Control of fine-structure splitting and excitonic binding energies in selected individual InAs/GaAs quantum dots

0.29 MB·English

by  R. Seguin

Control of fine-structure splitting and excitonic binding energies in selected individual
InAs/GaAs quantum dots
∗
R. Seguin, A. Schliwa, T. D. Germann, S. Rodt, K. Po¨tschke, A. Strittmatter, U. W. Pohl, and D. Bimberg
Institut fu¨r Festk¨orperphysik, Technische Universit¨at Berlin, D-10623 Berlin, Germany
M. Winkelnkemper
7
Institut fu¨r Festk¨orperphysik, Technische Universit¨at Berlin, D-10623 Berlin, Germany and
0
Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany
0
2
T. Hammerschmidt
n
Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany
a
J
2 P. Kratzer
Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany and

] Fachbereich Physik, Universit¨at Duisburg-Essen, D-47048 Duisburg, Germany
ci (Dated: February 5, 2008)
s
- A systematic study of the impact of annealing on the electronic properties of single InAs/GaAs
l quantumdots(QDs)ispresented. SingleQDcathodoluminescencespectraarerecordedtotracethe
r
t evolution of one and the same QD over several steps of annealing. A substantial reduction of the
m
excitonic fine-structure splitting upon annealing is observed. In addition, the binding energies of
. different excitonic complexes change dramatically. The results are compared to model calculations
at within8-bandk·ptheoryandtheconfigurationinteractionmethod,suggestingachangeofelectron
m and hole wave function shape and relative position.
-
d PACSnumbers: 78.67.Hc,73.21.La,71.35.Pq,78.60.Hk
n
o
c Singlequantumdots(QDs)arebuilding blocksfornu-
[ merous modern devices including single-photon emitters

[1] and storage devices [2, 3]. Targeted tailoring of their
1
v electronic properties is of utmost importance for device
1 functionality. Avanishingexcitonfine-structuresplitting
3 (FSS) ofQDs,forexample,is the keyparameterforgen-
0 erating entangled photon pairs [4, 5]. FSS post-growth
1
modification was recently demonstrated using external
0
electric [6] and magnetic fields [7] as well as externally
7
appliedstress[8]. Inordertolimitthecomplexityofafi-
0
/ naldevice,itisdesirabletomodifytheFSSpermanently,
t
a e.g., by precise variation of the QD structure. Anneal-
m ing can considerablyalter the electronic structure ofQD
ensemblesleadingtoachangeofFSS[9,10,11]andbiex-
-
d citonbindingenergy[11]. WhileRefs.9and10measured
n averagepropertiesofQDensembles,Youngetal.[11]de- FIG. 1: In the upper part, monochromatic CL images of the
o mesa are shown for the as-grown case and after two consec-
termined the electronic properties of individual QDs by
c utive annealing steps. The position of the examined QD is
: performing single QD spectroscopy. However, they ana- indicated by a white arrow. The lower part shows CL spec-
v lyzed QDs randomly chosen before and after annealing. tra of the QD before and after the two respective annealing
i
X In contrast to that, in this letter a systematic study of steps. Lines originating from neutral and charged excitonic
the influence ofannealingonthe emissioncharacteristics complexes are identified.
r
a of one and the same QD for consecutive steps of anneal-
ing is presented. Fine-structure splittings and excitonic
binding energies are determined. By comparing the ex- tion and orientation of the participating wave functions
perimental results to calculations within the framework is discussed.
of 8-band k·p theory and the configuration interaction
The InAs QDs were grown in an AIXTRON 200/4
(CI) method [12], the impact of annealing on size, posi-
metal-organicchemicalvapordeposition(MOCVD)reac-
tor in GaAs matrix on GaAs(001) substrates. A 300 nm
thickGaAsbufferlayerfollowedbya60nmAl0.6Ga0.4As
diffusion barrier and 90 nm GaAs were grown. For the
∗Electronicaddress: [email protected]
QDs nominally 1.9 monolayers of InAs were deposited
2
followed by a 540 s growth interruption. Subsequently,
theQDswerecappedwith50nmGaAs. Finally,a20nm
Al0.33Ga0.67As diffusion barrier and a 10 nm GaAs cap-
ping layer were deposited. During the growth interrup-
tion, the QDs undergo a ripening process, i.e., material
is transportedfromsmallto largeQDs, leading to a red-
shift ofthe ensemble luminescence [13]. Here the ensem-
ble peak is centered at 1.06 eV at T=10 K. While most
small QDs dissolve during the long growth interruption,
some remain, leading to an ultralow QD density (< 107
per cm2) in the 1.25-1.35eV spectral range.
The two consecutive annealing steps lasted five min-
◦ ◦
utes at 710 C and 720 C, respectively, performed un-
der As atmosphere in the MOCVD reactor in order to
stabilize the sample surface.
ThesamplewasexaminedusingaJEOLJSM840scan-
ning electron microscope equipped with a cathodolumi-
nescence(CL)setup. Theluminescencewasdispersedby
FIG.2: Effectoftwoconsecutiveannealingstepsonthespec-
a 0.3 m monochromator equipped with a 1200 lines/mm
trumofasingleQD.0meVcorrespondstotherespectiveneu-
grating. The light was detected using a liquid-nitrogen
tral exciton recombination energy (1.2738 eV for as-grown,
cooled Si charge-coupled-device camera. The resolution ◦ ◦ −
1.3002 for 710 C, and 1.3174 eV for 720 C). The X -line
of the setup is ≈140 µeV. Using line shape analysis, shifts to higher energies with respect to the X-line (i.e. the
the energeticpositionofsinglelines couldbe determined X− becomesless binding). Allotherlinesfollow theopposite
withtinanaccuracybetterthan20µeV.Thesamplewas trend (i.e. become more binding).
mounted onto the tip of a helium-flow cryostat provid-
ing temperatures as low as 6 K used for all experiments
throughout this letter. than20µeV.ItshouldthusbepossibletoreducetheFSS
Circular mesas of 24 µm in diameter were etched into in a controlled way below the homogeneous linewidth of
the sample surface. Figure 1 shows monochromatic CL the X-line (which is on the order of a few µeV at liq-
images of such a mesa viewed from the top. One can uid He temperatures), a prerequisite for the generation
clearlysee,thattheQDdensityislowenoughtoidentify ofpolarization-entangledphotonpairs[4,5]. Thegeneral
individual QDs and their position within the mesa. It is trendofdecreasingtheFSS[9,10,11]andincreasingthe
thuspossibletorelocateonespecificQDafterthesample XX binding energy [11] by annealing has also been ob-
has undergone an annealing step. servedbyotherauthors. However,onlybymeasuringthe
The QD spectra change dramatically due to a modifi- sameQDbeforeandafterannealingadetailedanalysisof
cation of the QD structure during the annealing proce- the interplay of QD morphology, wave function position
dure. Figure 2 shows the effect of the annealingsteps on and shape, and excitonic properties can be conducted.
the spectrum of a particular QD. Neutral excitons (X), While in this letter we only show results for one specific
biexcitons(XX)andcharged[positively(X+),negatively QD,thedescribedobservationsandtrendsaretypicalfor
(X−)] excitons could be identified following Ref. 18. For all analyzed QDs.
theQDshowninFig.2,theXtransitionenergyincreased The experimental results were modeled using 8-band
by43.6meVafterbothannealingsteps. Foreaseofcom- k·p theory for the single particle orbitals and the CI
parisonoftheannealinginducedvariations,theenergetic methodforthefew-particlestates. Theas-grownQDwas
position of the X line has been set to 0 meV. The XX assumed to have truncated pyramidal shape with {101}
shiftstolowerenergieswithrespecttothe Xline,chang- side facets,a heightof1.42nm, a lateralsize of11.3nm,
ing its character from anti-binding (EXBX =−2.1 meV) and an In content of 100 %. There is some uncertainty
to binding (EXBX = 2.6 meV) with a total change in concerningthese numbers since the determination of the
binding energy ∆EXBX = 4.7 meV. Likewise, the X+ structureofa fewsmallQDswithinanensembleoflarge
binding energyincreasesby∆EXB+ = 6.3 meV. The X−, QDs is very difficult. While reliable information about
on the other hand, shows the opposite trend, becom- the structure of similarly grown QDs exists [13], the in-
ing less binding with its binding energy decreasing by fluence of the long growth interruption on the morphol-
∆EXB− = -1.3 meV. The annealing process thus has a ogy of the QDs is unknown. Our model QD yields an
surprisingly large impact on all binding energies, sug- X transition energy of 1.08 eV. In our experiments it is
gesting a drastic change of the involved wave functions likelythataslightfractionofGaisincorporatedintothe
and/or their mutual position. QDs during growth, leading to a higher emission energy
Additionally, the excitonic FSS was recorded by per- than for the model QD. The annealing process and the
forming polarization dependent measurements (Fig. 3). resulting exchange of In and Ga atoms grade the inter-
For this particular QD it decreasedfrom170 µeV to less faces between matrix material and QD. This effect was
3
FIG. 4: Calculated binding energies for X−, X+, and XX.
FIG. 3: Polarization dependent measurements of the same
Open symbols correspond to a reduction of electron-hole
QDdepictedinFig.2revealtheexcitonicfine-structuresplit-
Coulomb interaction by 0.6 meV simulating a misalignment
ting. Itdecreasesfrom170±20µeVtolessthan20µeVafter
of electron and hole wave functions (see text).
thesecond annealing step.
not correctly modeled. Remarkably the disagreements
simulatedbyapplyingasmoothingalgorithmforeachan-
canberesolved,whentheattractiveCoulombinteraction
nealing step, correspondingto Fickian diffusion. The re-
betweenelectronandhole (Jeh) is artificiallyloweredfor
sulting atomistic structures were relaxed with a recently
the as-grownQD by 0.6 meV, corresponding to a reduc-
developedbond-orderpotential of the Abell-Tersofftype
tion of 3%, while repulsive electron-electron (Jee) and
that is particularly suited for InAs/GaAs heterostruc-
hole-hole (Jhh) Coulomb terms are left unaltered. Such
tures [14]. To be more precise, we performed slab calcu-
an effect may result from a reduced electron-hole wave
lations with periodic boundary conditions in the lateral
function overlapcausedby either a slightelongationand
directions, a conjugate-gradient scheme to minimize the
misalignment of the wave functions or a mutual vertical
total energy until the maximum force on an atom in the
displacement.
system was below 1 meV/˚A, and the scheme outlined in
Using the assumption of reduced Jeh for the as-grown
Ref. [15] to determine the atomistic strain tensor. The
QDweobserveboththebiexcitoncrossoveraswellasthe
single-particle orbitals were then derived from a strain- −
relative insensitivity of X binding energy to annealing
dependent 8-band k·p Hamiltonian accounting for band
as seen in the experiment (open symbols in Fig. 4). A
coupling and band mixing. The piezoelectric field was
symmetrization of the wave functions with annealing is
computed using the first and second order piezoelectric
further supported by the drastic reduction of FSS [9].
tensor [16, 17]. The excitonic states were calculated us-
In conclusion, we have recorded emission spectra of
ing the CI methodbyexpanding the respectiveexcitonic
singleQDsandfollowedtheirevolutionunderananneal-
Hamiltonian into a basis of antisymmetrized products of
ingprocedure. Thebindingenergiesofdifferentexcitonic
single particle wave functions built from a total of six
complexes change on the order of several meV and the
electron and six hole wave functions. This procedure ac-
FSS decreases from 170 µeV to less than 20 µeV. These
counts for direct Coulomb interaction, exchange, and in
results can be understood by a change of electron and
part correlation [18].
hole wave function shape and mutual position. We have
Results for the binding energies of X+, X−, and XX
thus demonstrated a powerful tool to tailor single QDs’
are shown in Fig. 4. The experimentally observed en-
electronic properties for their use in potential applica-
ergetic order of X− and X+ is well reproduced by our
tions. In particular, zero FSS, essential for emission of
theory. Also, the general trend of the binding energies
entangled photon pairs, can be enforced.
upon annealing (X− becomes less binding, X+ becomes
The calculations were performed on the IBM
more binding) is in good agreement. However, there
pSeries 690 supercomputer at HLRN within project
are some discrepancies between theory and experiment:
No.bep00014. ThisworkwassupportedbytheDeutsche
The change of character of the biexciton (i.e. from anti-
Forschungsgemeinschft in the framework of SfB 296 and
binding to binding) as observedin the experiment is not
the SANDiE Network of Excellence of the European
reproduced by the modeling. Also, the experiment re-
Commision, Contract No. NMP4-CT-2004-500101.
vealedamuchstrongerrelativeshiftforX+ andXXthan
−
for X (see Fig. 2).
These discrepancies imply that an important effect is
4
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