Spin lifetime from the Hanle effect and fine structure of excitonic levels in InAlAs/AlGaAs quantum dots

phys. stat. sol. (b) 244, No. 7, 2622–2628 (2007) / DOI 10.1002/pssb.200642520

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Spin lifetime from the Hanle effect and fine structure

of excitonic levels in InAlAs/AlGaAs quantum dots

A. Sahli1, A. Melliti*, 1, M. A. Maaref 1, C. Testelin2, A. Lemaitre3, R. Kuszelewicz3,

and P. Voisin3

1 Unité de Recherche de Physique des Semiconducteurs et Capteurs,

Institut Préparatoire aux Etudes Scientifiques et Techniques, La Marsa 2070, Tunisia 2 Institut des NanoSciences de Paris, Campus Boucicaut, Universités Paris 6 et 7, CNRS,

UMR7588, 140 rue de Lourmel, 75015 Paris, France 3 Laboratoire de Photonique et Nanostructures, CNRS, UPR20, France

Received 16 October 2006, revised 30 January 2007, accepted 1 February 2007

Published online 26 March 2007

PACS 78.20.Ls, 78.47.+p, 78.55.Cr, 78.66.Fd, 78.67.Hc

Excitation of electron–hole pairs by circularly polarized light yields an electron spin polarization in

InAlAs self-assembled quantum dots. This spin polarization causes circular polarization of the photolumi-

nescence light, its degree decreasing in a magnetic field perpendicular to the initial spin vector of the elec-

tron–hole pair (Hanle effect). The scaled spin lifetime e

sg T^

, where e

g^is the transverse electron Landé

factor and sT is the electron spin lifetime is deduced from the Hanle curves and is of the order of 100 ps. It

is attributed to the polarized spin confined in quantum dots. With increasing energy detection the width of

the Hanle curve is reduced. The corresponding scaled electron–hole spin lifetime increases with increas-

ing energy detection. We have also performed photoluminescence study of excitons localized in InAlAs

quantum dots, in a longitudinal magnetic field. The magnetic-field dependence of the linear and circular

polarization evidences the exciton fine structure and helps to determine the anisotropic part of the exciton

exchange, which is of the order of 14 µeV.

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

Semiconductor structures with quantum dots (QD) are currently the subject both of fundamental studies and of optical applications such as QD lasers and detectors. In the last few years much attention was given to the study of the spin relaxation in spin-dependent devices [1–3] and to develop new techniques for controlling the spin degrees of freedom in QD. These efforts are stimulated in part by some proposals to use the spin systems as quantum bits (qubits) in quantum information processing [4–6]. In fact, the electron confinement in QD is expected to inhibit the spin-relaxation mechanisms, which are active in bulk materials or in two-dimensional structures. Recent experimental studies at low temperature have shown that the spin relaxation of the lowest electron–hole (e–h) pair states is over tens of ns [2, 7], but also a fast spin relaxation has been observed under some conditions [8, 9]. For application of QDs as single-photon emitters, the anisotropic exchange interaction between elec-trons and holes is crucial as it can determine both the polarization and entanglement of the emitted pho-tons [10]. Assuming rotational symmetry of the QD along the growth axis Oz, one predicts two bright electron–hole pair states denoted |+1⟩ and | 1- ⟩ and with an angular momentum projection along the growth axis,

* Corresponding author: e-mail: [email protected]

phys. stat. sol. (b) 244, No. 7 (2007) 2623

www.pss-b.com © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

1z z z

M s j= + = ± where the electron spin 1/2zs = ∓ and the heavy hole angular momentum 3/2

zj = ± .

These states are degenerate and excited by orthogonal circularly polarized light states. In elongated QDs, the reduced symmetry of the confinement potential leads to a mixing of the exciton spin doublet through the exchange interaction. The new QD eigenstates correspond to two linearly polarized transitions X and Y, which are aligned along the orthogonal axes of the elongated QD. The anisotropic exchange splitting between X and Y ranges from a few tens of µeV [7] to several hundred µeV [11]. Here, we present a study of the fine structure of excitons in an ensemble of self-organized InAlAs/AlGaAs QDs, using po-larization-resolved photoluminescence experiments under a magnetic field applied along the growth axis (Faraday geometry). We also employ the Hanle effect to obtain the scaled electron spin lifetime e

sg T^

. The QD polarization has been studied in nonresonant excitation conditions (i.e. photogenerating the carriers in the wetting layer).

2 Sample growth and experimental details

The Al0.28In0.72As QDs embedded in Al0.28Ga0.72As were grown on a [1] oriented GaAs substrate by using a molecular beam epitaxy (MBE) system. The self-organized coherent AlInAs islands were formed by deposing of nominally 4.8 monolayers between 500 Å thick layers of Al0.28Ga0.72As, the QD density is ~4 × 1010 cm–2 per array. In continuous-wave (cw) photoluminescence (PL) the sample was placed at the center of a supercon-ducting solenoid and loaded into a cryostat with liquid helium. The helium was pumped down to a tem-perature T = 1.8 K. The magnetic field (B) was aligned normal or parallel to the growth axis. The sample was excited by a He–Ne laser (λ = 633 nm), above the energy of the wetting layer (WL) using a very low excitation density (~0.1 W/cm2). The polarization was analysed by a quarter-wave plate and a linear polarizer. The resultant PL is dis-persed by a monochromator and detected by a LN2-cooled charge-coupled-device camera. The ground-state emission is centered around 1.631 eV with a full width at half maximum (FWHM) of ~120 meV. The linear and circular polarization degrees of the luminescence are defined as

l( )/x y

P I I= - ( )x yI I+ and

c( )/( )P I I I I

+ - + -

= - + , respectively; where ( )x yI I and ( )I I

+ - denote, respectively, the ( )X Y linearly polarized and the right (left) circularly polarized luminescence components; X and Y are

chosen to be parallel or perpendicular to the ⟨110⟩ crystallographic directions. lP and

cP are, respectively,

obtained under linearly and circularly polarized excitation. Time-resolved photoluminescence measurements were made using a closed cycle He cryostat and mode-locked Ti:sapphire laser giving nearly Fourier-transform-limited pulse in the range of 1–1.5 ps with a repetition rate of 82 MHz. Its energy was tuned to 1.72 eV. The emission was spectrally dispersed using a monochromator. Next, temporal analysis was performed by a synchroscan streak camera. The time resolution was ~5 ps.

3 Results and discussion

3.1 Fine structure of exciton (Faraday configuration)

In the following, a magnetic field applied along the growth axis of the sample (B || [001]) was used to investigate the behavior of the excitonic fine structure states split by the magnetic field. The magnetic-field dependence of the circular and linear exciton polarization can be described in the framework of an effective pseudospin with 1/2S = [12]. In this formalism, the exciton state |+1⟩ and | 1- ⟩ are equivalent to a pseudospin polarized parallel or antiparallel to the Oz axis, respectively ( 1/2

zS = or 1/2- ), and the

linear exciton states | (|+1 | 1 )/ 2X = + -⟩ ⟩ ⟩ and | ( 1 1 )/ 2Y i= - + - -⟩ are described by a pseudospin 1/2

xS = and 1/2- , respectively. The circular and linear exciton PL polarization writes simply Pc = 2S

z

and Pl = 2Sx. The pseudospin Hamiltonian that takes into account the exchange and the Zeeman terms is

simply equal to ||[ ( )]/2x z

H ωσ Ω σ= + , where ћω is the anisotropic exchange splitting of the radiative

2624 A. Sahli et al.: Spin lifetime in InAlAs/AlGaAs quantum dots

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

X

zSr

//Ωr

Z

ωr0Sx

r

x Sr

Ωr

doublet and ћΩ|| =

ex

||g µBB, with ex

||g being the exciton longitudinal Landé factor. The schematic repre-sentation in Fig. 1 shows that the pseudospin rotates around the vector W = (ω, 0, Ω||) with the effective

Larmor frequency 2 2

||Ω ω Ω= + . A circularly polarized excitation is represented by an initial pseudo-

spin 0zS parallel to the Oz axis. Following linearly polarized excitation, the initial pseudospin 0

xS is paral-lel to the Ox axis. The average value of the pseudospin is obtained by projecting the initial pseudospin onto the W direction. Increasing the magnetic field yields a reduction of the average value of the PL linear polarisation, given by

l2

xP S= , and an increase of the average value of the PL circular polarization

given by c

2z

P S= . The observed magnetic field dependence of the PL circular and linear polarization are displayed in Figs. 2 and 3, respectively. The magnetic-field dependence of the linear and circular polarization allows the determination of the exciton fine structure. These dependences are described by [12]

2

||0

c c 2 2

||

,P PΩ

ω Ω=

+

(1)

2

0

l l 2 2

||

.P Pω

ω Ω=

+

(2)

Figure 2 displays the degree of circular polarization as a function of the magnetic field. One observes a substantial increase in the degree of radiation polarization, followed by saturation at a level of 14.4%.

-0,4 -0,2 0,0 0,2 0,4 0,69

10

11

12

13

14

15

Cir

cula

rP

olar

izat

ion

(%)

Magnetic Field (T)

Fig. 1 Schematic representation of the exciton pseudospin projec-

tion. 0

xS is the initial pseudospin vector under [110] linearly polar-

ized excitation; x

S and z

S are the components of the average pseu-

dospin.

Fig. 2 (online colour at: www.pss-b.com)

Longitudinal-magnetic-field dependence of the

circular polarization. The solid line is the best fit

obtained with Eq. (1). The energy detection is

1.58 eV.

phys. stat. sol. (b) 244, No. 7 (2007) 2625


Original

Paper

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

-14

-13

-12

-11

-10

MagneticField (T)

Line

arP

olar

izat

ion

(%)

The solid line displayed is the best fit of the experimental data obtained using Eq. (1) with 0

c4.4%P = and

a background of 10%. If we take the exciton g factor value given by [13] ( ex

||g = 2.1) we find 14 µeV.ω ª Figure 3 shows the effect of a longitudinal magnetic field upon the optical alignment of

excitons. Linear polarization decreases with increasing the longitudinal magnetic field in circular polari-zation. The linear polarization is suppressed in the same characteristic range of fields where an increase of circular polarization is observed. The solid line displayed is the best fit of the experimental data ob-tained using Eq. (2). If we take the exciton g factor value given by [13] we also find 14 µeVω ª . We note that suppression of

lP is determined by the difference of the degrees of linear polarization in

zero and strong magnetic fields, since an intensity modulation is superposed on the measured degree of effective linear polarization. This intensity modulation is due to the difference in the absorption coeffi-cients between light polarized along the [110] and [110] axes (linear dichroism), equal to 14%, and is independent of the magnetic field. Such linear dichroism was already observed in similar InAlAs QD [14] and InAs QD [15].

3.2 Hanle effect (Voigt configuration)

The Hanle effect uses the degree of circular polarization of photons from carrier recombination to meas-ure the component of the carrier spin along the direction of observation [16]. The degree of circular po-larization of the PL decreases in a transverse magnetic field. From this decrease the electron-spin lifetime can be deduced. In our experiment the carrier’s excitation is above the wetting-layer energy. Then, the hole spin is completely relaxed before the recombination [17]. Thus, the spin of the electron–hole pair is that of the electron. Consequently the photoluminescence polarization is related to the electron polarisa-tion. On the other hand, the relaxation of the electron to the ground state occurs in cascades. Each step of the cascade corresponds to a state with a certain lifetime and spin-relaxation time. The final spin polari-zation after n steps of the cascade, which determines the Hanle curve, is given by [17]

( ) ( )

( ) ( )1 s

( )( ) s

0 ( )1

1( ) (0) Re ,

1

(0) ,

n

n n

k k

k

n k

n

k

k

Bi T

T

ρ ρΩ

ρ ρτ

=

=

=

+

=

’

’

(3)

where ( ) ( )

s ,

k kT τ and ( )k

Ω are the spin lifetime, the lifetime and the Larmor frequency in the external per-pendicular magnetic field on the k-th step.


Longitudinal-magnetic-field dependence of the

linear polarization. The solid line is the best fit

obtained with Eq. (2). The energy detection is

1.58 eV.



-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0

0

2

4

6

8

10

ρ ρ ρ ρc(Β

) (Β

) (Β

) (Β

) (%

)(%

)(%

)(%

)

Magnetic Field (T)

If there exists only one particular state l for which the condition ( ) ( ) ( ) ( )

s s

l l k k

k l

T TΩ Ω

π

Â is fulfilled, we

can deduce from Eq. (1) that the Hanle curve has a single Lorentzian shape. The full width at half maxi-mum (FWHM) of the curve in this case is determined by e( )l

g^

and the spin lifetime in this state, e( ) ( )

B s∆ /l l

B g Tµ^

= . In contrast, when all (or some of) ( ) ( )

s

k kTΩ are of the same value the average spin in the final state

oscillates, with a change of the sign, as a function of the magnetic field [17]. Figure 4 shows the typical Hanle curve at temperature 2 K. The detection is kept at the peak of the QD ground state PL (1.631 eV). FWHM is 224 mT. The circular polarization decreases from 10% at zero magnetic fields to 1% at higher field. The best fit of our experimental data is obtained by a single Lor-entzian curve (solid lines). The fit with a single Lorentzian of the Hanle curve shows that one state (with e

sg T^

≈ 100 ps) imposes the dynamic of the spin. Two states are mainly involved in the spin dynamics: the state of the wetting layer conduction-band bottom and the localized state inside the quantum dots. Concerning the wetting layer the value of e

sg T^

can be estimated or bounded independently, as follows:

1,54 1,56 1,58 1,60 1,62 1,64 1,66 1,68 1,70 1,7290

95

100

105

110

115

Energy (eV)

gTs

Fig. 5 Electron spin lifetime s

g T^

vs. detection energy.


Photoluminescence circular polarization vs. trans-

verse magnetic field exciting with 0.1 W/cm3

and detecting at the QD ground state (1.631 eV).

phys. stat. sol. (b) 244, No. 7 (2007) 2627


Original

Paper

0 500 1000 1500 2000

Cou

nts

Time (ps)

Fig. 6 (online colour at: www.pss-b.com) Time decay of the ground-state emission obtained at 10 K at

the energy detection of 1.637 eV.

(i) The value of

sT is lower than the capture time of carriers in the quantum dots. This time can be

estimated from the PL decay curve fitted by an exponential decay and an exponential rise (Fig. 5). It is on the order of 70 ps. Therefore,

sT < 70 ps.

(ii) It was clearly shown in thin layers of InAs/GaAs with a thickness comparable to that of the wet-ting layer [18], that e

g^of the layer is equal to e

g^ in the barrier. Moreover, the Landé factor increases

when one substitutes Al to Ga. Indeed, in bulk material, e

g^(GaAs) = –0.44 [18] and e

g^(Al0.35Ga0.65As)

= 0.54 ± 0.05 [19, 20]. Assuming a linear dependence with Al content, one gets e

g^(Al0.28Ga0.72As)

= 0.34 ± 0.05. Finally, one can conclude that the scales spin lifetime

e

sg T^

in the wetting layer is lower than 23 ps, which is much lower than the value obtained experimentally ( e

sg T^

≈ 100 ps). Thus, one can deduce that the dynamics of spin is imposed by the localized state inside the quantum dots. In quantum dots the spin-relaxation time (

sτ ) is larger than the recombination time (

rτ ), at low tem-

perature [2, 7] so that sT is almost equal to

rτ . Figure 6 shows that

rτ is about 630 ps. Using the obtained

value of e

sg T^

, one can estimate that e

g^ is about 0.2.

Finally, we have performed the study of the scaled spin lifetime e

sg T^

versus energy detection (see Fig. 5). We note that e

sg T^

increases with QD emission energy. This behavior is in agreement with the increase of the spin lifetime versus QD emission energy, observed by Watanaki et al. [7] on similar InAlAs QD using heterodyne four-wave mixing.

4 Conclusion

In conclusion, we have studied the fine structure of excitons in InAlAs/AlGaAs self-assembled quantum dots, which arises from the electron–hole anisotropic exchange interaction. We have found an aniso-tropic exchange splitting on the order of 14 µeV. We have also realized Hanle-effect measurements on InAlAs quantum dots and we have found a value of e

sg T^

on the order of 100 ps. Using this value and the radiative recombination time we have found that e

g^ of InAlAs/AlGaAs QDs is on the order of 0.2.

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Documents

Spin lifetime from the Hanle effect and fine structure of excitonic levels in InAlAs/AlGaAs quantum dots