energy relaxation by multiphonon processes in … · energy relaxation by multiphonon processes in...

PHYSICAL REVIEW B 15 OCTOBER 1997-IIVOLUME 56, NUMBER 16

Energy relaxation by multiphonon processes in InAs/GaAs quantum dots

R. Heitz, M. Veit, N. N. Ledentsov, A. Hoffmann, and D. BimbergInstitut fur Festkorperphysik, Technische Universita¨t Berlin, 10623 Berlin, Germany

V. M. Ustinov, P. S. Kop’ev, and Zh. I. AlferovA. F. Ioffe Physical-Technical Institute, 194021, St. Petersburg, Russia

~Received 10 January 1997!

Carrier relaxation and recombination in self-organized InAs/GaAs quantum dots~QD’s! is investigated byphotoluminescence~PL!, PL excitation~PLE!, and time-resolved PL spectroscopy. We demonstrate inelasticphonon scattering to be the dominant intradot carrier-relaxation mechanism. Multiphonon processes involvingup to four LO phonons from either the InAs QD’s, the InAs wetting layer, or the GaAs barrier are resolved.The observation of multiphonon resonances in the PLE spectra of the QD’s is discussed in analogy to hotexciton relaxation in higher-dimensional semiconductor systems and proposed to be intricately bound to theinhomogeneity of the QD ensemble in conjunction with a competing nonradiative recombination channelobserved for the excited hole states. Carrier capture is found to be a cascade process with the initial captureinto excited states taking less than a few picoseconds and the multiphonon~involving three LO phonons!relaxation time of the first excited hole state being 40 ps. Theu001& hole state presents a relaxation bottleneckthat determines the ground-state population time after nonresonant excitation. For the small self-organizedInAs/GaAs QD’s the intradot carrier relaxation is shown to be faster than radiative~.1 ns! and nonradiative~'100 ps! recombination explaining the absence of a ‘‘phonon bottleneck’’ effect in the PL spectra.@S0163-1829~97!09340-5#

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I. INTRODUCTION

Carrier relaxation in quasi-0-dimensional semiconducsystems@dubbed quantum dots~QD’s!# has been widely dis-cussed in recent years.1–9 Inelastic phonon scattering ismall QD’s having large substate splittings as neededroom-temperature optoelectronic applications, is predicte3,4

to be slow since the discrete spectrum of eigenstates menergy and momentum conservation difficult. Carrirelaxation times of the order of radiative and nonradiatrecombination times are predicted,3,5 restricting the popula-tion of the ground state upon nonresonant excitation. Teffect has been termed ‘‘phonon bottleneck.’’ The expemental observation of intense ground-state pholuminescence10–15 ~PL! as well as the demonstration of injection lasing for self-organized QD’s~Refs. 16–18! indicatethat such a ‘‘phonon bottleneck’’ is no intrinsic propertysmall QD’s. Alternative relaxation mechanisms, e.g., Augrecombination6 and Coulomb scattering of free carriers,7,8

have been evaluated for their potential to remove the phobottleneck. However, a high density of hole states or lafree-carrier concentrations would be needed to obtain sciently high relaxation rates. At low excitation densitieboth conditions are not given for small self-organizQD’s,19 making phonons the most likely candidates to dispate the energy in carrier relaxation.

A proven method to demonstrate the dominating carrrelaxation process in higher-dimensional systems is theservation of hot exciton relaxation,20 revealing LO-phononresonances in PL excitation~PLE! spectra. Hot exciton relaxation can be observed when the exciton relaxation hacompete with other relaxation or recombination processThough for single QD’s the classical concept of hot excit

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relaxation does not work due to the discrete energy sptrum, we will show that for a QD ensemble an equivaleeffect can be observed in PLE, which then gives evidencethe dominating carrier-relaxation process.

The PLE spectra ofsingle QD’s reveal sharp excitationresonances that are unambiguously attributed to electrtransitions.21,22 However, comparatively broad excitatioresonances 30–130 meV above the detection energy areserved monitoringlarge ensemblesof self-organized QD’sand controversially discussed either as electronic transitreflecting the excited-state spectrum12,13,23or as multiphononresonances indicative for carrier-relaxation processes.10,24,25

Similar ~multi!phonon transitions have been observed in nresonance excited PL spectra.26–28 For InAs/GaAs QD’s upto four LO-phonon replica are resolved10 showing the cou-pling to LO modes from different regions of the Qstructure.24 The multiphonon resonances have been tentively explained invoking the inhomogeneity of the QD esemble and a nonradiative recombination channel for hoin excited states to compete with intradot relaxation.24 Re-cently, excited-state PL by itself has been proposed tosufficiently efficient to compete with intradot relaxation,25,28

implying the observation of multiphonon resonances to beintrinsic property. However, PLE results for uncouplestacked QD’s reveal the variation of the excited-stsplitting in dependence of the QD size,23 indicating excited-state transitions to be resolved in the spectra. The menisms determining the appearance of the PLE spectratherefore their interpretations are not clear yet. Furthermhole relaxation24 and exciton relaxation28 are controversiallydiscussed, depending on the assignment of the optical tsitions to either ‘‘forbidden’’19 or ‘‘allowed’’ 28 transitions.Both processes cannot be easily distinguished from the

10 435 © 1997 The American Physical Society

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Here, we present a detailed study of carrier relaxationself-organized InAs/GaAs QD’s combining PLE and timresolved PL~TRPL! results. This paper is structured as folows: Sec. III A gives detailed PLE results demonstratingmultiphonon nature of the observed excitation resonanceSec. III B the multiphonon resonances are shown to beincoherent phenomenon yielding information on carrierlaxation in the QD’s, and in Sec. III C we determine tmultiphonon ~three LO phonons! relaxation time to 40 psand show that for the excited hole states in the investigasamples a competing nonradiative recombination channeists. Finally, in Sec. IV we propose that the observed Pspectra are intricately bound to the inhomogeneity ofinvestigated InAs island QD’sand the nonradiative recombination channel leading to a model similar to hot excitrelaxation in higher-dimensional semiconductors.20 The non-radiative recombination is associated with defects inGaAs barrier and enables the characterization ofintrinsiccarrier-relaxation mechanisms in small InAs/GaAs QD’sing PLE.

II. SAMPLES AND EXPERIMENTAL SETUP

We report experimental results for two InAs/GaAs Qsamples grown by solid-source molecular beam epitaxyGaAs ~100! substrate as described in detail in Refs. 14,and 29. The single InAs layer enclosed by GaAs barriersandwiched between two GaAs/AlxGa12xAs superlatticesgrown at 600 °C defining an ‘‘optically active’’ region fromwhich carriers can be trapped into the QD’s. A GaAs buflayer is grown on the first superlattice before the temperais lowered to 480 °C for the growth of 12-Å InAs and10-nm-thick GaAs cap. Subsequently, the temperature iscreased back to 600 °C for the remaining growth. Sampleand B differ nominally only in the different thickness of thactive region being 15 and 116 nm, respectively. TEMsults indicate the InAs islands, which sit on top of an Inwetting layer~WL!, to be pyramid-shaped and to vary in siand shape showing side facets close to$101% and$203%.14,29,30 The QD’s have a base length of 12–14 nmheight of 4–6 nm, and an area density of about 1011 cm22.

For the PL and PLE experiments the samples wmounted in a continuous-flow He cryostat at 6 K. A tungslamp dispersed by a 0.27-m double-grating monochromserved as a tunable, low-excitation-density (,0.02W cm22) light source and the PL was detected through0.5-m single-grating monochromator using a cooled Geode. The TRPL measurements were performed in superHe with 150-fs pulses at a repetition rate of 76 MHz ofTi-sapphire laser for excitation and a 0.35-m subtractdouble-grating monochromator in combination with a strecamera with an infrared-enhanced photocathode for detion. The full width at half maximum~FWHM! of the systemresponse to the excitation pulses was between 25 and 6depending on the time-range setting. The transients wanalyzed taking into account the system response to thecitation pulses enabling the determination of time constadown to 5 ps under optimal conditions.

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III. EXPERIMENTAL RESULTS

Figure 1 compares low-excitation-density PL~thick lines!and PLE~thin lines! spectra of samplesA and B, with theintensities given on the same scale. Upon excitation abthe GaAs band gap the ground-state transition of the InQD’s leads to PL peaks at 1.105 and 1.079 eV wFWHM’s of 42 and 37 meV, respectively, indicating thaverage InAs island size to be slightly larger in sampleB.The QD PL peaks are almost of Gaussian shape as indicby the dotted fits in Fig. 1 and the FWHM is attributed to tinhomogeneity of the QD ensemble with each single Qcontributing only a sharp line~,150 meV!.15 Assuming thecarrier-capture cross section and quantum yield to beindependent, the PL peak represents the inhomogeneousdensity, indicating asize inhomogeneity of;5%.19 Theexcited-state spectrum of the InAs QD’s has been expmentally obtained from high excitation-density PL spectra31

Above 50 W cm22 the PL of the QD ground state saturatand two additional peaks appear on the high-energy sshifted by about 85 and 165 meV. The excited-state PL liare identified as recombination of holes in theu001& andu002& excited states with electrons in theu000& ground state,based on a good agreement with the energy spectrum calated for strained InAs pyramids.19 These transitions wouldbe dipole-forbidden in QD’s having inversion symmetry bare allowed for the strained InAs pyramids. Figure 2 giveschematic term scheme of the sample structure showingthe QD’s in addition to theu000& ground states theu001& andu002& excited hole states.

A. Multiphonon resonances in the PLE spectra

The excited-state transitions are not resolved in the Pspectra recorded on the maximum of the QD PL peaks~thin

FIG. 1. PL~thick lines! and PLE~thin lines! spectra for samplesA andB taken withI 0,0.02 W cm22 at T56 K. The PL is excitedat 1.67 eV and the PLE spectra are recorded on the respectivmaximum. The dotted lines represent Gaussian fits of the QDThe peak at 1.491 eV is attributed to carbon-related PL in GaA

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56 10 437ENERGY RELAXATION BY MULTIPHONON PROCESSES . . .

lines in Fig. 1!. Instead a series of resonances is observedexcitation energies (Eexc) below 1.25 eV, which we showbelow to result from intradot excitationand relaxation in theinhomogeneousQD ensemble. At higher energies the QD PLis excited via carrier capture, revealing absorption byInAs WL and the GaAs barrier. The GaAs free-excitonresolved for sampleB but not for sampleA, for which thenarrow width of the active region leads to quantization inGaAs barrier. The similar PL intensity in both samplesexcitation below the GaAs band gap reflects the comparQD density. Exciting above the GaAs band gap, the PLtensity is about 6 times higher for sampleB due to the largerthickness of the active region, providing a higher carrier ccentration at the same excitation density. Carriers fromwhole active region are equally captured by the QD’s. TPLE peaks at 1.388 and 1.465 eV in sampleA are attributedto the heavy~hh! and light ~lh! -hole absorption of the WL,respectively. Figure 3 shows the dependence of the Pspectra on the detection energy (Edet) for sampleA. Thespectra are shifted in they direction for clarity and the re-spectiveEdet is indicated by the crosses. The energy of tWL resonance is 1.388 eV independent of the detectionergy indicating that the QD size and the structural properof the surrounding WL are not correlated in one sample. Teffective thickness of the WL estimated from the transitienergy is 1.7 ML.19 For sampleB the heavy-hole absorptioappears at a higher energy~1.399 eV! indicating the WL tobe thinner in favor of larger QD’s.

Exciting below 1.35 eV the PLE spectra assume a chacteristic shape as shown in Figs. 1 and 3. Starting fromdetection energy, with increasing excitation energy a seof equidistant PLE resonances evolves. The first three rnances are well resolved and increase in intensity, thenfourth appears only weakly and is followed at higher en

FIG. 2. Schematic term scheme of the InAs QD structurespicting carrier relaxation (t rel) and radiative (t rad) as well as non-radiative (tnonrad) recombination for the excitedu001& hole state.

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gies by a weakly modulated broad excitation band. Theergy separation of the PLE resonances of about 32 meVin the range of typical phonon energies in the InAs/Gasystem. Thus, we refer to the PLE peaks as 1LO, 2LO,resonances as indicated in Fig. 3. The inset of Fig. 3 githe ground-state PL intensity excited in the maximum ofvarious LO resonances in dependence of the detectionergy. The PL intensity follows the inhomogeneous QD desity represented by the QD PL upon GaAs excitation, shoing the relative intensity of the first three LO resonancesbe independent of the QD size and theabsoluteintensity todepend on the QD density. The dominating 3LO resonafalls almost together with the absorption into theu001& ex-cited hole state for pyramids with$101% side facets.19 Welike to note that in our experiments stray light~not shown inthe figures! covers the resonantly excited PL of the Qground state. For QD’s having discrete energy levels,sorption and emission match each other within the homoneous FWHM~,150meV!.15 However, calorimetric absorption experiments have shown absorption matchingground-state PL.14

The strongly modulated near-resonant excitation eciency ~Figs. 1 and 3! enablesselectiveexcitation of QD’swith a ground-state transition energy one, two, or three Lphonon energies below the excitation energy as shownFig. 4. In the selectively excited PL spectra, the relativetensity of the LO resonances depends on the excitationergy. With decreasing excitation energy, first the 3LO, ththe 2LO, and finally the 1LO replica becomes dominantflecting the density of QD’s with a matching ground-statransition energy. We find no indication of phonon-assis

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FIG. 3. PLE spectra of sampleA in dependence on the detectioenergy (Edet). The spectra are shifted in they direction for clarityand the crosses mark the respectiveEdet. The inset compares the Pintensity for excitation in the maximum of the 1LO, 2LO, and 3Lresonances and above the GaAs band gap.

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emission processes consistent with the weak Fro¨hlich inter-action in the covalent III-V semiconductors. For excitatienergies above 1.25 eV the inhomogeneous QD peakcomes apparent indicatingnonselectiveexcitation. This be-havior is merely the result of the weak modulation of tPLE spectra above 1.25 eV~Fig. 3! and does not necessitaa nonlocal excitation mechanism as provided by GaAsWL absorption. Finally, thesets of PL and PLE spectrashown in Figs. 3 and 4 both contain the same informatie.g., the PL spectra can be unambiguously generatedthe PLE spectra. However,each single PL spectrum compares QD’s with different ground-state transition energiwhereas in PLE a subset of the QD ensemble defined byground-state transition energy is probed. Thus, in the folloing we prefer the PLE spectra for a more detailed analysithe phonon modes involved in the multiphonon processe

Higher resolution PLE spectra for samplesA and B aregiven in Fig. 5 as a function of the excess excitation eneDE5Eexc2Edet, revealing a threefold substructure for th2LO and 3LO resonances. In order to determine the eneand FWHM of the various PLE resonances, we performline-shape fits assuming Gaussian peaks. Full lines in Fishow the best fit to the PLE spectra~given as thick dots! andthe contributing Gaussians are indicated. The large numof Gaussians used is motivated by the rich fine structresolved for sampleB and gives also the best fit for sampA. The fit of the 2LO and 3LO resonances yields for bosamples the same three phonon energies of~29.660.5!, ~32.660.5!, and ~37.660.5! meV. The FWHM of the 29.6- and37.6-meV resonances is;7 meV, whereas the 32.6-meresonances are broader~;14 meV for 3LO!.32 For the 1LOresonance only the 32.6-meV mode is resolved. HowePL excited selectively with high density at 1064 nm showGaAs Raman scattering to contribute to the 1LO pea24

FIG. 4. PL spectra of sampleA for selective infrared excitationThe spectra are shifted in they direction for clarity and the crossemark the respective excitation energy (Eexc).

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Above 130 meV the resonances become broader andlonger correspond to multiples of the above phonon energA fit of a complete series of PLE spectra shows that the penergies of the various LO resonances and therefore theresponding phonon energies are independent of the deteenergy. This is illustrated in Fig. 6 for sampleB showing acontour plot of the PL intensity in dependence of the dettion wavelength andDE. Multiples of the three phonon energies determined in the line-shape fits are indicated by hzontal lines. We like to note that no resonances matchcombinations of the different phonon modes are resolved

The three phonon modes can be attributed to LO phonin different regions of the strained InAs/GaAs QD structutaking into account that the LO-phonon energy in a semicductor nanostructure is altered by strain and confinemen33

The effects of the biaxial strain and the strong vertical cofinement compensate each other for thin InAs quantum w~QW’s!.34 Thus, we identify the 29.6-meV mode, corresponding in energy to the bulk InAs LO phonon, with the Lphonon of the InAs WL. The 32.6-meV mode, which domnates the PLE spectra, is attributed to the LO phonon ofstrained InAs QD’s, for which phonon confinement canneglected. A LO phonon energy of 32.1 meV has been emated from the strain distribution in InAs pyramids wi$101% side facets,19 which is in excellent agreement with thexperimental value. The 37.6-meV mode is assigned toLO phonon in the GaAs barrier. The increased energy copared to bulk GaAs reflects the biaxial strain accommodaby the barrier in the immediate vicinity of the islands. Thlarge FWHM’s of the PLE resonances~.7 meV! might bethe result of weakenedk-selection rules, the shape inhomgeneity of the islands, which alters the strain distribution atherewith the phonon energies, or higher-order processevolving LA phonons.4 Further investigations are needed for

FIG. 5. Line-shape fits of the PLE spectra of the QD PLsamplesA and B recorded withI 0,0.02 W cm22 at T56 K. Thecombined experimental resolution of excitation and detection w3.6 meV.

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more detailed analysis. Figure 5 shows that compared toQD phonon replica, the WL and GaAs modes are mprominent for the 3LO resonance than for the 1LO and 2ones. The coupling to both modes depends on the extenof the excited-state wave function into the barrier. Thus,interaction with both modes becomes stronger with increing DE and therefore decreasing carrier localization inexcited state. The phonon replica in the PLE spectra ofQD’s are local probes of the strain in and around the ovegrown InAs islands. The observed phonon energies aresistent withcoherentInAs islands and can thus be takenindication for the detected, optically active QD’s to bdislocation-free.

B. The incoherent nature of the PLE resonances

Multiphonon resonances in the PLE spectra of bsemiconductors,20 QW’s,35 and corrugated superlattices36

have been controversially discussed in terms of hot excrelaxation and resonant Raman scattering~RRS!. The basicdifference between both processes is that hot exciton reation is an incoherent process, and RRS is a coherentcess. Thus, both processes usually proceed on a diffetime scale defined by energy relaxation and dephasingcesses, respectively. As shown by Toyozawa, Koyani,Sumi37 both processes become indistinguishable when btime scales become similar. In order to decide on the naof the multiphonon resonances observed for the InAs/GQD’s we studied TRPL in dependence of the excitationergy.

Typical transients observed for sampleA upon excitationabove the GaAs band gap with an excitation density

FIG. 6. Contour plot of the QD PL intensity in sampleB as afunction of the detection wavelength and the excess excitationergy (DE5Eexc2Edet). The horizontal lines represent multiplesthe phonon energies determined in the line-shape fits.

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100 W cm22 are shown in Fig. 7. The respective detectienergies are indicated by the arrows in the inset. Transidetected near the maximum~or on the low-energy side! ofthe QD peak decay monoexponentially, whereas thosetected on the high-energy side show an additional facomponent which we attribute to the superpositionexcited-state PL of larger QD’s and ground-state PLsmaller ones. The PL spectrum for pulsed excitation~fullline in the inset! shows a high-energy shoulder not presefor low-density cw excitation~broken line!. Though thetime-averaged excitation density of 100 W cm22 was chosenby avoiding saturation of the QD ground-state PL duringexperiments it was sufficient to saturate part of the QDleading to excited-state PL. At 100 W cm22 each excitationpulse generates about 431010 cm22 electron hole pairs inthe 15-nm-wide active GaAs barrier, which is close to tQD density (;1011 cm22).

Figure 8 compares transients of the QD ground-statefor various excitation energies. Most remarkable, we obsethe same time behavior exciting via GaAs or WL absorptiowhich are completely incoherent excitation processes,exciting via the 3LO resonance. This observation preseunambiguous justification to treat the multiphonon resnances as an incoherent phenomenon, i.e., as a threeprocess: first absorption into excited states, then relaxatand finally ground-state recombination. Raman scattermight contribute to the one LO resonance as observedselectively excited PL spectra.24 Recently, Raymondet al.27

reported for AlxIn12xAs/AlxGa12xAs QD’s fasterPL decayexciting 1LO and 2LO phonon energies above the detectThe authors used the fact that the observed decay isslower than the exciting laser pulse as argument to reRRS for the observed phonon resonances located on atense, broad PL background. This background is not pre

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FIG. 7. QD PL transients for sampleA excited above the GaAsband gap with a density of 100 W cm22, corresponding to431010 cm22 electron-hole pairs per pulse. The inset comparesspectra for pulsed and cw (;0.01 W cm22) excitation.

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in case of the InAs QD’s, Fig. 5. We like to note that thdephasing times of the carriers in the InAs/GaAs QD’shitherto unknown, but can be expected to be longer thahigher-dimensional systems. The spatial localization ofcarriers in the QD’s suppresses carrier-carrier scatterwhich is the dominant dephasing process in highdimensional systems, and thed-function density of statesdrastically restricts phonon scattering. Indeed, for boundcitons in bulk semiconductors recombination-limited dephing times of several hundred ps have been observed.38,39

C. Relaxation and recombination dynamics

The PL transients are analyzed taking into accountexponential decay processes for ground (t1) and excited(t2) -state recombination, and one exponential rise (t rise) toaccount for carrier capture and relaxation. Typical resultsa least square fit of the experimental data with the convotion of the assumed transient and the system responsetion are shown as full lines in Fig. 7. Figure 9 compares rand decay times deduced for samplesA andB upon excita-tion above the GaAs band gap in dependence of the deteenergy. The transients for sampleB, which have been measured at an excitation density of 1 W cm22 corresponding toan initial carrier density of 33109 cm22 much lower thanthe QD density (;1011 cm22), decay monoexponentiallyeven on the high-energy side of the QD PL confirmiexcited-state PL to be not detectable at such low-excitadensities.

The ground-state decay times of 10006100 ps and 10706100 ps for samplesA and B, respectively, observed neathe center or on the low-energy side of the QD PL peakin good agreement with previously reported valuesInxGa12xAs ~Ref. 40! and InAs ~Refs. 17 and 41! QD’s.With increasing ground-state transition energy and there

FIG. 8. Transients of the QD PL in sampleA for different ex-citation energies. The inset gives the PL rise time in dependencthe excitation energy. The combined spectral resolution of exction and detection was 20 meV for the time-resolved measurem

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decreasing QD size, the decay time decreases to about 3near 1.25 eV. Lateral phonon-assisted tunneling from smto large InAs QD’s has been proposed recently41 to explainthe shorter lifetime of the smaller QD’s. Though the Qdensity in our samples is similar to that of the sample invtigated in Ref. 41, we do not observe the reported characistic deformation of the QD PL peak. Indeed, a ground-stPL lifetime of 340 ps is found for samples having only smQD’s14 in good agreement with the present results. Thlateral energy transfer between QD’s is unlikely to besponsible for the energy dependence of the ground-statetime shown in Fig. 9. The observed decrease of the groustate lifetime with decreasing QD size could be the resulan increasing oscillator strength. However, for the invegated small InAs/GaAs QD’s carrier-quantization energare much larger than the exciton binding energy.19 In thisstrong confinement regime, the oscillator strength is pdicted to be size independent.42 We cannot exclude that nonradiative recombination, demonstrated below for the exciQD states, is also of importance for the ground-state tration of the smaller QD’s.

Carrier capture and the subsequent intradot relaxationtermine the PL rise after nonresonant excitation. Our TRresults~Figs. 8 and 9! suggest carrier capture to be a cascaprocess involving at least the excitedu001& hole state as in-termediate state. The evaluation of the excitation-enerdependent transients~Fig. 8!, yields a rise time of 2865 ps,which is within our temporal resolution~;5 ps! independentof the excitation process~see inset!, indicating that only thelast relaxation step, namely, the hole relaxation from thecited u001& state, is resolved. This is supported by the dettion energy-dependent data shown in Fig. 9. The groustate rise time is about 30 ps independent of the QD swhereas the excited-state PL rises much faster~,10 ps,

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sampleA for Edet.1.17 eV!. These observations show ththe observed PL rise time of 2865 ps is the lifetime of theu001& excited hole state and that we are not able to resocarrier capture in the excited hole states~,5 ps!. The initialcarrier capture time has been assessed to be on a 1-psscale from the PL yield of deep etched mesa structuredependence of the mesa diameter43 and from the observationof hot electron resonances in the QD excitation via the Gabarrier.23 We find no influence of carrier diffusion in thGaAs barrier, which we attribute to a long-range attractpotential caused by the strain field surrounding the QD19

leading to carrier drift.The lifetime of theu001& excited hole state depends o

relaxation (t rel) to the u000& ground-state, radiative recombnation (t rad) with electrons in theu000& state, and nonradiative recombination (tnonrad), as indicated in Fig. 2:

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As shown above, at low excitation densities radiative recobination of excited states is suppressed by hole relaxa(t rel!trad). The intensity distribution between the grounstate and excited-state PL at high-density cw excitation31 aswell as the results of the calculations19 indicate the oscillatorstrength of the excited-state transitions to be lower thanof the ground-state transition (t rad.1000 ps).

The nonradiative recombination (tnonrad) can be assessein high excitation density TRPL experiments. The saturatof the QD states with two carriers suppresses the intrarelaxation leading to excited-state PL~Refs. 26 and 31! andaltering the carrier dynamics. Figure 10 shows for samplBexcitation density-dependent PL spectra upon pulsed extion above the GaAs band gap~the spectra are normalizeand shifted in they direction for clarity!. At 1 W cm22

(33109 cm22 electron hole pairs per pulse! only ground-

FIG. 10. Excitation-density-dependent PL spectra for samplBand pulsed excitation. The spectra are normalized and shifted iny direction for clarity. An excitation density of 1 W cm22 corre-sponds to an initial carrier density of 33109 cm22.

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state PL is evident, and above 300 W cm22 the spectralshape saturates revealing emission from theu001& and u002&excited hole states 82 and 177 meV above the ground-stransition as well as weak signal in the region of the Wobserved at 1.399 eV in PLE~Fig. 1!. The excited-state transitions appear much weaker in PL for pulsed excitation thupon cw excitation, compare, e.g., Fig. 3 in Ref. 31, sincedecay of the excited-state population favors the ground-stransition. The saturation of the shape of the PL spectrabove 300 W cm22 indicates the QD’s to be initially completely filled by each pulse.

The fast intradot relaxation leads to a situation whereholes in each QD behave practically like a hole gas fillingenergy states starting from the ground state. Consequethe PL of the highest populated state will decay followithe decrease of the hole density and PL from lower-enestates will be constant as long as the higher ones act aservoir, supplying holes as soon as one recombines. Lowethe excitation density, the decay is entered at a later stcorresponding to the lower initial carrier density. Thisshown in Fig. 11 comparing for sampleB transients recordedwith different excitation densities at the spectral positionsthe various PL transitions~marked by the dotted lines in Fig10!. Though the QD’s are initially completely filled at thhighest excitation density (3000 W cm22), the transient ofthe WL follows the system response~dotted curve! to theexcitation pulses indicating fast recombination in the W

he

FIG. 11. Transients recorded for sampleB at the spectral posi-tions corresponding to PL from the ground state~u000&!, the excitedstates~u001&, u002&!, and the WL as indicated in Fig. 10 at variouexcitation densities. The transients are normalized for the slowcay component.

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~t,5 ps!. With decreasing detection energy the PL decbecomes slower, with time constants of 42610 and 95610ps ~100 ps in sampleA, Fig. 9! for recombination from theu002& and u001& excited hole states, respectively. Finally, tground-state PL intensity is initially nearly constant astarts to decay only after a delay of 250 ps. Reducingexcitation density, the intensity of the fast decay componeattributed to the excited-state PL decreases, but the dtimes remain constant. The decay time of the ground-stransition, however, shortens from 1070 to 800 ps increasthe excitation density from 1 to 3000 W cm2. These resultsshow that in the investigated samples the hole populadecays with time constants shorter than 100 ps until onlyground state is populated.

The fast decay of the excited-state PL under saturaconditions implies a nonradiative recombination channeindicated in Fig. 2, with the observed lifetimes being a msure for the recombination times. Thus, the nonradiativecombination times are of the order of 95 and 42 ps foru002& and u001& excited hole states and less than 5 ps forWL. Auger processes, proposed recently to explain the sration of the integrated PL intensity under high-densityexcitation in similar samples,17,29 could explain the increasing nonradiative recombination probability with increasioccupation of the QD’s. However, the recent observation23,44

of longer time constants for the decay of excited-state PLInAs QD’s suggests that the nonradiative recombinationnot an intrinsic property of the QD’s. Our experimental rsults can be explained assuming the nonradiative recombtion to be defect related. Since the PLE results showoptically active InAs islands to be coherent, we proposeergy transfer to deep defects in the vicinity of the InAslands. The decreasing localization of the holes in the excstates and, in particular, in the WL would then accountthe increasing nonradiative recombination probability. Rcently, Sercel9 discussed energy transfer between deepfects in the GaAs barrier and InxGa12xAs QD’s and pre-dicted transfer times in the 100-ps region for a QD/dedefect separation of up to 10 nm supporting the interpretaof the nonradiative recombination. The formation of dedefects in the GaAs cap or the 1.7-ML InAs WL might bintricately connected to the strain fields generated byInAs islands or be caused by the low-growth temperaturethe initial GaAs covering layer. For samples having smathree-dimensional islands and a thinner WL no signs for nradiative recombination are observed.17,29

From the low-excitation-density lifetime and the nonraative recombination time of theu001& excited hole state, amultiphonon relaxation time of 4067 ps is determined usingEq. ~1!. This result is in good agreement with recent resufor uncoupled, stacked InAs QD’s, offering no nonradiatirecombination channel,23 and for In0.3Ga0.7As QD’s.45 Thehole relaxation from theu001& state needs three LO phononto span the energy gap to theu000& ground state, and is thuat least a third-order effect. The relaxation time is of torder of that predicted for second-order scattering of1LA phonons at low temperatures,4 indicating that for thesmall InAs QD’s the multiphonon emission probability donot drastically decrease for higher-order processes. Theson might be an increased Fro¨hlich interaction in the smalInAs QD’s as proposed for II-VI nanocrystals,46,47 or the

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change in the local charge distribution for the excited staRecently, Arakawaet al.48 solved the time-dependent Schr¨-dinger equation using the coupled mode equations for etron capture into localized QD states, yielding a weak dcrease of the relaxation probability with increasing enespacingDE supporting our results. A detailed discussionmultiphonon relaxation processes between localizedstates should be based on calculations taking into accounactual QD shape~pyramids!, the finite-carrier confinementand proper confined phonon modes, which is beyondscope of this paper.

IV. DISCUSSION

In the preceding section we have shown that the QD Pspectra in the investigated samples are dominated by carelaxation leading to multiphonon resonances. Such a beior is well known as hot exciton relaxation in highedimensional systems20,35,36and is there inseparably boundthe continuous density of states. The present results indithat a similar effect can be observed for QD’s though thhave a discrete density of states. In the following, we wshow that the observation of ‘‘hot exciton’’ relaxation foQD’s depends critically on the fact that we probe an inhmogeneous QD ensemble providing an efficient comperelaxation channel, namely, defect-related nonradiativecombination for the excited hole states. Though, the inhomgeneity as well as the nonradiative recombination are unsired properties of the QD ensemble, they result for thevestigated samples in a situation where PLE spectra diredemonstrate the dominating carrier relaxation process.

The first excitedu001& hole state acts as bottleneck fohole relaxation in the small InAs/GaAs QD’s. Comparinwith Fig. 2, the quantum yieldh for hole relaxation from theu001& to the u000& state, which we assume to be also thatthe ground-state PL, is given by the competition betwehole relaxation and recombination in theu001& hole state:

h5t rel

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211tnonrad21 5

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tnonrad

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The lack of excited-state PL upon low-density nonresonexcitation shows that radiative recombination is too sl~.1 ns! to compete with intradot relaxation and, thus, canneglected in Eq.~2!. The nonradiative recombination in thinvestigated samples, however, is sufficiently fa(tnonrad;100 ps) to compete with hole relaxation. We likenote that the nonradiative recombination channel has nofect on the intensity ratio of excited- to ground-state Pwhich is given by the ratiot rel /trad at low excitation densitiesand the statistics of carrier capture at higher excitatdensities.49

The quantum yieldh for hole relaxation in a QD dependon the relaxation timet rel for the u001& hole state and thus isexpected to be a function of the excited-state splitting.3,4 Forsingle QD’s electronic transitions lead to sharp lines inPLE spectra, which are not correlated to LO-phonenergies,21,22 andh modulates only the intensity of the exctation resonances. The situation is the same for an enseof QD’s of well-defined shape, which have a clear corretion between the ground-state transition energy and

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excited-state splittings. However, the self-organized InGaAs QD’s investigated in this paper vary in sizeandshape.Consequently, the excited-state splitting of a subset of Qwith the same ground-state transition energy is inhomoneously broadened leading to a finite densityN(Eexc,Edet) ofQD’s, which are simultaneously in resonance with excitatand detection in a selective PL or PLE experiment. Temission intensityI is then given by

I}N~Eexc,Edet!h~Eexc2Edet!. ~3!

The dependence of the quantum yieldh on the excess excitation energyDE5Eexc2Edet determines which QD’s contribute to the selective PL or PLE spectra, revealingdominating relaxation processes if the inhomogenebroadening of the excited-state splitting is sufficiently largThe PLE spectra of the investigated samples, revealing 2and 3LO-phonon replica, indicate that the inhomogenebroadening of the excited-state spectrum covers this enrange for a given ground-state transition energy and thatdependence oft rel on DE strongly modulatesh. For h;1,i.e., when nonradiative recombination is negligible, Eq.~3!predicts the PLE spectra to reveal the inhomogeneobroadened excited-state splitting, as recently observeduncoupled, stacked InAs QD’s.23 The FWHM of the PLEresonances indicated the inhomogeneous excited-state bening to exceed 20 meV.23

The observation of multiphonon resonances in the Pspectra of small InAs/GaAs QD’s is thus unambiguous prfor multiphonon emission to be the dominant intradot relaation process. Every time the excited-state splittingDEequals multiples of one of the available LO-phonon energthe relaxation rate (t rel

21) has a maximum resulting in a PLpeak. The above discussion shows that the increasing insity from the 1LO to the 3LO resonance is the result ofinhomogeneity of the excited-state splittingN centeredaround 85 meV, which acts as envelope function. At higenergies the excitation process involves absorption inu002& or higher-excited hole states, subject to cascade reation. In this case,h is no longer defined by the experimentsettings, i.e.,Eexc andEdet but depends on the actual excitestate spectrum, resulting in an effectiveheff , averaged overthe QD ensemble, in Eq.~3!. Thus, we attribute the intensitdrop for the 4LO replica as well as the onset of the almstructureless PLE above 1.25 eV, Figs. 1 and 3, to multisrelaxation in the QD’s. The situation might be different inexternal magnetic field leading to a tunable splitting for tu001& hole state. In this case, the excited-state splittingtherefore also the two-step relaxation processes are welfined and can thus be resolved in the PLE spectra.

The multiphonon relaxation timet rel is 40 ps for QD’shaving an excited-state splitting in resonance with the 3process and expected to be faster for a lower-order proci.e., 2LO scattering. For QD’s out of resonancet rel is ex-pected to be much larger corresponding to the lower qutum efficiency observed in PLE. However, the TRPL mesurement are dominated by in-resonance QD’s, having aexcitation yield, due to the limited energy resolution~;20meV! in the near-resonant excited TRPL experiments athe fact that LO phonons with various energies contributethe relaxation process, allowing efficient carrier relaxat

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for a wide range of excited-state splittings. Using the expemental time constants and Eq.~2! we estimate a quantumyield of 70% for the majority of the QD’s in the investigatesamples, having an excited-state splitting allowing 3LO sctering. Thus, it is not justified to speak of a phonon bottneck as proposed by Benisty, Sotomayor Torres,Weisbuch,3 in particular, since the nonradiative recombintion channel is not an intrinsic property of the InAs/GaAQD’s. However, the impact of out-of-resonance QD’s is epected to increase in case of samples with higher islandformity.

The above discussion shows that PLE is a powerful tfor the characterization of an inhomogeneous QD ensemgiving access to the shape nonuniformity of the islands,carrier relaxation processes, and nonradiative recombinaA detailed knowledge of the energy dependence ofh, andtherewith of the relaxation and nonradiative recombinatprobabilities would be a precondition for a detailed modeliof the PLE spectra. However, the relative intensity of t1LO and 2LO resonances in our experiments are a sensmeasure for the shape inhomogeneity of the islands anchange in the mean excited-state energy would changeintensity distribution among the LO resonances. The relaintensity of the various LO resonances in our PLE expements~Fig. 3! is independent of the detection energy, indcating the average excited-state energy to be independethe ground-state transition energy. These results suggesaverage island height-to-width ratio to decrease with increing island size, as recently inferred from high-excitatiodensity PL spectra of a series of samples.31

V. CONCLUSION

We have investigated carrier relaxation and recombition for small self-organized InAs/GaAs QD’s. We obserphonon resonances involving up to 4LO phonons in the Pspectra of the QD ground state and demonstrate with TRmeasurements that these resonances can be discussedincoherent phenomenon, i.e., as a multistep process yielinformation on excited-state absorption and carrier relaxain the QD’s. The results present unambiguous proof forelastic phonon scattering to be the dominant carrier reation process at low excitation densities.

In particular, the present results show efficient carrier cture after nonresonant excitation in the GaAs barrier andInAs WL. The initial carrier capture takes place on a ps timscale resulting in the population of the excitedu001& holestate, which presents a bottleneck for hole relaxation toground state. The multiphonon emission limited lifetime4067 ps for QD’s with an excited-state splitting in resnance with a 3LO process. The results show that carrier cture is a cascade process involving at least the excitedu001&hole state. We observe ground-state lifetimes of about 1ps for InAs QD’s with a transition energy around 1.1 ewhich is over an order of magnitude slower than intradcarrier relaxation. The TRPL results for excitation densitsufficient to saturate the hole states in the QD’s, reveanonradiative recombination channel for holes in excitstates with recombination times shorter than 100 ps. Tenergy dependence of the nonradiative recombinationsuggests energy transfer to deep defects in the vicinity ofInAs islands.

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We propose an explanation for the observation of carrelaxation processes in the PLE spectra of the InAs Qhaving a discrete energy spectrum with substate splittilarger than LO-phonon energies, which is in close analoghot exciton relaxation in higher-dimensional semconductors.50 The continuous density of states being fundmental to hot exciton relaxation is thereby replaced byinhomogeneity of the InAs QD ensemble. The observationmultiphonon resonances is the result of the competing nradiative recombination channel in the investigated sampQD’s with an excited-state splitting in resonance with onethe multi-LO-phonon processes will allow efficient hole rlaxation to the ground state instead of nonradiative recomnation. From the experimentally derived time constantsestimate a yield of about 70% for hole relaxation in theQD’s. For the small InAs QD’s a wide energy window foefficient ground-state population results from the couplingthree different phonon modes with energies of 29.6, 32and 37.6 meV, attributed to the InAs WL, the InAs QD’and the strained GaAs barrier, respectively. The presensults show that PLE is a powerful tool to characterizeinhomogeneity and nonradiative recombination in a Qsample.

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The u001& hole state acts as a bottleneck for hole relaation. However, this bottleneck is not observed in PL expements, since intradot hole relaxation is found to be fasthan radiative or nonradiative recombination from the ecited states, but might be important for QD-based injectlasers, when stimulated emission accelerates carrier recbination. A hole relaxation time of 40 ps would limit thhigh-frequency capability and could cause excited statecontribute in the lasing. The present results, however,scribe carrier relaxation at low-excitation densities and thgive only a lower limit for the relaxation probability undelasing conditions, where Auger processes and Coulomb stering might accelerate carrier relaxation.

ACKNOWLEDGMENTS

We thank M. Grundmann for fruitful discussion. Variouparts of this work were funded by VolkswagenstiftunDeutsche Forschungsgemeinschaft in the framework of296 and INTAS Project No. 94-1028. N.N.L. is particularindebted to the Alexander von Humbold Foundation.

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1U. Bockelmann and G. Bastard, Phys. Rev. B42, 8947~1990!.2H. Benisty, Phys. Rev. B51, 13 281~1995!.3H. Benisty, C. M. Sotomayor Torres, and C. Weisbuch, Ph

Rev. B44, 10 945~1991!.4T. Inoshita and H. Sakaki, Phys. Rev. B46, 7260~1992!.5U. Bockelmann, Phys. Rev. B48, 17 637~1993!.6A. L. Efros, V. A. Kharchenko, and M. Rosen, Solid State Co

mun.93, 281 ~1995!.7U. Bockelmann and T. Egler, Phys. Rev. B46, 15 574~1992!.8J. L. Pan, Phys. Rev. B49, 2536~1994!.9P. C. Sercel, Phys. Rev. B53, 14 532~1996!.

10N. N. Ledentsov, M. Grundmann, N. Kirstaedter, J. Christen,Heitz, J. Bohrer, F. Heinrichsdorff, D. Bimberg, S. S. RuvimoP. Werner, U. Richter, U. Go¨sele, J. Heydenreich, V. M. Ustinov, A. Yu. Egorov, M. V. Maximov, P. S. Kop’ev, and Zh.Alferov, in Proceedings of the 22nd International Conferenon the Physics of Semiconductors, Vancouver, 1994, edited byD. J. Lockwood~World Scientific, Singapore, 1995!, Vol. 3, p.1855.

11J. Y. Marzin, J. M. Ge´rard, A. Israe¨l, D. Barrier, and G. BastardPhys. Rev. Lett.73, 716 ~1994!.

12S. Fafard, D. Leonard, J. L. Merz, and P. M. Petroff, Appl. PhLett. 65, 1388~1994!.

13Q. Xie, P. Chen, A. Kalburge, T. R. Ramachandran, A. Nafonov, A. Konkar, and A. Madhukar, J. Cryst. Growth150, 357~1995!.

14M. Grundmann, N. N. Ledentsov, R. Heitz, L. Eckey, J. ChristJ. Bohrer, D. Bimberg, S. S. Ruvimov, P. Werner, U. Richter,Heydenreich, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, PS. Kop’ev, and Zh. I. Alferov, Phys. Status Solidi B188, 249~1995!.

15M. Grundmann, J. Christen, N. N. Ledentsov, J. Bo¨hrer, D. Bim-berg, S. S. Ruvimov, P. Werner, U. Richter, U. Go¨sele, J. Hey-denreich, V. M. Ustinov, A. Yu. Egorov, A. E Zhukov, P. S

.

-

.

.

-

,.

Kop’ev, and Zh. I. Alferov, Phys. Rev. Lett.74, 4043~1995!.16N. Kirstaedter, N. N. Ledentsov, M. Grundmann, D. Bimberg,

Richter, S. S. Ruvimov, P. Werner, J. Heydenreich, V. M. Usnov, M. V. Maximov, P. S. Kop’ev, and Zh. I. Alferov, ElectronLett. 30, 1416~1994!.

17D. Bimberg, N. N. Ledentsov, M. Grundmann, N. Kirstaedter,Schmidt, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, P. SKop’ev, Zh. I. Alferov, S. S. Ruvimov, U. Go¨sele, and J. Hey-denreich, Jpn. J. Appl. Phys., Part 135, 1311~1996!.

18Q. Xie, A. Kalburge, P. Chen, and A. Madhukar, IEEE PhotonTechnol. Lett.8, 965 ~1996!.

19M. Grundmann, O. Stier, and D. Bimberg, Phys. Rev. B52,11 969~1995!.

20S. A. Permogorov, Phys. Status Solidi B68, 9 ~1975!.21D. Gammon, E. S. Snow, and D. S. Katzer, Appl. Phys. Lett.67,

2391 ~1995!.22M. Notomi, T. Furuta, H. Kamada, J. Temmyo, and T. Tam

mura, Phys. Rev. B53, 15 743~1996!.23R. Heitz, A. Kalburge, Q. Xie, M. Veit, M. Grundmann, P. Che

A. Madhukar, and D. Bimberg, inProceedings of the 23rd In-ternational Conference on the Physics of Semiconductors, Blin, 1996, edited by M. Scheffler and R. Zimmermann~WorldScientific, Singapore, 1996!, Vol. 2, p. 1425.

24R. Heitz, M. Grundmann, N. N. Ledentsov, L. Eckey, M. Veit, DBimberg, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, P. SKop’ev, and Zh. I. Alferov, Appl. Phys. Lett.68, 361 ~1996!.

25M. J. Steer, D. J. Mowbray, W. R. Tribe, M. S. Skolnick, M. DSturge, M. Hopkinson, A. G. Cullis, C. R. Whitehouse, andMurray, Phys. Rev. B54, 17 738~1996!.

26S. Fafard, R. Leon, D. Leonard, J. L. Merz, and P. M. PetroPhys. Rev. B52, 5752~1995!.

27S. Raymond, S. Fafard, S. Charbonneau, R. Leon, D. LeonarM. Petroff, and J. L. Merz, Phys. Rev. B52, 17 238~1995!.

28K. H. Schmidt, G. Medeiros-Ribeiro, M. Oestereich, P. M

R,I.

Uu

s.

so

ed

NS.

o

,

P.

.s.,

,,.d

. B

Y.

C.

a,

tesr hotnal


Petroff, and G. H. Do¨hler, Phys. Rev. B54, 11 346~1996!.29N. N. Ledentsov, M. Grundmann, N. Kirstaedter, O. Schmidt,

Heitz, J. Bohrer, D. Bimberg, V. M. Ustinov, V. A. ShchukinA. Yu. Egorov, A. E. Zhukov, S. Zaitsev, P. S. Kop’ev, Zh.Alferov, S. S. Ruvimov, A. O. Kosogov, P. Werner, U. Go¨sele,and J. Heydenreich, Solid-State Electron.40, 785 ~1996!.

30S. Ruvimov, P. Werner, K. Scheerschmidt, J. Heydenreich,Richter, N. N. Ledentsov, M. Grundmann, V. M. Ustinov, A. YEgorov, P. S. Kop’ev, and Zh. I. Alferov, Phys. Rev. B51,14 766~1995!.

31M. Grundmann, N. N. Ledentsov, O. Stier, J. Bo¨hrer, D. Bim-berg, V. M. Ustinov, P. S. Kop’ev, and Zh. I. Alferov, PhyRev. B53, R10 509~1996!.

32The FWHM’s are not limited by the combined experimental relution for excitationand detection of 3.6 meV.

33B. Jusserand and M. Cardona, inLight Scattering in Solids V,edited by M. Cardona and G. Guntherrodt, Topics in AppliPhysics Vol. 66~Springer, Berlin, 1989!, p. 49.

34P. D. Wang, N. N. Ledentsov, C. M. Sotomayor Torres, I.Yassievich, A. Pakhomov, A. Yu. Egorov, A. E. Zhukov, P.Kop’ev, and V. M. Ustinov, Phys. Rev. B50, 1604~1994!.

35R. P. Stanley, J. Hegarty, R. Fischer, J. Feldmann, E. O. Go¨bel,R. D. Feldmann, and R. F. Austin, Phys. Rev. Lett.67, 128~1991!.

36D. S. Jiang, X. Q. Zhou, M. Oestereich, W. W. Ru¨hle, R. Notzel,and K. Ploog, Phys. Rev. B49, R10 786~1994!.

37Y. Toyozawa, A. Koyani, and A. Sumi, J. Phys. Soc. Jpn.42,1495 ~1977!.

38H. Stolz, V. Langer, E. Schreiber, S. A. Permogorov, and W. v

.

.

-

.

n

der Osten, Phys. Rev. Lett.67, 679 ~1991!.39B. Lummer, R. Heitz, V. Kutzer, J.-M. Wagner, A. Hoffmann

and I. Broser, Phys. Status Solidi B188, 493 ~1995!.40G. Wang, S. Fafard, D. Leonard, J. E. Bowers, J. L. Merz, and

M. Petroff, Appl. Phys. Lett.64, 2815~1994!.41A. Takeuchi, Y. Nakata, S. Muto, Y. Sugiyama, T. Usuki, Y

Nishikawa, N. Yokoyama, and O. Wada, Jpn. J. Appl. PhyPart 234, L1439 ~1995!.

42E. Hanamura, Phys. Rev. B37, 1273~1988!.43N. N. Ledentsov, M. V. Maximov, P. S. Kop’ev, V. M. Ustinov

M. V. Belousov, B. Ya. Meltser, S. V. Ivanov, V. A. ShchukinZh. I. Alferov, M. Grundmann, D. Bimberg, S. S. Ruvimov, WRichter, P. Werner, U. Go¨sele, J. Heydenreich, P. D. Wang, anC. M. Sotomayor Torres, Microelectron. J.26, 871 ~1995!.

44K. Mukai, N. Ohtsuka, H. Shoji, and M. Sugawara, Phys. Rev54, R5243~1996!.

45B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, andArakawa, Phys. Rev. B54, 11 532~1996!.

46J. C. Marini, B. Stebe, and E. Kartheuser, Phys. Rev. B50,14 302~1994!.

47G. Scamarcio, V. Spagnolo, G. Ventruti, M. Lugara, and G.Righini, Phys. Rev. B53, R10 489~1996!.

48Y. Arakawa, M. Nishioka, H. Nakayama, and M. KitamurIEICE Trans. Electr.E79C, 1487~1996!.

49M. Grundmann and D. Bimberg, Phys. Rev. B55, 9740~1997!.50We would like to note that the discrete nature of the QD sta

leads to the same energy spacing of the PLE resonances foelectron and hot exciton relaxation unlike in higher-dimensiosystems~Ref. 20!.

energy relaxation by multiphonon processes in … · energy relaxation by multiphonon processes in...

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