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ACCADEMIA NAZIONALE DEI LINCEI
FONDAZIONE «GUIDO DONEGANI»
38
joint italo-german meeting on
CURRENT ISSUES IN CRYSTAL GROWTH
FROM THE VAPOUR
(Rome, 8-9 November 2005)
edited by
Sergio Carrà and Carlo Paorici
ROMA 2007
BARDI EDITORE
EDITORE COMMERCIALE
Luca Seravalli
(a)
, Giovanna Trevisi
(a)
, Paola Frigeri
(a)
, Secondo Franchi
(a)
SELF-ASSEMBLED ZERO-DIMENSIONAL SEMICONDUCTOR
NANOSTRUCTURES
Abstract – In this paper the fundamentals of the three-dimensional growth
mechanism that takes place during the Molecular Beam Epitaxy of highly lattice-mis-
matched semiconductor heterostructures will be reviewed; it will be shown that the
Stranski-Krastanow mechanism allows the preparation of self-assembled quantum dot
nanostructures of interest for a number of innovative devices. Aspects of the structural,
electronic and optical properties of said structures characterized by zero-dimensional
electronic carrier systems will be presented, along with a few innovative quantum dot
devices that have substantial advantages as compared to those with higher-dimension-
ality carrier systems.
1. Introduction
It is generally agreed upon that innovative nanoelectronic devices will
fulfil the requirements of the information society. Many of these devices
can be fabricated by means of semiconductor epitaxial nanostructures,
where electronic carriers are three-dimensionally confined in nanosized re-
gions of materials (quantum dots) by means of suitable potential barriers;
the quantum confinement takes place whenever both the mean free path and
the de Broglie wavelength of free carriers exceed the critical sizes of struc-
tures.
The barriers can be accurately designed by using composition, doping
and strain profiles of semiconductor layers. The zero-dimensionality of such
carrier systems gives rise to new optical, electronic and transport properties
that are of huge interest for both basic studies and technological applica-
tions [1-3].
The epitaxial growth under suitable conditions of highly lattice-mis-
matched semiconductor heterostructures results in the nucleation of three-
(a)
CNR – IMEM Institute – Parco delle Scienze, 37/a – 43100 Parma (Italy).
— 170 —
dimensional, self-assembled, coherent nanoislands that can be incorporated
in structures for innovative electronic devices, without having recourse to
sophisticated nanolithographic techniques.
In this Chapter we will review: i) the fundamental features of the so-
called three-dimensional or Stranski-Krastanow [4] growth mechanism that
takes place during the Molecular Beam Epitaxy (MBE) of highly lattice-
mismatched (> 2-3%) III-V semiconductor heterostructures and ii) the ad-
vantages that can be taken for the preparation of quantum dot (QD) nanos-
tructures (Section 2). Structural (Section 3), electronic and optical (Sections
4 and 5) properties of said structures will be briefly reviewed and special
emphasis will be placed on the engineering of optical properties of in-
terest for photonic devices; finally, a few new devices such as QD lasers,
single-photon emitters and QD photodetectors, will be shortly discussed
(Section 6).
2. Three-dimensional growth mechanism
In this Section we will present the experimental evidence of the so-
called self-assembled three-dimensional (3D) growth, with reference to the
growth of InAs on a (100) GaAs substrate by Molecular Beam Epitaxy [5-
7]. The dependence of the 3D growth process on the strain of the growing
system will be highlighted and a brief review of the most interesting the-
ories underlying the 3D growth mechanism will be presented.
2.1. The three-dimensional growth mechanism as a tool for strain relaxation
Figure 1 shows the evolution of the Reflection High Energy Electron
Diffraction (RHEED) pattern [8, 9] during the epitaxial growth of a
7% compressively mismatched InAs layer on a (100) GaAs substrate. The
streaky RHEED pattern that shows up during the homoepitaxial growth of
GaAs (Fig. 1 (a)) is peculiar of a growth front with a surface roughness in
the order of the monolayer (ML) (Fig. 1 (b)). The persistence of a streaky
pattern during the first stage of InAs deposition on GaAs (Fig. 1 (c)) is the
experimental evidence that in this phase the growth takes place according to
the two-dimensional (2D) layer-by-layer mechanism, with heterointerfaces
smooth on an atomic scale (Fig. 1 (d)). As soon as the amount of deposited
InAs exceeds the so-called critical coverage θ
c
, the streaky RHEED pattern
is replaced by the spotty one shown in figure 1 (e). This behaviour is related
to the formation of a 3D growth front characterized by the nucleation of
3D nanoislands on the growing surface (Fig 1 (f)). The 3D epitaxial growth
on a 2D epitaxial layer (wetting layer, -WL-) shown in figure 1 is usually
referred to as Stranski-Krastanow (SK) growth [4]; depending on material
— 171 —
properties, the occurrence of 3D island growth may not require the presence
of the 2D WL, in which case the growth mechanism is termed as Volmer-
Weber [10].
The existence of a high lattice-mismatch (> 2-3%) between the epilayer
and the substrate is the key-parameter for the occurrence of the SK growth
mechanism. Depending also on growth conditions, in fact, the elastic strain
energy accumulated in the deposit may be efficiently released through the
formation of coherent 3D nanoislands in which the in-plane lattice parameter
continuously relaxes along the growth direction towards the value of the
free-standing material. In this way the elastic energy is relaxed without the
introduction of misfit dislocations at the heterointerface, that is the favoured
strain-relaxation mechanism for the heteroepitaxy of low lattice-mismatched
materials [11, 12].
2.2. Modelling of the three-dimensional growth mechanism
In order to modelise the 3D self-assembling process, several theories
have been developed taking into account in different ways the thermody-
namics and the kinetics of the growth process.
Fig. 1 – RHEED patterns (panels (a), (c) and (e)) during the 2D deposition of GaAs
(b), the 2D deposition of InAs (d) and the 3D deposition of InAs (f) on a (100) GaAs
buffer layer, respectively. (Seravalli et al.).
— 172 —
Equilibrium energy models have been developed on the basis of the
balance between the energy of 2D and 3D configurations in the presence of
lattice-mismatch. Early studies on the evolution of the growing mismatched
epilayer [13, 14] were able to justify the nucleation of 3D coherent nanois-
lands by taking into account: i) the equilibrium between the energy nec-
essary for the formation of a network of dislocations at the heterointerface
and ii) the surface energy related to the nucleation of a 3D island, that de-
pends on the material parameters and on the island shape. More recently,
by means of complex energetic models [1, 15] the existence of equilibrium
shapes and dimensions of 3D islands was anticipated and some features of
3D island ensembles were justified, such as the reduced size broadening and
the lateral ordering on the growing surface, without the need for the intro-
duction of kinetic limiting steps.
Kinetic models of the SK growth mechanism, on the other hand, were
able to provide a deeper understanding of the mechanisms by which design
and growth parameters may affect the island features. In particular, the key-
roles of lattice-mismatch of the system and of cation surface mobility [16,
17] were highlighted by means of kinetic Monte Carlo simulations. Some
remarkable results of these simulations, confirmed by several experimental
observations, are that: i) in highly lattice-mismatched systems, the strain re-
lease is efficiently achieved by means of the formation of 3D islands, ii) in
3D islands, the density of elastic energy is higher at the island edges that,
consequently, are the most favourable regions for the occurrence of defects
or dislocations, iii) the island size decreases and their surface separation
increases with increasing lattice-mismatch, iv) at constant strain, the equi-
librium configuration of a system depends on the adatom diffusion length,
v) the adatom incorporation at the island edges is inhibited by the presence
of high strain fields, thus reducing the broadening of island dimensions and
vi) under conditions of high adatom surface mobility, the initial stage of
3D island formation is largely based on the incorporation of pre-deposited
adatoms which detach from the 2D strained layer.
3. Three-dimensional islands
Kinetic and energetic models highlight the dependence of 3D island
features on material parameters and growth conditions. These results are
confirmed by a number of experimental works performed by means of mi-
croscopy techniques, such as Atomic Force Microscopy (AFM), Scanning
Electron Microscopy (SEM), Transmission Electron Microscopy (TEM),
Scanning Tunnelling Microscopy (STM) and by high resolution X-ray dif-
fraction (HRXRD) (see Ref. 18 for a comprehensive review). Owing to the
— 173 —
complex nature of the investigated systems, the interpretation of measure-
ments is not always straightforward and several experimental results have
been largely reconsidered during the last years.
The analysis of size distributions and densities of uncapped 3D islands
is successfully performed by means of scanning probe techniques such as
AFM and STM. It is worth noting that, though the evaluation of the height
of 3D islands by means of AFM is quite straightforward, the measurement
of the island lateral size and the observation of the shape are affected by
convolution effects between islands and probing tips, that have sizes of the
same order of magnitude. Convolution effects can be taken into account if
the size and shape of the tip and the height of islands are known [19, 20].
Plan-view or cross-sectional TEM and STM may be used to investigate
the size, shape and composition of capped and uncapped 3D islands. One
of the main problems concerning the interpretation of TEM images is the
modelling and disentanglement of the strain- and composition-dependent
contrast which affects the measurements [21]. Valuable information may be
obtained by the analysis of cross-sections of 3D islands that allows the de-
termination of both the shape of 3D islands and their compositional profile
on an atomic scale. The analysis of cross-sections of 3D islands, however,
is affected by several additional problems as compared to plan-view meas-
urements [22], such as: i) the outwards relaxation of islands induced by the
absence of the surrounding material after cleaving and ii) the dependence of
the section of the island on the relative position of the cleavage plane with
respect to the island axis. Cross-sectional TEM measurements, moreover,
are affected by the additional problem of the superposition of the diffraction
information over the whole layer containing the island.
Investigations of the shape and surface correlation of the position of 3D
islands have been successfully carried out by means of grazing-incidence
X-ray techniques, such as X-ray reflectivity (XRR) and grazing-incidence
small-angle X-ray scattering (GISAXS) [23].
In the following, the main results concerning the study of island mor-
phology, density and composition will be reviewed.
3.1. Morphological and structural properties of three-dimensional islands
Figure 2 shows the AFM image of a InAs deposit with a 3 ML coverage
on a (100) GaAs substrate; since this coverage exceeds θ
c
(~ 1.6 ML) the
3D island nucleation occurs, as evidenced in the figure. By means of AFM
measurements, it is possible to infer that: i) the islands are nanometer-sized,
with heights and diameters of few nm and few tens of nm, respectively,
ii) the islands are homogeneously distributed on the growing surface with
maximum surface density in the order of 10
11
cm
-2
and iii) the island dimen-
— 174 —
sions have reduced dispersions that, depending on growth conditions, are in
the order of 10%.
The determination of the shape of 3D islands is still a controversial
matter; depending on both growth conditions and investigation techniques,
different shapes have been attributed to 3D islands. STM measurements per-
formed under ultra-high vacuum conditions [24] showed that the shape of
uncapped InAs 3D islands is characterised by high-index facet orientation
which forms an angle with the (100) GaAs surface as low as 20°, this result
suggests that self-assembled 3D islands are rather flat nanostructures with
lens-like shape [25]. A review regarding the experimental determination of
the shape of InAs 3D islands is given by Jacobi [26].
A very detailed study of the dependence of emission energies of InAs/
GaAs QDs on the InAs coverage in the early stages of QD formation has
shown that the experimental points are aligned on lines (Fig. 3); this result
has been interpreted as due to the formation of different families of dots,
with heights differing by MLs [27-29]; calculations of emission energies
from such QD families have supported the above interpretation [27]. This
behaviour strictly mimics the one related to “monolayer fluctuations” that
take place in quantum wells, where the widths change by integer values of
ML in different parts of the structures.
Very recently, the formation and evolution of multimodal InAs/GaAs
QD ensembles during growth interruptions prior to cap depositions have
been studied [30, 31]. Again, it was found that InAs QDs grown very closely
to the 2D-3D transition have heights that vary in steps of complete InAs
monolayers and have top and bottom interfaces both well-defined and flat.
An even more pronounced formation of said families was observed when
during growth interruptions the surface was irradiated by Sb, acting as a
surfactant. The photoluminescence spectra were in an excellent agreement
Fig. 2 – (500 x 500 nm
2
) AFM image of
InAs quantum dots (3 ML InAs coverage)
deposited on (100) GaAs. (Seravalli et al.).
— 175 —
to emission energies calculated by assuming shell-like size variations of
truncated pyramidal InAs/GaAs QDs with heights differing by 1 ML [31].
Several experimental observations evidenced the presence of non-uniform
composition profiles in the 3D islands and in the surrounding barriers, though
different results have been reported in the literature [32-34]. This may be at-
tributed not only to the difficult interpretation of high resolution measure-
ments, but also to the complex dependence of the 3D island features on both:
i) growth conditions, such as growth temperatures, growth rates, V-to-III flux
ratios and ii) capping procedure, as explained in the next Section.
3.2. Capping of three dimensional islands
The growth of overlayers on top of 3D islands is necessary for the
quantum confinement of carriers (Section 4); the capping procedure strongly
affects the 3D island strain, composition and morphology owing to both: i)
the island lattice distortion induced by the different lattice parameter of the
overlayer and ii) the interdiffusion of material between islands and over-
layers. Unless the growth temperature of the cap layer is extremely low
[35], it has been shown [36, 37] that interdiffusion takes place at the very
first stage of island encapsulation and is responsible for: i) a significant
change of 3D island shape due to mass transport from the top to the bottom
of islands and ii) the alloying of the islands. Zhi and co-workers [38] ob-
served that the effective In composition of InAs islands after encapsulation
is much lower than the nominal one (about 65%) and decreases away from
the central core. Regarding the composition of capped 3D islands, it is worth
noting that studies performed on In(Ga)As self-assembled islands prepared
by both MBE and Metalorganic Vapour Phase Epitaxy [39] suggested that
3D islands may reach an equilibrium composition that is independent of
nominal composition and growth technique.
Fig. 3 – Energies of decon-
voluted 10 K photolumi-
nescence emission peaks of
InAs/GaAs quantum dots
as functions of InAs cov-
erage. In the inset the 10 K
photoluminesce spectrum
of a structure with a 1.84
ML InAs coverage is
shown. Adapted from Ref.
29. (Seravalli et al.).
— 176 —
3.3. Three-dimensional island surface density
The initial stage of the formation of InAs 3D island on a (100) GaAs
surface is characterised by the fast evolution of the island surface density,
until it reaches a saturation value [40]. The additional material deposited
beyond the achievement of the surface density saturation increases the
volume of 3D islands, as deduced by STM measurements of uncapped struc-
tures. Both the island density saturation value and the size of 3D islands in
the post-saturation regime are strongly dependent on growth kinetics. The
enhancement of group-III adatom diffusion length, in particular, favours the
formation of ensembles of 3D islands with lower density and larger mean
size as compared to higher density and smaller mean size of islands nu-
cleated under conditions of low adatom surface mobility [40, 41]. This be-
haviour has been observed by a number of experimental works in which the
adatom diffusion length has been changed by changing growth conditions
such as: i) the growth temperature [42], ii) the growth rate [43], iii) the
V-to-III flux ratio [44] and iv) the growth technique [45]. High growth tem-
peratures, very low growth rates and sophisticated growth schemes, com-
bined with low island coverage, were used to affect the adatom diffusion
length in such a way to reduce the 3D island surface density down to 10
7
-
10
8
cm
-2
[46, 47], a necessary requirement for the preparation of structures
for single-photon emission purposes (Section 6).
3.4. Stacking of three-dimensional island planes
A key-demand for the fabrication of a number of optoelectronic de-
vices, such as QD lasers, is the large number of islands of active material
per unit volume. Since the maximum value of the 3D island surface density
is kinetically limited, the stacking of several planes of 3D islands is used in
order to achieve high volume densities. A consequence of stacking is that
the strain energy that builds up as the number of QD planes increases af-
fects the structural [48] and morphological [49] properties of 3D islands. For
structures consisting of InGaAs islands embedded in GaAs, three different
regimes were identified depending on the spacer layer thickness d [50]: i)
vertically correlated growth for low d, in which 3D islands tend to grow on
top of the underlying buried islands, ii) vertically anticorrelated growth for
intermediate d, in which 3D islands in neighbouring layers tend to grow in
between the underlying buried islands and iii) uncorrelated growth for high
d. In the cited work, the correlation-to-anticorrelation transition occurs for
d of about 150 ML [50]. These different behaviours have been thoroughly
investigated and the explanations were found to rely on the dependence of
cation diffusion length in successive layers on the strain induced by the
buried 3D islands, that propagates through the spacer layers [51-54].
— 177 —
3.5. Wetting layer depletion and alloying
Theoretical calculations [17] and experimental observations suggest
that the 2D WL plays an active role during the nucleation of 3D islands.
The measurement of the total volume of uncapped InAs 3D islands evi-
denced the increase in island size at high growth temperatures [43] and low
growth rates [55]; these experimental results were attributed to both: i) the
enhancement of adatom migration length and ii) the enhancement of strain
induced detachment of adatoms from WL which favours the incorporation
of additional amount of material into the 3D islands.
The additional effect of the In segregation process [56], along with the
strain-driven WL depletion, lead to a pronounced alloying of the InGaAs WL
during the 3D island nucleation. For this reason, it is usually an hard task
to control the composition and thickness of the 2D strained layer resulting
from the SK growth mechanism. Modified MBE growth techniques such
as heterogeneous droplet epitaxy [57], modified droplet epitaxy [58] and
sub-ML deposition [59] allow the preparation of 3D nanostructures without
WLs or with controlled WL thicknesses. As compared to the conventionally
prepared SK nanoislands, these structures may lead to improved optical per-
formances, owing to the absence of the channel for thermal escape of car-
riers represented by WLs (Section 4).
4. Three-dimensional confinement of carriers
Quantum dots (QDs) are semiconductor nanostructures where con-
finement of carriers in all three spatial directions is realized and, then, a
zero-dimensional (0D) system of carriers is obtained. This occurs when the
dimensions of the self-assembled islands are comparable to the de Broglie
wavelengths of carriers and to their mean free-path, as it is usually the case
for semiconductors. When such nanoislands are embedded into layers of
semiconductors with larger energy gap and appropriate band discontinuities,
carriers are effectively quantum confined inside the nanoislands.
In figure 4 a schematic of the InAs/GaAs QD structure along an arbitrary
direction is shown, where confined ground levels for electrons and holes and
pertaining energy quantities of the structure, such as confinement energies,
band discontinuities and optical QD transition energy, are indicated.
4.1. Zero-dimensional and two-dimensional quantum levels
Thanks to the zero dimensionality of the carrier system, within QDs
a very efficient radiative recombination between confined electrons and
— 178 —
holes takes place. For this reason, the study of the QD optical properties
has attracted considerable interest in these last years and was performed
by different techniques such as photoluminescence (PL) [60-62], excitation
of photoluminescence (PLE) [63, 64], micro-photoluminescence [65] and
scanning near field optical spectroscopy (SNOM) [66].
The electronic structure of QDs results from the interaction between
zero-dimensional QDs and the two-dimensional WL levels; the WL state is
believed to have an important role in determining the thermal quenching of
the light intensity emitted from QDs. In particular: i) the QD light intensity
may be quenched at increasing temperature, due to the thermally activated
escape of carriers from QD to WL levels [67-70], ii) the fast PL energy
redshift and the concomitant decrease of PL linewidth with increasing tem-
perature may be attributed to thermally-enhanced carrier relaxation among
dots, as mediated by the WL level [71-73]. Recent studies on WL-free QDs
[74] have helped in gaining insight on the WL role in the QD system, of
particular interest for room temperature QD-based optoelectronic devices.
4.2. Effects of QD properties on confined quantum levels
A wide and particularly active area of research on QDs is the study of
the dependence of the QD confined levels (and, therefore, of the emission
energy E) on parameters such as: i) QD sizes, ii) band discontinuities be-
tween confining layers (CLs) and QDs and iii) QD material energy gap. The
deep understanding of the different effects of the QD system properties is
necessary in order to tune the QD emission at wavelengths of technological
interest for optoelectronic devices, to be discussed in Section 5. As repre-
sented in figure 4, the emission energy E is given by the sum of the energy
Fig. 4 – Schematic diagram of conduction (CB) and valence (VB) band profiles for
an InAs/GaAs QD structure (right panel) along an arbitrary direction shown by the
arrow (left panel). The confined ground levels for electrons and holes are indicated.
E corresponds to the fundamental optical transition energy. The energy gap of the QD
material is indicated by E
g
, while E
e
and E
h
are the confinement energies for electrons
and holes, respectively. ∆V
e
and ∆V
h
are the band discontinuities for the CB and VB,
respectively. (Seravalli et al.).
— 179 —
gap of the QD material (E
g
) and of the confinement energies for electrons
and holes (E
e
and E
h
), neglecting exciton effects.
Confinement energies depend on: i) band discontinuities ∆V
e
and ∆V
h
for conduction and valence bands, respectively, determined mainly by the
QD and CL compositions and ii) QD dimensions and shape. On the other
hand, the energy gap of the QD material depends on the composition of the
QD and on the QD strain, due to the mismatch between CLs and QD. This
quantity, in turn, is related to the composition of the QD itself and of the
confining layers and to the CL residual strain, if they are not lattice-matched
to the substrate. Moreover, other effects may influence the energy values of
QD levels, such as: i) effective QD composition, that could substantially
differ from the nominal one and may depend on growth and design param-
eters, ii) spatially non-uniform composition profiles, both in QDs and CLs,
iii) spatially dependent strain fields, affecting locally QD and CL energy
gaps.
Therefore, it can be easily understood that the energy of QD confined
levels depends in a rather complex way on various parameters related to
both the QDs (shape, sizes, strain, composition) and the CLs (composition,
residual strain) and determined not only by the design of the structure, but
also by growth conditions.
5. Engineering of three-dimensional confined levels
One of the most interesting topics of research on QDs in these last years
has been the engineering of the QD structure aimed at tuning the emission
wavelength in the spectral windows of optoelectronic interest. Wavelengths
of particular technological importance are 0.98, 1.31 and 1.55 µm, used
for optical telecom and datacom networks (Section 6). As InAs/GaAs QDs
grown under typical conditions generally emit in the 1.05-1.10 µm range,
it is necessary to affect one or more of the parameters discussed in the pre-
vious Section, in order to redshift or blueshift the emission at room tem-
perature (RT). This requires a deep understanding of the effects of all pa-
rameters on the emission energy.
5.1. Engineering of QD nanostructures for 0.98 µm emission
The engineering of QD emission towards 0.98 µm at RT is of particular
interest since this wavelength matches the optical pumping level of Er
3+
doped fiber amplifiers (EDFA), used for long-haul telecom networks [75].
The most investigated system for this application consists of self-assembled
InGaAs QDs embedded in AlGaAs CLs (Fig. 5 (c)) that have emission energy
— 180 —
that increases by increasing the Al content in AlGaAs CLs [76-79]. This
result has been attributed to both: i) the enhanced carrier confinement poten-
tials in conduction (CB) and valence (VB) bands and ii) the change in QD
size, shape and composition as a function of the composition of underlying
AlGaAs surfaces. The presence of Al on the growing surface, in fact, proved
to affect the growth kinetics [80] leading to: i) the decrease in QD size [80,
81], ii) the increase in QD surface density [80, 81] and iii) the prevention of
In out-diffusion from the QDs towards the CLs [82]. A further experimental
approach used to blueshift the emission energy is based on the annealing
at high temperature of InGaAs QDs embedded in AlGaAs layers [83]. The
observed behaviour is generally attributed to structural and morphological
changes of the QD-CL system due to material interdiffusion and to thermally
activated segregation of In out of the QDs. Based on these experimental ob-
servations, 0.98 µm laser devices have been prepared by using InGaAs QDs
embedded in AlGaAs layers [84-86]. Owing to the high temperature growth
of the upper CL, required for high quality AlGaAs layers, a blueshifted laser
emission in the window of interest has been observed [87].
5.2. Tuning QD emission at 1.31 µm and 1.55 µm
In order to obtain a redshift in the QD emission it has been proposed to
increase QD sizes to reduce the confinement energies for carriers. However,
the increase of sizes cannot be obtained by simply increasing the InAs cov-
erage, because the concomitant increase of elastic energy stored in QDs may
result in the formation of dislocations that would spoil the optoelectronic
properties of structures. The increase of QD dimensions, instead, has been
obtained by using: i) the ALMBE technique to grow InAs coherent QDs
[45], ii) other variants of MBE growth based on the concept of alternating
molecular beams to grow InGaAs QDs [88-90], iii) very low growth rates
(LGR) for deposition of InAs [91-93].
A second approach to redshift the QD emission is the reduction of
CL-QD band discontinuities, by using InGaAs confining layers, instead of
GaAs ones. However, when InAs QDs are embedded in InGaAs layers also
the QD-CL mismatch is reduced and, then, both the QD strain and the QD
energy gap decrease. This is schematically shown in figure 5 (a) and (b),
where band profiles in function of one arbitrary spatial coordinate for the
InAs/GaAs and InAs/InGaAs/GaAs structures are presented, respectively. In
this way, two associated mechanisms, both contributing to the redshift of
the emission, are in action, making it difficult to single their role out.
As a matter of fact, InAs/InGaAs QD structures emitting at 1.31 µm
have been very often reported [91, 94-99], but the effect of the reduction
of band discontinuities and of QD energy gap has been debated. In some of
these works the major contribution is attributed to the QD strain reduction
— 181 —
[91, 96], while for other authors the principal effect is the reduction of band
discontinuities [97]. Other authors invoke yet another effect, namely the
increased QD dimensions and/or changed QD composition due to strain-
driven In migration from InGaAs confining layers to QDs [94, 95].
QD emission at 1.55 µm has proven to be a rather more difficult ob-
jective for research, but very recently some works opened the way to reach
this goal. Most of the results reported so far are based on the reduction of
the QD strain that stems from the decrease of the energy gap of the QD
material; the reduction of strain has been obtained by: i) partially-relaxed
InGaAs lower confining layers, acting as metamorphic buffers [100-103],
ii) AlGaAsSb LCLs [104], and iii) InAs QDs grown on InP substrates [105-
109]. The use of diluted nitride alloys in QDs is reported to be an inter-
esting approach to redshift the QD emission towards the 1.55 µm optoelec-
tronic window [110, 111], even if such alloys still have a number of material
problems related to their metastability.
5.3. QD strain engineering
It clearly emerges from the results of these last years that a deep un-
derstanding of the effects of different parameters in the redshift of the QD
emission light for InAs/InGaAs/GaAs is still lacking. To clarify the role of
the different mechanisms, Seravalli et al. [100] studied InAs QDs embedded
between In
x
Ga
1-x
As lower confining layers (LCLs) with different compo-
sitions and thicknesses and upper confining ones, with the same composi-
tions of LCLs. In LCLs with thicknesses exceeding the critical thickness
for plastic relaxation, misfit dislocations are formed to release the elastic
energy accumulated in the layers; different models have been put forward
Fig. 5 – Schematic diagram of band profiles for: (a) InAs/GaAs QD structures, (b)
InAs QDs embedded in InGaAs CLs and (c) InGaAs QDs embedded in AlGaAs CLs.
(Seravalli et al.).
— 182 —
to describe the decrease in residual strain, resulting from dislocation for-
mation, and, then, the increase in the LCLs lattice parameter as its thickness
increases (Ref. 112 and references therein quoted). As a consequence of the
dependence of LCL residual strain on its thickness, the QD strain decreases
in a predictable way, that was ascertained experimentally and compared with
model predictions [112]. Therefore, by controlling the band discontinuities
determined by: i) the QD and CL compositions and ii) the QD strain, related
to the LCL thickness and composition, it is possible to obtain emission en-
ergies at 10 K, corresponding to wavelengths beyond 1.55 µm at RT; this
approach can be termed as QD strain engineering [100]. In further works
[101, 113], the authors used a simple model to calculate the QD emission
energy as a function of the QD-CL mismatch (affecting the QD strain) and
of the CL composition in InAs/InGaAs/GaAs structures, where metamorphic
InGaAs buffers were used as lower confining layers. In figure 6 (a), the
calculated 10 K QD emission energy is plotted as a function of the two pa-
rameters. From these calculations it was possible to deduce the values of the
pairs of QD-CL mismatch and CL composition that correspond to emission
at given wavelengths at room temperature, as shown by the dashed lines in
the figure. QD strain engineered structures showed PL emission in good
agreement with model calculation, as presented in figure 7. Furthermore, as
there are two parameters available for structure design, it was also possible
to minimize the thermal quenching of the QD emission, by maximizing the
activation energy for thermal carrier escape from confined levels; this pa-
rameter is given [114] by the sum of the energy difference from QD levels
to CL states for electrons and holes (Fig. 6 (b)). The above considerations
Fig. 6 – (a) Model calculation for emission energies at 10 K for InAs QDs with In
x
Ga
1-
x
As relaxed LCLs in function of QD-CL mismatches f and CL compositions x. Lines
represent the pairs of values (x, f) that result in RT emission wavelengths at 1.3, 1.4
and 1.5 µm; (b) Model calculation for activation energy for confined-carriers thermal
escape (see text) for same structures of figure 6 (a). Lines indicate same (x, f) pairs
evidenced in figure 6 (a). Adapted from Ref. 113. (Seravalli et al.).
— 183 —
show that QD strain engineering is a viable method not only to engineer the
QD emission in the windows of optoelectronic interest at 1.31 µm and 1.55
µm, but also to enhance the RT emission efficiency, by maximizing the acti-
vation energy for the above intrinsic quenching mechanisms.
5.4. Vertical electronic coupling in QD stacks
A high surface density of QDs is necessary for some optoelectronic ap-
plications, in particular for QD lasers. A efficient method to increase this
parameter is to have QD stacks, separated by spacers. In structures with
vertically stacked QD layers, described in Section 3.4, the stacking details
have a relevant influence on the electronic properties. In particular, the QD
emission energy E depends on the vertical interaction among QDs, that
is related to the number of QD planes N and on the thickness of spacer
layers D [115, 116]. Different regimes can be identified: i) for D ≤ 20 ML,
confined carriers in different stacks may interact, causing a redshift of the
emission energy when N increases [115, 116], ii) for D ≥ 50 ML, there is
very little coupling and the emission energy is not affected by the increase
of N, iii) for intermediate values, as D increases E initially shows a blueshift
and then a small redshift. This last feature, typical of an intermediate-cou-
Fig. 7 – 10 K experimental QD emission energies in function of the QD-CL mismatch
with (x, f) pairs selected (Fig. 6 (a)) for 1.3, 1.4, 1.5 and 1.55 µm emission at room
temperature, as indicated by dashed lines. Adapted from Ref. 101. (Seravalli et al.).
— 184 —
pling regime, has been interpreted as due to complex dependence of the
confinement energies and of the exciton binding energy on N [117].
6. Zero-dimensional devices for nanoelectronics
Due to their peculiar properties that may lead to largely improved or
new device performances, zero-dimensional structures have attracted con-
siderable interest in these last years for optoelectronic applications, such as:
i) QD lasers, both edge-emitting laser and Vertical Cavity Surface Emitting
Laser (VCSEL) devices, ii) single photon emitters and other devices for
quantum computing, iii) Quantum Dot Infrared Photodetectors (QDIP), iv)
Semiconductor Optical Amplifiers (SOA) and v) memory devices.
The most studied and developed QD device so far is undoubtely the QD
laser. Indeed, as shown in figure 8 (a) the three-dimensional confinement of
carriers brings a unique energy dependence of the density of states (DOS)
that is given by δ-like functions centered at the discrete values of energy of
confined levels, with spectral widths related to the QD size-dishomogeneity
and not to kT. Therefore, laser gain was predicted to be higher and with
a sharper energy dependence as compared to that of higher-dimensionality
systems, as indicated in figure 8 (b) [119]. As a consequence, the threshold
current density J
th
is reduced, leading to a lower power dissipation and,
then, an increase of the device lifetime. These considerations lead to the
proposal of a QD laser device back in 1982 by Arakawa et al. [120]. Edge-
emitting QD lasers were fabricated since 1994 [121-123] and the lowest
threshold current density reported so far has a value as low as 20 A/cm
2
Fig. 8 – (a) Density of states in three-, two- and zero-dimensional systems (3D, 2D and
0D, respectively); adapted from Ref. 118. (b) Energy dependence of gain coefficients
for 3D, 2D, 1D and 0D structures. Adapted from Ref. 119. (Seravalli et al.).
— 185 —
[124, 125], that outperforms the quantum well laser one [126]. Another
advantage in using QDs as active materials for lasers is the lower sensi-
tivity of J
th
to the operation temperature. This is due to the discreteness
of electronic levels that forbids carrier losses with increasing temperature
T, leading to an higher characteristic temperature T
0
, defined by means
of J
th
(T) = J
0
exp(T/T
0
). The capability of having laser emission at 1.31
µm, and possibly at 1.55 µm using structures grown on GaAs substrates, as
discussed in Section 5, adds technological interest to QD lasers. The con-
ventional approach is based on InGaAsP/InP quantum well lasers on InP
substrates, notwithstanding that such substrates do not compare favourably
with GaAs ones due to: i) a lower crystalline quality, higher costs and a
less mature technology, ii) reduced carriers confinement in InGaAsP/InP
structures compared to AlGaAs/InGaAs ones and iii) lower refraction-index
mismatch in the InGaAs/InP system, as compared with that of the Al(Ga)
As/GaAs system, that prevents the fabrication of efficient Bragg reflectors.
This feature is of great importance, as it permits the fabrication of VCSELs
[127-129], devices of great interest for low-cost, high-performance lightwave
communications networks.
A second application of QDs that is attracting considerable interest re-
cently are single photon emitters to be used as building blocks in Quantum
Computing (QC), which combines computer science and quantum me-
chanics to realise computers where the elementary unit of information is the
quantum bit (qubit) [130, 131]. By reducing the surface density of QDs to
values less that 10
9
cm
-2
(Section 3) and using submicrometer-size device
fabrication, it has been possible to observe single photon emission [132,
133] and to develop single QD LEDs [134, 135].
Yet another QD device developed in these recent years is the Quantum
Dot Infrared Photodetector (QDIP) [136, 137]. Thanks to intersubband pho-
toexcitation of electrons from QD levels to the continuum, it is possible to
detect a photocurrent flow, for shining light in the 2-30 µm range. QDIPs
are attracting as they have: i) sensitivity to normal incidence radiation, that
is generally not allowed by selection-rules for optical transitions in Quantum
Wells Infrared Photodetectors (QWIPs), ii) reduced dark currents, iii) higher
photocurrent responsivities [136-139].
QDs have been used also as active materials in Semiconductor Optical
Amplifiers (SOAs) [140, 141], as they showed high operation speeds (likely
beyond 100 GHz) and the possibility of amplifying different wavelengths
at the same time. Lastly, QD structures have also been implemented in
memory devices, where single carriers confined in QDs are used as ele-
ments for write and read processes [142-144].
— 186 —
Conclusions
In this Chapter we have briefly reviewed the basic MBE growth
mechanism that takes place when the growth of highly lattice-mismatched
structures is carried out under controlled conditions. The so-called 3D or
Stranski-Krastanow growth mechanism allows the preparation of semicon-
ductor nanostructures (quantum dots) where the charge carriers are three-
dimensionally confined by suitable potential barriers in space regions with
sizes comparable to the de Broglie wavelength of carriers and to their mean
free path. Then, we have presented a few structural features of QD nano-
structures and some electronic and optical properties that stem from the 3D
quantum confinement. Finally, a brief review on innovative QD-based de-
vices for telecommunications, quantum computing and optical processing
of information and on their respective advantages has been given; this dis-
cussion justifies the expectations that QD nanostructures will have a con-
siderable impact in the development of next generation nanoelectronic de-
vices.
Acknowledgments
This work has been partially supported by the MIUR-FIRB project “Nanotec-
nologie e Nanodispositivi per la Società dell’Informazione” and by the SANDiE
Network of Excellence of EC, contract no. NMP4-CT-2004-500101.
— 187 —
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