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exciton relaxation and dephasing in InGaAs quantum dots (QDs) in the temperature range ... are performed with a sensitive heterodyne detection technique.
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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 8, NO. 5, SEPTEMBER/OCTOBER 2002

Exciton Relaxation and Dephasing in Quantum-Dot Amplifiers From Room to Cryogenic Temperature P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Member, IEEE

Abstract—We present an extensive experimental study of the exciton relaxation and dephasing in InGaAs quantum dots (QDs) in the temperature range from 10 K to 295 K. The QDs are embedded in the active region of an electrically pumped semiconductor optical amplifier. Ultrafast four-wave mixing and differential transmission spectroscopy on the dot ground-state transition are performed with a sensitive heterodyne detection technique. The importance of the population relaxation dynamics to the dephasing is determined as a function of injection current and temperature. Above 150 K dephasing processes much faster than the population relaxation are present, due to both carrier–phonon scattering and Coulomb interaction with the injected carriers. Only at low temperatures ( 30 K) does population relaxation of multiexcitons in the gain regime fully determine the dephasing. Index Terms—Four-wave mixing (FWM), quantum-dot (QD) amplifiers, ultrafast optics.

I. INTRODUCTION

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HE application of semiconductor quantum dots (QDs) in optoelectronics has progressed impressively since the first realization of electroluminescence from a semiconductor laser structure containing quantum boxes in 1987 [1]. With modern nanotechnologies, epitaxially grown semiconductor QDs with high crystalline and optical quality can be fabricated [2] and are very appealing as active components in improved-performance devices such as low threshold–current diode lasers [3], 1.3- m-wavelength vertical-cavity surface-emitting lasers on GaAs substrates [4], ultrafast amplifiers [5], [6], and high-temperature infrared photodetectors [7]. Besides optoelectronics, the application of QDs in cavity quantum electrodynamics [8], [9], photon antibunching [10], [11], and quantum computation [12] has also received increasing attention in the past few years. The homogeneous broadening of an optical interband transition in a QD is a physical property of basic importance for any application that relies on the atom-like character of QDs. The homogeneous broadening is inversely proportional to the dephasing time, which is the decay time of the optically induced polarization associated with the transition [13]. Intrinsic mechanisms such as radiative recombination, carrier–phonon scattering, and carrier–carrier scattering determine the dephasing

Manuscript received May 14, 2002. This work was supported by DFG in the frame of Wo477/17-1 and SFB296. The work of P. Borri was supported by the European Union with the Marie Curie Individual Fellowship Contract HPMF-CT-2000–00843. P. Borri, W. Langbein, S. Schneider, and U. Woggon are with the Experimentelle Physik IIb, Universität Dortmund, 44221 Dortmund, Germany. R. L. Sellin, D. Ouyang, and D. Bimberg are with the Institut für Festkörperphysik, Technische Universität Berlin, 10623 Berlin, Germany. Digital Object Identifier 10.1109/JSTQE.2002.804250

time which is, therefore, a direct probe of the ultrafast carrier dynamics in a QD. Transient four-wave mixing (FWM) spectroscopy is a powerful tool to directly measure the dephasing time even in an inhomogeneously broadened ensemble of transitions [13]. However, while it has been reported in GaAs islands [14] and in II–VI QDs [15], [16], FWM on self-assembled III–V QDs was found to be very difficult to measure and, thus, only very recently reported [17]–[19]. In electrically pumped InGaAs QD amplifiers, time-resolved FWM at room temperature was recently reported [6], [20]. In InAs–InGaAs QDs with 100-meV confinement energy, the dephasing time of the excitonic ground-state (GS) transition was measured to be about 260 fs without electrical injection [17] and decreasing to less than 50 fs in the gain region [20]. This corresponded to a homogeneous broadening going from 5 meV to more than 25 meV due to Coulomb scattering with the electrically injected carriers. These broadenings set an intrinsic limit to the delta-function-like density of states in the QDs. Note that a 25-meV homogeneous broadening is comparable to currently achieved inhomogeneous distributions in QD ensembles and implies a dominant homogeneous broadening behavior in QD lasers [21], important for continuous-wave high-power applications. Carrier dynamics in QDs have been intensively studied in recent years and effects such as long radiative lifetimes, inhibited interaction with phonons, and Auger-type carrier scattering have been widely debated in theory and experiments. For the application of QDs to devices, carrier dynamics are an important issue since they intrinsically limit their high-speed performance (see, e.g., [5] and [22]). Carrier relaxation dynamics in InGaAs QDs have been directly studied using time-resolved photoluminescence (see, e.g., [23] and [24] and references therein) or differential transmission spectroscopy (DTS) [25], [26]. Electrically pumped QD amplifiers showed an ultrafast gain recovery at room temperature [5], [27] promising for high-speed optical communications. It is important to point out that the dynamics of the carrier density is different from the dynamics of the induced polarization given by the dephasing time. In fact, the dephasing is ultimately limited by the population relaxation dynamics, but can be faster [13]. Processes that do not affect the population dynamics but influence the decay of the polarization are often called “elastic” or “pure” dephasing processes. A comparative study of population relaxation and dephasing times allows one to infer important new insights on the carrier dynamics and on the physical origin of the homogeneous line broadening in QDs. However, this comparison is hardly reported in the literature on self-assembled QDs. We showed that, at room temperature, a homogeneous broadening of 5–6 meV is

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BORRI et al.: EXCITON RELAXATION AND DEPHASING IN QUANTUM-DOT AMPLIFIERS

measured in the excitonic GS transition of In(Ga)As QDs with different confinement energies (from 100 meV to more than 200 meV) which, conversely, exhibit pronounced differences in the exciton population dynamics [28]. In the presence of electrically injected carriers, InAs QDs with large confinement energies ( 200 meV) showed a longer dephasing time compared to dots with smaller confinement. The comparison with the population dynamics indicated a quenching of the elastic dephasing by Coulomb scattering with carriers in the barrier/wetting layer material due to the low carrier density in the wetting layer [6]. In this paper, we study the exciton dephasing time and relaxation dynamics in an electrically pumped InGaAs QD amplifier in the temperature range from 10 K to 295 K, using heterodyne FWM and DTS techniques of high sensitivity. The contribution of the population relaxation to the dephasing is determined as a function of temperature and injection current. We find that pure dephasing processes due to both phonon scattering and Coulomb interaction with the injected carriers dominate above 150 K, while the dephasing is lifetime-limited only at temperatures below 30 K. The paper is organized as follows. In Section II, the investigated sample and the experimental techniques are described. In Section III, the gain properties of the QD amplifier are shown versus temperature and electrical injection, and the transition from thermal equilibrium to a nonthermal distribution of carriers among the dots in the ensemble is distinguished. In Section IV, we present FWM results that allow us to measure the dephasing time of the excitonic GS transition. In Section V, the DTS measurements are shown and the relation between dephasing and population relaxation is discussed. Section VI gives a summary of the work.

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Fig. 1. Sketch of the experimental heterodyne setup and of the QD waveguide structure. ! and ! are radio-frequency shifts of the optical laser frequency of pump and probe pulses with a relative time delay  in a quasi-degenerate scheme. The signal is detected at the probe frequency for DTS or at the FWM frequency for coherent spectroscopy.

II. SAMPLES AND EXPERIMENT The investigated sample is a p-i-n structure grown by metal–organic chemical vapor deposition containing three layers of self-organized In Ga As QDs separated by 35-nm-thick GaAs spacers. Two AlGaAs cladding layers and a ridge structure of 5 m width and 500 m length provide optical waveguiding. The end facets were tilted to avoid multiple reflections and lasing. A sketch of the structure is shown in Fig. 1. In the presence of an injection current ( ), amplified spontaneous emission (ASE) is detected and spectrally resolved, as shown in Fig. 2, at a temperature of 25 K. At exciton recombination (GS small , the ASE shows the are the lowest lying twofold spin transitions), where and degenerate states of electrons and holes in the dot, respectively. At 25 K, thermalization among the dots does not occur and reflects the inhomogeneous distribution of the ASE at low the GS transitions due to the random capture of the injected carriers by the dots [29]. We infer a Gaussian inhomogeneous broadening of 60-meV full-width at half-maximum (FWHM) due to fluctuations in dot size and indium concentration. At , saturation of the GS exciton occupation occurs higher and (Pauli blocking allows no more than two carriers in ) and recombination of electron and holes in the first two [excited-state (ES) transitions], which excited levels are nearly degenerate in dots with good cylindrical symmetry [30], is visible 65 meV above the center of the GS transitions.

Fig. 2. ASE spectra at 25 K at low (0.5 mA) and high (20 mA) injection current. The excitonic ground state transition (GS) is inhomogeneously broadened and separated from the first excited-state transition (ES) by 65 meV. The spectrum of the pulse used in the experiment is shown. The curves are vertically displaced for clarity.

Photoluminescence on a reference sample shows a wetting layer transition 210 meV above the dot ground state, quantifying the strong confinement. QD lasers fabricated from the same structure showed efficient GS lasing at room temperature with low transparency current densities ( 6 A/cm per quantum-dot layer) indicating the good crystal quality and the high quantum efficiency of the dots [31]. The DTS and FWM experiments are performed using an optical parametric oscillator providing Fourier-limited 150-fs pulses at 76-MHz repetition rate, with a wavelength tuned to the center of the GS transitions (as shown in Fig. 2) which ranges from 1170 nm at 300 K to 1070 nm at 7 K. At this wavelength, we estimate a negligible contribution (2%) of the excited states to the optical density of states. Two colinearly polarized pulses

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are coupled into the transverse electric waveguide mode with a (see sketch of the experiment in Fig. 1). relative delay time and the Pulse 1 (pump) leads pulse 2 (probe) for positive signal is detected using a heterodyne technique similar to the one discussed in our previous work [32], but modified for high repetition rates with an improved signal-to-noise ratio [33]. In this technique, the pulse 1 (2) is frequency shifted by ( ) and the DTS signal is detected the radio-frequency while the FWM signal is detected at the frequency shift . In the FWM experiment, the intensities of the at exciting pulses were in the limit of small absorption bleaching ( 0.1 electron–hole pair excited per dot on average) and the FWM signal was in the third-order regime. Note that in the heterodyne detection, a reference pulse interferes with the signal, and its delay time relative to the signal can be varied in order to time-resolve the signal [33]. Therefore, the signal field amplitude is measured via its interference with the electromagnetic field of the reference pulse. The sample was held in a specially designed cryostat that allowed light-coupling with high numerical aperture into and out of the waveguide. III. GAIN PROPERTIES It has been shown in several reports that at high temperatures (typically above 200 K), thermal carrier emission out of the dot and recapture into adjacent dots occurs before recombination in InGaAs QD ensembles [34]–[36]. In this case, the equilibrium carrier distribution function across the ensemble is close to a Fermi function which, with increasing temperature, spreads over the excited states of the dots [37]. At low temperatures (typically below 100 K), the carrier escape time out of a QD is longer than the recombination lifetime, and different QDs are isolated from each other in the ensemble. Due to the random capture of carriers, the nonthermal equilibrium among the dots implies that dots with different GS energies are equally occupied on average, which is a highly non-Fermi distribution [37]. These carrier distributions have been shown to result in a peculiar temperature-dependent threshold current density in QD lasers. The threshold is independent of temperature for nonthermal equilibrium, decreases in the transition toward thermal coupling among the dots, and then increases with temperature [29], [38], [39]. We have investigated the transition from thermal to nonthermal carrier distribution in the QD ensemble, both considering the temperature dependence of the ASE spectra as well as the temperature dependence of the GS small-signal gain. The temperature dependence of the ES occupation for a given GS (average) population is qualitatively indicated in Fig. 3. ASE spectra at the injection currents corresponding to on average) of the optically probed transparency (i.e., one center of the GS transitions (see Fig. 2) are shown in Fig. 3, normalized to the GS peak, and spectrally shifted to coincide with the GS low-energy tail at room temperature. The minimum occupation of the ES transitions occurs at 150 K, where the GS emission spectrum is also the narrowest. This behavior indicates that thermalization among the dots occurs down to 150 K. At this temperature, the most selective occupation occurs with only the lower energy GS states within the ensemble preferentially occupied and a strong quenching of the thermal

Fig. 3. ASE spectra at different temperatures, as indicated, for the injection current corresponding to transparency at the center of the GS transitions. The spectra are normalized, spectrally shifted to coincide on the low-energy tail at 295 K, and vertically displaced for clarity.

spread into the excited states. When the carrier distribution becomes nonthermal at low temperatures, the occupation of the excited states reincreases. This is consistent with calculations of the carrier distribution in [37]. It can be understood as a consequence of the random capture and the increased Pauli blocking of the ground state for the same GS gain [37]. The temperature dependence of the small-signal modal gain of the GS transition is shown in Fig. 4 versus . The modal gain is measured by the transmission of a weak 150-fs pulse in the center of the inhomogeneous distribution (see Fig. 2). Negative (positive) values indicate absorption (gain) and the current at (gain ) is shown in the inset as a function transparency of temperature.1 The transparency current decreases from room temperature to 150 K, and reincreases below 150 K as expected in the transition from thermal to nonthermal equilibrium among the dots [29], [39]. However, the increase below 50 K is not should be temperature independent in the expected, since limit of nonthermal distribution [29], [39]. We believe that at low temperature an increased diffusion of the injected carriers out of the ridge stripe occurs, as confirmed from the observation of the spatial profile of the ASE from the output facet of the device. Before closing this Section, we would like to comment on a puzzling aspect of the data in Fig. 4, namely the value of the saturated modal gain which is strongly varying with temperature and is always smaller than the maximum absolute value for absorption. The absorption coefficient of a two-level system is known to be proportional to the transition energy [40], which however changes by only 10% from 300 K to 10 K in the investigated sample (see Fig. 3). The observed change of the 1Transparency current I was inferred from the DTS data (see Section V) and thus the modal gain in Fig. 5 does not include waveguide losses (see also [5]).

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Fig. 4. Small-signal gain versus injection current at different temperatures, as indicated. In the inset, the transparency current versus temperature is shown. The data at zero bias, where a built-in electric field is present due to the diode structure of the sample, are shown as separated points.

maximum modal gain from 10 cm to 20 cm between 300 K and 150 K could be due to a temperature-dependent confinement factor and/or free carrier absorption. Even more surprising is the difference between the maximum absorption and the maximum gain observed at all temperatures. At saturation the maximum modal gain should be equal to the maximum absorption, being given by the density of states and the transition oscillator strength. At room temperature, one can speculate that full saturation can be reached only at very high injection current where strong Coulomb renormalization spectrally shifts and reshapes the gain [41]. We can also comment that the maximum absorption value was obtained with the device being unbiased and, thus, not in flat-band condition of the intrinsic region which occurs in forward bias. To emphasize the difference, the absorption for the unbiased device is indicated as a separated point in Fig. 4, while at forward bias the data are joined with a solid line. In flat-band conditions at low temperature the maximum absorption/gain ratio is almost 1 : 1. This might suggest that the oscillator strength is changed in the presence of the built-in electric field in the unbiased device, giving rise to an increased absorption. However, it remains unexplained why this effect is temperature dependent. We also observed no further increase of the absorption for reverse bias. At this stage, we do not have a conclusive interpretation of these findings which should await further study. IV. FOUR-WAVE MIXING SPECTROSCOPY: EXCITON DEPHASING TIME We have recently reported on the temperature-dependent dephasing time of the GS transition without injection current in order to investigate the dephasing processes due to , the excitonic exciton–phonon interactions [18]. At (labeled 0– ) is transition from the crystal ground state to probed in the experiment. While the dephasing time is ultrafast at room temperature ( 200 fs), we measured 630-ps dephasing time at 7 K corresponding to only 2 eV homogeneous

Fig. 5. Time-integrated FWM field amplitude of the GS transitions at different temperatures, as indicated, without electrical injection (dotted lines) 20 mA (solid lines). Curves at different temperatures are vertically and at I displaced for clarity. Labels of the different excitonic transitions probed in the experiments are shown. Thin dashed lines mark the two distinct decays of the signal at 10 K and I = 20 mA. An exponential fit to the data is shown at 150 K and I = 0 (solid line) and a numerical simulation to the data is shown at 295 K and I = 20 mA (dashed line).

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broadening close to the radiative lifetime limit. Moreover, below 100 K, we found a strongly nonexponential polarization decay corresponding to a non-Lorentzian lineshape of the 0– transition. These results suggested a new description of the line broadening in InGaAs QDs in terms of a sharp zero-phonon line (ZPL) and of a broadband from exciton–acoustic phonon interactions, similar to findings in II–VI QD’s [42]. Inelastic dephasing processes such as radiative decay and phonon absorption into higher energy excitonic states influence the broadening of the ZPL, while the broad band arises from an elastic dephasing of the 0– transition due to the local lattice distortion associated with the excitonic excitation in dots of small sizes [18], [42]. The effect of electrically injected carriers to the dephasing time of the GS transition is shown in Fig. 5 at different temperatures. In the figure, the time-integrated FWM field amplitude for 0 mA (dotted lines) and 20 mA (sold is shown versus lines) injection current, as indicated. From 300 K to 150 K, the polarization dynamics are dominated by a fast decay with a dephasing time ( ) below 1 ps. We showed in [18] that the corre) of the 0– sponding homogeneous broadening ( transition ( ) linearly increases with temperature from 3 to 6 meV from 125 K to 300 K. The dephasing time was taken from an exponential fit of the data, as shown, e.g., at 150 K in mA saturation of the , occupation and Fig. 5. At excitons is evident in the ASE spectra filling of the at all temperatures (see also Figs. 2–4). We found that transmA at room temparency of the ES transition occurs at

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Fig. 6. Power spectrum of the time-integrated FWM field at 25 K, with and without injection current as indicated.

perature and at mA at 10 K [44]. In the presence of excitons, the probed GS transition in the FWM exper) to a iment goes from a multiexciton ground state (labeled exciton [lamultiexciton excited state which has only one ) ]. This transition has a strong final state damping beled ( due to the relaxation of the excited multiexciton into its ground excitons resulting in a fast FWM decay [43]. state with two When the FWM decay became close to the pulse duration, we numerically calculated the third-order polarization by solving the optical Bloch equations for a two-level model assuming Gaussian excitation pulses and an inhomogeneous broadening much wider than the pulse spectral width, as explained in our previous works in [17], [20]. An example of the simulated FWM mA signal is shown in Fig. 5 at room temperature and and the inferred dephasing time is indicated. The corresponding –( ) transition versus homogeneous broadening of the is shown in Fig. 8 (closed squares) and will be compared with the population dynamics in Section V. Below 100 K, the decay of the polarization is strongly nonmA, together with the –( ) exponential. At transition, a weak contribution of the biexciton to exciton tran– ) is also present (see Fig. 5 at 10 K). sition (labeled – transition has a much smaller final state damping The –( ) , and its polarization decay can be disthan the tinguished at low temperatures when the fast dephasing from the exciton–acoustic phonon interaction is reduced [44]. In the presence of a strongly nonexponential FWM decay, we have Fourier transformed the polarization decay and fitted the lineshape as superposition of a narrow and a broadband, as described in [18]. At low temperature ( 30 K), the lineis dominated by the sharp Lorentzian ZPL shape at of the 0– transition. A sizeable Lorentzian broadband apcorresponding to the homogeneous pears with increasing –( ) transition superimposed with broadening of the – line. The width of this broad band a sharp Lorentzian mA is shown in Fig. 6 together with at 25 K and for comparison. The homogeneous the lineshape at –( ) transition versus at broadening of the

Fig. 7. Pump-induced change of the gain in decibels, deduced from the probe differential transmission, at different temperature and injection currents as indicated. In the inset the shortest time constant of the recovery inferred from a multi-exponential fit to the gain dynamics is shown. An example of best fit to 3 mA by the thin solid line. the data is shown at 150 K and I

=

25 K is shown in Fig. 8 and will be commented on in Section V, – transition while the homogeneous broadening of the at low temperatures is reported elsewhere [44]. V. DIFFERENTIAL TRANSMISSION SPECTROSCOPY: POPULATION RELAXATION DYNAMICS The population relaxation dynamics of the GS transition probed in the gain region are shown in Fig. 7, where the pump-induced change of the gain, deduced from the probe differential transmission, is plotted. A QD in the gain case excitons. By stimulated is initially populated by two exciton, the pump pulse leads to a reducemission of one tion in the gain experienced by the probe (gain compression) that recovers by the relaxation of one – pair into the state. In Fig. 7, the presence of excitons in the excited states is shown to be important for the GS relaxation dynamics. At room temperature the recovery of the gain compression is very fast, while at 150 K a much slower gain recovery dynamics is observed for injection currents just above transparency. We fitted the DTS data by convoluting a multiexponential response function with the pulse intensity autocorrelation, and carefully accounting for instantaneous contributions such as two-photon absorption and coherent artifacts [5]. An example of a fit to the data is shown by the thin solid line at 150 K and mA. In the inset of Fig. 7, the time constant ( ) of the initial recovery of the gain compression obtained from the . We interpret this time constant as fit is shown versus the population lifetime of the ( ) state, which gives the final state damping of the –( ) transition. At room temperature, due to the thermal spread of carriers into the ) consists of excited states, the excited multiexciton ( with several spectators even for values of one just above transparency. This multiexciton relaxes quickly into its ground state via phonon relaxation mediated by Auger-type carrier–carrier scattering with one excited carrier promoted into

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dephasing due to phonons quenched and and coincide, i.e., the homogeneous broadening is lifetime-limited. Note that has a steeper dependence on than at 150 K. at 25 K, This is in agreement with the findings in Fig. 3, where the occupation of the excited states at 25 K is higher than at 150 K allowing for faster relaxation dynamics. are average time We should comment that the inferred constants. A more accurate evaluation of the DTS and FWM data under electrical injection should follow a microstates model [47]. The microstate of a QD is a configuration with the dot being occupied by an integer number of carriers, generally distributed between ground and excited states. In a QD ensemble, a macroscopic configuration for a given electrical injection is a superposition of microstates. However, a high number of microstates have to be considered at high temperatures where the thermal occupation of the excited states is important, making such description beyond the scope of this paper. On the other hand, at low temperature a satisfactory model can be made using only a few microstates where the carriers are distributed in the lowest energy configurations, and is reported elsewhere [44]. Fig. 8. Homogeneous broadening (solid squares) deduced from the dephasing time measured with FWM, and broadening (open squares) deduced from the population lifetime measured with DTS of the X –(X ) transitions. The homogeneous broadening of the 0–X transition without electrical injection is also shown for comparison.

the wetting layer (and subsequently relaxing) and one excited carrier scattered into the ground state [45]. With lower temperatures, the thermal spread of carriers into the excited states is at the transparency for the reduced. As shown in Fig. 3, with GS transitions the minimum occupation of the ES transitions occurs at 150 K. At this temperature, we suggest that the slow recovery time (see inset) just above transparency is mainly due to the relaxation dynamics of the states with only one carrier in the first excited state that relaxes to its ground state via phonon emission, not mediated by carrier–carrier scattering. Finally, we compare in Fig. 8 the homogeneous broadening of the –( ) transition deduced from the FWM decay as discussed in Section IV, with the broadening from the population lifetime of the ( ) state. In the absence of pure dephasing these two broadenings should be equal. From the results in Fig. 8, the presence of a pure dephasing which depends both on temperature and injection current is evident. and occurs at room The strongest difference between temperature. Here, is higher than and has a steeper dependence on . Therefore, the dephasing due to phonon interaction (which can be extrapolated considering at ) is dominantly pure dephasing at room temperature, as already discussed in [28]. Moreover, the interaction with the electrically injected carriers gives rise to a strong elastic dephasing, probably from elastic Coulomb collisions with carriers in the wetting layer present at room temperature by thermal population [46]. When the temperature decreases and the thermal occupation on the wetting layer is quenched, this elastic contribution is and have the same dependence reduced, and at 150 K on . Still, the phonon contribution is dominated by a pure dephasing. Only at very low temperatures ( 30 K) is the pure

VI. SUMMARY We have reported an extensive experimental study of the relaxation dynamics and dephasing of the excitonic GS transition in an electrically pumped InGaAs QD amplifier from 10 K to 295 K. Population relaxation dynamics of multiexcitons are measured in the gain regime with DTS and are compared with the dephasing time measured using FWM. This comparison allowed us to distinguish inelastic from pure dephasing processes. Dephasing processes much faster than the population relaxation are measured above 150 K and are due to both carrier–phonon scattering and Coulomb interaction with the injected carriers. Elastic Coulomb interaction with carriers in the barrier/wetting layer material is quenched below 150 K due to the decreased thermal occupation of the high-energy states with decreasing temperature. At very low temperature ( 30 K), the pure dephasing arising from the lattice deformation in dots of small size is also quenched and the dephasing is fully inelastic. These results represent an important progress in the fundamental understanding of the line broadening and of the carrier dynamics in self-assembled QDs. Our findings indicate that barrier engineering could reduce the homogenous line broadening by reducing the carrier concentration in the barrier/wetting layer material. On the other hand, the Auger-like intradot carrier–carrier scattering that occurs once the dot excited states are occupied allows the ultrafast gain recovery dynamics that are very important for high-speed applications. Therefore, a convenient design for an ultrafast laser/amplifier which retains a density of states with sharp resonances could involve intentional doping inside the dots, allowing for intradot carrier–carrier scattering, and strong confinement energies to reduce the elastic dephasing from Coulomb interactions with the carriers in the barrier. ACKNOWLEDGMENT R. L. Sellin is grateful to Agilent Technologies.

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BORRI et al.: EXCITON RELAXATION AND DEPHASING IN QUANTUM-DOT AMPLIFIERS

P. Borri, photograph and biography not available at the time of publication.

W. Langbein, photograph and biography not available at the time of publication.

S. Schneider, photograph and biography not available at the time of publication.

U. Woggon, photograph and biography not available at the time of publication.

R. L. Sellin, photograph and biography not available at the time of publication.

D. Ouyang, photograph and biography not available at the time of publication.

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D. Bimberg (M’92) was born in Schrozberg, Germany, on July 10, 1942. He received the Diploma in physics and the Ph.D. degree from Goethe University, Frankfurt, Germany, in 1968 and 1971, respectively. From 1972 to 1979, he was a Senior Scientist with the Max Planck-Institute for Solid State Research, Grenoble, France, and Stuttgart, Germany. From 1979 to 1981, he was an Associate Professor with the Department of Electrical Engineering, Technical University of Aachen, Aachen, Germany. Since 1981, he has held the Chair of Applied Solid State Physics and, since 1990, has been Executive Director of the Solid State Physics Institute at the Technical University of Berlin, Berlin, Germany. Since 1994, he has been chairman of the National Research Council “Center of Excellence” on “Growth Related Properties of Nanostructures” and, since 1998, chairman of the National “Center of Competence” on “Nano-Optoelectronics” of the German Federal Ministry of Research. Among others, he hold guest professorships at the University of California, Santa Barbara, and at Hewlett-Packard, Palo Alto, CA. He has authored more than 800 papers, patents, and books. His research interests include the physics of nanostructures and nanostructured devices, wide-gap semiconductor heterostructures, and high-speed photonic devices. Dr. Bimberg holds an honorary membership at the A.F. Ioffe Institute at St. Petersburg. He received the Russian State Prize in Science and Technology in 2001.