Nonequilibrium LO Phonons Research Articles

The role of nonequilibrium LO phonons, Pauli exclusion, and intervalley pathways on the relaxation of hot carriers in InGaAs/InGaAsP multi-quantum-wells

Under continuous-wave laser excitation in a lattice-matched In0.53Ga0.47As/In0.8Ga0.2As0.44P0.56 multi-quantum-well (MQW) structure, the carrier temperature extracted from photoluminescence rises faster for 405 nm compared with 980 nm excitation, as the injected carrier density increases. Ensemble Monte Carlo simulation of the carrier dynamics in the MQW system shows that this carrier temperature rise is dominated by nonequilibrium LO phonon effects, with the Pauli exclusion having a significant effect at high carrier densities. Further, we find a significant fraction of carriers reside in the satellite L-valleys for 405 nm excitation due to strong intervalley transfer, leading to a cooler steady-state electron temperature in the central valley compared with the case when intervalley transfer is excluded from the model. Good agreement between experiment and simulation has been shown, and detailed analysis has been presented. This study expands our knowledge of the dynamics of the hot carrier population in semiconductors, which can be applied to further limit energy loss in solar cells.

Transient energy relaxation in scattering-assisted terahertz quantum cascade lasers

We adopt a self-consistent Maxwell–Bloch method to investigate the energy relaxation process from unsaturated to saturated in the scattering-assisted terahertz quantum cascade laser. In the lasing-establishment process, more nonequilibrium LO phonons are accumulated and more electrons are thermalized. At the same time, more efficient energy relaxation of the saturated situation can be found compared with the unsaturated situation. These phenomena stem from the improved electron transport efficiency across the active region, due to the lasing-induced lifetime reduction of electrons in the upper lasing subband. The simulation results are qualitatively identical with previous experimental results.

Hot phonon effect on electron velocity saturation in GaN: A second look

A theoretical model is developed for electron velocity saturation in high power GaN transistors. It is shown that electron velocity at high electric fields is reduced due to heating of electron gas since the high density of nonequilibrium LO phonons cannot efficiently transfer heat to the lattice. However, the resulting degradation of electron velocity is found to be weaker than previously reported. The results are compared with experimental data, and the ways to improve the efficiency of cooling the electron gas to increase the drift velocity are discussed.

Enhancement by electric field of high-speed photoconductivity in AlGaN∕GaN heterostructures

The authors report a large response in the conductivity of AlGaN∕GaN heterostructures to a 10ns UV laser pulses. The dynamics of the conductivity response follows the time evolution of the laser pulse. This fast photoconductivity component shows a remarkable enhancement in high electric fields. For the field ≈15kV∕cm, it increases by at least one order of magnitude at temperatures of 4.2 and 300K. This photoconductivity enhancement is found to be related to the hot electron effect. The authors propose an explanation for the observed phenomena. The mechanism of the photoconductivity enhancement involves nonequilibrium LO phonons generated by hot carriers.

Lifetime of nonequilibrium zone-center longitudinal optical phonons in zinc-blende materials

We employ a theoretical model to assess the importance of Ridley’s channel in limiting the lifeitime of nonequilibrium zone-center LO phonons in zinc-blende materials. For comparison, we also present results for the decay through Klemens’s channel as well as via Vallée–Bogani’s intraband combination channel.

Influence of Nonequilibrium LO Phonons on High-frequency Performance of One-dimensional Hot Electrons in Quantum Wires of Polar Semiconductors

Small-signal ac transport of degenerate one-dimensional hot electrons in quantum wires of GaAs and In0.53Ga0.47As is studied for lattice temperatures of 77 K and 300 K. The carrier energy loss via polar optic phonons and momentum losses via polar optic phonons, acoustic phonons and ionized impurities are included in the calculations. Alloy disorder scattering in momentum loss is additionally incorporated for (In,Ga)As. The consideration of nonequilibrium optical phonons or hot phonons is found to enhance the 3dB cut-off frequency (f3dB) considerably, where the ac mobility falls to 0.707 of its low frequency value. f3dB is generally higher for (In,Ga)As quantum wire than for GaAs.

Nonradiative capture of hot photoelectrons by multiphonon emission in highly excited polar semiconductors

Room-temperature recombination dynamics of hot electron-hole plasma in highly excited polar semiconductors is analysed. A rate equation with Arrhenius dependence of carrier lifetime on the effective temperature is employed to consider the capture by deep centres via multiphonon emission (MPE) with the nonequilibrium LO phonons taken into account. The luminescence-intensity dependence on the pump intensity under quasistationary excitation conditions, as well as the shape of the luminescence-intensity transient kinetics, are shown to be strongly dependent on the height of the localization barrier. Typical manifestation of carrier-temperature-activated capture by MPE is experimentally demonstrated both for quasi-steady-state and transient conditions in CdSe and CdS single crystals, respectively. Additionally, evidence, testifying that surface recombination in CdS nanocrystals embedded in a glass matrix exhibits features characteristic of nonradiative capture by MPE for carrier and phonon systems far from thermal equilibrium with the lattice, is presented. The relevant localization barriers are shown to lie within the 100–200 meV range.

Influence of the energy transport of electrons by optical phonon emission on the superluminescence and reversible bleaching of a thin GaAs layer excited by a strong picosecond light pulse

The dependence of the superluminescence and optical bleaching of GaAs during the interband absorption of a strong picosecond light pulse on the photon energy ℏωex of the exciting pulse is investigated experimentally. The bleaching (transmission enhancement, i.e., greater transparency) mainly reflects the density of the photogenerated electron-hole plasma. Several events are observed when the distance between the energy level at which electrons are generated and the level from which they undergo stimulated recombination is a multiple of the longitudinal optical phonon energy. These events are: 1) amplification of recombination superluminescence; 2) slowing of the increase in optical bleaching as ℏωex is increased; and 3) an increase in the shift of the edge of the emission spectrum toward longer wavelengths. These phenomena are qualitatively attributed to an increase in the fraction of transitions involving the emission of LO phonons in the energy transport of electrons toward the bottom of the conduction band and to the influence of this process on the heating of the electron-hole plasma and the density of nonequilibrium LO phonons.

Dense electron-hole plasma cooling due to second nonequilibrium-phonon bottleneck in CdS crystallites

Quantitative evidence on the existence of a second nonequilibrium-phonon bottleneck for dense electron-hole plasma cooling in a highly excited polar semiconductor is presented. The bottleneck is caused by recurrent fusion of nonequilibrium LO phonons from their decay products (daughter phonons). Carrier cooling was experimentally investigated in CdS, which offers a favorable phonon dispersion. Crystallites of 50-nm radius were utilized to prevent stimulated recombination and diffusion of photoexcited electron-hole plasma with a density around $1.5\ifmmode\times\else\texttimes\fi{}{10}^{19} {\mathrm{cm}}^{\ensuremath{-}3}.$ A transient of carrier effective temperature, deduced from time-resolved luminescence spectra, exhibit a slow-relaxation component with the time constant of 70 ps at room temperature. The transient was shown to be in quantitative consistence with the theoretical model based on Boltzmann equations for two generations of nonequilibrium phonons and degenerate-carrier energy rate equation with the energy income due to recombination effects (nonradiative capture via multiphonon emission, fermion self-heating, and band-gap renormalization) taken into account. The observed cooling rate agrees with two nonequilibrium-phonon bottlenecks with the depopulation time constants deduced from the available Raman data (0.5 ps for LO phonons and 12.4 ps for daughter phonons).

Second nonequilibrium-phonon bottleneck for carrier cooling in highly excited polar semiconductors

Cooling of high-density electron-hole plasma excited in direct-gap polar semiconductors by a picosecond pulse of an extreme intensity is considered. Convenient models of carrier coupling with LO phonons via screened Fr\"ohlich interaction, nonequilibrium LO-phonon creation by free-carrier intraband relaxation, and fermion recombination-induced heating were combined with a description of second-generation nonequilibrium phonons produced by anharmonic decay of the nonequilibrium LO phonons. An additional source of nonequilibrium LO phonons due to nonradiative capture by deep centers via multiphonon emission was also introduced. A numerical simulation for a CdS crystal was performed. Even at room temperature, the carrier cooling is shown to exhibit a noticeable slow component for plasma densities above ${10}^{19}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ At the late stage of the relaxation, the relevant time constant $(\ensuremath{\sim}100\mathrm{ps})$ is found to be comparable with the carrier lifetime, while the magnitude of the excess effective temperature is determined by nonequilibrium population of the second-generation phonons. The ``width'' of the second nonequilibrium-phonon bottleneck is demonstrated to be determined by peculiarities of the lattice vibration spectrum.

Effects of carrier heating, nonequilibrium LO phonons and lattice heating on small-signal modulation response of semiconductor lasers

A small-signal analysis is presented for the modulation response of semiconductor lasers by simultaneously incorporating the effects of carrier heating, nonequilibrium LO phonons and lattice heating. The authors theoretically investigate, without the definition of steady-state carrier energy relaxation time, the effects of the lifetime of LO phonons and the thermal conduction time of acoustic phonons on the small-signal modulation response of semiconductor lasers. They show that, if the LO phonon lifetime approaches the inverse of modulation frequency, the assumption about the quasistatic population variation of LO phonons may lose its validity in discussing the modulation response of semiconductor lasers.

The Coupled Optoelectronic Problems of Quantum WellLaser Operation

The treatment of several aspects of quantum well laser simulation are discussed in terms of the Minilase‐II simulator. The discussion involves the optical problem and several components of the electronic problem, including bulk transport, carrier scattering into and within the quantum well, and the nonequilibrium LO phonon temperature within the well. Descriptions of these problems are followed by simulation results which show the ways in which they each affect the laser characteristics.

Effects of electron–hole energy transfer on the nonlinear gain coefficients in the small-signal modulation response of semiconductor lasers

The effects of energy transfer between electrons and holes on the small-signal modulation response of semiconductor lasers are theoretically investigated. We calculate the electron energy relaxation time due to electron–hole scattering from the first principle. We show that its value is comparable to the electron energy relaxation time due to the electron–LO phonon scattering with the effect of nonequilibrium LO phonons. In such a case, the nonlinear gain coefficient due to carrier heating defined in the small-signal modulation response of semiconductor lasers is no longer a simple sum of the term due to electron heating and that due to hole heating.

Femtosecond investigation of the hot-phonon effect in GaAs at room temperature

Slowing down of the hot electron-lattice thermalization by generation of nonequilibrium phonons (hot-phonon effect) is investigated in GaAs at room temperature using high-sensitivity femtosecond single- and double-wavelength absorption saturation techniques. Measurements were performed for different amplitudes of the hot-phonon effect by changing either the individual excess energy of the photoexcited carriers or their density in the range 7\ifmmode\times\else\texttimes\fi{}${10}^{15}$--4\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. After an initial regime dominated by nonequilibrium LO-phonon k-space redistribution, the long-time delay (\ensuremath{\ge}3 ps) electron thermalization is found to occur with a characteristic time of \ensuremath{\sim}1.9 ps, independent of the total energy initially injected into the carriers and essentially reflecting the LO-phonon energy relaxation. This is in agreement with numerical simulations of the coupled carrier-phonon relaxation dynamics, indicating that energy transfers to holes are responsible for this slight reduction of the thermalization time compared to the LO-phonon lifetime (identified with the dephasing time ${\mathit{T}}_{2}$/2\ensuremath{\sim}2.1 ps). \textcopyright{} 1996 The American Physical Society.

Nonequilibrium phonon dynamics and electron distribution functions in InP and InAs

We have used subpicosecond laser pulses to study the generation of nonequilibrium LO phonons in both InP and InAs. These two semiconductors provide a contrast in that the decaying of the Raman signal probes different relaxation mechanisms. In InP, for example, we find that the decay of the Raman signal is dominated by the lifetime of the LO phonons. On the contrary, in InAs, our studies show that the decay of the Raman signal is governed by the time required for electrons to return to the \ensuremath{\Gamma} valley from the L valleys of the conduction bands. In addition, nonequilibrium electron distributions were also studied in InP and InAs. We have found that the single-particle-scattering spectrum in InAs can only be observed with the use of a much longer laser pulse width than subpicosecond as a result of electron intervalley scattering and very small electron effective mass. \textcopyright{} 1996 The American Physical Society.

Nonequilibrium optical-phonon population by sequential resonant tunneling in GaAs-AlAs superlattices.

We report on the observation of nonequilibrium GaAs LO phonons generated by the relaxation of hot electrons due to sequential resonant tunneling in strongly coupled superlattices. Raman-scattering experiments were performed at 5 K with low optical excitation density. The anti-Stokes LO-phonon intensity, which gives a measure of the nonequilibrium LO-phonon population, exhibits maxima at the resonant tunneling voltages. The transport data show that the electrical heating power increases linearly with voltage. Our results suggest that hot-electron cooling via acoustical phonon emission is suppressed under sequential resonant tunneling conditions.

Relaxation of a hot-electron-two-mode-phonon system in highly excited CdS1-xSex crystals.

An investigation of the electron-hole-plasma effective-temperature relaxation in highly excited ${\mathrm{CdS}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Se}}_{\mathit{x}}$ mixed crystals is presented. The slow (\ensuremath{\sim}100-ps) relaxation stage, attributed to the depopulation of the fragments (decay products) of the initially produced nonequilibrium LO phonons, is examined with variation of the alloy composition. The relevant relaxation time dependence on x exhibiting a remarkable drop at small CdSe mole fractions is analyzed in terms of a two-route energy relaxation model considering hot-carrier plasma and two generations of nonequilibrium phonons each originating from both pure constituents of the alloy. The disorder-enhanced cross relaxation between two sublattices of the alloy is inferred to account for the experimental results.

Theoretical study of the anharmonic decay of nonequilibrium LO phonons in semiconductor structures.

Using a model cubic anharmonic crystal potential and Fermi's golden rule, an expression for the anharmonic relaxation time for a nonequilibrium long-wavelength LO phonon is rigorously derived. Decay times for various bulk, alloy, and quantum-well semiconductor systems are calculated. Comparison with time-resolved Raman measurements indicates that a relatively high value of the Gr\"uneisen constant (1.8 for GaAs) gives the best agreement between experiment and theory.

Direct observation of a reduced cooling rate of hot carriers in the presence of nonequilibrium LO phonons in GaAs:As.

We have directly observed the influence of nonequilibrium optical phonons on the cooling rate of hot carriers in GaAs:As. Carriers with density g${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ were generated by an 80-fs, 1.72-eV pulse and cooled as well as recombined on a 1-ps time scale leaving behind only nonequilibrium phonons. The cooling rate of low-density (${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) carriers generated by a second delayed pulse was studied through time-resolved luminescence. The rate changes with the intensity of the first pulse and delay of the second pulse in a manner consistent with reabsorption of the nonequilibrium phonons.

Numerical solution of coupled steady-state hot-phonon-hot-electron Boltzmann equations in InP.

A matrix method for the numerical determination of steady-state hot-phonon and nondegenerate hot-electron distribution functions is presented. The coupled Boltzmann equations for the longitudinal-optical phonons and for the electrons, in the \ensuremath{\Gamma} and L valleys of III-V semiconductor compounds, are iteratively solved with high accuracy under typical hot-electron conditions. The phonon distribution is shown to be significantly disturbed from thermal equilibrium. In turn, nonequilibrium phonons induce a substantial disturbance of the hot-electron distribution. Computations are performed for InP at 300 K, taking into account all relevant scattering mechanisms. It turns out that the electron transport parameters are strongly affected in the field range from 0 to 10 kV/cm: the drift velocity is increased by about 42% at 2 kV/cm and the Ohmic mobility by 37%. These effects are shown to be due to the drag and reduced cooling of the carriers by the nonequilibrium LO phonons.