Nonequilibrium Phonon Population Research Articles

Role of interface optical phonons in cooling hot carriers in GaAs-AlAs quantum wells.

We present an experimental study of the nonequilibrium phonon population generated by the relaxation of hot carriers photoexcited in GaAs-AlAs quantum wells. The optical phonon population is measured by anti-Stokes Raman scattering performed in the plane of the layers. The measured occupation numbers suggest that interface phonon modes contribute significantly to the relaxation dynamics over the lifetime of an electron-hole pair. These results are explained on the basis of the interplay between emission and reabsorption of hot phonons, which leads to a large population of interface phonons under steady-state conditions.

Anharmonic interactions of nonequilibrium phonons in LiYF4:Pr3+

We have investigated the decay of nonequilibrium phonons in ${\mathrm{LiYF}}_{4}$:${\mathrm{Pr}}^{3+}$ (1 at. %) at a temperature of 9.5 K. Nonequilibrium phonon populations at 51.9, 66.0, and 113 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are generated monochromatically with a high-power pulsed far-infrared laser via defect-induced one-phonon absorption, and their temporal and spectral evolution detected using anti-Stokes absorption. We observe the broadband distribution that results from the anharmonic decay of the initial monochromatic phonon population. The experimental data are modeled using a Monte Carlo simulation based on spontaneous three phonon processes. The simulation is in good agreement with the experimental data.

Time resolved nonequilibrium phonon dynamics in the nonradiative decay of photoexcited forsterite

Information on the nonequilibrium phonon dynamics of the 225 cm−1 and 335 cm−1 modes on forsterite has been obtained using time resolved Raman scattering. The observed nonequilibrium phonon population is associated with the overall complex nonradiative decay following the excitation of the impurity ion.

Subpicosecond real-space charge transfer in GaAs/AlAs type II superlattices

The authors report time-resolved anti-Stokes Raman scattering measurements of short-period GaAs/AlAs type II superlattices which reveal directly that q approximately 0 confined and interface optical phonons are emitted by electrons when they transfer from the Gamma valley in the GaAs layers to the Xz valley in the AlAs layers in structures where the Gamma -Xz separation is greater than the optical phonon energy. The transfer time is estimated from the risetime of the non-equilibrium phonon population to be approximately=1 ps.

Electron-optical-phonon interactions in ultrathin GaAs/AlAs multiple quantum wells.

Nonequilibrium populations of both confined and interface phonons generated by picosecond laser pulses in a series of GaAs/AlAs quantum wells have been studied by time-resolved picosecond Raman scattering as a function of well width. The dependence of the nonequilibrium phonon populations on well width is found to be sensitive to the theoretical model which is used to describe the electron-phonon interaction. Our data disagree with the macroscopic model of electron-phonon interaction, but they are in excellent agreement with the microscopic model proposed recently by Huang and Zhu.

Anharmonic decay time, isotopic scattering time, and inhomogeneous line broadening of optical phonons in 70Ge, 76Ge, and natural Ge crystals.

High-accuracy (0.02-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) first-order Raman spectra of two different isotopically enriched Ge crystals (95.9% $^{70}\mathrm{Ge}$ and 86.0% $^{76}\mathrm{Ge}$) and a Ge crystal of natural isotopic composition as well as time-resolved picosecond Raman spectra of the isotopically enriched $^{70}\mathrm{Ge}$ and natural Ge were measured and compared with theoretical calculations using the self-consistent Born approximation and the coherent-potential approximation. The broadening of the Raman line in the frequency domain was found to be predominantly caused by the anharmonic decay of optical phonons into lower-energy acoustic phonons, resulting in a line broadening that is inversely proportional to the average isotopic mass m\ifmmode\bar\else\textasciimacron\fi{}. Isotopic disorder contributes only a little to the line broadening and depends on the isotopic composition of the material. From the phonon linewidths the anharmonic decay time of optical phonons in Ge at 80 K was determined to be m\ifmmode\bar\else\textasciimacron\fi{}(8.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ ps (m\ifmmode\bar\else\textasciimacron\fi{} is the average isotopic mass in atomic-mass units). The isotopic (elastic) scattering time of optical phonons depends strongly on the isotopic composition and is two orders of magnitude longer than the decay time in all samples. The asymmetry observed in the Raman lines is explained in terms of the opacity of the material and the asymmetric phonon self-energies (due to isotopic disorder). The decay time of the time-resolved incoherent anti-Stokes Raman signal is 8\ifmmode\pm\else\textpm\fi{}1 ps for both the isotopically enriched and the natural Ge. It is suggested that the discrepancy between the phonon decay time (determined from the frequency-domain measurements) and the nonequilibrium phonon population decay time (determined from the time-domain measurements) is due to effects related to the phonon-generation process in the transient experiment.

Effect of valence-subband structure on the energy relaxation dynamics of electrons in GaAs quantum wells grown on Si.

Different electron energy relaxation dynamics are observed in narrow and wide modulation Be-doped GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum wells grown on Si substrates (GaAs QW's/Si) arising from different valence-subband structure. The combination of built-in biaxial stress and spatial hole confinement results in a reversal of light- and heavy-hole subbands in narrow GaAs QW's/Si structures. For narrow (wide) quantum-well structures of 40 (188) \AA{} at 4.3 K in which there is a two-dimensional light- (heavy-) hole gas, the energy-loss process of photoexcited hot electrons is extremely rapid (slow) due to strong (weak) energy exchange with the cool light (heavy) holes. The nonequilibrium phonon population was found to build up from the relaxation of hot electrons in the 188-\AA{} wells but not in the 40-\AA{} wells.

Spectral and temporal dynamics of nonequilibrium phonons in LaF3:Pr3+

Defect-induced one-phonon absorption is used to generate high-occupation-number narrow-band nonequilibrium phonon populations at a range of frequencies in ${\mathrm{LaF}}_{3}$:${\mathrm{Pr}}^{3+}$. The spectral and temporal dynamics associated with the return to equilibrium of these phonons is observed. Processes that dominate the spectral evolution are shown to be narrow-band phonon confluence, anharmonic decay, and the broadband confluence of anharmonic decay products. The experimental data are shown to be in good agreement with a phonon-occupation-number rate-equation analysis that incudes the above processes.

Decay processes of nonequilibrium phonons in Pr3+-doped yttrium aluminum garnet.

We have investigated the decay of nonequilibrium phonons in YAG:${\mathrm{Pr}}^{3+}$ (1.0 at.%) at a temperature of 16 K. Nonequilibrium phonon populations are generated monochromatically with a high-power pulsed far-infrared laser using defect-induced one-phonon absorption and their temporal and spectral evolution determined using a time-resolved vibronic sideband spectrometer. We find that two decay mechanisms dominate the nonequilibrium phonon relaxation: anharmonic decay via three-phonon interactions and two-phonon--one-electron inelastic-scattering processes. The latter mechanism leads to the evolution of a highly peaked phonon distribution that persists for several phonon generations.

Correlation of hot-phonon and hot-carrier kinetics in Ge on a picosecond time scale.

We report room-temperature measurements of time-resolved reflectivity from intrinsic crystalline Ge induced and probed by \ensuremath{\lambda}=0.575 \ensuremath{\mu}m, 2-ps pulses and for photogenerated carrier densities up to \ensuremath{\sim}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. These data are used together with our earlier picosecond-time-resolved Raman-scattering data at 77 and 300 K to self-consistently determine transient nonequilibrium carrier and phonon effects. The combined data sets are modeled with a Boltzmann transport description of coupled electron and phonon kinetics to understand the temporal and spatial evolution of carrier density and temperature and the generation and decay of Raman-active phonons. Using known material parameters in the model, we can account for the magnitude and temporal evolution of the electron, hole, and phonon thermodynamic parameters. In particular, the model accounts for the relative delay between the peak of the pulse and the nonequilibrium phonon population, the number of nonequilibrium phonons generated, and the initially rapid diffusion of hot carriers away from the sample surface on a 5-ps time scale.

Dynamics of monochromatically generated nonequilibrium phonons in LaF3:Pr3+

The temporal evolution of nonequilibrium phonon populations in ${\mathrm{LaF}}_{3}$:${\mathrm{Pr}}^{3+}$ is investigated at low temperatures (1.8 K) utilizing pulsed, tunable, monochromatic generation and time-resolved, tunable, narrow-band detection. High occupation number, narrow-band phonon populations are generated via far-infrared pumping of defect-induced one-phonon absorption. Time-resolved, frequency-selective detection is provided by optical sideband absorption. Nonequilibrium phonon decay times are measured and attributed to anharmonic decay.

Hot-carrier dynamics in Ge on single picosecond timescales: Comparing Raman and reflectivity experiments with a self-consistent kinetic model

Through comparisons of picosecond Raman and transient reflection experiments with a comprehensive kinetic model of photo-excited carrier and lattice dynamics in Ge, we demonstrate the ability of these techniques to probe subtle aspects of non-equilibrium carrier dynamics in group IV materials at moderate injected carrier densities. Using material parameters taken from the literature, the temporal evolution of the non-equilibrium optical phonon population generated by the relaxation of photo-excited electrons and holes is obtained by solving a coupled set of Boltzmann equations for the electron and hole particle and thermal currents. The results of the calculation agree, in absolute terms, with the experimentally observed evolution of the non-equilibrium optical phonon population. The calculation also predicts that the hot plasma initially diffuses rapidly away from the sample surface, on a 5 picosecond timescale, and subsequently diffuses much slower as the carrier temperature decays to the lattice temperature, and the density gradient diminishes due to the hot carriers which have already migrated into the material. This prediction is verified by comparison of the calculated change in reflectivity due to the plasma, and picosecond reflectivity measurements performed at room temperature with 575 nm pulses.

Polar optical phonon scattering of charge carriers in alloy semiconductors: Effects of phonon localization

The effects of spatial localization of phonons or their correlation functions to finite distances in alloy semiconductors on polar optical phonon scattering of hot carriers are modeled analytically. Despite the possibility of increased numbers of carrier-scattering-active phonon modes, it is demonstrated that phonon localization in alloys should have little if any effect on the total polar optical scattering rate for charge carriers coupled to equilibrium phonon populations. Further, it is demonstrated that phonon localization may have a beneficial effect on hot carrier transport by reducing the possibility of exciting nonequilibrium phonon populations. These results are obtained without assuming any specific functional form or degree of phonon localization; rather, calculations rely on the inherent orthogonality and mathematical completeness of the classical vibrational modes over the crystal lattice degrees of freedom.

Effects of nonequilibrium phonons on the energy relaxation and recombination lifetime of photogenerated carriers in undoped GaAs quantum wells.

Time-resolved and time-integrated photoluminescence studies of an undoped multiple GaAs quantum-well structure excited by 0.5-ps laser pulses have revealed several important experimental observations on the behavior of photoexcited carriers. A large population of nonequilibrium longitudinal optical phonons produced in the energy relaxation process of hot carriers manifests itself by the nonequilibrium phonon-stimulated phonon replica which is located at \ensuremath{\sim}30 meV below n=1 electron-hole transition. The energy relaxation is substantially suppressed due to the existence of nonequilibrium phonons after an initial rapid cooling (0--5 ps). The number of photoexcited carriers decreases anomalously fast within the first 30 ps after the excitation by laser pulse. An effective carrier depletion time is determined to be as short as 10 ps. A mechanism which leads to such a short carrier depletion time is associated with the nonequilibrium phonon-stimulated phonon replica.

Nonequilibrium phonon effects on the time-dependent relaxation of hot carriers in GaAs MQW

The existence of a large population of nonequilibrium (hot) phonons after an initial rapid carrier cooling in an undoped multiple GaAs quantum well structure excited by 500fs laser pulses is experimentally verified. An effective carrier depletion time is determined to be as short as 10ps. A mechanism which leads to such a short carrier depletion time is associated with hot phonon enhanced phonon-replica-emission.

Picosecond Raman scattering from non-equilibrium LO and TO phonons in germanium

The temporal evolution of non-equilibrium LO and TO phonon populations in photo-excited Ge was monitored at 77K and 300K using a picosecond Raman scattering technique. In addition to demonstrating that significant non-equilibrium populations are produced in non-polar semiconductors, the results also indicate that carrier-TO phonon interactions are of similar strength to carrier-LO phonon interactions. The phonon lifetimes and non-equilibrium populations are discussed and compared with data obtained by others in GaAs.

Nonequilibrium longitudinal-optical phonon effects in GaAs-AlGaAs quantum wells.

We use an ensemble Monte Carlo technique to study the electron and phonon dynamics in a single quantum well of GaAs-AlGaAs under optical excitation. The cooling of the photoexcited quasi two-dimensional electron distribution is studied in the presence of a nonequilibrium longitudinal-optical phonon population and electron-electron interaction. It is found that the presence of hot phonons due to emission from the photoexcited carriers in the quantum well reduces the electron relaxation rate in qualitative agreement with available experimental results in such systems.

Picosecond luminescence measurements of hot carrier relaxation in III–V semiconductors using sum frequency generation

Abstract We review here studies of the effect of the presence of a hot carrier plasma on carrier-phonon interactions in semiconductors. We have measured the luminescence spectra under picosecond excitation of several different semiconductors from 1.55 to 0.75 microns wavelength, with time resolution of a few picoseconds. We discuss the influence of nonequilibrium phonon populations, screening, and alloy composition on carrier energy relaxation in both alloy semiconductor systems and p-type modulation on doped quantum wells.

Raman probe studies of Nd: YAlG laser generated non-equilibrium excitations in GaAs

A survey is presented of the non-equilibrium excitations in GaAs that can be probed by Raman scattering. Intense Q-switched Nd:YAlG laser pulses are used both for generating the non-equilibrium excitations at low temperature, and for in-situ Raman scattering probe measurements. Particular emphasis is placed on the search for non-equilibrium, zone-edge slow TA phonons. We discovered that the difference frequency combination spectrum involving slow TA phonons is surprisingly coincident with the acceptor excitation line spectrum for the Zn impurity. The discrimination between the non-equilibrium phonon population and a non-equilibrium hole population on minority acceptors in n-GaAs is discussed.

Spectral hole burnings at high energy tails in spontaneous emission and hot carrier relaxation in InGaAsP lasers

Spectral hole burnings in spontaneous emission spectra from 1.3 μm InGaAsP lasers were found. The results are understood on the basis of population burnings of holes associated with the saturation of intervalence-band absorption. Theoretical results on hot carrier relaxation are shown to explain the population burnings, pointing out an importance of nonequilibrium optical phonon populations in the active layers of long wavelength InGaAsP lasers and light emitting diodes (LED's).