Molecular-Beam Epitaxy and Characterization of Ge Quantum Dots

Molecular-Beam Epitaxy and Characterization of
Ge Quantum Dots on Si (001) Substrates
Practical Course in the frame of the Ferienpraktikum
¨
Supervisor: Gregor Mussler, Julich
Summer 2011
Contents
1 Introduction
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2 Properties of SiGe Heterostructures
2.1 Growth mechanism of SiGe quantum dots . . . . . . . . . . . . . . . . . .
2.2 Structural properties of self-assembled SiGe quantum dots . . . . . . . .
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3 Growth and Characterization of Ge Quantums Dots
3.1 Chemically cleaning of the Si substrates . . . . .
3.2 Molecular Beam Epitaxy . . . . . . . . . . . . . .
3.3 Structural Characterization . . . . . . . . . . . .
3.3.1 X-ray reflectivity . . . . . . . . . . . . . .
3.3.2 Atomic force microscopy . . . . . . . . .
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4 Experimental Tasks
4.1 Molecular-beam epitaxy of Ge QDs and Si cap layers . . . . . . .
4.1.1 Chemical cleaning of the Si substrate . . . . . . . . . . . .
4.1.2 Transfer of substrate into the growth chamber . . . . . . .
4.1.3 Growth of the Ge quantum dots . . . . . . . . . . . . . . .
4.2 X-ray reflectivity on the Ge QD samples . . . . . . . . . . . . . . .
4.2.1 Alignment and measurement of the XRR curve . . . . . . .
4.2.2 Analysis of the surface roughness by the Leptos program .
4.3 Atomic Force Microscopy on the Ge QD layer . . . . . . . . . . . .
4.3.1 Performing the AFM measurements . . . . . . . . . . . . .
4.3.2 Analysis of the AFM images . . . . . . . . . . . . . . . . .
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1 Introduction
Quantum dots are quasi-zero dimensional semiconductor structures on the nanometer
scale, which provide a confining potential for charge carriers in all three dimensions.
Hence, these artificial atoms have a completely different energy structure compared to
bulk material or other semiconductor nanostructures, such as quantum wells or quantum wires. Therefore, novel device applications based on QDs in the field of optoelectronics [1–3], spintronics [4–6] or even quantum computation [7–9] are envisioned.
A possible avenue to realise QDs is to harness the so called Stranski Krastanov growth
mode, i.e. owing to different lattice constants between the semiconductor epitaxial
film and the planar substrate, dislocation-free QDs are formed as a result of an energy
minimisation process. Figure 1 depicts the band gap of several elemental or binary
semiconductors in dependence of the lattice constant. Large lattice mismatches exist
of several percent between different semiconductor materials. For example the lattice
mismatch between the direct semiconductors InAs and GaAs amounts to 7.2% and
therefore InAs QDs grown on GaAs substrates is a prominent example of semiconductor QDs for optoelectronic applications in the near infrared regime [10, 11].
Figure 1: Lattice constants and band gaps of several elementary and binary semiconductors with a
zinc-blende structure. The lines that connect different semiconductors denote the band gaps and lattice
constants of the pertinent semiconductor alloys.
For the Si and Ge semiconductors, the lattice mismatch amounts to 4.2%. Consequently, when exceeding a critical thickness of the deposited Ge, self-organised Ge
QDs are formed on planar Si substrates. Details on the formation of Ge QDs will be
given in section 2. A main drawback of the Si and Ge material system is the indirect
nature of their band gaps. As a result, Ge QDS in a Si matrix has poor light emitting
properties, making optoelectronic applications based on Ge QDs a daunting challenge.
However, electronic applications based on Ge QDS are very promising, as the Si and
Ge material system are compatible to CMOS technology. The general trend in CMOS
technology is to approach towards smaller and more effective devices. Over decades,
CMOS technology has followed the predictions of Moore’s Law which suggests that
2
Figure 2: SEM image of a DotFET with the short-gate and long-gate segments indicated (a). TEM image
of a DotFET cross-section (b). Close-up of a Si/SiGe/Si stack (c). Image taken from reference [12]
the number of transistors on an integrated circuit is increasing exponentially, doubling
approximately every two years. Naturally, further down scaling of integrated circuits
will reach its limit sooner or later and new concepts are required to continue the successful advancements of semiconductor technology.
Possible applications of Ge QDs in the field of next-generation CMOS devices are for
example the Ge QD field effect transistor (DotFET). This novel type of transistor consists of germanium dots grown in the Stranski Krastanov mode and a subsequently
grown biaxially strained Si cap layer. The biaxial strain in the Si cap layer results in a
warping of the conduction band dispersion, which consequently causes a reduction in
the effective electron mass and thus an increase in electron mobility. Figure 2 depicts
a scanning electron microscopy (SEM) image of a processed Ge DotFET. Owing to the
large biaxial strain in the Si cap layer, an average drain current increase up to 22.5% is
achieved [12].
Figure 3: Planar view and a cross-sectional view of a Ge QDC. The image is composed of two transmission electron micrograph and one atomic force micrograph. Image taken from reference [13]
3
Besides applications based on properties of individual QDs, SiGe quantum dot crystals (QDCs), i.e. a periodic arrangement of QDs that interact with each other, are a
completely new class of materials, offering prospects to realise novel devices. Identical
to conventional crystals, the periodic arrangement of Ge QDs results in the formation
of an electronic band structure [14]. Additionally, modified carrier transport [15, 16]
as well as unique phonon and thermal conductivity properties [17–19] are expected
for these artificial crystals. In order to place the Ge QDs in well-defined positions, templated Si substrates, i.e. substrates with a lithographically structured surface, is usually
employed [20–22]. Figure 3 shows a 11-period Ge QDC with a spatial extend of 100 nm
× 90 nm × 11 nm, which was realized on a Si substrate templated by means of x-ray
interference lithography [13]. The properties of such Ge QDC depends on the shape
and size of the QDs and the distance between neighbouring dots, i.e. the lattice constant of these artificial crystals. Therefore, unlike conventional crystals, the properties
of the QDCs can be tailored by choosing proper templated Si substrates and growth
parameters. As a result, SiGe QDC-based applications in the field of infrared photodetectors [23, 24] or high temperature thermoelectric elements [25] are envisioned.
4
2 Properties of SiGe Heterostructures
2.1 Growth mechanism of SiGe quantum dots
Si and Ge are group IV elements and they crystallize in the diamond cubic crystal structure. Hence, each atom is tetragonally bound to its four neighbour atoms as shown in
Figure 4. The lattice constants of Si and Ge are aSi = 0.543 nm and aGe = 0.566 nm,
respectively, which results in a large lattice mismatch of 4.2%. To calculate the lattice
parameters of a Si1−x Gex alloy, linear fit between the lattice parameters of Si and Ge is
assumed (Vegard’s law). However, a better fit to the experimental values is given by
a(Si1−x Gex ) = (0.5431 − 0.00125x + 0.01957x2 + 0.00436x3 ) nm [26].
Figure 4: Left: the elements Si and Ge in the periodic table. Right: lattice structure of Si and Ge
As mentioned in the last section, the epitaxial growth of Ge on Si develops in the
Stranski-Krastanov growth mode (SK). This growth mode occurs for almost any semiconductor system with a certain lattice mismatch of the involved materials. SK proceeds in a two step process (see Fig. 5). During the initial deposition of material A
on B, a strained wetting layer (WL) is formed. By reaching a critical thickness dc of
the WL (dc = 3-4 ML [27] for the Si/Ge system) strain relaxation occurs during island
nucleation. Certainly, the formation of islands increases the surface energy, but on the
other hand, this is overcompensated by the reduction of strain energy within the dot.
Thus, the total energy is reduced through island formation.
2.2 Structural properties of self-assembled SiGe quantum dots
The formation of SiGe islands via SK on Si(100) substrates was evidentiary demonstrated for the first time by Eaglesham et al., using TEM [28] and Mo et al., using
STM [29] in 1990. Since then, the interest in SiGe QDs increased dramatically and especially the structural properties of these islands were investigated extensively. Dots
were prepared using different growth techniques, such as MBE, CVD or magnetron
sputter epitaxy. For all of the mentioned techniques a similar behaviour of the island
morphology has been found. In this section the basic observation of heteroepitaxial
growth of Ge on Si(100) will be briefly resumed.
5
Figure 5: Schematics of the Stranski-Krastanov growth mode.
In the SK growth mode an energy barrier has to be overcome to activate the transition
from two-dimensional WL growth to three-dimensional island nucleation. Tersoff et
al. [31] calculated the change in free energy which is required to form an SiGe island.
They suggest that by reaching a critical thickness, island nucleation is energetically
favoured compared to further wetting. Secondly, they point correctly that QD formation starts with (105)-faceted dots (see also Ref. [32, 33] for the stability of (105) facets),
since the deposition of pure Ge results in the initial nucleation of (105)-faceted clusters1. These so-called hut clusters are coherent with the substrate lattice, i.e. free of
dislocations between the substrate and the hut clusters, which make them technologically desirable. XRD measurements indicate that the huts are almost fully strained at
Figure 6: Typical Ge island shapes obtained by STM. (a) A hut cluster with pyramidal shape, (b) a Ge
dome and (c) a superdome cluster. The corresponding facet plots are shown on the right side. (image
taken from [30]
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the Si/Ge interface and relax their strain gradually towards their apex [34]. A STM
image of such a hut cluster is shown in Figure 6 (a). These huts have always a pyramidal shape with either a rectangular (elongated hut clusters) [29, 35] or a square shaped
base [36–38]. Latter is the thermodynamic equilibrium shape of Ge hut clusters [31,39].
Their principal axes are aligned along two orthogonal (100) directions.
With further Ge deposition hut clusters undergo a number of shape transitions that
finally results in the formation of multi-faceted islands, so called dome clusters [28, 37,
40]. As indicated in Figure 6 (b), these dome clusters are bound by steeper (113) and
(15 3 23) facets which allow them to grow larger and to relief more strain than (105)faceted hut clusters [41], while they are still coherent with the substrate [28]. Over a
wide range of growth conditions SiGe islands show a bimodal size distribution with
smaller hut clusters and larger dome clusters. This bimodal behaviour and the related
shape transitions are described by an anomalous coarsening process [42–44], which
is similar to Ostwald ripening. At a critical island volume the dome energy becomes
lower than the pyramid energy, resulting in an abrupt change of the chemical potential
of an island and the described shape transition occurs. As far as some islands reach
the critical volume for changing to the dome shape, the hut density starts to decrease.
Huts which do not reach the critical volume start to shrink and disappear [45]. The
kinetics of this anomalous coarsening process is very slow and can take up to hours as
investigated during post-growth annealing [40, 43].
By depositing even larger amounts of Ge, an extended coherent island shape, so called
barns, with steep (111) facets is found [46, 47]. The dome to barn transition has strong
similarities to the hut to dome transition described above. At even higher Ge coverage, strain relaxation occurs via plastic relaxation and coherent islands transform into
large dislocated islands, so-called superdomes as shown in Figure 6 (c) [43, 48]. Additionally to the (113) and (15 3 23) dome facets, superdomes exhibit (111), (126), (4
20 23) and a (001) top facet [30]. STM investigations observe a (2 × 1) reconstruction
of the (001) top facet, suggesting a full relaxation of the superdome lattice [30]. The
described morphological transitions of the islands are driven by kinetic processes and
hence strongly depend on the growth parameters, such as the growth temperature. In
a bimodal distribution a higher growth temperature results in a relative increase of
the dome fraction compare to the hut fraction because of the stronger surface diffusion [49, 50]. With increasing deposition temperature, Si/Ge intermixing also becomes
more important.
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3 Growth and Characterization of Ge Quantums Dots
3.1 Chemically cleaning of the Si substrates
Prior to the deposition of the Si and Ge epilayers by means of MBE, the Si substrates
have to be chemically cleaned in order to remove organic contaminants and the native
oxide and to passivate the Si surface with hydrogen. For epitaxial deposition it is of
enormous importance that the substrate surface is free of contaminations or particles to
avoid any kind of impurities. We employ the RCA cleaning procedure, which consists
of three steps:
1. The substrates are put into a Caros etch (2 parts H2 SO4 1 part H2 O2 ) for 10 minutes at 90◦ C to remove organic materials from the surface by oxidizing the surface.
2. The remaining acid is removed by flushing the wafers in deionized water.
3. Subsequently the substrates are dipped for 2 minutes into aqueous hydrofluoric
(HF) acid solution (5%).
The dip removes the silicon oxide from the surface and passivates the dangling bonds
at the surface with hydrogen1. The hydrogen passivation protects the surface against
oxidation in ambient conditions for times of sim 30 minutes. This three step procedure
is repeated two times. Immediately after the cleaning procedure the substrates are
placed into the epitaxy chambers. Further improvements of the surface quality are
achieved by in-situ annealing inside the growth chambers. Inside the MBE chamber
an in-situ annealing for 5 min at 550◦ C is performed. This temperature is sufficient to
desorb residual organic compounds as well as hydrogen from the surface which occurs
at around 500◦ C [51].
3.2 Molecular Beam Epitaxy
Molecular beam epitaxy (MBE) is one of several methods of depositing single crystals
which takes place in high vacuum or ultra high vacuum (p ∼ 10−9 mbar). The most
important aspect of MBE is the slow deposition rate (typically less than 1000 nm per
hour), which allows the films to grow epitaxially. The slow deposition rates require
proportionally better vacuum to achieve the same impurity levels as other deposition
techniques
The principle idea of the MBE technique is the formation of an atomic beam directed
towards a substrate on which the atoms are deposited in an ordered way. The calibration of a MBE is relatively facile, since the growth rate depends only on the fluxes of
the Si and Ge beams, and it is independent of the growth temperature. The processing in the ultra-high vacuum (UHV) regime is mandatory to guarantee an undisturbed
atomic beam without collision with residual atoms as well as to prevent incorporation
of impurities from residual gases [52]. A cross section of the SiGe MBE system (Balzers
UMS 500), which will be used in this practical course, is shown in Figure 13. The solid
Si and Ge sources are placed in Si shielded, water cooled Cu crucibles and consist of
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Figure 7: Photograph and a cross-sectional drawing of the MBE system at the FZJ.
single crystals of high purity (Si: 99.9999%, Ge: 99.9999%, Holm Siliciumbearbeitung).
The atomic beams are generated by means of electron beams by evaporation of the
source material. The deposition time is controlled by closing/opening of pneumatic
shutters. The Si and Ge fluxes of the electron beam evaporators are controlled by the
emission currents of the filaments as well as by the focus of the e-beams on the solid
sources. The fluxes are permanently recorded by a quadrupole mass spectrometer. Its
signal enters a feedback loop in order to regulate the actual flux exactly to the set point
value by changing the electron emission current and the focus of the electron beams.
This approach allows a fast change of the atomic fluxes as well as flux stability and flux
accuracy. Furthermore the MBE system is equipped with a high temperature effusion
cell for p-type doping with boron, a low temperature effusion cell for n-type doping
with antimony and a carbon sublimation source. The effusion cells are driven at constant temperature using a constant filament current adjusted by Eurotherm controllers.
The substrate (whole 100 mm wafer or smaller chip) is placed upside down in 100 mm
diameter substrate holder, directly below a graphite filament which allows heating up
to 1000◦ C. The temperature of the filament is measured with a thermocouple mounted
directly above the heater. The long distance between sources and substrate of about
0.5 m guarantees a high degree of uniformity of the epitaxial layers across the whole
wafer. The sources and the heater are equipped with water cooled shieldings to reduce
the heat load of the MBE chamber. To improve the pressure during growth, a cryogenic
shield cooled by liquid nitrogen is mounted above the sources. The MBE chamber is
pumped with a turbo molecular pump combined with a Ti sublimation pump which
achieves a base pressure of ∼ 10−11 mbar. The advantages of the MBE growth technique can be listed as follows:
1. Low growth rate of ∼ 1 monolayer (lattice plane) per second, and hence good
control of the epilayer thickness on the atomic level
2. Low growth temperature (∼ 300◦ C for SiGe), and thus a low degree of atomic
diffusion during growth
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3. Atomically smooth growth surface with steps of atomic height and large flat terraces with a spatial extent of several µm
4. Precise control of surface composition and morphology
5. Abrupt variation of chemical composition at interfaces
6. In-situ control of crystal growth at the atomic level
7. Unity sticking coefficient for the impinging Si and Ge adatoms, which results in
a linear dependence between the growth rates and Si and Ge material fluxes
8. Extremely low impurity concentration in MBE-grown films, owing to the ultrahigh vacuum condition and the extremely pure source materials.
3.3 Structural Characterization
3.3.1 X-ray reflectivity
X-ray reflectometry (XRR) is a non-destructive technique to obtain information about
layer thicknesses and surface roughnesses on the nanometer scale. For this measurement x-ray radiation is focused on a sample in the θ/2θ-geometry under a very small
angle θ. The sample is moved in small step sizes around θ and the reflection is detected
under the 2θ angle (Fig. 8 a). When the incident angle is larger than the critical angle
θc , for which total reflections occurs when the incident angle is equal or lower than this
value, the beam penetrates the layer and is reflected at the interface layer - substrate.
When the beam exits the layer, the radiation interferes with the reflected beam from
the sample surface (Fig. 8 b). Thus, characteristic oscillations in the intensity (“Kiessig
fringes”) are observed (Fig. 9) due to destructive and constructive interference. The
occurrence of the interference pattern is apparent by taking into account the Bragg
equation (Eq. 1):
m · λ = 2 · d · sin(θ2 )
(1)
Constructive interference occurs when the optical path difference ∆ (marked red in Fig.
8 b) is a multiple integer m of the wavelength λ. The angle θ2 is calculated by means
of Snell’s law (Eq. 2), taking into account the small angular approximation and the
refractive index n. For x-ray radiation, the refractive index n is complex number, and
its value is given by n = 1 − δ + βi.
cos(θ1 ) = (1 − δ) · cos(θ2 )
q
⇒ θ2 =
θ12 − 2δ
(2)
(3)
By inserting Eq. 3 into Eq. 1 and assuming small angles (cos θ ≈ θ 2 ), one finds the
following relation [53]:
λ2
2
θ1 = 2 · m2 + 2δ
(4)
4d
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Figure 8: Schematics of a XRR setup and its working principle.
To estimate the thickness d of the layer out of this equation, one has to plot θ12 of the
oscillation minima or maxima over the squared order m2 and from the slope of straight
line the thickness is calculated. The intersection with the y-axis yields the squared
critical angle θc2 = 2δ.
Another way to determine the thickness is by fitting the curve with the help of a software based on Fresnel equations. Thereby the thickness and the roughness are the free
parameters. For convenience the thicknesses is usually determined with the software
Leptos and an example of a fitting is shown in Fig. 9.
Figure 9: Left: structure of the investigated sample. Right: XRR curve of a SiGe/Si stack grown on a Si
substrate. The black curve denotes the experimental data and the red curve represents the simulation.
Besides determining the thickness of semiconductor films, XRR measurements are also
beneficial for determining the interface and surface roughness. Mathematically spoken, XRR curves are Fourier transforms in reciprocal space of the epilayer structures
in real space. As a consequence, the features of the Fourier transform diminish if the
translational symmetry of the epilayer is real space is reduced. Surface and interface
roughnesses represent a reduction of the translational symmetry of the epilayer structures, and therefore a diminishing of the satellite peaks is observed. By means of the
Leptos software package, it is possible to enter roughnesses to the epilayer structures
in order to simulate XRR curves of epilayers with with smeared out interfaces and sur-
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faces. Figure 10 depicts depth-dependent concentration profile of a Si/SiGe stack for
different interface and surface roughnesses (cf. figure 9). A diminishing of the XRR
curves is seen for structures with a more pronounced interface and surface roughness.
This technique is also applicable for Ge QDs grown on Si substrates.
Figure 10: Left: depth-dependent concentration profile of a Si/SiGe stack for different interface and
surface roughnesses. Right: simulated XRR curves of the profiles depicted in the right image.
3.3.2 Atomic force microscopy
Atomic force microscopy (AFM) is a very high-resolution type of scanning probe microscopy, with demonstrated resolution on the order of fractions of a nanometer, more
than 1000 times better than the optical diffraction limit. The AFM is one of the foremost tools for imaging, measuring, and manipulating matter at the nanoscale. The
information is gathered by ”feeling” the surface with a mechanical probe. Piezoelectric elements that facilitate tiny but accurate and precise movements on (electronic)
command enable the very precise scanning.
The AFM consists of a cantilever with a sharp tip at its end that is used to scan the specimen surface. The cantilever is typically silicon or silicon nitride with a tip radius of
curvature on the order of nanometers. When the tip is brought into proximity of a sample surface, forces between the tip and the sample lead to a deflection of the cantilever
according to Hooke’s law. Depending on the situation, forces that are measured in
AFM include mechanical contact force, van der Waals forces, capillary forces, chemical
bonding, electrostatic forces, magnetic forces, Casimir forces, solvation forces, etc. The
deflection is measured using a laser spot reflected from the top surface of the cantilever
into an array of photodiodes.
If the tip was scanned at a constant height, a risk would exist that the tip collides with
the surface, causing damage. Hence, in most cases a feedback mechanism is employed
to adjust the tip-to-sample distance to maintain a constant force between the tip and the
sample. The sample is mounted on a piezoelectric tube, that can move the sample in
the z direction for maintaining a constant force, and the x and y directions for scanning
the sample. The resulting map of the area s = f(x,y) represents the topography of the
sample.
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Figure 11: Left: schematics of the working principle of an AFM. Right: AFM image of s sample showing
atomic steps.
The AFM can be operated in a number of modes, depending on the application. In
general, possible imaging modes are divided into static (also called contact) modes
and a variety of dynamic (or non-contact) modes where the cantilever is vibrated. One
type of the non-contact mode is the so called tapping mode, which will be employed
in this practical course.
In tapping mode, the cantilever is driven to oscillate up and down at near its resonance
frequency by a small piezoelectric element mounted in the AFM tip holder similar
to non-contact mode. However, the amplitude of this oscillation is greater than 10
nm, typically 100 to 200 nm. Due to the interaction of forces acting on the cantilever
when the tip comes close to the surface, Van der Waals force, dipole-dipole interaction,
electrostatic forces, etc. cause the amplitude of this oscillation to decrease as the tip
gets closer to the sample. An electronic servo uses the piezoelectric actuator to control
the height of the cantilever above the sample. The servo adjusts the height to maintain
a set cantilever oscillation amplitude as the cantilever is scanned over the sample. A
tapping AFM image is therefore produced by imaging the force of the intermittent
contacts of the tip with the sample surface.
By employing an AFM in tapping mode, the damage done to the surface and the tip
is less pronounced compared to the amount done in contact mode. Tapping mode is
gentle enough even for the visualization of atomic steps at the surface of a sample.
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4 Experimental Tasks
4.1 Molecular-beam epitaxy of Ge QDs and Si cap layers
4.1.1 Chemical cleaning of the Si substrate
The Si substrates are cleaned by means of the Piranha recipe described in section 3 in
the class 100 clean room of the institute. Owing to the fact that special instructions
are needed to enter the clean room, the cleaning procedure of the 100 mm diameter Si
substrates will be performed by the supervisor.
Figure 12: Class 100 clean room of the institute.
4.1.2 Transfer of substrate into the growth chamber
Immediately after the cleaning procedure, the substrate has to be inserted into the load
lock subsequently transferred through the central chamber into the growth chamber
(see figure 13).
The following steps have to be done:
1. Turning off the turbo pump of the load lock at the pump control unit (see left
image in figure 13).
2. Venting the load lock with nitrogen by gently turning the faucet at the right hand
side.
3. Opening the load lock window and inserting the cleaned Si substrate, turned
upside down, into the sample holder ring
4. Closing the faucet and shutting the window of the load lock.
5. Turning on the turbo pump again, and wait for 30 minutes until the vacuum is
below 1 × 10−6 mbar.
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Figure 13: Left: The MBE system consisting of a load lock, a central chamber, and a growth chamber.
Right: control unit of the MBE system.
6. Opening the valves of the central chamber to the growth chamber and the load
lock.
7. Using wheel A to rotate transfer rod and wheel B (see figure 13 to move out the
arm in order to pick up the substrate onto the sample holder and to transfer it
into the growth chamber.
8. Employing the substrate movement command at the VAX station to mount the
substrate to the MBE head in the growth chamber.
9. Transferring the transfer rod out of the growth chamber and closing all valves.
4.1.3 Growth of the Ge quantum dots
For this practical course, a 20 nm hick Si buffer layer and a 8.4 monoloayer (ML) thin Ge
QD film will be grown. The sample structure and additional growth parameter, such
as the growth rates, flux values and substrate temperatures, are depicted in figure 14.
The following tasks need to be accomplished:
1. Setting the EHV 214 unit in the Standby ON mode.
2. Turnng on the filament of the quadrupole mass spectrometer.
3. Loading the recipe “QD-sample” into the VAX system.
4. Starting the growth of the QD sample by punching the “Start Program” button.
5. When the e-beam evaporators start, set the Si and Ge electron beams to the center
of the crystals and write down the growth parameters.
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6. When the growth is finished and the substrate temperature is below 200◦ C, transfer the sample out of the system.
Figure 14: Left: The structure of the Ge QD sample that will be grown in the MBE system. Right: the
growth parameters employed.
4.2 X-ray reflectivity on the Ge QD samples
4.2.1 Alignment and measurement of the XRR curve
A screenshot of the program Diffrac to operate the x-ray diffractometer is shown in
figure 15. The tasks to align and to measure the XRR curves are listed as follows:
1. Mount the sample on the sample holder by using adhesive tape.
2. Move the omega and theta drives to zero.
3. Set the absorber to automatic and the antiscattering slit to 0.1 mm.
4. Start a z scan and set the z value to 50% of the maximum value.
5. Start a rocking curve and set omega to the maximum.
6. Carry out a 2theta/theta scan and save the data.
7. Repeat the procedure with a plain Si substrate for comparison.
4.2.2 Analysis of the surface roughness by the Leptos program
For analyzing the surface roughness by means of the XRR technique, the program Leptos is employed. Figure 16 illustrates a screenshot of the program’s command window.
The following steps have to be carried out.
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Figure 15: Screenshot of the Diffrac program to operate the x-ray diffractometer.
1. Load the experimental data into the program by pressing the load data button
(see figure 16).
2. Create a sample structure, consisting of a Si substrate, a 20 nm thick Si buffer
layer with 0.5 nm roughness, and a 1.2 nm thick Ge film with 0.8 nm roughness.
3. Set the angular range for the simulation and simulate the XRR curve.
4. Use the right-hand side mouse button to click on both, the experimental and
simulated curve, to create a fit curve window.
5. Adjust the simulation parameters, i.e. the Ge thickness and the interface and
surface roughness to find an agreement.
6. Repeat the same procedure for the XRR curve of the plain Si substrate for comparison.
4.3 Atomic Force Microscopy on the Ge QD layer
4.3.1 Performing the AFM measurements
Prior to performing AFM scans, the sample has to be cut into 1 × 1 cm2 large pieces.
A screenshot of the program to control the AFM system is found in figure 17. The
following tasks need to be done:
1. Removing the cantilever box and placing the sample piece on the sample holder.
2. Mounting the cantilever box and moving the cantilever to the sample surface
manually.
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Figure 16: Screenshot of the Leptos program to analyze the XRR curves.
3. Pressing the “automatic approach” button (see figure 17) to move the cantilever
to the sample surface automatically.
4. Adjusting the aplitute setpoint to obtain stable measurement condition.
5. Perform several AFM scans with areas between 0.2 × 0.2 µm2 and 10 × 10 µm2 .
Figure 17: Screenshot of the Nanoscope program to to operate the AFM system.
4.3.2 Analysis of the AFM images
For the analysis of the AFM images, the program WSxM is used. A screenshot of the
program is seen in figure 18. The following aspects have to be scrutinized.
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1. Investigate the type of QDs, i.e. the shape, the size, the lateral extent, and the
facets. For the latter, the cosine feature is a beneficial tool.
2. Determine the density of the QDs and the surface roughness.
3. Create two-dimensional and three-dimensional images of the Ge QDs.
Figure 18: Screenshot of the WSxM program to to analyze the AFM images.
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