ARTICLE IN PRESS

Journal of Crystal Growth 267 (2004) 405–411

*Corresp

42-868-504

E-mail

0022-0248/

doi:10.101

Evolution of bimodal size-distribution on InAs coveragevariation in as-grown InAs/GaAs quantum-dot

heterostructures

S.J. Leea, S.K. Noha,*, J.W. Choeb, E.K. Kimc

aQuantum Dot Technology Laboratory, Materials Evaluation Center, Korea Research Institute of Standards and Science, P.O. Box 102,

Yusong, Daejeon 305-600, South KoreabDepartment of Electrical Engineering and Computer Science, Kyunghee University, Suwon 449-701, South Korea

cDepartment of Physics, Quantum Photonics Science Research Center, Hanyang University, Seoul 133-781, South Korea

Received 11 January 2004; accepted 7 April 2004

Communicated by H. Ohno

Abstract

We report photoluminescence (PL) spectra associated with bimodal size-distribution observed in a series of self-

assembled InAs/GaAs quantum-dot (QD) heterostructures with different InAs coverages. The PL spectra exhibit a

well-defined doublet-like QD peak with invariable energy positions regardless of the coverage attributed to large and

small QD groups. The excitation-power dependence reveals that the high-energy peak is composed by two

contributions, one from the excited state of large QDs and the other from the ground state of small QDs. The power-

and the temperature-dependent plots on the integrated PL-intensity ratios show distinctive features supporting an

evolution of bimodal size-distribution on the InAs coverage variation in the QD ensembles. These suggest that, in as-

grown InAs QD ensembles with appropriate InAs coverage grown under an optimized condition, there can exist a

specific bimodal size-distribution consisting of two groups of large and small QDs whose sizes are fixed, but whose

numbers vary with the amount of InAs coverage with no rearrangement of the overall size-distribution profile.

r 2004 Elsevier B.V. All rights reserved.

PACS: 78.55.Cr; 78.67.Hc

Keywords: A1. Low-dimensional structures; A1. Photoluminescence; A1. Bimodal size-distribution; A3. Molecular beam epitaxy; A3.

Self-assembled quantum dots; B1. Indium arsenide

onding author. Tel.: +82-42-868-5127; fax: +82-

7.

address: sknoh@kriss.re.kr (S.K. Noh).

$ - see front matter r 2004 Elsevier B.V. All rights reserve

6/j.jcrysgro.2004.04.014

1. Introduction

Self-assembled quantum dot (QD) and itsrelated heterostructures have been receiving con-siderable attention as potential semiconductor

d.

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S.J. Lee et al. / Journal of Crystal Growth 267 (2004) 405–411406

nanostructures applicable to QD-based optoelec-tronic devices such as laser diodes [1], infraredphotodetectors [2,3]. By virtue of unique zero-dimensional features and strong confinement ofthe carrier wave functions in QDs, the structureshave emerged as scientifically important systemsnot only in device applications but also infundamental studies. Although a number of effortshave been made on (InGa)As-based QDs in orderto clarify the formation mechanism and the relatedcharacteristics by using a variety of theoretical andexperimental approaches so far [4–18], unusualbehaviors associated with the QD size-distributionare still rather ambiguous and unsettled.

Previously, a number of research groups havepresented some discussions on distinctive beha-viors that appeared in photoluminescence (PL)spectra of QD ensembles with bimodal or multi-modal size-distribution. Tackeuchi et al. [10] havedemonstrated multi-coupled quantum dot(MCQD) structures consisting of QDs coupledwith adjacent dots in which the photoexcitedcarriers tunnel into the large quantum dots withlower energy states. In addition, on the basis of thesigmoidal temperature dependence of the emissionenergy observed in InAs QDs, Brusaferri et al. [11]presented some experimental evidences on themulti-modal QD size-distribution and the ther-mally activated carrier transfer between adjacentQDs with different sizes. Lee et al. [12] reportedthat a double-peak PL spectrum observed in in situannealed InAs QD samples contrasted with asingle peak emission in as-grown one, and the QDsize bifurcated during annealing. In addition, astrong dependence on the QD size-distribution onthe growth temperature assisting the carriertransfer mechanism was given by Kissel et al.[13]. A few anomalous behaviors associated withmodes of size-distribution in PL spectra stillremain as points of issue, and the thermalredistribution of photocarriers has been discussedas one of the dominant mechanisms [11–18].

In this paper, we report some interestingfeatures associated with the bimodal size-distribu-tion in the PL spectra taken from a series of InAsQD ensembles grown with different InAs cover-age. The analysis is made on the excitation-powerand the temperature dependences of doublet-like

PL spectra consisting of a couple of low- and high-energy peaks on the basis of the bimodal size-distribution of large and small QD groups. Ingeneral, both size and density of QDs are functionsof InAs coverage and growth temperature [18]. Asthe amount of InAs coverage increases, the size ofQD ensemble continuously increases and the PLpeak gradually shifts to longer wavelength. In thispaper, however, we present a schematic viewillustrating an evolution of bimodal size-distribu-tion on the InAs coverage variation that shows achange of the numbers of large and small QDgroups in the ensembles with pinned energypositions.

2. Experimental procedures

For a systematic study on spectroscopic effectsarising in QD ensembles with bimodal size-distribution, a series of single-layered InAs-QD/GaAs heterostructures with different InAs cov-erages were grown by using a molecular beamepitaxy (MBE) system (RIBER 32P). All struc-tures basically have the same layer profile exceptfor the equivalent thickness of InAs to control thesize-distribution of QD ensembles. The sampleswere grown under the same conditions, and InAsQDs were fabricated by using a self-assemblingtechnique of the Stranski–Krastanow (S–K) mode.The growth was initiated from the GaAs bufferlayer with a thickness of 0.3 mm at a temperatureof 560�C, and the QD formation was conductedon the GaAs layer at 480�C. Three different QDstructures with the equivalent InAs thicknesses of2.0, 2.5, and 3.0 monolayers (MLs) were preparedby completing a 25-nm-thick undoped GaAs layer.The growth rates of GaAs and the InAs layerswere 12.4 and 1.4 nm/min, respectively, and the V/III beam-equivalent pressure (BEP) was approxi-mately 25.

The dot formation was in situ confirmed duringthe growth by observing the two- to three-dimensional (2D–3D) transition in the reflectionhigh-energy electron diffraction (RHEED) pattern[4]. The PL measurements were performed byusing a typical visible-to-near-infrared monochro-mator system (f ¼ 3=4m) with an Ar-ion laser

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Eo(L) E

1(L)+E

o(S)

3.0 MLs

ity (

a.u.

)

InAs/GaAs SQDInAs=2.0/2.5/3.0 MLsT = 15 K / P = 20 mW

S.J. Lee et al. / Journal of Crystal Growth 267 (2004) 405–411 407

(l ¼ 514:5 nm) and a closed-cycle He refrigerator(10K). Excitation-power- and temperature-depen-dent PL spectra were taken in the ranges ofnominal output power of 1–110mW and tempera-ture of 15–250K, respectively, and the lumines-cence signal was detected and recovered by aliquid-nitrogen-cooled Ge detector and a lock-inamplifier. The details of the epitaxial growth andthe basic properties have been reported elsewhere[3–5].

0.9 1.0 1.1 1.2 1.3 1.4

1.24 eV

E1(S)

1.165 eV

1.085 eV

2.0 MLs

2.5 MLsPL

Inte

ns

Emission Energy (eV)

Fig. 1. Representative PL spectra for three kinds of self-

assembled InAs QD ensembles with different InAs coverages of

2.0, 2.5, and 3.0MLs taken at a temperature of 15K with an

excitation power of 20mW. All spectra exhibit a doublet-like

feature and can be decomposed into a couple of dominated

peaks, one centered at 1.085 eV and the other at 1.165 eV within

an error of 75meV.

3. Results and discussion

Three representative PL spectra for the self-assembled InAs QD ensembles with different InAscoverages of 2.0, 2.5, 3.0MLs taken at a tempera-ture of 15K and an excitation power of 20mW arecompared in Fig. 1. Each spectrum exhibits adoublet-like feature with a weak high-energyshoulder, and can be decomposed into a coupleof dominated peaks, one centered at 1.085 eV andthe other at 1.165 eV with a shoulder near 1.24 eV.As the InAs coverage increases, the PL intensity oflow-energy peak (LEP) becomes stronger but thatof high-energy peak (HEP) becomes relativelyweaker with no change in the energy positionswithin an error of 75meV. In this case, there is analternative in the size mode of QD ensembles. Oneis a monomodal size-distribution with a pair ofstates, and the other a bimodal size-distributionconsisting of two size groups of large and smallQDs. In order to clarify the exact nature of thedoublet-like peak, we have investigated excitation-power and temperature dependences of the PLspectra.

Three sets of excitation-power-dependent PLspectra obtained from QD samples with InAscoverages of (a) 2.0MLs, (b) 2.5MLs, and (c)3.0MLs are presented in Fig. 2. All spectra show acouple of well-resolved PL peaks with invariableenergy positions pinned at 1.085 eV (LEP) and1.165 eV (HEP), even at low excitation-power.While the 2.0-ML spectra (a) have almost nopower dependence, the 3.0-ML ones (c) show astrong dependence. In other words, as the excita-tion power increases, there is almost no change inthe intensity profiles for the 2.0-ML sample but

HEP of the 3.0-ML spectra gradually grows andbecomes distinguishable. According to the power-dependent behaviors of the PL spectra shown inFig. 2, it is clear that HEP is involved with both aground state (major in the 2.0-ML spectra) and anexcited state (major in the 3.0-ML spectra).Assuming that LEP (1.085 eV) is due to the groundstate of large QDs [EoðLÞ], [16] we can say thatHEP (1.165 eV) is composed of two contributions,one from the excited state of large QDs [E1ðLÞ] andthe other from the ground state of small QDs[EoðSÞ], as denoted in Fig. 1. On the other hand,the PL spectra for the 2.5-ML sample (b) with anintermediate InAs coverage show only a weakpower dependence inbetween the two profiles for2.0MLs (a) and 3.0MLs (c) samples. This meansthat the numbers of large and small QDs are

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0.9 1.0 1.1 1.2 1.3 1.4

(a) 2.0 MLs

Po

10Po

5Po

20Po

50Po

110Po

Emission Energy (eV)

InAs/GaAs SQDT=15 K/P

o=1 mW

(c) 3.0 MLs

Po

5Po

10Po

20Po

50Po

110Po

(b) 2.5 MLs1.165 eV1.085 eV

110Po

50Po

20Po

10Po

5Po

Po

PL

Inte

nsity

(a.

u.)

Fig. 2. Three sets of excitation-power-dependent PL spectra

(15K) taken from QD samples with InAs coverages of (a) 2.0,

(b) 2.5, and (c) 3.0MLs. All spectra show two well-resolve PL

peaks with invariable energy positions pinned at 1.085 and

1.165 eV. While the 2.0-ML spectra (a) show almost no power

dependence, the 3.0-ML ones (c) show a strong dependence.

The 2.5-ML sample (b) with an intermediate coverage of InAs

shows only a weak dependence at the middle of the two profiles.

10 1000

1

2

3

4

3.0 MLs

2.5 MLs

2.0 MLs

200525 020

x 2

InAs/GaAs QDInAs = 2.0/2.5/3.0 MLsT = 15 K

Inte

grat

ed P

L In

tens

ity R

atio

I o(L

)/[I 1

(L)+

I o(S

)]

Excitation Power (mW)

Fig. 3. Plots for the integrated PL-intensity ratios of LEP to

HEP, IoðLÞ=½I1ðLÞ þ IoðSÞ], as a function of the excitation

power. The curves show that the 2.0-ML sample with the least

number of large QDs has almost no dependence with increased

power, and the decreasing behavior becomes stronger as the

InAs coverage increases up to 3.0MLs.

S.J. Lee et al. / Journal of Crystal Growth 267 (2004) 405–411408

comparable to each other in the 2.5-ML sample,thus, HEP is superposed by competing intensitiesdue to the excited state of large QDs [E1ðLÞ] andthe ground state of small QDs [EoðSÞ]. Here, it isadequate to mention the non-Gaussian waveformof HEP. Taking into account that the asymme-tricity is severest in the 2.0-ML sample having amajority of small QDs, we can conclude that thenon-Gaussian profile appeared near 1.24 eV iscaused by an excited state of small QDs [E1ðSÞ].Therefore, it is clear that there exists a pair of

conduction-band sublevels corresponding to thePL emission energies of 1.085/1.165 eV and 1.165/B1.24 eV for large and small QD groups, respec-tively, in all the samples used in this study [16,17].

A quantitative approach was taken to demon-strate the existence of bimodal size-distribution byanalyzing the integrated intensities of PL spectradecomposed into three Gaussian peaks[EoðLÞ;E1ðLÞ þ EoðSÞ;E1ðSÞ]. Fig. 3 shows threeplots for the integrated PL-intensity ratios of LEPto HEP, IoðLÞ=½I1ðLÞ þ IoðSÞ], as a function ofexcitation-power. All curves decrease as theexcitation power increases, and the decreasingbehavior becomes stronger with increase of theInAs coverage. In general, the power-dependentPL spectrum offers information on the excited-state transition as more electron–hole pairs aregenerated by higher excitation-power and thusmore excited states are occupied by electrons.Thus, the power dependence of the intensity ratioreflects a contribution from excited states, andsuggests a criterion on the number of QDsinvolved in the excited-state transition. Thedecreasing behavior shown in Fig. 3 is mainlydue to an enhancement of the excited-statetransition in large QDs [I1ðLÞ]. So we cansuggest that the 2.0-ML sample with almost no

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15 K

30 K

50 K

77 K

90 K

120 K

150 K

200 K

250 K(b) 2.5 MLs

PL

Inte

nsity

(a.

u.)

0.9 1.0 1.1 1.2 1.3 1.4

15 K

30 K

50 K

77 K

90 K

120 K

150 K

200 K

250 K(a) 2.0 MLs

Emission Energy (eV)

InAs/GaAs SQD/P=90 mW(c) 3.0 MLs

15 K

30 K

50 K

77 K

90 K

120 K

150 K

200 K

250 K

Fig. 5. Three series of temperature-dependent PL spectra taken

S.J. Lee et al. / Journal of Crystal Growth 267 (2004) 405–411 409

dependence contains the least number of largeQDs, and the number of large QDs becomes largerwith increased InAs coverage. That is, while the2.0-ML/3.0-ML sample consists mostly of small/large QDs, the 2.5-ML sample has a comparablenumber of large and small QDs. Fig. 4 is aschematic sketch showing the evolution of thenumbers of the bimodal sized QDs on the InAscoverage variation.

An additional behavior supporting the bimodalsize-distribution of QD ensembles can be found inthe temperature dependence of PL spectra. Threeseries of temperature-dependent PL spectra takenfrom the same QD samples with InAs coverages of(a) 2.0MLs, (b) 2.5MLs, and (c) 3.0MLs arepresented in Fig. 5. With increasing temperature,all the spectra show a typical red shift of the PLpeak energies, which is known to be mainly due tothermal expansion of the lattice constant andelectron–phonon scattering, as in bulk semicon-ductors. However, an interesting behavior can beobserved in the temperature dependences on theintegrated PL-intensity ratio of LEP to HEP,IoðLÞ=½I1ðLÞ þ IoðSÞ], as presented in Fig. 6. Thecurves show that the dependence becomes strongerwith increased InAs coverage, and two distinctfeatures appear in the profile. First, a decreasingbehavior in the intensity ratio is observed at thelow-temperature region below around 50K. Tak-

2.5 MLs

2.0 MLs

Small QDs

Large QDs

3.0 MLs

Fig. 4. A schematic sketch showing the evolution of the

numbers of the bimodal sized QDs on the InAs coverages of

2.0, 2.5, and 3.0MLs. While the 2.0-ML/3.0-ML sample

consists mostly of small/large QDs, the numbers of large and

small QDs for the 2.5-ML sample are comparable to each other.

from the same QD samples with InAs coverages of (a) 2.0-MLs,

(b) 2.5-MLs, and (c) 3.0-MLs. With increasing temperature, all

the spectra show a typical red shift of the PL peak energies, as

in bulk semiconductors.

ing into account that the 3.0-ML sample withmostly large QDs shows the strongest change, itcan be interpreted as due to the intersublevelthermal excitation from the ground states to theexcited states in large QDs [EoðLÞ-E1ðLÞ]. So, wecan expect a reduction of the ratio,IoðLÞ=½I1ðLÞ þ IoðSÞ], by both decrease of IoðLÞand increase of I1ðLÞ with the temperatureenhancement, especially in the 3.0-ML samplewith mostly large QDs. The second is the rapidincreasing behavior that appears at the hightemperature region over 50K, in which thevariation becomes stronger with increased InAscoverage. Considering that the temperature is high

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10 1000

1

2

3

4

3.0 MLs

2.5 MLs

2.0 MLs

50

x 2

20 200 30030

InAs/GaAs QDInAs = 2.0/2.5/3.0 MLsP = 90 mW

Inte

grat

ed P

L In

tens

ity R

atio

I o(L

)/[I 1

(L)+

I o(S

)]

Temperature (K)

Fig. 6. Plots for the integrated PL intensity ratios of LEP to

HEP, IoðLÞ=½I1ðLÞ þ IoðSÞ], as a function of temperature. The

curves show that the dependence becomes stronger with

increased InAs coverage, and the decreasing and the increasing

behaviors appear in low and high temperature below and above

around 50K.

10 1000.9

1.0

1.1

1.2

20020 50

Eg(T)=E

g(0) - [αT2/(T+β)]

500

High-Energy Peak

Low-Energy Peak

InAs/GaAs SQDInAs = 2.5 MLsP = 90 mW

PL

Pea

k E

nerg

y (e

V)

Temperature (K)

Fig. 7. The temperature dependence of PL emission energies

for LEP and HEP determined from a series of PL spectra for

the 2.5-ML QD sample presented in Fig. 5. The curve on LEPs

(squares) obeys the Varshni function (dotted lines), but the data

on HEPs (circles) digress from the functional curve at high

temperatures above 100K.

S.J. Lee et al. / Journal of Crystal Growth 267 (2004) 405–411410

enough for carrier thermalization, this may beexplained by the thermal excitation from theexcited state of large QDs [E1ðLÞ] and the groundstate of small QDs [EoðSÞ] to the above states. Incase of the 2.5-ML sample consisting of a mixtureof a comparable number of large and small QDs,the slow change may be associated with thethermally activated carrier transfer from EoðSÞ toEoðLÞ � E1ðLÞ states through E1ðSÞ level thatresults in a reduction of IoðSÞ and enhancementsof IoðLÞ and I1ðLÞ: The temperature behavior maybe in support on the thermal redistribution ofphotocarriers [19,20] resulted from the existence ofbimodal size-distribution consisting of large andsmall QD groups whose numbers depend on theamount of InAs coverage.

Finally, we present the temperature dependenceof PL peak energies as another piece of evidencefor the bimodal size-distribution in QD ensembles.Fig. 7 shows the temperature dependences of theemission energies for LEP and HEP determinedfrom a series of PL spectra for the 2.5-ML QDsample presented in Fig. 5. An anomalousbehavior has been found on the energy shift. Thecurve on LEPs (squares) designated as the groundstate of large QDs [EoðLÞ] follows the Varshni

equation expressed as EgðTÞ ¼ Egð0Þ2aT2=ðT þbÞ (dotted lines) over the whole temperature range,but that on HEPs (circles) superposed by twopeaks due to large and small QDs [E1ðLÞ þ EoðSÞ]does not obey the functional form at hightemperatures above 100K. Here, we used para-meters of a ¼ 3:158� 10�4 eV/K and b ¼ 93K forInAs bulk [21], and each curve was fitted to thecorresponding experimental data by adjustingEgð0Þ; the 0-K bandgap energy. As discussed insome research works devoted to the anomaloustemperature dependence of PL spectra in various(InGa)As QD ensembles [11,13,15–20], this maypossibly be due to the carrier redistribution by thethermally activated carrier transfer between ad-jacent QDs with different sizes through the wettinglayer as a carrier transfer channel. We think thatthe digression from the functional curve may be anadditional feature assisting the above discussionson the bimodal QD size distribution.

4. Summary and conclusion

In summary, we have studied some distinctivefeatures associated with bimodal size-distribution

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S.J. Lee et al. / Journal of Crystal Growth 267 (2004) 405–411 411

observed in excitation-power- and temperature-dependent PL spectra for a series of self-assembledInAs/GaAs quantum-dot (QD) heterostructureswith different InAs coverages. The PL spectraexhibited a well-defined doublet-like QD peak withinvariable energy positions pinned at 1.085 eV(LEP) and 1.165 eV (HEP) regardless of thecoverage attributed to large and small QD groups.The power dependence revealed that LEP was dueto the ground state of large QDs and HEP wascomposed by two contributions, one from theexcited state of large QDs and the other from theground state of small QDs. On the basis of theanalyses on the excitation-power and the tempera-ture dependences of the integrated PL-intensityratios, we suggested that the 2.0-ML/3.0-MLsample consisted mostly of small/large QDs andthe 2.5-ML sample had the numbers of large andsmall QDs comparable to each other. Finally, asanother piece of evidence for the bimodal size-distribution in QD ensembles, we presented thetemperature dependence of PL peak energies witha digression from the functional curve that mightpossibly be due to the thermal carrier redistribu-tion between adjacent QDs with different sizes.

In conclusions, we proposed that, in as-grownInAs QD ensembles with appropriate InAs cov-erages grown under an optimized condition, therecould exist a specific bimodal size-distributionconsisting of two groups of large and small QDswhose sizes are fixed, but whose numbers varywith the amount of InAs coverage with norearrangement of the overall size-distributionprofile.

Acknowledgements

This work was mainly carried out at theNational Research Laboratory on Quantum DotTechnology (Contract No. M1-0104-00-0127) atKRISS designated by the Ministry of Science andTechnology. The authors acknowledge the partialsupports provided by KOSEF through Quantum-Functional Science Research Center at DonggukUniversity and Quantum Photonics Science Re-search Center at Hanyang Univeristy.

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