Emission Of Longitudinal Optical Phonons Research Articles

Fundamental limitations on gain of terahertz quantum cascade lasers

We analyze the main physical processes in quantum cascade lasers with a spatial separation between the region of photon radiation and longitudinal optical (LO) phonon emission, which facilitates the depopulation of the lower level of the optical transition. Our objective is to identify the reasons for the reduction of population inversion at low photon energy and explore methods to enhance it. The expression for population inversion is derived from an equation for a simplified density matrix. This approach allows us to consider the coherence of tunneling between different levels and comprehend its influence on transition probabilities in a straightforward manner. We have found out that the energy uncertainty principle is the fundamental factor limiting population inversion in terahertz lasers. By optimizing the tunneling matrix element between the two regions and the LO phonon emission time, it is possible to significantly increase the population inversion. The optimal value for the matrix element is smaller than its maximum possible value, while the optimal LO phonon emission time exceeds the time achieved during LO phonon resonant emission.

Absorption and emission of longitudinal optical phonons by confined electrons in Pöschl–Teller quantum wells under the effects of the aluminum concentration, temperature, and hydrostatic pressure

In this study, we investigated the simultaneous effects of the alloy concentration, electron temperature, and hydrostatic pressure on the magneto-optical transport properties (MOTPs) of GaAs/AlηGa1−ηAs Pöschl–Teller quantum wells (QW) by using the operator projection method and profile technique. The optical absorption power and full width at half maximum were calculated and compared for the optically detected magneto-phonon resonance peaks with phonon absorption and emission. In addition, the main results were compared with those for the rectangular potential QW. The results showed that the alloy concentration, electron temperature, and hydrostatic pressure greatly influenced the MOTPs of the GaAs/AlηGa1−ηAs Pöschl–Teller QW in both cases with the absorption and emission of phonons. In addition, these effects were greater when the degree of asymmetry was stronger for the Pöschl-Teller QW. Our results also demonstrated that the combined effects of the alloy concentration, electron temperature, and hydrostatic pressure on the MOTPs of the GaAs/AlηGa1−ηAs Pöschl-Teller QW were always greater in the phonon absorption case than the phonon emission case. Furthermore, the combined effects of these three parameters on the MOTPs of the Pöschl-Teller potential QW were greater than those on the rectangular potential QW in both the phonon emission and absorption processes.

Impact of compositional disorder on electron migration in lutetium–yttrium oxyorthosilicate scintillator

A general description of the dynamics of nonequilibrium carriers in multicomponent activated scintillation materials with a compositional disorder of the crystalline matrix is developed and applied for studying the excitation transfer and timing properties of lutetium–yttrium oxyorthosilicate (LYSO). The energy structure, the density of states, and the effective potential of LSO and YSO crystals have been calculated by using the Quantum Espresso package. An analytical form of the potential fluctuations due to compositional disorder is suggested in the pseudopotential approximation. The spatial distribution of lutetium and yttrium cations in the LYSO crystal has been simulated by the Monte Carlo method using the thermodynamic approach for three qualitatively different cases of cation distribution: uniform, heterogeneous neighboring, and clustered. The impact of the compositional disorder on electron migration is found to be qualitatively different in four typical regions of electron energy. The density of localized states in LYSO calculated using the coherent potential approximation (CPA) and the quasiclassical approach is comparable to the density of secondary carriers expected in an ionization track and might have significant influence on the migration of thermalized carriers. The transport mean free path of nonlocalized electrons limited by elastic scattering on pseudopotential fluctuations is shown to be substantially longer than that due to longitudinal optical phonon emission in the low-energy region (calculated using CPA) and the high-energy region (calculated using the Born approximation). The scattering on pseudopotential fluctuations is important for intermediate-energy electrons due to a substantial influence of the core potential fluctuations on high-energy branches.

Transient surface photovoltage spectroscopy of diamond

Contactless and highly sensitive probing of electronic transitions in diamond over a wide spectral range from near infrared to deep ultraviolet is still challenging. Surface photovoltage (SPV) signals depend on electronic transitions and transport phenomena leading to charge separation in space and allow for a contactless study of electronic transitions. Here, transient SPV spectroscopy in an arrangement with a charge amplifier and a laser tunable over a wide range was applied to study an undoped diamond single crystal between 0.8 and 5.9 eV at room temperature in ambient air. SPV transients were measured without and with weak visible bias light, which allowed for suppression of possible parasitic contributions in SPV signals not related to diamond and distinction of processes of charge separation that were independent of band bending. Transitions at 1.0 and 3.1 eV led to preferential separation of photogenerated holes toward the surface. In contrast, a transition at 1.8 eV caused preferential separation of photogenerated electrons toward the surface. Transitions near the indirect bandgap of diamond were observed at 5.27, 5.32, 5.48, and 5.53 eV and could be assigned to absorption assisted (i) by an indirect exciton and absorption of longitudinal optical and acoustic phonons, (ii) by absorption of transverse acoustic phonons, (iii) by emission of transverse acoustic phonons, and (iv) by emission of longitudinal optical and acoustic phonons, respectively. Charge separation under excitation at 5.27 eV was caused by directed charge transfer at/near the diamond surface after exciton diffusion followed by exciton dissociation.

Terahertz oscillations in gallium nitride quantum-well channels predicted by hot-electron noise temperature behavior at microwave frequency

The almost periodic streaming motion of accelerated electrons under moderate electric fields coupled with almost periodic emission of longitudinal optical (LO) phonons is studied in a gallium nitride quantum-well—a promising pathway for terahertz (THz) oscillations. The optimal conditions for the LO-phonon-terminated streaming depend, among others, on the density of the electron gas, the low-field electron mobility, the lattice temperature, and the electric field in a very specific way. The present manuscript exploited the electron noise temperature measured at an X band frequency as a marker for the oscillations at THz frequencies. The idea was tested on a deterministic model for a GaN two-dimensional electron gas (2DEG) through calculation of the electron noise temperature spectra in the Langevin approach for the frequency range from 1 GHz to 10 THz. The noise temperature at 10 GHz was found to be in a strong anticorrelation with the THz peaks in the noise temperature spectrum. In particular, a weaker dependence on the applied electric field at 10 GHz implies stronger THz oscillations. In an experiment, the microwave hot-electron noise measurements were carried out for AlGaN/AlN/GaN heterostructures with the 2DEG channel at 10 GHz under pulsed electric field conditions in order to mitigate the effect of Joule heating of the channel. The plateau-like behavior of the noise temperature, in its dependence on the electric field, was obtained for the 2DEG channels with rather low electron densities (2.5×1012 cm−2) in a good agreement with the model. The aforementioned plateau in the electron noise temperature observed at 10 GHz can be used as an indicator for the THz oscillations.

Confined and interface optical phonon emission in GaN/InGaN double barrier quantum well heterostructures.

In GaN-based high electron mobility transistors (HEMTs), the fast emission of longitudinal optical (LO) phonons can result in the formation of hot spots near the gate region where high electric fields produce hot electrons. In this work, we investigate the probability of phonon emission as a function of electron energy for confined and interface (IF) phonon modes for wurtzite GaN/InGaN/GaN heterostructures. Hot electrons radiate optical phonons which decay, anharmonically, into acoustic phonons that are essentially heat carriers. Herein, phonon engineering concepts are introduced which facilitate thermal management through the production of polar optical phonons. Some of the electrons near a semiconductor gate which manifests a strong electric field, are accelerated and the resulting hot electrons will produce confined and interface modes when the electrons are incident on a suitably-placed quantum well. This paper focuses on the production of confined and interface phonons. It is shown that interface modes may be preferentially produced which lead to elongated, lower-temperature hot spots.

Dynamic Screening and Slow Cooling of Hot Carriers in Lead Halide Perovskites.

Among the exceptional properties of lead halide perovskites (LHPs) is the ultraslow cooling of hot carriers. Carrier densities below the Mott density for large polarons (≤ ≈1018 cm-3 ) are focused on here. As in other semiconductors, a nascent hot electron distribution initially cools down via emission of longitudinal optical (LO) phonons on the 10-14 -10-13 s timescale. What distinguishes LHPs from conventional semiconductors is the exceptionally efficient screening in the former. The dielectric screening in LHPs on the 10-13 s timescale results in an order-of-magnitude reduction in the Coulomb potential upon the formation of a large polaron, likely with ferroelectric-like local ordering. Further LO-phonon emission is inhibited, and this leads to partial retention of hot electron energy on the 10-12 s timescale, more so in hybrid LHPs than in their all-inorganic counterparts. Further cooling of hot polarons occurs on the 10-10 s timescale, and this can be attributed to the slow diffusion of heat out of the large polaron volume due to the low thermal conductivity of LHPs. Like other carrier properties, slow hot carrier cooling in LHPs can be intimately related to efficient screening in a soft, anharmonic, and dynamically disordered lattice.

Energy loss rate of hot electrons due to polar-optical phonon modes in a semiconductor nanowire under transverse electric field

Within the frame of electron-temperature model we calculate the average energy loss rate due to interface and confined longitudinal optical (LO) phonon emission from a hot-electron gas to a cold lattice in polar semiconductor nanowire surrounded by non-polar material. The system both with and without hot-phonon effect is investigated. The impact of a perpendicular electric field on average energy loss rate is explored. The energy loss rate dependences on electric field strength, wire radius and electron temperature are obtained. It has been shown that the energy loss rate is more sensitive to the electric field when the wire radius is larger. The presented results indicate that the electric field applied perpendicularly to the wire axis can serve as a means to control the energy loss rate. There is an experimental evidence concerning to the increase of energy loss rate with increasing electron temperature as we have obtained.

Competition Between Hot-Electron Cooling and Large Polaron Screening in CsPbBr3 Perovskite Single Crystals

Lead halide perovskites (LHPs) are solution processable semiconductors characterized by long carrier lifetimes. Recent studies have suggested that electrons and holes in LHPs interact with phonons to form large polarons on subpicosecond time-scales and polaron formation may also slow down hot carrier cooling. Using femtosecond time-resolved two-photon photoemission (TR-2PPE) and transient reflectance (TR) spectroscopies, we follow the initial electron cooling and polaron formation dynamics in single-crystal CsPbBr3 perovskite. We find that the hot electrons cool down initially (≤0.2 ps) with rates of −0.64 ± 0.06 eV/ps and −0.82 ± 0.08 eV/ps at 300 and 80 K, respectively. This weakly temperature-dependent rate is attributed to the initial relaxation of unscreened hot electrons by the emission of longitudinal optical (LO) phonons. On longer time scales, we observe dynamic changes in the photoemission cross-section and in the red-shift of the optical bandgap. We attribute these dynamic changes to large pola...

Hot carrier cooling mechanisms in halide perovskites

Halide perovskites exhibit unique slow hot-carrier cooling properties capable of unlocking disruptive perovskite photon–electron conversion technologies (e.g., high-efficiency hot-carrier photovoltaics, photo-catalysis, and photodetectors). Presently, the origins and mechanisms of this retardation remain highly contentious (e.g., large polarons, hot-phonon bottleneck, acoustical–optical phonon upconversion etc.). Here, we investigate the fluence-dependent hot-carrier dynamics in methylammonium lead triiodide using transient absorption spectroscopy, and correlate with theoretical modeling and first-principles calculations. At moderate carrier concentrations (around 1018 cm−3), carrier cooling is mediated by polar Fröhlich electron–phonon interactions through zone-center delayed longitudinal optical phonon emissions (i.e., with phonon lifetime τLO around 0.6 ± 0.1 ps) induced by the hot-phonon bottleneck. The hot-phonon effect arises from the suppression of the Klemens relaxation pathway essential for longitudinal optical phonon decay. At high carrier concentrations (around 1019 cm−3), Auger heating further reduces the cooling rates. Our study unravels the intricate interplay between the hot-phonon bottleneck and Auger heating effects on carrier cooling, which will resolve the existing controversy.

Carrier capture in InGaN/GaN quantum wells: Role of electron-electron scattering

The competition of electron-electron interband scattering (ee) and longitudinal optical phonon emission (e-ph) as electron capture mechanisms is theoretically investigated in III-nitride quantum wells. The non-trivial separation of their scattering probabilities is discussed, and compact expressions for capture time are obtained in the framework of the quantum many-body formalism. At the typical operating conditions of light emitting diodes (LEDs), the model predicts an increasing importance of ee scattering as a capture mechanism with increasing carrier density. Verifications against recent experiments are presented to support this finding and confirm the need for population-dependent capture time expressions including both ee and e-ph mechanisms for an accurate description of LED carrier dynamics and efficiency.

Fast Relaxation of Photo-Excited Carriers in 2-D Transition Metal Dichalcogenides

We predict a fast relaxation of photo-excited carriers in monolayer transition metal dichalcogenides (TMDCs), which is mediated by the emission of longitudinal optical (LO) phonons. By evaluating Born effective charges for ${\rm MoS_2, MoSe_2,WS_2}$, and ${\rm WSe_2}$, we find that, due to the polar coupling of electrons with LO phonons, the relaxation times for hot electrons and holes are of the order of a few ps.

The electron-longitudinal optical phonon scattering rate in GaInAsP/InP stepped quantum well

Within the framework of effective mass approximation, the scattering rate via longitudinal optical (LO) phonon emission for an electron and the mean scattering rate via LO phonons emission for electrons initially in the first excited sub-band and finally in the ground sub-band in [Formula: see text] stepped quantum well (QW) is calculated adopting the shooting method and Fermi’s golden rule. The results show that the scattering rate and the mean scattering rate are highly dependent on alloy compositions, well width, initial electron energy, electron temperature and sub-band separation [Formula: see text] between the ground sub-band and the first excited sub-band. When [Formula: see text] is larger than the LO phonon energy, the scattering rate and the mean scattering rate increases with increasing Ga composition, decreasing As composition and increasing well width. However, when [Formula: see text] is smaller than the LO phonon energy, its change tendency is contrary. The scattering rate increases with decreasing initial electron energy if the separation between the initial electron energy and the ground state energy [Formula: see text] is not smaller than the LO phonon energy. The scattering rate and the mean scattering rate increases with rising electron temperature. The mean scattering rate reaches the maximum value when [Formula: see text] is equal to the LO phonon energy. The interruption in the scattering rate happens when the separation between the initial electron energy and [Formula: see text] is smaller than the LO phonon energy. The rapid decrease of the mean scattering rate happens when [Formula: see text] is smaller than the LO phonon energy if [Formula: see text] continues decreasing. In addition, both the scattering rate and the mean scattering rate show little change with different stepped layer widths.

Amplified spontaneous emission of phonons as a likely mechanism for density-dependent velocity saturation in GaN transistors

We show that density-dependent velocity saturation in a GaN high electron mobility transistor (HEMT) can be related to the stimulated emission of longitudinal optical (LO) phonons. As the drift velocity of electrons increases, the drift of the Fermi distribution in reciprocal space results in population inversion and gain for the LO phonons. Once this gain reaches a threshold value, the avalanche-like increase in LO phonon emission causes a rapid loss of electron energy and momentum and leads to drift velocity saturation. Our simple model correctly predicts both the general trend of decreasing saturation velocity with increasing electron density, and the measured experimental values of saturation.

Phonon emission and arrival times of electrons from a single-electron source

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy.

Density-dependent electron transport and precise modeling of GaN high electron mobility transistors

We report on the direct measurement of two-dimensional sheet charge density dependence of electron transport in AlGaN/GaN high electron mobility transistors (HEMTs). Pulsed IV measurements established increasing electron velocities with decreasing sheet charge densities, resulting in saturation velocity of 1.9 × 107 cm/s at a low sheet charge density of 7.8 × 1011 cm−2. An optical phonon emission-based electron velocity model for GaN is also presented. It accommodates stimulated longitudinal optical (LO) phonon emission which clamps the electron velocity with strong electron-phonon interaction and long LO phonon lifetime in GaN. A comparison with the measured density-dependent saturation velocity shows that it captures the dependence rather well. Finally, the experimental result is applied in TCAD-based device simulator to predict DC and small signal characteristics of a reported GaN HEMT. Good agreement between the simulated and reported experimental results validated the measurement presented in this report and established accurate modeling of GaN HEMTs.

Femtosecond cooling of hot electrons in CdSe quantum-well platelets.

Semiconductor quantum wells are ubiquitous in high-performance optoelectronic devices such as solar cells and lasers. Understanding and controlling of the (hot) carrier dynamics is essential to optimize their performance. Here, we study hot electron cooling in colloidal CdSe quantum-well nanoplatelets using ultrafast two-photon photoemission spectroscopy at low excitation intensities, resulting typically in 1-5 hot electrons per platelet. We observe initial electron cooling in the femtosecond time domain that slows down with decreasing electron energy and is finished within 2 ps. The cooling is considerably faster at cryogenic temperatures than at room temperature, and at least for the systems that we studied, independent of the thickness of the platelets (here 3-5 CdSe units) and the presence of a CdS shell. The cooling rates that we observe are orders of magnitude faster than reported for similar CdSe platelets under strong excitation. Our results are understood by a classic cooling mechanism with emission of longitudinal optical phonons without a significant influence of the surface.

Excitonic states and energy relaxation in low-dimension CdSe/ZnSe structures with isolated ZnCdSe islands

Photoluminescence (PL) and PL excitation (PLE) spectra of structures containing MBE-grown CdSe layers with a nominal thickness tCdSe of 1.4–2.7 monolayers (MLs) in a ZnSe matrix have been studied. It is shown that the main features of the PLE spectra in structures with different amounts of deposited CdSe can be described in terms of two different models: in structures with tCdSe exceeding approximately 1.7 ML, the properties of electronic states correspond to the frequently used model of the quantum well formed by an inhomogeneous ZnCdSe solid solution with nanosize inclusions constituted by planar ZnCdSe islands whose composition is strongly enriched with CdSe, whereas the properties of electronic states in structures with tCdSe < 1.6 ML can be described in the model of isolated uncoupled ZnCdSe nanoislands. It was found that the main channel by which emitting states are occupied under excitation with photons in a wide energy range both in the region of quantum-dot states and in that of free states in the ZnSe barrier is the cascade relaxation of hot excitons, with emission of longitudinal optical phonons. Other properties of electronic states in nano-objects of this kind are discussed.

Unique properties of photoluminescence excitation spectra in a Eu-doped GaN epitaxial film

We have investigated the temperature dependence of photoluminescence-excitation (PLE) spectra of Eu3+ emission due to the intra-4f shell transitions in a Eu-doped GaN epitaxial film from the viewpoint of the energy transfer process by carriers and excitons from the host GaN to Eu3+ ions. It was found that the excitonic band of the PLE spectrum disappears in a low temperature region below ∼140 K in spite of the fact that the optical transitions of the A and B excitons are clearly observed in a reflectance spectrum. The excitonic PLE band becomes remarkable with an increase in temperature. This fact indicates that carriers originating from the thermal dissociation of photogenerated excitons contribute to the Eu3+ emission. In other words, excitons play no role in the energy transfer process. Furthermore, the PLE spectrum at room temperature exhibits an oscillatory structure resulting from longitudinal-optical phonon emission in a hot carrier relaxation process.

Terahertz Electron-Hole Recollisions inGaAs/AlGaAsQuantum Wells: Robustness to Scattering by Optical Phonons and Thermal Fluctuations

Electron-hole recollisions are induced by resonantly injecting excitons with a near-IR laser at frequency fNIR into quantum wells driven by a 10 kV/cm field oscillating at fTHz=0.57 THz. At T=12 K, up to 18 sidebands are observed at frequencies fsideband=fNIR+2nfTHz, with -8≤2n≤28. Electrons and holes recollide with total kinetic energies up to 57 meV, well above the ELO=36 meV threshold for longitudinal optical (LO) phonon emission. Sidebands with order up to 2n=22 persist up to room temperature. A simple model shows that LO phonon scattering suppresses but does not eliminate sidebands associated with kinetic energies above ELO.