon coupling increases, in consistency with a corresponding expected increase of the Fröhlich coupling constant with decreasing ħωLO.

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to the full first-principles theory and the Fröhlich polaron

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $\epsilon_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,\omega)=-{\Im m}G_R(k,\omega) /\pi$, where $G_R$ is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fr\"ohlich Hamiltonian by Mishchenko $\textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fr\"ohlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fr\"ohlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.

Design strategy for terahertz quantum dot cascade lasers.

The development of quantum dot cascade lasers has been proposed as a path to obtain terahertz semiconductor lasers that operate at room temperature. The expected benefit is due to the suppression of nonradiative electron-phonon scattering and reduced dephasing that accompanies discretization of the electronic energy spectrum. We present numerical modeling which predicts that simple scaling of conventional quantum well based designs to the quantum dot regime will likely fail due to electrical instability associated with high-field domain formation. A design strategy adapted for terahertz quantum dot cascade lasers is presented which avoids these problems. Counterintuitively, this involves the resonant depopulation of the laser's upper state with the LO-phonon energy. The strategy is tested theoretically using a density matrix model of transport and gain, which predicts sufficient gain for lasing at stable operating points. Finally, the effect of quantum dot size inhomogeneity on the optical lineshape is explored, suggesting that the design concept is robust to a moderate amount of statistical variation.

Normal Incident Long Wave Infrared Quantum Dash Quantum Cascade Photodetector.

We demonstrate a quantum dash quantum cascade photodetector (QDash-QCD) by incorporating self-assembled InAs quantum dashes into the active region of a long wave infrared QCD. Sensitive photoresponse to normal incident light at 10 μm was observed, which is attributed to the intersubband (ISB) transitions in the quantum well/quantum dash (QW/QDash) hybrid absorption region and the following transfer of excited electrons on the extraction stair-like quantum levels separated by LO-phonon energy. The high density InAs quantum dashes were formed in the Stranski-Krastanow mode and stair-like levels were formed by a lattice matched InGaAs/InAlAs superlattice. A stable responsivity from 5 mA/W at 77 K to 3 mA/W at as high as 190 K was observed, which makes the QDash-QCD promising in high temperature operation.

P-State Luminescence in CdSe Nanoplatelets: Role of Lateral Confinement and a Longitudinal Optical Phonon Bottleneck.

We evidence excited state emission from p states well below ground state saturation in CdSe nanoplatelets. Size-dependent exciton ground and excited state energies and population dynamics are determined by four independent methods: time-resolved PL, time-integrated PL, rate equation modeling, and Hartree renormalized k·p calculations-all in very good agreement. The ground state-excited state energy spacing strongly increases with the lateral platelet quantization. Depending on its detuning to the LO phonon energy, the PL decay of CdSe platelets is governed by a size tunable LO phonon bottleneck, related to the low exciton-phonon coupling, very large oscillator strength, and energy spacing of both states. This is, for instance, ideal to tune lasing properties. CdSe platelets are perfectly suited to control the exciton-phonon interaction by changing their lateral size while the optical transition energy is determined by their thickness.

Resonant surface-enhanced Raman scattering by optical phonons in a monolayer of CdSe nanocrystals on Au nanocluster arrays

Here we present the results on an investigation of resonant Stokes and anti- Stokes surface-enhanced Raman scattering (SERS) by optical phonons in colloidal CdSe nanocrystals (NCs) homogeneously deposited on arrays of Au nanoclusters using the Langmuir–Blodgett technology. The thickness of deposited NCs, determined by transmission and scanning electron microscopy, amounts to approximately 1 monolayer. Special attention is paid to the determination of the localized surface plasmon resonance (LSPR) energy in the arrays of Au nanoclusters as a function of the nanocluster size by means of micro-ellipsometry. SERS by optical phonons in CdSe NCs shows a significant enhancement factor with a maximal value of 2×103 which depends resonantly on the Au nanocluster size and thus on the LSPR energy. The deposition of CdSe NCs on the arrays of Au nanocluster dimers enabled us to study the polarization dependence of SERS. It was found that a maximal SERS signal is observed for the light polarization along the dimer axis. Finally, SERS by optical phonons was observed for CdSe NCs deposited on the structures with a single Au dimer. A difference of the LO phonon energy is observed for CdSe NCs on different single dimers. This effect is explained as the confinement-induced shift which depends on the CdSe nanocrystal size and indicates quasi-single NC Raman spectra being obtained.

Analysis of the exciton–LO-phonon coupling in single wurtzite GaN quantum dots

In this study, we analyze the interaction between excitons and longitudinal-optical phonons (LO phonons) in single, wurtzite GaN quantum dots (QDs) by means of micro-photoluminescence $(\ensuremath{\mu}\mathrm{PL})$ spectroscopy. We report on Stokes-shifted emission lines measured for hundreds of single QDs. A decrease of the Huang-Rhys factor $(\ensuremath{\sim}0.5\text{--}0.01)$ is observed with increasing QD emission energy that can be modeled in an adiabatic approximation applying two-particle eight-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ wave functions. In order to obtain the QD dimensions and shape needed for these calculations, we conduct a scanning transmission electron microscope (STEM) analysis, not only focusing on the QD dimensions, but also on alloying effects. The QD height is identified as the most detrimental parameter for the exciton-LO-phonon interaction in strongly polar QD systems based on nitrides. Additionally, we extract the LO-phonon energy for a significant number of individual QDs from our $\ensuremath{\mu}\mathrm{PL}$ data set scaling in-between the bulk values for the QD (GaN) and the matrix material (AlN). Such a large variation of the LO-phonon energy cannot be explained by the alloying effects attested by our STEM analysis. Hence, the exciton-LO-phonon interaction resides in a volume that encloses the QD in the growth direction and a fraction of the matrix material depending on the QD height. We approximate this exciton-LO-phonon interaction volume by a sphere with a constant diameter of $2.6\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.16em}{0ex}}0.2$ nm.

Controllable synthesis of CdS nanowire by a facile solvothermal method and its temperature dependent photoluminescent property

CdS nanowires with controllable size, orientation, and morphology were synthesized on a large scale by a solvothermal method. The mechanism for the formation of CdS nanowires evolved from CdS spherical particles can be divided into a short-period solid–solid transformation process and a long-period ripening process. Near-band-emission without distinct split phenomenon was observed in the PL spectrum of CdS nanowires at 10 K. The best fit results based on Varshni empirical equation support our assignment of FX. Temperature dependent integrated peak intensity and linewidth of FX were analyzed by means of a two-step quenching process model and well fitted by Toyozawa's theory. All fitted results including thermal activation energy, LO-phonon energy were close to that observed in bulk CdS, indicating high quality of nanomaterial but also revealing its promising applications in photonics.