Observation of long-lived excitons in InAs quantum dots under thermal redistribution temperature

Physics Letters A 376 (2012) 1495–1498

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Physics Letters A

www.elsevier.com/locate/pla

Observation of long-lived excitons in InAs quantum dots under thermal

redistribution temperature

Chun Cheng, Sheng-Di Lin

∗

, Chien-Hung Pan, Chien-Hung Lin, Ying-Jhe Fu

Department of Electronics Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan

a r t i c l e

i n f o

a b s t r a c t

Article history:

Received 30 January 2012 Accepted 6 March 2012 Available online 9 March 2012 Communicated by V.M. Agranovich Keywords:

Quantum dot

Time-resolved photoluminescence Spin-flip

We study the temperature-dependent time-resolved photoluminescence (TRPL) of self-assembled InAs quantum dots (QDs). Under low excitation power, a surprisingly long PL decay time is observed at about 60 K, under the thermal redistribution temperature. The long decay time decreases with increasing excitation power but is nearly independent of the detection energy of TRPL measurements. A model considering the spin relaxation through the excited excitonic state is proposed to quantitatively explain the unusual phenomena. The rate equation analysis indicates that the observation of long-lived excitons is caused by the shortened spin-flip time.

©2012 Elsevier B.V. All rights reserved.

1. Introduction

Self-assembled semiconductor quantum dots (QDs) have been a central topic for two decades. The potential applications on optoelectronic devices and quantum information processing are promising because of their defect-free quality and superior optical properties[1–3]. Recently, the dark excitons in QDs received grow-ing attention due to the possibility of usgrow-ing them as spin storage and qubits [4–6]. To process spin information using QD, it is es-sential to study the interplay between bright and dark excitons and many related works have been reported recently[5–9]. In this Letter, we report the first observation of long-lived exciton in indi-vidual InAs QDs, which is strongly related to the optically-inactive dark exciton. Revealing by the proposed model and by the numeri-cal analysis of rate equations, we claim that the very long PL decay time is caused by the thermal-induced spin-flip which turns dark excitons into bright ones. This work provides a piece to understand the complex dynamics in QDs and paves the way of using QDs as a spin qubit at elevated temperature.

To study the carrier dynamics in QDs, temperature-dependent TRPL is one of the most common methods. The temperature-dependent exciton dynamics in InAs QDs ensembles has been extensively studied but its physical mechanism in whole tempera-ture range is not well understood[8]. Typically, for InAs QDs, the measured carrier decay time keeps nearly constant at tempera-tures less than 100 K. In middle temperature range (

∼

100–200 K),

*

Corresponding author. Tel.: +886 3 5131240; fax: +886 3 5724361. E-mail address:[email protected](S.-D. Lin).

a moderate rise of decay time is commonly observed, owing to the thermal redistribution among QDs [10,11]. That is, when the car-rier emission/re-capture time is comparable with the recombina-tion time of ground states, the thermal redistriburecombina-tion among QDs begins so the thermal equilibrium between individual QDs grad-ually builds up. As a result, the PL decay time increases and the full-width-half-maximum (FWHM) of PL spectra decreases. At near room temperature, the non-radiative recombination becomes dom-inant so a rapid decrease of carrier lifetime was observed in most samples[10,12–16]. In this work, we present the first observation of an anomalous behavior of long-lived excitons in the tempera-ture range of 50–75 K. A three-level model, including bright, dark, and hot excitonic states is proposed to explain the unusual phe-nomena. A consistent fit between the theory and the experiment is obtained with the rate equation simulation, which reveals the important role of hot excitonic state in spin relaxation of carriers in QDs.

2. Sample growth and measurement setup

The QDs were grown by a solid-source molecular beam epi-taxy system (Varian Gen II) on (100) GaAs substrate. More than 20 samples were studied but we focus on two representative samples here, noted as sample A (LM3572) and sample B (LM4682). The QDs were centrally embedded in 300 nm GaAs and sandwiched with two AlGaAs confinement layers. For the QDs growth, the InAs nominal thickness, growth rate and substrate temperature are 2.4 (3.0) monolayers (MLs), 0.05 (0.05) ML/s and 500 (480)◦C for sam-ple A (samsam-ple B), respectively. The growth ended with an uncapped QDs layer grown at the same condition for surface morphology 0375-9601/$ – see front matter ©2012 Elsevier B.V. All rights reserved.

1496 C. Cheng et al. / Physics Letters A 376 (2012) 1495–1498

Fig. 1. (Color online.) Temperature-dependent PL decay times detected at the peak

energies of samples A and B (solid symbols), as well as those detected at subgroups QDs of sample A (open symbols). Inset: the PL spectra of two samples and the indication of detection energies.

observation. All layers were undoped. The QDs area density mea-sured with atomic force microscopy is about 8

.

0

×

1010_cm−2 _for sample A and about 6

.

0

×

1010cm−2 for sample B. Continuous-wave low-temperature (

∼

20 K) PL measurements show that the PL ground state energy and FWHM of sample A (sample B) are 1.21 eV (1.09 eV) and 95 meV (33 meV), respectively. To per-form TRPL measurements, the samples were excited with a pulsed diode laser (

λ

=

780 nm, pulse width

∼

50 ps and repetition rate

=

10 MHz) with a spot size of about 60 μm. By considering the spot size and the net absorption of GaAs matrix, the number of photo-generated electron–hole pairs per dot is less than 0.13 at the aver-age excitation power of 2 μW for sample A (QDs’ area density

=

8

.

0

×

1010cm−2). The PL were dispersed by a monochromator and then detected by an InGaAs photo-multiplier tube (PMT) using time-correlated single photon counting technique. The time resolu-tion of TRPL system is about 0.3 ns, limited by the response time of InGaAs PMT. At each temperature, the PL spectra were taken prior to the TRPL measurements to decide the detection wavelength. The PL decay time is extracted by fitting the measured decay curves with the bi-exponential function below. For clarity, we define the fast part of the decay curve as the PL decay time (i.e. the smaller

τ

, denoted as

τ

1)

IPL

(

t

)

=

A1exp

(

−

t

/

τ

1

)

+

A2exp

(

−

t

/

τ

2

).

(1)

3. Result and discussion

Fig. 1shows the extracted PL decay times from 25 to 300 K. The excitation power of sample A (sample B) is 20 μW (25 μW). First, the decay times of sample B (BP) exhibit the typical temperature dependence but those of sample A detected at peak wavelength (AP) shows an unusual spike between 50 and 75 K. A surpris-ing lone decay time of about 4.0 ns is obtained. To see the decay times of the subgroups of the QDs ensemble, we also plotted the decay time of sample A detected at the energies lower (AL) and higher (AH) than its peak energy, by the half of FWHM. In the middle temperature range (125–225 K), the decay times of these three subgroup QDs have different trends due to thermal redistri-bution among QDs. This is exactly what we expected as mentioned above. The carriers in smaller QDs can escape the confinement before radiative recombination and re-capture by the larger QDs. Obviously, in this temperature range, the thermal redistribution of carriers causes the different decay times between QDs’ sub-groups. Nevertheless, the long decay time at 60 K appears with all of the three subgroups. It reveals that the increase of decay

Fig. 2. (Color online.) (a) Measured PL time traces of sample A for T=35–75 K. At each temperature, the black line is a fit of bi-exponential function to the data. (b) The fast and slow decay times and the amount ratio of slow part, extracted from (a).

time is irrelevant with the carrier transfer among QDs thereby it occurs in all individual QDs. In addition, the integrated PL in-tensity in 25–100 K is nearly constant (within

±

10%) so the non-radiative recombination is probably unrelated to the unusual behavior.

To see the long decay time in detail, we show the time traces of sample A from 35 to 75 K under the excitation power of 2 μW in Fig. 2(a). Note that the vertically-shifted PL intensity is plot-ted in logarithmic scale so their slopes are proportional to the inverse of decay times. At T

=

35 K, a typical bi-exponential decay (

τ

1

∼

0

.

8 ns,

τ

2

∼

32 ns) is clearly seen. The fast one comes from the bright exciton recombination and the slow one is attributed to the spin-flip of dark excitons [5–9]. In 35–50 K, the slopes of fast decay decrease with increasing temperatures. The longest

τ

1 is seen at 55 K, which is caused by the replacement of the fast de-cay part with the slow one. The numerical fitting is also plotted in Fig. 2(a) with detailed results shown in Fig. 2(b). With rais-ing temperatures,

τ

1 increases and

τ

2reduces, where they become closest at 55 K. The replacement of the fast part with the slow one is clearly revealed by the A2 ratio, defined as A2

/(

A1

+

A2

)

, which reaches its peak value also around 55 K. For T

>

55 K, the slow part is negligible. Accordingly, we can say that the decays are basically two components at temperatures less than about 55 K then they become mono-exponential decay for higher tempera-tures. That is, the fast one dominates at low temperatures but, with

C. Cheng et al. / Physics Letters A 376 (2012) 1495–1498 1497

Fig. 3. (Color online.) Temperature-dependent PL decay times measured with various

excitation powers.

Fig. 4. (Color online.) Measured and simulated PL decay time of sample A. Inset: the

schematic of proposed three-excitonic-states model.

increasing temperatures, the slow one fastens and then takes over at about 55 K.

We have also performed power-dependent TRPL measurement on sample A, as shown in Fig. 3. It is clearly observed that the anomalous spike becomes much more significant as the excitation power decreases. At the lowest excitation power in our measure-ment (2 μW), the peak decay time is as high as 7.6 ns. As the exci-tation power increases, the spike gradually flattens out. This can be easily understood as follows. The increasing excitation power en-hances the possibility of bi-exciton generation and the bi-exciton decay leaves the exciton in bright state so the dark state is less occupied. As a result, the slow decay arising from the spin-flip of dark excitons has little chance to replace the fast one when the temperature increases.

To explain the unusual behavior quantitatively, we propose a three-level model including hot, bright and dark excitonic states (see the inset ofFig. 4). The energy difference between bright and dark excitonic states (



E2) is of hundreds μeV[7,17,18]. Compar-ing with the radiative recombination time (

τ

r

∼

1 ns) of bright exciton, the spin-flip time between dark and bright states is very long at low temperature (

τ

spin-flip

∼

100 ns) [9,17,18]. The effec-tive hot excitonic state could arise from the exciton formed by a hole (an electron) at the excited state and an electron (a hole) at the ground state, as well as other combinations of higher states. The relaxation time to either bright or dark state, noted as

τ

relax (

∼

a few ps), is believed to be much faster than

τ

r. Based on the model, we performed calculation with the rate equation in the fol-lowing: dNb dt

= −



Nb

τ

r

+

Nb

τ

bd



1

−

Nd nd



+

Nb

τ

bh



1

−

Nh nh



+



Nd

τ

db



1

−

Nb nb



+

Nh

τ

hb



1

−

Nb nb



,

dNd dt

= −



Nd

τ

db



1

−

Nb nb



+

Nd

τ

dh



1

−

Nh nh



+



Nb

τ

bd



1

−

Nd nd



+

Nh

τ

hd



1

−

Nd nd



,

dNh dt

= −



Nh

τ

hb



1

−

Nb nb



+

Nh

τ

hd



1

−

Nd nd



+



Nb

τ

bh



1

−

Nh nh



+

Nd

τ

dh



1

−

Nh nh



.

(2)

The variables Ni and ni (i

=

b

,

d

,

h) are the occupation num-ber and the maximum allowed numnum-ber of excitons for each state, respectively.

τ

i j is the transition time between states i and j. Be-cause the energy difference between the bright and dark states (



E2) is much smaller than the thermal energy kBT at T

=

50 K, we assume that

τ

db

=

τ

bd

=

τ

spin-flip,

τ

hb

=

τ

hd

=

τ

relax but

τ

bh

=

τ

hb

×

eE1/kBT. With the following parameters,

τ

r

=

1 ns,

τ

relax

=

10 ps,

τ

spin-flip

=

30 ns,



E1

=

30 meV,



E2

=

0

.

3 meV, and with an odd but necessary unbalanced initial condition of Nd

(

0

)

=

4Nb

(

0

)

, where Nd

(

0

)

and Nb

(

0

)

are the initial occupa-tion numbers of dark and bright states, respectively, we can fit the simulated results with the measured ones very well below 80 K (see Fig. 4). The discrepancy at higher temperatures could be be-cause of the slight involvement of thermal redistribution between QDs.

Here we give an intuitive explanation to the observation. At the lowest temperature, the dark excitons can only become the bright ones with the slow spin-flip rate. However, with increasing tem-peratures, there is an additional path as sketched in the inset of Fig. 4. Dark excitons can turn into bright ones through the hot excitonic states. This path has an effective transition time

τ

eff, ex-pressed as follows:

τ

eff

=

τ

relax

×

exp

(

E1

/

kBT

).

(3)

When the thermal energy is much smaller than the energy spacing between dark and hot excitonic states (i.e. kBT

 

E1),

τ

eff is much longer than

τ

r and the exciton supply through this additional path is negligible so

τ

1

=

τ

r. However, when kBT is large enough to make

τ

effis comparable with

τ

r, the exciton comes from the additional path could compensate the consumption of ra-diative recombination so the measured decay time is significantly prolonged. For even higher temperatures, the additional path be-comes even more efficient so the decay time is limited by

τ

ragain. Besides, in the measured more than 20 samples, the long decay time was obtained with about one third of them. No obvious cor-relation between the growth conditions and the unusual behavior is spotted. The sample dependence of observing the long decay time could probably be understood by Eq.(3). The

τ

effis governed by two parameters,

τ

relax and



E1. They are strongly correlated because the energy spacing between two states could affect the re-laxation time between them[2]. Accordingly, to observe the effect, proper values of these two parameters could be quite important. Of course, the size-dependent energy difference between dark and bright states could also be a factor[18]but further investigations are certainly needed to clarify this issue.

4. Conclusion

In conclusion, we presented the first observation of long-lived exciton in individual InAs QDs. The rate equation analysis indicates

1498 C. Cheng et al. / Physics Letters A 376 (2012) 1495–1498

that the effective spin-flip time could become comparable with the radiative recombination time when the thermal-induced spin-flip is fastened. Our work is useful for using dark excitons as spin stor-age at elevated temperatures.

Acknowledgements

This work was supported by NSC and MOE in Taiwan. The equipment support from CNST at NCTU is appreciated. We thank Profs. C.P. Lee, W.H. Chang and S.J. Cheng for their inspiring dis-cussions.

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