PHYSICAL REVIEW B 68, 235301 ~2003!

Continuum transitions and phonon coupling in single self-assembled Stranski-Krastanowquantum dots

R. Oulton1,* J. J. Finley,1,2 A. I. Tartakovskii,1 D. J. Mowbray,1 M. S. Skolnick,1 M. Hopkinson,3 A. Vasanelli,4

R. Ferreira,4 and G. Bastard41Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

2Walter Schottky Institute, Technische Universita¨t Munchen, Garching D85748, Germany3Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom

4Laboratoire de Physique de la Matie`re Condense´e, Ecole Normale Supe´rieure, F75005 Paris, France~Received 19 June 2003; revised manuscript received 2 September 2003; published 3 December 2003!

Continuum transitions in the absorption spectra of self-assembled InGaAs quantum dots are demonstrated tohave an intrinsic origin, and to arise from transitions between the wetting layer quantum well and quantum dotconfined states, in agreement with recent theory predictions. The spectra are shown to fall into two distinctgroups, below 50 meV corresponding to sharp line transitions expected in an ideal atom picture, and above 50meV where coupling of discrete transitions to the continuum is demonstrated. Electric-field-controlled resonantcoupling to LO phonons is also demonstrated.

DOI: 10.1103/PhysRevB.68.235301 PACS number~s!: 78.67.Hc, 73.40.Kp, 73.63.Kv, 78.55.2m

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Semiconductor quantum dots~QDs! are frequently de-scribed as atoms in the solid state.1 This description impliesthat the quantum states and exciton transitions are welllated from the environment in which the dots are embeddSuch isolation from the environment and accompanying lodephasing times underlies much of the present interesQD’s for applications in quantum information processin2

QD’s grown by the Stranski-Krastanow technique havemajor advantage that the quantum dots are embeddedsemiconductor matrix and can be accessed electricallywell as optically, a key point for many applications. However, since the dots are embedded in semiconductor matand furthermore sit on top of an underlying wetting lay~WL! quantum well~QW! from which they form above acritical thickness, potential intrinsic mechanisms exist forteraction of the QD states and transitions with their surrouing environment.

In this paper we identify unambiguously the origincontinuum transitions in the absorption spectra of single sassembled In0.5Ga0.5As QD’s. We demonstrate that they arisfrom ‘‘crossed’’ transitions from the WL QW valence bandthe lowest confined electron state, in agreement with rectheoretical predictions.3 We show that the QD spectra fainto two distinct categories: low-energy transitions up tomeV above the exciton ground state which exhibit shatomlike spectra, and above 50 meV where the onset ofcontinuum is observed. Transitions which overlap the ctinuum exhibit much increased linewidth, strong temperatdependence, and field broadening, all clear evidence forpling of the confined state transitions to their WL enviroment. From field-dependent studies we show that certransitions below 50 meV exhibit coupling to LO phononsthe system, a further breakdown of the ideal atom pictur

The absorption spectra are obtained from photolumincence excitation~PLE! and photocurrent spectroscopy~PC!measurements. The PLE and PC mechanisms are depschematically in Fig. 1~a!. PLE is a three-step processwhich absorption into an excited state is followed by carrrelaxation to the ground state and subsequent photolumi

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cence~PL! emission, whereas in PC, photon absorptionfollowed by tunneling out of the dot leading to a measuracurrent. The experiments were performed on In0.5Ga0.5AsQD’s in a Schottky diode structure on ap1 substrate whichenables vertical electric fields to be applied.4

The PL spectrum from the ground state of dot 1, coposed of a single line,XPL

0 of energy 1232.7 meV is shownin Fig. 2 ~left side! at a field of 90 kV/cm. ImmediatelyaboveXPL

0 , theX0 spectrum in PC is shown at a very similafield, and is composed of a single line at the same energXPL

0 , arising from absorption into theX0 ground state andsubsequent tunneling out of the dot.4,5 Combining the PL andPC data enables the Stark shift of theX0 ground state of

FIG. 1. ~a! Schematic showing processes giving rise to photominescence~PL!, PL excitation and photocurrent under applieelectric field.~b! Energy-band diagram for quantum dot studieddetail.

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R. OULTON et al. PHYSICAL REVIEW B 68, 235301 ~2003!

23.6 meV between 60 and 140 kVcm21 to be obtained.6

The PLE spectrum recorded for detection ofXPL0 is shown

on the right side of Fig. 2~lower!. It is composed of a serieof sharp lines (100–300meV width, experimental resolution;100 meV) at 16, 22, and 34–39 meV aboveX0 withbroader features (;1 meV linewidth! in the 29–32 meV re-gion. Most notably there is no discernible background tospectra in the energy range up to 50meV aboveXPL

0 , incontrast to results of Refs. 7–11. However for higher ene@final 10 meV range of Fig. 2 and 3~dot 1! up to 110 meVaboveX0] a steadily increasing continuum signal with ons50 meV aboveXPL

0 is found, superimposed on which isnumber of closely spaced sharp lines.12 PLE spectra of verysimilar form are found for dots 2 and 3~Fig. 3, X0 energies1269, 1243 meV, respectively!. Even though the ground-statenergies for dots 1, 2, and 3 differ by;40 meV, the onset ofthe continuum is still observed;50 meV aboveXPL

0 , sug-gesting that the continuum arises from properties intrinsicthe dot.

FIG. 2. Lower—PL~left! and PLE~right! for dot 1 at 90 kV/cm.The lower-energy scale is absolute and the upper relative toX0.Middle ~left!—ground-state PC. Upper—dIPC /dE. Inset—ensemble PL spectrum showing wetting layer signal at 1425 mand dot ensemble peaking at;1310 meV.

FIG. 3. Wide range PLE spectra for dots 1, 2, and 3, showcontinuum onset;50 meV aboveX0. The lowest ~absorption!spectrum is calculated following the theory of Ref. 3.

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We now show that consideration of known energiesthe system enables unambiguous attribution of the ctinuum. The WL energy (EWL) for the region of the waferinvestigated is 1425 meV~see Fig. 2 inset!. In previous workon a similar dot from the same wafer we determinedionization energy in the conduction band (EI

e) to the WLband edge to be 150620 meV, from field-dependentX0 tun-nel broadening.4 Combining this with theX0 energy of 1233meV @E(X0)# for dot 1 leads to the energy-band diagramFig. 1~b!, in which the relative dot and WL level energies aknown. The onset of transitions from the valence-band ctinuum to the electron ground state is expected at the hionization energy from dot to WL@EI

h5EWL2E(X0)2EIe

545620 meV# aboveX0 @see Fig. 1~b!#. This predicted en-ergy is in very good agreement with 50 meV found for tonset of the continuum aboveX0 for dots 1, 2, and 3 in Fig.3, providing strong support to the attribution of the cotinuum to crossed WL valence band, electron ground-stransitions.3,13

Further support to this attribution is given by the calclated spectrum in Fig. 3 obtained by using the methodsRef. 3. A model truncated-cone-shaped dot was employeheight 6 nm, radius~bottom! 14 nm, radius~top! 11 nm, WLthickness 1.5 nm, In concentrationx50.3, the parametersbeing adjusted to give reasonable agreement withground-state and first allowed excited-state transition engies. Good semiquantitative agreement with the obserspectra is seen, particularly for the relative strength ofdiscrete and continuum transitions, providing strong suppto the above attribution of the continuum. These results shthat previous discussion in terms of WL or GaAs band tattributions of the continuum is unlikely to bcorrect.7,10–12,14A previous study in large area samples cotaining WL only, and WL plus QD’s, also showed that thcontinuum was not related to the WL band tail.15

We now present three pieces of evidence demonstrathe interaction of excited states with the continuum. First,transitions at.50 meV aboveX0 in Fig. 3 have linewidthsof .0.5–1.0 meV, a factor of 2–3 greater than the resotion limited linewidths for the sharp lines below 50 meV. Thlarge linewidths correspond to dephasing times,2 ps, aris-ing from Coulomb coupling16 with the overlapping con-tinuum transitions. Second, the lines above 50 meV exhstrong temperature dependence due to acoustic phonoduced coupling to the continuum as predicted in Ref. 3,ing fully quenched at 60 K~Ref. 17!, as shown in Fig. 4,whereas the lines to lower energy exhibit negligible tempeture dependence. Third, the.50 meV lines exhibit strongelectric-field broadening, probably due to tunneling into tcontinuum. In Fig. 5 a series of PLE spectra of dot 1 from 4to 100 kV/cm are shown. It is seen that lineC shows signifi-cant broadening at high field. These results are presequantitatively in Fig. 6. Figure 6 shows linewidth data asfunction of field for peaks below the continuum~1,3,4! andoverlapping the continuum~C! taken from the results of Fig5. A factor of 3 increase in linewidth of peakC with field isseen, in marked contrast to the lower-energy lines 1, 3, anof Fig. 6 whose widths are field independent.

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CONTINUUM TRANSITIONS AND PHONON COUPLING . . . PHYSICAL REVIEW B68, 235301 ~2003!

separations@Eexc2E(X0)# less than the hole ionization energy @EI

h5EWL2E(X0)2EIe# to the WL are necessary i

order to have excited-state transition energies below theset of the continuum. This is required for quantum informtion applications involving dot excited states where dephing due to scattering into the continuum must be avoidFor a WL energy ofEWL51425 meV@Figs. 1~b! and 2 in-set#, and for excited states occurring at 30–40 meV as inpresent dots, this requires ground-state transition enerless than 1300 meV to achieve excited-state transitionslow the continuum onset. ForEexc2E(X0).60 meV, asfrequently occurs for In~Ga!As dots,E(X0) must be less than1250 meV. The use of low-energy dots can thus minimizeeliminate excited-state-continuum interactions, but at thepense of moving below the range of sensitive silicon dettors ~cutoff 1230 meV!, desirable for applications involvingemission detection. The growth of a thin Al-containing rgion above the dots could also be employed. This has bshown to lead to incorporation of Al into the WL,18 and will

FIG. 4. PLE spectra for dot 2 as a function of temperature.

FIG. 5. PLE spectra for dot 1 as a function of field (F). Thedashed vertical line indicates 36.6 meV above the field-depenground-state energy. PeakB shows enhancement of its intensirelative to other sharp features with increasingF.

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lead to a shift of the continuum onset to higher energy, pviding an alternative route to eliminate the excited-stacontinuum overlap.19

Finally we discuss the sharp features in the,50 meV,continuum-free region. The PLE spectra for dot 1 were psented in Fig. 5 from 40 to 100 kV/cm. The energy positioof each peak are plotted in Fig. 7~a!, on a scale relative to thefield-dependentX0 energy. All lines shift relative toXPL

0 dueto the more extended excited-state wave functions, confiing their origin as excitonic absorption, and not Raman sctering, as suggested in the first PLE spectra on single do7

The absorption origin of the sharp line features is furthconfirmed by differential PC spectradIPC /dE, an exampleof which is shown in the top part of Fig. 2, all the sharp lin

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FIG. 6. Linewidths~full width at half maximum! of peaks C, 1,3, and 4~see Fig. 5! vs field.

FIG. 7. ~a! Transition energies vs electric field for higher-enertransitions, PLE—circles, PC—squares.~b! Intensity of peakB nor-malized to peaks 1, 2, and 3~see Fig. 5! as a function of energyrelative toX0.

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R. OULTON et al. PHYSICAL REVIEW B 68, 235301 ~2003!

in PLE being observed in the two-step PC process@Fig.1~a!#.20

The most likely origin for the sharp lines isX0 (e1-h1),lines 35–40 meV aboveX0 (e2-h2), the multiplicity of linesarising from symmetry lowering toC2v or below, and the 16and 22 meV lines to nominally forbiddene1-h2, e1-h3transitions, allowed by symmetry lowering in the real dpotential.21 It is notable that the two peaks labeledA, 29–31meV aboveX0 have much greater linewidth~0.9 meV! thanthe other lines~width 100–300meV). The A lines have en-ergy close to that of InAs-like LO phonons in the dot.22 Wesuggest that theA lines arise from exciton-LO phonocoupled modes, the large linewidth arising from the rangeInAs phonon energies in the dots.

Conclusive evidence for interaction with LO phononsobtained from the study of the relative intensity of peakBwith field in Fig. 7~b!. The intensity ofX0 PL, and hence ofall PLE features, first increases with field as the dots are fdepleted of excess holes~above 40 kV/cm!. At fields greaterthan 80 kV/cm by contrastX0 PL is quenched due to tunneing out of the dot.4 By normalizing the intensity ofB relativeto other peaks~labeled 1, 2, 3! its variation is obtained independent of any variation of theX0 intensity. The results areshown in Fig. 7~b! where the normalized lineB intensity isplotted as a function of energy aboveX0 ~the Stark shiftresults of Fig. 7~a! are used to convert the field-depende

*Email address: php00ro@shef.ac.uk1For review, see D. Bimberg, M. Grundmann, and N.N. Ledents

Quantum Dot Heterostructures~Wiley, New York, 1999!.2See, e.g., E. Biolatti, R.C. Iotti, P. Zanardi, and F. Rossi, Ph

Rev. Lett.85, 5647~2000!.3A. Vasanelli, R. Ferreira, and G. Bastard, Phys. Rev. Lett.89,

216804~2002!.4R. Oulton, J.J. Finley, A.D. Ashmore, I.S. Gregory, D.J. Mo

bray, M.S. Skolnick, M.J. Steer, S.-L. Liew, M.A. Miglioratoand A.J. Cullis, Phys. Rev. B66, 045313~2002!.

5F. Findeis, M. Beier, E. Beham, A. Zrenner, and G. AbstreiAppl. Phys. Lett.78, 2958~2001!.

6P.W. Fry, I.E. Itskevich, D.J. Mowbray, M.S. Skolnick, J.J. FinleJ.A. Barker, E.P. O’Reilly, L.R. Wilson, I.A. Larkin, P.AMaksym, M. Hopkinson, M. Al-Khafaji, J.P.R. David, A.G. Culis, G. Hill, and J.C. Clark, Phys. Rev. Lett.84, 733 ~2000!.

7Y. Toda, O. Moriwaki, M. Nishioka, and Y. Arakawa, Phys. ReLett. 82, 4114~1999!.

8J.J. Finley, A.D. Ashmore, A. Lemaıˆtre, D.J. Mowbray, M.S.Skolnick, I. Itskevich, P.A. Maksym, T.K. Krauss, and M. Hokinson, Phys. Rev. B63, 073307~2001!.

9A. Lemaıtre, A.D. Ashmore, J.J. Finley, D.J. Mowbray, M.SSkolnick, M. Hopkinson, and T.F. Krauss, Phys. Rev. B63,161309~R! ~2002!.

10F. Findeis, A. Zrenner, G. Bohm, and G. Abstreiter, Phys. Rev61, R10579~2000!.

11C. Kammerer, C. Voisin, G. Cassabois, C. Delalande, Ph. Rosignol, F. Klopf, J.P. Reithmaier, A. Forchel, and J.M. GeraPhys. Rev. B66, 041306~R! ~2002!.

12H. Htoon, D. Kulik, O. Baklenov, A.L. Holmes, Jr., T. Takaga

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results of Fig. 5 to energy relative toX0). It is seen that lineB shows a resonant enhancement as it is scanned up toGaAs LO phonon energy of 36.6 meV@Figs. 5 and 7~b!#.Excitons and LO phonons in QD’s are strongly coupledform polaron eigenstates:23,24photon absorption creates a plaron coupled mode which decays by LO phonon conversinto two acoustic phonons, enhancing the productionground-state PL for excitonic states close in energy to anphonon.24,25

In conclusion, absorption spectra for InGaAs seassembled quantum dots have been reported. The spectrinto two distinct regions, a low-energy region of sharp linfree of any background, followed by a higher-energy regof discrete transitions superimposed on a continuum. Tcontinuum has been shown to have an origin intrinsic toStranski-Krastanow growth process. Interactions betwdiscrete states and the continuum have been demonstrTechniques to reduce or eliminate such interactions, delrious to quantum information applications, have been sgested. Such applications may otherwise require techniqwhich probe dot ground states, such as direct absorptiophotocurrent.

EPSRC is acknowledged for support to this work throuGrant No. GR/N20997.

v,

s.

,

B

s-,

hara, and C.K. Shih, Phys. Rev. B63, 241303~R! ~2001!. Theseparation of single dot spectra into distinct regions wasserved in this work.

13Similar transitions for quantum wells have been reported by MSkolnick, P.R. Tapster, S.J. Bass, A.D. Pitt, N. Apsley, and SAldred, Semicond. Sci. Technol.1, 29 ~1986!.

14C. Kammerer, G. Cassabois, C. Voisin, C. Delalande, P. Rosignol, and J.M. Gerard, Phys. Rev. Lett.87, 207401~2001!.

15P.W. Fry, I.E. Itskevich, S.R. Parnell, J.J. Finley, L.R. WilsoK.L. Schumacher, D.J. Mowbray, M.S. Skolnick, M. Al-KhafajA.G. Cullis, M. Hopkinson, J.C. Clark, and G. Hill, Phys. ReB 62, 16 784~2000!.

16R. Ferreira and G. Bastard, Appl. Phys. Lett.74, 2818~1999!.17Marked increase of linewidth with temperature was observed

PLE in Ref. 11, and was attributed to coupling to continuustates.

18A.F. Tsatsulnikov, A.R. Kovsh, A.E. Zhukov, Y.M. ShernyakoY.G. Musikhin, V.M. Ustinov, N.A. Bert, P.S. Kop’ev, Zh.I. Al-ferov, A.M. Mintairov, J.L. Merz, N.N. Ledentsov, and D. Bimberg, J. Appl. Phys.88, 6272~2000!.

19Absorption~PLE! spectra with sharp transitions but no continuuhave been reported by P. Hawrylak, G.A. Narvaez, M. Bayand A. Forchel, Phys. Rev. Lett.85, 389 ~2000!. This may arisefrom the ‘‘In-flush-annealing’’ growth technique@S. Fafard, Z.R.Wasilewski, C.Ni. Allen, D. Picard, M. Spanner, J.P. McCaffreand P.G. Piva, Phys. Rev. B59, 15 368~1999!#, possibly leadingto reduction of the amount of In in the WL.

20A broad background signal is seen in PC from 1200 to 1400 mprobably arising from absorption of scattered laser light byensemble of dots. Field modulation techniques (DV510 mV,1.6 kHz!, sensitive only to field-dependent features, were eployed, enabling the background to be eliminated. Lock-in

tection leads to the differential spectra of Fig. 2.

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CONTINUUM TRANSITIONS AND PHONON COUPLING . . . PHYSICAL REVIEW B68, 235301 ~2003!

21Very similar sharp line structure is seen for dots 2 and 3~Fig. 3!.For dot 3 however, the 15–25 meV features are much wearelative to the higher-energy lines, supporting a perturbationgin for the observation of the nominally forbiddene1-h2,e1-h3 lines. The cylindrical symmetry assumed in the theoaccounts for the relatively small number of discrete lines intheory spectra.

22See, e.g., M. Grundmann, O. Stier, and D. Bimberg, Phys. Re

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52, 11 969~1995!.23O. Verzelen, R. Ferreira, and G. Bastard, Phys. Rev. Lett.88,

146803~2002!.24O. Verzelen, G. Bastard, and R. Ferreira, Phys. Rev. B66, 081308

~2002!.25The polaron splitting for theue1-h1,1LO&, ue2-h2& resonance is

only expected to be;0.1 meV due to the similar polarisatiocharges for electron and hole states of the same symmetry.

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