Optical excitations of a self assembled artificial ion

8 Pages·0.1 MB·English

by  F. Findeis

Optical excitations of a self assembled artificial ion
F. Findeis, M. Baier, A. Zrenner, M. Bichler, and G. Abstreiter
Walter Schottky Institut, Technische Universit¨at Mu¨nchen
Am Coulombwall, 85748 Garching, Germany
1
U. Hohenester and E. Molinari
0
0 Istituto Nazionale per la Fisica della Materia (INFM) and Dipartimento di Fisica
2 Universit`a di Modena e Reggio Emilia, Via Campi 213/A, 41100 Modena, Italy
(January 16, 2001)
n
a
J
Byuseofmagneto-photoluminescencespectroscopywedemonstratebiascontrolledsingle-electron

6 charging ofasingle quantumdot. Neutral,single, anddoublecharged excitonsareidentifiedinthe
1 opticalspectra. AthighmagneticfieldsoneZeemancomponentofthesinglechargedexcitonisfound

to be quenched, which is attributed to the competing effects of tunneling and spin-flip processes.
]
l Our experimental data are in good agreement with theoretical model calculations for situations
l
a where the spatial extent of the hole wave functions is smaller as compared to the electron wave
h functions.
-
s
e
m
. Semiconductorquantumdots (QDs)areoften referred creasing number of electrons probed by magneto-PL.
t
a toasartificialatoms. Differentlevelsofneutraloccupan- For controlled charging of individual QDs a special
m
ciesinQDshavebeenobtainedinthelastyearsbypower electric field tunable n-i structure has been grown by
d- dependent optical excitation. The associated few parti- molecular beam epitaxy. The In0.5Ga0.5As QDs are em-
n cle states have been intensively studied by multi-exciton bedded in an i-GaAs region 40 nm above an n-doped
o photoluminescence(PL)spectroscopyandcorresponding GaAs layer (5×1018cm−3) which acts as back contact.
c theoretical investigations [1–7]. Occupancies with dif- The growth of the QDs is followed by 270 nm i-GaAs, a
[
ferent numbers of electrons and holes result in charged 40 nm thick Al0.3Ga0.7As blocking layer, and a 10 nm i-

1 exciton complexes. In analogy to QDs with neutral oc- GaAs cap layer. As a Schottky gate we use a 5 nm thick
v cupancy —artificial atoms— charged exciton complexes semitransparent Ti layer. The samples were processed
0 may be considered as artificial ions. In the field of low as photodiodes combined with electron beam structured
4
dimensional semiconductors charged excitons have been shadowmaskswithaperturesrangingfrom200nmto800
2
1 observed first in quantum well structures [8]. In QDs, nm. Schematicoverviewsofthe sampleandthe banddi-
0 charged excitons have been studied in inhomogeneously agram are shown in Figs. 1 a and b. The occupation
1 broadened ensembles by PL [9] as well as in interband of the QD with electrons can be controlled by an exter-
0 transmissionexperiments[10],andrecentlyalsoinsingle, nal bias voltage VB on the Schottky gate with respect
/
at optically tunable QDs [11] as well as electrically tunable to the back contact. For increasing VB the band flattens
m quantum rings by PL [12]. and the electron levels of the QD are shifted below the
Few-particle theory predicts binding energies for Fermi energy of the n-GaAs back contact, which results
-
d charged QD excitons in the order of some meV [11,13]. in successive single electron charging of the QD. In our
n This allows for the controlled manipulation of energeti- experiments excitons are generated optically at low rate
o
callywellseparatedfewparticlestatesundertheactionof andformchargedexcitons togetherwith the VB induced
c
an external gate electrode. Discrete and stable numbers extra electrons in the QD. We used a HeNe laser (632.8
:
v
of extra charges are thereby possible via the Coulomb nm) for optical excitation and a cooled CCD camera for
i
X blockademechanism. Infutureexperiments andpossible detectionofthePL.Thesamplewasmountedinaconfo-
r applications the resonant optical absorption and emis- callow-temperature,highmagneticfieldmicroscope[14].
a sion of such systems is expected to be tunable between In Fig. 2 a and b we present PL spectra as a function
discrete and characteristic energies. Moreover such few- of VB in the range of -550 mV to +400 mV correspond-
particle systems are expected to exhibit an interesting ing to electric fields of 37.5 kV/cm to 11.1 kV/cm. The
variety of spin configurations, which can be controlled PL intensity is displayedas gray scale plot for B=0 T in
by external magnetic field, gate induced occupancy, and Fig. 2 a and for B=12 T in Fig. 2 b. As a function of
spin selective optical excitation. VB we find a series of lines with discrete jumps in the
In the present contribution we present for the first emission energy. Those lines are assigned to radiative
time experimental and theoretical results on the gate- s-shell transitions of neutral (X0), single charged (X−),
controlled charging of a single InGaAs QD with an in- and double charged (X2−) excitons, as marked in Figs.
1
2 a and b and discussed in the following. For B=0 T despiteitssimplicity,suchconfinementisknowntomimic
(Fig. 2a)andlargenegativeVB (VB <−0.5V)theelec- the most important characteristics of InxGa1−xAs dots,
tron levels in the QD are far above the Fermi energy of and has recently proven successful in comparison with
the n-GaAs back contact and the QD is electrically neu- experiment [7,18]. We take 5 nm for the well width in
tral. OpticallygeneratedexcitonscanrelaxintotheQD, z-direction and h¯ωe = 30 meV (¯hωh = 15 meV) for the
0 0
but before radiative recombination (τ ∼ 1ns) the carri- electron (hole) confinement energies due to the in-plane
ers tunnel out ofthe QDdue to the highapplied electric parabolic potential; material parameters are computed
field. For VB ≃ −0.5 V the QD is still uncharged, but accordingtoRefs.[19,20](notethatwiththesevalueswe
in the smaller electric field radiative recombination gets alsowellreproducethe∼40meVsplittingbetweenthe1s
more likely and the X0 emission line appears at 1307 and 1p shells measured at higher photo-excitation pow-
meV. The weak satellite about 0.4 meV below is tenta- ers). Finally,becauseofthestrongquantumconfinement
tively explained in terms of QD asymmetry [15]. With in z-direction we safely neglect minor effects due to the
increasing VB, the X0 line shifts to higher energies due applied external electric field. PL spectra for X0, X−,
to the quantum confined Stark effect in the decreasing and X2− are computed within a direct-diagonalization
electric field. For VB =−0.35 V a new emission line ap- approachaccountingforallpossiblee-eande-hCoulomb
pears below the X0 line at 1302.5 meV, indicating the interactions [11,21]
static occupation of the QD with one electron. The X− The black lines in Fig. 3 show the dependence of the
binding energy with respect to the X0 is determined to luminescence spectra of the X0, X−, and X2− lines as
∆EX− = 4.6 meV by the measured difference in emis- functionoftheextensionLh0 oftheholewavefunction(for
sion energies. For −0.35V < VB < 0V the X0 and X− definition see figure caption). In accordance with exper-
line coexist, which is a consequence of the statistical na- iment and related work [11,12] we find (for Lh ≤ Le)
0 0
ture of non-resonant optical excitation. In the presence in the PL spectra: a red-shift of the charged-exciton
of one extra electron, the capture and subsequent decay emission peak X−; a further, much smaller, red-shift of
of an electron hole pair leads to the emission of a X− the main X2− emission peak, which is accompanied by
photon. If only a single hole is captured we expect a a weak satellite peak at even lower photon energy (see
X0 photon, and if a single electron is captured we ex- arrows). A quantitative comparison between theory and
pectnophoton,butinsteadelectronbacktransfertothe experiment,however,revealsthatforthesameextension
n+ region. At VB = 0 V the QD is charged with a sec- of electron and hole wavefunctions (Le0 = Lh0) the calcu-
ond electron. This leads to the appearance of two new lated charged-exciton binding of 1.5 meV is by a factor
characteristic emission lines (marked in Fig. 2 a and b), of ∼3 smaller than the measured value; we checked that
which are assigned to the X2− decay. The main line of this finding does not depend decisevly on small modifi-
the X2− emission appears only 0.3 meV below the X− cations of the chosen dot and material parameters. As
line, whereas a much weaker satellite peak appears 4.6 can be inferred from Fig. 3, the VB binding energy is a
meV below the main line at 1298.1 meV. The appear- quite sensitive measure of the relative extension of elec-
ance of two emission lines is characteristic for the X2− tronandholewavefunctions: DecreasingLh andkeeping
0
decay. The energy difference between the two X2− lines all other parameters (ωe, ωh, Le) fixed, one clearly ob-
0 0 0
correspondstothedifferenceinthes-pexchangeenergies serves in Fig. 3 an increased binding (moderate param-
between the two possible final states with parallelor an- eter changes turn out to have no impact on this general
tiparallel spin orientation of the two remaining electrons trend; see, e.g., gray lines).
[4]. Again X2− and X− can be observedsimultaneously We thus conclude that the large experimental X−
over a certain range in VB. At VB > 0.19V only one binding energy of 4.6 meV can only be explained by
broad emission line remains. This indicates filling of the more localized hole wavefunctions, which we attribute
wetting layer (WL) states with electrons. Here, weakly to effects of heavier hole masses and of possible piezo-
confinedelectronsareinteractingwiththecarriersinthe electric fields. Additional evidence for this interpreta-
QD,causingabroadeningofthedetecteds-shelldecayin tioncomesfromthe ratiobetweentheexchangesplitting
the QD. A roughestimationof the VB incrementneeded of the two X2− lines and the X− binding energy. The
to bring the WL states below the Fermi energy (starting experimentally observed exchange splitting of about 4.6
from the onset of the X− line), taking charging energy meV between the weak low energy and intense high en-
and the electrostatics of the structure into account [16], ergybranchoftheX2− lineisfoundtobeapproximately
results in a reasonable value of ∆VB = 530 mV in good equaltotheX− bindingenergy. Fromourtheoreticalin-
agreement with our experimental data. vestigations such a scenario can only be obtained if the
For a quantitative analysis of the experimental results hole confinement is considerably stronger than the elec-
we performed theoretical model calcualtions. Follow- tron confinement.
ing the approach presented in Ref. [17], we assume for Finally we discuss the magnetic field dependence
electronsandholes,respectively,aconfinementpotential shown in Fig. 2 b for B=12 T. From comparison with
whichisparabolicinthe(x,y)-planeandbox-likealongz; the B=0 T data (Fig. 2 a) it is clear that single elec-
2
tron charging versus VB is mostly unaffected by mag- is smaller as compared to the electron wave functions.
netic field. The centers of s-shell emission for X0, X−, Spin polarization and lifting of the Zeeman degeneracy
and X2− are shifted to higher energies due to diamag- athighmagneticfieldsallowsfurtheraccesstosofarun-
netic shift and each emission line splits into two lines, exploredspindependentpropertiesoffewparticlestates.
separated by the Zeeman energy. The observed weak ThesuppressionofoneZeemancomponentoftheX−de-
differences between the Zeeman energies of the X0 and cayisexplainedintermsofstateselectivetunnelingfrom
X− lines seem to indicate, that the spin orientation of a spin triplet configuration.
an extra electron in the QD does not change during the This work has been supported financially by the DFG
radiative decay from the s-shell. via SFB 348, by the BMBF via 01BM917, in part by
In the following we concentrate on the asymmetry in INFM through PRA-99-SSQI, and by the EU under
thePL-intensitiesofthetwoZeemanbranchesoftheX− theTMRNetwork“UltrafastQuantumOptoelectronics”
line for −0.35 V < VB < −0.13 V (see Fig. 2 b). This and the IST programme “SQID”.
asymmetry is observed only for the X− line, not for the
X0 and X2− lines. The explanation of this phenomenon
involves spin polarization, Pauli blocking, and state se-
lective tunneling as summarized in Fig. 4 a and b. At
B=12 T a single electron in a QD is spin polarized in
thermal equilibrium. The optical excitation of excitons
canhappenwithtwodifferentspinorientations,whichre- [1] Forarecentreviewsee: A.Zrenner,J.Chem.Phys.112,
7790 (2000).
sults in the states showninFig. 4 a and b. Due to Pauli
[2] E. Deckelet al.,Phys. Rev.Lett. 80, 4991 (1998)
blocking in the conduction band, parallel electron spin
[3] L. Landin et al.,Science 280, 262 (1998).
orientation leads to a metastable triplet state with one
[4] P. Hawrylak, Phys. Rev.B 60, 5597 (1999).
electroninthes-shellandoneinthep-shell(seeFig. 4a).
[5] U. Hohenester, F. Rossi, and E. Molinari, Solid State
If the tunneling time from the p-shell to the continuum Comm. 111, 187 (1999).
is shorter than the electron spin-flip time, an electron is [6] F. Findeis, A. Zrenner, G. B¨ohm, G. Abstreiter, Solid
lostandweendupwithaneutralexcitonandhencewith State Commun. 114, 227 (2000).
a contributionto one Zeeman componentof the X0 line, [7] M. Bayer et al.,Nature405, 923 (2000).
i.e. weloseoneZeemancomponentoftheX−decay. The [8] K. Khenget al.,Phys.Rev.Lett. 71, 1752 (1993).
introductionofanexcitonwithoppositespinorientation, [9] K. H. Schmidt, G. Medeiros-Ribeiro, and P. M. Petroff,
however, produces a singlet state as shown in Fig. 4 b. Phys. Rev.B 58, 3597 (1998).
[10] R.J.Warburtonetal.,Phys.Rev.Lett.79,5282(1997).
The radiative decay of this configuration contributes to
the other Zeeman component of the X− line. Our find- [11] A. Hartmann et al., Phys.Rev.Lett. 84, 5648 (2000).
[12] R. J. Warburton et al., Nature405, 926 (2000).
ings also imply that the associated heavy hole spin flip
[13] A.WojsandP.Hawrylak,Phys.Rev.B55,13066(1997).
time should be at least of the same order or longer than [14] A. Zrenner et al., Physica B 256-258, 300 (1998).
the e-h lifetime. Long spin-flip times and conservation [15] D. Gammon et al.,Phys.Rev. Lett.76, 3005 (1996).
of the exciton spin within the exciton lifetime has been [16] H. Drexler et al.,Phys.Rev. Lett.73, 2252 (1994).
reported already earlier for zero-dimensional systems at [17] G. A. Navarez and P. Harylak, Phys. Rev. B 61, 15753
high magnetic fields [22]. The suppression of one X− (2000).
Zeeman component persists over a VB range of 0.22 V, [18] P. Hawrylak, G. A. Navarez, M. Bayer, and A. Forchel,
whichtranslatestoanenergyshiftoftheQDstateswith Phys. Rev.Lett. 85, 389 (2000).
respect to the n-GaAs Fermi energy of 28 meV (about [19] O.Stier,M.Grundmann,andD.Bimberg,Phys.Rev.B
tbootchonZdeuecmtiaonncboamnpdosn-epnstespoafratthieonX).−FloinreVBare>r−ec0o.v1e3reVd [20] W59e, 5u6s8e8m(1hz99=9)1./(γ1 −2γ2) and mhk = 1/(γ1 +γ2) for
theholemass inthez andlateral directions,with γi the
as a consequence of the increased tunneling time, which
Luttinger parameters.
allowsnowforthecompetingspinflipandrelaxationpro-
[21] For details of our computational approach see: U. Ho-
cesstothes-shell. FortheX0andX2− linesaquenching henester and E. Molinari, phys. stat. sol. (b) 221, 19
of Zeeman lines is not expected and also not observed, (2000); cond-mat/0005253. In our calculations we con-
since the p-shell is either never (X0) or always (X2−) sider a single-particle basis of the 6 electron and hole
populated, regardless of the spin orientation of the opti- states with lowest energy,respectively.
cally excited e-h pair. [22] W. Heller and U. Bockelmann, Phys. Rev. B 55, R4871
In summary, we have demonstrated bias controlled (2000).
charging of a single QD in magneto-optic PL experi-
ments. The few-particle interaction energies determined
experimentally for the X− and X2− states are found to FIG.1. (a)Photodiodecombinedwithanearfieldshadow
beingoodagreementwithourtheoreticalmodelforsitu- mask. (b) Schematic band diagram of the structure for zero
ationswherethespatialextentoftheholewavefunctions bias.
3
FIG.2. GrayscaleplotofPLintensityasafunctionofPL FIG. 3. Dependence of luminescence spectra on the ex-
i i
energy and VB. The series of lines can be assigned to emis- tension of theholewavefunction. L0 =1/p(miω0) (i=e,h)
sions from s-shell transitions of X0, X−, and X2−. At zero is a characteristic length scale of the parabolic confinement,
e h
magnetic field (a) and at B=12 T (b) with me (mh) the electron (hole) mass and ¯hω0 (h¯ω0) the
confinement energies dueto the in-plane parabolic potential.
Black lines: ¯hω0e = 30 meV (Le0 = 7.5 nm) and h¯ω0h = 15
meV; the thickness of each line corresponds to the oscillator
strength of thecorresponding transition (photon energy zero
given by the X0 energy for same extension of electron and
h e e
hole wavefunctions, i.e., L0 = L0). Gray lines: ¯hω0 = 35
e h
meV (L0 =7 nm) and ¯hω0 =10 meV.
FIG.4. Triplet (a) and singlet (b) electron configurations
for the X−. The triplet state is subjected to tunnel decay
from the p-shell.
4
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1.4
1.2
e 0
L

/ 1.0
h 0
L
0.8
2- - 0
X X X
0.6
-15 -10 -5 0 5
Energy (meV)
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