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Copyright copy 2011 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofNanoelectronics and Optoelectronics

Vol 6 51ndash57 2011

Single Neutral Excitons Confined in AsBr3In Situ Etched InGaAs Quantum Rings

F Ding12 daggerlowast B Li3 N Akopian4 U Perinetti4 Y H Chen2F M Peeters3 A Rastelli1 V Zwiller4 and O G Schmidt1

1Institute for Integrative Nanosciences IFW Dresden Helmholtzstr 20 D-01069 Dresden Germany2Key Laboratory of Semiconductor Materials Science Institute of Semiconductors

Chinese Academy of Sciences PO Box 912 Beijing 100083 China3Departement Fysica Universiteit Antwerpen Groenenborgerlaan 171 B-2020 Antwerpen Belgium

4Kavli Institute of Nanoscience Delft University of Technology PO Box 5046 2600 GA Delft The Netherlands

We observe the evolution of single self-assembled semiconductor quantum dots into quantumrings during AsBr3 in situ etching The direct three-dimensional imaging of In(Ga)As nanostructuresembedded in GaAs matrix is demonstrated by selective wet chemical etching combined with atomicforce microscopy Single neutral excitons confined in these quantum rings are studied by magneto-photoluminescence Oscillations in the exciton radiative recombination energy and in the emissionintensity are observed under an applied magnetic field Further we demonstrate that the period ofthe oscillations can be tuned by a gate potential that modifies the exciton confinement The exper-imental results combined with calculations indicate that the exciton Aharonov-Bohm effect mayaccount for the observed effects

Keywords Quantum Ring Quantum Dot Neutral Exciton Aharonov Bohm Effect GateControlled Selective Etching

1 INTRODUCTION

Self-assembled semiconductor nanostructures such asquantum dots (QDs) and rings (QRs) are being inten-sively investigated both because of their possible appli-cation in quantum information science and because theyare ideal test beds for fundamental physical research TheAharonov-Bohm (AB) effect1 modifies the wave functionphase of a charged particle traveling around a regionenclosing a magnetic field During the 50 years since itsdiscovery this effect has made a significant impact onthe development of physics2 The AB effect has beenobserved independently for electrons and holes in variousmicro-nanoscale structures3ndash5

An interesting question arises here Is it possible toobserve the AB effect when considering a single neutralexciton (an electronndashhole pair) confined in a QR Theoret-ical investigations have predicted that the phases accumu-lated by the electron and the hole will be different after one

lowastAuthor to whom correspondence should be addresseddaggerPresent address IBM Research Zuumlrich Saumlumerstrasse 4 8803

Ruumlschlikon Switzerland

revolution leading to modulations between different quan-tum states6 And this so called neutral exciton AB effectcan be probed from the photoluminescence (PL) emissionin semiconductor QRs since the change in the phase ofthe exciton wave function is accompanied by a change inthe exciton total angular momentum making the PL emis-sion magnetic field dependent6ndash10 Similar effect has beenreported for a charged exciton confined in a lithographi-cally defined QR However for neutral excitons the exper-imental optical observation of this AB-type effect has sofar been limited to quantum ring ensembles11ndash13 Consider-ing the relatively small electronndashhole separation the questfor the AB effect in a single neutral exciton in a type-Isystem is quite challengingHere we study single self-assembled In(Ga)AsGaAs

QRs fabricated by molecular beam epitaxy (MBE) com-bined with in situ AsBr3 etching14 In order to unveilthe morphology of buried nanostructures we use selectivechemical etching to remove the GaAs capping layer andinvestigate the structures with atomic force microscopy(AFM) We observe a progressive morphological evolu-tion of the buried In(Ga)AsGaAs nanostructures namelyfrom quantum dots (QDs) to volcano-shaped QRs as the

J Nanoelectron Optoelectron 2011 Vol 6 No 1 1555-130X20116051007 doi101166jno20111132 51

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

AsBr3 etching depth is increased Due to a radial asymme-try in the effective confinement for electrons and holes weexpect the neutral exciton AB effect We observe magneticfield dependent oscillations in the PL energy and intensityof a single neutral exciton in agreement with previous the-oretical predictions We also show that a vertical electricfield which modifies the exciton confinement is able tocontrol this quantum interference effect15

2 EXPERIMENTAL DETAILS

21 Fabrication and Characterization ofIn(Ga)AsGaAs QRs

All samples examined in this work are grown onsemi-insulating GaAs (001) substrates in a solid-sourcemolecular-beam epitaxy system equipped with an AsBr3gas source After oxide desorption a 300-nm GaAs buffer

0 nm 6 nm ndash26ordm 26ordm

1 nm AsBr3 etching

2 nm AsBr3 etching

3 nm AsBr3 etching

as-grown

G aAsG aAs

G aAsG aAs

G aAsG aAs

G aAsG aAs

Fig 1 Fabrication of In(Ga)AsGaAs QRs by MBE combined with AsBr3 in situ etching The first column images show schematic representationsof the fabrication processes with different AsBr3 etching depths 500times500 nm2 AFM images illustrate the sample surface morphology before (secondcolumn) and after (third column) the removal of GaAs capping layer The last column shows the progressive morphological evolution of a single buriednanostructure namely from QD to volcano-shaped QR

layer is grown at 570 C A 18-monolayer (ML) InAslayer is then deposited at 500 C a temperature which canbe easily reproduced by observing the change in surfacereconstruction from (2times4) to c(4times4) using an In growthrate of 001 MLs After 30 s growth interruption the sub-strate temperature is lowered to 470 C and a 10-nm GaAscap is deposited at a rate of 06 MLs while the tempera-ture is ramped back to 500 C After GaAs deposition theAsBr3 etching gas is subsequently supplied to produce thenanoholes (see the first and second columns of Fig 1)The etching rate of GaAs was 024 MLs which was cali-brated by reflection high-energy electron diffraction inten-sity oscillationsThe surface morphology develops into a rhombus-

shaped structure with a tiny hole in the middle after10 nm GaAs overgrowth (see the first row of Fig 1)After supplying the AsBr3 etching gas there is a pref-erential removal of the central part of the buried QDs

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

due to the local strain field induced by the buried QDs14

In order to characterized the underlying QR structuresa selective chemical etchant [ammonium hydroxide (28NH4OH) hydrogen peroxide (31 H2O2) and deionizedwater (1125)] is used to remove the GaAs cappinglayer NH4OHH2O2 solutions are known to etch selec-tively GaAs over InGaAs alloys16ndash19 The mixture usedhere etches GaAs at a rate of sim10 nms17 Figure 1 sug-gests that the GaAs cap is completely removed by thesolution and the etching process significantly slows downat the In(Ga)As wetting layer (WL) (see also Fig 2) Pro-longed etching ( 2ndash3 seconds) results in the removal ofthe WL and the undercut of the QDs We verified that dif-ferent etching experiments with the same nominal duration(1 second) performed on the same sample yield compat-ible results Slower etching rates of GaAs are achievablewith diluted solutions20

We observe from Figure 1 that by varying the nominalAsBr3 etching depth the morphology of the ring struc-ture can be tuned (see the second third and fourth rows)The statistical structural analysis of the uncapped In(Ga)Asnanostructures as a function of the nominal etching depthis given in the right part of Figure 2 A cross sectionaltransmission electron microscopy (TEM) image of a sin-gle QR from a similar sample is also presented (Fig 2)further supporting the validity of our method We arguethat the selective chemical etching combined with AFM isa reliable fast and convenient way to characterize buriedIn(Ga)AsGaAs nanostructures it provides information onthe three-dimensional morphology and does not requireany special sample preparationWe focus now on the QRs with a nominal etching depth

of 3 nm Both AFM and TEM (see Fig 2) confirm that theaverage inner radius r1 of the QR is about 85 nm whilethe average outer radius r2 is about 19 nm and the heightH is about 4 nm The inner height h is less than 1 nmSuch a ring structure could produce different confinement

0 1 2 30

2

4

6

8

Hh

GaAs

InAs WL

Hh10 nm

Hei

ght (

nm)

Nominal etching depth (nm)

100 nm

TE

MA

FM

r1

r2

Fig 2 AFM image shows the QRs with nominal AsBr3 etching depthof 3 nm after removal of the GaAs capping layer by selective chemicaletching The lower graph shows the cross sectional TEM image of a sin-gle QR from the similar sample The statistical structural analysis of theuncapped In(Ga)As nanostructures as a function of the nominal etchingdepth is given in the right part H is the height of the embedded nano-structures and h is the distance between the InAs WL and the bottom ofthe dip at the nanostructure apex

potentials for the electron and the hole thus the neutralexciton AB can be expected

22 Magneto-Photoluminescence

We use magneto-PL to probe the energy changes andintensity changes related to the nature of the ground stateThe samples are placed in a cryostat tube which is evac-uated and then refilled with a small amount of heliumexchange gas The tube is then inserted into a 42 Khelium bath dewar equipped with a superconducting mag-net capable of providing fields up to 9 T The sample isexcited by a 532 nm laser beam and the PL is collected byan objective with 085 numerical aperture The PL signalis dispersed by a spectrometer with 075 m focal lengthequipped with a 1800 gmm grating and captured by aliquid nitrogen cooled Si charge-coupled device (CCD)Figure 3(a) shows a typical PL spectrum for a single QRat B = 0 T We use power-dependent PL polarization-dependent PL (Fig 3(c)) and charging experiments21 toidentify the neutral exciton X the biexciton XX and thecharged exciton X+We have carefully optimized and tested the system to

minimize drifts associated with magnetic field rampingAn optimum resolution of 25 eV can be achieved byfitting the PL peaks with Lorentzian functions The accu-racy of this peak-determination procedure is determined byusing the quantum confined Stark effect (QCSE) Some ofthe QRs are embedded in an n-i-Schottky structure con-sisting of 20 nm n+ GaAs layer followed by a 20 nm thickspacer layer under the QRs 30 nm i-GaAs and a 116 nmthick AlAsGaAs short period superlattice With a 5 nmthick semi-transparent Ti top gate an electric field can beapplied to modify the energy band of the ring2122 When

Raw peak position

Fit peak position

Fig 3 (a) Typical PL spectrum for a single QR (b) The PL peak isshifted by QCSE both fit peak positions and the measured raw peakpositions are plotted (c) Linear polarization dependent energy shift of Xand XX The solid lines are sine wave fittings

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

a forward bias Vg is scanned from 03 to 032 V (withsteps of 05 mV) the PL emission energy of a single QRis tuned by about 30 eV (see Fig 3(b)) We observe thatin contrast to the discretized raw data (diamond points)the Lorentzian fit data show a smooth blue-shift of thepeak positions (round points) We plot the 95 predictionband of the fit function in Figure 3(b) (solid lines) fromwhich an error of plusmn15 eV for this Lorentzian analysisprocedure is estimated For the evaluation of the system-atic error repeated measurements (B field increasing anddecreasing) are performed on the same QR and the fitpeak positions are reproducible to within plusmn25 eV Wecan therefore expect an overall error of plusmn25 eV in thepeak-determination procedure used in this workTo further support the validity of this peak determina-

tion procedure we perform the FSS measurements for Xand XX lines (Fig 3(c)) The data points are given byLorentzian fits with an uncertainty of 25 eV Solid linesin the exciton and biexciton plots are sine wave fittingcurves As expected X and XX show anti-correlated shiftsas we rotate the half-wave plate The FSS of this QD isonly 13 eV which is near the resolution limit of our PLsystem and would be undetectable without the Lorentzianfitting processA magnetic field up to 9 T is applied along the sample

growth direction and we observe the characteristic Zee-man splitting as well as the diamagnetic shift of the PLemission energy (see Fig 4(a)) similar to previous reportson single QRs23 In Figure 4(b) we plot the neutral excitonemission energies of the QR after averaging the emissionenergy values of the Zeeman split lines It is observed

0

15

00

05

10

Nor

m P

L I

nt

Ene

rgy

(microeV

)

ndash15

(c)

(d)

13484

13488

13492

13496

PL e

nerg

y (e

V)

13483

13485

13487

13489

Quantum ring(3 nm etched)

(b)

(a)

Magnetic field (T)0 2 4 6 8 10

Magnetic field (T)0 2 4 6 8 10

Fig 4 Fitted PL peak position versus B field before (a) and after (c) averaging the Zeeman splitting for the neutral exciton emission in a 3 nm-etchedQR The blue dashed line in (b) indicates a parabolic fit Oscillations in PL energy and corresponding normalized PL intensity as a function of B fieldare shown in (c) and (d) respectively The solid lines represent the smoothed data using a Savitzky-Golay filter The arrows in (b) and (d) indicatechanges in the ground state transitions

that the emission energy does not scale quadratically withincreasing B field From its shape Figure 4(b) looks quitesimilar to the one shown in a very recent report13 inwhich AB oscillations in ensemble InAsGaAs QRs wereobserved However the diamagnetic shift for a single QRstudied in our work is sim6 times smaller than the valuefor the ensemble QRs in Ref [13] and the oscillationamplitude is much smaller Also no Zeeman splitting wasobserved in Ref [13] because of the broad ensemble emis-sion In order to visualize the magnetic field induced oscil-lations we subtract a single parabola from Figure 4(b) andplot the results in Figure 4(c) We observe two maxima atsim4 T and sim7 T (the solid line here which represents thesmoothed data using a Savitzky-Golay filter is guide to theeye) suggesting changes in the ground state transitionsAnother significant feature observed is the decrease

in PL intensity with increasing magnetic field seeFigure 4(d) The change in PL intensity is one of thesignatures expected for a QR and is attributed to oscilla-tions in the ground state transitions611ndash13 Two knees canbe observed at sim4 T and sim7 T (Fig 4(c)) which cor-respond well with the peak energy oscillation maxima inFigure 4(c) (indicated by arrows)All the observations here are well above the system

resolution and they strongly contrast with the experimen-tal results on a conventional QD where no peak energyoscillation and PL intensity quenching were observed seeRef [15] Especially the PL intensity of this QR quenchesby more than 70 with increasing magnetic field whichis confirmed by repeating the measurements and similarobservations in other QRs A recent study on single GaAs

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

QR obtained by droplet epitaxy also revealed a signifi-cant reduction in the PL intensity by more than 20 atB gt 6 T24 the exciton AB effect may account for theobservation

23 Gate-Controlled Oscillations

We use the above mentioned gated-QR structure to demon-strate the possibility of controlling the observed effect withan external electric field The oscillations for a single QR(with a nominal AsBr3 etching depth of 3 nm) under aforward bias of 28 V are clearly seen in Figure 5(a) withthe two transition points at 26 T and 8 T The PL intensityalso shows similar quenching behavior as in Figure 4(d)(not shown here) When we decrease the bias from 28 V to08 V it is clear that the transition points shift smoothly tohigher magnetic fields (Fig 5(b)) indicating that the effec-tive radii of the electron and the hole are modified by theexternal gate potential The PL intensity is also stronglymodified at different electric fields which is a consequenceof the QCSE At sim18 V the PL intensity reaches an over-all maximum and then decreases see Ref [15] Interest-ingly the PL intensity at 18 V shows clear modulation bythe magnetic field ie first quenches by more than 25

Fig 5 (a) Under a forward bias of 28 V the PL energy shows cleartransitions at sim26 T and sim8 T (b) When the bias changes from 28 Vto 08 V the transitions shift smoothly to higher magnetic fields (c) At18 V the PL energy shows transitions at sim3 T and sim82 T while thenormalized PL intensity also shows oscillations

and then recovers fully to its original value with increasingmagnetic field (Fig 5(c)) This observation is quite simi-lar to the long-existed theoretical prediction for a weaklybound neutral exciton confined in a QR6

3 DISCUSSIONS

Previous theoretical works distinguish between excitonscomposed of strongly and weakly bound electronndashholepairs6 In Ref [7] the effectiveness of the electronndashholeCoulomb interaction is expressed as

vq =e2

rradicReRh

Qqminus12

(1+ ReminusRh

2ReRh

)(1)

where r is the dielectric constant and Qx is the Leg-endre function In the strongly bound regime where vq isdominant the exciton moves along the ring as one tightlybound particle and AB effect manifests itself in a brightto dark transition in the ground state with increasing mag-netic field While in the opposite limit of a weakly boundelectronndashhole pair an interesting modulation between dif-ferent bright and dark states should appear The electronndashhole pairs in above-mentioned QRs are close to the weaklybound regime this is because(i) in the ring geometry the ratio of Coulomb to kineticenergies is proportional to the ring radius while for smallrings (R lt alowast the effective Bohr radius) the quantizationdue to kinetic motion is strong625 and the effectiveness ofvq becomes weaker(ii) in our structure the n-doped layer which locates 20 nmunder the QRs (also the metal contact in the gated struc-ture) can sufficiently screen the effectiveness of vq

7

(iii) in experiment we also observe that the changes in thebinding energies EBXX asymp EBX

+ when E changes(not shown here) indicating that the strongly confinedfew-particle picture is valid in our QRs and the effectiveradii of electron and hole are very different2627

However the theory in Ref [6] is not sufficient toexplain our results We model a simplified QR as depictedin Figure 2 with the main aim to explain the gate-controlled oscillation effect (Fig 5) The ground stateenergy of the neutral exciton inside the In1minusxGaxAs ring(surrounded by GaAs barrier) is calculated within theconfiguration interaction (CI) method For simplicity thepresence of a wetting layer azimuthal anisotropy28 andstructural asymmetry23 are not included in calculationMore details of the calculation can be found in Ref [15]The indium composition inside the ring and the large

lattice mismatch between the ring and barrier materialsresult in a considerably large strain and this strain hasa different effect on the electron and hole confinementpotential With finite element methods we can calculate thestrain induced shift to the band offset Uc and Uv Note thatwe take the opposite value of the hole confinement poten-tial so that the larger value of Uv stands for higher energy

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

Z

Uv Uc UcUv

Fig 6 (a) Strain induced shift to the band offset Uc and Uv along horizontal direction and (b) along vertical direction Z The inset shows halfcross-section of the QR structure The effective radius of the electron (c) and the hole (d) is calculated at two different electric fields (e) The radiusex = mh+memh lt e gt

2 +me lt h gt205 shows similar behavior to e

We plot Uc and Uv along different directions and Z inFigures 6(a and b) It is clear that the strain induced bandoffset for the electron is smaller in the area with smaller and Z while for the hole the top area of the QR has thelowest value So the presence of strain makes the electronand the hole apart from each other which is important forthe observation of the neutral exciton AB effectWe now examine the effects of electric field and mag-

netic field on the effective radius of the electron (hole)e (h) From Figure 6(c) we know that with decreas-ing vertical electric field from 200 kVcm to 20 kVcmthe electron is attracted to the bottom area of the ringdecreasing its effective radius while the hole is pushedto the top of the ring and its effective radius increases(Fig 6(d)) However from the change of e and halone we can not conclude that the period of the AB oscil-lation decreases Theoretical study reveals that the oscil-lation comes from a change in the value of the angularmomentum pair (le lh) not from the single electron orhole angular momentum The period of the oscillation isnot only related to the effective radius of the electron andthe hole but also to their effective massesIn our calculation it is found that the magnetic field

at which the first transition takes place is proportional toe2

ex where 12ex = mhe2+mee2me+mh

We plot ex as a function of magnetic field for differ-ent values of electric field in Figure 6(e) Because theeffective mass of the hole is much larger than that ofthe electron (also because the electron and the hole radiichange within the same magnitude) ex should have a

similar behavior as the electron effective radius e Thisis clearly observed in Figure 6(e) and ex decreases mono-tonically with decreasing electric field As a result the firsttransition takes place at a higher magnetic field when wedecrease the electric field (see Fig 5(b)) The explanationfor the second transition is similar although the formulafor the magnetic field at which it takes place is different(it also has the dominant term mhe2) which shifts tohigher magnetic field when the electric field decreasesPrevious reports revealed that the PL intensity also

oscillates with magnetic field and the oscillation ampli-tudes are around 5sim101213 This should explain theintensity oscillation in Figure 5(c) However for the QRsstudied in Figures 4 and 5 (at 28 V) we observe strongquenching in the PL intensity This phenomenon originatespartly from the AB-like quantum interference effect butthere is also contribution from the imperfect ring geome-try Grochol et al demonstrated that even a slightly eccen-tric ring geometry can smooth the oscillations and rendersthe total angular momentum a non-well defined quantumnumber10 The selection rules are only strictly applicablein a system with perfect rotational symmetry and at highmagnetic fields an oscillator strength transfer is expectedbetween excitonic bright states and dark states

4 CONCLUSION

In conclusion we fabricate a novel self-assembledIn(Ga)AsGaAs QR structure by MBE combined within situ AsBr3 etching The morphology of In(Ga)As

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

nanostructures embedded in GaAs matrix is unveiled byselective wet chemical etching combined with AFM andwe find that the structural parameters of the QRs can bewell controlled by the AsBr3 etching depth Single neu-tral excitons confined in the volcano-like QRs are stud-ied by magneto-photoluminescence Oscillations in bothPL energy and intensity are observed under an appliedmagnetic field We also show that the oscillations can betuned by applying a vertical electric field which modifiesthe electron and hole effective radii Although the experi-mental features are not fully understood yet a theoreticalinvestigation is able to explain the main results We con-clude that the exciton Aharonov-Bohm effect may accountfor the observed effects

Acknowledgment We acknowledge L PKouwenhoven and Z G Wang for support C C BofBufon C Deneke V Fomin A Govorov S Kiravittayaand Wen-Hao Chang for their help and discussions Weare grateful for the financial support of NWO (VIDI)the CAS-MPG programm the DFG (FOR730) BMBF(No 01BM459) NSFC China (60625402) and FlemishScience Foundation (FWO-Vl)

References and Notes

1 Y Aharonov and D Bohm Phys Rev 115 485 (1959)2 S Popescu Nat Phys 6 151 (2010)3 A G Aronov and Y Sharvin Rev Mod Phys 59 755 (1987)4 S Zaric G N Ostojic J Kono J Shaver V C Moore M S

Strano R H Hauge R E Smalley and X Wei Science 304 1129(2004)

5 A Fuhrer S Luscher T Ihn T Heinzel K EnsslinW Wegscheider and M Bichler Nature 413 822 (2001)

6 A O Govorov S E Ulloa K Karrai and R J Warburton PhysRev B 66 081309 (2002)

7 Luis G G V Dias da Silva S E Ulloa and T V ShahbazyanPhys Rev B 72 125327 (2005)

8 R A Roumlmer and M E Raikh Phys Rev B 62 7045 (2000)9 A Chaplik JETP Lett 62 900 (1995)10 M Grochol F Grosse and R Zimmermann Phys Rev B

74 115416 (2006)11 E Ribeiro A O Govorov W Carvalho and G Medeiros-Ribeiro

Phys Rev Lett 92 126402 (2004)

12 I R Sellers V R Whiteside I L Kuskovsky A O Govorov andB D Mccombe Phys Rev Lett 100 136405 (2008)

13 M D Teodoro V L Campo Jr V Lopez-Richard E Marega JrG E Marques Y Galvatildeo Gobato F Iikawa M J S P Brasil Z YAbuWaar V G Dorogan Yu I Mazur M Benamara and G JSalamo Phys Rev Lett 104 086401 (2010)

14 F Ding L Wang S Kiravittaya E Muumlller A Rastelli and O GSchmidt Appl Phys Lett 90 173104 (2007)

15 F Ding N Akopian B Li U Perinetti A Govorov F M PeetersC C Bof Bufon C Deneke Y H Chen A Rastelli O G Schmidtand V Zwiller Phys Rev B 82 075309 (2010)

16 D G Hill K L Lear and J S Harris Jr J Electrochem Soc137 2912 (1990)

17 S-J Paik J Kim S Park S Kim C Koo S-K Lee and D DCho 42 326 (2003)

18 Z M Wang L Zhang K Holmes and G J Salamo Appl PhysLett 86 143106 (2005)

19 B N Zvonkov I A Karpovich N V Baidus D O Filatov S VMorozov and Y Y Gushina Nanotechnology 11 221 (2000)

20 L Wang A Rastelli S Kiravittaya P Atkinson F Ding C C BofBufon C Hermannstaumldter M Witzany G J Beirne P Michler andO G Schmidt New J Phys 10 045010 (2008)

21 R J Warburton C Schaflein D Haft F Bickel A LorkeK Karrai J M Garcia W Schoenfeld and P M Petroff Nature405 926 (2000)

22 B D Gerardot S Seidl P A Dalgarno R J Warburton D Grana-dos J M Garcia K Kowalik O Krebs K Karrai A Badolatoand P M Petroff Appl Phys Lett 90 041101 (2007)

23 T-C Lin C-H Lin H-S Ling Y-J Fu W-H Chang S-D Linand C-P Lee Phys Rev B 80 081304 (2009)

24 T Kuroda T Belhadj T Mano B Urbaszek T Amand X MarieS Sanguinetti K Sakoda and N Koguchi Phys Stat Sol (b)246 861 (2009)

25 M Korkusinski P Hawrylak and M Bayer Phys Stat Sol (b)234 273 (2002)

26 F Ding R Singh J D Plumhof T Zander V Kraacutepek Y H ChenM Benyoucef V Zwiller K Doumlrr G Bester A Rastelli and O GSchmidt Phys Rev Lett 104 067405 (2010)

27 M-F Tsai H Lin C-H Lin S-D Lin S-Y Wang M-C Lo S-JCheng M-C Lee and W-H Chang Phys Rev Lett 101 267402(2008)

28 V M Fomin V N Gladilin J T Devreese N A J M KleemansM Bozkurt and P M Koenraad Phys Stat Sol (b) 245 2657(2008)

29 M Bayer M Korkusinski P Hawrylak T Gutbrod M Michel andA Forchel Phys Rev Lett 90 186801 (2003)

30 R J Warburton C Schulhauser D Haft C Schaumlflein K KarraiJ M Garcia W Schoenfeld and P M Petroff Phys Rev B65 113303 (2002)

Received 28 September 2010 Accepted 26 November 2010

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

AsBr3 etching depth is increased Due to a radial asymme-try in the effective confinement for electrons and holes weexpect the neutral exciton AB effect We observe magneticfield dependent oscillations in the PL energy and intensityof a single neutral exciton in agreement with previous the-oretical predictions We also show that a vertical electricfield which modifies the exciton confinement is able tocontrol this quantum interference effect15

2 EXPERIMENTAL DETAILS

21 Fabrication and Characterization ofIn(Ga)AsGaAs QRs

All samples examined in this work are grown onsemi-insulating GaAs (001) substrates in a solid-sourcemolecular-beam epitaxy system equipped with an AsBr3gas source After oxide desorption a 300-nm GaAs buffer

0 nm 6 nm ndash26ordm 26ordm

1 nm AsBr3 etching

2 nm AsBr3 etching

3 nm AsBr3 etching

as-grown

G aAsG aAs

G aAsG aAs

G aAsG aAs

G aAsG aAs

Fig 1 Fabrication of In(Ga)AsGaAs QRs by MBE combined with AsBr3 in situ etching The first column images show schematic representationsof the fabrication processes with different AsBr3 etching depths 500times500 nm2 AFM images illustrate the sample surface morphology before (secondcolumn) and after (third column) the removal of GaAs capping layer The last column shows the progressive morphological evolution of a single buriednanostructure namely from QD to volcano-shaped QR

layer is grown at 570 C A 18-monolayer (ML) InAslayer is then deposited at 500 C a temperature which canbe easily reproduced by observing the change in surfacereconstruction from (2times4) to c(4times4) using an In growthrate of 001 MLs After 30 s growth interruption the sub-strate temperature is lowered to 470 C and a 10-nm GaAscap is deposited at a rate of 06 MLs while the tempera-ture is ramped back to 500 C After GaAs deposition theAsBr3 etching gas is subsequently supplied to produce thenanoholes (see the first and second columns of Fig 1)The etching rate of GaAs was 024 MLs which was cali-brated by reflection high-energy electron diffraction inten-sity oscillationsThe surface morphology develops into a rhombus-

shaped structure with a tiny hole in the middle after10 nm GaAs overgrowth (see the first row of Fig 1)After supplying the AsBr3 etching gas there is a pref-erential removal of the central part of the buried QDs

52 J Nanoelectron Optoelectron 6 51ndash57 2011

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

due to the local strain field induced by the buried QDs14

In order to characterized the underlying QR structuresa selective chemical etchant [ammonium hydroxide (28NH4OH) hydrogen peroxide (31 H2O2) and deionizedwater (1125)] is used to remove the GaAs cappinglayer NH4OHH2O2 solutions are known to etch selec-tively GaAs over InGaAs alloys16ndash19 The mixture usedhere etches GaAs at a rate of sim10 nms17 Figure 1 sug-gests that the GaAs cap is completely removed by thesolution and the etching process significantly slows downat the In(Ga)As wetting layer (WL) (see also Fig 2) Pro-longed etching ( 2ndash3 seconds) results in the removal ofthe WL and the undercut of the QDs We verified that dif-ferent etching experiments with the same nominal duration(1 second) performed on the same sample yield compat-ible results Slower etching rates of GaAs are achievablewith diluted solutions20

We observe from Figure 1 that by varying the nominalAsBr3 etching depth the morphology of the ring struc-ture can be tuned (see the second third and fourth rows)The statistical structural analysis of the uncapped In(Ga)Asnanostructures as a function of the nominal etching depthis given in the right part of Figure 2 A cross sectionaltransmission electron microscopy (TEM) image of a sin-gle QR from a similar sample is also presented (Fig 2)further supporting the validity of our method We arguethat the selective chemical etching combined with AFM isa reliable fast and convenient way to characterize buriedIn(Ga)AsGaAs nanostructures it provides information onthe three-dimensional morphology and does not requireany special sample preparationWe focus now on the QRs with a nominal etching depth

of 3 nm Both AFM and TEM (see Fig 2) confirm that theaverage inner radius r1 of the QR is about 85 nm whilethe average outer radius r2 is about 19 nm and the heightH is about 4 nm The inner height h is less than 1 nmSuch a ring structure could produce different confinement

0 1 2 30

2

4

6

8

Hh

GaAs

InAs WL

Hh10 nm

Hei

ght (

nm)

Nominal etching depth (nm)

100 nm

TE

MA

FM

r1

r2

Fig 2 AFM image shows the QRs with nominal AsBr3 etching depthof 3 nm after removal of the GaAs capping layer by selective chemicaletching The lower graph shows the cross sectional TEM image of a sin-gle QR from the similar sample The statistical structural analysis of theuncapped In(Ga)As nanostructures as a function of the nominal etchingdepth is given in the right part H is the height of the embedded nano-structures and h is the distance between the InAs WL and the bottom ofthe dip at the nanostructure apex

potentials for the electron and the hole thus the neutralexciton AB can be expected

22 Magneto-Photoluminescence

We use magneto-PL to probe the energy changes andintensity changes related to the nature of the ground stateThe samples are placed in a cryostat tube which is evac-uated and then refilled with a small amount of heliumexchange gas The tube is then inserted into a 42 Khelium bath dewar equipped with a superconducting mag-net capable of providing fields up to 9 T The sample isexcited by a 532 nm laser beam and the PL is collected byan objective with 085 numerical aperture The PL signalis dispersed by a spectrometer with 075 m focal lengthequipped with a 1800 gmm grating and captured by aliquid nitrogen cooled Si charge-coupled device (CCD)Figure 3(a) shows a typical PL spectrum for a single QRat B = 0 T We use power-dependent PL polarization-dependent PL (Fig 3(c)) and charging experiments21 toidentify the neutral exciton X the biexciton XX and thecharged exciton X+We have carefully optimized and tested the system to

minimize drifts associated with magnetic field rampingAn optimum resolution of 25 eV can be achieved byfitting the PL peaks with Lorentzian functions The accu-racy of this peak-determination procedure is determined byusing the quantum confined Stark effect (QCSE) Some ofthe QRs are embedded in an n-i-Schottky structure con-sisting of 20 nm n+ GaAs layer followed by a 20 nm thickspacer layer under the QRs 30 nm i-GaAs and a 116 nmthick AlAsGaAs short period superlattice With a 5 nmthick semi-transparent Ti top gate an electric field can beapplied to modify the energy band of the ring2122 When

Raw peak position

Fit peak position

Fig 3 (a) Typical PL spectrum for a single QR (b) The PL peak isshifted by QCSE both fit peak positions and the measured raw peakpositions are plotted (c) Linear polarization dependent energy shift of Xand XX The solid lines are sine wave fittings

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

a forward bias Vg is scanned from 03 to 032 V (withsteps of 05 mV) the PL emission energy of a single QRis tuned by about 30 eV (see Fig 3(b)) We observe thatin contrast to the discretized raw data (diamond points)the Lorentzian fit data show a smooth blue-shift of thepeak positions (round points) We plot the 95 predictionband of the fit function in Figure 3(b) (solid lines) fromwhich an error of plusmn15 eV for this Lorentzian analysisprocedure is estimated For the evaluation of the system-atic error repeated measurements (B field increasing anddecreasing) are performed on the same QR and the fitpeak positions are reproducible to within plusmn25 eV Wecan therefore expect an overall error of plusmn25 eV in thepeak-determination procedure used in this workTo further support the validity of this peak determina-

tion procedure we perform the FSS measurements for Xand XX lines (Fig 3(c)) The data points are given byLorentzian fits with an uncertainty of 25 eV Solid linesin the exciton and biexciton plots are sine wave fittingcurves As expected X and XX show anti-correlated shiftsas we rotate the half-wave plate The FSS of this QD isonly 13 eV which is near the resolution limit of our PLsystem and would be undetectable without the Lorentzianfitting processA magnetic field up to 9 T is applied along the sample

growth direction and we observe the characteristic Zee-man splitting as well as the diamagnetic shift of the PLemission energy (see Fig 4(a)) similar to previous reportson single QRs23 In Figure 4(b) we plot the neutral excitonemission energies of the QR after averaging the emissionenergy values of the Zeeman split lines It is observed

0

15

00

05

10

Nor

m P

L I

nt

Ene

rgy

(microeV

)

ndash15

(c)

(d)

13484

13488

13492

13496

PL e

nerg

y (e

V)

13483

13485

13487

13489

Quantum ring(3 nm etched)

(b)

(a)

Magnetic field (T)0 2 4 6 8 10

Magnetic field (T)0 2 4 6 8 10

Fig 4 Fitted PL peak position versus B field before (a) and after (c) averaging the Zeeman splitting for the neutral exciton emission in a 3 nm-etchedQR The blue dashed line in (b) indicates a parabolic fit Oscillations in PL energy and corresponding normalized PL intensity as a function of B fieldare shown in (c) and (d) respectively The solid lines represent the smoothed data using a Savitzky-Golay filter The arrows in (b) and (d) indicatechanges in the ground state transitions

that the emission energy does not scale quadratically withincreasing B field From its shape Figure 4(b) looks quitesimilar to the one shown in a very recent report13 inwhich AB oscillations in ensemble InAsGaAs QRs wereobserved However the diamagnetic shift for a single QRstudied in our work is sim6 times smaller than the valuefor the ensemble QRs in Ref [13] and the oscillationamplitude is much smaller Also no Zeeman splitting wasobserved in Ref [13] because of the broad ensemble emis-sion In order to visualize the magnetic field induced oscil-lations we subtract a single parabola from Figure 4(b) andplot the results in Figure 4(c) We observe two maxima atsim4 T and sim7 T (the solid line here which represents thesmoothed data using a Savitzky-Golay filter is guide to theeye) suggesting changes in the ground state transitionsAnother significant feature observed is the decrease

in PL intensity with increasing magnetic field seeFigure 4(d) The change in PL intensity is one of thesignatures expected for a QR and is attributed to oscilla-tions in the ground state transitions611ndash13 Two knees canbe observed at sim4 T and sim7 T (Fig 4(c)) which cor-respond well with the peak energy oscillation maxima inFigure 4(c) (indicated by arrows)All the observations here are well above the system

resolution and they strongly contrast with the experimen-tal results on a conventional QD where no peak energyoscillation and PL intensity quenching were observed seeRef [15] Especially the PL intensity of this QR quenchesby more than 70 with increasing magnetic field whichis confirmed by repeating the measurements and similarobservations in other QRs A recent study on single GaAs

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

QR obtained by droplet epitaxy also revealed a signifi-cant reduction in the PL intensity by more than 20 atB gt 6 T24 the exciton AB effect may account for theobservation

23 Gate-Controlled Oscillations

We use the above mentioned gated-QR structure to demon-strate the possibility of controlling the observed effect withan external electric field The oscillations for a single QR(with a nominal AsBr3 etching depth of 3 nm) under aforward bias of 28 V are clearly seen in Figure 5(a) withthe two transition points at 26 T and 8 T The PL intensityalso shows similar quenching behavior as in Figure 4(d)(not shown here) When we decrease the bias from 28 V to08 V it is clear that the transition points shift smoothly tohigher magnetic fields (Fig 5(b)) indicating that the effec-tive radii of the electron and the hole are modified by theexternal gate potential The PL intensity is also stronglymodified at different electric fields which is a consequenceof the QCSE At sim18 V the PL intensity reaches an over-all maximum and then decreases see Ref [15] Interest-ingly the PL intensity at 18 V shows clear modulation bythe magnetic field ie first quenches by more than 25

Fig 5 (a) Under a forward bias of 28 V the PL energy shows cleartransitions at sim26 T and sim8 T (b) When the bias changes from 28 Vto 08 V the transitions shift smoothly to higher magnetic fields (c) At18 V the PL energy shows transitions at sim3 T and sim82 T while thenormalized PL intensity also shows oscillations

and then recovers fully to its original value with increasingmagnetic field (Fig 5(c)) This observation is quite simi-lar to the long-existed theoretical prediction for a weaklybound neutral exciton confined in a QR6

3 DISCUSSIONS

Previous theoretical works distinguish between excitonscomposed of strongly and weakly bound electronndashholepairs6 In Ref [7] the effectiveness of the electronndashholeCoulomb interaction is expressed as

vq =e2

rradicReRh

Qqminus12

(1+ ReminusRh

2ReRh

)(1)

where r is the dielectric constant and Qx is the Leg-endre function In the strongly bound regime where vq isdominant the exciton moves along the ring as one tightlybound particle and AB effect manifests itself in a brightto dark transition in the ground state with increasing mag-netic field While in the opposite limit of a weakly boundelectronndashhole pair an interesting modulation between dif-ferent bright and dark states should appear The electronndashhole pairs in above-mentioned QRs are close to the weaklybound regime this is because(i) in the ring geometry the ratio of Coulomb to kineticenergies is proportional to the ring radius while for smallrings (R lt alowast the effective Bohr radius) the quantizationdue to kinetic motion is strong625 and the effectiveness ofvq becomes weaker(ii) in our structure the n-doped layer which locates 20 nmunder the QRs (also the metal contact in the gated struc-ture) can sufficiently screen the effectiveness of vq

7

(iii) in experiment we also observe that the changes in thebinding energies EBXX asymp EBX

+ when E changes(not shown here) indicating that the strongly confinedfew-particle picture is valid in our QRs and the effectiveradii of electron and hole are very different2627

However the theory in Ref [6] is not sufficient toexplain our results We model a simplified QR as depictedin Figure 2 with the main aim to explain the gate-controlled oscillation effect (Fig 5) The ground stateenergy of the neutral exciton inside the In1minusxGaxAs ring(surrounded by GaAs barrier) is calculated within theconfiguration interaction (CI) method For simplicity thepresence of a wetting layer azimuthal anisotropy28 andstructural asymmetry23 are not included in calculationMore details of the calculation can be found in Ref [15]The indium composition inside the ring and the large

lattice mismatch between the ring and barrier materialsresult in a considerably large strain and this strain hasa different effect on the electron and hole confinementpotential With finite element methods we can calculate thestrain induced shift to the band offset Uc and Uv Note thatwe take the opposite value of the hole confinement poten-tial so that the larger value of Uv stands for higher energy

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

Z

Uv Uc UcUv

Fig 6 (a) Strain induced shift to the band offset Uc and Uv along horizontal direction and (b) along vertical direction Z The inset shows halfcross-section of the QR structure The effective radius of the electron (c) and the hole (d) is calculated at two different electric fields (e) The radiusex = mh+memh lt e gt

2 +me lt h gt205 shows similar behavior to e

We plot Uc and Uv along different directions and Z inFigures 6(a and b) It is clear that the strain induced bandoffset for the electron is smaller in the area with smaller and Z while for the hole the top area of the QR has thelowest value So the presence of strain makes the electronand the hole apart from each other which is important forthe observation of the neutral exciton AB effectWe now examine the effects of electric field and mag-

netic field on the effective radius of the electron (hole)e (h) From Figure 6(c) we know that with decreas-ing vertical electric field from 200 kVcm to 20 kVcmthe electron is attracted to the bottom area of the ringdecreasing its effective radius while the hole is pushedto the top of the ring and its effective radius increases(Fig 6(d)) However from the change of e and halone we can not conclude that the period of the AB oscil-lation decreases Theoretical study reveals that the oscil-lation comes from a change in the value of the angularmomentum pair (le lh) not from the single electron orhole angular momentum The period of the oscillation isnot only related to the effective radius of the electron andthe hole but also to their effective massesIn our calculation it is found that the magnetic field

at which the first transition takes place is proportional toe2

ex where 12ex = mhe2+mee2me+mh

We plot ex as a function of magnetic field for differ-ent values of electric field in Figure 6(e) Because theeffective mass of the hole is much larger than that ofthe electron (also because the electron and the hole radiichange within the same magnitude) ex should have a

similar behavior as the electron effective radius e Thisis clearly observed in Figure 6(e) and ex decreases mono-tonically with decreasing electric field As a result the firsttransition takes place at a higher magnetic field when wedecrease the electric field (see Fig 5(b)) The explanationfor the second transition is similar although the formulafor the magnetic field at which it takes place is different(it also has the dominant term mhe2) which shifts tohigher magnetic field when the electric field decreasesPrevious reports revealed that the PL intensity also

oscillates with magnetic field and the oscillation ampli-tudes are around 5sim101213 This should explain theintensity oscillation in Figure 5(c) However for the QRsstudied in Figures 4 and 5 (at 28 V) we observe strongquenching in the PL intensity This phenomenon originatespartly from the AB-like quantum interference effect butthere is also contribution from the imperfect ring geome-try Grochol et al demonstrated that even a slightly eccen-tric ring geometry can smooth the oscillations and rendersthe total angular momentum a non-well defined quantumnumber10 The selection rules are only strictly applicablein a system with perfect rotational symmetry and at highmagnetic fields an oscillator strength transfer is expectedbetween excitonic bright states and dark states

4 CONCLUSION

In conclusion we fabricate a novel self-assembledIn(Ga)AsGaAs QR structure by MBE combined within situ AsBr3 etching The morphology of In(Ga)As

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

nanostructures embedded in GaAs matrix is unveiled byselective wet chemical etching combined with AFM andwe find that the structural parameters of the QRs can bewell controlled by the AsBr3 etching depth Single neu-tral excitons confined in the volcano-like QRs are stud-ied by magneto-photoluminescence Oscillations in bothPL energy and intensity are observed under an appliedmagnetic field We also show that the oscillations can betuned by applying a vertical electric field which modifiesthe electron and hole effective radii Although the experi-mental features are not fully understood yet a theoreticalinvestigation is able to explain the main results We con-clude that the exciton Aharonov-Bohm effect may accountfor the observed effects

Acknowledgment We acknowledge L PKouwenhoven and Z G Wang for support C C BofBufon C Deneke V Fomin A Govorov S Kiravittayaand Wen-Hao Chang for their help and discussions Weare grateful for the financial support of NWO (VIDI)the CAS-MPG programm the DFG (FOR730) BMBF(No 01BM459) NSFC China (60625402) and FlemishScience Foundation (FWO-Vl)

References and Notes

1 Y Aharonov and D Bohm Phys Rev 115 485 (1959)2 S Popescu Nat Phys 6 151 (2010)3 A G Aronov and Y Sharvin Rev Mod Phys 59 755 (1987)4 S Zaric G N Ostojic J Kono J Shaver V C Moore M S

Strano R H Hauge R E Smalley and X Wei Science 304 1129(2004)

5 A Fuhrer S Luscher T Ihn T Heinzel K EnsslinW Wegscheider and M Bichler Nature 413 822 (2001)

6 A O Govorov S E Ulloa K Karrai and R J Warburton PhysRev B 66 081309 (2002)

7 Luis G G V Dias da Silva S E Ulloa and T V ShahbazyanPhys Rev B 72 125327 (2005)

8 R A Roumlmer and M E Raikh Phys Rev B 62 7045 (2000)9 A Chaplik JETP Lett 62 900 (1995)10 M Grochol F Grosse and R Zimmermann Phys Rev B

74 115416 (2006)11 E Ribeiro A O Govorov W Carvalho and G Medeiros-Ribeiro

Phys Rev Lett 92 126402 (2004)

12 I R Sellers V R Whiteside I L Kuskovsky A O Govorov andB D Mccombe Phys Rev Lett 100 136405 (2008)

13 M D Teodoro V L Campo Jr V Lopez-Richard E Marega JrG E Marques Y Galvatildeo Gobato F Iikawa M J S P Brasil Z YAbuWaar V G Dorogan Yu I Mazur M Benamara and G JSalamo Phys Rev Lett 104 086401 (2010)

14 F Ding L Wang S Kiravittaya E Muumlller A Rastelli and O GSchmidt Appl Phys Lett 90 173104 (2007)

15 F Ding N Akopian B Li U Perinetti A Govorov F M PeetersC C Bof Bufon C Deneke Y H Chen A Rastelli O G Schmidtand V Zwiller Phys Rev B 82 075309 (2010)

16 D G Hill K L Lear and J S Harris Jr J Electrochem Soc137 2912 (1990)

17 S-J Paik J Kim S Park S Kim C Koo S-K Lee and D DCho 42 326 (2003)

18 Z M Wang L Zhang K Holmes and G J Salamo Appl PhysLett 86 143106 (2005)

19 B N Zvonkov I A Karpovich N V Baidus D O Filatov S VMorozov and Y Y Gushina Nanotechnology 11 221 (2000)

20 L Wang A Rastelli S Kiravittaya P Atkinson F Ding C C BofBufon C Hermannstaumldter M Witzany G J Beirne P Michler andO G Schmidt New J Phys 10 045010 (2008)

21 R J Warburton C Schaflein D Haft F Bickel A LorkeK Karrai J M Garcia W Schoenfeld and P M Petroff Nature405 926 (2000)

22 B D Gerardot S Seidl P A Dalgarno R J Warburton D Grana-dos J M Garcia K Kowalik O Krebs K Karrai A Badolatoand P M Petroff Appl Phys Lett 90 041101 (2007)

23 T-C Lin C-H Lin H-S Ling Y-J Fu W-H Chang S-D Linand C-P Lee Phys Rev B 80 081304 (2009)

24 T Kuroda T Belhadj T Mano B Urbaszek T Amand X MarieS Sanguinetti K Sakoda and N Koguchi Phys Stat Sol (b)246 861 (2009)

25 M Korkusinski P Hawrylak and M Bayer Phys Stat Sol (b)234 273 (2002)

26 F Ding R Singh J D Plumhof T Zander V Kraacutepek Y H ChenM Benyoucef V Zwiller K Doumlrr G Bester A Rastelli and O GSchmidt Phys Rev Lett 104 067405 (2010)

27 M-F Tsai H Lin C-H Lin S-D Lin S-Y Wang M-C Lo S-JCheng M-C Lee and W-H Chang Phys Rev Lett 101 267402(2008)

28 V M Fomin V N Gladilin J T Devreese N A J M KleemansM Bozkurt and P M Koenraad Phys Stat Sol (b) 245 2657(2008)

29 M Bayer M Korkusinski P Hawrylak T Gutbrod M Michel andA Forchel Phys Rev Lett 90 186801 (2003)

30 R J Warburton C Schulhauser D Haft C Schaumlflein K KarraiJ M Garcia W Schoenfeld and P M Petroff Phys Rev B65 113303 (2002)

Received 28 September 2010 Accepted 26 November 2010

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

due to the local strain field induced by the buried QDs14

In order to characterized the underlying QR structuresa selective chemical etchant [ammonium hydroxide (28NH4OH) hydrogen peroxide (31 H2O2) and deionizedwater (1125)] is used to remove the GaAs cappinglayer NH4OHH2O2 solutions are known to etch selec-tively GaAs over InGaAs alloys16ndash19 The mixture usedhere etches GaAs at a rate of sim10 nms17 Figure 1 sug-gests that the GaAs cap is completely removed by thesolution and the etching process significantly slows downat the In(Ga)As wetting layer (WL) (see also Fig 2) Pro-longed etching ( 2ndash3 seconds) results in the removal ofthe WL and the undercut of the QDs We verified that dif-ferent etching experiments with the same nominal duration(1 second) performed on the same sample yield compat-ible results Slower etching rates of GaAs are achievablewith diluted solutions20

We observe from Figure 1 that by varying the nominalAsBr3 etching depth the morphology of the ring struc-ture can be tuned (see the second third and fourth rows)The statistical structural analysis of the uncapped In(Ga)Asnanostructures as a function of the nominal etching depthis given in the right part of Figure 2 A cross sectionaltransmission electron microscopy (TEM) image of a sin-gle QR from a similar sample is also presented (Fig 2)further supporting the validity of our method We arguethat the selective chemical etching combined with AFM isa reliable fast and convenient way to characterize buriedIn(Ga)AsGaAs nanostructures it provides information onthe three-dimensional morphology and does not requireany special sample preparationWe focus now on the QRs with a nominal etching depth

of 3 nm Both AFM and TEM (see Fig 2) confirm that theaverage inner radius r1 of the QR is about 85 nm whilethe average outer radius r2 is about 19 nm and the heightH is about 4 nm The inner height h is less than 1 nmSuch a ring structure could produce different confinement

0 1 2 30

2

4

6

8

Hh

GaAs

InAs WL

Hh10 nm

Hei

ght (

nm)

Nominal etching depth (nm)

100 nm

TE

MA

FM

r1

r2

Fig 2 AFM image shows the QRs with nominal AsBr3 etching depthof 3 nm after removal of the GaAs capping layer by selective chemicaletching The lower graph shows the cross sectional TEM image of a sin-gle QR from the similar sample The statistical structural analysis of theuncapped In(Ga)As nanostructures as a function of the nominal etchingdepth is given in the right part H is the height of the embedded nano-structures and h is the distance between the InAs WL and the bottom ofthe dip at the nanostructure apex

potentials for the electron and the hole thus the neutralexciton AB can be expected

22 Magneto-Photoluminescence

We use magneto-PL to probe the energy changes andintensity changes related to the nature of the ground stateThe samples are placed in a cryostat tube which is evac-uated and then refilled with a small amount of heliumexchange gas The tube is then inserted into a 42 Khelium bath dewar equipped with a superconducting mag-net capable of providing fields up to 9 T The sample isexcited by a 532 nm laser beam and the PL is collected byan objective with 085 numerical aperture The PL signalis dispersed by a spectrometer with 075 m focal lengthequipped with a 1800 gmm grating and captured by aliquid nitrogen cooled Si charge-coupled device (CCD)Figure 3(a) shows a typical PL spectrum for a single QRat B = 0 T We use power-dependent PL polarization-dependent PL (Fig 3(c)) and charging experiments21 toidentify the neutral exciton X the biexciton XX and thecharged exciton X+We have carefully optimized and tested the system to

minimize drifts associated with magnetic field rampingAn optimum resolution of 25 eV can be achieved byfitting the PL peaks with Lorentzian functions The accu-racy of this peak-determination procedure is determined byusing the quantum confined Stark effect (QCSE) Some ofthe QRs are embedded in an n-i-Schottky structure con-sisting of 20 nm n+ GaAs layer followed by a 20 nm thickspacer layer under the QRs 30 nm i-GaAs and a 116 nmthick AlAsGaAs short period superlattice With a 5 nmthick semi-transparent Ti top gate an electric field can beapplied to modify the energy band of the ring2122 When

Raw peak position

Fit peak position

Fig 3 (a) Typical PL spectrum for a single QR (b) The PL peak isshifted by QCSE both fit peak positions and the measured raw peakpositions are plotted (c) Linear polarization dependent energy shift of Xand XX The solid lines are sine wave fittings

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

a forward bias Vg is scanned from 03 to 032 V (withsteps of 05 mV) the PL emission energy of a single QRis tuned by about 30 eV (see Fig 3(b)) We observe thatin contrast to the discretized raw data (diamond points)the Lorentzian fit data show a smooth blue-shift of thepeak positions (round points) We plot the 95 predictionband of the fit function in Figure 3(b) (solid lines) fromwhich an error of plusmn15 eV for this Lorentzian analysisprocedure is estimated For the evaluation of the system-atic error repeated measurements (B field increasing anddecreasing) are performed on the same QR and the fitpeak positions are reproducible to within plusmn25 eV Wecan therefore expect an overall error of plusmn25 eV in thepeak-determination procedure used in this workTo further support the validity of this peak determina-

tion procedure we perform the FSS measurements for Xand XX lines (Fig 3(c)) The data points are given byLorentzian fits with an uncertainty of 25 eV Solid linesin the exciton and biexciton plots are sine wave fittingcurves As expected X and XX show anti-correlated shiftsas we rotate the half-wave plate The FSS of this QD isonly 13 eV which is near the resolution limit of our PLsystem and would be undetectable without the Lorentzianfitting processA magnetic field up to 9 T is applied along the sample

growth direction and we observe the characteristic Zee-man splitting as well as the diamagnetic shift of the PLemission energy (see Fig 4(a)) similar to previous reportson single QRs23 In Figure 4(b) we plot the neutral excitonemission energies of the QR after averaging the emissionenergy values of the Zeeman split lines It is observed

0

15

00

05

10

Nor

m P

L I

nt

Ene

rgy

(microeV

)

ndash15

(c)

(d)

13484

13488

13492

13496

PL e

nerg

y (e

V)

13483

13485

13487

13489

Quantum ring(3 nm etched)

(b)

(a)

Magnetic field (T)0 2 4 6 8 10

Magnetic field (T)0 2 4 6 8 10

Fig 4 Fitted PL peak position versus B field before (a) and after (c) averaging the Zeeman splitting for the neutral exciton emission in a 3 nm-etchedQR The blue dashed line in (b) indicates a parabolic fit Oscillations in PL energy and corresponding normalized PL intensity as a function of B fieldare shown in (c) and (d) respectively The solid lines represent the smoothed data using a Savitzky-Golay filter The arrows in (b) and (d) indicatechanges in the ground state transitions

that the emission energy does not scale quadratically withincreasing B field From its shape Figure 4(b) looks quitesimilar to the one shown in a very recent report13 inwhich AB oscillations in ensemble InAsGaAs QRs wereobserved However the diamagnetic shift for a single QRstudied in our work is sim6 times smaller than the valuefor the ensemble QRs in Ref [13] and the oscillationamplitude is much smaller Also no Zeeman splitting wasobserved in Ref [13] because of the broad ensemble emis-sion In order to visualize the magnetic field induced oscil-lations we subtract a single parabola from Figure 4(b) andplot the results in Figure 4(c) We observe two maxima atsim4 T and sim7 T (the solid line here which represents thesmoothed data using a Savitzky-Golay filter is guide to theeye) suggesting changes in the ground state transitionsAnother significant feature observed is the decrease

in PL intensity with increasing magnetic field seeFigure 4(d) The change in PL intensity is one of thesignatures expected for a QR and is attributed to oscilla-tions in the ground state transitions611ndash13 Two knees canbe observed at sim4 T and sim7 T (Fig 4(c)) which cor-respond well with the peak energy oscillation maxima inFigure 4(c) (indicated by arrows)All the observations here are well above the system

resolution and they strongly contrast with the experimen-tal results on a conventional QD where no peak energyoscillation and PL intensity quenching were observed seeRef [15] Especially the PL intensity of this QR quenchesby more than 70 with increasing magnetic field whichis confirmed by repeating the measurements and similarobservations in other QRs A recent study on single GaAs

54 J Nanoelectron Optoelectron 6 51ndash57 2011

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Fri 06 May 2011 211221

RESEARCH

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LE

Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

QR obtained by droplet epitaxy also revealed a signifi-cant reduction in the PL intensity by more than 20 atB gt 6 T24 the exciton AB effect may account for theobservation

23 Gate-Controlled Oscillations

We use the above mentioned gated-QR structure to demon-strate the possibility of controlling the observed effect withan external electric field The oscillations for a single QR(with a nominal AsBr3 etching depth of 3 nm) under aforward bias of 28 V are clearly seen in Figure 5(a) withthe two transition points at 26 T and 8 T The PL intensityalso shows similar quenching behavior as in Figure 4(d)(not shown here) When we decrease the bias from 28 V to08 V it is clear that the transition points shift smoothly tohigher magnetic fields (Fig 5(b)) indicating that the effec-tive radii of the electron and the hole are modified by theexternal gate potential The PL intensity is also stronglymodified at different electric fields which is a consequenceof the QCSE At sim18 V the PL intensity reaches an over-all maximum and then decreases see Ref [15] Interest-ingly the PL intensity at 18 V shows clear modulation bythe magnetic field ie first quenches by more than 25

Fig 5 (a) Under a forward bias of 28 V the PL energy shows cleartransitions at sim26 T and sim8 T (b) When the bias changes from 28 Vto 08 V the transitions shift smoothly to higher magnetic fields (c) At18 V the PL energy shows transitions at sim3 T and sim82 T while thenormalized PL intensity also shows oscillations

and then recovers fully to its original value with increasingmagnetic field (Fig 5(c)) This observation is quite simi-lar to the long-existed theoretical prediction for a weaklybound neutral exciton confined in a QR6

3 DISCUSSIONS

Previous theoretical works distinguish between excitonscomposed of strongly and weakly bound electronndashholepairs6 In Ref [7] the effectiveness of the electronndashholeCoulomb interaction is expressed as

vq =e2

rradicReRh

Qqminus12

(1+ ReminusRh

2ReRh

)(1)

where r is the dielectric constant and Qx is the Leg-endre function In the strongly bound regime where vq isdominant the exciton moves along the ring as one tightlybound particle and AB effect manifests itself in a brightto dark transition in the ground state with increasing mag-netic field While in the opposite limit of a weakly boundelectronndashhole pair an interesting modulation between dif-ferent bright and dark states should appear The electronndashhole pairs in above-mentioned QRs are close to the weaklybound regime this is because(i) in the ring geometry the ratio of Coulomb to kineticenergies is proportional to the ring radius while for smallrings (R lt alowast the effective Bohr radius) the quantizationdue to kinetic motion is strong625 and the effectiveness ofvq becomes weaker(ii) in our structure the n-doped layer which locates 20 nmunder the QRs (also the metal contact in the gated struc-ture) can sufficiently screen the effectiveness of vq

7

(iii) in experiment we also observe that the changes in thebinding energies EBXX asymp EBX

+ when E changes(not shown here) indicating that the strongly confinedfew-particle picture is valid in our QRs and the effectiveradii of electron and hole are very different2627

However the theory in Ref [6] is not sufficient toexplain our results We model a simplified QR as depictedin Figure 2 with the main aim to explain the gate-controlled oscillation effect (Fig 5) The ground stateenergy of the neutral exciton inside the In1minusxGaxAs ring(surrounded by GaAs barrier) is calculated within theconfiguration interaction (CI) method For simplicity thepresence of a wetting layer azimuthal anisotropy28 andstructural asymmetry23 are not included in calculationMore details of the calculation can be found in Ref [15]The indium composition inside the ring and the large

lattice mismatch between the ring and barrier materialsresult in a considerably large strain and this strain hasa different effect on the electron and hole confinementpotential With finite element methods we can calculate thestrain induced shift to the band offset Uc and Uv Note thatwe take the opposite value of the hole confinement poten-tial so that the larger value of Uv stands for higher energy

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RESEARCH

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

Z

Uv Uc UcUv

Fig 6 (a) Strain induced shift to the band offset Uc and Uv along horizontal direction and (b) along vertical direction Z The inset shows halfcross-section of the QR structure The effective radius of the electron (c) and the hole (d) is calculated at two different electric fields (e) The radiusex = mh+memh lt e gt

2 +me lt h gt205 shows similar behavior to e

We plot Uc and Uv along different directions and Z inFigures 6(a and b) It is clear that the strain induced bandoffset for the electron is smaller in the area with smaller and Z while for the hole the top area of the QR has thelowest value So the presence of strain makes the electronand the hole apart from each other which is important forthe observation of the neutral exciton AB effectWe now examine the effects of electric field and mag-

netic field on the effective radius of the electron (hole)e (h) From Figure 6(c) we know that with decreas-ing vertical electric field from 200 kVcm to 20 kVcmthe electron is attracted to the bottom area of the ringdecreasing its effective radius while the hole is pushedto the top of the ring and its effective radius increases(Fig 6(d)) However from the change of e and halone we can not conclude that the period of the AB oscil-lation decreases Theoretical study reveals that the oscil-lation comes from a change in the value of the angularmomentum pair (le lh) not from the single electron orhole angular momentum The period of the oscillation isnot only related to the effective radius of the electron andthe hole but also to their effective massesIn our calculation it is found that the magnetic field

at which the first transition takes place is proportional toe2

ex where 12ex = mhe2+mee2me+mh

We plot ex as a function of magnetic field for differ-ent values of electric field in Figure 6(e) Because theeffective mass of the hole is much larger than that ofthe electron (also because the electron and the hole radiichange within the same magnitude) ex should have a

similar behavior as the electron effective radius e Thisis clearly observed in Figure 6(e) and ex decreases mono-tonically with decreasing electric field As a result the firsttransition takes place at a higher magnetic field when wedecrease the electric field (see Fig 5(b)) The explanationfor the second transition is similar although the formulafor the magnetic field at which it takes place is different(it also has the dominant term mhe2) which shifts tohigher magnetic field when the electric field decreasesPrevious reports revealed that the PL intensity also

oscillates with magnetic field and the oscillation ampli-tudes are around 5sim101213 This should explain theintensity oscillation in Figure 5(c) However for the QRsstudied in Figures 4 and 5 (at 28 V) we observe strongquenching in the PL intensity This phenomenon originatespartly from the AB-like quantum interference effect butthere is also contribution from the imperfect ring geome-try Grochol et al demonstrated that even a slightly eccen-tric ring geometry can smooth the oscillations and rendersthe total angular momentum a non-well defined quantumnumber10 The selection rules are only strictly applicablein a system with perfect rotational symmetry and at highmagnetic fields an oscillator strength transfer is expectedbetween excitonic bright states and dark states

4 CONCLUSION

In conclusion we fabricate a novel self-assembledIn(Ga)AsGaAs QR structure by MBE combined within situ AsBr3 etching The morphology of In(Ga)As

56 J Nanoelectron Optoelectron 6 51ndash57 2011

Delivered by Ingenta toAlexander BalandinIP 16923512206

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RESEARCH

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LE

Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

nanostructures embedded in GaAs matrix is unveiled byselective wet chemical etching combined with AFM andwe find that the structural parameters of the QRs can bewell controlled by the AsBr3 etching depth Single neu-tral excitons confined in the volcano-like QRs are stud-ied by magneto-photoluminescence Oscillations in bothPL energy and intensity are observed under an appliedmagnetic field We also show that the oscillations can betuned by applying a vertical electric field which modifiesthe electron and hole effective radii Although the experi-mental features are not fully understood yet a theoreticalinvestigation is able to explain the main results We con-clude that the exciton Aharonov-Bohm effect may accountfor the observed effects

Acknowledgment We acknowledge L PKouwenhoven and Z G Wang for support C C BofBufon C Deneke V Fomin A Govorov S Kiravittayaand Wen-Hao Chang for their help and discussions Weare grateful for the financial support of NWO (VIDI)the CAS-MPG programm the DFG (FOR730) BMBF(No 01BM459) NSFC China (60625402) and FlemishScience Foundation (FWO-Vl)

References and Notes

1 Y Aharonov and D Bohm Phys Rev 115 485 (1959)2 S Popescu Nat Phys 6 151 (2010)3 A G Aronov and Y Sharvin Rev Mod Phys 59 755 (1987)4 S Zaric G N Ostojic J Kono J Shaver V C Moore M S

Strano R H Hauge R E Smalley and X Wei Science 304 1129(2004)

5 A Fuhrer S Luscher T Ihn T Heinzel K EnsslinW Wegscheider and M Bichler Nature 413 822 (2001)

6 A O Govorov S E Ulloa K Karrai and R J Warburton PhysRev B 66 081309 (2002)

7 Luis G G V Dias da Silva S E Ulloa and T V ShahbazyanPhys Rev B 72 125327 (2005)

8 R A Roumlmer and M E Raikh Phys Rev B 62 7045 (2000)9 A Chaplik JETP Lett 62 900 (1995)10 M Grochol F Grosse and R Zimmermann Phys Rev B

74 115416 (2006)11 E Ribeiro A O Govorov W Carvalho and G Medeiros-Ribeiro

Phys Rev Lett 92 126402 (2004)

12 I R Sellers V R Whiteside I L Kuskovsky A O Govorov andB D Mccombe Phys Rev Lett 100 136405 (2008)

13 M D Teodoro V L Campo Jr V Lopez-Richard E Marega JrG E Marques Y Galvatildeo Gobato F Iikawa M J S P Brasil Z YAbuWaar V G Dorogan Yu I Mazur M Benamara and G JSalamo Phys Rev Lett 104 086401 (2010)

14 F Ding L Wang S Kiravittaya E Muumlller A Rastelli and O GSchmidt Appl Phys Lett 90 173104 (2007)

15 F Ding N Akopian B Li U Perinetti A Govorov F M PeetersC C Bof Bufon C Deneke Y H Chen A Rastelli O G Schmidtand V Zwiller Phys Rev B 82 075309 (2010)

16 D G Hill K L Lear and J S Harris Jr J Electrochem Soc137 2912 (1990)

17 S-J Paik J Kim S Park S Kim C Koo S-K Lee and D DCho 42 326 (2003)

18 Z M Wang L Zhang K Holmes and G J Salamo Appl PhysLett 86 143106 (2005)

19 B N Zvonkov I A Karpovich N V Baidus D O Filatov S VMorozov and Y Y Gushina Nanotechnology 11 221 (2000)

20 L Wang A Rastelli S Kiravittaya P Atkinson F Ding C C BofBufon C Hermannstaumldter M Witzany G J Beirne P Michler andO G Schmidt New J Phys 10 045010 (2008)

21 R J Warburton C Schaflein D Haft F Bickel A LorkeK Karrai J M Garcia W Schoenfeld and P M Petroff Nature405 926 (2000)

22 B D Gerardot S Seidl P A Dalgarno R J Warburton D Grana-dos J M Garcia K Kowalik O Krebs K Karrai A Badolatoand P M Petroff Appl Phys Lett 90 041101 (2007)

23 T-C Lin C-H Lin H-S Ling Y-J Fu W-H Chang S-D Linand C-P Lee Phys Rev B 80 081304 (2009)

24 T Kuroda T Belhadj T Mano B Urbaszek T Amand X MarieS Sanguinetti K Sakoda and N Koguchi Phys Stat Sol (b)246 861 (2009)

25 M Korkusinski P Hawrylak and M Bayer Phys Stat Sol (b)234 273 (2002)

26 F Ding R Singh J D Plumhof T Zander V Kraacutepek Y H ChenM Benyoucef V Zwiller K Doumlrr G Bester A Rastelli and O GSchmidt Phys Rev Lett 104 067405 (2010)

27 M-F Tsai H Lin C-H Lin S-D Lin S-Y Wang M-C Lo S-JCheng M-C Lee and W-H Chang Phys Rev Lett 101 267402(2008)

28 V M Fomin V N Gladilin J T Devreese N A J M KleemansM Bozkurt and P M Koenraad Phys Stat Sol (b) 245 2657(2008)

29 M Bayer M Korkusinski P Hawrylak T Gutbrod M Michel andA Forchel Phys Rev Lett 90 186801 (2003)

30 R J Warburton C Schulhauser D Haft C Schaumlflein K KarraiJ M Garcia W Schoenfeld and P M Petroff Phys Rev B65 113303 (2002)

Received 28 September 2010 Accepted 26 November 2010

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

a forward bias Vg is scanned from 03 to 032 V (withsteps of 05 mV) the PL emission energy of a single QRis tuned by about 30 eV (see Fig 3(b)) We observe thatin contrast to the discretized raw data (diamond points)the Lorentzian fit data show a smooth blue-shift of thepeak positions (round points) We plot the 95 predictionband of the fit function in Figure 3(b) (solid lines) fromwhich an error of plusmn15 eV for this Lorentzian analysisprocedure is estimated For the evaluation of the system-atic error repeated measurements (B field increasing anddecreasing) are performed on the same QR and the fitpeak positions are reproducible to within plusmn25 eV Wecan therefore expect an overall error of plusmn25 eV in thepeak-determination procedure used in this workTo further support the validity of this peak determina-

tion procedure we perform the FSS measurements for Xand XX lines (Fig 3(c)) The data points are given byLorentzian fits with an uncertainty of 25 eV Solid linesin the exciton and biexciton plots are sine wave fittingcurves As expected X and XX show anti-correlated shiftsas we rotate the half-wave plate The FSS of this QD isonly 13 eV which is near the resolution limit of our PLsystem and would be undetectable without the Lorentzianfitting processA magnetic field up to 9 T is applied along the sample

growth direction and we observe the characteristic Zee-man splitting as well as the diamagnetic shift of the PLemission energy (see Fig 4(a)) similar to previous reportson single QRs23 In Figure 4(b) we plot the neutral excitonemission energies of the QR after averaging the emissionenergy values of the Zeeman split lines It is observed

0

15

00

05

10

Nor

m P

L I

nt

Ene

rgy

(microeV

)

ndash15

(c)

(d)

13484

13488

13492

13496

PL e

nerg

y (e

V)

13483

13485

13487

13489

Quantum ring(3 nm etched)

(b)

(a)

Magnetic field (T)0 2 4 6 8 10

Magnetic field (T)0 2 4 6 8 10

Fig 4 Fitted PL peak position versus B field before (a) and after (c) averaging the Zeeman splitting for the neutral exciton emission in a 3 nm-etchedQR The blue dashed line in (b) indicates a parabolic fit Oscillations in PL energy and corresponding normalized PL intensity as a function of B fieldare shown in (c) and (d) respectively The solid lines represent the smoothed data using a Savitzky-Golay filter The arrows in (b) and (d) indicatechanges in the ground state transitions

that the emission energy does not scale quadratically withincreasing B field From its shape Figure 4(b) looks quitesimilar to the one shown in a very recent report13 inwhich AB oscillations in ensemble InAsGaAs QRs wereobserved However the diamagnetic shift for a single QRstudied in our work is sim6 times smaller than the valuefor the ensemble QRs in Ref [13] and the oscillationamplitude is much smaller Also no Zeeman splitting wasobserved in Ref [13] because of the broad ensemble emis-sion In order to visualize the magnetic field induced oscil-lations we subtract a single parabola from Figure 4(b) andplot the results in Figure 4(c) We observe two maxima atsim4 T and sim7 T (the solid line here which represents thesmoothed data using a Savitzky-Golay filter is guide to theeye) suggesting changes in the ground state transitionsAnother significant feature observed is the decrease

in PL intensity with increasing magnetic field seeFigure 4(d) The change in PL intensity is one of thesignatures expected for a QR and is attributed to oscilla-tions in the ground state transitions611ndash13 Two knees canbe observed at sim4 T and sim7 T (Fig 4(c)) which cor-respond well with the peak energy oscillation maxima inFigure 4(c) (indicated by arrows)All the observations here are well above the system

resolution and they strongly contrast with the experimen-tal results on a conventional QD where no peak energyoscillation and PL intensity quenching were observed seeRef [15] Especially the PL intensity of this QR quenchesby more than 70 with increasing magnetic field whichis confirmed by repeating the measurements and similarobservations in other QRs A recent study on single GaAs

54 J Nanoelectron Optoelectron 6 51ndash57 2011

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Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

QR obtained by droplet epitaxy also revealed a signifi-cant reduction in the PL intensity by more than 20 atB gt 6 T24 the exciton AB effect may account for theobservation

23 Gate-Controlled Oscillations

We use the above mentioned gated-QR structure to demon-strate the possibility of controlling the observed effect withan external electric field The oscillations for a single QR(with a nominal AsBr3 etching depth of 3 nm) under aforward bias of 28 V are clearly seen in Figure 5(a) withthe two transition points at 26 T and 8 T The PL intensityalso shows similar quenching behavior as in Figure 4(d)(not shown here) When we decrease the bias from 28 V to08 V it is clear that the transition points shift smoothly tohigher magnetic fields (Fig 5(b)) indicating that the effec-tive radii of the electron and the hole are modified by theexternal gate potential The PL intensity is also stronglymodified at different electric fields which is a consequenceof the QCSE At sim18 V the PL intensity reaches an over-all maximum and then decreases see Ref [15] Interest-ingly the PL intensity at 18 V shows clear modulation bythe magnetic field ie first quenches by more than 25

Fig 5 (a) Under a forward bias of 28 V the PL energy shows cleartransitions at sim26 T and sim8 T (b) When the bias changes from 28 Vto 08 V the transitions shift smoothly to higher magnetic fields (c) At18 V the PL energy shows transitions at sim3 T and sim82 T while thenormalized PL intensity also shows oscillations

and then recovers fully to its original value with increasingmagnetic field (Fig 5(c)) This observation is quite simi-lar to the long-existed theoretical prediction for a weaklybound neutral exciton confined in a QR6

3 DISCUSSIONS

Previous theoretical works distinguish between excitonscomposed of strongly and weakly bound electronndashholepairs6 In Ref [7] the effectiveness of the electronndashholeCoulomb interaction is expressed as

vq =e2

rradicReRh

Qqminus12

(1+ ReminusRh

2ReRh

)(1)

where r is the dielectric constant and Qx is the Leg-endre function In the strongly bound regime where vq isdominant the exciton moves along the ring as one tightlybound particle and AB effect manifests itself in a brightto dark transition in the ground state with increasing mag-netic field While in the opposite limit of a weakly boundelectronndashhole pair an interesting modulation between dif-ferent bright and dark states should appear The electronndashhole pairs in above-mentioned QRs are close to the weaklybound regime this is because(i) in the ring geometry the ratio of Coulomb to kineticenergies is proportional to the ring radius while for smallrings (R lt alowast the effective Bohr radius) the quantizationdue to kinetic motion is strong625 and the effectiveness ofvq becomes weaker(ii) in our structure the n-doped layer which locates 20 nmunder the QRs (also the metal contact in the gated struc-ture) can sufficiently screen the effectiveness of vq

7

(iii) in experiment we also observe that the changes in thebinding energies EBXX asymp EBX

+ when E changes(not shown here) indicating that the strongly confinedfew-particle picture is valid in our QRs and the effectiveradii of electron and hole are very different2627

However the theory in Ref [6] is not sufficient toexplain our results We model a simplified QR as depictedin Figure 2 with the main aim to explain the gate-controlled oscillation effect (Fig 5) The ground stateenergy of the neutral exciton inside the In1minusxGaxAs ring(surrounded by GaAs barrier) is calculated within theconfiguration interaction (CI) method For simplicity thepresence of a wetting layer azimuthal anisotropy28 andstructural asymmetry23 are not included in calculationMore details of the calculation can be found in Ref [15]The indium composition inside the ring and the large

lattice mismatch between the ring and barrier materialsresult in a considerably large strain and this strain hasa different effect on the electron and hole confinementpotential With finite element methods we can calculate thestrain induced shift to the band offset Uc and Uv Note thatwe take the opposite value of the hole confinement poten-tial so that the larger value of Uv stands for higher energy

J Nanoelectron Optoelectron 6 51ndash57 2011 55

Delivered by Ingenta toAlexander BalandinIP 16923512206

Fri 06 May 2011 211221

RESEARCH

ARTIC

LE

Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

Z

Uv Uc UcUv

Fig 6 (a) Strain induced shift to the band offset Uc and Uv along horizontal direction and (b) along vertical direction Z The inset shows halfcross-section of the QR structure The effective radius of the electron (c) and the hole (d) is calculated at two different electric fields (e) The radiusex = mh+memh lt e gt

2 +me lt h gt205 shows similar behavior to e

We plot Uc and Uv along different directions and Z inFigures 6(a and b) It is clear that the strain induced bandoffset for the electron is smaller in the area with smaller and Z while for the hole the top area of the QR has thelowest value So the presence of strain makes the electronand the hole apart from each other which is important forthe observation of the neutral exciton AB effectWe now examine the effects of electric field and mag-

netic field on the effective radius of the electron (hole)e (h) From Figure 6(c) we know that with decreas-ing vertical electric field from 200 kVcm to 20 kVcmthe electron is attracted to the bottom area of the ringdecreasing its effective radius while the hole is pushedto the top of the ring and its effective radius increases(Fig 6(d)) However from the change of e and halone we can not conclude that the period of the AB oscil-lation decreases Theoretical study reveals that the oscil-lation comes from a change in the value of the angularmomentum pair (le lh) not from the single electron orhole angular momentum The period of the oscillation isnot only related to the effective radius of the electron andthe hole but also to their effective massesIn our calculation it is found that the magnetic field

at which the first transition takes place is proportional toe2

ex where 12ex = mhe2+mee2me+mh

We plot ex as a function of magnetic field for differ-ent values of electric field in Figure 6(e) Because theeffective mass of the hole is much larger than that ofthe electron (also because the electron and the hole radiichange within the same magnitude) ex should have a

similar behavior as the electron effective radius e Thisis clearly observed in Figure 6(e) and ex decreases mono-tonically with decreasing electric field As a result the firsttransition takes place at a higher magnetic field when wedecrease the electric field (see Fig 5(b)) The explanationfor the second transition is similar although the formulafor the magnetic field at which it takes place is different(it also has the dominant term mhe2) which shifts tohigher magnetic field when the electric field decreasesPrevious reports revealed that the PL intensity also

oscillates with magnetic field and the oscillation ampli-tudes are around 5sim101213 This should explain theintensity oscillation in Figure 5(c) However for the QRsstudied in Figures 4 and 5 (at 28 V) we observe strongquenching in the PL intensity This phenomenon originatespartly from the AB-like quantum interference effect butthere is also contribution from the imperfect ring geome-try Grochol et al demonstrated that even a slightly eccen-tric ring geometry can smooth the oscillations and rendersthe total angular momentum a non-well defined quantumnumber10 The selection rules are only strictly applicablein a system with perfect rotational symmetry and at highmagnetic fields an oscillator strength transfer is expectedbetween excitonic bright states and dark states

4 CONCLUSION

In conclusion we fabricate a novel self-assembledIn(Ga)AsGaAs QR structure by MBE combined within situ AsBr3 etching The morphology of In(Ga)As

56 J Nanoelectron Optoelectron 6 51ndash57 2011

Delivered by Ingenta toAlexander BalandinIP 16923512206

Fri 06 May 2011 211221

RESEARCH

ARTIC

LE

Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

nanostructures embedded in GaAs matrix is unveiled byselective wet chemical etching combined with AFM andwe find that the structural parameters of the QRs can bewell controlled by the AsBr3 etching depth Single neu-tral excitons confined in the volcano-like QRs are stud-ied by magneto-photoluminescence Oscillations in bothPL energy and intensity are observed under an appliedmagnetic field We also show that the oscillations can betuned by applying a vertical electric field which modifiesthe electron and hole effective radii Although the experi-mental features are not fully understood yet a theoreticalinvestigation is able to explain the main results We con-clude that the exciton Aharonov-Bohm effect may accountfor the observed effects

Acknowledgment We acknowledge L PKouwenhoven and Z G Wang for support C C BofBufon C Deneke V Fomin A Govorov S Kiravittayaand Wen-Hao Chang for their help and discussions Weare grateful for the financial support of NWO (VIDI)the CAS-MPG programm the DFG (FOR730) BMBF(No 01BM459) NSFC China (60625402) and FlemishScience Foundation (FWO-Vl)

References and Notes

1 Y Aharonov and D Bohm Phys Rev 115 485 (1959)2 S Popescu Nat Phys 6 151 (2010)3 A G Aronov and Y Sharvin Rev Mod Phys 59 755 (1987)4 S Zaric G N Ostojic J Kono J Shaver V C Moore M S

Strano R H Hauge R E Smalley and X Wei Science 304 1129(2004)

5 A Fuhrer S Luscher T Ihn T Heinzel K EnsslinW Wegscheider and M Bichler Nature 413 822 (2001)

6 A O Govorov S E Ulloa K Karrai and R J Warburton PhysRev B 66 081309 (2002)

7 Luis G G V Dias da Silva S E Ulloa and T V ShahbazyanPhys Rev B 72 125327 (2005)

8 R A Roumlmer and M E Raikh Phys Rev B 62 7045 (2000)9 A Chaplik JETP Lett 62 900 (1995)10 M Grochol F Grosse and R Zimmermann Phys Rev B

74 115416 (2006)11 E Ribeiro A O Govorov W Carvalho and G Medeiros-Ribeiro

Phys Rev Lett 92 126402 (2004)

12 I R Sellers V R Whiteside I L Kuskovsky A O Govorov andB D Mccombe Phys Rev Lett 100 136405 (2008)

13 M D Teodoro V L Campo Jr V Lopez-Richard E Marega JrG E Marques Y Galvatildeo Gobato F Iikawa M J S P Brasil Z YAbuWaar V G Dorogan Yu I Mazur M Benamara and G JSalamo Phys Rev Lett 104 086401 (2010)

14 F Ding L Wang S Kiravittaya E Muumlller A Rastelli and O GSchmidt Appl Phys Lett 90 173104 (2007)

15 F Ding N Akopian B Li U Perinetti A Govorov F M PeetersC C Bof Bufon C Deneke Y H Chen A Rastelli O G Schmidtand V Zwiller Phys Rev B 82 075309 (2010)

16 D G Hill K L Lear and J S Harris Jr J Electrochem Soc137 2912 (1990)

17 S-J Paik J Kim S Park S Kim C Koo S-K Lee and D DCho 42 326 (2003)

18 Z M Wang L Zhang K Holmes and G J Salamo Appl PhysLett 86 143106 (2005)

19 B N Zvonkov I A Karpovich N V Baidus D O Filatov S VMorozov and Y Y Gushina Nanotechnology 11 221 (2000)

20 L Wang A Rastelli S Kiravittaya P Atkinson F Ding C C BofBufon C Hermannstaumldter M Witzany G J Beirne P Michler andO G Schmidt New J Phys 10 045010 (2008)

21 R J Warburton C Schaflein D Haft F Bickel A LorkeK Karrai J M Garcia W Schoenfeld and P M Petroff Nature405 926 (2000)

22 B D Gerardot S Seidl P A Dalgarno R J Warburton D Grana-dos J M Garcia K Kowalik O Krebs K Karrai A Badolatoand P M Petroff Appl Phys Lett 90 041101 (2007)

23 T-C Lin C-H Lin H-S Ling Y-J Fu W-H Chang S-D Linand C-P Lee Phys Rev B 80 081304 (2009)

24 T Kuroda T Belhadj T Mano B Urbaszek T Amand X MarieS Sanguinetti K Sakoda and N Koguchi Phys Stat Sol (b)246 861 (2009)

25 M Korkusinski P Hawrylak and M Bayer Phys Stat Sol (b)234 273 (2002)

26 F Ding R Singh J D Plumhof T Zander V Kraacutepek Y H ChenM Benyoucef V Zwiller K Doumlrr G Bester A Rastelli and O GSchmidt Phys Rev Lett 104 067405 (2010)

27 M-F Tsai H Lin C-H Lin S-D Lin S-Y Wang M-C Lo S-JCheng M-C Lee and W-H Chang Phys Rev Lett 101 267402(2008)

28 V M Fomin V N Gladilin J T Devreese N A J M KleemansM Bozkurt and P M Koenraad Phys Stat Sol (b) 245 2657(2008)

29 M Bayer M Korkusinski P Hawrylak T Gutbrod M Michel andA Forchel Phys Rev Lett 90 186801 (2003)

30 R J Warburton C Schulhauser D Haft C Schaumlflein K KarraiJ M Garcia W Schoenfeld and P M Petroff Phys Rev B65 113303 (2002)

Received 28 September 2010 Accepted 26 November 2010

J Nanoelectron Optoelectron 6 51ndash57 2011 57

Delivered by Ingenta toAlexander BalandinIP 16923512206

Fri 06 May 2011 211221

RESEARCH

ARTIC

LE

Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

QR obtained by droplet epitaxy also revealed a signifi-cant reduction in the PL intensity by more than 20 atB gt 6 T24 the exciton AB effect may account for theobservation

23 Gate-Controlled Oscillations

We use the above mentioned gated-QR structure to demon-strate the possibility of controlling the observed effect withan external electric field The oscillations for a single QR(with a nominal AsBr3 etching depth of 3 nm) under aforward bias of 28 V are clearly seen in Figure 5(a) withthe two transition points at 26 T and 8 T The PL intensityalso shows similar quenching behavior as in Figure 4(d)(not shown here) When we decrease the bias from 28 V to08 V it is clear that the transition points shift smoothly tohigher magnetic fields (Fig 5(b)) indicating that the effec-tive radii of the electron and the hole are modified by theexternal gate potential The PL intensity is also stronglymodified at different electric fields which is a consequenceof the QCSE At sim18 V the PL intensity reaches an over-all maximum and then decreases see Ref [15] Interest-ingly the PL intensity at 18 V shows clear modulation bythe magnetic field ie first quenches by more than 25

Fig 5 (a) Under a forward bias of 28 V the PL energy shows cleartransitions at sim26 T and sim8 T (b) When the bias changes from 28 Vto 08 V the transitions shift smoothly to higher magnetic fields (c) At18 V the PL energy shows transitions at sim3 T and sim82 T while thenormalized PL intensity also shows oscillations

and then recovers fully to its original value with increasingmagnetic field (Fig 5(c)) This observation is quite simi-lar to the long-existed theoretical prediction for a weaklybound neutral exciton confined in a QR6

3 DISCUSSIONS

Previous theoretical works distinguish between excitonscomposed of strongly and weakly bound electronndashholepairs6 In Ref [7] the effectiveness of the electronndashholeCoulomb interaction is expressed as

vq =e2

rradicReRh

Qqminus12

(1+ ReminusRh

2ReRh

)(1)

where r is the dielectric constant and Qx is the Leg-endre function In the strongly bound regime where vq isdominant the exciton moves along the ring as one tightlybound particle and AB effect manifests itself in a brightto dark transition in the ground state with increasing mag-netic field While in the opposite limit of a weakly boundelectronndashhole pair an interesting modulation between dif-ferent bright and dark states should appear The electronndashhole pairs in above-mentioned QRs are close to the weaklybound regime this is because(i) in the ring geometry the ratio of Coulomb to kineticenergies is proportional to the ring radius while for smallrings (R lt alowast the effective Bohr radius) the quantizationdue to kinetic motion is strong625 and the effectiveness ofvq becomes weaker(ii) in our structure the n-doped layer which locates 20 nmunder the QRs (also the metal contact in the gated struc-ture) can sufficiently screen the effectiveness of vq

7

(iii) in experiment we also observe that the changes in thebinding energies EBXX asymp EBX

+ when E changes(not shown here) indicating that the strongly confinedfew-particle picture is valid in our QRs and the effectiveradii of electron and hole are very different2627

However the theory in Ref [6] is not sufficient toexplain our results We model a simplified QR as depictedin Figure 2 with the main aim to explain the gate-controlled oscillation effect (Fig 5) The ground stateenergy of the neutral exciton inside the In1minusxGaxAs ring(surrounded by GaAs barrier) is calculated within theconfiguration interaction (CI) method For simplicity thepresence of a wetting layer azimuthal anisotropy28 andstructural asymmetry23 are not included in calculationMore details of the calculation can be found in Ref [15]The indium composition inside the ring and the large

lattice mismatch between the ring and barrier materialsresult in a considerably large strain and this strain hasa different effect on the electron and hole confinementpotential With finite element methods we can calculate thestrain induced shift to the band offset Uc and Uv Note thatwe take the opposite value of the hole confinement poten-tial so that the larger value of Uv stands for higher energy

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RESEARCH

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Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

Z

Uv Uc UcUv

Fig 6 (a) Strain induced shift to the band offset Uc and Uv along horizontal direction and (b) along vertical direction Z The inset shows halfcross-section of the QR structure The effective radius of the electron (c) and the hole (d) is calculated at two different electric fields (e) The radiusex = mh+memh lt e gt

2 +me lt h gt205 shows similar behavior to e

We plot Uc and Uv along different directions and Z inFigures 6(a and b) It is clear that the strain induced bandoffset for the electron is smaller in the area with smaller and Z while for the hole the top area of the QR has thelowest value So the presence of strain makes the electronand the hole apart from each other which is important forthe observation of the neutral exciton AB effectWe now examine the effects of electric field and mag-

netic field on the effective radius of the electron (hole)e (h) From Figure 6(c) we know that with decreas-ing vertical electric field from 200 kVcm to 20 kVcmthe electron is attracted to the bottom area of the ringdecreasing its effective radius while the hole is pushedto the top of the ring and its effective radius increases(Fig 6(d)) However from the change of e and halone we can not conclude that the period of the AB oscil-lation decreases Theoretical study reveals that the oscil-lation comes from a change in the value of the angularmomentum pair (le lh) not from the single electron orhole angular momentum The period of the oscillation isnot only related to the effective radius of the electron andthe hole but also to their effective massesIn our calculation it is found that the magnetic field

at which the first transition takes place is proportional toe2

ex where 12ex = mhe2+mee2me+mh

We plot ex as a function of magnetic field for differ-ent values of electric field in Figure 6(e) Because theeffective mass of the hole is much larger than that ofthe electron (also because the electron and the hole radiichange within the same magnitude) ex should have a

similar behavior as the electron effective radius e Thisis clearly observed in Figure 6(e) and ex decreases mono-tonically with decreasing electric field As a result the firsttransition takes place at a higher magnetic field when wedecrease the electric field (see Fig 5(b)) The explanationfor the second transition is similar although the formulafor the magnetic field at which it takes place is different(it also has the dominant term mhe2) which shifts tohigher magnetic field when the electric field decreasesPrevious reports revealed that the PL intensity also

oscillates with magnetic field and the oscillation ampli-tudes are around 5sim101213 This should explain theintensity oscillation in Figure 5(c) However for the QRsstudied in Figures 4 and 5 (at 28 V) we observe strongquenching in the PL intensity This phenomenon originatespartly from the AB-like quantum interference effect butthere is also contribution from the imperfect ring geome-try Grochol et al demonstrated that even a slightly eccen-tric ring geometry can smooth the oscillations and rendersthe total angular momentum a non-well defined quantumnumber10 The selection rules are only strictly applicablein a system with perfect rotational symmetry and at highmagnetic fields an oscillator strength transfer is expectedbetween excitonic bright states and dark states

4 CONCLUSION

In conclusion we fabricate a novel self-assembledIn(Ga)AsGaAs QR structure by MBE combined within situ AsBr3 etching The morphology of In(Ga)As

56 J Nanoelectron Optoelectron 6 51ndash57 2011

Delivered by Ingenta toAlexander BalandinIP 16923512206

Fri 06 May 2011 211221

RESEARCH

ARTIC

LE

Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

nanostructures embedded in GaAs matrix is unveiled byselective wet chemical etching combined with AFM andwe find that the structural parameters of the QRs can bewell controlled by the AsBr3 etching depth Single neu-tral excitons confined in the volcano-like QRs are stud-ied by magneto-photoluminescence Oscillations in bothPL energy and intensity are observed under an appliedmagnetic field We also show that the oscillations can betuned by applying a vertical electric field which modifiesthe electron and hole effective radii Although the experi-mental features are not fully understood yet a theoreticalinvestigation is able to explain the main results We con-clude that the exciton Aharonov-Bohm effect may accountfor the observed effects

Acknowledgment We acknowledge L PKouwenhoven and Z G Wang for support C C BofBufon C Deneke V Fomin A Govorov S Kiravittayaand Wen-Hao Chang for their help and discussions Weare grateful for the financial support of NWO (VIDI)the CAS-MPG programm the DFG (FOR730) BMBF(No 01BM459) NSFC China (60625402) and FlemishScience Foundation (FWO-Vl)

References and Notes

1 Y Aharonov and D Bohm Phys Rev 115 485 (1959)2 S Popescu Nat Phys 6 151 (2010)3 A G Aronov and Y Sharvin Rev Mod Phys 59 755 (1987)4 S Zaric G N Ostojic J Kono J Shaver V C Moore M S

Strano R H Hauge R E Smalley and X Wei Science 304 1129(2004)

5 A Fuhrer S Luscher T Ihn T Heinzel K EnsslinW Wegscheider and M Bichler Nature 413 822 (2001)

6 A O Govorov S E Ulloa K Karrai and R J Warburton PhysRev B 66 081309 (2002)

7 Luis G G V Dias da Silva S E Ulloa and T V ShahbazyanPhys Rev B 72 125327 (2005)

8 R A Roumlmer and M E Raikh Phys Rev B 62 7045 (2000)9 A Chaplik JETP Lett 62 900 (1995)10 M Grochol F Grosse and R Zimmermann Phys Rev B

74 115416 (2006)11 E Ribeiro A O Govorov W Carvalho and G Medeiros-Ribeiro

Phys Rev Lett 92 126402 (2004)

12 I R Sellers V R Whiteside I L Kuskovsky A O Govorov andB D Mccombe Phys Rev Lett 100 136405 (2008)

13 M D Teodoro V L Campo Jr V Lopez-Richard E Marega JrG E Marques Y Galvatildeo Gobato F Iikawa M J S P Brasil Z YAbuWaar V G Dorogan Yu I Mazur M Benamara and G JSalamo Phys Rev Lett 104 086401 (2010)

14 F Ding L Wang S Kiravittaya E Muumlller A Rastelli and O GSchmidt Appl Phys Lett 90 173104 (2007)

15 F Ding N Akopian B Li U Perinetti A Govorov F M PeetersC C Bof Bufon C Deneke Y H Chen A Rastelli O G Schmidtand V Zwiller Phys Rev B 82 075309 (2010)

16 D G Hill K L Lear and J S Harris Jr J Electrochem Soc137 2912 (1990)

17 S-J Paik J Kim S Park S Kim C Koo S-K Lee and D DCho 42 326 (2003)

18 Z M Wang L Zhang K Holmes and G J Salamo Appl PhysLett 86 143106 (2005)

19 B N Zvonkov I A Karpovich N V Baidus D O Filatov S VMorozov and Y Y Gushina Nanotechnology 11 221 (2000)

20 L Wang A Rastelli S Kiravittaya P Atkinson F Ding C C BofBufon C Hermannstaumldter M Witzany G J Beirne P Michler andO G Schmidt New J Phys 10 045010 (2008)

21 R J Warburton C Schaflein D Haft F Bickel A LorkeK Karrai J M Garcia W Schoenfeld and P M Petroff Nature405 926 (2000)

22 B D Gerardot S Seidl P A Dalgarno R J Warburton D Grana-dos J M Garcia K Kowalik O Krebs K Karrai A Badolatoand P M Petroff Appl Phys Lett 90 041101 (2007)

23 T-C Lin C-H Lin H-S Ling Y-J Fu W-H Chang S-D Linand C-P Lee Phys Rev B 80 081304 (2009)

24 T Kuroda T Belhadj T Mano B Urbaszek T Amand X MarieS Sanguinetti K Sakoda and N Koguchi Phys Stat Sol (b)246 861 (2009)

25 M Korkusinski P Hawrylak and M Bayer Phys Stat Sol (b)234 273 (2002)

26 F Ding R Singh J D Plumhof T Zander V Kraacutepek Y H ChenM Benyoucef V Zwiller K Doumlrr G Bester A Rastelli and O GSchmidt Phys Rev Lett 104 067405 (2010)

27 M-F Tsai H Lin C-H Lin S-D Lin S-Y Wang M-C Lo S-JCheng M-C Lee and W-H Chang Phys Rev Lett 101 267402(2008)

28 V M Fomin V N Gladilin J T Devreese N A J M KleemansM Bozkurt and P M Koenraad Phys Stat Sol (b) 245 2657(2008)

29 M Bayer M Korkusinski P Hawrylak T Gutbrod M Michel andA Forchel Phys Rev Lett 90 186801 (2003)

30 R J Warburton C Schulhauser D Haft C Schaumlflein K KarraiJ M Garcia W Schoenfeld and P M Petroff Phys Rev B65 113303 (2002)

Received 28 September 2010 Accepted 26 November 2010

J Nanoelectron Optoelectron 6 51ndash57 2011 57

Delivered by Ingenta toAlexander BalandinIP 16923512206

Fri 06 May 2011 211221

RESEARCH

ARTIC

LE

Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings Ding et al

Z

Uv Uc UcUv

Fig 6 (a) Strain induced shift to the band offset Uc and Uv along horizontal direction and (b) along vertical direction Z The inset shows halfcross-section of the QR structure The effective radius of the electron (c) and the hole (d) is calculated at two different electric fields (e) The radiusex = mh+memh lt e gt

2 +me lt h gt205 shows similar behavior to e

We plot Uc and Uv along different directions and Z inFigures 6(a and b) It is clear that the strain induced bandoffset for the electron is smaller in the area with smaller and Z while for the hole the top area of the QR has thelowest value So the presence of strain makes the electronand the hole apart from each other which is important forthe observation of the neutral exciton AB effectWe now examine the effects of electric field and mag-

netic field on the effective radius of the electron (hole)e (h) From Figure 6(c) we know that with decreas-ing vertical electric field from 200 kVcm to 20 kVcmthe electron is attracted to the bottom area of the ringdecreasing its effective radius while the hole is pushedto the top of the ring and its effective radius increases(Fig 6(d)) However from the change of e and halone we can not conclude that the period of the AB oscil-lation decreases Theoretical study reveals that the oscil-lation comes from a change in the value of the angularmomentum pair (le lh) not from the single electron orhole angular momentum The period of the oscillation isnot only related to the effective radius of the electron andthe hole but also to their effective massesIn our calculation it is found that the magnetic field

at which the first transition takes place is proportional toe2

ex where 12ex = mhe2+mee2me+mh

We plot ex as a function of magnetic field for differ-ent values of electric field in Figure 6(e) Because theeffective mass of the hole is much larger than that ofthe electron (also because the electron and the hole radiichange within the same magnitude) ex should have a

similar behavior as the electron effective radius e Thisis clearly observed in Figure 6(e) and ex decreases mono-tonically with decreasing electric field As a result the firsttransition takes place at a higher magnetic field when wedecrease the electric field (see Fig 5(b)) The explanationfor the second transition is similar although the formulafor the magnetic field at which it takes place is different(it also has the dominant term mhe2) which shifts tohigher magnetic field when the electric field decreasesPrevious reports revealed that the PL intensity also

oscillates with magnetic field and the oscillation ampli-tudes are around 5sim101213 This should explain theintensity oscillation in Figure 5(c) However for the QRsstudied in Figures 4 and 5 (at 28 V) we observe strongquenching in the PL intensity This phenomenon originatespartly from the AB-like quantum interference effect butthere is also contribution from the imperfect ring geome-try Grochol et al demonstrated that even a slightly eccen-tric ring geometry can smooth the oscillations and rendersthe total angular momentum a non-well defined quantumnumber10 The selection rules are only strictly applicablein a system with perfect rotational symmetry and at highmagnetic fields an oscillator strength transfer is expectedbetween excitonic bright states and dark states

4 CONCLUSION

In conclusion we fabricate a novel self-assembledIn(Ga)AsGaAs QR structure by MBE combined within situ AsBr3 etching The morphology of In(Ga)As

56 J Nanoelectron Optoelectron 6 51ndash57 2011

Delivered by Ingenta toAlexander BalandinIP 16923512206

Fri 06 May 2011 211221

RESEARCH

ARTIC

LE

Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

nanostructures embedded in GaAs matrix is unveiled byselective wet chemical etching combined with AFM andwe find that the structural parameters of the QRs can bewell controlled by the AsBr3 etching depth Single neu-tral excitons confined in the volcano-like QRs are stud-ied by magneto-photoluminescence Oscillations in bothPL energy and intensity are observed under an appliedmagnetic field We also show that the oscillations can betuned by applying a vertical electric field which modifiesthe electron and hole effective radii Although the experi-mental features are not fully understood yet a theoreticalinvestigation is able to explain the main results We con-clude that the exciton Aharonov-Bohm effect may accountfor the observed effects

Acknowledgment We acknowledge L PKouwenhoven and Z G Wang for support C C BofBufon C Deneke V Fomin A Govorov S Kiravittayaand Wen-Hao Chang for their help and discussions Weare grateful for the financial support of NWO (VIDI)the CAS-MPG programm the DFG (FOR730) BMBF(No 01BM459) NSFC China (60625402) and FlemishScience Foundation (FWO-Vl)

References and Notes

1 Y Aharonov and D Bohm Phys Rev 115 485 (1959)2 S Popescu Nat Phys 6 151 (2010)3 A G Aronov and Y Sharvin Rev Mod Phys 59 755 (1987)4 S Zaric G N Ostojic J Kono J Shaver V C Moore M S

Strano R H Hauge R E Smalley and X Wei Science 304 1129(2004)

5 A Fuhrer S Luscher T Ihn T Heinzel K EnsslinW Wegscheider and M Bichler Nature 413 822 (2001)

6 A O Govorov S E Ulloa K Karrai and R J Warburton PhysRev B 66 081309 (2002)

7 Luis G G V Dias da Silva S E Ulloa and T V ShahbazyanPhys Rev B 72 125327 (2005)

8 R A Roumlmer and M E Raikh Phys Rev B 62 7045 (2000)9 A Chaplik JETP Lett 62 900 (1995)10 M Grochol F Grosse and R Zimmermann Phys Rev B

74 115416 (2006)11 E Ribeiro A O Govorov W Carvalho and G Medeiros-Ribeiro

Phys Rev Lett 92 126402 (2004)

12 I R Sellers V R Whiteside I L Kuskovsky A O Govorov andB D Mccombe Phys Rev Lett 100 136405 (2008)

13 M D Teodoro V L Campo Jr V Lopez-Richard E Marega JrG E Marques Y Galvatildeo Gobato F Iikawa M J S P Brasil Z YAbuWaar V G Dorogan Yu I Mazur M Benamara and G JSalamo Phys Rev Lett 104 086401 (2010)

14 F Ding L Wang S Kiravittaya E Muumlller A Rastelli and O GSchmidt Appl Phys Lett 90 173104 (2007)

15 F Ding N Akopian B Li U Perinetti A Govorov F M PeetersC C Bof Bufon C Deneke Y H Chen A Rastelli O G Schmidtand V Zwiller Phys Rev B 82 075309 (2010)

16 D G Hill K L Lear and J S Harris Jr J Electrochem Soc137 2912 (1990)

17 S-J Paik J Kim S Park S Kim C Koo S-K Lee and D DCho 42 326 (2003)

18 Z M Wang L Zhang K Holmes and G J Salamo Appl PhysLett 86 143106 (2005)

19 B N Zvonkov I A Karpovich N V Baidus D O Filatov S VMorozov and Y Y Gushina Nanotechnology 11 221 (2000)

20 L Wang A Rastelli S Kiravittaya P Atkinson F Ding C C BofBufon C Hermannstaumldter M Witzany G J Beirne P Michler andO G Schmidt New J Phys 10 045010 (2008)

21 R J Warburton C Schaflein D Haft F Bickel A LorkeK Karrai J M Garcia W Schoenfeld and P M Petroff Nature405 926 (2000)

22 B D Gerardot S Seidl P A Dalgarno R J Warburton D Grana-dos J M Garcia K Kowalik O Krebs K Karrai A Badolatoand P M Petroff Appl Phys Lett 90 041101 (2007)

23 T-C Lin C-H Lin H-S Ling Y-J Fu W-H Chang S-D Linand C-P Lee Phys Rev B 80 081304 (2009)

24 T Kuroda T Belhadj T Mano B Urbaszek T Amand X MarieS Sanguinetti K Sakoda and N Koguchi Phys Stat Sol (b)246 861 (2009)

25 M Korkusinski P Hawrylak and M Bayer Phys Stat Sol (b)234 273 (2002)

26 F Ding R Singh J D Plumhof T Zander V Kraacutepek Y H ChenM Benyoucef V Zwiller K Doumlrr G Bester A Rastelli and O GSchmidt Phys Rev Lett 104 067405 (2010)

27 M-F Tsai H Lin C-H Lin S-D Lin S-Y Wang M-C Lo S-JCheng M-C Lee and W-H Chang Phys Rev Lett 101 267402(2008)

28 V M Fomin V N Gladilin J T Devreese N A J M KleemansM Bozkurt and P M Koenraad Phys Stat Sol (b) 245 2657(2008)

29 M Bayer M Korkusinski P Hawrylak T Gutbrod M Michel andA Forchel Phys Rev Lett 90 186801 (2003)

30 R J Warburton C Schulhauser D Haft C Schaumlflein K KarraiJ M Garcia W Schoenfeld and P M Petroff Phys Rev B65 113303 (2002)

Received 28 September 2010 Accepted 26 November 2010

J Nanoelectron Optoelectron 6 51ndash57 2011 57

Delivered by Ingenta toAlexander BalandinIP 16923512206

Fri 06 May 2011 211221

RESEARCH

ARTIC

LE

Ding et al Single Neutral Excitons Confined in AsBr3 In Situ Etched InGaAs Quantum Rings

nanostructures embedded in GaAs matrix is unveiled byselective wet chemical etching combined with AFM andwe find that the structural parameters of the QRs can bewell controlled by the AsBr3 etching depth Single neu-tral excitons confined in the volcano-like QRs are stud-ied by magneto-photoluminescence Oscillations in bothPL energy and intensity are observed under an appliedmagnetic field We also show that the oscillations can betuned by applying a vertical electric field which modifiesthe electron and hole effective radii Although the experi-mental features are not fully understood yet a theoreticalinvestigation is able to explain the main results We con-clude that the exciton Aharonov-Bohm effect may accountfor the observed effects

Acknowledgment We acknowledge L PKouwenhoven and Z G Wang for support C C BofBufon C Deneke V Fomin A Govorov S Kiravittayaand Wen-Hao Chang for their help and discussions Weare grateful for the financial support of NWO (VIDI)the CAS-MPG programm the DFG (FOR730) BMBF(No 01BM459) NSFC China (60625402) and FlemishScience Foundation (FWO-Vl)

References and Notes

1 Y Aharonov and D Bohm Phys Rev 115 485 (1959)2 S Popescu Nat Phys 6 151 (2010)3 A G Aronov and Y Sharvin Rev Mod Phys 59 755 (1987)4 S Zaric G N Ostojic J Kono J Shaver V C Moore M S

Strano R H Hauge R E Smalley and X Wei Science 304 1129(2004)

5 A Fuhrer S Luscher T Ihn T Heinzel K EnsslinW Wegscheider and M Bichler Nature 413 822 (2001)

6 A O Govorov S E Ulloa K Karrai and R J Warburton PhysRev B 66 081309 (2002)

7 Luis G G V Dias da Silva S E Ulloa and T V ShahbazyanPhys Rev B 72 125327 (2005)

8 R A Roumlmer and M E Raikh Phys Rev B 62 7045 (2000)9 A Chaplik JETP Lett 62 900 (1995)10 M Grochol F Grosse and R Zimmermann Phys Rev B

74 115416 (2006)11 E Ribeiro A O Govorov W Carvalho and G Medeiros-Ribeiro

Phys Rev Lett 92 126402 (2004)

12 I R Sellers V R Whiteside I L Kuskovsky A O Govorov andB D Mccombe Phys Rev Lett 100 136405 (2008)

13 M D Teodoro V L Campo Jr V Lopez-Richard E Marega JrG E Marques Y Galvatildeo Gobato F Iikawa M J S P Brasil Z YAbuWaar V G Dorogan Yu I Mazur M Benamara and G JSalamo Phys Rev Lett 104 086401 (2010)

14 F Ding L Wang S Kiravittaya E Muumlller A Rastelli and O GSchmidt Appl Phys Lett 90 173104 (2007)

15 F Ding N Akopian B Li U Perinetti A Govorov F M PeetersC C Bof Bufon C Deneke Y H Chen A Rastelli O G Schmidtand V Zwiller Phys Rev B 82 075309 (2010)

16 D G Hill K L Lear and J S Harris Jr J Electrochem Soc137 2912 (1990)

17 S-J Paik J Kim S Park S Kim C Koo S-K Lee and D DCho 42 326 (2003)

18 Z M Wang L Zhang K Holmes and G J Salamo Appl PhysLett 86 143106 (2005)

19 B N Zvonkov I A Karpovich N V Baidus D O Filatov S VMorozov and Y Y Gushina Nanotechnology 11 221 (2000)

20 L Wang A Rastelli S Kiravittaya P Atkinson F Ding C C BofBufon C Hermannstaumldter M Witzany G J Beirne P Michler andO G Schmidt New J Phys 10 045010 (2008)

21 R J Warburton C Schaflein D Haft F Bickel A LorkeK Karrai J M Garcia W Schoenfeld and P M Petroff Nature405 926 (2000)

22 B D Gerardot S Seidl P A Dalgarno R J Warburton D Grana-dos J M Garcia K Kowalik O Krebs K Karrai A Badolatoand P M Petroff Appl Phys Lett 90 041101 (2007)

23 T-C Lin C-H Lin H-S Ling Y-J Fu W-H Chang S-D Linand C-P Lee Phys Rev B 80 081304 (2009)

24 T Kuroda T Belhadj T Mano B Urbaszek T Amand X MarieS Sanguinetti K Sakoda and N Koguchi Phys Stat Sol (b)246 861 (2009)

25 M Korkusinski P Hawrylak and M Bayer Phys Stat Sol (b)234 273 (2002)

26 F Ding R Singh J D Plumhof T Zander V Kraacutepek Y H ChenM Benyoucef V Zwiller K Doumlrr G Bester A Rastelli and O GSchmidt Phys Rev Lett 104 067405 (2010)

27 M-F Tsai H Lin C-H Lin S-D Lin S-Y Wang M-C Lo S-JCheng M-C Lee and W-H Chang Phys Rev Lett 101 267402(2008)

28 V M Fomin V N Gladilin J T Devreese N A J M KleemansM Bozkurt and P M Koenraad Phys Stat Sol (b) 245 2657(2008)

29 M Bayer M Korkusinski P Hawrylak T Gutbrod M Michel andA Forchel Phys Rev Lett 90 186801 (2003)

30 R J Warburton C Schulhauser D Haft C Schaumlflein K KarraiJ M Garcia W Schoenfeld and P M Petroff Phys Rev B65 113303 (2002)

Received 28 September 2010 Accepted 26 November 2010

J Nanoelectron Optoelectron 6 51ndash57 2011 57