Radiative recombination lifetime of excitons in self-organized

InAs/GaAs quantum dots

A. Mellitia,*, M.A. Maarefa, F. Hassenb, M. Hjirib, H. Maarefb, J. Tignonc, B. Sermaged

aUnite de Recherche de Physique des Semiconducteurs, Institut Preparatoire aux Etudes Scientifiques et Technologiques,

La Marsa 2070, TunisiabLaboratoire de Physique des Semiconducteurs, Faculte des Sciences de Monastir, Monastir, Tunisia

cLaboratoire de Physique de la Matiere Condensee, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris cedex 05, Paris, FrancedLaboratoire de Photonique et de Nanostructures, CNRS, Route de Nozay, 91460 Marcoussis, France

Received 22 May 2003; accepted 26 August 2003 by T.T.M. Palstra

Abstract

We report an investigation of the exciton dynamics in self-organized InAs/GaAs quantum dots (QD’s) grown by molecular-

beam epitaxy on (001)-oriented GaAs substrate. We have combined continuous wave and time resolved luminescence as a

function of temperature to obtain quantitative information on the recombination processes in the dots. We have found that the

excitonic radiative lifetime of two monolayers InAs QD’s is almost independent of temperature.

q 2003 Elsevier Ltd. All rights reserved.

PACS: 78.67.HC; 81.16.Nd; 78.55.Ap; 81.07.Ta

Keywords: A. InAs/GaAs; A. Quantum dots; D. Decay time; D. Radiative lifetime; E. Photoluminescence; E. Temperature

1. Introduction

The quest for high performance optoelectronic devices

has promoted a growing interest for zero-dimensional

semiconductor quantum dots (QD’s). In these systems,

indeed, the strong localization of the electronic wave

function leads to an atomic-like electronic density of states

and to the possible realization of novel and improved

photonic and electronic devices [1–3]. Furthermore, the

self-aggregation of defect-free QD’s during the epitaxial

deposition of strained semiconductor layers [4] has

stimulated a large number of experimental works. QD

injection-laser prototypes, made from InAs/GaAs hetero-

structures, have now characteristics as good as quantum

well based devices [5]. In order to assess QD for application

in photonic devices parameters such as carrier radiative

lifetime must be measured. A systematic study of this

parameter in quantum boxes formed naturally along the axis

of a V-shaped GaAs/AlGaAs quantum wires by means of

time and spatially resolved resonant photoluminescence

(PL) has been reported by Bellessa et al. [6]. They have

found that the radiative recombination rate varies linearly

with the length of the box. Heitz et al. [7] have investigated

by time resolved PL spectroscopy the recombination in self-

organized InAs/GaAs luminating at about 1.1 eV. They

have found that the radiative lifetime is around 1 ns at

1.8 K. As regards the excited states in self-assembled InAs/

GaAs QD’s Raymond et al. [8] have proposed a model that

allows to calculate the radiative rates at low temperature.

The calculated rates decline from 109 to 1.4 £ 108 s21 as

higher energy states are probed. On the other hand, using PL

spectroscopy and a Monte Carlo model Buckle et al. [9]

have shown that the radiative decay time of the emission

from the ground, first excited, second excited and third

excited states are about 1, 3.7, 4, and 1.4 ns at 6 K. Weaker

values of radiative lifetime have been reported for self-

assembled AlInAs/AlGaAs QD’s (500 ps) [10] and single

CdSe/ZnSe QD (290 ps) [11].

0038-1098/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ssc.2003.08.020

Solid State Communications 128 (2003) 213–217

www.elsevier.com/locate/ssc

* Corresponding author. Tel.: þ216-989-996-46; fax: þ216-717-

465-51.

E-mail address: adnenmelliti@yahoo.fr (A. Melliti).

In this paper, we investigate the effect of the temperature

on the excitonic radiative lifetime in self-organized

InAs/GaAs QD’s by time resolved (TR) and continuous

wave (CW) PL. The sizes of these structures are not

uniform. The carriers diffuse from small QD’s to larger ones

[12–19]. This process causes the refilling of large QD’s at

high temperature during the decay. Consequently, the direct

determination of the radiative lifetime of these QD’s is

impossible. To avoid this problem, we have limited the

study of this process to the small QD’s. We have calculated

the radiative lifetime using the rate equation model [12].

The decay constant of the ground state has been modeled

correctly by this model [12,20].

2. Sample growth and experimental details

The InAs QD’s embedded in GaAs were grown on an

(001)-oriented GaAs substrate by using a molecular beam

epitaxy system. An undoped GaAs buffer layer was grown

on the substrate at 580 8C. The self-organized coherent InAs

islands were formed at 520 8C by deposition of nominally

two monolayers grown between two 200 A thick layers of

GaAs. The temperature was then increased to 580 and a

300 A GaAs cap layer was grown. The morphology of the

InAs islands, grown under the same conditions as an

uncapped sample, were investigated in air by contact mode

by atomic force microscopy using a digital Nanoscope III

system. The results show two main size distributions (larger

20 nm diameter and smaller 14 nm diameter QD’s). The

QD’s density was estimated as 3 £ 1010 cm22

The CWPL emission was spectrally resolved by a

monochromator blazed at 1 m. The excitation source was

a frequency-doubled Nd: vanadate laser emitting at 2.33 eV

(into the GaAs barrier) with an excitation power density of

the order of 5 W cm22. The luminescence was detected with

a silicon avalanche photodiode. The sample was held in a

closed cycle He cryostat.

TRPL measurements were made using a closed cycle He

cryostat and mode-locked Ti-saphir laser giving nearly

Fourier-transform limited pulse in the range of 1–1.5 ps

with a repetition rate of 82 MHz. Its energy was tuned to

1.46 eV (into the wetting layer (WL)). The excitation power

density is of the order of 80 W cm22. The emission is

spectrally dispersed using a monochromator. Next, temporal

analysis is performed by a synchro scan streak camera.

Finally, the signal is detected using a charge-coupled

device. The time resolution lies around 5 ps.

3. Results and discussion

Fig. 1 shows a broad CWPL band associated to the

luminescence of QD’s at different temperatures. The PL

band obtained at 10 K is centered around 1.24 eV. The

luminescence results from the radiative recombination on

the ground and excited states of two QD’s size distributions

[16].

Fig. 2 shows the TRPL decays measured at different

Fig. 1. QD’s PL bands at different temperatures.

Fig. 2. Each figure shows PL decay obtained at different

temperatures for a particular emitting state (solid line), (a) and (b)

correspond, respectively, to emitting states of energies 1.128 and

1.299 eV at 10 K. The detection energy is redshifted as the

temperature increases to account for the energy band-gap-shift

with temperature. The dotted lines show fit curves.

A. Melliti et al. / Solid State Communications 128 (2003) 213–217214

temperatures and at detection energies corresponding to the

low and high-energy sides of the QD’s PL spectra. Each

detection energy corresponds to a particular emitting state.

As the temperature varies from 10 K toward higher values,

the detection energies are redshifted to take into account the

energy band-gap-shift with temperature. For the first order

of approximation, the band gap shift is estimated using the

formula described in Ref. [21]. For the low energy detection

ðE1 ¼ 1:179 eVÞ (Fig. 2(a)), the PL decay can be well fitted

by a monoexponential for low temperatures (,90 K) and

high temperatures (.200 K). In the intermediate tempera-

ture range, the PL intensity is initially constant over a few

hundred of picoseconds. This result may be due to two

processes: the refilling of the large QD’s by carriers escaped

from small QD’s and the state blocking caused by the effects

of Pauli exclusion [9]. For the high-energy detection ðE3 ¼

1:318 eVÞ (Fig. 2(b)) we have not observed the PL intensity

saturation vs. time. This behavior indicates that the

recapture by small QD’s is weak. On the other hand, for

the high-energy detection, the PL decay is fitted by two

exponentials. We attribute the two components to the

superposition of excited states PL of large QD’s and ground

states PL of smaller ones.

Fig. 3 shows the PL decay times for various emission

energies plotted vs. sample temperature. The luminescence

decay times were determined by fitting the experimental

decay curves at a particular emission energy to a single

exponential over a time windows selected to avoid the

possible influence of excited state emission. The arrows in

the inset indicate the positions of detection energies within

the QD’s PL band. We remark that the decay time associated

to the high-energy extremity of the PL band ðE3 ¼ 1:318

eVÞ is almost constant (750 ps) up to 100 K. Then it

decreases with temperature. For lower detection energies,

the decay time curves show a maximum. The greater

maximal value is obtained for E1 ( ¼ 1.179 eV). We note

that the maximal decay times and the PL saturation vs. time

(shown in Fig. 2(a)) are obtained in the same temperature

range.

The model developed in Ref. [12] explains the behavior

of decay time corresponding to a given detection energy. At

sufficiently high temperature, the small QD’s experience a

relatively large rate of thermal emission of electron-hole

pairs back into the WL, leading to a reduction of the PL

decay time for these QD’s. Meanwhile, recapture from the

WL causes the repopulation of the other lower-energy QD’s

and leads to an increase of their PL decay time. At higher

temperatures, thermally activated emission ultimately

begins to cause a decrease of the PL decay times of the

lower-energy QD states. This model allows us to interpret

the variation as a function of temperature of the decay time

corresponding to a given energy detection, but it does not

explain its increase as the detection energy vary from E0

( ¼ 1.16 eV at 10 K) to E1 ( ¼ 1.179 eV at 10 K).

We note that the variation of the decay time of QD’s

corresponding to the high-energy extremity of the PL

spectra (HEQD’s), that does not increase at low tempera-

tures, indicates that the recapture has no significant effect on

the evolution of the population of these QD’s.

We have analyzed our results using the rate equation

deduced from the model developed in Ref. [12]:

dn

dt¼ cMJ 2

1

tr

þ1

te

� �n ð1Þ

Where n is the population of QD’s excitons, c is the capture

rate coefficient, M is the number of WL excitons per unit

area, JðEÞ is the normalized density of ground states of QD’s

excitons, it is related to the inhomogeneous broadening of

QD’s PL band, tr and te correspond, respectively, to the

radiative lifetime and to the time for thermal emission to the

WL.

We neglect the recapture of carriers by HEQD’s. This

approximation is supported by the fact that for these QD’s:

† The decay does not present a saturation vs. time (Fig.

2(b))

† The decay time does not increase with temperature (Fig.

3)

† The value of JðEÞ is small.

Using this approximation, the rate equation of excitons

in these QD’s is given in the case of pulsed excitation by:

dn

dt< 2

1

tr

þ1

te

� �n ¼ 2

1

tn ð2Þ

solution of this equation corresponding to RTPL

Fig. 3. PL decay times vs. temperature. Solid lines provide a guide

to the eye. The values of E0 ¼ 1:16 eV; E1 ¼ 1:179 eV; E2 ¼

1:227 eV and E3 ¼ 1:318 eV represent the detection energies at

what the PL is measured at 10 K. As one moves along each line

from 10 K toward higher temperatures, the energy detection is

redshifted to account for the energy-band-gap shift with tempera-

ture. The arrows in the inset indicate the positions of the detection

energies within the PL band obtained at 10 K for pulsed excitation.

A. Melliti et al. / Solid State Communications 128 (2003) 213–217 215

measurements is given by n ¼ n0 expð2t=tÞ: The decay time

corresponding to energy close to E3 can be directly

interpreted as t: For a continuous excitation, n is given

by: n ¼ cJMt: The CWPL intensity (IPL) can be written as:

IPL ¼ cJMt=tr

Considering two detection energies corresponding to

HEQD’s (E01 ¼ 1:31 eV and E0s2 ¼ 1:32 eV) we obtain the

following equations:

IPLðE1Þ

IPLðE2Þ¼

tr2

tr1

t1

t2

JðE01Þ

JðE02Þ

ð3Þ

1

t1

¼1

tr1

þ1

te1

ð4Þ

1

t2

¼1

tr2

þ1

te2

ð5Þ

Where t1 ðt2Þ; tr1 ðtr2Þ and te1 ðte2Þ are, respectively, the

decay time, the radiative lifetime and the thermal emission

time corresponding to E01 ðE

02Þ: te1 and te2 are related by the

relationship [12]:

te1 ¼ te2 expE0

2 2 E01

2kbT

� �ð6Þ

To estimate J we have used the CWPL band obtained with

excitation power of 0.5 W cm22 and at 10 K, to avoid the

excited states contribution and the influence of inter-dots

diffusion. The Eqs. (3)–(6) allow to calculate the radiative

lifetime from the CWPL and RTPL measurements. The

values of tr are presented in Fig. 4. We note that tr is of the

order of 800 ps and is almost independent of temperature.

The calculated value of tr is smaller than that measured

by Heitz et al. [7] and Buckle et al. [9] (1 ns). The QD’s

studied by Heitz and Buckle are larger than those studied

here. Indeed, the transition energy of QD’s studied by Heitz

and Buckle are 1.1 and 1.13 eV, respectively, and those of

QD’s studied here are 1.31 and 1.32 eV. The decrease of the

radiative lifetime with decreasing QD size is connected with

a reduction of confinement effects [20].

The flat temperature dependence of the exciton radiative

lifetime is expected [13,22]. Indeed, the density of states

consists of a series of d functions. Increasing, the

temperature cannot redistribute excitons within a band of

adjacent states since these do not exist.

4. Conclusion

We have determined the radiative lifetime of small QD’s

(diameter ¼ 140 A) using CWPL and TRPL measurements.

We have found that the excitonic radiative lifetime is of the

order of 800 ps and is almost independent of temperature.

On the other hand, we have observed that for intermediate

temperature range, the PL intensity of large QD’s remains

constant over a few hundred of picoseconds. We have

attributed this behavior to two processes: the refilling of the

large QD’s by carriers escaped from small QD’s and the

state blocking caused by the effects of Pauli exclusion.

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