Henini M. Handbook of Self Assembled Semiconductor Nanostructures for Novel devices in Photonics and Electronics
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Quantum Dot Charge and Spin Memory Devices 499
In the last few months we applied our optical charge storage techniques to probe single hole –
spin relaxation in small ensembles of self-assembled InGaAs QD [102] . Time and polarization
resolved magneto-optical spectroscopy were performed to obtain as a function of static mag-
netic fi eld and lattice temperature, as for the electron storage samples discussed above. Most
remarkably, our results demonstrated that single hole–spin relaxation can proceed over times-
cales which are comparable to electrons in nominally identical QDs. This shows that the valence
band SO coupling does not necessarily set the timescale for hole–spin relaxation as is the case in
higher-dimensional systems. Explicit expressions for due to SO-mediated single-phonon scatter-
ing produce very good quantitative agreement, demonstrating that hole-spin relaxation in self-
assembled QDs is mediated by the same mechanism as for electrons.
Figure 15.18 shows the temporal evolution of the peak intensity of the resonant peak at B f o r
storage times in the range 0.3 μ s 60 μ s, recorded with circularly polarized excitation and detec-
tion. Here, denotes the intensity of peak R recorded with polarization in both excitation and detec-
tion channels, the other three curves completing the four polarization permutations. The full dark
grey lines in Fig. 15.18 show the storage EL intensities and for the corresponding excitation polariza-
tion averaged over the two detection polarizations. Within experimental error and are independent
of, confi rming that holes are not thermally redistributed between the dots via wetting layer states
during the range of storage times investigated. Careful examination of the data presented in Fig.
15.18 indicates the presence of a signifi cant polarization memory effect; the storage EL is co-polar-
ized with the excitation laser for short storage times () with a degree of circular polarization up to
10% as shown in the upper panel of Fig. 15.18 . As Δ t increases, the DoP decreases exponentially for
both and excitation, reaching an equilibrium value close to zero for long storage times ( Δ t 4 0 μ s).
B 10 T
4000
I
/
(t)
I
/
(t)
I
/
(t)
I
/
(t)
Storage signal (arb. units)
3000
4000
<l>
<l>
3000
0.1 10
Storage time – Δt (μs)
100
3/2
3/2
1
ΓΓ
Figure 15.18 Polarization resolved intensity of resonant hole storage signal as a function of storage time. The four
curves show data for the four combinations of excitation and detection polarizations. Inset: Two-level model used to
represent hole spin states.
Quantitative information can be extracted from these data using rate equations applicable to
a non-interacting ensemble of two-level systems to represent the total population of 3/2 and
3/2 holes in the QDs probed by the experiment ( Fig. 15.18 (inset)). The rates for up-scatter-
ing ( 3/2 → 3/2) and down-scattering ( 3/2 → 3/2) are represented by and, respectively.
Using this model the population of a specifi c spin species, a time t after generation, is given by:
Nt N N
t
T
N
equ
h
↑↓ ↑↓
↑↓
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
() ()
()
() ( ( ) ) 0
2
exp
(15.4)
where
Nt
↑↓ ↑ ↑ ↓()
() ( / )ΓΓΓω
is the Boltzmann distribution at thermal equilibrium,
T
h
1
1/(Γ
↑
is the hole–spin lifetime and N
↑ ( ↓ )
the initial population of spin up (down) holes at
CH015-I046325.indd 499CH015-I046325.indd 499 6/24/2008 5:06:35 PM6/24/2008 5:06:35 PM
500 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
Δ t . Since the intensity of the storage luminescence a time after generation is proportional to the
curves presented in Fig. 15.18b can each be fi tted by
ItI I tT
nm nm
nh
//
exp ( /()( () ) )ΔΔ 0
2
,
where I
n
/
m
is the corresponding intensity at Δ t and { n , m } { , } , { , } { , } , and
I
I
is the saturation value for long storage times. The best fi ts to all four decay curves
are presented as full lines in Fig. 15.18b . Most importantly, all four traces are well described using
a single value for the hole–spin lifetime of
T
h
1
11
using this method.
The observation of such remarkably slow hole–spin relaxation dynamics in QDs contrasts
strongly with bulk III–V materials where spin–fl ip scattering occurs over subpicosecond times-
cales due to SO mixing of the valence band spin states close to the Γ -point in the bandstructure
[96] . This mixing is partially inhibited by motional quantization effects in quantum wells, lead-
ing to enhanced hole–spin lifetimes longer than 1 ns at low temperatures [98] . In contrast, the
fully quantized electronic structure in QDs restricts the phase space for such quasi-elastic scatter-
ing processes and results in much longer hole–spin lifetimes in the present experiment [101] .
Finally, we discuss the dependence of on external magnetic fi eld B along the growth direc-
tion and lattice temperature T , as for the electron sample discussed in the previous section.
Fig. 15.19a shows the excess degree of circular polarization following excitation and detection
plotted as a function of Δ t for B 5 11 T at T 8 K. In all cases the time dependence of the
polarization is well described by a monoexponential decay (Eq. 15.4 ), with a time constant that
becomes longer as the B -fi eld is reduced. The values of obtained are presented in Fig. 15.19b and
directly compared with equivalent data recorded from an electron spin memory device measured
under the same experimental conditions. As the B -fi eld is reduced from 12 to 1.5 T the hole–spin
lifetime is found to increase from 8 3 μ s to 270 180 μ s. The spin relaxation time measured at
B 1.5 T is more than four orders of magnitude longer than recent reports for single CdSe dots
where a lower limit of 10 ns was measured [100] . Furthermore, the ratio
T
h
1
lies in the range
5–10 over the whole range of the B -fi eld investigated, in strong contrast with quantum wells
where
T
h
1
is smaller than 10
3
due to SO mixing of HH and LH valence bands. In the absence
of such SO mixing we expect hole–spin relaxation to be dominated by SO-mediated spin–lattice
coupling, as is the case for electron spin relaxation in self-assembled QDs. To test this hypothesis
we studied the temperature dependence of. Fig. 15.19c shows the temperature dependence of for
10
(l
/
(t)-<|> (10
3
counts/cycle)
1000
T
1
(s)
T
h
1
(s)
(a)
(b)
T
h
1
T
e
1
(c)
6T
Theory
10 T
100
100
10
1
10
0510
10 100
15
8
5T
6T
8T
T 8K
T 10 K
11 T
6
4
2
01020
Storage time Δt (μs)
Magnetic field (T)
Temperature (K)
30
Figure 15.19 (a) Temporal dependence of polarization intensity as a function of Δ t for magnetic fi eld ranging
from 5 to 11 T. (b) Comparison of the B -fi eld dependence of and (fi lled symbols) for identical QD material and exper-
imental conditions. The fi lled line shows the calculated hole spin relaxation time using the model of [101] and the
following parameters: g
h
, 6 meV, 100 meV, m
*
h
0.03 m
0
and T 8 K. (c) Comparison of measured and
calculated dependence of on lattice temperature.
CH015-I046325.indd 500CH015-I046325.indd 500 6/24/2008 5:06:36 PM6/24/2008 5:06:36 PM
Quantum Dot Charge and Spin Memory Devices 501
magnetic fi elds of B 6 T and 10 T. For both magnetic fi elds a very clear
T
h
1
∝
dependence is
observed, exactly as was found previously for electron spin relaxation in the previous section. The
observation of mono-exponential decays and comparable spin lifetimes for electrons and holes
combined with temperature and strong B -fi eld dependencies strongly indicates that the domi-
nant relaxation mechanism for hole spins is, indeed, due to SO-mediated spin–lattice coupling as
has been shown to be the case for electrons.
15.4 Outlook
One of the major challenges for investigations in the immediate future is the determination of
coherence ( T
2
) and inhomogeneous spin dephasing ( T
2
*
) times for single electrons and holes in
self-assembled QD nanostructures. These quantities may be accessible using time resolved coher-
ent optical measurements or by combining the spin storage experiments with electron spin reso-
nance techniques. Another important aspect is the effi cient readout of single electron spins. This
may be achieved optically by incorporating the dots within microcavities with enhanced collec-
tion effi ciency and, thus, enhanced sensitivity. In addition, high-effi ciency electrical readout of
such optically prepared spin systems may also be feasible [103] . The use of the spin degree of
freedom in quantum dots for more complex quantum operations will also require extension of
the present techniques to coupled dots or arrays of dots. Here, frequency selective optical address-
ing provides maximum fl exibility when compared to spin to charge conversion. Furthermore, we
have very recently demonstrated that coupling of self-assembled InGaAs quantum dots is indeed
possible by electric fi eld tuning [104] . This is a fi rst step towards up-scaling of the spin control
from single quantum dots to more complex coupled quantum systems for spin-based quantum
information processing.
Acknowledgements
This work was fi nanced by the Deutsche Forschungsgemeinschaft via SFB631 ( Festkörperbasierte Quan
teninformationsverarbeitung: Physikalische Konzepte und Materialaspekte ) and the Nanosystems Initiative
Munich (NIM) Cluster of excellence. I would like to acknowledge the important contributions from
many of my colleagues and, above all, the hard work and dedication of many PhD, Diploma and
Masters students over the past few years researching the topics presented in this chapter.
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Engineering of Quantum Dot Nanostructures for Photonic Devices
L. Seravalli , G. Trevisi , M. Minelli , P. Frigeri , and S. Franchi
CNR-IMEM Institute, Parco delle Scienze, 37a, I-43100 Parma, Italy
In order to take full advantage of the peculiar optical properties of quantum dot (QD) nano-
structures, their band structure must be engineered to optimize a few relevant parameters.
In this chapter we review some approaches used to design and prepare structures for both the
1.3–1.6 μ m spectral window of low hydroxyl-content optical fi bres, and the 0.98–1.04 μ m one
for telecom and medical applications.
As for long wavelength applications, we discuss fi rst the approach termed as QD strain engi-
neering : in InAs/InGaAs structures on GaAs substrates the composition of InGaAs confi ning
layers and the thickness of the metamorphic lower one determine both the band discontinuities
between QDs and confi ning layers and the energy gap of the QD material, through its strain; the
availability of the two degrees of freedom make it possible to tune both the emission energy and
the activation energy for thermal quenching of emission, a parameter that determines the room
temperature (RT) emission effi ciency. By using QD strain engineering we obtained from struc-
tures grown by molecular beam epitaxy photoluminescence emission at RT up to 1.44 μ m under
excitation power densities as low as 5 W/cm
2
. A simple effective-mass model, validated by our
experimental results, offers a rationale for the achievement of effi cient RT emission at long wave-
length; the results also show that in long wavelength structures the inevitably low-band disconti-
nuities hamper the achievement of room temperature operation.
We review our results on the insertion of InAlAs additional barriers embedding QDs and set
amid the InGaAs confi ning layers; it is shown that the blue shift of emission wavelength due to
the additional barriers can be effectively counterbalanced by the red shift induced by QD strain
engineering; as a consequence, in QD strain engineered structures with enhanced barriers the
activation energies can be signifi cantly increased so that RT emission wavelengths in excess of
1.5 μ m are experimentally obtained.
AlGaAs confi ning layers and InGaAs QDs have been successfully used in order to respectively
increase the band discontinuities and the QD energy gap for 0.98–1.04 μ m emitting structures.
Experimental results and model calculations allow us to discuss the effect of QD and confi n-
ing layer composition on the QD morphology. In particular, we show how the CL composition,
besides band discontinuities, affects also the QD dimensions and other details of the QD band
structure. Furthermore, by studying the effect of the change in composition of InGaAs QDs, we
identify different mechanisms contributing to the blue shift of the emission; 0.98 μ m RT emission
was achieved from structures consisting of InGaAs QDs embedded in Al
0.30
Ga
0.70
As CLs.
16.1 Introduction
Self-assembled semiconductor quantum dots (QDs) have unique properties that make them
extremely interesting for photonic devices with improved performances such as QD lasers [1–4] .
CHAPTER 16
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506 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
Such properties are intrinsic and are related to the zero-dimensional confi nement of carriers in
the structures.
Moreover, by using QD structures advantage may be taken of the lattice mismatch between
components of the structure (about 7% when growing InAs QDs on GaAs substrates) that – in
the case of quantum well (QW) structures – would be intolerably high, whereas in QD structures
can be profi tably used as the driving force for the self-assembly of coherent nanostructures; these
structures grown on GaAs may have a suffi ciently high quality to show room temperature (RT)
emission at 1.3 μ m, a very important advantage with respect to the current technology based on
QW structures on InP substrates [2] .
These considerations explain why a considerable amount of research is devoted worldwide to the
study of QD structures with effi cient RT emission in the spectral windows for lightwave communi-
cations (0.98 μ m and 1.3–1.6 μ m) and medical applications (1.04 μ m). However, the extension of
RT emission to wavelengths up to 1.6 µm is still problematic for QD structures grown on GaAs.
In order to tune the QD emission in regions of interest, it is necessary to control the band struc-
ture details that determine the optical properties of QD structures. Therefore, it is crucial to reach
a fi rm understanding of the complex dependence of QD band structure on material properties,
growth conditions and design parameters. Ultimately, this knowledge will not only allow the QD
band structure to be effectively engineered, but in some cases will also hint at new methods to
extend the spectral range of QD operation.
In this contribution, we thoroughly discuss the engineering of QD emission in InAs/InGaAs
and InGaAs/AlGaAs QD structures intended for 1.3–1.6 μ m and 0.98–1.04 μ m operation,
respectively. In section 16.2, we review different approaches proposed to red shift InAs QD emis-
sion towards the long wavelength spectral region and discuss the various parameters considered.
Then, in section 16.3, we present the q uantum dot strain engineering approach, which relies on the
control of the band structure of InAs/InGaAs QDs by means of both the composition of InGaAs
confi ning layers (CLs) and the strain of QDs, determined by the thickness of a metamorphic lower
CL (LCL) on which QDs are deposited. By using a single-band effective-mass model validated by
the experimental results obtained on QD structures with different CL composition and QD strain
we show how QD strain engineering allows the separate control of QD–CL band discontinuities
and energy gap of the QD material. These band structure parameters can be considered as two
degrees of freedom that can be used simultaneously to tune the emission energy and to optimize
the activation energy for emission quenching at RT, a parameter that determines the emission
effi ciency; this approach results in structures grown on GaAs with RT emission up to 1.44 μ m
under excitation power densities as low as 5 W/cm
2
.
Moreover, a deeper analysis of model calculations leads us to discuss a rationale for the
achievement of effi cient RT emission at long wavelength; in particular, we highlight that the
inevitable requisite for red shifting the emission towards 1.6 μ m is the decrease of the potential
barriers that confi ne carriers which results in the decrease of the emission effi ciency at RT; then,
we show how the use of additional InAlAs barriers embedding QDs increases the emission effi -
ciency of such structures so that 1.51 μ m RT emission is obtained under low excitation power
densities, an interesting step in the quest for 1.6 μ m operation.
In section 16.4 we show how In(Ga)As/AlGaAs structures allow the achievement of blue shifted
QD emission necessary to match the 0.98–1.04 μ m window of operation. The use of compositions
of both CLs and QDs as tuning parameters is thoroughly discussed. In the former case, an analysis
of the physical mechanisms responsible for the blue shift is carried out, thanks to the comparison
between experimental emission energies and model calculations in InAs/AlGaAs structures; in the
latter case the effects of the change of QD composition on QD morphology and band structure are
discussed and the causes of the increase of the emission energies are identifi ed. Finally, in section
16.5 we draw some conclusions and envision possible paths for future work.
16.2 QD nanostructures for long wavelength emission
The emission energy of InAs QDs embedded in GaAs confi ning layers depends on a number
of parameters of structures, such as InAs coverages, QD shapes and dimensions, as well as on
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Engineering of Quantum Dot Nanostructures for Photonic Devices 507
growth conditions, as it is shown, for instance in [5] , where it was reported that the emission
energy at 10 K of structures may range between 1.05 and 1.31 eV, which would correspond to
1.25–1.00 μ m at RT.
In order to red shift the InAs QD emission towards longer wavelengths, a fi rst proposed
approach has been the increase of QD sizes to reduce the confi nement energies for carriers.
This can be obtained by an increase of the InAs coverage; anyway the enlargement of QDs may
result in non-coherent structures, leading to the nucleation of dislocations with deleterious
consequences on the optoelectronic properties. Therefore, various methods to increase QD sizes
have been used, including: (i) the use of the ALMBE technique [6–8] , (ii) other variants of MBE
growth based on the concept of alternating molecular beams [9–11] , (iii) very low growth rates
for InAs deposition [12–15] and (iv) the use of a seed layer of dots in order to control shape, size
and density of QDs grown on a second layer [14, 16–18] .
The second approach to red shift the emission, which has been more generally used in the
last decade, consists in embedding InAs QDs in InGaAs confi ning layers (CLs) instead of GaAs
ones [19–31] . The interpretation of this effect, however, is still debated due to the concomitant
presence of different mechanisms all contributing to the red shift of QD emission energy: (i) the
reduction of QD–CL band discontinuities, which we denote here by the sum Δ E of the conduc-
tion and valence band offsets, (ii) the decrease of the energy gap E
QD
of the QD material, due to
the reduced QD strain ensuing from the reduction of the lattice mismatch between InAs QDs and
InGaAs CLs, and (iii) the change in QD sizes due to intermixing effects between CLs and QDs.
Such contributions cannot be easily singled out, therefore for some authors the most relevant
effect is the reduction of E
QD
[14, 20, 21, 25, 31] , while others have identifi ed the most impor-
tant mechanism in the substantial changes in QD composition and sizes stemming from the
strain-driven In migration from InGaAs CLs to InAs QDs (activated alloy phase separation) [19,
26, 29, 32, 33] .
A comprehensive understanding of the complex interplay of design and growth parameters is
therefore a crucial need in order to be able to reliably engineer InAs/InGaAs QD nanostructures
for photonics devices operating in the long wavelength range.
16.3 Quantum dot strain engineering
When the emission energy is tuned by using the CL composition two effects are to be consid-
ered that are changes of: (i) E
QD
related to the QD strain variation and (ii) QD–CL band discon-
tinuities. In order to disentangle these effects the quantum dot strain engineering [34] approach
has been proposed which is based on the control of: (i) CL composition and (ii) QD–CL mismatch
and, then, the QD strain by using the thickness of the InGaAs lower confi ning layer (LCL). Such a
LCL acts as a metamorphic buffer [34–38] , the lattice parameter of which depends on its thick-
ness through the mechanism of strain relaxation that takes place to minimize the elastic energy
stored in the lattice-mismatched LCL [39] .
InGaAs layers grow on GaAs in two different regimes, depending on their thickness: (i) the
pseudomorphic regime, for thicknesses t smaller than the so-called critical thickness t
c
for plastic
relaxation, where the lattice parameter in the plane of the heterointerface equals that of GaAs,
and (ii) the metamorphic regime, for thicknesses larger than t
c
, where for increasing t the lattice
parameter increases up to that of free-standing (unstrained) InGaAs ( a
InGaAs
).
The lattice constant a
InGaAs
is calculated according to Vegard’s law:
aaaax
InGaAs GaAs InAs GaAs
⫽⫹⫺()
(16.1)
where a
InAs
and a
GaAs
are the free-standing lattice parameters of InAs and GaAs, respectively, and
x is the In composition; the in-plane lattice parameter a
LCL
of the InGaAs metamorphic buffers is
given by:
a
a
InGaAs
LCL
res
⫽
⫹1 ε
(16.2)
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508 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
where ε
res
is the in-plane residual strain of the metamorphic buffer that, independently of the
considered strain relaxation model, does depend on the thickness t of the buffer layer, as it will be
discussed below. Then, the lattice mismatch f between InAs QDs and InGaAs LCL is:
fa a a
InAs
⫽⫺()/
LCL LCL
(16.3)
Photorefl ectance (PR) experiments [38] have shown that the upper confi ning layers (UCL) grow
pseudomorphically on the lower ones with the same composition x . Therefore, both upper and
lower CLs have the same lattice parameter a
CL
and the same mismatch f with respect to the QDs.
Two classes of models have been put forward to describe the residual strain due to plastic
relaxation; they are the so-called non-equilibrium models of strain relaxation (energy-balance
[40] and nucleation models [41] ) and the equilibrium ones that take into account the thermo-
dynamic equilibrium between a rectangular grid of misfi t dislocations and the strained epitaxial
layer [42, 43] . The former and the latter models predict a ε
res
⬀ t
⫺ n
dependence, with n ⫽ 1 / 2
[41] and n ⫽ 1 [44] , respectively.
By PR measurements [45] , as well as by X-ray diffraction and Raman scattering experiments
[46] performed on structures similar to those considered here, it was shown that the measured
values of the residual strain compare quite favourably with the Marée et al. [41] ones, while they
defi nitely do not support predictions of equilibrium models [44] .
0.080
0.070
0.060
0.050
0.58
QD–CL mismatchLCL residual strain
0.030
0.020
0.010
0.000
x ⫽ 0.15
x ⫽ 0.15
x ⫽ 0.15
⫺x ⫽ 0.35
x ⫽ 0.35
InAs QDs/In
x
Ga
1⫺x
As CLs
x ⫽ 0.35
x ⫽ 0.35
110
LCL thickness (nm)
100 1000
0.57
CL lattice parameter (nm)
0.56
Figure 16.1 Dependencies of LCL residual strain, CL lattice parameter and QD–CL lattice mismatch on LCL
thickness in In
x
Ga
1 ⫺
x
As structures in the pseudomorphic (dashed lines) and metamorphic (continuous lines)
regimes. The strain relaxation in LCLs has been calculated according to [41]. Reprinted with permission from [38].
Copyright 2007, American Institute of Physics.
The LCL in-plane residual strain ε
res
following the t
⫺
1/2
dependence, the CL lattice parameter
a
CL
and the QD–CL mismatch f are plotted in Fig. 16.1 as functions of t for different values of x ,
highlighting that by growing QDs on metamorphic InGaAs buffers the QD–CL mismatch can be
controlled in a wide range by acting on both x and t . As discussed in [47] both the hydrostatic
( ε
h
) and biaxial ( ε
b
) components of the QD strain defi ned as ε
h
⫽ ε
xx
⫹ ε
yy
⫹ ε
zz
and ε
b
⫽ 2 ε
zz
⫺
ε
xx
⫺
ε
yy
(where ε
ij
are the components of the strain tensor, z being the direction parallel to the
QD axes) are proportional to the mismatch f , with proportionality constants that depend on the
QD sizes and shapes. The heavy-hole energy gap E
QD
of the QD material (the smallest one in com-
pressively strained semiconductors) is given by [48, 49] :
EE EE
E
Hc
S
QD QD
=++−
0
2
δδ
δ
(16.4)
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