Asymmetry of localised states in a single quantum ring: polarization dependence of excitons and biexcitons

2.8 MB·English

by  H. D. Kim

Asymmetry of localised states in a single quantum ring: polarization dependence of
excitons and biexcitons
H. D. Kim1, K. Kyhm2,3,∗ R. A. Taylor1,† G. Nogues2, K. C. Je4, E. H. Lee5, and J. D. Song5
1Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, OX1 3PU, U.K
2Department of NANOscience, Institut N´eel, CNRS, rue des Martyrs 38054, Grenoble, France
3Department of Physics Education, RCDAMP, Pusan Nat’l University, Busan 609-735, South Korea
4College of Liberal Arts and Sciences, Anyang University, Gyeonggi-do 430-714, South Korea and
5Nano-Photonics Research Center, KIST, Seoul, 136-791, South Korea
(Dated: January 28, 2013)
We performed spectroscopic studies of a single GaAs quantum ring with an anisotropy in the
3
rimheight. Thepresenceofanasymmetriclocalisedstatewassuggestedbytheadiabaticpotential.
1
Theasymmetrywasinvestigatedintermsofthepolarizationdependenceofexcitonsandbiexcitons,
0
wherealargeenergydifference(∼0.8meV)intheexcitonemissionenergyforperpendicularpolar-
2
izationswasobservedandtheoscillatorstrengthswerealsocomparedusingthephotoluminescence

n decay rate. For perpendicular polarizations the biexciton exhibits twice the energy difference seen
a for the exciton, a fact that may be attributed to a possible change in the selection rules for the
J lowered symmetry.

5
2
Currently, quantum ring (QR) structures are of great were grown successively at 580◦C. The substrate tem-

] interest for the optical Aharonov-Bohm (AB) effect [1– perature was decreased to 310◦C, and Ga metal equiva-
l
l 5]. While the rotating charge in the shell of a type-II lent to 2 monolayers of GaAs was introduced to the sub-
a
h quantumdot(QD)determinestheABoscillationperiod, strateatthemainchamberpressureof∼3×10−10Torr.
- the orbital radius difference of the electrons and holes is When the substrate temperature reached 200◦C, arsenic
s
the crucial parameter in a QR, for which the coupling tetramers were introduced to form GaAs rings. Finally,
e
m to the magnetic flux is of opposite sign. Nevertheless, theringswerecappedwith60nm-thickAl0.3Ga0.7Asand
the individual behaviour of each of the particles is not 3 nm-thick GaAs for optical measurements. The photo-
.
t clear in a QR; either the radius is larger or one of them luminescence (PL) of a single QR was collected at 4K
a
m is localised as in the case of a type-II QD. using a confocal arrangement, where frequency-doubled
(400nm) Ti:sapphire laser pulses (120fs pulse duration
- Recent measurements have shown that the morphol-
d ogy of a QR is anisotropic, where the rim height is not at a 80-MHz repetition rate) were focused on the QR
n sample (∼ 6QRs/µm2) with a spot-size of 0.8µm2. A
constant around the azimuthal angle. In the case of this
o time-correlated single photon counting system was used
so-called volcano-like structure [5], the azimuthal quan-
c to obtain the time-resolved PL (TRPL).
[ tum number is no longer valid, and the wavefunction
in the anisotropic QR can be either localised or delo- AsshowninFig.1(a),thevolcano-likeringstructurewas
1 modelled in cylindrical coordinates (z = z(r,φ)) based
calised through tunnelling [6]. Nevertheless, a persis-
v on atomic force microscope (AFM) images of uncapped
tent current can be observed in a QR as evidence of
3
GaAs QRs (Fig.1(b)), where both anisotropy and asym-
AB-oscillation, when an external magnetic field is large
8
metry are present [7, 10]. The rim height is maximum
9 enough to overcome the anisotropy-induced potential
at the azimuthal angles of 0◦ and 180◦ along the [1¯10]
5 barrierorasymmetricexchangeinteraction[4]. Asymme-
. try and anisotropy seem to have been overlooked in the direction, and a minimum at the perpendicular angles
1 of 90◦ and 270◦ along the [110] direction, respectively.
0 spectroscopy of QRs [1–3, 7–9]. In this work, the pres-
The in-plane shape is elliptical with the long axis along
3 ence of a localised state in a single GaAs/Al0.3Ga0.7As [1¯10], and the height in the middle of the QR is ∼3nm.
1 QRarisesfromthevolcano-likeQRstructure,whichcor-
: responds to an excited state of the vertical confinement. Since the vertical height (7∼12nm) is smaller than the
v
ringsize(∼50nm),thefastverticalwavefunctioncanbe
i Also, the asymmetry of the localised state has been in-
X separated by the adiabatic approximation [5], where the
vestigatedintermsofthepolarizationdependenceofex-
r citons and biexcitons. potentialofelectronandholedependsonthevolcano-like
a ring structure respectively as V (z,r,φ)(cid:39)V (z(r,φ)).
GaAs rings [7] were grown on an n-doped GaAs (001) e,h e,h
Consequently, the adiabatic potential εk (r,φ) can be
substrate using a molecular beam epitaxy system with e,h
obtained for electron and hole separately by solving the
an ion getter pump. After thermal cleaning of the sub-
vertical part of the Schr¨odinger equation, where the ver-
strate under arsenic ambient at 600◦C, a 100 nm-thick
tical confinement is represented by the vertical quan-
GaAs buffer layer and a 50 nm-thick Al Ga As layer
0.3 0.7 tum number k. In the case of an ideal isotropic ring,
εk (r) can be simplified by using a parabolic function
e,h
(∼ (r −r )2), where the maximum ring height is posi-
0
tioned at r [11]. Although the fine structure of the PL
∗Electronicaddress: [email protected] 0
†Electronicaddress: [email protected] spectruminaQRhasoftenbeenattributedtoquantized
2
(a)
(b) (a)
h =10 nm
m
(c)
(d)
m)
n
(
(b)
FIG. 2: Adiabatic potentials (εk=3) of the electron (a) and
e,h
the hole (b) for a vertical quantum number of k = 3 are
(nm) shown,wheretheinsetsshowtheenergyrangeoftheradially
confined levels for the azimuthal angle for the electron and
FIG. 1: (a) Volcano-like ring model for the rim height the hole, respectively.
based on the AFM morphology (b), where the localised adi-
abatic potentials of the electron for a vertical quantum num-
ber of k = 3 are shown for three rim height parameters
vertical confinement states than the lower rim. In other
(h = 8,9,10nm) (c). (d) PL intensity corresponding to
m words,excitedconfinementstatesareallowedonlyatthe
thek=3statesfromtheXXiscomparedwiththatfromthe
limited azimuthal angles of the high rim region as the k
X with increasing the excitation power.
quantum number increases [5]. We found that vertical
confinement states can be defined at all of the azimuthal
angles up to k = 2. Therefore, the vertical excited state
rotational motion along the rim [7], the cylindrical sym- of k = 3 is a criterion of the localisation. As shown
metry of a QR can easily break down, which is similar in Fig.1(c), the electron adiabatic potentials for k = 3
to the case of an elliptical QD. Also, the anisotropy in (εk=3(r,φ)) are localised at limited azimuthal angles for
e
the rim height requires an azimuthal angle-dependence three different QR heights (h =8,9,10nm), where the
m
of the vertical confinement. Both the asymmetry of the rim height is characterized by a parameter h [10]. As
m
in-plane ellipticity and the height anisotropy have been the QR height is decreased, the localized potential area
mostlyoverlookedinpreviousspectroscopy. Theseeffects becomes reduced.
canbeparamaterizedintermsofεke,h(r,φ),whichissim- Theadiabaticpotentialsoftheelectron(εke=3)andhole
ilar to an inversion of the asymmetric and anisotropic (εk=3) are compared for h =10nm in Fig.2 [12]. Also,
h m
structure morphology. the radially confined energy of the adiabatic potential
Provided that the potential hill in εk (r,φ) is found for φ=0◦ and φ=90◦ are estimated with the parabolic
e,h
neartheazimuthalangles90◦and270◦,thewavefunction approximation for the electron and the hole (insets in
delocalisation of the ground state depends on the tun- Fig.2), respectively. Whilst the holes are confined for
neling efficiency, which determines either localised [6] or all azimuthal angles (Fig.2-(b)), the electron is confined
extendedstates. However, itshouldberememberedthat to the limited azimuthal angles (−38◦ ∼ 38◦) (Fig.2-
thenumberofconfinementstatescanbeameasureofthe (a)) due to the shallow potential well when compared
confinement size, i.e., the higher rim (z) contains more to the barrier energy in the conduction band (262meV).
3
Therefore, the ground eigen-energy of the electron and
the hole should be located in the range of the radially
confined levels for allowed azimuthal angles (εk=3(φ)).
e,h
For example, suppose the ground state of the electron
(a)
is located near 240meV, then the confined wavefunction
becomes localised in a crescent-like structure. However,
the tunnelling wavefunction is extended up to ∼ 4.5nm
in the barrier. On the other hand, the hole wavefunc-
tion also becomes localised when the hole ground state
is assumed to be ∼ 60meV, but the tunnelling length
is small (∼ 0.7nm) as the barrier energy in the valence
band(195meV)isstilllarge. Consequently,thelocalised
(c)
area of the electron would be larger due to the large (b)
tunnelling, and PL quenching becomes significant with
increasing temperature. We found the PL intensity is
nearly quenched beyond ∼45K.
The exact ground state energy of the electron-hole (e-
h) pair can be refined by adding the Coulomb interac-
tion to the independent e-h pair, i.e., the total energy
is determined by the ground state energy sum of each
adiabatic potential and the Coulomb energy. In the case
(d)
of strong confinement, the effective Coulomb interaction
is known to be enhanced by a factor of 1.786. However,
both the vertical and the lateral confinement energy are
far larger than the Coulomb interaction (∼ 4.2meV for
bulk GaAs). Thus, the energy levels are dominated by
the confinement effect, and this rough model predicts
the energy range of the e-h pair at the k = 3 state
(1.814∼1.864eV). As shown in Fig.3, the PL spectrum
was measured near the barrier (Al Ga As) energy. It FIG. 3: PL spectrum of the X (a) and XX (d) at various
0.3 0.7
analyzer angles in a single QR. (b) Normalized PL intensity
exhibits a strong polarization dependence for the exci-
asafunctionofanalyzerangleismappedinpolarcoordinates
ton(X)andbiexciton(XX)statesat1.6kWcm−2,where
at various energies, whereby the relative angular delay (θ) of
the nature of the XX emission appearing 5meV below
each dumbbell-like trace can be obtained for the X and XX.
that of the X was characterised by a quadratic rise in
(c) Schematic diagram of a multitude of transitions between
its PL intensity (Fig.1(d)) and the fast decay of the TR-
the fine structure states of XX and X.
PL (Fig.4(b)) relative to the X. The X and XX emission
spectrawerebothmeasuredsimultaneouslyataseriesof
analyzer angles. We also observed the PL spectrum in
and |Y(cid:105) in an elliptical QD can be spectrally isolated
the predicted k =3 range (1.813eV, 1.821eV, 1.832 eV,
by a linear polarizer [13–15], the fine structure states at
and 1.842eV) at different QRs; they all show the similar
different angles in the asymmetric εk=3(r,φ) can overlap
polarization dependence.
in the PL spectrum of X. Therefore, the analyzer angle
The wavefunction of the electron and the hole can be dependence of the PL intensity is mapped at different
imagined roughly as an inversion structure of the adia- energiesinpolarcoordinatesasshowninFig.3(b),where
batic potential in Fig.2. Since both εke=3 and εkh=3 are the maximum intensity of each PL spectrum is normal-
anisotropic, the e-h pair is likely to be localised in either ized to make a comparison possible. For example, the
of the two crescent structures instead of delocalization maximumPLintensityofXat1.8208eVmeasuredat0◦
around the whole rim. The localised e-h pair can be is gradually reduced until the analyzer angle rotates to
verified in terms of the large energy splitting for perpen- 90◦, but increases again up to 180◦. Consequently, this
dicular polarizations. Since the localised states are of a sinusoidal behavior gives rise to a dumbbell-like trace.
crescent shape, the fine structure states resulting from All of the dumbbell-like traces obtained at different en-
various different confinement dimensions may depend on ergies are similar, but rotated in a regular manner. The
the analyzer angle. Additionally, during sample growth, relative angular delay (θ) between the traces varies with
identical crescents are unlikely to form in an anisotropic emission energy. The trace at 1.8200eV is 90◦-rotated
QRandtheresonanceatthek =3statebetweenthetwo with respect to that at 1.8208eV, and an energy dif-
crescents is vulnerable to small size differences. In this ference (∆) of 0.8meV is obtained. This value is re-
case, localisation of the e-h pair is favored at the larger markablylargeincomparisontotheasymmetricsplitting
crescent-like structure. (∆ ∼0.1meV) of an elliptical quantum dot.
XY
Whilst the two orthogonally polarized states of |X(cid:105) In the case of an elliptical quantum dot, an asymmet-
4
ricelectron-holeexchangeinteractionleadsto asplitting
(∆ )ofthedoubleexcitonstate(|±1(cid:105))intotwosinglet
XY √
states (|X,Y(cid:105)=(|+1(cid:105)±|−1(cid:105))/ 2), where two linearly
andorthogonallypolarizeddipoles(|X(cid:105)and|Y(cid:105))arede-
finedalongtheprincipalaxesofanellipticalQD[13–15].
This also gives rise to the same splitting of the biexciton
emission(∆ ),whichinvolvesthetransitionfrombiex-
XY
citon to two singlet exciton states (|X,Y(cid:105)), respectively.
However, the energy difference for the perpendicular po-
larization in the XX spectrum (Fig.3(d)) is nearly twice
6
(∼ 1.75meV) that of X, where the angular delay of 90◦ y
is measured by the dumbbell-like trace of XX. We have nsit 5
e
alsoconfirmedthisphenomenoninQRsofdifferentsizes. d Int 4
When considering XX in this structure, two kinds of ze 3
generation are possible; either two Xs in the same lo- mali 2
calised crescent structure or separate Xs located in two Nor 1 (a)
identical crescent structures are bound, respectively. Al- Ln Angle (degrees)
though the binding energy of the latter case was known
tobesub-meV[6], thegenerationcanbeinhibitedbythe
5
smallsizedifferencebetweenthetwocrescentstructures. sity
For large GaAs QDs (30 ∼ 40nm in radius), the XX en 4
bindingenergyisknowntobeafewmeV[17,18]. There- d Int 3
fore, the large binding energy (∼5meV) in this result is ze
likely to arise from a localised XX, which consists of two mali 2
Xs localised at the same crescent structure. The large or
N 1 (b)
asymmetric splitting (∆XY ∼ 1.75meV) of the XX also Ln Angle (degrees)
supportsalocalisedXX.Whenthesymmetryislowered,
it is known that the selection rules change significantly
[16,19]. Thiscangiverisetoanincreaseinthenumberof
dipole-allowedtransitions,i.e.,amultitudeoftransitions FIG. 4: TRPL of the of the localised state of X (a) and
XX (b) in a single QR measured at 1.6kWcm−2 for various
betweenthetwo-excitonandone-excitonstates,resulting
analyzer angles, where each PL rate shown in the inset.
in a broad PL spectrum for the XX. It is also noticeable
that the XX PL spectrum in Fig.3(d) is rather broad.
Consequently, asshownschematicallyinFig.3(c), amul-
titude of transitions between the fine structure states of
tron and hole. However, extended states keep feeding
XXandX,whicharedenotedbytherelativeangularde-
electrons to localised states. State saturation in the
lay (θ), may result in twice the splitting when compared
plateausuggeststhepresenceofafeedingsourceforintra-
to the X for perpendicular polarizations because of the
relaxation of localised electrons (k = 3) to lower states
change in the ideal selection rules.
(k = 2 or k = 1). Furthermore, it is noticeable that the
Although the wavefunction distribution of the fine
decaytime(532±56ps)oftheXislongerthanthatseen
structurestatesisnotclear,theoscillatorstrengthdiffer-
in GaAs QDs (250±50ps) [13]. When compared to the
ence of these states can be observed in terms of the size
recombination rate of a hole near localised electrons, the
dependence of the PL decay rate, where the PL spectra
recombination rate of a hole far from such localised elec-
for different confinement sizes are isolated by the ana-
trons can be reduced. This effect possibly results in the
lyzer angle. As shown in Fig.4, TRPL of X and XX was
reduction of the total decay rate in the k = 3 localised
measured at various analyzer angles (θ), where the PL
structure.
decay rates were obtained by a linear fit to the mono-
tonic decay section on a log scale (shown in the inset). In conclusion, the presence of an asymmetric localised
We found that the PL decay rates of both X and XX stateinasingleGaAs/Al Ga AsQRwasobservedby
0.3 0.7
increase for increasing analyzer angle up to 90◦. Inter- itspolarizationdependenceinthePLspectrum,whichis
estingly, XX shows a novel feature in the size dependent in agreement with the adiabatic potential arising from
oscillator strength. a volcano-like anisotropic morphology. The fine struc-
Whilst the radiative recombination of the e-h pair ture states of the crescent-like adiabatic potential were
is characterized by a single exponential decay after ∼ resolvedbychangingtheanalyzerangle, wherebyalarge
400ps, a plateau range is observed up to ∼ 300ps in energy difference in the exciton (∼ 0.8meV) and biexci-
Fig.4(a). This may be associated with extended states ton (∼1.75meV) splitting was observed for perpendicu-
oftheelectron. Initially,e-hrecombinationoccursatthe lar polarizations, and oscillator strength differences were
wavefunction overlap range between the localised elec- also compared in terms of the PL decay rate.
5
Acknowledgments 2011-013-C00025 and NRF-2010-008942) and GRL pro-
gram, and the KIST institutional program. Authors are
This work was supported by the National Research also grateful to the late Dr. Lee for organizing the inter-
Foundation of Korea Grant funded by MEST (NRF- national collaboration.
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