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InAs Quantum Dot Formation Studied at the Atomic Scale
by Cross-sectional Scanning Tunnelling Microscopy
J. M. Ulloa, P. Offermans and P. M. Koenraad
Department of Applied Physics, Eindhoven University of Technology, The Netherlands
5.1 Introduction
5.1.1 Quantum dot formation
Self-assembled quantum dots (QDs) have attracted much attention in the last years [1, 2] . These
nanostructures are very interesting from a scientifi c point of view because they form nearly
ideal zero-dimensional systems in which quantum confi nement effects become very important.
These unique properties also make them very interesting from a technological point of view.
For example, InAs QDs are employed in QD lasers [3, 4] , single electron transistors [5] , mid-
infrared detectors [6, 7] , single-photon sources [8, 9] , etc. InAs QDs are commonly created by the
Stranski–Krastanov growth mode when InAs is deposited on a substrate with a bigger lattice con-
stant, like GaAs or InP [10] . Above a certain critical thickness of InAs, three-dimensional islands
are spontaneously formed on top of a wetting layer (WL) to reduce the strain energy. Once cre-
ated, the QDs are subsequently capped, a step which is required for any device application.
For any application based on InAs QDs, an accurate control of their electronic properties is
required. The electron and hole states in the dot are very sensitive to the QD size, shape and com-
position (as well as to the surrounding material), and therefore an accurate control of the QD
structural properties is necessary for applications. This explains the strong effort dedicated in the
last years to the structural characterization of QDs [11] , which is essential in order to have a deep
understanding of the QD formation process. Although a lot of effort has been dedicated to study
surface QDs, there are relatively few studies focused on the effect of the capping process [12–20] .
Some of these studies have already shown signifi cant differences in size, shape and composition
between uncapped and capped QDs. For example, an important collapse of the QD height has
been reported for InAs/GaAs QDs capped with GaAs [14, 15, 17–19] , revealing the big infl uence
of the capping process on the structural properties of the QDs. Indeed, critical issues affecting the
dot take place during capping like dot decomposition, intermixing, segregation, As/P exchange
and composition modulation in the capping layer. This means that the real buried QDs must be
studied in order to understand the complete QD formation process. Cross-sectional scanning tun-
nelling microscopy is an especially useful technique for this purpose, because it allows the struc-
ture of the capped dots at the atomic scale to be assessed.
5.1.2 Cross-sectional scanning tunnelling microscopy (X-STM)
The scanning tunnelling microscope is part of the family of scanning probe microscopes, which
are able to provide direct real space information of a physical property at the atomic scale. This
CHAPTER 5
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166 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
is done by scanning a probe across the surface of a sample while recording the measured signal,
which results in an image of the surface. In the case of scanning tunnelling microscopy (STM),
invented in 1981 by Binnig and Rohrer [21] , the probe consists of a metallic tip which is brought
into tunnelling contact with a (semi-)conducting surface. The quantum mechanical tunnelling
effect allows the electron to tunnel through the vacuum barrier even when the energy of the
electrons is lower than the potential barrier ( Fig. 5.1a ). Since the tunnelling current depends
exponentially on the distance between tip and sample, an atomic-scale height map of the sur-
face density of states and topography can be acquired by adjusting the tip sample distance during
scanning, using a feedback loop that keeps the tunnelling current constant ( Fig. 5.1b ).
Feed
back
Height
motion
of the tip
Scanning direction
Piezo scanning unit
Tip Fermi level E
F
(a) (b)
Sample Fermi level
Vacuum level
Sample
V
d
Tip
eV
Metallic tip
Sample surface
V
e
Figure 5.1 (a) Schematic showing the overlap and decay of tip and sample wave functions in the vacuum barrier.
(b) Schematic of a scanning tunnelling microscopy with feedback loop.
In cross-sectional scanning tunnelling microscopy (X-STM), the direct visualization of nano-
structures, which are generally embedded in several layers of semiconducting material, is possible
by cleaving the sample and thereby exposing the cross-sectional surface of the buried nanostruc-
tures. The semiconductor wafers are cleaved along a natural cleavage plane to expose a cross-
section of the epitaxial layers grown on the wafer. In the case of III/V semiconductors, the (110)
and
()110
cleavage planes of the zinc-blende crystal show a 1 1 surface unit cell reconstruc-
tion where the group III elements move into the surface while the group V elements move outward
( Fig. 5.2 ). This buckling behaviour causes the energetic position of the dangling bond surface
states of the type III and type V elements to move above and below the semiconductor band gap
in the bulk, respectively. Therefore, depending on the polarity of the applied bias between tip and
sample, either the empty states of the type III elements (Vsample 0) or the fi lled states of the
type V elements (Vsample 0) are imaged ( Fig. 5.3 ). Since the (110) and
()110
surface planes
contain only half of the (001) layers within the zinc-blende crystal, the atomic rows observed in
the cross-sectional STM image are separated by a bilayer distance in the growth [001] direction,
which is equal to the lattice constant a
0
. Because there are no surface states present in the band
gap of most cleaved III/V semiconductors, the Fermi level at the cleaved surface is unpinned,
i.e. it is not forced to assume a specifi c value in the band gap independent of its value in the bulk
material. This allows the electronic properties of the bulk to be probed at energies near the band
gap. The bulk states generally contribute with an electronic contrast to STM images that is not
related to the actual physical topography of the surface, but governed by factors such as varia-
tions in the band gap, doping level and electron affi nity.
The electronic contribution to the apparent height in the STM image can be suppressed to a
large extent by scanning at high voltages [22, 23]. Since the tunnelling probability decays expo-
nentially with the height of the effective tunnelling barrier, the states with the highest energy
contribute most to the tunnelling current. If a suffi ciently large voltage is applied during empty
state imaging of a heterostructure, the states contributing most to the tunnelling current have
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InAs Quantum Dot Formation Studied at the Atomic Scale 167
Filled surface states
Sample
Tip
Sample
E
v
E
e
e
1.7 V
1.7 V
eV
E
v
E
e
e
eV
Empty surface states
Tip
Figure 5.3 Schematic of tunnelling into empty and fi lled surface states, and STM image showing the atomic cor-
rugation at both polarities.
Surface
layer
Dangling bonds
Sub-surface
layer
Side view of
(110) surface
Sub-surface row
a
Top view of
(110) surface
Anion (type V element) Cation (type III element)
Surface row
Figure 5.2 Schematic top and side view of III/V semiconductor (110) surface.
energies far above the conduction band edge and the contribution of the lower lying states is
negligible. Similarly, the voltage dependent sensitivity of the tunnelling current on doping level
can be overcome by injecting electrons above the depletion region. In the case of fi lled states tun-
nelling (electron tunnelling from sample to tip), the valence band offset in a heterostructure is
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168 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
smaller with respect to the total barrier height than the conduction band offset, since the effec-
tive barrier height for tunnelling is increased by the band gap. Therefore, the resulting electronic
contrast is smaller than in the case of empty states tunnelling (electron tunnelling from tip to
sample). Thus, as demonstrated in [22, 23] , at high (preferably negative) sample voltages, the
electronic contribution to the height contrast is minimized, enabling the acquisition of the true
(fi lled states) topography of the structure, such as the outward relaxation of the cleaved surface.
5.1.2.1 X-STM topography and strain analysis
When two materials with a different lattice constant are used in a heterostructure, it will accu-
mulate strain. Stranski–Krastanov grown InAs quantum dots are the ultimate example of such
strained heterostructures, but also (In,Ga) As quantum wells have built-in strain. When such a
structure is cleaved, it reduces its built-in tensile or compressive strain by deforming the cleaved
surface. Regions under compressive strain bulge outward while tensile strain depresses the
cleaved surface ( Fig. 5.4 ). The strain can be measured in two ways with cross-sectional scanning
tunnelling microscopy:
● Strain in the plane of the surface can be deduced from the lattice spacing.
● Distortion normal to the surface can be measured using (fi lled states) topography imaging,
as described before.
Free-standing
GaAs and InAs
(a) (b) (c)
GaAs InAs GaAs 2a
Y
Strained InAs/GaAs
quantum well
Surface of cleaved
InAs quantum well
Z
(1
22
)
a
Figure 5.4 Strain relaxation at the cleaved surface of a strained quantum well. (a) Natural lattices of freestanding
GaAs and InAs. (b) Due to lattice mismatch the InAs well is strained in GaAs. (c) The strain is released at the cleaved
surface by outward relaxation.
The measured outward displacement and strain (measured by the change in lattice spacing)
can be used to determine the indium composition of a strained (In,Ga) As nanostructure, by
comparing the experimental data with the calculated relaxation and strain using elasticity the-
ory [24] . In the case of quantum wells with a low concentration of indium ( 30%), or wetting
layers, the indium distribution can also be obtained directly by counting the indium atoms, as
will be shown in the next sections. However, in the case of InAs quantum dots the indium con-
centration is too high to distinguish individual indium atoms, and the only way to determine its
composition is by fi tting to the measured outward relaxation or change in lattice constant. To cal-
culate the outward relaxation of a cleaved QD we use the package ABAQUS. It is based on contin-
uum elasticity theory and performs a fi nite element calculation to solve the 3D problem, in which
an isotropic material is considered. The measured size and shape of the QDs is introduced in the
model and the composition is varied until the calculated profi le fi ts to the experimental one. The
real size and shape of the QDs can only be known after scanning a large number of dots, since
they will be cleaved at a random position. Figure 5.5 shows the calculated outward relaxation
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