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We show that the initial dynamics of resonantly excited excitons in quantum wells is controlled by several processes, such as radiative recombination, spin-relaxation of excitons, electrons and holes, and scattering between different momentum states of excitons. We present results of experiments designed to simultaneously probe these processes. By a unified analysis of the results we extract quantitative information about radiative, spin-relaxation and momentum- relaxation rates, obtaining a good physical understanding of the initial dynamics of non- equilibrium excitons.
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We report the direct experimental determination of the energy loss rate of photoexcited minority electrons in highly doped p-GaAs. At 300 K, the luminescence spectra are measured with high time-resolution (approximately 100 fs, using up-conversion) after low excitation (n < 1017 cm-3) of additional electron-hole pairs. The hole concentration due to doping is by two orders of magnitude higher, which ensures that the hole energy distribution stays thermal at 300 K. Within the first picosecond after excitation a rapid change of the luminescence spectra is observed, which can be clearly attributed to the energy distribution of the photoexcited minority electrons. The electron temperature decreases within 500 fs from 900 K down to less than 350 K. The energy loss rate per electron exceeds the energy loss rate by electron-phonon interaction by almost an order of magnitude. Indications of nonthermal distributions in the temporal range of 0 to 200 fs are present.
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We show that a lineshape analysis of the photoluminescence spectra of GaAs/AlGaAs quantum wells can provide valuable information on the processes ruling the exciton recombination. In particular the relevance of resonant Rayleigh scattering in the case of resonant excitation at various lattice temperatures and the validity of the thermalization hypothesis under different experimental conditions have been investigated.
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We present an experimental and theoretical study of the carrier capture time into a semiconductor quantum well. The carrier capture time was obtained by measuring both the rise of the quantum well population using time-resolved luminescence measurements and the decay of the barrier population using pump-probe correlation experiments. In the first technique we compare the QW rise times after direct (below the barrier band gap) and indirect (above the barrier band gap) excitation, in order to eliminate the effects of relaxation and exciton formation in the quantum well. We report the first experimental observation of oscillations in the carrier capture time between 3 and 20 ps as a function of quantum well thickness, obtained from both techniques. The observed capture times are for the first time in agreement with theoretical predictions from an ambipolar capture model.
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Dynamics of free and bound excitons in CdSe, localized excitons in CdSexS1-x, and confined two-dimensional excitons in GaAs/AlGaAs quantum wells have been studied by degenerate four-wave mixing and light-induced grating experiments. In the coherent range, the dephasing of excitons has been determined as a function of temperature, density, and energy. For incoherent excitons, we have determined recombination lifetimes and diffusion coefficients. In particular, we have studied the mobility of excitons in CdSexS1-x near the mobility edge. Quantum interferences are observed in the nonlinear signal from these exciton systems, and the nature of these four-wave mixing beats are being discussed.
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We report a spectroscopic investigation of the stationary and transient recombination processes in rectangular GaAs quantum well-wires. The ground level exciton states are studied by linear and non linear photoluminescence excitation spectroscopy, providing information on the one-dimensional exciton binding energy and on the actual band gap edge of the wires. The carrier density dependence and the temporal evolution of the band gap renormalization in GaAs quantum wires have been determined by a line-shape analysis of the time resolved electron-hole plasma luminescence. The obtained data are compared with recent theoretical calculations.
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Ensemble Monte Carlo simulations of hot nonequilibrium electron relaxation in rectangular GaAs quantum wires is carried out. The simulations demonstrate that the initial stage of hot photoexcited electron cooling dynamics is determined by cascade emission of optical phonons. The second relaxation stage is controlled by inelastic electron interaction with acoustic phonons and exhibits strong dependence on the cross-section of a quantum wire. If electron concentration exceeds 105 cm-1 nonequilibrium (hot) phonon effects come into play and hot phonon thermalization time defines the characteristic electron gas cooling time. In contrast to bulk materials and quantum wells, hot phonon effects in quantum wires are strongly dependent on the initial broadening of energy distribution of photoexcited electrons.
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The Hamiltonian describing the deformation potential interaction of confined acoustic phonons with carriers is derived by quantizing the appropriate, experimentally verified approximate compressional acoustic phonon modes in a rectangular quantum wire. The scattering rate due to the deformation potential interaction is calculated for a range of quantum wire dimensions.
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We report systematic studies of the femtosecond transient reflectivity and transmission in low- temperature-grown III-V semiconductors. By using a 2-eV-pump/white-light-probe system as well as a tunable infrared laser we are able to investigate different materials and shed new light on the processes governing the photoexcited carrier dynamics in these compounds.
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We report new experimental results on the internal thermalization of the electron-hole plasma (EHP) in bulk GaAs. Time-resolved differential transmission spectra have been systematically studied for different pump photon energies (1.45 eV < $HBAR(omega) < 1.51 eV) and different excitation intensities. The experimental data demonstrate that the plasma thermalization is achieved within a stable interval of 150 - 200 fs for plasma densities ranging from 2 X 1017 to 2 X 1018/cm3. Experimental results are in good agreement with the thermalization times deduced from plasma dynamics calculations using dynamic screening of the interactions in the framework of Boltzmann's equations.
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We time-resolve the transient, photoinduced transmission and reflectivity changes near the direct bandedge of crystalline germanium (at 295 K) with 120-fs, tunable, infrared pulses from a 76-MHz optical parametric oscillator. The data show a rich collection of phenomena including bandgap renormalization, carrier-carrier scattering, carrier cooling and (Gamma) yields L intervalley scattering. An apparent carrier density dependence in the measured intervalley scattering time is attributed to plasma screening of the Coulomb enhanced continuum absorption.
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Energy relaxation of electrons in the X6 and X7, satellite, X6 (reversible reaction) (Gamma) and X7 (reversible reaction) (Gamma) , have been investigated using time-resolved UV pump-IR probe absorption spectroscopy in GaAs and GaP. Energy band renormalization of the X6 and X7 valleys, band filling effects in the X6 yields X7 spectra, and O.D. spectral relaxation of electrons in the X6 and X7 valleys by intervalley scattering, X6 (reversible reaction) (Gamma) and X7 (reversible reaction) (Gamma) , were all observed as a function of photoexcited electron density. From the observed energy relaxation dynamics it is determined that X7 yields (Gamma) intervalley scattering is faster than X6 yields (Gamma) intervalley scattering in GaAs. These experiments were performed by measuring the absorption spectra of 500-fs IR probe pulses induced by 500-fs UV pump pulses, as a function of delay time and pump pulse fluence. The spectra, at different pump pulse fluences and pump-probe delay times, are interpreted in terms of free carrier absorption, X6 yields X7 direct interconduction band absorption, and indirect interconduction band absorption.
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Coherent states of optical phonons and polaritons are created through coherent Raman excitation (CRE) and their dephasing is determined through pico- and femtosecond time resolved coherent anti-Stokes Raman spectroscopy (TRCARS). The temperature dependence of the dephasing is used to identify the acoustic phonons generated from the decay of coherent optical states. The general decay channel involves the decay of the optical phonons and polaritons into two acoustic phonons each with one half the optical phonon energy and with compensating wave vectors. In some cases the decay channel is more complicated. In order to conserve momentum one of the phonons is near the positive X-point and the other near the negative X-point of the Brillouin zone. The TA phonon is on the lowest dispersion branch and, therefore, cannot further decay into lower energy phonons and still obey energy and momentum conservation. Thus to third order in the decay kinetics the TA phonons should have infinite lifetime. Our observations lead to a TA phonon lifetime of 66.5 +/- 5 ns.
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We present recent time-resolved measurements of the linear dielectric constant of GaAs at 2.2 eV and 4.4 eV following femtosecond laser pulse excitation. In sharp contrast to predictions based on the widely used Drude model, the data show an interband absorption peak coming into resonance first with the 4.4 eV probe photon energy and then with the 2.2 eV probe photon energy, indicating major changes in the band structure. The time scale for these changes ranges from within 100 fs to a few picoseconds, depending on the incident pump pulse fluence.
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Utilizing transform-limited time-resolved light scattering with simultaneously optimum temporal and spectral resolution, it is possible to investigate on a picosecond time scale energy and phase relaxation processes of excitons in semiconductors. Thereby quantum-beating as a measure of exciton coherence allows us to discriminate Raman scattering from hot luminescence as exemplified for indirect free excitons in AgBr. In order to distinguish resonant Rayleigh scattering occurring in disordered systems from ordinary fluorescence, the experimental setup has to be fully included in the theoretical description of the light scattering process. Experiments at the (n equals 1, e-hh) exciton in GaAs/AlGaAs quantum well structures confirm the predicted finite decay of this process and allow us to measure the exciton relaxation dynamics.
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A picosecond laser excited GaAs p-i-n structure is studied using an ensemble Monte Carlo method to determine the temporal and spatial evolution of the hot electron distribution function. The experimental set-up we simulate is a novel method based on Raman scattering of light from the electrons to measure the drift velocity of electrons in GaAs at high electric fields. It is observed that the simulation agrees with the experimental results, however, the measured velocity is actually averaged over the time evolution of the spatial distribution of the Raman probe in the sample and underestimates the average velocity of electrons over the pulselength excited in the (Gamma) conduction band of a 1.909 eV laser pulse, which is calculated to be in the order of 8.5 X 107 cm/sec for fields of 25 kV/cm at a temperature of 77 K.
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Eric D. Grann, Shou Jong Sheih, C. Chia, Kong-Thon F. Tsen, Otto F. Sankey, George N. Maracas, R. Droopad, Arnel A. Salvador, Andrei Botchkarev, et al.
Electric-field-induced non-equilibrium carrier distributions in GaAs-based p-i-n nanostructure semiconductors has been studied by transient Raman spectroscopy on a picosecond time scale and at T approximately equals 80 K. For an injected carrier density of n approximately equals 2.2 X 1018 cm-3 and electric field intensity E equals 25 KV/cm, the drift velocity of electrons as high as Vd equals 2.5 X 107 cm/sec was observed. We demonstrate in this work that time-resolved Raman spectroscopy is a feasible technique to interrogate both ballistic transport and velocity overshoot phenomena in nanostructure semiconductors.
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A modified coherent model, which includes the inhomogeneous broadening effect of the excitonic linewidth, of the resonant tunneling (RT) of electrons in double quantum wells is presented. The validity of the model is confirmed with the experiments and shows that the resonant tunneling process of electrons can be mostly explained by the simple coherent theory. We discuss the influence of linewidth on resonant tunneling time, which is strongly dependent on the barrier thickness LB, by introducing the contrast-ratio (Lambda) and the full width at half depth (FWHD) of the RT valley, and we found that (Lambda) first increases with increasing barrier thickness, reaches a maximum, and then decreases with a further increase of LB, in striking contrast to the Fabry-Perot (FP) analogy where a monotonous increase of the current peak-to-valley ratio is predicted. A decrease of the FWHD monotonously with increase of LB is also found. We discuss the potential application of our results in the design of tunneling devices.
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For bulk GaAs as representative material we estimate the possibility of experimentally detecting oscillatory coherence effects in the transient nonlinear pump-and-probe absorption spectroscopy of semiconductors involving highly energetic and dense photo-excited electron- hole plasmas. Under such high-excitation conditions coherence effects in the nonlinear optical response are very difficult to observe because the carrier dynamic is strongly dominated by phase-breaking scattering processes, and here predominantly by carrier-carrier scatterings. Our theoretical framework consists of a hybridization of the quantum-mechanical equations of motion for the two-particle density matrix in k space with an ensemble-Monte-Carlo simulation of the single-particle scattering dynamics. Within the well-established Markov approximation this allows us to consistently obtain the leading scattering contributions to the electron-hole amplitude and thereby to the induced polarization and to the nonlinear optical susceptibility. For pump-and-probe absorption spectroscopy we propose, in terms of the excitation density and energy and of the temporal widths of the pump and the probe pulse, realizable experimental scenarios as candidates for detectable `Rabi'-type oscillatory coherence effects in the transient absorption change (bleaching) at the excitation frequency.
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We studied intersubband relaxation of carries during ultrafast photoexcitation in single and coupled quantum wells using ensemble Monte Carlo simulation, Intra- and intersubband scattering due to polar and nonpolar optical phonons, acoustic phonons, and intercarrier scattering are included in the simulation. The polar optical mode description is given in terms of a two-pole dielectric continuum model for the alloy barriers. In the present work we focus on relaxation when the 2-1 subband spacing is smaller than the optical phonon energy so that suppression of the intersubband polar optical phonon scattering rate occurs. Our results for a single well show that intercarrier intersubband scattering dominates over acoustic phonon scattering during the initial relaxation of carriers from 2-1, with a strong contribution due to polar optical phonon emission from the tails of the heated distributions as well. We have studied optical pumping for a 3 level coupled quantum well system in which (Delta) E12 is less than h(omega) 0, and calculate the change in occupancy of the excited subbands through pumping of the 1-3 transition.
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A rigorous theory of the optical rectification in the zinc-blende semiconductors is developed. This theory combines the bonding orbitals representation of the electrons in the semiconductor with the band structure representation. It is shown that when the semiconductor is excited above the absorption edge there is a strong resonant enhancement of the optical rectification signal and connected with it emission of the terahertz radiation. Both the magnitude and the temporal characteristics of this signal are closely related to the intraband relaxation processes in the valence band.
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Electron-hole correlations play an important role for understanding the conditions of thermalization and the optical properties of the electron-hole plasma (EHP) in the subpicosecond regime. We first discuss the consideration of the dynamic screening in the framework of Boltzmann's transport equations. Carrier-carrier scattering rates are computed and compared for different approximations. We show that the dynamic screening significantly increases the electron-electron collision rate. Then we discuss the variation of the absorption coefficient in the presence of a non-thermalized EHP. We show that the change of the electron-hole correlations induces a small oscillation of the absorption around the excitation energy.
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The transition from a nonthermal into a thermal distribution of electrons at low densities (< 1014 cm-3) is traced on a picosecond time-scale by the time evolution of a band-to-acceptor transition in GaAs:Be. Two narrow, nonthermal electron distributions are detected during the first picoseconds originating from the heavy- and light-hole valence band, respectively. Measurements with circular polarization of excitation and luminescence confirm this assignment. The variation of their energetic peak-positions with excitation energy allows the experimental determination of the valence band dispersions for very small wave vectors near k equals 0, where only parabolic energy terms contribute to the dispersions. The results are consistent with the commonly used effective hole masses.
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Momentum relaxation of photo-excited carriers in GaAs was investigated using the Monte Carlo approach. A laser of 1.51 eV photon energy and 9 fs width was assumed. Simulations were performed for excitation densities ranging from 1016 cm-3 to 8 X 1017 cm-3. For nexc equals 8 X 1017 cm-3, the distribution of the carrier momentum was found to approximate a Maxwell-Boltzmann distribution 25 fs after laser excitation, which concurs with recent experimental data. The relaxation time was shown to increase with decreasing carrier density and to be shorter when the carrier-carrier scattering was treated dynamically rather than statically.
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We introduce a scaled ensemble Monte Carlo technique for the simulation of semiconductor plasmas at ultrashort times after excitation. The error, from counting statistics, can be decreased directly either by a computationally expensive increase in the number of simulation trajectories or by averaging over long times. The latter approach cannot be applied in studying ultrafast, far-from-equilibrium phenomena. The remaining alternative is to redistribute the computational effort to weight more heavily those regions with low densities. Scaled EMC uses ordinary EMC weighting, but simulates a different function, related by an energy- dependent scaling factor to the usual particle distribution. The simulation trajectories obey the same free-flight equations of motion as ordinary EMC, with no `splitting' of particles or iteration of trajectories. We describe simulations of modulation-doped GaAs structures under applied fields. G-, L- and X-valley carrier populations are determined across more than seven orders of magnitude in density, using only ten thousand simulation points, with fractionally small sampling error across a one-volt energy range. Using standard EMC with the same number of points, sampling statistics necessarily limits the range of simulable densities to less than four decades overall.
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Ultrafast relaxation of photo-excited electrons in p-doped and intrinsic GaAs has been investigated using the Monte Carlo method. Dynamic screening of the carrier-carrier (c-c) interaction has been implemented using a momentum and frequency dependent dielectric function. Compared to the static c-c scattering model, the current approach results in faster cooling of the electron-hole plasma, due to enhanced carrier-carrier scattering rates. In p- GaAs, the energy relaxation shows that the electron-hole plasma (EHP) cools faster with increasing hole concentration. The transient luminescence intensity and the effective carrier temperature computed from luminescence spectra compare favorably with experimental data.
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At high electric fields negative differential resistance and oscillatory behavior of the current is observed in 2-dimensional electron gases in modulation doped heterostructures. We develop a model in which the understanding of these phenomena is provided by the ohmic contacts to the 2-dimensional electron gas. The key phenomenon is that at a high electric field, well below the threshold field for real space transfer across the interface between the GaAs and the AlxGa1-xAs, injection of electrons from the contacts into the AlxGa1-xAs layer opens a conductive channel in the AlxGa1-xAs parallel to the 2-dimensional electron gas in the GaAs layer. We show that avalanche ionization in the AlxGa1-xAs layer leads to current filamentation. We studied this behavior for various experimental conditions by means of a novel technique which we developed for this purpose: the technique of time resolved optical beam induced current.
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We have measured the time-resolved photoconductive response of a strained InGaAs/InGaAsP/InP multiple quantum well laser structure as a function of temperature and bias. It is found that the hole escape is dominated by tunneling at reverse biases of greater than -0.5 V at all temperatures. Under forward bias, recombination is dominant at temperatures below approximately 90 K while thermal escape processes prevail at higher temperatures. From Arrhenius plots of the hole escape time, the activation energy from the ground level has been determined as a function of bias and is in good agreement with a valence band offset of 75% of the total band offset. The intercepts of the plots yielded a scattering parameter of 6 ps. The carrier dynamics within the well were simulated using a simple model of thermionic emission and gave good qualitative agreement. The calculations indicate that the structures have the potential for extremely fast detection.
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Negative differential velocity is evidenced in semiconductor superlattices through several experimental approaches: temperature dependence of the current-voltage characteristics, frequency spectrum of the microwave S-parameters, and time-resolved photocurrent induced by a short optical pulse. In particular, new experimental data for GaInAs/AlInAs superlattices matched to InP are analyzed owing to classical models. They yield the miniband width dependence of the mobility, critical field and peak velocity which describe the electron velocity laws. The latter are in fair agreement with a semiclassical model based on numerical solutions of the Boltzmann equation, i.e., a rigorous extension of the simpler Esaki-Tsu model of miniband conduction. In the dynamical experiments, the temporal evolution of the electron distribution in the superlattice structure is represented in terms of propagating space charge waves, which can give rise to amplification and oscillation. Consequences of miniband conduction regarding maximum frequency and noise of superlattice-based oscillators are also examined.
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The electron and hole transport in a triple-barrier resonant tunneling diode are investigated using photoluminescence spectroscopy on a picosecond and nanosecond time scale. Time- resolved populations are created by exciting only the GaAs contact layers on either side of the tunneling structure but luminescence signals are detected from each of the two consisting quantum wells. Under external bias, several alignment conditions are investigated. First, the resonance of the ground state of the accumulation layer with either the narrow or the wide well depending on the bias direction. Second, the alignment of the accumulation layer with both quantum well subbands. For most external biases, the excess photocreated electron density is small with respect to the steady-state injected current density and the transient luminescence reflects the hole population. Both rise and decay of the transient photoluminescence are governed by the hole tunneling rate which increases with increasing bias. The sequential process of tunneling from the first to the second quantum well is apparent from a comparison of the signals in opposite bias direction. In the low current regime, time- resolved electron tunneling manifests, which adds a fast component to the transient luminescence signal.
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High frequency modulation properties of distributed feedback (DFB) lasers are analyzed by optical excitation with picosecond pulses. Typical time constants of the large signal response were investigated. Measurements at different temperatures demonstrate that capture of carriers from the adjacent barrier energy levels into the active region of the laser are dominant mechanisms for laser dynamics. This carrier transfer consists of the intrinsic processes of carrier-carrier scattering, carrier energy relaxation, carrier diffusion, and quantum mechanical capture of carriers into the quantum wells. In order to separate the limiting processes for laser speed, the influence of relaxation processes from different energy levels on the device response was tested by varying the wavelength of the excitation pulse. To investigate modulation limitations due to intrinsic band structure parameters, the laser emission wavelength was detuned against the gain spectrum by varying the grating period of a DFB laser. Longer time constants at higher wavelengths demonstrate that the differential gain constant is the most important contribution for modulation speed. A theoretical description based on a 3 level system model yields rate equations which explain our experimental results.
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Relaxation of photoconductivity (PC) in Ga-doped PbTe under picosecond pulse excitation was investigated in the temperature range of 77 - 200 K. Processes of nano-, micro-, and millisecond time scale were observed depending on excitation level and temperature. At 160 K PC response shortened up to 1 ns making it possible to resolve single pulses of picosecond pulse train. Studies of temperature dependence of PC lifetime revealed additional low- frequency process (far less 800 Hz) which was closely connected to long-term relaxation of PC at low temperatures. The two-level model was shown to explain qualitatively main PC processes observed in PbTe(Ga) crystals.
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Electronic interference effects in the ballistic conductivity of 1-D and 2-D quantua structures •ith two-diaensional nonunifora potential relief created by the lateral controlling electrode are theoretically investigated It is shown that in such structures one can create quasi-localized electronic states, this results in appearance of sharP. singularities in dependencies of the structure transaission coefficient ITl 2 on particle energy and controlling field.
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We present results of a theoretical study of tunneling of laser-generated conduction-band electrons between two adjacent GaAs-AlGaAs quantum wells. Carriers are excited in the left well by a suitable sub-picosecond laser pulse. Damping of ensuing charge oscillations due to the electron-electron interaction is studied within the density-matrix formalism. A tractable set of generalized Boltzmann equations is derived which accounts for carrier generation, an exact treatment of the tunneling process, and the Coulomb interaction between electrons within the adiabatic (scattering) approximation. A detailed study of the evolution of the electron distribution is presented. We have found that, depending on structural parameters and excitation levels, the Coulomb interaction provides an efficient agent to destroy phase coherence in the system and to drive the system back towards equilibrium.
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