InxGa1−xAs quantum dots

PHYSICAL REVIEW B 74, 205302 共2006兲

Carrier thermodynamics in InAs/ InxGa1−xAs quantum dots S. Sanguinetti, D. Colombo, M. Guzzi, and E. Grilli Dipartimento di Scienza dei Materiali, Universitá di Milano Bicocca, Via Cozzi 53, I-20125, Milano, Italy

M. Gurioli LENS and Dipartimento di Fisica, Universitá di Firenze, Via Sansone 1, I-50019, Sesto Fiorentino, Italy

L. Seravalli, P. Frigeri, and S. Franchi CNR-IMEM Institute, Parco delle Scienze 37a, I-43100 Parma, Italy 共Received 29 November 2005; revised manuscript received 7 June 2006; published 1 November 2006兲 We present a detailed study of the carrier thermodynamics in InAs/ InxGa1−xAs self-assembled quantum dots performed via an accurate determination of the dependence of the quantum dot photoluminescence efficiency on temperature, excitation power density and wavelength. We have found experimental evidences that the electron and hole populations in the dots are highly correlated. We also show that other puzzling effects, like the onset of the superlinear dependence of the quantum dot integrated photoluminescence intensity on the excitation power density, stem from the saturation, by the photogenerated carriers, of nonradiative centers in barrier. DOI: 10.1103/PhysRevB.74.205302

PACS number共s兲: 78.47.⫹p, 78.67.Hc, 73.21.La, 78.55.Cr

The quantum dots 共QDs兲 are designable mesoscopic atoms easily integrable in nanoelectronics. These zerodimensional structures, being solid state systems with an atomic-like density of states, have initially attracted large interest for improving the performances of optoelectronic devices, like lasers and optical amplifiers.1,2 Recently, the research in the field of QD materials is committed to the exploitation of the peculiar electronic properties of these systems. Potential applications in the field of quantum cryptography3 and quantum computing4 have been recently demonstrated using single QD devices. In both fields a good knowledge of the recombination kinetics and carrier dynamics at high temperature 共T兲 of the QDs are of great importance for most of the foreseen devices. Semiconductor QDs are known to efficiently capture the carriers generated by optical absorption. The electron hole pairs created in the barrier region rapidly relax to the QD ground state from where they radiatively recombine. The role of nonradiative channels on the T dependence of the QD recombination efficiency has been analyzed in many details and with different experimental techniques.5–8 It is nowadays well established that the high-T thermal quenching of the photoluminescence 共PL兲 is due to the escape of carriers from the QD to the wetting layer 共WL兲 or barrier material, where they undergo nonradiative recombination.9 The presence of PL thermal quenching at intermediate temperatures has been attributed to the loss of carriers within the barriers during the relaxation path.9,10 Despite the large experimental and theoretical effort devoted to the understanding of the carrier thermodynamics in QDs a few aspects still need a better understanding. In particular, two recent papers8,11 target the relevant aspect of the carrier dynamics in the QD system. In the literature it has been long debated, and still not completely clarified, whether the capture and escape of the carriers in QDs occurs via single carrier,12 uncorrelated electron-hole pairs13 or excitons.7 Le Ru et al.8 show that a clear superlinear dependence of the QD integrated photoluminescence 共IL兲 on 1098-0121/2006/74共20兲/205302共6兲

the excitation power density 共Pexc兲 is present at high T in QD samples. Le Ru et al. claim that such observation is the fingerprint of a bimolecular recombination inside the QDs, thus inferring that single carrier dynamics dominates in the QDs. They remark that at high T the average thermal energy is much larger than the exciton binding energy in the bulk, so that a carrier dynamics dominated by excitons is very unlikely. However, it should be mentioned that the exciton binding energy in QDs is ⬇20 meV,14 therefore very close to kT at room temperature. The conclusion that the carrier dynamics in QD system is ruled by uncorrelated electron-hole pairs were also drawn by Dawson and co-workers,11 basing their discussion on the observation that none of the models, which describe the carriers dynamics in QDs6,7,13 under the assumption of electron-hole pair dynamics, is able to describe the correct effect of the increasing Pexc on the IL dependence on T. It is worth noticing that both papers use the nonlinear behavior of the IL on Pexc at high T as the more stringent proof that carrier dynamics in QDs is dominated by uncorrelated electrons and holes. In this paper we present a detailed study of the T behavior of both cw and time resolved PL as a function of Pexc and excitation wavelength ␭exc. We show that the thermal quenching of the PL in InAs/ InxGa1−xAs QDs is highly affected by the photon energy of the exciting light, i.e., on whether the excitation is in the barrier, from where the carriers thermalize in the QDs and then recombine 共nonresonant excitation photoluminescence, NPL兲, or directly in the dots, where the carriers recombine 共resonant photoluminescence, RPL兲. Provided that similar QD occupancies are scanned in NPL and RPL conditions, the dependence of IL on Pexc at high T can be linear or superlinear, depending on the use of resonant or nonresonant excitation of PL, respectively. The comparative analysis of the PL data as a function of temperature, ␭exc and Pexc allows us to identify that a nonradiative recombination channel in the barrier is responsible for the PL superlinearity at high T. We discuss the escape carrier kinetics in QDs on the basis of the observed phenomenology con-

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©2006 The American Physical Society

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cluding that only the presence of correlation in the hole and electron population statistics of the QDs could explain the observed behavior. The investigated samples are strain-engineered QD structure, where the partially relaxed InGaAs lower confining layer 共LCL兲 is used to control the QD strain:15 The reduction of strain allows for the redshift the QD emission and, then, for the match of the 1.3– 1.5 ␮m transparency windows of silica fibers.15 The QD structures, grown on 共100兲 GaAs substrate, consist of 共i兲 a 100 nm thick GaAs buffer layer, 共ii兲 a InxGa1−xAs lower confining layer of thickness d grown by MBE at 490 ° C, with x ranging in the 0.15– 0.35 interval, 共iii兲 a plane of InAs QDs with a three-monolayer 共ML兲 coverage, deposited by ALMBE16 at 460 ° C, 共iv兲 a 20 nm thick InxGa1−xAs upper confining layer grown by ALMBE at low temperature 共360 ° C兲 in order to reduce the interaction between upper confining layers and QDs. Before and after the deposition of QDs, the growth was interrupted for 210 s to change the substrate temperature. More details on the growth can be found in Ref. 15. The CW-PL was excited with a Nd:Yag duplicated laser 共␭exc = 532 nm兲 for nonresonant excitation in the barrier 共NPL conditions兲, or with Nd:Yag laser 共␭exc = 1064 nm兲 for excitation resonant with the QD excited states 共RPL conditions兲. The power density was in the 1 – 100 W / cm2 range for NPL and 4 – 400 W / cm2 for RPL, respectively. The spot lateral size was about 100 ␮m in both NPL and RPL conditions. PL spectra were measured by a grating monochromator with a Peltier-cooled InGaAs photodiode. A picosecond Tisapphire laser 共␭exc = 780 nm, 2 ps, 82 MHz兲 has been used as the excitation source in the time-resolved measurements, while the detection has been performed by means of time correlated single photon counting technique with a time resolution of 300 ps. In the following, we will concentrate our analysis on a single sample of the series, characterized by a lower confining layer with d = 60 nm and a concentration of In in the barrier x = 0.15. Of course, the phenomenology here presented is a common feature of all the measured samples in the series. Figure 1 reports the sample PL spectrum excited nonresonantly 共␭exc = 532 nm兲 in the barrier or resonantly with the QD excited states 共␭exc = 1064 nm兲 at low temperature 共T = 13 K兲. In the NPL spectrum the emission peaks at 1.027 eV, with a FWHM of 38 meV. The RPL spectrum shows the same shape and energy. It is worth noticing the RPL laser is resonant with the QD excited states of a subgroup of the QD ensemble thus giving rise to the well-known selective photoexcitation modulation of the spectra.17 NPL spectra at high injection 共not shown兲 show a sharp line at 1.25 eV, well below the barrier energy 共EB = 1.33 eV, taking into account In concentration and strain relaxation15兲, that we attribute to the WL emission. We accurately measured the dependence of the IL on the excitation density Pexc over two decades and at different temperatures. The data are reported in Figs. 2共a兲 and 2共b兲 for both NPL and RPL excitation conditions. The data are nicely fitted by a power law ␣ IL = ␰ Pexc .

共1兲

FIG. 1. Photoluminescence spectrum under NPL 共circles兲 and RPL 共squares兲 excitation conditions measured at T = 13 K with an exciting power density of about 100 W / cm2 共NPL兲 and 400 W / cm2 共RPL兲, respectively. Each spectrum is normalized to its maximum.

The solid lines in Figs. 2共a兲 and 2共b兲 are the fits of the experimental data with Eq. 共1兲. The exponent ␣ obtained from the fits is reported in Fig. 2共c兲 as a function of the temperature. The ␣ values of the RPL data are between 1.0 and 1.2 in the entire temperature range thus showing a linear dependence. At low-T NPL data show a nearly linear dependence as well. However, above 120 K, IL shows a strong superlinear dependence on Pexc, with ␣ up to 1.5. All these measurements have been performed in an excitation density regime where the average number of electron-

FIG. 2. Integrated PL intensity versus excitation density at different temperatures. 共a兲 Resonant excitation; 共b兲 nonresonant excitation. P0 = 100 W / cm2 for resonant excitation and 400 W / cm2 for nonresonant excitation, respectively. The solid lines are the best fit of the experimental points with a power-law dependence. 共c兲 Exponent ␣ obtained from the fit of IL vs excitation density with Eq. 共1兲. Squares and circles refer to RPL and NPL conditions, respectively.

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CARRIER THERMODYNAMICS IN InAs/ InxGa1−xAs QUANTUM DOTS

FIG. 3. Arrhenius plot of the temperature dependence of IL 共normalized at T = 10 K兲 under RPL 共squares兲 and NPL 共circles兲 conditions measured at Pexc = 10 W / cm2 共NPL兲 and Pexc = 400 W / cm2 共RPL兲, respectively.

hole pairs per QD is below one. In fact, the QD-PL showed no emission from excited states. It is worth noticing that, in the measured Pexc range, NPL and RPL IL differ by less than an order of magnitude 关the ordinate scales in Figs. 2共a兲 and 2共b兲 are exactly the same兴. Because we do not expect any change in intrinsic QD recombination probability ␩rec when carriers are injected in the QD resonantly or not, this means that our data scan, under both NPL and RPL excitation conditions, similar, within one order of magnitude, average population range of electron-hole pairs in the QDs. IL共T兲, under both NPL and RPL conditions 共see Fig. 3兲, shows a similar temperature dependence. Above ⬇100 K a consistent reduction of the emission efficiency takes place, which arrives at about three orders of magnitude at room temperature. Such behavior implies that, at high T, the carrier dynamics is dominated by a temperature activated quenching. Time resolved PL measurements, as a function of Pexc, were performed both at low T 共10 K兲 and at a temperature sufficiently high 共200 K兲 so that the recombination efficiency is dominated by nonradiative decay channels. At low T the QD-PL decay time is ␶D = 600 ps and it does not depend on Pexc, unless ground state filling effects come into play. When T is raised to 200 K, ␶D acquires a slight Pexc dependence, continuously increasing from 300± 30 ps to 400± 40 ps when Pexc is increased from 1 to 100 W / cm2 共see Fig. 4兲. No state filling effects were observed in the whole measured Pexc range. Superlinear emission means that the PL internal quantum efficiency ␩PL increases with increasing the excitation power. Since the efficiency is limited to 1, it follows that superlinearity implies ␩PL
1 since when ␩PL = 1 all the absorbed photons are reemitted and the PL must be linear in Pexc. Thus the observation of superlinearity requires the copresence of efficient nonradiative channels and of a nonlinear mechanism in the recombination efficiency. The nonlinearity can either be due to an increase of the intrinsic relaxation rates or to a saturation of the nonradiative processes. In general the PL efficiency ␩PL can be expressed as a product of the efficiency

PHYSICAL REVIEW B 74, 205302 共2006兲

FIG. 4. Time resolved PL traces recorded at different Pexc : 1.5 W / cm2 共circles, ␶D = 300± 30 ps兲, 17 W / cm2 共squares, ␶D = 340± 30 ps兲, and 100 W / cm2 共triangles, ␶D = 400± 40 ps兲. ␭exc = 780 nm.

of each process involved in the carrier thermalization and recombination: 共a兲 the carrier energy relaxation and diffusion in the barrier and WL, 共b兲 the carrier capture and relaxation within the QDs, and 共c兲 the recombination probability in the QDs. Thus the identification of the role of each temperaturedependent contribution to the PL quenching is a crucial point in order to understand the recombination kinetics of the carriers in QD systems. Carrier relaxation, diffusion and capture processes are skipped by RPL measurements which essentially probe the T dependence of the recombination probability in QDs. The finding that RPL is linear with increasing Pexc allows us to exclude that the superlinearity stems from variations in the QD internal recombination efficiency. Our data unambiguously show that the superlinear behavior in the integrated intensity at high temperatures is controlled by ␭exc thus depending on the carrier injection loci. However, it is well known from spectral diffusion and blinking measurements,18,19 that the presence of charged traps in the QD environment may strongly influence the carrier thermalization and recombination processes in the QDs. Therefore one can still picture out the possible presence of traps in the barriers which can be photopassivated in NPL condition leading to the observed IL superlinearity.12 Within this framework the PL decay time ␶D must depend on the excitation power density and be proportional, in Pexc ranges not dominated by state filling effects, to the ratio IL / Pexc. A direct test of this model is given by time resolved PL, that significantly shows that ␶D undergoes a small variation with Pexc, at high temperatures. In fact, at T = 200 K, ␶D only slightly changes 共⬇30% 兲 while the IL / Pexc ratio increases more than one order of magnitude. This rules out interpretation of the superlinear behavior as due to the saturation, by means of photogenerated carriers, of nonradiative recombination channels located in the QD close environment.12 Auger processes are very efficient nonlinear mechanisms in the QD carrier capture and relaxation, leading to a speed up of the PL risetimes in time-resolved measurements, and possibly to a superlinear increase with Pexc of the capture probability. However, Auger mechanisms are present also at low T and they occur at very high excitation density, corre-

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sponding to state filling effects. Here we are always below this limit and NPL is almost linear in the low T region. Thus we can rule out also Auger processes as possible explanation for the observed NPL superlinearity. We conclude that the observed IL superlinearity on Pexc must be associated to an increase of the diffusion efficiency. As already mentioned, the QD yield in NPL conditions is mostly determined by carrier energy relaxation and diffusion in the barrier. Only a small fraction of the photogenerated carriers are actually captured by the QDs, even at low temperature. IL depends on QD capture rate ⌫C, on the nonradiative recombination rate in the barrier ⌫NR ⬘ 共associated with the carrier diffusion process in the barrier兲, on the QD recombination efficiency ␩rec and, naturally, on Pexc as IL ⬅ ␩rec

⌫C Pexc . ⬘ ⌫C + ⌫NR

共2兲

We may expect a combined temperature and Pexc dependence of ⌫NR ⬘ . Actually, the presence of temperature activated traps, affecting the temperature dependence of the QD PL yield, has been already demonstrated in QD systems.9,10 The saturation of such traps by the capture of the photogenerated carrier in the barrier could induce a temperature activated reduction of ⌫NR ⬘ . Typical activation energies of the traps responsible for the quenching of the QD PL yield are in the range 30– 80 meV,10,20,21 thus fully compatible with the observed temperature onset of the NPL IL superlinearity. We interpret the superlinear dependence of NPL IL on Pexc as stemming from the saturation of nonradiative decay channels active during the thermalization and the diffusion of the photogenerated carriers in the barrier. The absence of superlinearity in RPL IL dependence is clearly the outcome of the lack of this step in the resonantly photogenerated carrier thermalization path to the QD ground state. Let us now discuss the implications of the observation of a linear dependence of RPL IL vs Pexc in the whole measured range. As a matter of fact, as also pointed out by Le Ru et al.,8 it is very unlikely that the electron and hole pairs persist as excitons at high T, due to the fact the binding energy in the bulk is smaller than kT. This observation naturally forces the modelization of the QD system by decoupled electron and hole rate equations, with a bimolecular recombination rate. Such model predicts a linear dependence of IL on Pexc at low T which switches to a quadratic law at high T. This can be easily appreciated using the simple, steady state, QD model sketched in Fig. 5共a兲. Here the carriers flux in the QD, P ⬀ Pexc, of the two carriers is the same, thus simulating RPL conditions. The carriers trapped in the QD can recombine or escape through a thermally activated channel. The rate equations governing the model of Fig. 5共a兲 in steady state conditions are

FIG. 5. 共a兲 Schematics of a decoupled electron and hole steady state model of the QD system. 共b兲 PL integrated intensity measure in RPL conditions 共circles兲 with the fit 共continuous line兲 obtained using Eq. 共5兲. The fit parameters were R = 1 / ␶D 共fixed兲, P = 0.1/ ␶D 共fixed兲, EQUE = ⌬Ee + ⌬Eh = 170 meV 共fitted兲, ␬e␬h = 5 ⫻ 104 / ␶D 共fitted兲. ␶D was set to the experimental value at low T 共␶D = 600 ps, see text兲. We choose P = 0.1/ ␶D in order to maintain the QD occupation below one in all the T range 共as observed experimentally兲. 共c兲 Temperature dependence of the exponent ␣ obtained from the fit of PL integrated intensity vs excitation density with Eq. 共1兲. Circles refer to the experimental measurements in RPL conditions. The continuous line represents the dependence of the ␣ exponent as calculated via the Pexc dependence of the PL integrated intensity predicted by the model with the parameter set reported above.

⬅ 具n共t , T兲典t and p共T兲 ⬅ 具p共t , T兲典t are the time-average electron and hole populations in the QD at the temperature T. When performing broad area PL measurements of IL, what is measured is the ensemble average of the single QD emission IL ⬀ 具ILj典ENS, where the superscript j identifies the QD in the ensemble. Because QDs lack of an efficient coupling channel, it is impossible to define common quasiequilibrium quantities for the QD ensemble up to very high T. The average over the QD ensemble can be therefore approximated by a sum over uncorrelated systems, IL ⬇ 兺 jILj共T兲. So that, for understanding the IL dependence on Pexc, it is not necessary to introduce the spreading in energy of the QD ground states. As well documented in the literature, the inhomogeneous nature of the PL line broadening plays its main role determining the anomalous behavior of the PL energy peak and full width at half-maximum.7,11 It is possible to find an analytical solution of the equation system 共3兲,

P − Rn共T兲p共T兲 − p共T兲␤ = 0, P − Rn共T兲p共T兲 − n共T兲␥ = 0,

p= 共3兲

where R is the recombination rate, ␤ = ␬e exp共−⌬Ee / kT兲, ␥ = ␬h exp共−⌬Eh / kT兲 共⌬Ee and ⌬Eh are the quenching activation energies of electrons and holes, respectively兲 and n共T兲

n= In the model

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− ␤␥ + 冑␤2␥2 + 4␤␥RP , 2␤R − ␤␥ + 冑␤2␥2 + 4␤␥RP 2␥R

共4兲 .

CARRIER THERMODYNAMICS IN InAs/ InxGa1−xAs QUANTUM DOTS

IL = Rn共T兲p共T兲.

共5兲

The result of the fit of IL共T兲, measured in RPL conditions, using Eq. 共5兲, is reported in Fig. 5共b兲. The IL共T兲 curve is nicely reproduced, despite the simplicity of the model. Regarding the dependence of the RPL IL on Pexc, the model, at low T, when the main carrier depletion channel is through bipolar recombination of electrons and holes trapped in the QD, predicts IL = P. On the contrary, at high T, the thermal excitation of the carrier toward the quenching channel dominates the model carrier dynamics 共␤␥  R兲 and IL =

R 2 P , ␤␥

共6兲

thus showing a quadratic dependence on Pexc and an activation energy of the quenching process EQUE = ⌬Ee + ⌬Eh. The transition between the two regimes should take place in the 100– 170 K range, as can be appreciated in Fig. 5共c兲 where the calculated temperature dependence of the power law coefficient ␣, determined via the dependence on P of Eq. 共5兲 at different temperatures, is reported. There is therefore a clear contradiction between the model outcomes, which predict a switch from the linear to the superlinear dependence of IL on Pexc, and the experimental data 关see Fig. 5共c兲兴. In RPL condition the experimental dependence of IL vs Pexc remains linear in all the measured T range 共␣ ⬇ 1兲. It is worth noticing that the carrier dynamics, as determined experimentally in RPL conditions, clearly switches from a regime dominated by the radiative recombination, at low T, to the thermal activated escape toward a quenching channel, at high T 共the PL efficiency drops about three orders of magnitude between 10 K and 270 K兲. So that, the constancy of ␣ over the measured T range cannot be attributed to the lack of transition between the two carrier dynamics regimes in RPL conditions. This contradiction between model and experimental results is not the outcome of the simplicity of the model. Similar results are reported by Dawson et al.11 with a model which takes into account the more relevant aspects of the QD system physics. A critical analysis of the steady state equations used to modelize the QD system is therefore necessary. As a matter of fact, IL is proportional to the time average of the instantaneous product of the electron and hole populations in the QD, IL ⬅ 具n共t , T兲p共t , T兲典t. Steady state models assume a completely uncorrelated population of electrons and holes in the QD, that is the dynamics of the carrier population of one species, in the QD, is not influenced by that of the other. This leads to 具n共t,T兲p共t,T兲典t = 具n共t,T兲典t具p共t,T兲典t

共7兲

and then, under the assumptions of the model sketched in Fig. 5, to the Eqs. 共5兲 and 共3兲.

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To our judgment, the assumption of completely uncorrelated electron and hole populations in the QD 关Eq. 共7兲兴 is at the basis of the failure of steady state models to predict the correct dependence of IL on Pexc, as observed in RPL measurements. Although the electron and hole pairs cannot be considered, at high T, as excitons, they still retain a high degree of correlation due to their Coulomb interaction. The contemporaneous presence of the two carriers inside the QD reduces the escape probability of both carriers due to the Coulomb interaction energy 共which is ⬇20 meV,14 thus comparable to kT even at room temperature兲. In addition, Coulomb interaction enhances 共or reduces兲 the trapping cross section of QDs which trap the complementary 共or the same兲 carrier species. Therefore, Coulomb interaction enhances the time average of the product 具n共t , T兲p共t , T兲典t above the uncorrelated value 关please note n共t , T兲 and p共t , T兲 oscillate between 0 and 1兴. An exact calculation of the effects of electron-hole Coulomb interaction on the correlation of the QD carrier populations should require kinetic Monte Carlo simulations which are outside the scope of this work. However we may consider the correlated pair 共exciton兲 dynamics as an upper 共although unrealistic兲 limit for the effect of carrier-carrier correlation. The excitonic description of carrier dynamics in QDs can be found in Ref. 7. The model predicts a linear dependence of IL on Pexc at all the temperatures and an activation energy of the quenching process equal to the difference between the PL emission and the quenching state energies in quite close agreement with the experimental findings.9 Summarizing our discussion, our experimental findings suggest that the electron and hole populations in the QD are highly correlated. The degree of correlation is evidenced by the almost linear dependence of IL on Pexc, which is closer to the correlated pair 共linear兲 rather than to the uncorrelated pair 共quadratic兲 behavior. In conclusion, we have demonstrated that the superlinear dependence of the QD emission intensity on the excitation power density in NPL condition, taken as the fingerprint of a decoupled electron and hole dynamics in the QDs must, instead, be attributed to the saturation of temperature activated trap states, which affect the carrier diffusion in the barrier. We observed a linear dependence of IL on Pexc, when the QDs are excited in RPL conditions, up to room temperature. Such behavior suggests the presence of a high correlation of the time dependence of electron and hole populations in the QDs. The authors thank F. Casati for help during the measurements. The work was partially supported by the MIUR-FIRB project “Nanotecnologie e Nanodispositivi per la Società dell’Informazione” and by the SANDiE Network of Excellence of EC, Contract No. NMP4-CT-2004-500101 共CNRIMEM兲.

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