Anomalous shift of the recombination energy in single asymmetric quantum wells

Anomalous Shift of the Recombination Energy in

Single Asymmetric Quantum Wells

N.O. Dantas a

, FanyaoQu a

, and P.C. Morais b

a

UniversidadeFederaldeUberl^andia, FaculdadedeFsica,CEP38400-902,Uberl^andia-MG,Brazil

b

UniversidadedeBraslia,Institutode Fsica,N ucleodeFsicaAplicada

CEP70919-970,Braslia-DF,Brazil

Receivedon23April,2001

Self-consistentnumericalcalculationandphotoluminescence(PL)measurementshavebeenusedto

investigatethetemperaturedependenceoftheopticalStarkeectinn-dopedGaAs/AlGaAssingle

asymmetricquantumwells(SAQWs),grownby molecularbeamepitaxy. Inthe low-temperature

regime(5 to 40K) a remarkable blueshift (9.8meV)is observedinthe PL peak energy, as the

opticalexcitationintensityincreasesfrom0.03to90W/cm 2

. Theblueshiftiswellexplainedbythe

reductionofthetwo-dimensionalelectrongas(2DEG)density,duetoacharge-transfermechanism.

Atabout80K,however,ananomalousbehaviorofthePLpeak energywas found,i.e. aredshift

hasbeenobservedastheoptical excitationintensityincreases. Thisanomalousbehaviorhasbeen

explainedbycombiningtheeectsofbandgaprenormalization,bandbending,temperaturedepen-

denceofthebandgap,temperaturedependenceofthe2DEGdensity,andtemperaturedependence

ofthefundamentalenergyposition.

I Introduction

One-sidemodulation-dopedorsingleasymmetricquan-

tum wells (SAQWs) have been used as ideal systems

to investigate dierent aspects related to many-body

eectsintwo-dimensional(2D),one-componentcarrier

plasmas[1]. TheSAQWisaspecialcaseofmodulation-

doped quantumwell(MDQW)where theremotedop-

ingismadeonlyinonesideofthesinglequantumwell.

The typicalgrowthprole of aGaAs/AlGaAsSAQW

includes athickGaAs buerlayerontopof theGaAs

substrate, a short-period GaAs/AlGaAs superlattice,

the GaAs SAQW, the undoped AlGaAs spacer layer,

the n- or p-type doped AlGaAs layer, and nally the

GaAs cap layer. Among the many-body eects inves-

tigated using SAQWs are the Fermi-edge singularity

(FES) [2], the band gap renormalization [3], and di-

mensionalitycrossover[4], allof themstrongly depen-

dent upon the carrier temperature and their density

(N

S

). Forinstance,thelowtemperatureandhighcar-

rierconcentrationfavortheFESobservationinPLex-

periments, while FES would be smeared out by high

temperatureandlowcarrierdensity. BesidesFES,band

gap renormalization also strongly depends upon the

carrierdensity,N

S

,accordingto(N

S )

. Theexponent

is relatedto thedimensionalityof thesystem,being

=1/2 for three-dimensional (3D) carrier plasma and

size the great interest of using SAQWs to investigate

many-body eects in 2D semiconductor heterostruc-

tures,oncethecarriergasdensityinsuchstructurecan

becontinuouslyvariedfromitsmaximumvaluedownto

zero. Continuouschangeofthe 2Dcarrierdensity has

beenachievedbyapplyingabiasvoltageinaeldeect

transistor conguration[5] {electric Stark eect. Al-

ternatively,continuouschangeofthe2Dcarrierdensity

has been obtainedthroughillumination of thesample

with increasing optical excitation intensity (P) { op-

tical Stark eect. The signature of the optical Stark

eect is a remarkableenergy shift (typically 10 meV)

inthefundamentalopticaltransition. Theexplanation

ofthePLblue shiftwiththeincreaseofthelaserexci-

tation intensitywasrstput forwardby Chaveset al.

[6]. Thereupon, it was further conrmed by following

works [3]. The established optical control mechanism

used to explain the experiment requires illumination

with photonshavingenergy higherthantheband gap

of theundoped spacer layer. Theattentionis focused

on the electron-hole pairs photocreated in the spacer

layer. Inthen-typedopedstructure,thephotocreated

electron initially moves back to the spatially distant

donorswhile the photocreatedhole is driftedinto the

quantumwellbythebuilt-inelectriceld,thererecom-

bining with 2D electrons. Later on, the photocreated

electron movesfrom thedonor into the quantum well

bytunnelingthroughthespacerlayer. Atagivenopti-

cal excitation intensitythesteady-state2DEGdensity

is lowerthan thedensity (N 0

S

)at ornear zeroexcita-

tion. Althoughthecharge-transfermechanismhasbeen

successfullyusedtoexplaintheexperimental,allthere-

portedstudiesconcerningtheopticalStark eecthave

beenperformedat low-temperatures. However,thein-

uence of nite temperatures on the optical Stark ef-

fect is obviously important for both applied purposes

and fundamental physics. Nevertheless, the tempera-

ture dependence of optical Stark eect has not been

investigated yet,in spiteof thehugetechnologicalim-

pact ofthemicro-electronic-opticaldevicesandoptical

communications,bothoperatingatnitetemperatures.

Investigationof theeectsofnitetemperaturesupon

theopticalStarkeectisthemainissueofthepresent

study.

II Experimental details and re-

sults

ThePLexperimentsreportedinthisstudywerecarried

out using two GaAs/Al

0:35 Ga

0:65

As SAQW samples

(W1506 and W1413), grown by molecular beam epi-

taxy. SampleW1506consistsofasemi-insulatingGaAs

substratefollowedbya1.3m-thickGaAsbuerlayer,

aGaAs/Al

0:35 Ga

0:65

Assuperlattice (typically735

A

+ 8100

A), andby thenominally 152

A-thickGaAs

SAQW. The2Delectrongas(2DEG) inside theGaAs

SAQW is a result of the electron-transfer, through a

295

A-thickundopedAl

0:35 Ga

0:65

Asspacerlayer,from

a385

A Si-dopedAl

0:35 Ga

0:65

Aslayer. A250

A-thick

GaAs caplayerwasgrownontopof theoverallstruc-

ture. SamplesW1413andW1506havesimilargrowth

proles. Inthe W1413sample, theasymmetric quan-

tumwellwidthis150

A,thethicknessofspacerlayeris

300

A,andthethicknessoftheSi-dopedAl

0:35 Ga

0:65 As

barrierregionis380

A.Bothsampleshaveelectronmo-

bility higher than 410 4

cm 2

/Vs at liquid Helium

temperature. Sampleswereopticallyexcitedabovethe

band gap of theundoped Al

0:35 Ga

0:65

As spacerlayer,

using the 5145

A argon-ion laser line. The PL spec-

trawererecordedusingaSPEX-750Mmonochromator

equipped with a Joban-Yvon CCD 2000800-3. The

NEOCERA LTC-11 temperature controller was used

during thePLmeasurements.

Fig. 1showsthePLspectraofsampleW1506under

P =0.4W/cm 2

,atdierenttemperatures(10,30,50,

and80K).ThePLpeak-A,locatedat1521.7meV(10

K),isassociatedtothen=0transition,i.e. between

the ground state conduction subband to the ground

stateheavy-holesubband ofthe GaAs SAQW.As the

opticalexcitationintensityincreasesthe2DEGdensity

decreases due to the electron-transfer mechanism. At

2

outfromtheGaAsSAQW.Then,theelectron-transfer

turnsthe152

A-thickGaAsSAQWintoanalmostper-

fectsquare potentialwell. Inthis case, thecalculated

n =0 recombination energy is 1538.7 meV and the

excitonbinding energy associated to theground state

in the GaAs SAQW is 8.2 meV. Thus, a free exciton

transitioninasquareGaAspotentialwellwouldbeex-

pected to occurat about 1530.5meV. Note the good

agreementbetween thecalculatedvalue (1530.5meV)

andtheobservedPLpeak-A position (1531.7meV) at

higheropticalexcitation intensity(P =90W/cm 2

).

Figure 1. PL spectra of sample W1506 under P = 0.4

W/cm 2

,atdierenttemperatures(10,30, 50,and80K).

The PLpeak-B, located at 1514.8 meV (10 K), is

attributed to the recombination from the thick GaAs

buer layer. It is worthy to mention that the PL

peaks A and B are very much close together in the

weakopticalexcitationintensityregime,becauseofthe

strongband bendingandbandgap renormalizationef-

fects. However,asP increasesthePLpeak-A tendsto

separate from the PL peak-B. Finally, they are com-

pletely separated at the higher optical excitation in-

tensity regime. Moreover,PL peaks A and B demon-

stratequitedierent temperature dependence. Asex-

pected, PL peak-B shows normal temperature depen-

dence,onceintensityandenergypeakpositiondecrease

monotonicallywiththeincreaseintemperature. Incon-

trast,PLpeak-Aexperiencesadierentbehavioronce

its intensity with respect to the PL peak-B intensity

increasesmonotonically, asthetemperatureincreases.

ThePLpeak-C(1493.8meV)isassignedtothecarbon

acceptortransitionintheGaAssubstrate. PLpeaksC

ior,asfarastheincreaseoftheopticalexcitationinten-

sityisconcerned. Incontrast,PLpeaksCandDshow

dierenttemperaturedependence. Thus, thePL peak

D may originatefrom the residualacceptor transition

in thenominally undoped GaAs SAQW,accompanied

by LO-phonon emission. Finally, PL peak E (1668.7

meV)hasitspositionalmostindependentoftheoptical

excitation intensity, being associated to theinterband

transition from the short-periodGaAs/Al

0:35 Ga

0:65 As

superlattice.

Fig. 2 shows the optical excitation intensity de-

pendence of the recombination energy of the W1413

sample,atdierenttemperatures. Atlowtemperature

(10K), astrong blue shift in recombinationenergy, as

theoptical excitation intensity increases,is found. As

thetemperatureincreasesfrom 10Kto40K,theblue

shiftin recombination energyis still observed, though

reduced from 9.2 meV (10K) to 8.4 meV (40K). As

thetemperatureisfurtherincreasedabreakdownofthe

blueshiftisobserved,asshownbytheopencircles(80

K) in Fig. 2. Above about 80 K the recombination

energydecreasesmonotonicallyasthetemperaturein-

creases. At100K,aslightblueshift(2meV)hasbeen

found.

III Discussion

Atverylowtemperature,residualacceptorstatesplaya

keyroleintheopticalpropertiesofintentionallydonor-

doped semiconductormaterials. Undersuch condition

fewacceptorstatesaectthepositionoftheFermien-

ergy, forelectronsfrom donorsgetcaptured at accep-

tor sites,resultingin someionizeddonors. Under low

optical excitation intensity, thephotogenerated excess

holes collected by the SAQW are less than the num-

beroftheionizedacceptorsintroducedbytheresidual

doping. Then, the ionized residual acceptors rapidly

localizephotoholes. Since in k space thestate ofthe

localized holesis extended, recombinationof all occu-

pied conduction-band states with dierent k, from 0

up to the Fermi wavevector, k

F

, and localized holes

isallowed. Atasuitableacceptorconcentrationthere-

strictionofthek-selectionruleimposedontherecombi-

nationprocess isrelaxed. So,at lowtemperature,the

free photoelectron-localized-hole transitions dominate

theopticalemissionprocess. Sincethetrappingofholes

byelectronsisveryeÆcient,theopticaltransitionsre-

main k-nonconserving. As aconsequence, in SAQWs,

low-temperaturePLspectrapresentbroadandstep-like

bands with sharp edgesat theeective band gap and

attheFermi energycuto(seeFig. 1).

In SAQWs, the optical Stark eect clearly shows

three dierent behaviorsas a function of bothoptical

excitationintensityandtemperature(seeFig. 2). First,

at low opticalexcitation intensity,and in thetemper-

turedependenceofthePLrecombinationenergyisob-

served. As thetemperature increasesfrom5to 100K

thePLpeakenergymovesupwardstoapeakvalue,at

intermediatetemperatures,tofurthercomedownatthe

high-temperatureend(100K).Second,athighoptical

excitation intensity, the PLpeak energyassociated to

the SAQW presents normal temperature dependence,

i.e. thePLpeakenergymovesmonotonically tolower

energy as the temperature increasesfrom 5to 100 K.

Third,a continuoustransition betweenthe twodier-

entregimeshasbeenobservedatintermediatevaluesof

opticalexcitationintensity.

Figure2. Recombinationenergyasafunctionoftheoptical

excitationintensity,forsampleW1413, atT=10K(open

squares),T=40K(soliduptriangles),T=80K(opencir-

cles),and (soliddowntriangles). Thelinesare justguides

fortheeye.

To understand the complexfeatures in theoptical

spectraofSAQWs,particularlytheirdependenceupon

the optical excitation intensity and temperature, the

combined eects of band gap energy shrinkage, band

bending, band gap renormalization, temperature de-

pendence of the 2DEG, and relaxation of ionized ac-

ceptorsshouldbetakenintoaccount. Thismeansthat

a quantitative description of the temperature depen-

dence ofboth 2DEGdensity andground state energy

hastobeperformed. Therefore,self-consistentcalcula-

tion,which numericallysolvesthecoupledSchrodinger

andPoissonequations,hasbeencarriedoutforsample

W1413. Thecorrespondentresultwillbepublished in

a forthcoming paper. The following parameters have

beenusedinthecalculation: donorboundenergyxed

at E

D

= 50meV, lowfrequency dielectricconstantin

thewell("

W

=13.2"

0

)andinthebarrier("

B

=12.2"

0 ),

andeectiveelectronmassinthewell(m W

e

=0.067m

0 )

and in the barrier (m B

e

=0.092m

0

). It is found that

theelectronarealdensityincreasesasthetemperature

increases. Inaddition,thehigherthedonorconcentra-

tionthelargertheelectronarealdensityanditsincreas-

ingrate. Reductionoftheelectronfundamentalenergy

tually, in the low optical excitation intensity regime,

the blue shift due to the electron-transfer mechanism

is negligible. Asthetemperatureincreasesthermalef-

fectstend tospreadthe2DEGoverthefull densityof

states. Then, thePLpeakenergyshiftstowardhigher

values. Ontheotherside,asthetemperatureincreases,

theshrinkageofthebandgapandthereductionofthe

groundstateenergyleadtoaredshiftofthePLpeak

energy. Reduction of the PLpeak energy, due to the

shrinkage of the band gap energy, is about 8.5 meV

(0.69meV)asthetemperatureincreasesfrom40to80

K (10 to 40 K). Then, in the low optical excitation

regime and below80K,the resultanteect leadsto a

blueshiftinthePLpeakenergy. Withfurtherincrease

intemperature(above80K),theshrinkageoftheband

gap becomes dominant (12.1meV in thetemperature

rangeof 80to100K),leadingto aredshift inthePL

peak energy. At intermediatevaluesof optical excita-

tion intensities, however,the electron-transfer mecha-

nismgovernstheopticalemissionprocess,reducingthe

2DEG density in the SAQW. The band bending and

the band gap renormalizationdecrease as the optical

excitation intensity increases. ThePL peak energyis

expectedto movetowardhigher energyvalues. Even-

tually, in the high optical excitation intensity regime,

all electrons are removed out from the SAQW by the

photogeneratedholes. TheSAQWturnsintoaperfect

square potentialwell. Then,asexpected, normaltem-

perature dependence of the PL recombination energy

aswellassymmetricPLspectraareobserved. Inother

words, theanomalous dependence of the PL recombi-

intensity increases. This feature supports the picture

ofthecompetitionbetweentheopticalStarkeectand

theelectron-transfermechanisminexplainingtheopti-

calpropertiesofSAQWs,atnitetemperaturesandin

awiderangeofopticalexcitationintensities.

In summary, the band gap renormalization, band

bending, temperature dependence of the 2DEG den-

sity, and temperature dependence of the fundamental

energy position are all coupled together to determine

theverycomplexbehaviorof theSAQW PLpeak po-

sition.

Acknowledgments

SupportfromtheBrazilianagenciesFAPMIG,FAP-

DF,andCNPqisgratefullyacknowledged.

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