Optical properties of wurtzite GaN/AlN quantum dots grown on non-polar planes: the effect of stacking faults in the reduction of the internal electric field

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by  J. A. Budagosky

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Optical properties of wurtzite GaN AlN quantum dots grown on non-polar planes: the
ff
e ect of stacking faults in the reduction of the internal electric field
J.A.Budagosky,N.Garro,A.Cros,andA.Garc´ıa-Cristo´bal
InstitutdeCie`nciadelsMaterials(ICMUV),UniversitatdeVale`ncia,E-46071Vale`ncia,Spain
S.FountaandB.Daudin
CEA,INAC-SP2M,”Nanophysiqueetsemiconducteurs”group,F-38000Grenoble,France
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1
0
2
Abstract

n
aThe optical emission of non-polar GaN/AlN quantum dots has been investigated. The presence of stacking faults inside these
Jquantumdotsisevidencedinthedependenceofthephotoluminescencewithtemperatureandexcitationpower.Atheoreticalmodel

9fortheelectronicstructureandopticalpropertiesofnon-polarquantumdots,takingintoaccounttheirrealisticshapes,ispresented
1which predicts a substantial reduction of the internal electric field but a persisting quantum confined Stark effect, comparable to

that ofpolar GaN/AlN quantumdots. Modeling theeffect ofa 3 monolayerstacking faultinside the quantumdot, whichacts as
]
lzinc-blendeinclusionintothewurtzitematrix,resultsinanadditional30%reductionoftheinternalelectricfieldandgivesabetter
l
aaccountoftheobservedopticalfeatures.
h
-Keywords:
s
e
m
.1. Introduction these systems [9]. The absorption spectrum is calculated us-
t
a ingaplane-waveexpansionmethodanda8×8k·pmodel. The
m Thecurrentinterestingroup-IIInitridequantumdots(QDs) comparison of polar and non-polar QD absorption shows that
-ismostlyrelatedtothepossibilityofdevelopinganewgenera- thelatterarestilldominatedbyQCSE,inagreementwithpre-
d
tionofoptoelectronicdevicesoperatingintheultravioletwave- vious theoretical models [10, 11, 12, 13], not fitting, however,
n
olengthrange[1]. Asamatteroffact,self-assembledGaN/AlN our experimental observations. The influence of basal plane
cQDsgrownintheStranski-Krastanovmodebymolecularbeam stacking faults on the QD optical properties is revealed in the
[epitaxy(MBE),whichpresenthexagonalwurtzite(WZ)struc- temperatureandpowerdependenceoftheiremission. Weshow

1 ture preferably, are free of structural defects, such as disloca- howsuchstackingfaults,actingaszinc-blende(ZB)inclusions,
vtions [2]. The great potential of these systems is somehow modifytheelectricpolarizationinsidetheQDsandcanaccount
2frustratedbythepresenceofstrongbuilt-inelectrostaticfields for additional electric field reductions. Such reduction, united
4which induce the quantum confined Stark effect [3] (QCSE), totheeffectsofCoulombcorrelation[12]ortherealisticshape
9
i.e. the emission exhibits large red-shifts and the oscillator of the dots [9, 13], could complete the picture of the QCSE
4
0strengthsoftheopticaltransitionsarereducedconsiderablydue suppressioninnon-polarQDs.
.to electron and hole spatial separation. These fields are origi-
1
natedbythedifferenceinthemacroscopicpolarizationbetween
0 2. Experimentalresults
6thedotandthebarriermaterialsandaremainlyparalleltothe
1polar c-axis of the WZ structure [4]. Non-polar heterostruc- We have investigated a sample consisting of a 18-period
v:tureshavebeengrownwiththeaimofreducingorsuppressing multi-layer of GaN/AlN QDs grown by MBE on commercial
ithe internal electric field. In the case of non-polar quantum a-plane 6H-SiC substrate. Self-assembled GaN QDs (a-QDs)
X
wells,wherethemacroscopicpolarizationlaysontheplaneof formed by the Stranski-Krastanow growth method at 700 ◦C
rthewellandundergoesnodiscontinuity,built-inelectricfields under Ga-rich atmosphere. The mean diameter and height of
a
are completely suppressed [5]. The lack of electric field ef- the GaN QDs are 20 nm and 3 nm, respectively. More details
fectsreportedforGaN/AlNQDsgrownonthea-planebyMBE aboutthegrowthofthissamplecanbefoundelsewhere[7].
is more intriguing. These QDs present strong emission in the The spectral content and the dynamics of the emission of
UVwithfastlifetimesindicatinganeffectivesuppressionofthe the a-QDs have been explored by time-integrated and time-
QCSE[6,7,8]. resolved photoluminescence (PL) spectroscopy. Figure 1 (a)
In this paper we study the emission of a-plane GaN/AlN showsthea-QDPLspectrarecordedbetween30and300K.We
QDsandcompareitwiththepredictionsofatheoreticalmodel observe that the emission peaks above the GaN band-gap en-
which takes into account the realistic arrow-head shapes of ergyindicatinganeffectivesuppressionoftheQCSE,inagree-
PreprintsubmittedtoMaterialScienceinSemiconductorProcessing January20,2016
whicharecommonina-planeAlN,asshowninTEMimageof
30 K theupperinsetofFig. 1(a).
60 K BSFs are ZB inclusions in the WZ matrix and can be re-
90 K
s) 120 K gardedastype-IIquantumwellsforelectrons. Holesareinthe
ituni 322022000 KKK surrounding WZ area and stay bound to the electrons thanks
b. to Coulomb attraction. Therefore, transition I in Fig. 1 cor-
ar 1.0 1
nsity (nten II1 X ormalized INo100..05 rtionesngpsto.hneTdhesexrtcmoitoathlne.exArcacidttauiataitloilvnye,ctrahenecodamcetlbiovicanataliitozinoenetnhoeefrhgsoyulceohsbtbtayyipndee-idsIIseoxecpxiecarit---
I 0.01 0.02 0.03 imentally, 30±3 meV, matches the binding energy of the ex-
1/T(K-1) (a)
citon[14]. Increasingtheexcitationpower, ontheotherhand,
33..66 33..77 33..88 33..99 44..00 44..11 44..22 leadstotheband-fillingoftheelectronsubbandsandthepartial
Energy (eV) screening of the electric field in the inclusion, which is orig-
LIow T inated by the discontinuity of the polarization at the WZ/ZB
nits) 104 RX1T interface[15]. Thiscanexplaintheblue-shiftoftheI1PLpeak
b. uy (arb 1033 showninFig. 1(c).
ensit 102 (b) 3. Theoreticalresults
nt
I
3.1. Descriptionofthemodel
3.82 LIo1w T
RXT We have implemented a model for the optical properties of
gy (eV) 3.80 GpoalNar/AorliNenQtaDtisonwsi.thTahrebfiitrrsatrystgeepoimneoturyrmanoddbeloitshtphoelacralacnudlantoionn-
ere
En 3.78 (c) of the three-dimensional strain and built-in potential distribu-
tions in the dot and the surrounding barrier. Our approach to
0.1 1 10
the strain distribution is based in a reformulation of Eshelby’s
Power (mW)
inclusions model [16]. The displacement, u(r), associated to
therelaxationoftheQDinclusionwithintheinfinitematrixis
Figure1:(Coloron-line)(a)PLspectraoftheGaNa-QDsasafunctionofthe calculatedfromtheelasticequilibriumequation,
sampletemperature. Theupperinsetshowsa100×80nm2 plan-viewTEM
(cid:34) (cid:35)
imagewhereBSFscrossingtheAlNbarriersandmostofthea-QDsappearas ∂ ∂ ∂ (cid:104) (cid:105)
verticallines,asextractedfromRef.[9].ThelowerinsetcontainsanArrhenius ∂x Cijkl(r)∂x uk(r) =−∂x σ(i0j)χ(r) , (1)
plotoftheintensityofthe I1 peakprovidinganactivationenergyof30±3 j l j
meV.Thedependenceofthepeakintensity(b)andenergy(c)ontheexcitation
whereχ(r)isthecharacteristicshapefunctionoftheinclusion,
poweroftheI1 andX transitions. Thedashedlinein(b)correspondstothe
lineardependence. Cijkl(r)aretheelasticconstantsoftheinhomogeneoussystem,
andσ(0) theinitialstress, relatedtothemismatchbetweenthe
ij
latticeparametersofthematrixandtheinclusion. Theanalysis
ment with previous reports [6, 7, 8]. On the other hand, two is simplified by taking the same elastic constant values in the
transitions can be identified (labeled as I and X) peaking at dot and matrix, which is a good approximation for GaN and
1
3.785 eV and 3.87 eV at 30 K, which evolve differently with AlN. Since the shape of the non-polar QDs can be crucial for
temperature. While I dominatestheemissionatlowtempera- theiropticalproperties[13],weturntotheFourierspacewhere
1
tures, its intensity decays rapidly as the temperature is raised, itisalwayspossibletoobtaintheanalyticalsolutionsforu˜i(q)
asshownbytheArrheniusplotinsettedinFig. 1(a). Atroom foranyQDshape. Finally,thebuilt-inelectrostaticpotentialis
temperature,justonegaussianpeakcorrespondingtotransition computed considering the spontaneous, Psp = (0,0,Pszp), and
X is observed. The dynamics of the PL (not shown) is also piezoelectric, Ppz = (Ppxz,Ppyz,Ppzz), contributions for the total
different for X and I with decay times of 1.23 and 2.38 ns, materialpolarization.Thelatterarecalculatedassuminghomo-
1
respectively. Inordertostudythedependenceofthetwotran- geneous piezoelectric constants for the inclusion and the ma-
sitionsontheexcitationpower, experimentshavebeencarried trix. Then,weusethesepolarizationsandthePoissonequation
outatlowandroomtemperature,whenthePLisdominatedby tocomputethebuilt-inelectrostaticpotential,
I and X, respectively. Thepowerdependenceoftheintensity
1 i
andthePLpeakenergiesareexemplifiedinFigs. 1(b)and(c). φ˜(q)=− q·P˜tot(q) . (2)
q2(cid:15) (cid:15)
The integrated intensities increase with power almost linearly 0 r
in both cases. The peak energy, however, blue-shifts clearly The electronic structure is calculated within the multi-band
withincreasingpowerforthe I transition, whilebeingnearly envelopefunctionapproximationbasedonthe8×8k·pHamil-
1
constantforX. Theoverallphenomenologyreportedfortransi- tonianderivedbyChuangetal[17]takingintoaccountthecon-
tionI iscompatiblewiththatattributedtobasalstackingfaults tribution of the strain field and the built-in electrostatic poten-
1
(BSFs)[14,15]. Non-polarQDscanbeoftencrossedbyBSFs tial. Aplane-waveexpansionwithinthefirstBrillouinzoneis
2
performed [18]. Excitonic correlation has been taken into ac- 2
countperturbatively. Then,foreachelectron-holepairthecor- ((aa)) ((bb)) φpiezo
respondingexcitonenergyisgivenbyEX,ij =(Ecj−Eiv)−Eb,ij, 1 φspont
where Eb,ij is calculated from the direct matrix element of the φpiezo+φspont
electron-holeCoulombinteraction
0
Eb,ij =−4eπ2εr (cid:90)re(cid:90)rh (cid:112)(xe−xh|)ψ2cj+(r(ey)|e2|−ψviy(hr)h2)|+2 (ze−zh)2 .(3 (eV)φ) -1 yy zz α
D D
Here,ψc (Ec)andψv (Ev)arethewavefunctions(energies)of -2 x y 1
j j i i
D
the jth electron state and the ith hole state, respectively. We 22
finally obtain the absorption spectrum from the exciton ener- -3 z yy h x z h
gies and the computed polarization dependent dipolar matrix
elements
-4
-6 -4 -2 0 2 4 6 -10 -5 0 5 10
α((cid:126)ω)= C (cid:88) f Γ , (4) z (nm) z (nm)
(cid:126)ω i,j T,ij(cid:16)EX,ij−(cid:126)ω(cid:17)2+Γ2
Figure2: (Coloron-line)Variationoftheelectrostaticpotentialcomponents
whereCisaconstant,(cid:126)ωthephotonenergy,Γprovidesaphe-
alongthewurtzitec-axisofa(a)c-QDanda(b)a-QD.TheshapesoftheQDs
nomenological description of the line broadening, and fT rep- foreachorientationaresketchedintheinsets.Thedimensionsofthec-QDare
resentsthetransitionoscillatorstrength,definedas D=20nmandh=4nm;andofthea-QD,D1 =24nm,D2 =16nm,h=3
nm, andα = 30◦. Thedashedarrowsindicatethelineswherethepotential
fT = m2(cid:126)E2 (cid:12)(cid:12)(cid:12)(cid:104)ψcj|eˆ·p|ψvi(cid:105)(cid:12)(cid:12)(cid:12)2 . (5) profilesaretakenfrom.
0 X
Finally, an important property of the confined electron-hole
value. The value obtained for the potential can be partially
transitionsistheirradiativelifetime,τ [8]
r understood through geometrical arguments: the GaN-AlN in-
3m c32π(cid:126)2(cid:15) terface along z in the a-QD is not perpendicular to the c-axis,
τr = n0e2E2 f 0 , (6) leadingtoareductioninthepolarizationcharge. Additionally,
X T the magnitude of the potential does not increase linearly with
wherenistherefractionindexofthematerial. Theparameters distance, since the a-QD geometry hardly resembles a planar
usedinourcalculationsarethoseofRef[19]. capacitor. AsecondstrikingdifferencebetweenFigs. 2(a)and
(b) arises from the piezoelectric contribution to the potential
3.2. Comparative study of the optical properties of polar and induced by strain which has now opposite sign due to the dif-
non-polarGaN/AlNQDs ferences in the strain distribution [7]. As a consequence, the
TwodifferentQDorientationsarestudied,whichinvolvetwo totalpotentialisconsiderablyreduced.
distinctiveQDgeometries. PolarQDs,withthedotaxisparal- Theabsorptionspectraofpolarandnon-polarQDsarecom-
lel to the c-axis (c-QDs), are modeled as truncated hexagonal paredinFig3. Thelabelsindicatetheelectronandholestates
basedpyramids[2],asdepictedinFig2(a). Ontheotherhand, involvedinthetransitionsforbothorientations. Forthec-QD,
a-QDs have the truncated trapezoidal based pyramidal shape theabsorptionpeakscorrespondingtothegroundstatearewell
[9]showninFig2(b). Weshalltakethez-axisalwaysparallel belowtheGaNband-gapenergy(2.922eVand2.930eV).The
tothecrystal[0001]direction. Figure2showsthevariationof smallenergydifferencebetweenbothpeaksisattributedtothe
theelectrostaticpotentialalongthez-directionforbothtypesof bandcouplingincludedinthemodel. Remarkably, theoptical
QDs. Thecontributionsfromthepiezoelectricandthesponta- transitionsofthea-QDarejust20meVhigherthanthoseofthe
neouspolarizationsareexplicitlydisplayed. Forthec-QD,the c-QD,whichcanbeexplainedbythesmallervolumeofthea-
piezoelectricandspontaneouscontributionsarefoundtobeof QDwithrespecttothepolarcaseandtheconsequentincrease
similarmagnitudeand,moreimportantly,ofthesamesign,re- ofthequantumconfinementenergy. Despitethesimilaritiesin
sultinginatotalpotentialthatchangesalmost2.4Vinalength termsofenergyrange,wefindprofounddifferencesinthetwo
ofonly4nm. Noticethat, fromtheelectrostaticpointofview, spectra. Firstofall,theabsorptionspectrumofa-QDsisthree
a QD of this geometry resembles a planar capacitor, with its ordersofmagnitudeweakerthanthatofthec-QDs. Suchade-
oppositelychargedsheetsseparatedadistanceequaltotheQD creaseintheoscillatorstrengthisduetothelargerspatialsep-
height. Therefore,thepotentialdifferencebetweenthetopand arationbetweentheelectronandholestatesinnon-polarQDs,
bottomoftheQDincreasesalmostlinearlywithheight. Asim- ascanbeobservedintheinsetsofFig. 3forthegroundstates
ilaranalysisforthea-QD,seeFig. 2(b),conveysverydifferent of electrons and holes confined in such QDs. In relation with
results. First, we notice that the contribution to the potential that, the calculated lifetime of the radiative recombination of
arisingfromthespontaneouspolarizationhasalmostthesame thegroundtransitionis18msfora-QDs. Thisvalueisfouror-
magnitudethanthatforthec-QD.However,withtheimageof dersofmagnitudegreaterthanthelifetimeofthegroundtransi-
the planar capacitor in mind, we would expect a much larger tioninc-QDs,(2.3µs). Fromthetheoreticalsimulationwecan
3
X (a) ×103 (b)
Y e (a) X (b)
Intensity (arb.units)2.900 e-h200. 9Z25e-h01 2.95e-h005 e-hh0620.0975 2.900 2.925 e-hhe00200.9e-h5001 e-h022e-h.90375 es (eV)Band Edge)nd Edges (eV)Ban 1000...6450005 C.B. aaa--QQQDDD++BBSSFF arb. units)Intensity (a I x10-7 ZZY -he000e-he-h0102-he030
V.B.
Energy (eV) -0.5
-10 -5 0 5 10 33.992255 33.995500 33.997755 44.000000
z (nm) Energy (eV)
Figure3: (Coloron-line)Firsttransitionsoftheopticalabsorptionspectraof
(a)thec-QDand(b)a-QDasafunctionofthelightpolarization.Thelabeling Figure4:(Coloron-line)(a)Conductionandvalenceband-edgeprofilesforthe
foreachtransitionsisrealizedbytheuseoftheelectronandholelevels. The a-QDcorrespondingtothefirststatesforelectronsandholescontaininga3
insetsshowthewavefunctionsoftheelectronandholegroundstatesforthetwo mono-layerZBinclusioninthez=0plane. (b)Firsttransitionsoftheoptical
geometries. absorptionspectrumofelectricfield-freea-QD.Thescaleoftheintensityisthe
sameasinFig.3.
concludethattheQCSEendsupbeinghigherina-QDsthanin
c-QDs. importantly,theoscillatorstrengthissevenordersofmagnitude
largerthanthoseobtainedforc-QDs.
In conclusion, the optical properties of GaN/AlN non-polar
4. Discussion quantum dots show a drastic suppression of the quantum con-
fined Stark effect in these systems. Theoretical calculations
The almost full suppression of the QCSE evidenced exper- predict a strong reduction of the internal electric field which
imentally cannot be explained by our theoretical simulations. doesnotensure,however,aneffectivesuppressionofthequan-
This puts forward the need for other mechanisms that should tum confined Stark effect due to the orientation of non-polar
accountforadditionalreductionsoftheinternalelectricfieldsin quantumdots. Thecomputationofthepotentialprofileofbasal
non-polarQDs.Whilesomeauthorshavedemonstratedthatthe stackingfaultsinsidethequantumdotsprovidesadditionalre-
shapeofthedots[13]orthepresenceoffreecarriers[20]can ductionoftheinternalelectricfield. Excitonictransitionsasso-
increasetheoscillatorstrengthofthetransitionsorscreenbuilt- ciatedtostackingfaultscandominatetheemissionspectrumat
inelectricfields,noattentionhasbeenpaidtotheexistenceof lowtemperaturesandmoderateexcitationpowers.
structural defects, such as BSFs, revealed in the PL spectra of
Fig. 1. TheeffectofBSFsistwofold: firstofall,thebandoff-
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