electron energy loss spectroscopy of iii-nitride...
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Linköping Studies in Science and Technology Licentiate Thesis No. 1487
Electron Energy Loss Spectroscopy of
III-Nitride Semiconductors
Justinas Palisaitis
LIU-TEK-LIC-2011:26 Thin Film Physics Division
Department of Physics, Chemistry and Biology (IFM) Linköping University
SE-58 183 Linköping, Sweden
© Justinas Palisaitis ISBN: 978-91-7393-161-8
ISSN: 0280-7971 Printed by LiU-Tryck
Linköping, Sweden, 2011
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Abstract
This Licentiate Thesis covers experimental and theoretical investigations of the bulk
plasmon response to different compositions and strain states of group III-nitride
materials. Investigated materials were grown using magnetron sputtering epitaxy and
metal organic chemical vapour deposition and studied by Rutherford backscattering
spectrometry, X-ray diffraction, electron microscopy and electron energy loss
spectroscopy (EELS).
It is shown that low-loss EELS is a powerful method for a fast compositional
determination in AlxIn1-xN system. The bulk plasmon energy of the investigated
material system follows a linear relation with respect to lattice parameter and
composition in unstrained layers.
Furthermore, the effect of strain on the bulk plasmon peak position has been
investigated by using low-loss EELS in group III-nitrides. We experimentally
determine the AlN bulk plasmon peak shift of 0.156 eV per 1% volume change. The
AlN peak shift was corroborated by full potential calculations (Wein2k), which reveal
that the bulk plasmon peak position of III-nitrides varies near linearly with unit cell
volume variations.
Finally, self-assembled ternary Al1-xInxN nanorod arrays with variable In concentration
have been realized onto c-plane sapphire substrates by ultra-high-vacuum magnetron
sputtering epitaxy with Ti0.21Zr0.79N or VN seed layer assistance. The nanorods exhibit
hexagonal cross-sections with preferential growth along the Al1-xInxN c-axis. A coaxial
rod structure with higher In concentration in the core was observed by scanning
transmission electron microscopy in combination with low-loss EELS.
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Preface The work presented in this Licentiate Thesis is a part of my PhD studies from
September 2007 to April 2011 in the Thin Film Physics Division at Department of
Physics, Chemistry and Biology (IFM) at Linköping University. My project, which is
a part of the NanoN program, is funded by Stiftelsen för Strategisk Forskning (SSF) as
well as CeNano. The goal of my licentiate project is to gain insight in low-loss EELS
capabilities for group III-nitride semiconductors characterization on the nanoscale.
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Acknowledgements I would like to acknowledge everyone who contributed to this thesis and especially:
- Per Persson, my supervisor
- Lars Hultman and Jens Birch, my co-supervisors
- Co-authors
- My colleagues at Thin Film, Plasma and Nanostructured Materials groups
- My colleagues at IFM
- Family and friends
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Papers Included in This Thesis
Paper 1
Standard-free composition measurements of AlxIn1-xN by low-loss electron energy loss spectroscopy
J. Palisaitis, C.-L. Hsiao, M. Junaid, M. Xie, V. Darakchieva, J.F. Carlin, N. Grandjean,
J. Birch, L. Hultman and P.O.Å. Persson
Physica Status Solidi – Rapid Research Letters 5, 50 (2011)
Paper 2
Effect of strain on low-loss electron energy loss spectra of group III-nitrides
J. Palisaitis, C.-L. Hsiao, M. Junaid, J. Birch, L. Hultman and P.O.Å. Persson
Manuscript in Final Preparation
Paper 3
Composition tunable Al1-xInxN nanorod arrays grown by ultra-high-vacuum magnetron sputter epitaxy
C.-L. Hsiao, J. Palisaitis, M. Junaid, P.O.Å. Persson, J. Jensen, Q.-X. Zhao, L.-C. Chen,
K.-H. Chen and J. Birch
Manuscript in Final Preparation
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Papers Not Included in This Thesis
Paper 4
Electronic-grade GaN(0001)/Al2O3(0001) growth by reactive DC-magnetron sputter epitaxy using a liquid Ga sputtering target
M. Junaid, C.-L. Hsiao, J. Palisaitis, J. Jensen, P.O.Å. Persson,
L. Hultman and J. Birch
Applied Physics Letters 98, 141915 (2010)
Paper 5
Face-Centered Cubic (Al1-xCrx)2O3
A. Khatibi, J. Palisaitis, C. Höglund, A. Eriksson, P.O.Å. Persson, J. Jensen, J. Birch,
P. Eklund and L. Hultman
Thin Solid Films 519, 2426 (2010)
Paper 6
Trimming of aqueous chemically grown ZnO nanorods into ZnO nanotubes and their comparative optical properties
M.Q. Israr, J.R. Sadaf, L.L. Yang, O. Nur, M. Willander,
J. Palisaitis and P.O.Å. Persson
Applied Physics Letters 95, 073114 (2009)
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Table of Contents
1. INTRODUCTION ..................................................................................................... 1
1. 1. Material Analysis .................................................................................................. 1
2. MATERIALS ............................................................................................................ 3
2.1. Crystal Structure and Properties of III-Nitrides ................................................ 3 2.1.1. Template for Growing III-Nitrides ................................................................... 5
2.2. Growth Methods .................................................................................................... 7 2.2.1. Magnetron Sputtering Epitaxy (MSE) .............................................................. 7 2.2.2. Metal Organic Chemical Vapour Deposition (MOCVD) ................................ 8
3. CHARACTERIZATION ....................................................................................... 11
3.1. Composition Analysis .......................................................................................... 11 3.1.1. Rutherford Backscattering Spectrometry (RBS) ............................................ 11
3.2. Structure Analysis ................................................................................................ 12 3.2.1. X-ray Diffraction (XRD) ................................................................................ 12 3.2.2. Transmission Electron Microscopy (TEM) .................................................... 15
3.2.2.1. Basic TEM Working Principle ................................................................ 16 3.2.2.2. Imaging Techniques ................................................................................ 17 3.2.2.3. Diffraction in TEM .................................................................................. 23 3.2.2.4. TEM Sample Preparation ........................................................................ 25
3. 3. Analytical Methods in the STEM ...................................................................... 27 3.3.1. High Energy Electron Interaction with Material ............................................ 27 3.3.2. STEM Analysis ............................................................................................... 29 3.3.3. Energy-Dispersive X-ray Spectroscopy (EDX) ............................................. 30 3.3.4. Electron Energy Loss Spectroscopy (EELS) .................................................. 31 3.3.5. Energy Loss Spectrum .................................................................................... 32
3.3.5.1. Zero-Loss Region .................................................................................... 32 3.3.5.2. Low-Loss Region and Bulk Plasmon Losses .......................................... 34 3.3.5.3. Low-loss EELS Spectrum Simulations ................................................... 36 3.3.5.4. High-Loss Region ................................................................................... 37 3.3.5.5. Data Post-Processing ............................................................................... 38
4. STRESS-STRAIN IN THIN FILMS ..................................................................... 39
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5. SUMMARY OF RESULTS ................................................................................... 41
5.1. Paper 1 .................................................................................................................. 41
5.2. Paper 2 .................................................................................................................. 42
5.3. Paper 3 .................................................................................................................. 43
6. REFERENCES ........................................................................................................ 45
PAPER 1-3 ................................................................................................................... 49
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1. Introduction
1. 1. Material Analysis
To understand and explain phenomena as well as applying this knowledge to improve
everyday life is the core of human nature. Knowledge about materials has been
important for humanity since ancient times. Understanding material behavior is one of
the major driving forces for development of new technologies.
III-Nitrides are a material group which attracts interest due to promising applications
for contemporary and future optoelectronic and electronic devices [1]. Alloying two
binary nitrides InN and AlN produces the ternary compound AlxIn1-xN, with a bandgap
which spans from 0.64 eV to 6.2 eV [2]. AlxIn1-xN is particularly attractive since it can
be grown lattice matched to GaN and AlxGa1-xN, ensuring stress-free heterostructures
with tunable bandgap. Simultaneously, the constant size reductions of group III–nitride
device structures are accompanied by a need for increased control and understanding
of growth and diffusion mechanisms along with accurate compositional and structural
information.
The material analysis is usually performed at a macroscopic and/or micro/nano scale.
The techniques for material analysis can be divided into different categories depending
on resolution, signal detected, etc. A short summary of the most common techniques
are given in Table 1.
Table 1. Analysis techniques employing electrons, ions and photons beams.
Incident beam
Signal detected
Technique Probes
Electron Electron Electron Photon
Electron microscopy Auger spectroscopy
X-ray emission spectroscopy
Structure & Chemistry Chemistry Chemistry
Ion Ion Rutherford backscattering spectrometry Composition Photon Photon
Electron X-ray diffraction
X-ray photoelectron spectroscopy Structure Chemistry
Rutherford backscattering spectrometry (RBS) and X-ray diffraction (XRD) are
commonly used for macroscopic compositional and structural investigations.
However, these methods are not adequate to investigate confined structures like
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quantum wells and dots, or single precipitates. To achieve this, a high spatial
resolution is required and possible to reach only by using the transmission electron
microscope (TEM) where presently the resolution is below the atomic level. TEM is
frequently combined with spectroscopy methods for compositional analysis such as
energy dispersive X-ray spectroscopy (EDX) and electron energy loss spectroscopy
(EELS). In this thesis the low-loss EEL spectra were evaluated while investigating
group III-nitride materials.
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2. Materials 2.1. Crystal Structure and Properties of III-Nitrides
The core material for today’s semiconductor industry remains Si, however due to
limitations of the physical properties it cannot meet future challenges in emerging
electronic applications, requiring device operation at high temperature, power and
frequency. For such applications high thermal conductivity, high breakdown electric
field, tunable band gap as well as thermal, mechanical and chemical stability are the
main prerequisites. The material group exhibiting such physical properties is III-nitride
semiconductors (AlN, GaN and InN), their ternary (e.g. AlInN) and quaternary alloys
(AlGaInN). Some of the designed properties are given by the big electro-negativity
difference between the group III elements and N, establishing strong chemical bonds
[3-9].
Group III-nitrides are the key materials for contemporary and future electronic devices
such as high-brightness blue and white LEDs, high-frequency transistors, chemical
sensors, surface acoustic wave and quantum structure devices [1, 10-12].
III-Nitrides can be synthesized in two basic structures. The most common is the
hexagonal wurtzite crystal structure (P63mc) (see Figure 1 a), although the cubic
zincblende structure (F4 3m) (see Figure 1 b) is commonly reported [9, 13, 14].
Figure 1. Ball-and-stick model of two GaN polytypes: a) hexagonal (h-GaN), b) cubic (c-
GaN).
a) b)
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In both structures each atom (Ga or N) is tetrahedrally coordinated between the
corresponding atom (N or Ga respectively) with a strong chemical bond, giving high
stability to the material. The general material properties for some typical examples are
summarized in Table 2.
Table 2. General material properties of III-nitrides, Si, SiC, ZnO and Al2O3 [9, 13].
# Band gap [eV]
Lattice parameter a
[Å]
Lattice parameter c
[Å]
Thermal expansion
[K -1]
Thermal conductivity [Wcm-1K -1]
h-AlN 6.2 3.11 4.98 4.21·10-6 1.3
c-AlN - 4.36 - 4.56·10-6 2.8
h-GaN 3.44 3.18 5.18 5.59·10 -6 2.0
c-GaN 3.23 4.5 - 4.78·10 -6 1.3
h-InN 0.64 3.54 5.76 - 0.8
c-InN - 4.98 - 5.03·10 -6 -
Al 2O3 9 4.75 12.99 7.5·10-6 0.3
6HSiC 3.05 3.08 15.12 4.2·10-6 4.9
ZnO 3.3 3.25 5.2 - -
Si 1.11 5.30 - 3.59·10 -6 1.5
As an example, GaN grown directly on Al2O3 is shown in Figure 2. In this particular
sample, GaN close to interface is found to be synthesized in the hexagonal as well as
cubic structure. This phenomenon is typically explained by the big lattice mismatch
(Al2O3 and GaN) resulting in competing growth mechanisms. After ~25 nm of film
thickness, the cubic inclusions are overgrown by hexagonal GaN, since it is a more
thermodynamically stable phase.
Alloying two binary wurtzite nitrides (InN and AlN) generates the ternary compound
(Al xIn1-xN). Depending on the alloying composition a direct room temperature (RT)
bandgap from 0.64 eV to 6.2 eV (near infrared to ultraviolate) is achievable, which is
attractive for optoelectronic applications where the bandgap is directly related to the
emission and absorption properties of optical devices [1, 15]. AlxIn1-xN is particularly
attractive since Al0.83In0.17N can be grown lattice matched to GaN [16]. This allows
realization of stress free heterostructures with tunable bandgap and high quality strain
free heterointerfaces [2].
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Figure 2. HRTEM micrograph of GaN grown on Al2O3 close to the interface. The cubic
GaN inclusion is visible and overgrown by a hexagonal GaN layer. The stacking fault
(SF) in the cubic GaN and interface between Al2O3 and GaN are indicated by arrows.
2.1.1. Template for Growing III-Nitrides
In the growth of epitaxial III-nitride semiconductor structures, substrates of different
materials (hetero-epitaxy) are mostly used since natural (homo-epitaxy) substrates are
not always commonly available [17]. This generally results in a degradation of crystal
quality of the grown film due to the different physical properties of the substrate and
III-nitride film (see Table 2). Lattice mismatch and thermal expansion differences,
crystal structure, price, etc. influence the choice of substrate used in the growth of III-
nitride films. Moreover, by using various growth strategies high quality epitaxial
layers can still be fabricated [18, 19]. For instance, buffer layers can be used to
minimize stress and defect densities in the final structure.
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Examples of Al0.84In0.16N structures are shown in Figure 3. The samples were grown
using different techniques (discussed in Chapter 2.2). Both samples contain buffer
layers (GaN, AlN) for reducing stress and the number of threading defects, which are
generated at the interface.
Figure 3. Same compostion Al0.84In 0.16N structures grown by two different growth
techniques. a) Overview of the Al0.84In0.16N structure grown on GaN/SiC by chemical
vapour deposition, b) Al0.84In0.16N film grown on AlN/Al 2O3 by physical vapour
deposition.
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2.2. Growth Methods
Growth of III-nitrides can be challenging in achieving a homogenous solution of
different composition AlxIn1-xN, due to different material properties (Table 1) and
growth conditions. E.g. InN should be grown at a much lower temperature compared
to AlN due to the lower dissociation temperature [20, 21]. In this work the investigated
samples were grown using two different growth techniques: Magnetron sputtering
epitaxy (MSE) and metal organic chemical vapour deposition (MOCVD). The
compositional range and structural quality differ depending on which technique was
implemented. MSE deposited films experiences more roughness and higher point
defect density. Although MOCVD films have better structural quality, the
incorporation of In is challenging (maximum ~30%), thus MOCVD grown films are
Al-rich.
2.2.1. Magnetron Sputtering Epitaxy (MSE)
Most of the III-nitride films investigated in this thesis were grown using MSE, which
is a growth method based on the sputtering process [22-24]. To initiate the sputtering
process, inert gases like Ar is introduced into the chamber. The basic MSE working
principle is shown in Figure 4. After igniting the plasma in the chamber, high kinetic
energy ions (I) are accelerated towards one or more targets (II), which are kept at
negative potential. In the sputtering process secondary electrons are generated at the
target surface and help sustaining Ar gas ionization. Ions and neutrals are ejected from
the target towards the substrate surface (III) where film growth takes place. At the
same time, for initiating the nitride film growth, nitrogen (N2) gas is also introduced
into the chamber. Nitrogen acts as sputtering gas and reacts with sputtered atoms to
form a compound. Compositional variations in the growing film are achieved by
varying the magnetron power. The main characteristic of the MSE process is that the
energy of adatoms is determined by temperature and kinetics, which can be varied by
applying a bias to the substrate. Also, growth occurs at non-thermal equilibrium
conditions.
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Figure 4. MSE system scheme and fundamental working principle: I - Generated
plasma, II - Ejection of the target atoms, III - Deposition on the substrate.
2.2.2. Metal Organic Chemical Vapour Deposition (MOCVD)
MOCVD is another commonly used growth technique for depositing III-nitride films
of various compositions [25, 26]. This method is based on a thermally induced
reaction of gas-phase precursor molecules on the heated surface of the substrate [27,
28]. In this case the precursor is supplied as a metal-organic molecule, such as tri-
methyl In (TMIn) or tri-methyl Al (TMAl) while ammonia (NH3) is used as a nitrogen
source. The basic principle of MOCVD together with schematics of the reactor scheme
is illustrated in Figure 5. Different precursor gases carrying In/Al elements flow
through the system in one direction (I). After entering the high temperature reaction
zone the heat dissociate molecules (II) initiating the condensation on the substrate
surface (III). The heat is supplied using radio frequency (RF) coils around the
chamber. Compositional variations in the film are achieved by varying the gas flow
ratio (composition of gases). The remaining reaction products are removed from the
reactor (IV). High purity and structural quality III-V semiconductors with growth rate
~2 µm/h can be produced using MOCVD. The growth temperature is close to
thermodynamic equilibrium, such that the energy of adatoms is given by temperature
only.
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Figure 5. MOCVD reactor basic scheme and fundamental working principle: I -
Precursor, II - Cracking, III - Deposition and IV - Removal of residual gases.
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3. Characterization
3.1. Composition Analysis
3.1.1. Rutherford Backscattering Spectrometry (RBS)
Rutherford backscattering spectrometry is a routine technique for compositional
analysis of thin films [29]. The investigated material is bombarded with high energy
light ions (e.g. He), which are incident almost perpendicular to the surface of the
analyzed sample. The He ions interact with atoms in the sample. Consequently some
ions are backscattered from the sample atoms through elastic collisions. Compositional
analysis is based on the interpretation of the energy spectrum of backscattered ions
though conservation of momentum. The energy loss of backscattered ions depends on
the material and the energy dependent scattering cross-section. Experimental and
simulated spectra of analyzed Al0.66In0.34N sample are shown in Figure 6.
Figure 6. Experimental and simulated RBS spectra from Al0.66In0.34N sample grown on
Al 2O3 substrate with AlN buffer layer.
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3.2. Structure Analysis
3.2.1. X-ray Diffraction (XRD)
X-ray diffraction is a result of the wave nature of X-rays (λ=1.54 Å, Cu Kα1), which
allows them to diffract and interfere constructively when interacting with the periodic
structure of the crystal. As an example, the semiconductor crystal exhibits a lattice
periodicity of a few Å (a=3.11 Å and c=4.98 Å for AlN). Diffracted waves provide
information for determining the crystallographic structure, orientation, composition,
strain state, etc. of the materials [30, 31]. In order to determine the condition for
constructive interference, which gives the maximum intensity of scattered X-rays from
the crystal, Bragg’s law (eq.1) is commonly used.
�λ � 2� sin� (1)
where n is the integer number, λ – the wavelength, d – the lattice spacing and θ is the diffraction angle.
This rule states that the maximum(-a) of the scattered intensity is(are) found when the
incident and scattered angles are θ for the periodic lattice spacing d (in the crystal).
Since λ and θ in an experimental setup are known, d can be calculated. This is
schematically illustrated in Figure 7. Fulfilling Bragg’s law is however not enough for
obtaining scattered intensity, since the scattering intensity is related to the structure
factor of the investigated material. The structure factor takes into account atomic
positions and scattering powers in the unit cell, making some reflections appear
stronger, weaker or completely forbidden.
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Figure 7. The schematic principle of X-ray diffraction according to Bragg’s law is
shown in the high resolution TEM image, indicating lattice spacing d, incident and
diffraction angle θ.
In the simplest XRD experiment one can vary incident and detection angle
simultaneously and record the X-ray intensities as they are scattered from the sample.
This is the basis of θ/2θ measurements, which is the routine method for identifying
crystal phases and extracting the lattice parameters that are parallel to the surface from
the as-grown samples. As an example, a θ/2θ measurement from Al0.24In0.72N (0002)
grown on an AlN (0002) buffer layer is shown in Figure 8, with distinct peaks owing
to the different lattice parameters.
In order to evaluate the crystal quality, strain, relaxation, coherency, in-plane and out-
plane lattice parameters, so called reciprocal space maps (RSM) can be recorded. RSM
scans record continuously varying θ and ω to form an area image around given
reciprocal lattice points. Afterwards all desired information is extracted from position,
shape, and orientation of those reciprocal space points. Reciprocal space mapping was
used to extract the lattice parameters by examining the symmetric (0002) and
asymmetric (1015) reflections in AlN samples and an example of a reciprocal space
map is given in Figure 9.
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Figure 8. θ/2θ XRD measurement for Al0.24In0.72N (0002) grown on AlN (0002) buffer
layer.
Figure 9. RSM from AlN (0002) and (1015) reciprocal lattice points.
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3.2.2. Transmission Electron Microscopy (TEM)
The properties of a material are governed by its structure and composition, where both
have to be investigated in order to be fully understood. For achieving this, structural
and compositional characterization must be performed with high accuracy.
Characterization on the atomic level can be achieved from a combination of imaging
and spectroscopy techniques which are realized in the Scanning TEM (STEM). It is a
powerful technique, which allows structural and chemical material characterization
based on the same imaging principle as in optical microscopy. Electrons are used in
the TEM as the radiation, which has shorter wavelength (λ=2.5 pm for 200kV) as the
main benefit. The resolution is conventionally defined by the Rayleigh criterion. This
criterion states that minimum resolvable details are directly proportional to the
illumination wavelength and inversely proportional to the aperture size. Thus, the
consequence of shorter electron wavelength makes atomic resolution possible. The
resolution in a TEM is not diffraction limited as in the case for optical microscopes,
but rather by instrumentation stability, lens defects, inelastic scattering, etc. All this
defines imaging resolution around 1 Å. Moreover, the TEM offers a wide range of
complimentary information (crystallographic information about defects, strain,
interfaces and boundaries, etc.), which are available as a result of different operation
modes and imaging techniques, like bright-field (BF), dark-field (DF), selective area
electron diffraction (SAED) and high resolution TEM (HRTEM). If an electron probe
is formed by focusing electrons into a fine spot, and scanned across the sample, is the
operation mode for STEM. It enables imaging (~1 Å) and analytical information on
the nanometer scale, including precise electron energy loss spectroscopy (EELS) and
energy-dispersive X-ray spectroscopy (EDX) analyses, etc (see Chapter 3.3.2).
The typical limitations of TEM: sample preparation, which is a difficult and
destructive process (see Chapter 3.2.2.4), small sampling volume, electron beam
damage to the material, interpretation of images, etc. For more information on
different imaging techniques references [32-34] are recommended.
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3.2.2.1. Basic TEM Working Principle
The TEM operates at high vacuum and high voltage conditions. A basic TEM scheme
is shown in Figure 10. In this thesis an Tecnai G2 TF 20 UT (S)TEM equipped with a
field emission gun (FEG) was employed. The benefits of this gun are more brightness
and spatial coherence compared to ˝older˝ generation LaB6 [32]. The electrons are
extracted from the tip of the gun and accelerated by a 200 kV potential, meaning that
the electrons reach relativistic speeds resulting in an electron wavelength of ~2.5 pm.
State of the art technology can use different kind of electron sources [35-38] combined
with monochromators [39] to improve the beam characteristics, which improves
imaging and analysis.
Figure 10. Basic outline of the TEM.
After leaving the gun, the electrons are focused by electromagnetic lenses. The first set
of lenses the electron beam encounter is the condenser lens system. This lens system is
used to control the illumination of the sample (intensity and intensity spread). A
number of apertures are used to control the coherency, convergence angle, current and
centering of the beam.
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In the conventional TEM, the beam impinges on the top sample surface as a nearly
planar wave. As the electrons interact with the sample, they are either transmitted or
scattered. Different scattering mechanisms are used for different imaging techniques
(Chapter 3.2.2.2). As the electrons emerge from the bottom sample surface they are
focused again by the objective lens to form an image. This image is transmitted by the
projection system, consisting of intermediate and projection lenses onto a fluorescent
viewing screen or CCD camera.
3.2.2.2. Imaging Techniques
Image contrast appears as a consequence of different imaging mechanisms [32, 34].
Examples are:
• density/thickness contrast
• diffraction contrast
• phase contrast
• Z-contrast
Density/Thickness Contrast
The sample atoms act as absorbing/scattering centers for the beam electrons.
Density/thickness contrast dominates at low magnifications. Heavier atoms and/or
denser material absorb or scatter the electrons stronger, causing this contrast.
Diffraction Contrast (Bright/Dark Imaging Modes)
As the coherent electron beam passes through the sample, it experiences coherent
elastic scattering. The scattering occurs as a result of an interaction of the beam with
the periodicity of a crystal structure and is defined to a first approximation by Bragg’s
law (Chapter 3.2.1). Coherent elastic scattered beam from the same set of atomic
planes (at the same Bragg’s angle) is brought to one diffraction spot in the diffraction
plane (back focal plane of the objective lens). In this way a diffraction pattern is
formed, where the central spot consists of the transmitted beam and other spots
originate from the diffracted beams (Figure 11).
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Figure 11. The scattered incident beam is focused by the objective lens (O.L.) to form a
diffraction pattern in the diffraction plane (D.P.) and the image in the image plane
(I.P.).
It is possible to generate different images by selecting a specific spot or set of spots in
the diffraction plane (transmitted or diffracted electrons). The selection is made by the
objective aperture, which is inserted in the diffraction plane. Depending on which
electrons are allowed to pass through the objective aperture, the image can be BF,
which contains the transmitted beam (Figure 12 a) or DF, which does not (Figure 12
b). The objective aperture is primarily used to increase the contrast of the image and to
investigate different features, where the contrast depends on the scattering vector of a
selected electrons and reveal dislocation of the different character, local variations of
strain, bending and thickness changes in the sample, etc.
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Figure 12. Schematics of different image formation mechanism in TEM a) BF b) DF.
Phase Contrast (HRTEM)
High resolution imaging is used for ‘direct’ observation of the sample lattice (atomic
column projections). Phase contrast is dominant at high magnifications (>500 kx)
where the electron wave experiences a phase shift as they interact with the projected
atomic potentials of the sample atoms. When the transmitted and scattered waves
interfere they again overlap in the image plane, thus lattice fringes are formed (Figure
13). More than one beam is required for phase contrast imaging.
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Figure 13. a) HRTEM image of ZnO. b) line intensity profile is indicated (S-F), showing
separation between the atomic columns of ~3 Å.
In addition to the phase shift due to the crystal potential, the wave is phase shifted by
the microscope phase factor which is a complex function, depending on many different
parameters, such as: defocus (∆f), different order lens aberrations (astigmatism (A),
spherical aberrations (C), coma (B), etc.) and is conventionally defined by the so called
contrast transfer function (CTF) [34].
(2)
where ∆f is the defocus, A – the astigmatism, Cs – the spherical aberration and B is the coma.
The contrast dependence for different lattice spacing at certain microscope settings is
shown by the contrast transfer function (see Figure 14).
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Figure 14. Tecnai F20 UT contrast transfer function.
In HRTEM, the additional phase shift of the sample scattering in combination with the
phase shift from the lens defects produce the image contrast. As a result, the HRTEM
image interpretation is not straightforward in terms of object structure. Therefore, the
HRTEM image, Figure 12, is not generally the real representation of the structure in
the sample, but an interference pattern of the scattered electrons which contribute to
the image.
Z-Contrast (STEM)
STEM is another TEM mode in which a fine electron probe is formed and converged
on the sample into a small point. The sample is scanned by the probe in order to
generate the image. Each pixel of the STEM image is generated as the scattered
intensity at this point is recorded. Typically, STEM images are recorded by means of a
high angle annular dark field (HAADF) detector (Figure 15). The amount of scattered
electrons onto the HAADF from each point depends on the local atomic scattering
power, which is defined by the Rutherford scattering cross-section and at high angles
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this is the dominating contrast mechanism [40]. As a result HAADF-STEM images are
sensitive to atomic mass number (Z) and sample thickness (t) [32]:
~�� (3)
Higher Z results in more scattered electrons from the atomic columns. The image is
then formed by collecting the scattered intensity for each pixel. The image is rarely
pure mass-thickness contrast (incoherent scattering from atoms), but commonly
contain more or less diffraction contrast (coherent scattering from lattice) depending
on the camera length. With smaller camera length the electrons incident on the
HAADF have higher scattering angle, which reduces the coherent scattering
contribution to the image significantly.
Figure 15. STEM – BF, DF, HAADF detectors.
The major benefit with STEM is that analytical information may be retrieved from an
individual area or feature with spatial resolution near the size of the probe (~0.5 Å
probe have been reported [41, 42]). Analytical signals can be recorded in STEM using
detectors for EDX and EELS (Chapter 3.3) [43, 44].
23
3.2.2.3. Diffraction in TEM
Electron diffraction is a powerful tool for crystal structure determination together with
TEM imaging from the same area. An electron diffraction pattern of a multilayer
Al xIn1-xN grown on Al2O3 substrate is shown in Figure 16.
Figure 16. Electron diffraction pattern from Al xIn 1-xN multilayer grown on Al 2O3
substrate. Distinct diffraction spots belonging to different composition of AlxIn 1-xN
layers and the substrate (indicated by ‘s’) can be seen.
The diffraction pattern (DP) provides information about crystal structure, lattice
spacing, orientation, etc. It is also used to orientate the sample to a low index zone
axis, which is of key importance for HRTEM imaging.
Selective Area Electron Diffraction (SAED)
SAED is used for obtaining diffraction patterns from specific sample areas. The area
selection is made by inserting the SAED aperture in an image plane. This is a very
important tool for obtaining information from a desired area, for example of a single
grain in polycrystalline sample, precipitate, orientation relationships between different
24
phases, etc. As an example, a SAED pattern obtained from the Al2O3 substrate and the
first two layers, AlN and Al0.82In0.18N, is shown in Figure 17.
Figure 17. STEM image and SAED pattern taken from Al2O3 and the first two layers of
AlN and Al 0.82In0.18N (aperture position indicated by circle).
25
3.2.2.4. TEM Sample Preparation
For samples to be used in TEM analysis the thickness requirement is the most critical,
since sample must be electron transparent. This is achieved by reducing sample
dimensions from mm to µm and nm. Typical requirements for a ‘perfect’ TEM
sample: it is thin over a large area, contains little or no artifacts from the sample
preparation process, represents the entire sample, is clean and free from contamination
products, preferably conductive and non-magnetic. If the sample is thick and exhibits
considerably damaged surface layers, dynamic scattering and multiple interference
take place, complicating the interpretation of the TEM results.
The choice of the sample preparation method depends on the sample itself (single
crystal, biological, nanoparticles, etc.) and the projection (zone axis) one wants to
observe the sample. The typical zone axis are parallel to the c axis (plan view), and
perpendicular to the c axis (cross-section).
Conventional Cross-Sectional Sample Preparation
Initial sample with typical dimensions of 1 cm x 1 cm is cut with low speed diamond
saw into small 1.8 mm x 0.8 mm pieces which are mounted into Ti grid (diameter 3
mm), see Figure 18.
Figure 18. TEM sample preparation procedure: initial sample (a) cut to small pieces (b)
and put in Ti grid (c) which is glued (d) polished and ion milled from both sides until
final TEM sample (e) is ready, f) overview TEM image from this sample.
26
The grid is glued for ~2 hours at 180 oC. The sample is mechanically polished by
diamond polishing papers with different grain sizes. The polishing is typically finished
when the sample thickness is ~50 µm. The final sample polishing is done by argon ion
milling typically at 5 keV. The final step in milling is at low energy (2 keV), which
should reduce the amorphous layer on the sample surface.
Focused Ion Beam (FIB) Sample Preparation
Another sample preparation method used in this study is FIB. This was used since
some samples were small and conventional sample preparation was not possible. The
biggest advantage by using FIB is the selectivity of area from which the TEM sample
could be prepared. The FIB working platform is based on SEM principle, with an
additional Ga ion column, which is used for both sample milling and deposition. Gas
injection system (GIS) is used for letting gases into the chamber and manipulator is
needed for sample lift out. The disadvantage with FIB is that sample surface is
affected by implanted Ga ions, as well as FIB operation cost is rather high.
27
3. 3. Analytical Methods in the STEM
3.3.1. High Energy Electron Interaction with Material
The fast electrons impinging on the sample may be transmitted or scattered. When
scattered, the scattering event may be elastic or inelastic. After the scattering event the
electron waves may be either coherent or incoherent with other waves [45]. The basic
types of interactions with a single atom are shown in Figure 19.
Figure 19. High energy electron interaction with material.
• Electrons can be scattered coherently or incoherently. Elastic scattering is
typically coherent at low angles (from periodic array of atoms) which is used
for electron diffraction. Scattering becomes predominantly incoherent at higher
scattering angles (detected by HAADF).
• Elastic scattering is defined as an event where there is no change of the
electron energy (Figure 19–1,3,4), but the electron may change direction from
1. Unscattered electrons 2. Inner shell inelastic
scattering 3. High angle elastic
scattering 4. Back scattering 5. Valence electron
inelastic scattering
I. Electron ejection from inner shell
II. Emission of X-rays
28
the initial path. If the electrons pass closer to the atomic core (Figure 19–3) the
change of direction will be much bigger, due to Rutherford scattering (high
angle elastic scattering). This phenomenon is used primarily for STEM imaging
(Chapter 3.2.2.2). Electrons that pass far from the atom core and interact with
the electron cloud (low angle elastic scattering) form the basis of the coherently
scattered electrons, which contribute to the diffraction pattern and generate
strong TEM image contrast. The elastic scattering intensity is determined by the
atomic scattering amplitude.
• In the event of inelastic scattering the incident fast electrons transfers some
energy to the sample atoms by exciting outer shell and/or core electrons to
higher levels. Measuring the energy loss of the fast electrons forms the basis for
EELS analysis (Figure 19–2,5) (see Chapter 3.3.4). Atom deexcitation occurs
by emission of either an X-ray photon and forms the basis for EDX analysis
(Figure 19–I,II), or an Auger electron (see Chapter 3.3.3).
29
3.3.2. STEM Analysis
The basis for retrieving analytical information in STEM is the inelastic fast electrons
scattered by the sample atoms and the resulting different measurable physical signals
(see Figure 20).
Figure 20. Interaction between electron beam and material.
Generally, not all of the signals are used. In STEM, the typical signals which are
recorded are X-rays emitted (EDX) or energy loss electrons (EELS). The common
principle for analytical STEM is to focus the electron beam into a small probe (<1nm)
and perform a line or area scan across the sample or keep it at one position of interest.
For each scanned pixel the spectrum (EDX and/or EELS) is recorded and a single
spectrum or a spectrum image is formed. These can later be used for e.g.
compositional analysis of the investigated region. EDX analysis, in general, is more
efficient in collecting information about heavier elements while EELS for lighter.
Together with EELS and EDX, STEM is capable of delivering compositional,
bonding, thickness, etc. information from each data point, making it an efficient
analytical tool with nm or better resolution.
30
3.3.3. Energy-Dispersive X-ray Spectroscopy (EDX)
STEM is frequently combined with spectroscopy like energy dispersive X-ray
spectroscopy (EDX). Basis for this is discussed (Chapter 3.3.1 and Figure 19–II).
Recorded EDX signal gives a fingerprint of the atoms present in the sample. The
detected EDX signal is affected by elemental fluorescence yield, sample orientation,
detector response, thickness, etc. making precise elemental quantification challenging.
An example of EDX measurement from an AlInN multilayer is shown in Figure 21.
Figure 21. Combined STEM and EDX spectroscopy. a) STEM image of a Al1-xIn xN
multilayer, b) Al line profile obtained using a line scan across the structure, c) Single
EDX spectrum acquired from the AlN layer.
3.3.4. Electron Energy Loss Spectroscopy (
EELS measures the amount of energy lost in the beam
20). The amount of the lost energy can give insight into the composition and properties
of the sample being investigated
concentrated in a much narrower angular distribution compared to the elastically
scattered electrons. TEM can be equipped with
the column (in-column filter)
filter). Electrons entering the
according to the amount of energy lost in
increasing electron energy loss
Figure 22. Basic working principle
Magneticprism
31
. Electron Energy Loss Spectroscopy (
the amount of energy lost in the beam-specimen interaction (Figure
lost energy can give insight into the composition and properties
investigated [45-48]. Electrons undergoing inelastic scattering are
much narrower angular distribution compared to the elastically
attered electrons. TEM can be equipped with a spectrometer which is integrated into
column filter) or mounted under the projection chamber
the EEL spectrometer are dispersed by a magnetic prism
ing to the amount of energy lost in the scattering process, see Figure 22. With
ncreasing electron energy loss the deflection angle increases.
asic working principle of an EELS spectrometer
E0
E0-∆E Magnetic
CCD
prism
. Electron Energy Loss Spectroscopy (EELS)
specimen interaction (Figure
lost energy can give insight into the composition and properties
nelastic scattering are
much narrower angular distribution compared to the elastically
spectrometer which is integrated into
projection chamber (post-column
EEL spectrometer are dispersed by a magnetic prism
scattering process, see Figure 22. With
EELS spectrometer.
32
3.3.5. Energy Loss Spectrum
A typical EELS spectrum is shown in Figure 23. This spectrum can be divided into
three main regions depending on the energy loss of the electrons. Each region contains
different information about the properties of the sample.
Figure 23. Typical EELS spectrum recorded from AlN.
3.3.5.1. Zero-Loss Region
The zero-loss region (transmitted electrons) contains the zero-loss peak. These
electrons do not lose energy when interacting with the sample. This is however not
entirely true. The loss of energy when creating phonons, Auger electrons, etc. is often
smaller than spectrometer resolution. The full width at half maximum (FWHM) of the
zero-loss peak in vacuum serves as a measure of the spectrometer resolution. As an
example see Figure 24.
33
Figure 24. Aligned zero-loss peak (FWHM ~0.8eV).
The energy resolution depends primarily on the initial electron energy spread which is
convoluted with the spectrometer resolution as electrons are emitted from the gun and
spectrometer alignment. In general, the zero-loss peak provides useful information
only when it is compared with the rest of the spectrum. A measurement of the
scattered versus unscattered intensity gives an indication of the sample thickness by
using the Log ratio method [32]. This is performed by taking ratios of intensities of the
entire spectrum and the zero-loss peak:
�� � �� ��
�� (4)
where t is the sample thickness, λ – the average mean free path, IT – the area under
entire spectrum and I0 is the area under zero-loss peak.
34
3.3.5.2. Low-Loss Region and Bulk Plasmon Losses
The low-loss region contains information about excitation where the energy loss is
typically between 2 eV and 50 eV (Figure 19-5) and contains information about the
optical properties of the sample [49]. This region has not been extensively used for
analytical purposes as compared to the ionization edges (core loss region). It can be
divided even into very low-loss region, containing interface and surface plasmons,
Cherenkov losses, material bandgap, and the low-loss region which is mainly
dominant by bulk plasmon losses and interband transitions [50-55].
The bulk plasmon peaks comes from plasmon resonances that are excited in the
material, when the beam electrons interact with weakly bound outer shell electrons.
The energy of bulk plasmon loss primarily depends on the valence electron density.
Bulk plasmon oscillations runs through the crystal as a longitudinal collective electron
wave of loosely bound electrons with a characteristic frequency. The simple
description of valence electron oscillations is given by the Drude model [56], which
gives the free electron plasma energy. In this model valence electrons are treated as
free particles, and no damping is present in the electron plasma. The only parameters
influencing the plasma oscillations are the valence electron density and the lattice
parameter. If the number of valence electrons is constant, only the lattice parameter
will affect the plasma frequency. This model works very well for metals.
In mathematical treatment, if impinging fast electrons are considered as a time varying
electric field, the response of medium induced electric field will be governed by the
dielectric response function:
� � �� � ��� (5)
where ε is the dielectric function, ε1 its real part and ε2 imaginary part.
Electron losses can be described by differential cross-section characteristic of bulk loss
function:
������ ~lm � ��
� !"# (6)
where ������ is the differential cross-section.
35
In free electron theory the dielectric function of material is given by:
� $" � 1 & $' ( �)�*+)/-. (7)
where t is the relaxation constant and ωp –the plasma frequency. The frequency of the bulk plasmon oscillations according to the Drude model can be
expressed as:
$' � /01�2�3 (8)
where m is the electron effective mass, n – the valence electron density per unit volume and 45 is the permittivity of free space.
This generally holds for metals, but in other crystals more factors affect the appearance
and shape of the bulk plasmon frequency like: material bandstructure, momentum
transfer to plasma, bonds between atoms, etc. Some effects can be taken into account
by treating free electrons as damped harmonic oscillators using the more advanced
Drude-Lorentz model and other approximations [56].
36
3.3.5.3. Low-loss EELS Spectrum Simulations
To retrieve the energy loss function and the optical properties of a material by
theoretical means, full potential calculations of the dielectric function can be
performed. One software package for this kind of calculation is Wien2k, which is
based on quantum mechanics using density functional theory (DFT) [57]. In this
package, the interaction between electrons is treated as a series of one-electron Kohn-
Sham partial differential equations. The Wien2k simulation package employs the
linearized augmented plane wave (LAPW) method and has been established as one of
the most exact method for the computation of the electronic structure of solids. As an
example, the simulated low-loss EELS spectra of AlN, where unit cell volume was
linear increased while a/c ratio constant was kept constant is shown in Figure 27.
Figure 27. Simulated low-loss EELS spectrum of AlN by changing unit cell volume
(-3% to +3%) for a) xx and b) zz components and keeping a/c ratio constant.
37
3.3.5.4. High-Loss Region
The high energy loss region (ionization edges with fine structure) contains information
about the electrons interacting with core shell electrons of a specimen atom, causing
excitation to higher unoccupied levels, range from 50 eV up to >1000eV. These
characteristic excitations appear in form of edges in the EELS spectrum. The signal
intensity is weaker due to the smaller ionization cross-section compared to the low-
loss region. As an example Al0.44In0.56N and AlN samples containing characteristic N
K-edges are shown in Figure 25.
Figure 25. EELS spectra with N (K-edge) from AlN and Al0.44In 0.56N layers (raw
spectrum).
As it can be seen, the fine features of the two spectra are different. The edge fine
structure provides information about the chemical bond of the atom to surrounding
structure. While the fine structure is usually significantly different, it can be used to
determine the compound (from a library of fine structures).
38
3.3.5.5. Data Post-Processing
In order to generate reliable spectrum of good quality, post-processing of the data must
be performed. For this purpose, low-loss EEL spectra for each measured structure
were obtained by initial zero-loss peak fitting and drift correcting. This was followed
by Fourier-log deconvolution for plural scattering removal. Finally the bulk plasmon
peak position was acquired by using non-linear least squares fitting (NLLS) in the
central part of the bulk plasmon peak [32]. Gatan DigitalMicrograph was employed to
average all spectra in a spectrum image and determine exact bulk plasmon position.
These procedure results in the alignment and noise reduction of the final spectrum (see
Figure 28).
Figure 28. Comparison of single spectrum and noise reduced spectrum obtained by
averaging 500 spectra.
39
4. Stress-Strain in Thin Films Epitaxially grown hetero structures experience an adaptive challenge as two lattices
with different physical properties are forced together. The typical solution is either to
nucleate defects, such as dislocations, or to nucleate the new layer under strain. This
causes the structure atoms to deviate from their natural equilibrium positions. Strain is
an important parameter and affects the physical properties of the film.
Modern electronic devices are increasingly integrating structures that are dimensioned
on the nanoscale [10], such as optical devices based on quantum wells. As the
structures are growing smaller, the impact of strain, which appears as one material
structure is adapting to another, has a significant impact on the device characteristics.
It is commonly used to increase performance e.g. in strained SiGe layer devices [58,
59]. Thus, ability to evaluate strain with nanometer resolution is of great importance.
Existing strain is mostly due to the difference in the lattice parameters (mismatch)
between the grown structure and its substrate, thermal expansion coefficient
differences, etc. In order to reduce strain in the film, its thickness should be increased.
Also a sign of strain relaxation is generation of defects in the grown film. The film can
be tensely or compressively strained resulting in increasing or decreasing unit cell
volume respectively. An example of differently strained layers is shown in Figure 26.
Figure 26. Schematics showing a) bulk lattices (separate substrate and film), b) strained
thin film on the top of the substrate, c) partly relaxed film on the top of the substrate.
a) b) c)
Substrate Substrate Substrate
Relaxed film Strained film Partly relaxed film
40
41
5. Summary of Results 5.1. Paper 1
In the first study (Paper 1), a standard-free method to retrieve compositional
information in relaxed AlxIn1-xN thin films by measuring the bulk plasmon energy
(Ep), employing STEM-EELS was demonstrated. Two series of samples were
grown by MSE and MOCVD, covering together full compositional range 0 ≤ x ≤ 1.
Complementary compositional measurements were obtained using RBS and the
lattice parameters were obtained by XRD. It is shown that Ep follows a linear trend
with respect to composition and lattice parameter between the alloying elements
from AlN to InN. This allows a straightforward compositional analysis by a single
measurement of the bulk plasmon energy (Figure 29).
Figure 29. Ep dependence for both series of the AlxIn 1-xN samples as a function of
composition and lattice parameter c.
42
5.2. Paper 2
In the Paper 2, the effect of strain on the low-loss response of III-nitrides is
evaluated experimentally by low-loss EELS and theoretically by full potential
simulations using Wien2k. Three AlN layers were grown by MSE by different
growth schemes which resulted in different strain states. Our three investigated AlN
layers are in relaxed and oppositely strained states as was shown by RSM. The
different states are the outcome of different growth conditions with substrates,
growth temperature and thickness. It is shown that Ep is shifted between the
differently strained AlN layers (Figure 30). The tensile strained AlN resulted in a
blue shift (-0.17 eV) of the bulk plasmon peak position, while the compressively
strained AlN was red shifted (+0.25 eV) with respect to the strain free AlN (20.46
eV). To support our experimental findings a number of simulations were performed.
Through these simulations the strain state of AlN as well as GaN and InN was
continuously changed. Experiments and simulations reveal that the bulk plasmon
peak position varies linearly with unit cell volume (strain state). It is concluded that
strain should be taken into account as an additional factor when interpreting low-
loss spectra.
Figure 30. Low-loss EELS spectra from the three differently strained AlN layers, a)
simulated and b) experimental.
43
5.3. Paper 3
This paper reports growth of a self-assembled ternary Al1-xInxN nanorod arrays with
variable In concentration, 0.10 ≤ x ≤ 0.32 onto c-plane sapphire substrates by ultra-
high-vacuum magnetron sputter epitaxy with Ti0.21Zr0.79N or VN seed layers
assistance. It was shown that the growth of nanorods is very sensitive to the substrate.
The rods exhibit hexagonal cross-sections with preferential growth of the c-axis along
the rod-length direction. The compositional inhomogeneity of higher In concentration
in the core of the rod, and higher Al concentration in the sheet was confirmed by low-
loss EELS and EDX in STEM (See Figure 31).
Figure 31. a) EDX line scan and b) bulk plasmon peak dependence shows higher In
concentration in the core of the rod compared to the edges. c) STEM image of AlInN
rod together with line scan place (indicated by arrow).
44
45
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