ABSTRACT
Title of dissertation: ANALYTICAL MICROSCOPY APPLICATIONS TO
WIDE-BANDGAP SEMICONDUCTORS AND
NANOCARBON-METAL COMPOSITE MATERIALS
Christopher J. Klingshirn
Doctor of Philosophy, 2020
Dissertation directed by: Professor Lourdes Salamanca-Riba
Department of Materials Science and Engineering
Understanding the atomic structure of materials lies at the heart of materials
science. Electron microscopy offers myriad techniques to both probe processing-
structure-property relationships in materials, and to manipulate those relationships
directly. In this thesis, analytical transmission electron microscopy (TEM) was used
to investigate two distinct material systems with applications to energy-efficient
technologies: wide-bandgap semiconductors and nanocarbon-metal composites.
In the first project, TEM and electron energy loss spectroscopy were used to
investigate the structure, composition and bonding of metal-oxide-semiconductor
devices based on silicon carbide (SiC) and gallium oxide (Ga2O3). The performance
of SiC falls short of ideal due to electrically active interfacial defect states. This work
confirms that boron doping at the SiC/SiO2 interface is feasible and improves the
device channel mobility likely through a stress-relaxation mechanism. Separately,
no adverse structural effects were found after antimony ion implantation into the
SiC substrate, which independently raises mobility via a counter-doping mechanism.
Few atomic-scale studies on Ga2O3 have been reported to date; this thesis
aims to bridge the knowledge gap by investigating gate oxide materials and process
conditions from a structural perspective. Elevated annealing temperatures reduced
interface quality for both SiO2 and Al2O3 gate oxides. Separately, amorphous Al2O3
layers were crystallized under moderate electron irradiation in TEM. One-fourth the
dose was required for crystallization with 100-keV electrons compared to 200 keV, in-
dicating an ionization-induced atomic rearrangement mechanism. This unexpected
phenomenon will have implications for devices operating in extreme environments.
The second project investigated structure-property relationships in novel nano-
carbon metal-matrix composites called covetics, which exploit the superior mechan-
ical and electrical properties of carbon nanostructures such as graphene. Aluminum
covetics were characterized using TEM and various spectroscopy techniques; com-
plementary quantum-mechanical and effective-medium models were used to predict
the performance of covetics with a range of structures. The models suggest that
an electrical conductivity enhancement of ? 10% is feasible with a 5 vol.% carbon
loading, but oxides and poor Al/C contact often diminish the performance of real
covetics.
ANALYTICAL MICROSCOPY APPLICATIONS TO
WIDE-BANDGAP SEMICONDUCTORS AND
NANOCARBON-METAL COMPOSITE MATERIALS
by
Christopher J. Klingshirn
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2020
Advisory Committee:
Professor Lourdes G. Salamanca-Riba, Chair/Advisor
Professor John Cumings
Professor Neil Goldsman, Dean?s Representative
Professor Manfred Wuttig
Dr. Tsvetanka S. Zheleva
?c Copyright by
Christopher J. Klingshirn
2020

Acknowledgments
I am grateful to everyone who has made this work possible.
First I would like to thank my advisor, Professor Lourdes Salamanca-Riba, for
the opportunity to work and study among such a great group of people. She and
my fellow group members never hesitated to support my work in whatever way they
could?especially by sharing ideas, which is the best part of doing research. Thank
you for so many hours of valuable and interesting discussion.
Thanks are due to my thesis committee members, Profs. John Cumings and
Manfred Wuttig of the Materials Science department, Prof. Neil Goldsman of Elec-
trical Engineering, and Dr. Tsvetanka Zheleva of the U.S. Army Research Labora-
tory for their time, advice and support. I would also like to thank my internship
supervisor, Dr. Philipp Mu?ller of BASF Ludwigshafen?s TEM lab, for showing me
what it?s like to conduct research in German industry. The experience of working
in a different environment taught me new ways to make research both productive
and fun, and certainly expanded my career horizons.
I would like to acknowledge funding support for this work from several sources1:
The U.S. Army Research Laboratory, for their support of the wide-bandgap semi-
conductor research; the U.S. Department of Energy, for sponsoring the work on
nanocarbon-metal composites; and the U.S. Department of Education?s Graduate
Assistance in Areas of National Need (GAANN) Fellowship for supporting my pro-
fessional development during my final year.
1Army Research Laboratory Contract No. W911NF1420110, and Department of Energy, Office
of Energy Efficiency and Renewable Energy, Award No. DE-EE0008313.
ii
No one person can know and do everything required for such a wide-ranging
thesis. I will always appreciate the support of my fellow research group members
during my time at UMD: Xiaoxiao Ge and Madeline Morales for their expertise
in covetics fabrication and characterization; Josh Taillon, for guiding me through
the steep learning curve of the FIB/SEM and introducing me to EELS and hyper-
spectral decomposition; and Romaine Isaacs for valuable discussion about covetics
and Raman spectroscopy. Thanks to Prof. Sarit Dhar and his group at Auburn
University for providing gallium oxide samples and frequently helping me put my
TEM findings in a broader context. To the UMD NanoCenter microscopists Dr.
Jiancun Rao and Dr. Sz-Chian Liou, thanks for your help and support through the
many hours I spent using the FIB and TEM. I would also like to acknowledge the
dedication of all the staff members in the department business office, who made sure
we got our packages and funding on-time. And thanks to my friends in the depart-
ment, especially Naila Al Hasan, Zoey Warecki, Joy Chao, and all the members of
the TEM users? group meeting at UMD, who were there when I needed someone to
challenge, distract, and encourage me.
iii
Table of Contents
Table of Contents iv
List of Tables vii
List of Figures viii
List of Abbreviations xi
1 Introduction 1
1.1 SiC and Ga2O3 wide-bandgap semiconductors . . . . . . . . . . . . . 2
1.1.1 Silicon carbide . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1.1 Processing techniques and challenges . . . . . . . . . 4
1.1.2 Gallium oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.3 Goals of this research . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Nanocarbon-metal composites (NCMCs) . . . . . . . . . . . . . . . . 8
1.2.1 Unique properties of graphene . . . . . . . . . . . . . . . . . . 8
1.2.1.1 Electrical conductivity . . . . . . . . . . . . . . . . . 9
1.2.2 Established NCMC production strategies . . . . . . . . . . . . 12
1.2.3 Novel fabrication method: Electrocharging assisted process . . 13
1.2.4 Goals of this research . . . . . . . . . . . . . . . . . . . . . . . 14
2 Methodology 16
2.1 Analytical transmission electron microscopy . . . . . . . . . . . . . . 16
2.1.1 Conventional and scanning TEM modes . . . . . . . . . . . . 17
2.1.2 Electron energy loss spectroscopy (EELS) . . . . . . . . . . . 18
2.1.2.1 Energy-filtered TEM (EFTEM) . . . . . . . . . . . . 22
2.1.2.2 Multivariate analysis of EELS data . . . . . . . . . . 23
2.2 Focused ion beam sample preparation . . . . . . . . . . . . . . . . . . 27
2.3 Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4 Effective medium model for bulk properties of composites . . . . . . . 33
3 Characterization of wide-bandgap MOS interfaces 37
3.1 SiC: Passivation of electrically active defects with chemical treat-
ments beyond NO annealing . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.1 Boron interdiffusion and incorporation into SiO2 . . . . . . . . 38
3.1.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 39
iv
3.1.1.2 Results and discussion . . . . . . . . . . . . . . . . . 40
3.1.2 Sb ion implantation in conjunction with NO annealing . . . . 47
3.1.3 Summary and future research directions . . . . . . . . . . . . 53
3.2 Ga2O3 with deposited SiO2 and Al2O3 gate oxides . . . . . . . . . . . 54
3.2.1 Post-deposition annealing effects on the Ga2O3/gate oxide in-
terface structure . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.1.1 Experimental methods . . . . . . . . . . . . . . . . . 55
3.2.1.2 Results and discussion . . . . . . . . . . . . . . . . . 57
3.2.2 Electron beam-induced crystallization of Al2O3 gate oxides . . 68
3.2.2.1 Experimental methods . . . . . . . . . . . . . . . . . 69
3.2.2.2 Quantification of the crystalline transformation . . . 71
3.2.2.3 Factors contributing to crystallization of the Al2O3
gate layer . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.2.4 Device performance implications and recommenda-
tions for future work . . . . . . . . . . . . . . . . . . 81
4 Modeling and characterization of nanocarbon-metal composites 83
4.1 Analysis of C distribution and structure by Raman spectroscopy . . . 84
4.1.1 Distribution of the nano-graphite crystallite size, La . . . . . . 84
4.1.1.1 Characteristic long-tailed distribution of La after con-
version . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.1.2 Estimating the thickness of embedded GNRs . . . . . . . . . . 90
4.2 TEM investigation of metal-carbon interface structures . . . . . . . . 93
4.2.1 Specimen preparation and experimental approach . . . . . . . 93
4.2.2 Large-scale graphitic carbon structures in Al covetics . . . . . 95
4.2.3 Well-integrated carbon nanostructures in Al covetics: Analyt-
ical TEM-EELS . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.4 Dislocation structure, microstructure, and mechanical prop-
erties of covetics . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 Effective medium model of electrical conductivity . . . . . . . . . . . 119
4.3.1 The need for a new model . . . . . . . . . . . . . . . . . . . . 120
4.3.2 Structural inputs to the model . . . . . . . . . . . . . . . . . . 122
4.3.3 Electronic inputs to the model . . . . . . . . . . . . . . . . . . 125
4.3.3.1 Charge transfer at the metal?graphene interface . . . 125
4.3.3.2 Width dependence of GNR conductivity due to quan-
tum confinement . . . . . . . . . . . . . . . . . . . . 127
4.3.4 The effective conductivity of a composite with randomly-oriented
inclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5 Conclusions 148
5.1 Summary of research . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.1.1 Wide-bandgap MOS interfaces . . . . . . . . . . . . . . . . . . 148
v
5.1.2 Nanocarbon-metal composites (Covetics) . . . . . . . . . . . . 150
5.2 Recommendations for future work . . . . . . . . . . . . . . . . . . . . 152
5.2.1 Wide-bandgap MOS interfaces . . . . . . . . . . . . . . . . . . 152
5.2.2 Nanocarbon-metal composites . . . . . . . . . . . . . . . . . . 153
A Measurement of electron-beam currents in the field-emission TEM 155
A.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
A.2 Estimating the electron dose rate on the specimen . . . . . . . . . . . 159
B Publications and presentations related to this work 161
Bibliography 165
vi
List of Tables
1.1 Physical properties of Si, SiC, and Ga2O3 semiconductors . . . . . . . 4
3.1 Material and deposition parameters for gate oxide films on Ga2O3
MOS devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Electron beam conditions (accelerating voltage and current density)
and resulting crystallization effects on the Al2O3 gate oxide layer . . . 71
vii
List of Figures
1.1 Figure of merit for selected wide-bandgap semiconductors . . . . . . . 3
2.1 Schematic of TEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Schematic of EEL spectrometer . . . . . . . . . . . . . . . . . . . . . 20
2.3 Reference EELS spectrum for Si . . . . . . . . . . . . . . . . . . . . . 21
2.4 Example ?scree plot? ordering of principal components by relative
significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Schematic of FIB/SEM . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6 TEM lamella extraction process using the FIB/SEM . . . . . . . . . 29
2.7 Raman reference spectrum of defective graphite . . . . . . . . . . . . 31
2.8 Example Lorentzian fit to a Raman spectrum in a C-rich region of an
Al covetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.9 Examples of the graphitic crystallite size (La) distribution . . . . . . 34
2.10 Illustration of a composite with an unknown property to be modeled 34
2.11 Example composite geometries with varying degrees of ordering . . . 35
3.1 HR-TEM of abrupt SiC/BSG interface . . . . . . . . . . . . . . . . . 40
3.2 Boron pile-up at the interface between SiC/BSG layers revealed by
STEM-EELS mapping . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Uniform O-K EELS intensity across the SiC/BSG interface . . . . . . 44
3.4 MCR-LLM decomposition of the BSG interface . . . . . . . . . . . . 45
3.5 High-resolution TEM of the Sb-doped SiC/SiO2 interface . . . . . . . 49
3.6 Si-L2,3 EELS edges after Sb+NO annealing . . . . . . . . . . . . . . . 50
3.7 Elemental O-K and Sb-M4,5 EELS edges . . . . . . . . . . . . . . . . 51
3.8 MCR-LLM decomposition of SiC Sb+NO-annealed EELS spectrum
image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.9 HRTEM of Ga2O3/SiO2 interface roughness following post-deposition
annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.10 EELS spectrum image of Ga2O3/SiO2 interface . . . . . . . . . . . . 59
3.11 O-K EELS map showing roughness of Ga2O3/SiO2 interface following
1000 ?C PDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.12 Ga2O3/Al2O3 interface before and after crystallization of the gate
oxide under electron irradiation . . . . . . . . . . . . . . . . . . . . . 62
viii
3.13 NMF decomposition of EELS at the Ga2O3/ALD Al2O3 interface . . 64
3.14 NMF decomposition of EELS at the Ga2O3/ALD Al2O3 interface
after 500 ?C PDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.15 MCR-LLM decomposition of EELS data showing asymmetric diffu-
sion following PDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.16 Lower-magnification TEM of the crystallized Al2O3 layer . . . . . . . 70
3.17 Average inelastic energy loss from the Al2O3 gate oxide as determined
by the EELS spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.18 Finite element model of beam-induced heating in Ga2O3/Al2O3 TEM
lamella . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.19 Electron diffraction pattern of the fully crystallized Al2O3 layer . . . 77
3.20 Oxygen sub-lattices of the (2?01) ?-Ga2O3 and (111) ?-Al2O3 planes . 78
3.21 Raw EELS data from bulk ?-Ga2O3 and ?-Al2O3 layers with and
without PDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.22 Line profile of the relative Ga-M2,3 EELS edge in samples subjected
to 500 ?C PDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.1 Distribution of the nano-graphite crystallite size, La, in activated C
source material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2 Asymmetric La distributions following covetics conversion . . . . . . . 87
4.3 The fraction of C converted increased monotonically with reaction
residence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4 Linear increase in mean La with residence time . . . . . . . . . . . . 90
4.5 11 Raman spectra from covetic sample cv20190408 with clearly de-
fined 2D bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.6 Optical imaging and Raman spectra of a polished covetic cross-section 94
4.7 EDS mapping of a graphitic C feature prior to lamella extraction . . 95
4.8 SEM and TEM survey images of covetic lamella cv20190408 . . . . . 96
4.9 Higher-resolution TEM imaging of the graphitic C bulk . . . . . . . . 97
4.10 EFTEM composition imaging of a graphitic cluster in a covetic lamella 99
4.11 EFTEM of the graphitic carbon/Al interface . . . . . . . . . . . . . . 100
4.12 Color-enhanced EFTEM images from the C/Al interface . . . . . . . 100
4.13 Survey of cv20190408-IM TEM specimen prepared by ion milling . . 101
4.14 STEM-EDS of the Al/C interface structure after ion milling . . . . . 102
4.15 MCR-LLM decomposition of EDS spectra at the Al/C interface . . . 103
4.16 Cross-sectional TEM lamella of cv20190502 . . . . . . . . . . . . . . . 105
4.17 Diffraction- and high-resolution imaging of 2 graphitic regions in
cv20190502 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.18 EDS line scan across Al/C interface in cv20190502 . . . . . . . . . . . 107
4.19 HRTEM inspection of Al structure near interface with C . . . . . . . 108
4.20 TEM-EELS of rod-like graphitic structures in electropolished Al 6061
covetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.21 TEM imaging of aligned GNRs along a < 111 > zone axis . . . . . . 112
4.22 Characterization of a covetic sample subjected to nano-indentation . 114
4.23 Dislocation density estimate under the nanoindented covetic surface . 116
ix
4.24 Trends in covetics? electrical and mechanical performance as functions
of charge applied during fabrication . . . . . . . . . . . . . . . . . . . 118
4.25 Optical micrographs indicating typical grain sizes of Al 1350 covetic
and control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.26 Projected conductivity of nanocarbon-metal composites following the
rule of mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.27 Schematic illustrating the orientation of GNRs in a polycrystalline
metal matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.28 Structure of the Al-GNR-Al interface modeled via DFT . . . . . . . . 126
4.29 Width dependence of the electron mean free path in GNRs . . . . . . 129
4.30 Effects of W and EF on the quantum conductance of GNRs . . . . . 130
4.31 Band bending at the Al-GNR interface . . . . . . . . . . . . . . . . . 132
4.32 The conceptual finite potential well . . . . . . . . . . . . . . . . . . . 133
4.33 Graphical solution for electrons confined to a GNR with a finite po-
tential barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.34 Detailed schematic of the interaction between metal matrix and em-
bedded few-layer graphene . . . . . . . . . . . . . . . . . . . . . . . . 137
4.35 Projected effective conductivity of Al-matrix covetics with randomly
aligned GNRs based on c-AFM measurements . . . . . . . . . . . . . 139
4.36 Effective-medium model based on the GNR ideal quantum conductance142
A.1 Equipment used for measuring beam currents in TEM . . . . . . . . . 156
A.2 TEM beam current measurements using the EELS drift tube . . . . . 157
A.3 TEM beam current density measurements using the phosphorescent
screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
A.4 Estimate of beam diameter via Al2O3 gate oxide thickness . . . . . . 160
x
List of Abbreviations
AFM Atomic force microscopy
ALD Atomic layer deposition
BF Bright field
CLA Condenser lens aperture
CVD Chemical vapor deposition
DF Dark field
DFT Density-functional theory
DOS Density of states
EDS Energy-dispersive X-ray spectroscopy
EAP Electrocharging assisted process
EELS Electron energy loss spectroscopy
EFTEM Energy-filtered TEM
ELNES Energy loss near-edge structure
EMA Effective medium approximation
FFT Fast Fourier transform
FIB Focused ion beam
FWHM Full-width at half-maximum
GIF Gatan image filter
GNR Graphene nanoribbon
HAADF High-angle annular dark field
HRTEM High-resolution transmission electron microscopy
MCR-LLM Multivariate curve resolution by log-likelihood maximization
MOS Metal-oxide-semiconductor
MOSFET Metal-oxide-semiconductor field-effect transistor
MSA Multivariate statistical analysis
NCMC Nano-carbon metal composite
NMF Non-negative matrix factorization
PCA Principal component analysis
PDA Post-deposition anneal
POA Post-oxidation anneal
SEM Scanning electron microscopy
SI Spectrum image
SIMS Secondary-ion mass spectrometry
STEM Scanning transmission electron microscopy
TEM Transmission electron microscopy
WBG Wide-bandgap
XPS X-ray photoelectron spectroscopy
XRD X-ray diffraction
ZLP Zero-loss peak
xi
xii
Chapter 1: Introduction
Microscopy offers powerful techniques for the observation, measurement and
alteration of material systems in many fields. In recent decades electron and ion
microscopes have enabled in-situ modification of materials, atomic-resolution imag-
ing, and sub-nanometer resolution measurement of chemical composition and bond-
ing. In this work, dual focused ion beam (FIB)/SEM and transmission electron
microscopy (TEM) are utilized to illuminate the processing-structure-property re-
lationships of two distinct material systems: wide-bandgap semiconductors and
nanocarbon-metal composites. Each of these systems presents significant poten-
tial to enhance power transmission and conversion efficiency on large scales, and is
therefore of significant societal as well and scientific interest.
In the first half of this thesis, two wide-bandgap semiconductor material sys-
tems, silicon carbide (SiC) and gallium oxide (Ga2O3), were investigated using ana-
lytical electron microscopy methods to identify features of semiconductor/gate-oxide
interfaces that affect the performance of microelectronic devices based on these sys-
tems. The latter portion of this work is focused on understanding the processing-
structure-property relationship of novel nano-carbon metal composites (NCMCs),
known as ?covetics,? which aim to exploit the superior mechanical and electrical
1
properties of graphitic nanostructures such as carbon nanotubes and graphene to
enhance the bulk properties of alloys based on aluminum and copper. Intended ap-
plications for covetics range from microelectronic interconnects to grid-scale power
transmission lines as well as structural alloys.
1.1 SiC and Ga2O3 wide-bandgap semiconductors
Scientific understanding of semiconductor materials and processes has revolu-
tionized numerous technologies during the 20th century, enabling rapid development
of small, efficient computers and power electronics. However, these mainly silicon-
based devices are limited to moderate operating temperatures and voltages due to
the intrinsic properties of Si, such as its bandgap and thermal conductivity. Wide-
bandgap (WBG) semiconductors such as silicon carbide, gallium nitride and gallium
oxide have therefore attracted significant interest in recent years. Such materials?
wide bandgaps allow devices to operate at higher temperatures and voltages than
conventional semiconductors. In addition to greatly extending the range of possi-
ble high-temperature and high-voltage applications, wide-bandgap power electronics
are anticipated to cut AC-DC- and voltage-conversion losses in consumer electronics,
electric vehicle charging, and grid-scale applications by 50?90 % [1].
Inspection of Baliga?s figure of merit (BFOM), a metric of semiconductor per-
formance for switching applications defined by breakdown voltage VBR and specific
on-resistance RON further illustrates the potential of wide-gap materials, as depicted
in Fig. 1.1 [2]. Furthermore, reductions in the size and weight of power conversion
2
Figure 1.1: Log-log plot showing contours of Baliga?s figure of merit (BFOM) for Si and
selected WBG semiconductors. Performance for low-frequency switching devices increases
toward the lower-right. Adapted from [2].
equipment will lead to energy savings in the transportation sector, presently one of
the most energy-intensive human activities. However, each material system presents
its own set of scientific and engineering challenges, exposing gaps in our understand-
ing that will need to be filled in order to unlock their full potential.
1.1.1 Silicon carbide
Silicon carbide (SiC) is an ideal wide-bandgap (WBG) semiconductor for de-
vices operating in high-temperature, high-voltage, high-power and high-radiation
environments. Major advantages of SiC relative to Si are presented in Table 1.1;
these include high thermal conductivity, large electric field breakdown strength, high
bulk mobility, and the ability to form a native thermally-grown SiO2 oxide [3]. Over
200 polytypes of SiC exist in cubic (C), hexagonal (H), and rhombohedral (R) con-
figurations; hexagonal 4H-SiC is often preferred due to its relatively larger bandgap
3
Property Si 4H-SiC Ga2O3
Bandgap Eg [eV] 1.12 3.25 4.85
Dielectric constant  11.8 9.7 10
Breakdown field Ec [MV/cm] 0.3 2.5 8
Electron mobility ? [cm2/V s] 1500 1000 300
Thermal conductivity ? [W/cm K] 1.5 4.9 0.23
Baliga?s figure of merit = ?E3c 1 317 3214
Table 1.1: Comparison of the properties of the WBG semiconductors SiC and Ga2O3
relative to Si. Adapted from Ref. [8].
and higher intrinsic mobility and breakdown voltage [4]. Devices based on SiC have
the potential to substantially improve the performance and efficiency of electric ve-
hicles, aerospace and defense systems, and the electric grid itself [5]. Doping of SiC
is only possible via ion implantation, as the diffusion coefficients of the common n-
type dopants N or P, and the p-type dopants Al or B, are too low to make diffusion
doping practical [6]. Growth and processing technology have matured to the point
where SiC-based metal oxide semiconductor (MOS) devices are now commercially
available. However, their performance and reliability are far from ideal due to the
presence of electrically active defects at the SiC/SiO2 interface, which reduce the
channel mobility and cause threshold voltage instability in SiC MOS field-effect
transistors (FETs), especially at high operating temperatures and under thermal
cycling [7].
1.1.1.1 Processing techniques and challenges
Greater than 2 orders of magnitude separated the electron mobility of bulk SiC
(1000 cm2/Vs) and the mobility in the active region of early experimental SiC-based
4
devices (less than 10 cm2/Vs [9]). Improvement of the channel mobility has therefore
been a major focus of SiC device research. Li et al. found in 1997 that annealing in
a nitrous oxide (NO) atmosphere could reduce the interface trap density Dit in a SiC
MOS capacitor [10]. This discovery was followed in 2001 by the demonstration of
an NO-annealed SiC MOSFET with an order of magnitude reduction in Dit, which
corresponded to a five-fold increase in channel mobility, up to 30?35 cm2/Vs [9].
Nitrogen is believed to passivate electrically active interfacial defects which may
include, for example, Si interstitials contributing to near interface traps (NITs) [11].
Recent experimental treatments based on phosphorus [12] and boron [13] con-
verts the SiO2 layer into a phosphosilicate or borosilicate glass (PSG or BSG, re-
spectively) and improves carrier mobility upon NO passivation by a factor of 3, to
over 100 cm2/Vs in the case of either P [14] or B passivation [13]. Doping the SiO2
layer with B appears to be the more suitable treatment for device applications, as it
avoids the problem of threshold voltage instabilities generated by the polar nature
of the PSG material [15, 16]. Antimony (Sb) ion implantation of the SiC channel
region in conjunction with NO post-oxidation annealing has also been shown to pro-
duce channel mobilities greater than 100 cm2/Vs [17]. Furthermore, combinations
of these techniques have been shown to produce even higher channel mobilities, for
instance Sb + BSG (180 cm2/Vs, [18]) or an N2O anneal in conjunction with B dop-
ing and additional deposited SiO2 layer (170 cm
2/Vs, [19]). Each of these techniques
contribute to improved field-effect mobility ?FE through different mechanisms and
present different drawbacks, which require further structural investigation.
5
1.1.2 Gallium oxide
Despite being among the newest and least mature of the ultra-wide-bandgap
(UWBG) semiconductors, gallium oxide (Ga2O3) has notable advantages over SiC
for certain applications, including the ability to grow wafers economically from the
melt [2]. Its bandgap of ?4.9 eV gives rise to a breakdown strength of ?9 MV/cm,
making Ga2O3 especially well suited to very high-power applications (above 1 kV),
for example in defense and wireless communications [8, 20]. In addition, the large
bandgap opens up possibilities for deep UV sensing in a truly solar-blind configura-
tion [21]. Its inherent stability as an oxide will be useful for electronics intended for
harsh or high-temperature environments [8]. However, significant challenges remain,
including low thermal conductivity, difficulty of p-type doping, and an incomplete
understanding of the role played by interfacial defects in limiting device perfor-
mance [8]. Charge trapping at the interface adversely affects channel mobility and
threshold voltage stability, an ongoing challenge in the SiC/SiO2 system which per-
sists in Ga2O3 [2].
Additionally, the choice of gate oxide material (typically SiO2 or Al2O3), de-
position method, and process conditions will have significant implications for device
performance and reliability that require further investigation [22]. Recent work by
Jayawardena et al. [23] indicates that SiO2 may be the better choice among the
gate dielectrics SiO2, HfO2, and Al2O3 in terms of lower gate leakage and higher
breakdown field, consistent with its larger band offset on Ga2O3. Despite these
advantages, the density of electrically active defect states at the interface (Dit) was
6
higher with SiO2 gate dielectric as compared to interfaces with Al2O3, suggesting
that there is room for improvement.
1.1.3 Goals of this research
Wide-bandgap MOS technology based on SiC has been well validated in recent
years and has been rapidly expanding in the market, largely owing to the success
of NO post-oxidation annealing [24]. Nevertheless, there is still significant room for
improvement before approaching the bulk mobility of SiC, and the mechanisms of
recently developed passivation treatments are not yet well understood. This work
provides nanoscale structural characterization via (HR)TEM and STEM-EELS of
previously little-known phenomena such as boron doping and antimony ion implan-
tation of 4H-SiC.
Gallium oxide MOS technology is significantly less mature, with the first field-
effect transistor only reported in 2012 [25]. Consequently, many aspects of the
structure-property relationships governing Ga2O3 device performance remain poorly
understood. This work aims to address open questions regarding the semiconduc-
tor/gate oxide interface structures responsible for recently observed degradation in
devices? electrical characteristics depending on the choice of gate oxide, its deposi-
tion parameters and post-deposition annealing conditions.
7
1.2 Nanocarbon-metal composites (NCMCs)
The addition of carbon to metals is an ancient technique for improving desir-
able properties, such as tensile strength, resistance to oxidation and wear resistance,
of metals such as iron. Unlike steel, the solubility of C in common alloys based on
Al and Cu is generally limited to a few parts per million [26]. Thus, traditional met-
allurgy techniques cannot be used to enhance the desired properties of these metals,
primarily strength and electrical and thermal conductivity, which are significant
for applications in electricity transmission from the smallest integrated circuit (IC)
interconnects to the largest grid-scale transmission lines. Since Al and Cu are ubiqui-
tous in these applications, and nanostructured forms of C such as graphene [27] and
carbon nanotubes (CNTs) [28] have exceptionally high tensile strength and charge
carrier mobility with demonstrated commercial applications in polymer-nanocarbon
composites [29], it stands to reason that significant industrial gains may be realized
through the incorporation of nanostructured carbon in metals.
1.2.1 Unique properties of graphene
Graphene, the first readily available two-dimensional (2D) atomic crystal, ex-
hibits exceptional properties that may enable a range of new technologies encom-
passing energy transfer and storage, sensors, electronics, and structural applica-
tions [30, 31]. Its properties have been predicted theoretically since the 1940s [32],
but the stability of free single layers of graphene was not demonstrated experimen-
tally until 2004, by Novoselov, Geim and co-workers using the ?Scotch tape method?
8
to reproducibly isolate single atomic layers from bulk graphite [27]. Within 10 years
scientific interest in graphene had grown exponentially into the thousands of publi-
cations [31].
1.2.1.1 Electrical conductivity
The electrical conductivity of graphene is affected by a number of factors. It is
instructive to consider the conductivity ? as a function of the carrier concentrations
and mobilities:
? = e(n?e + p?h) (1.1)
where e is the elementary charge of the electron, n and p are the electron and
hole number densities, and ?e and ?h are their respective mobilities. All of these
variables are affected by extrinsic factors, including the choice of substrate (or lack
thereof) and associated impurities [33, 34], adsorbates on the surface [35], external
potential [36], temperature [37, 38], as well as the defects inherent in the graphene
itself, such as edges [39].
Factors affecting carrier density in graphene
The band structure of ideal graphene is semimetallic, with zero band gap and
approximately linear density of states as a result of its 2D structure [32, 35]:
2|E|
D2D(E) =
?h?2
(1.2)
?2F
9
Mobile charge carriers (electrons or holes) are induced by an applied gate
voltage Vg, with linear dependence demonstrated experimentally: n = ?Vg , where
? = 7.3?1010 cm?2 V?1, in good agreement with theory (? = 7.2?1010 cm?2 V?1),
which implies that all of the induced carriers are mobile [36]. Many fundamental
studies have been undertaken to study unusual phenomena at low carrier densities,
for example Ref. [33]. The development of specialized structures such as ionic-liquid
gates has also enabled the exploration of high carrier-density regimes where n > 1014
cm?2 [40]. In that work it was shown that bi- and tri-layer graphene are capable
of sustaining large conductivities, beyond the point at which the conductivity of
single-layer graphene would saturate, due to the availability of additional energy
bands.
The carrier density of graphene is also controllable via doping. This may be
done through surface transfer (electron exchange between graphene and adsorbates
or surfaces in close proximity), or by substitution of species into the graphene lat-
tice, such as B or N for p- and n-type doping, respectively, as with conventional
semiconductor technology [41]. Some degree of doping is inevitable in real systems,
whether from the substrate, residual chemical species used in processing, or the
ambient atmosphere. Graphene is also doped by adsorption on to a metal surface.
First-principles calculations at the level of density-functional theory (DFT) show
that graphene is weakly adsorbed on metals including Cu, Al, and Ag, where it
is doped with electrons depending on the difference in work function between the
metal and graphene [42, 43]. The transfer of electrons was greatest on the Al(111)
surface, followed by Ag and Cu [43]. (111) metal surfaces were chosen in that work
10
to minimize lattice mismatch with the graphene sheet, which was 0.8?3.8% depend-
ing on the metal. Further DFT studies have predicted electron densities on the
order of 1014 cm?2 in bilayer graphene trapped between Cu [44] and Al [45].
Factors affecting carrier mobility in graphene
The mobility of carriers in graphene is substantially influenced by the sub-
strate. The highest mobilities have been reported for suspended graphene, on the
order of 2?105 cm2/Vs, but only after removal of impurities adsorbed on the surface,
which are responsible for significant (extrinsic) scattering [34]. On ideal substrates
such as hexagonal boron nitride (h-BN), which is atomically smooth with relatively
few charged impurities, graphene can exhibit carrier density-independent mobilities
of around 60,000 cm2/Vs, three times larger than for graphene on SiO2 [46].
In addition to the extrinsic scattering of carriers due to charged impuri-
ties, there are intrinsic scattering mechanisms such as electron-phonon interactions,
which cannot be eliminated from a system in a real device. Fortunately, these have
been shown theoretically to be quite small [37, 47], such that the intrinsic mobility
?in can exceed 300,000 cm
2/Vs for bilayer graphene at 300 K, even greater than
in single-layer graphene, with a corresponding mean free path on the scale of mi-
crons [47]. Unlike the extrinsic mobility, the intrinsic mobility depends on the carrier
density as ?in ? 1/n [37, 38, 48]. Ballistic transport with path lengths in excess of
10 ?m has been observed experimentally in graphene nanoribbons grown on SiC
substrates, corresponding to a sheet resistance on the order of 1 ?/sq. [49].
11
1.2.2 Established NCMC production strategies
The first major Al-CNT composites prepared by powder metallurgy and ball
milling have shown increasing yield strength with volume fraction of multiwall car-
bon nanotubes (MWNTs); however, the mechanism of strengthening could not be
determined by TEM imaging [50]. Al-CNT composites have also been prepared us-
ing a chemical vapor deposition (CVD) technique in order to address the problems
of CNT agglomeration and damage caused by traditional metal-matrix-composite
preparation techniques, nearly doubling the tensile strength compared with the
traditionally-prepared composite [51]. Al?0.3 wt.% graphene nanosheet composites
prepared by flake powder metallurgy have resulted in 62% improvement in tensile
strength [52]. However, a similar Al-graphene composite prepared by ball milling ex-
hibited diminished strength and hardness, likely due to the formation of aluminum
carbide (Al4C3) at the defect sites of graphene, such as the edges of nanosheets [53].
Much variation exists in the nanostructured C distribution, effect of carbide
formation and performance of Al-CNT and Al-graphene composites produced using
the above mechanical methods. It is therefore desirable to investigate alternative
methods to produce nanocarbon-metal composites with fewer processing steps and
greater retention of the sp2 carbon network responsible for the composite?s enhanced
structural and electrical properties. Model systems indicating the potential gains
of such improvements have recently been modeled and fabricated. Mu Cao and
co-workers embedded graphene within Cu by growing monolayer graphene on Cu
foils via a chemical vapor deposition (CVD) process, followed by stacking and hot
12
pressing [44]. Bulk improvement in electrical conductivity attributed to the presence
of graphene was reported to be 5.2% with as little as 0.008% volume fraction of C,
with local conductivity up to 3 orders of magnitude greater than the Cu matrix at
the Cu/Graphene interface. Extending the technique to Al foil was possible but
required that the graphene be grown apart from the foil and transferred externally,
as Al is not a suitable substrate for CVD of graphene [45]. A further drawback of
the fabrication technique used here is the limited sample size, which were under 2
cm ? 2 cm, precluding economies of scale.
1.2.3 Novel fabrication method: Electrocharging assisted process
A fabrication process amenable to efficient scale-up will be important for com-
mercialization of nanocarbon-metal composite materials. One such technique is the
electrocharging assisted process (EAP), developed by Third Millennium Materials,
LLC in 2010 [54]. By applying a large direct current to a metal melt containing on
the order of 1 wt.% C (powdered activated carbon), it is possible to incorporate car-
bon into a matrix of various metals including Au, Ag, Al, Cu and other metals. The
resulting high-carbon composites are known as covetics. Carbon structures in cov-
etics remain incorporated even after subsequent re-melting, indicating the presence
of carbon-metal bonding. Electron-beam and pulsed laser deposition of Cu covetics
made by EAP have been demonstrated with potential applications in transparent
conducting electrodes [55]. Additionally, Al covetics made with commercially avail-
able Al 6061 alloy and 3 wt.% C have been shown to contain primarily sp2-bonded
13
C [56] and to exhibit up to 30% greater tensile strength and up to 43% greater
electrical conductivity than a typical Al 6061 alloy [57].
The ability of electric current to induce ordering in amorphous carbon (a-
C) has been demonstrated in well-controlled fundamental studies. A transition
from amorphous to graphitic C was observed in an investigation of flash sintering
of electronic conductors, which applied current densities of up to 175 A/mm2 to
fibers of a-C over periods of several minutes [58]. The graphitic transformation
was confirmed by Raman spectroscopy and X-ray diffraction (XRD), which both
indicated the narrowing of characteristic peaks. Transformation of a-C to graphene
was also observed in real time on a suspended graphene substrate via in-situ TEM
experiments [59]. C was naturally present in the form of hydrocarbon contamination
in the TEM column or adsorbed on the sample holder, and a-C was deposited
through the assistance of the electron beam, which caused decomposition of the
contamination. Crystallization of a-C into graphene was subsequently facilitated by
current-induced heating to 2000 ?C or greater via electrical contacts integrated in
the holder.
1.2.4 Goals of this research
Covetics may ultimately lead to commercially available alloys that have greater
mechanical strength, wear resistance, and electrical and thermal conductivities suit-
able for many applications. To reach this point, several outstanding challenges must
be understood and resolved. These include ensuring complete sp2 conversion of the
14
carbon precursor material, ordering into graphitic structures with superior electri-
cal transport properties, and ensuring uniform distribution of incorporated carbon.
Furthermore, structural features of the metal matrix such as grain size, distribution
of secondary phases, and dislocation density continue to be relevant in governing
the electrical and mechanical properties. Even the magnitude of potential enhance-
ments to electrical and thermal conductivity and mechanical strength in covetics
have not yet been quantitatively estimated.
Fundamental characterization studies such as those facilitated by electron mi-
croscopy provide much needed structural information that can be correlated to prop-
erties and ultimately used to improve the processing techniques, leading to commer-
cially viable covetics with uniformly enhanced properties. The goal of this work
is to build understanding of processing-structure-property relationships in covetics
via microscopy studies of covetics fabricated and post-processed under a range of
conditions. Additionally, the effective properties of the bulk covetic composites are
predicted using numerical models and properties of metal-carbon systems measured
from characterization studies. Modeling is an important complement to experimen-
tal fabrication and characterization of covetics, which often exhibit non-uniform or
non-ideal structures (e.g. due to imperfect mixing of C particles in the melt). A
theoretical approach will serve to demonstrate the full potential of covetics with
different compositions and structures, thus providing a roadmap for future research
and development within this class of materials.
15
Chapter 2: Methodology
2.1 Analytical transmission electron microscopy
The transmission electron microscope (TEM) is a versatile instrument for
many types of high-resolution imaging and spectroscopy. The basic design of a
TEM is similar to that of an optical microscope, except using a beam of electrons
instead of visible light to obtain much greater resolution?down to the level of
the atomic lattice. Electron energies in TEMs typically range from about 80?200
keV, but can be greater than 1 MeV in the highest-energy implementations. The
advantage of electrons over visible light is approximately illustrated by the Abbe
diffraction limit, representing the theoretical smallest resolvable feature (d) in an
optical system illuminated by a wavelength ?:
?
d = (2.1)
2n sin ?
where n is the refractive index of the medium and ? the half-angle of conver-
gence. For the highest energy visible light, d ? 200 nm. In contrast, 80?300 keV
16
electrons travel at relativistic speeds, with a de Broglie wavelength ? given by
h
? = = ? (h ) (2.2)p
2m eV0eV 1 + 2m c20
where h is Plank?s constant, m0 is the rest mass of the electron, e is the elementary
charge of the electron, p is the momentum of the electron, V is the accelerating
voltage of the electron beam, and c is the speed of light.
Analytical electron microscopy refers to the capability for identifying specific
chemical composition and bonding configurations within the specimen, e.g. from
inelastic scattering of the electrons with characteristic energy transitions. This prin-
ciple is commonly implemented in electron microscopy via energy-dispersive X-ray
spectroscopy (EDX or EDS), which makes use of characteristic X-rays emitted due
to incident electrons causing excitations within the specimen?s inner-shell electrons.
Another technique specific to TEM is electron energy loss spectroscopy (EELS),
which is capable of providing extremely high spatial- and energy-resolution chemi-
cal information from the specimen and is obtained from the energy lost by incident
electrons after interaction with the sample.
2.1.1 Conventional and scanning TEM modes
The primary instrument used in this work is the JEOL JEM 2100F field-
emission TEM at the University of Maryland Advanced Imaging and Microscopy
Laboratory (UMD AIMLab). It is capable of 0.19 nm point-to-point resolution in
conventional TEM mode and a spot size as small as 0.2 nm in STEM mode. Fig. 2.1
17
illustrates a typical TEM operating in conventional mode, where a broad parallel
electron beam illuminates the sample. This mode is used for high-resolution (HR)
TEM and selected area diffraction (SAD). It is also possible to focus the beam to a
point in the specimen plane using scanning TEM (STEM) mode, which is particu-
larly useful for high spatial-resolution analytical techniques such as EDS or EELS.
STEM enables imaging and spectroscopy utilizing the electrons transmitted through
the specimen at a particular point, but with a much smaller excitation volume than
from a thick sample as in scanning electron microscopy (SEM); therefore, the spa-
tial resolution of analytical techniques such as EDS is vastly improved over SEM. In
order to make full use of the scanning probe?s spatial resolution, sample drift and
vibrations must be minimized.
2.1.2 Electron energy loss spectroscopy (EELS)
Electron energy loss spectroscopy (EELS) is a highly sensitive material char-
acterization technique that is capable of sub-nanometer spatial resolution when per-
formed in STEM mode. In EELS, the energy lost by electrons? interactions with
the sample is recorded by a spectrometer below the TEM column, which separates
and counts electrons by their energy remaining after passing through the specimen
using a magnetic prism and CCD detector. A schematic illustration of an EEL
spectrometer similar to the instrument used in this work, the Gatan Image Filter
(GIF), is shown in Fig. 2.2 [61]. The energy loss for each scattering event is simply
the reduction from the known initial value (e.g., typically 200 keV in this work).
18
Figure 2.1: A typical TEM operating in conventional TEM mode, with a parallel electron
beam (formed by the condenser lenses) illuminating the sample. The image is projected
by the intermediate and projector lenses on to a fluorescent screen or captured on a CCD
located below the screen. Apertures are used to reduce the beam intensity or to select
certain regions of the sample or diffraction pattern for analysis. Adapted from FEI [60].
19
Figure 2.2: Schematic of an EEL spectrometer similar to that employed for this work.
After passing through an entrance aperture suitable for the chosen measurement (imaging
or spectroscopy), the beam is split by energy through the magnetic prism and projected on
to the CCD for counting (in spectroscopy) or constructing an image (as in energy-filtered
(EF)TEM). The slit inserted after the prism is used to select signals within a chosen
energy range for EFTEM imaging. Adapted from eels.info (Gatan, Inc.)
The magnitude of energy loss is characteristic of the elemental composition of the
sample as well as the specific physical phenomena involved in the scattering event.
If the specimen thickness is on the order of or greater than the electron mean free
path for the material and electron excitation voltage in question, a substantial frac-
tion of incident electrons may be scattered multiple times, resulting in energy loss
counts that represent the sum of all the interactions; for this reason it is essential
that TEM specimens be thinner than 100?150 nm for EELS analysis [62].
A related challenge is the build-up of hydrocarbon contamination under the
STEM probe which interferes with STEM-EELS spectrum imaging. Adsorbed con-
taminants can diffuse along the specimen surface toward the probe, building up a
thick layer that obscures the specimen. This effect makes it particularly challenging
to acquire large maps or weak EELS edges that require longer exposure times. A
simple preventive measure is the ?beam shower,? in which the sample is illuminated
20
100000
Zero loss
10000
Plasmon losses
1000
Core loss
100
0 20 40 60 80 100 120 140
Energy loss (eV)
Figure 2.3: A reference EEL spectrum for elemental Si plotted on a logarithmic scale,
showing typical features from the strong zero-loss peak through the first Si core-level
excitation. Adapted from the Gatan EELS Atlas [64].
with a broad beam in conventional mode for a few tens of minutes, which serves to
polymerize and immobilize contaminants on the surface [63].
Since most electrons pass through the sample without measurable energy
loss?by passing through undeflected or scattering elastically?the strongest peak
of the EEL spectrum is the zero-loss peak, centered at 0 eV by definition. The width
of the peak (typically reported as full-width at half-maximum, or FWHM) is also
used to determine the resolution of the spectrometer. In this work the zero-loss peak
FWHM ranged from 0.9?1.1 eV.
Peaks between about 4?40 eV are due to inelastic scattering via excitations of
outer shell electrons, primarily plasmon oscillations within the lamella. This region
is known as the low-loss region of the spectrum [62]. At higher energies, excitations
from the core-shell comprise the core-loss region, which for example in Si (the Si-L2,3
edge) is visible at 99 eV in Fig. 2.3. This value corresponds to the approximate
binding energy of the 2p electrons in Si, and is therefore the minimum energy or
21
Counts
ionization threshold required to excite a core-shell electron in Si into the conduction
band. This mechanism explains the asymmetrical edge shape of many core-shell
EELS excitations; some core-shell electrons are excited to above the conduction
band edge, giving the EELS signal some intensity at energies above the edge?the
fine structure?which typically exhibits small variations in intensity within a few
tens of eV beyond the edge onset [62]. When viewed at sufficiently high energy
resolution, the fine structure of EELS edges provides information about the energy
band structure and chemical bonding configuration of the corresponding element in
the specimen [62]. The fine structure can be used to distinguish between different
forms of an element or compound, such as the Si-L2,3 shift distinguishing between
Si in SiC vs. SiO2 [65] or the valence state of an ion. Thus, insight may be gained
into the relationship between physical and electronic structure and properties of
materials such as at the semiconductor/oxide interface of SiC and Ga2O3 MOS
devices.
2.1.2.1 Energy-filtered TEM (EFTEM)
In addition to spectroscopy, the magnetic prism of the EEL spectrometer is
capable of filtering the transmitted electrons in conventional TEM mode, to pro-
duce an image using only a selected range of transmitted electron energies. This
technique is known as energy-filtered TEM (EFTEM) and can be used to enhance
contrast of phases with energy-loss signals at the selected energies. With its ability
to image a large spatial area at low energy resolution, EFTEM may be considered
22
complementary to STEM-EELS. An application of EFTEM to an Al-C composite
system is presented in Sec. 4.2.2.
2.1.2.2 Multivariate analysis of EELS data
Challenges in EELS data analysis
Several factors complicate the analysis of EELS data in comparison to other
types of spectroscopy. The first is simply the large volume of data collected from
each sample. In EEL spectrum imaging, the scanning TEM probe is rastered across
the region of interest to collect a spectrum at each point in an array of up to several
hundred pixels per side. A single experiment can easily produce over one gigabyte
of raw data, rendering any less-than-fully-automated signal processing impractical.
Specific to EELS, the signal intensity can vary by several orders of magnitude across
the range of energies observed, as in the semi-log plot in Fig. 2.3. Some aspects of the
fine structure are weak relative to the background, especially at high energies, and
the long tails of core-loss edges can overlap strongly with each other. Furthermore,
the regions of greatest interest are often interfaces or inclusions occupying only a
small part of the total area in the spectrum image, and whose EELS signature is
not independently known.
One traditional method to interpret EELS spectra includes multiple linear
least squares (MLLS) fitting [66]. The spectra collected are assumed to be linear
combinations of chosen reference spectra, and the fitting algorithm computes each
component?s weight and the overall residual. Large residual indicates the need
23
for one or more additional components; however it does not suggest what these
components may look like. The MLLS technique is additionally subject to the bias
inherent in manually choosing reference spectra.
Algorithms for multivariate statistical analysis
Multivariate statistical analysis (MSA) is a broad class of techniques that offer
an approach for dealing with data in multiple dimensions. They are well suited to
datasets that are large and contain multiple variables (i.e. physical contributions
to the EEL spectra) or subtle correlations between variables [67]. MSA began to
attract attention within the EELS community several decades ago [68?70] and has
been demonstrated as a tool for describing localized interface-specific phenomena
since around that time [70]. Essentially, an EELS spectrum image, with spatial
dimensions (x, y) and spectral data E, may be considered as a matrix D(x,y),E [71,72].
Using the Principal Component Analysis (PCA) approach, D may be decomposed
into a product of
D T(x,y),E = S(x,y),n ? L (E,n) (2.3)
where the rows of the loading matrix LT(E,n) represent the eigenvalues (independent,
orthogonal component spectra), and the columns of S(x,y),n, the score matrix, rep-
resent their spatially varying intensities. The eigenvectors of LT comprise a new set
of basis vectors for the dataset which are oriented along the directions of maximum
variance. Sorting the components by relative intensity, one can estimate which are
physically significant and which are simply noise. PCA is not ideally suited to EELS,
24
however, as its primary constraint?orthogonality between principal components?
rarely applies to EEL spectra, which share background and elemental features in
common within a dataset.
The application of physically relevant constraints makes multivariate statis-
tical analysis more meaningful. Non-negative matrix factorization (NMF) is well
suited to EELS data for this reason. Like PCA, NMF seeks to identify components
which maximize variance within the dataset?subject to the requirement that all el-
ements in S and L be greater than or equal to zero, as in real physical spectra. NMF
is always an additive process for this reason, leading to a ?parts-based representa-
tion? of the dataset [73]. This technique is applicable to a wide range of problems in
the computer science community, such as image recognition, and interest is growing
quickly among material scientists and microscopists; the number of Google Scholar
results for the relevant terms taken together (?transmission electron microscopy,?
?EELS,? and ?non-negative matrix factorization?) increased from only 10 articles
in June 2016 [72] to 135 by November 2020.
Beyond NMF, the microscopy community continues to innovate in the area
of multivariate statistical analysis. Multivariate curve resolution (MCR) is a sub-
class of NMF which applies additional physically meaningful constraints including
that components? intensities always sum to unity. This algorithm was successfully
applied to a challenging 7-phase, low-intensity EELS dataset by Braidy and co-
workers in 2019 using a Poisson log-likelihood maximization (MCR-LLM) [74]. In
low-signal datasets MCR-LLM was demonstrated to outperform other multivariate
signal decomposition approaches including NMF. Due to rapid evolution at the
25
Figure 2.4: Example of a scree plot generated by PCA of a B-doped SiC/SiO2 interface
(discussed in Sec. 3.1.1). Each orthogonal component is presented in descending order of
significance as indicated by the fraction of overall variance it represents. A qualitative
guideline to distinguish physically meaningful components from noise is that the compo-
nents above the elbow are significant; in this case, 3 or plausibly 4.
intersection of multivariate statistical analysis and its applications to microscopy, an
additional goal of this work is to explore and document the use of novel techniques,
such as MCR-LLM, to draw meaningful conclusions from weak-signal EELS data.
Software and approach for applying multivariate statistical analysis to EELS SIs
Thanks to recent interest in ?big data,? machine learning, and related areas,
open-source software packages implementing PCA and NMF algorithms are freely
available. The HyperSpy software package [75] is a powerful Python package for
analysis of EELS, EDS and other spectral data and was used extensively in this
work. In general, the approach is to estimate the number of physically meaningful
components by inspection of a scree plot (a ranking of orthogonal components in
26
descending order of significance) generated by PCA, as depicted in Fig. 2.4. The
number of components above the elbow provides a reasonable initial guess of how
many are physically meaningful, as opposed to random noise. Subsequently, the
dataset is analyzed by NMF using the number of components suggested by the scree
plot, plus or minus one, and the resulting factorizations are compared to identify
the most reasonable explanation of the EELS data. A similar approach was taken
to apply the MCR-LLM algorithm via a publicly available Python code provided
by the algorithm?s authors [74]. Applications of this technique to wide-bandgap
semiconductor interfaces are discussed in Chapter 3.
2.2 Focused ion beam sample preparation
The focused ion beam (FIB) is a microscope in its own right, with a principle of
operation similar to that of an SEM, except with a beam formed by ions, e.g. Ga+,
instead of electrons. When accelerated to energies of 2?30 keV, the beam of massive
ions is capable of localized sputtering of the sample surface; thus the FIB/SEM is a
powerful tool for material modification and analysis. A typical dual-beam FIB/SEM
is illustrated in Fig. 2.5. The combination of both beams in one system with a single
vacuum chamber allows for near-simultaneous imaging and specimen modification.
A gas injection system (GIS) is used in conjunction with the ion beam to selectively
deposit materials such as W or Pt via organometallic precursor gases; the metal
is selectively deposited only where the gas is impacted and decomposed by the ion
beam. This functionality allows protective capping layers to be laid down prior to
27
e- beam
micro-
manipulator
?
GIS
SE detector
sample
Figure 2.5: Dual FIB/SEM schematic showing the 2 primary beams separated by the
angle ? (55? for the tools used in this work). The ion beam is used to mill around the
region of interest and to thin the final TEM lamella. A W micromanipulator probe is used
to transfer the lamella from the bulk material to the grid, and the gas injection system
(GIS) is used to deposit protective Pt or W capping layers and to attach the lamella to
the probe and the grid. Figure adapted from [72] and [76].
milling in order to protect shallow features from ion implantation damage, or to
adhere objects together, as when attaching the specimen to a specialized TEM grid
(e.g. Fig. 2.6 at left).
Cross-sectional transmission electron microscopy (TEM) specimens in this
work were prepared using the Tescan GAIA (Ga+) dual FIB/SEM at the UMD
AIMLab. The GAIA FIB was also equipped with a W micromanipulator probe to
extract sample cross-sections (TEM lamellas) and mount them to Cu TEM grids. It
was therefore possible to precisely select a region of interest on a device, extract the
specimen, and thin the lamella to electron transparency (typically < 100 nm) com-
pletely inside the FIB/SEM chamber. Analytical instruments commonly present in
SEMs were also available in the GAIA and other FIBs, such as Energy Dispersive X-
28
G
b a +e  a iom n
in-beam detector
(a) (b) (c)
Micro-
manipulator 
probe
tedpella.com
Grid (d) (e) (f)
post
Pt
SiO2
SiC
3 mm Lamella
Low-mag. TEM
Figure 2.6: Process of TEM lamella preparation in the dual FIB/SEM. (a?b) Selection
of the region of interest, deposition of protective Pt layer, and milling of trenches; (c)
Lift-out using W micromanipulator probe and (d) attachment to Cu TEM grid; (e) SEM
image of the final thinning result at low beam energy and current; (f) Low-magnification
TEM image showing the electron-transparent lamella. Adapted from Ref. [72].
ray Spectroscopy (EDS) and Electron Backscatter Diffraction (EBSD), which make
the FIB/SEM a uniquely powerful microscopy tool.
Fig. 2.6 outlines the process of TEM lamella preparation in the FIB. After
selecting the area of interest, a 2?3 ?m thick W or Pt protective cap is deposited
using the GIS to prevent amorphous damage from the ion beam from reaching the
interface during later stages of the process (Fig. 2.6(a?b)). The depth of damage
is beam voltage- and material-dependent, but can be 35 nm or more for a 50 keV
Ga beam on Si [77]. After rough milling at 30 kV and cutting under the lamella
with the ion beam, a W nanomanipulator probe is used to transfer the lamella to
a Cu TEM grid as shown in Fig. 2.6(c?d). Finally, the specimen is thinned at low
29
ion beam current and low voltage (first 5 kV, then 2 kV) to reduce the sample
thickness to 50?90 nm while minimizing surface amorphization damage from the
ion beam. The finished lamella (Fig. 2.6(e), in SEM) is electron-transparent in the
TEM (Fig. 2.6(f)).
2.3 Raman spectroscopy
Raman spectroscopy is a versatile way to identify molecules and bonding con-
figurations. It is an optical technique whereby a small fraction of incident photons
(on the order of 1 in 107) are inelastically scattered due to interaction with vibra-
tional modes of the molecules under illumination [78]. The energy shift is equal
to the energy lost to (or gained from) the vibrational mode, which is specific to
the atomic configuration. Raman spectroscopy is effective for preliminary non-
destructive characterization of bulk samples.
Characterization of carbon materials by Raman is well established in the lit-
erature. Graphite exhibits 3 distinct Raman signatures: a first order ?graphitic?
or G peak around 1582 cm?1, a disorder or D peak near 1350 cm?1, and second
order G? peak at 2700 cm?1 (also known as the 2D peak since its energy shift is
about twice the magnitude of the D peak at 1350 cm?1) [79, 80]. These features
are illustrated in Fig. 2.7. Defects contributing to the D peak include the edges of
graphene nanoribbons where the symmetry of the structure is broken. For the case
of more disordered or amorphous carbon (e.g. activated C), the D band appears
30
Figure 2.7: Raman spectrum of a graphite sample with defects. The G and G? peaks
arise from sp2 bonding of carbon, while the D and D? are due to broken symmetry such
as at the edges of graphene nanoribbons. Adapted from [80].
stronger relative to the G band than in more ordered C, and both the D and G
bands are broader; and the 2D band is substantially weaker or absent [81].
Raman spectra in this work were obtained using a Horiba LabRAM ARAMIS
confocal Raman system with a 532 nm laser excitation source. Using the highest
available optical magnification (100x) produced a laser spot size slightly smaller
than 1 ?m in diameter. To capture the spatial variability of C distributions in
covetics and to increase the volume of data available for statistical analysis, Raman
spectrum images (maps) of 11 ? 11 1??m square pixels were typically collected at
each region of interest.
Graphitic peak information was extracted from Raman data via non-linear
iterative curve fitting routines implemented in Matlab [82]. Lorentzian peaks were
fit to the D, G, and 2D bands, at 1350, 1580, and 2700 cm?1, respectively, with initial
31
Figure 2.8: Example of Lorentzian fits (green curves) to the D, G, and 2D features of a
single-point Raman spectrum (blue data points) in a C-rich region of an Al covetic. The
strong G and 2D peaks are indicative of a high degree of graphitic ordering. Note the
break in scale.
positions given by the literature [79, 83]. The best of three iterations was chosen
for each fit. Example fits from a single graphitic Raman spectrum in an Al6061
covetic alloy are displayed in Fig. 2.8. Customized Matlab scripts written for this
work were used to compile statistics of Raman data relevant to graphitic carbon and
to covetics. These scripts applied the curve-fitting routines from Ref. [82] to each
spectrum in a dataset which typically consisted of a collection of several spectrum
images taken from representative points on a cross-section of the sample. To obtain
accurate statistics it was necessary to filter out artifacts in the Raman spectra, such
as poor background fits or spurious Raman signals from adsorbed hydrocarbons and
other contaminants. These were excluded from the subsequent analyses by removing
poor fits with r2 < 0.9 or where any peak was shifted by greater than 50 cm?1 away
from its initial position, which would be likely to have a non-physical origin.
A commonly used metric of disorder in graphitic carbon is the ratio of the D
peak intensity, I(D), to the G peak intensity I(G), first introduced by Tuinstra and
32
Koenig [79]. The domain of validity of this relationship extends to nano-crystallites
as small as ? 2 nm [81]. It has been demonstrated that the I(D)/I(G) ratio is
inversely related to the width of the graphitic crystallites, La, by a constant which
depends on the excitation laser energy following Eq. 2.4 [84,85]:
( )
560 I ?1D
La = (2.4)
E4l IG
where El is the excitation laser energy in eV (in this work, 2.33 eV, equiva-
lent to 532 nm) and 560 is an empirically determined constant. This relationship
was validated by comparison with scanning tunneling microscopy (STM) and X-
ray diffraction (XRD) measurements [84]. Ultimately, Eq. 2.4 made it possible to
compute the nano-graphite crystallite size corresponding to every spectrum in each
Raman map, and therefore to both identify the locations of ordered graphitic carbon
produced in the covetics process (for further localized characterization) and to build
a statistical distribution of crystallite sizes representative of the sample in question
overall. An example of the reduced Raman spectrum image showing the spatial dis-
tribution of La and the corresponding histogram is shown in Fig. 2.9. Applications
of this approach to the characterization of covetic materials are presented in Sec. 4.1.
2.4 Effective medium model for bulk properties of composites
TEM, EELS, and Raman spectroscopy are critical techniques for identifying
the structure of NCMCs, which can then be related to properties including tensile
strength and electrical and thermal conductivity. However, it is also desirable to
33
La (nm)
26.1 ? 5.9 nm
Figure 2.9: Left: Spatial distribution of the nano-graphite crystallite size La in a 21 ?
21-?m Raman spectrum image. Black pixels were excluded from the subsequent analysis
due to poor fit quality. Right: the distribution of La in the spectrum image.
Figure 2.10: The macroscopic properties of a composite depend on many variables in
addition to the bulk properties of the constituents (matrix and inclusions), for instance
the inclusion orientation, dimensions, and interfacial interactions. There is no general
closed-form solution to predict the properties of composites.
predict the properties of covetics with certain graphitic structures in order to fully
understand their potential to offer enhanced properties, and to provide a reference
against which to gauge progress in their development.
The essence of this problem is illustrated by the schematic in Fig. 2.10. Various
attempts have been made since the time of Maxwell to calculate the bulk proper-
ties of a composite, which is by definition locally inhomogeneous [86, 87]. Several
additional variables become relevant for the properties of composites in addition to
the bulk properties of the matrix and inclusions. The volume fraction of inclusions,
34
Figure 2.11: Example configurations of composite inclusions with increasing complexity.
Adapted from Ref. [88].
as well as the inclusion geometry (shape and aspect ratio) and distribution within
the matrix (orientation and agglomeration) are generally significant. Fig. 2.11 gives
examples of the many possible configurations of inclusion geometries and distribu-
tions with varying degrees of ordering [88]. The relationship between anisotropy
in the inclusions? property to be simulated and the anisotropy of their distribution
within the matrix, if any, is relevant to composites which comprise graphitic inclu-
sions, such as carbon nanotubes or graphene sheets, whose electrical and mechanical
properties are highly anisotropic.
Interactions at interfaces between the matrix and inclusions can be significant,
but difficult to predict theoretically. Nan and co-workers effectively modified an ef-
fective medium model for thermal conductivity to include the interfacial thermal
resistance following Kapitza and Maxwell [89]. Deng [90] used this model to predict
thermal conductivities of CNTs embedded in insulating media, but did not extend
the interfacial-resistance calculations to electrical conductivity [91]. Fabrication of
model systems and/or nanoscale characterization are desirable to understand these
phenomena and to validate predictions. Finally, for certain inclusion geometries
35
above a critical volume fraction, the potential arises for long-range interaction (per-
colation effects) between series of adjacent inclusions. Predicting percolation effects
is mathematically complex and they are often safely neglected in dilute systems [86].
Several methods to model the properties of composites fall under the umbrella
of effective medium theory, or effective medium approximation (EMA), first devel-
oped by Bruggeman and Landauer [92]. Following this approach, a fraction of the
matrix with a given property (for the sake of this example, the electrical conductivity
?1) is replaced by a dilute, random dispersion of inclusions with a different property
(ex. ?2). For each inclusion it is assumed that, rather than being surrounded by
some combination of matrix and other inclusions (the exact configuration of which
could not be known), the inclusion is surrounded by the effective medium with the
property ?e of the bulk composite. Applications of the effective medium approxi-
mation to predict electrical conductivity enhancement in covetics are discussed in
Sec. 4.3.
36
Chapter 3: Characterization of wide-bandgap MOS interfaces
Recent developments in wide-bandgap semiconductor processing have enabled
commercialization of silicon carbide-based devices. Nevertheless, fundamental ques-
tions remain regarding the SiC/SiO2 interface which prevent SiC-based electronics
from reaching their full potential in terms of performance and reliability. In addi-
tion, several new wide-gap semiconductor technologies such as gallium oxide have
emerged within the last decade that may eventually surpass SiC in performance
under very high voltage conditions as their technology matures. Various TEM in-
vestigations were conducted to gain insight into the semiconductor-insulator inter-
face of these systems. Sec. 3.1 presents results of two experimental post-oxidation
annealing treatments in SiC based devices, respectively based on B and Sb doping,
while Sec. 3.2 explores the interface structure of two deposited gate oxide materials,
SiO2 and Al2O3 on ?-Ga2O3 devices processed under various conditions.
37
3.1 SiC: Passivation of electrically active defects with chemical treat-
ments beyond NO annealing
3.1.1 Boron interdiffusion and incorporation into SiO2
Nitridation annealing of the SiC/SiO2 system has dramatically improved the
channel mobility and enabled the first commercially successful SiC MOS devices.
Nevertheless, the resulting channel mobilities of 35?50 cm2/Vs [9, 93] fall far short
of the bulk field effect mobility in SiC. Within the past 10 years, efforts have been
underway to identify new chemical treatments that are able to enhance the perfor-
mance and/or reliability of the SiC/SiO2 system better than NO. Several electrical
characterization experiments have identified the dopants phosphorus [14?16, 94, 95]
and boron [13, 96, 97] as promising ways to passivate electrically active defects and
increase the field-effect mobility, ?FE. In both cases, doping is performed as a
post-oxidation anneal (POA) step which converts the thermally grown SiO2 oxide
into a phosphosilicate glass (PSG) or borosilicate glass (BSG), whose structure and
chemistry lower the interface trap density Dit and lead to enhanced ?FE: up to
75?105 cm2/Vs in the case of PSG [16] and approximately 100 cm2/Vs in the case
of BSG [13,98], about 2?3 times greater than NO POA alone. Furthermore, nitrida-
tion in combination with boron incorporation into a deposited oxide layer can lead
to ?FE of up to 170 cm
2/Vs [97].
Few structural studies have been conducted to date of the PSG and BSG oxide
layers on SiC. Analytical electron microscopy is especially important to understand-
38
ing the mechanisms by which P and B incorporation lead to enhanced mobility, in
order to optimize the potential for engineering devices with superior performance.
Prior to this work, one specimen each of PSG and BSG gate oxide was studied us-
ing TEM-EELS by Joshua Taillon, a former member of the research group of Prof.
Salamanca-Riba, whose results are reported in his 2016 PhD dissertation [72]. This
section of the present work details the confirmation of Dr. Taillon?s TEM work on
BSG-gated SiC and extends it using a larger dataset and new analytical tools. This
work is collectively published in Ref. [99].
3.1.1.1 Methods
The BSG sample was prepared by collaborators in the research group of Prof.
Sarit Dhar of Auburn University Department of Physics. In order to validate the
previous results in Ref. [72], the sample was prepared under the same conditions. A
5 mm ? 5 mm piece was diced from a 4?-miscut, n-type doped (1016 cm?3) 4H-SiC
wafer. After standard RCA cleaning (Radio Corp. of America [100]), the SiO2 oxide
was thermally grown at 1150 ?C to a target thickness of 75 nm. Subsequently, the
BSG layer was formed by annealing the sample in the presence of a planar B2O3
diffusion source at 950 ?C for 30 min., followed by a 2 hour drive-in anneal without
the B2O3 plate at the same temperature in Ar atmosphere. Electrical measurements
for this sample are detailed in Ref. [18]
Cross-sectional TEM specimens were prepared using the standard techniques
described in Sec. 2.2. The sample thickness was ultimately reduced to 50?60 nm
39
5 1/nm
SiC BSG
Figure 3.1: High-resolution TEM image of the SiC/BSG interface, which was abrupt and
smooth except for the steps resulting from the 4? substrate miscut.
using a 2 keV Ga+ ion beam in order to minimize the depth of amorphization
damage. High-resolution TEM imaging, HAADF-STEM, and EELS were performed
to characterize the structural and chemical composition of the SiC/BSG interface.
Analysis of the EELS data was performed by non-negative matrix factorization
(NMF). For this work the analysis was also performed using multivariate curve
resolution by log-likelihood maximization (MCR-LLM), a subclass of NMF that is
better suited to weak and/or low signal-to-noise ratio data by applying additional
constraints [74].
3.1.1.2 Results and discussion
High resolution TEM imaging revealed a flat and abrupt interface similar in
quality to those produced by the established NO anneal, as shown in Fig. 3.1. The
40
interface was abrupt, the only roughness being atomic steps arising from the 4?
miscut of the wafer.
HAADF imaging and EELS mapping were also performed in STEM mode to
probe the elemental composition and bonding of the interfacial region. Two phys-
ically significant components were identified for the NMF decomposition. These
results are presented in Fig. 3.2 for a 23 nm ? 50 nm region along the interface.
The first component, called silicon background in Fig. 3.2, was stronger in the SiC
substrate (left side of the map) but also weakly present in the BSG layer. It can
be attributed to background signal from the extended fine structure of the Si-L1
EELS edge. The spectrum of this component is shown in blue in Fig. 3.2(a). The
second component (green) matches the shape and energy of the B-K EELS edge
and thus confirms the presence of boron within the BSG layer. The corresponding
intensity map (?Boron,? top center) shows how the boron is homogeneously dis-
tributed throughout the bulk of the BSG layer, and concentrated in a narrow band
at the interface.
Linear profiles of relative intensity as a function of position across and per-
pendicular to the interface were constructed by summing each intensity map in
the vertical axis (parallel to the interface) and normalized relative to its maximum
(Fig. 3.2(b)). The B-K signal exhibits a maximum about 1 nm away from the in-
terface, as it is defined by the inflection point of the Si-L signal. At its maximum
the B-K signal is 2 times its intensity in the bulk of the BSG layer. The width
(FWHM) of the interfacial B accumulation was 2.8? 0.4 nm, with the uncertainty
41
Silicon Background Boron HAADF-STEM
40 18
5 nm
10 0
1.0
Si-L edge (a) Silicon (b)background
0.8
0.6
B-K edge 0.4
0.2 Boron
Interface
0.0
180 190 200 210 220 230 0 5 10 15 20
Energy loss (eV) x (nm)
Figure 3.2: Relative EELS intensity maps and simultaneously collected HAADF-STEM
image of the SiC/BSG interface (top). The HAADF-STEM image shows a ? 2.1-nm wide
dark band at the interface, most visible at the bottom of the image, which corresponds
to a lower-Z element such as B. Intensity maps reflect the relative abundance of the two
components identified by NMF decomposition, shown in (a): the residual background
from the Si-L edge, and the B-K edge. (b) Normalized line profiles of each component?s
intensity as a function of displacement across the interface. The B-K signal has a well-
defined peak at the interface, with a width (FWHM) of 2.8 nm and peak B concentration
roughly twice that of the bulk BSG.
42
Norm. Intensity (a.u.)
estimated to be half the step size of the EEL spectrum image, equal to the STEM
probe size of 0.7 nm.
As shown in Fig. 3.2(a), the primary peak of the B-K edge has an energy of
193.8 ? 0.7 eV, which corresponds to the ?? antibonding orbital of boron in an
sp2-hybridized state such as in B2O3 or trigonally-coordinated BO3 units [101?103].
Uncertainty in the edge-onset energy was estimated as the standard deviation of 7 B-
K edge positions extracted from NMF decompositions of EELS maps from different
areas along the interface. The evidence of trigonally-coordinated boron provided by
EELS lends support to the predicted mechanism of Dit reduction in B-doped SiC,
which suggests that the relief of interfacial stress is the cause [13,98]. The presence
of B in the glassy SiO2 layer contributes to a higher concentration of non-bonding
O atoms, making the BSG layer?and the interfacial part of it in particular?more
fluid [104], and less prone to large interfacial stresses that give rise to electrically
active defects. Elemental B did not appear to be present, as its B-K edge shape
is much different than that for B2O3 [103]. This observation is consistent with the
O-K EELS edge profile (Fig. 3.3) across the interface, which indicated that the
stoichiometry of oxygen within the oxide layer was uniform with depth, in spite of
the peak in B-K intensity profile.
The presence of the weak, but well-defined B-K edge and its uniform distribu-
tion along the interface meant that this dataset was well suited to additional MSA
algorithms beyond NMF, both to confirm the results produced by NMF and to
identify promising algorithms for use with other material systems elsewhere in this
thesis. Multivariate curve resolution by log-likelihood maximization (MCR-LLM)
43
Background O-K
SiC   BSG SiC   BSG
(a) (b) SiC BSG
O-K Background O-K signal
signal
Background
? Interface
Figure 3.3: STEM-EELS spectrum imaging at the energy-loss range of the O-K edge
from the SiC/BSG interface, near the region shown in Fig. 3.2. (a) A well-defined O-K
edge component was identified by NMF and localized to the gate oxide (BSG) layer. (b)
The line profile of O-K intensity did not indicate an interfacial peak of O concentration,
unlike with B.
is one such algorithm first published in 2019 [74] and introduced in Sec. 2.1.2.2.
It is particularly well-suited to low signal-to-noise ratio datasets. The MCR-LLM
decomposition results of the BSG sample are presented in Fig. 3.4. No background
subtraction was performed prior to decomposition. The 2 spatial dimensions of the
spectrum image were reduced to 1 prior to the analysis by summing each column
parallel to the interface, as required by the MCR-LLM Python code (available from
the repository indicated in Ref. [74]).
Three significant components were identified by MCR-LLM, as shown in Fig.
3.4(b). This is one more component than NMF was able to clearly resolve, as in
Fig. 3.2. The difference appears to arise from the additional constraints applied by
MCR-LLM. Specifically, the requirement that relative intensities (termed ?abun-
44
(a)
SiC
Si-L1
B-K BSG
MCR-LLM Decomposition of (a)
(b) (c) SiC  ?   B-rich BSG  ?  Bulk BSG
Si-L FWHM = 2.4 nm1
B-K
Figure 3.4: (a) Raw EELS data in the range 150?240 eV, from the same spectrum image
analyzed in Fig. 3.2. Each spectrum is one 50-nm long ? 0.7-nm wide line scan running
parallel to the interface. The spectra are separated by their raw intensities such that the
progression from SiC across the interface to BSG can be seen, as marked by the thick arrow.
(b) MCR-LLM components for each of 3 phases identified and (c) corresponding abundance
profiles. The interfacial phase (green curve) in (c) displayed the most prominent B-K edge
in (b), followed by the BSG phase (orange). The SiC phase (blue) of the decomposition
contained no discernible B-K signal.
45
dances? for the purpose of this algorithm) always sum to one led to the separation
of the BSG signal into two phases, one interfacial and one bulk, on the basis that
the B-K edge was stronger at the interface. Despite making this distinction, MCR-
LLM did not suggest that there was a chemical difference between the interface and
bulk BSG components, as they both exhibited the same fine-structure, albeit with
different intensities (Fig. 3.4(b)).
It is important to note that MCR-LLM has different criteria for distinguishing
between phases as a result of its constraints. The requirement for closure in partic-
ular seems to create a tendency to resolve intensity differences into distinct phases,
in addition to distinguishing between chemical differences in the EELS fine struc-
ture, whereas NMF relies more exclusively on the shape of the fine structure. Aside
from this distinction in the two algorithms? approaches, the results of NMF and
MCR-LLM decomposition are qualitatively similar. For instance, the width of the
interfacial boron pile-up in MCR-LLM was 2.4 nm, compared to 2.8 nm for NMF;
these values are within the margin of error, estimated to be 0.4 nm. These results
show that MCR-LLM is a viable way to apply multivariate statistical techniques to
EELS data, and support the qualitative results of NMF.
In summary, the SiC/BSG MOS interface was analyzed using analytical TEM-
EELS in combination with multivariate statistical analysis techniques in order to
validate and expand on previous findings, which indicated a uniform band of B-
rich SiO2 located at the interface. The present work supports that conclusion with
considerably more data. NMF decomposition reveals a 2.8-nm wide band of boron
accumulated at the interface, roughly twice the intensity as in the bulk oxide layer.
46
The fine structure of the B-K edge indicates sp2 hybridization, which is expected to
relieve interfacial stresses in the device and therefore presents a plausible mechanism
for the reduction in Dit observed in B-doped SiC MOS devices.
3.1.2 Sb ion implantation in conjunction with NO annealing
Another technique to improve channel mobility in SiC MOS devices is to im-
plant ions directly into the substrate prior to the formation of the gate oxide layer.
This approach has been utilized to help elucidate the mechanisms by which NO
and PSG annealing improve channel mobility. By implanting antimony ions into
the surface channel (Sb counter-doping), the effects of n-type doping could be dis-
tinguished from the passivation of interface traps. N, P, and Sb are all n-type
dopants in SiC, but Sb was not expected to have a passivating effect due to its
large atomic size [17]. The use of Sb counter-doping in conjunction with previously
demonstrated passivating treatments suggest that the effects are additive, with each
treatment acting independently to improve mobility. This has been the case with
Sb+NO (peak ?FE = 110 cm
2/Vs, compared with 32 cm2/Vs for NO and 80 cm2/Vs
for Sb alone) [17] and BSG+NO (peak ?FE = 180 cm
2/Vs vs. 135 cm2/Vs for BSG
alone) [18].
The interface structure of Sb counter-doped SiC MOS systems have primar-
ily been probed by electrical methods [105] or composition-analysis techniques with
resolution limitations, such as secondary ion mass spectrometry (SIMS) [18]. As
such, even preliminary results from TEM and EELS will be of interest to the SiC
47
device community. This subsection presents a case-study of TEM-EELS investiga-
tions performed on one sample subjected to the Sb+NO process by collaborators at
Auburn University as described in Ref. [18]. In brief, a 5 mm ? 5 mm piece of a 4?
off-axis, p-type (? 1016 cm?3) 4H-SiC wafer was implanted with a dose of 2.5?1013
cm?2 Sb ions at an energy of 80 keV. After a 1650 ?C post-implantation activation
anneal, the gate oxide layer was thermally grown to a target thickness of 75 nm
and an NO post-oxidation anneal was preformed for 30 min. The cross-sectional
TEM specimen was prepared by FIB using the approach presented in Sec. 2.2 and
ultimately thinned to a thickness of ? 50 nm using a 2 keV Ga+ beam.
TEM-EELS results from the cross-sectional TEM lamella are presented in
this section. High-resolution imaging of the interface region (Fig. 3.5) does not
suggest any significant deviation from a device prepared with only the NO anneal.
The interface was abrupt and smooth, with few steps, mostly corresponding to the
substrate miscut.
The objectives of STEM-EELS spectrum imaging of this sample was to deter-
mine whether the Sb could be detected and if so, to observe how it was spatially
distributed in the device. Contamination and drift were particular challenges during
spectrum imaging of this sample. Performing a ?beam shower? [63] and allowing the
specimen position to stabilize over a few minutes prior to STEM imaging and EELS
helped to mitigate these problems. 6 spectrum images were collected to encompass
the Si-L, C-K, Sb-M4,5, and O-K edges, using a probe step size of 0.7 nm and an
energy channel width of 0.3 eV.
48
SiO2
SiC 
(Sb-doped)
Figure 3.5: High-resolution TEM image and associated diffraction pattern of the Sb-
doped SiC/SiO2 interface.
There is an indication that the SiC/SiO2 transition region was narrower after
the Sb+NO treatment than in a comparable device treated only with NO. Fig. 3.6(a)
shows the progression of the chemical shift of the Si-L2,3 edge from 99 eV in SiC
to ? 105 eV in SiO2, as the STEM probe moved across the interface. This shift
occurred within 5 ? 1 adjacent spectra, so the transition width wTL was therefore
0.7 nm ? (5? 1) = 3.5? 0.7 nm. This is smaller than transition widths previously
reported for NO annealing alone, where a 30-minute post-oxidation anneal process
led to a wTL of about 7? 1 nm [93]. Sb ion implantation does not, however, appear
to have affected the Si-L2,3 edge in SiC, which is not distinguishable from that in
an un-doped SiC substrate (Fig. 3.6(b)) from a device treated with NO only.
Higher-energy signals were also collected using longer dwell times. The energy
range around the Sb-M4,5 edge at 528 eV and the O-K edge at 532 eV were of par-
49
(a) Si-L2,3 edge evolution across interface
SiC SiO2
99.1 eV
104.8 eV
(b)
Si-L2,3 edge in
Native SiC
Sb-doped SiC
100 105 110 115 120
Energy loss (eV)
Figure 3.6: (a) Si-L2,3 EELS edge evolution after Sb+NO annealing. Each curve repre-
sents the sum parallel to the interface of one 60-nm long column in the spectrum image
array. The edge onset energy shifts from 99 eV in SiC to ? 105 eV in SiO2 across 4?6 steps
with intermediate onset energies, indicating that the transition width was about 3.5 nm.
This is narrower than the equivalent process utilizing NO annealing only. (b) No shift in
the Si-L2,3 onset energy was identified between the Sb-implanted SiC in this sample and
a reference SiC wafer from the NO-only process without ion implantation.
50
532 eV O-K
Sb-M4,5
528 eV
Figure 3.7: Normalized reference spectra for elemental O-K and Sb-M4,5 edges. Source:
Gatan, Inc. / eels.info
ticular interest. These edges exhibit different fine structures (Fig. 3.7) and it should
in principle be possible to distinguish the two by multivariate analysis methods.
The NMF algorithm was able to resolve clear C-K and O-K edges in SiC and SiO2,
respectively, as with similar devices not doped with Sb. However, NMF was not able
to identify a clear Sb EELS signal. This was most likely due to a combination of the
lack of an abrupt onset or well-defined peak in the Sb-M4,5 edge, and the relatively
low concentration of Sb dopants (nominally 2.5? 1013 cm?2, but with up to 85% of
the Sb being lost during the fabrication process [17,18]). The 2019 publication and
release of the MCR-LLM algorithm [74] provided a new analytical tool to search
for this signal. The 2D spectrum image was converted into a 1D line-scan with
one spectrum for each column of the original dataset prior to being resolved into 2
principal components by the MCR-LLM algorithm, one for Sb-doped SiC and one
for the SiO2 oxide. These components are shown in Fig. 3.8(a). The corresponding
51
(a) O-K (b) Sb-M4,5 signal O-K signal
Sb-M 4.2 ? 0.4 nm4,5
Figure 3.8: MCR-LLM decomposition of EELS spectrum image in the energy range cap-
turing the O-K and Sb-M4,5 edges. (a) The two principal components resolved by the
MCR-LLM algorithm corresponded to the O-K (blue) and Sb-M4,5 (red) edges. The
fine structures match the published references in Fig. 3.7 after decaying-exponential back-
ground subtraction from the raw components (as displayed in the insets with the same
energy-loss range). (b) Relative abundance profile of the two components across the
SiC/SiO2 interface, with a 5?95% intensity transition width of 4.2? 0.4 nm.
line-profile transition width in Fig. 3.8(b) between the Sb-M4,5 and O-K edges was
4.2?0.4 nm, which is within the range estimated using the Si-L2,3 edge. MCR-LLM
is not capable of identifying absolute intensities, however the more prominent noise
in the Sb signal indicates that it is probably much weaker than the simultaneously
collected O signal.
The results from a single device do not represent the complete picture of the
interface structure, composition and bonding changes that result from the Sb+NO
processing technique. Nevertheless, the TEM-EELS analysis presented in this work
illustrates a promising path forward. HRTEM and spectrum imaging of the Si-L2,3
EELS edge indicate that the interface is at least as abrupt and smooth as in com-
parable devices treated with an NO post-oxidation anneal only, and possibly with
52
a smaller wTL. Higher-energy spectrum imaging interpreted using the MCR-LLM
multivariate statistical method indicates that Sb is present throughout the sub-
strate at relatively low concentrations. Previously reported SIMS depth profiles of
Sb concentrations in a similarly prepared device suggest that the Sb accumulates in
a Gaussian intensity profile which peaks ? 10 nm below the SiC/SiO2 interface [17].
The presence of this feature could not be confirmed by the MCR-LLM decomposi-
tion due to the absence of a third EELS edge, for instance Si-L or C-K, that could
serve as a reference to show intensity variations of the Sb signal with depth into
the substrate. A deeper EELS line profile over a sufficiently wide energy range to
capture an EELS edge unique to the substrate would help to confirm this report.
3.1.3 Summary and future research directions
In this section, new methods to improve the performance and reliability of
SiC MOS devices have been explored. Although SiC is now a commercially avail-
able technology, its performance still falls short of the theoretically expected mo-
bilities, largely due to electrically active interfacial defects at the substrate/gate
oxide interface which are traditionally passivated using a NO post-oxidation anneal.
Experimental treatments based on boron and antimony doping each serve to in-
crease channel mobility in SiC devices through different mechanisms. In Sec. 3.1.1,
HAADF-STEM and EELS spectrum imaging are used to confirm the link between
the spatial distribution of B in the B-doped SiO2 layer, the sp
2-hybridized nature of
the chemical bonding and the relaxation of interfacial stress known to inhibit car-
53
rier mobility. The B-K spectrum image also presented an opportunity to validate
the recently published MCR-LLM multivariate analysis algorithm for wide-bandgap
heterostructures. This technique became relevant for Sec. 3.1.2, where it was used
to identify a weak Sb-M4,5 EELS edge that could not be found with NMF. The rel-
atively smaller wTL in this device and overall abrupt, stable structure is also cause
for encouragement regarding Sb counter-doping as a method to improve channel
mobility.
Novel SiC processing techniques are often only characterized by electrical
methods, with an eye towards processing-performance relationships. Analytical elec-
tron microscopy techniques provide the physical and chemical structure information
to build a complete picture of the processing-structure-property relationships in SiC
MOS devices, which will ultimately inform the design of more efficient and robust
devices.
3.2 Ga2O3 with deposited SiO2 and Al2O3 gate oxides
3.2.1 Post-deposition annealing effects on the Ga2O3/gate oxide in-
terface structure
As described in Sec. 1.1.2, gallium oxide-based MOS technology is not yet
mature. One of the principal challenges is the selection of appropriate gate oxide
material and growth parameters to produce a device with a suitable interface struc-
ture to obtain the desired electrical properties. This section describes a series of
comparative TEM investigations conducted to investigate the Ga2O3 interface with
54
deposited SiO2 and Al2O3 gate oxides, with the goal of developing structure-based
understanding of electrical behavior previously observed on the same set of samples
by Jayawardena et al. [23].
3.2.1.1 Experimental methods
A set of six samples were provided for this work by collaborators in the research
group of Prof. Sarit Dhar at Auburn University. A summary of the sample prepara-
tion conditions is presented in Table 3.1. Ga2O3 MOS capacitors were prepared by
chemical vapor deposition (CVD) of the gate oxide layer on unintentionally Si-doped,
(2?01)-oriented ?-Ga2O3 substrates obtained from Tamura Corporation [106]. The
substrate surfaces were treated with a chemical-mechanical polishing (CMP) process
during manufacture, leading to initial surface roughness of 0.21 nm as-received [23].
After 5 mm ? 5 mm pieces were diced from the wafer and cleaned, a Piranha etch
step was performed for 15 min. (1:1 H2SO4:H2O2).
The SiO2 layer was deposited on one sample by low pressure CVD (LPCVD) at
650 ?C for 35 min., followed by densification in N2 at 850
?C for 2 h. For the second
SiO2 gate, a low-temperature oxide (?LTO?) was grown by CVD at 400
?C followed
by annealing in Ar at 1000 ?C for 60 sec. Four Al2O3 gate oxide samples were
prepared by atomic layer deposition (ALD) at 250 ?C using a trimethylaluminum
(TMA) precursor gas. Two of the samples were later annealed at 500 ?C, one in
forming gas (FG; 95% N2 : 5% H2) and one in pure H2. The others were not
subjected to post-deposition annealing (PDA). Al gate contact pads were thermally
55
Sample # Process Material Dep. T (?C) PDA T (?C) PDA Time
531 LPCVD SiO2 650 850 2 hrs.
324 LTO SiO2 400 1000 60 sec.
454 ALD Al2O3 250 ? ?
24 ALD Al2O3 250 ? ?
25 ALD Al2O3 250 500 (in FG) 2 min.
26 ALD Al2O3 250 500 (in H2) 2 min.
Table 3.1: Gate-oxide materials and CVD deposition parameters of the studied Ga2O3
MOS devices. FG = Forming Gas (mixture of N2 and H2).
evaporated on to the devices in order to perform electrical characterization prior to
TEM; the details of these measurements are published in Ref. [23].
Cross-sectional TEM specimens were prepared by focused ion beam using the
techniques described in Sec. 2.2. Lamellas were cut parallel to the cleaved edges of
the (2?01)-oriented Ga2O3 wafers, i.e. [010] or [102], such that the TEM zone axis was
ultimately one of these two directions. Final FIB polishing used a 2 kV Ga+ beam
to reduce the thickness of FIB-related damage (amorphization and Ga+ ion implan-
tation) and resulted in lamellas ranging between 50?100 nm in overall thickness.
High-resolution (HR) TEM imaging, high angle annular dark field scanning TEM
(HAADF-STEM) and electron energy loss spectroscopy (EELS) were performed on
the JEOL JEM 2100F TEM/STEM located at the University of Maryland Ad-
vanced Imaging and Microscopy Laboratory (AIMLab). EELS data were collected
at 200 kV in STEM mode as spectrum images (SIs) with a probe size of 0.7 nm,
convergence semi-angle of 12 mrad and collection semi-angle of 57 mrad. Typical SI
dimensions were 30?60 nm wide (across the interface) and 30?60 nm long (parallel
56
Figure 3.9: HRTEM images from Ga2O3 MOS capacitors subjected to post-deposition
annealing (PDA) at different process temperatures. (a) The sample treated with 850 ?C
PDA exhibited localized peak-to-valley roughness of about 1 nm, while the sample treated
with 1000 ?C PDA showed roughness of 2?3 nm.
to the interface). Several SIs were collected at different locations along the interface
of each specimen to increase the accuracy of the results.
3.2.1.2 Results and discussion
SiO2 gate oxides
Interfacial roughening of Ga2O3/SiO2 correlated with PDA temperature
High-resolution TEM imaging was performed first to identify the structural
characteristics of the Ga2O3/SiO2 interfaces. SiO2 layers were amorphous, as is
typical for the LPCVD and LTO processes. Localized roughness was observed along
the interfaces of both devices with SiO2 gates (Samples #531 and 324) as shown in
Fig. 3.9. The peak-to-valley roughness amplitude was approximately 1 nm in the
sample exposed to an 850 ?C, 2-hour post-deposition anneal (PDA), and 2?3 nm in
the sample exposed to a 1000 ?C, 60-second PDA. The larger interfacial roughness
57
may be attributed to the higher PDA temperature, since both Ga2O3 substrates
were treated by the same chemical-mechanical polishing process during manufacture,
leading to surface roughness values of 0.21 nm before gate oxide deposition [23,107].
It has been previously shown that the RMS surface roughness of a (100)-oriented ?-
Ga2O3 substrate increases after annealing, from 0.2 nm on the as-received substrate,
to 2.67 nm after a 950 ?C, 3-min. anneal, to greater than 14 nm after 3 min. at
1100 ?C [108].
The roughness of gate oxides is closely linked with the performance and reli-
ability of semiconductor devices. In the ubiquitous Si/SiO2 system, roughness on
the order of 2 nm is known to develop during the standard growth of SiO2 at 900
?C, which leads to undesirable electrical properties (reduced breakdown field and
increased probability of failure for a given bias); both the roughness and poor reliabil-
ity were ameliorated by post-oxidation annealing at 1050 ?C [109]. Extreme surface
roughness on the order of several (4?9) nm has been found to increase tunneling
current, to the detriment of the gate oxide reliability [110]. With thermally grown
SiO2 on SiC, roughness is detrimental to the charge-to-breakdown metric (QBD) in
time-dependent dielectric breakdown (TDDB) measurements, as increased rough-
ness can contribute to more intensive local field stress in the gate oxide, leading to
increased risk of failure over time [111]. For these reasons it is desirable to minimize
roughness or large thickness variations in gate oxides of Ga2O3 MOS devices as well.
58
HAADF-STEM SiO2 Ga2O3
(a)
Ga2O3 SiO2
10 nm
(b) (c)
Ga-M2,3
Ga2O3 1.8 nm
Si-L
SiO 2,32
Interface ?
Figure 3.10: EELS principal components from a Ga2O3/SiO2 MOS capacitor treated
with 1000 ?C PDA. (a) Relative intensities of the HAADF-STEM (Z-contrast) signal
and the two principal components belonging to SiO2 and Ga2O3, respectively. (b) Line-
profile averages showing the change in relative intensities across the interface, which was
abrupt, with minimal roughness in this region. (c) Constituent NMF component spectra
corresponding to the maps in (a).
Electron energy loss spectroscopy of Ga2O3/SiO2 interfaces
Scanning TEM and EEL spectrum imaging were performed in the energy range
of the Si-L2,3 and Ga-M2,3 edges in order to study the chemical composition and
bonding features of the interface. The onset energies of the two edges differed by
only 2 eV, which can be resolved by the spectrometer, but severe overlap between
the edges? extended fine structure made it difficult to separate them using traditional
methods. In addition, EELS edges can exhibit a chemical shift of up to several eV
depending on the bonding state, as with the elemental Si L2,3 edge (99 eV in pure Si)
59
HAADF-STEM Background Ga2O3 SiO2
Ga2O3 SiO2 Ga2O3
SiO2
5 nm
10 nm Localized roughness (~3 nm)
5.6 ? 0.4 nm
SiO2 (greater width attributed to 
roughness in this region)
Ga2O
Ga-L2,3 
3 edge
Background
Figure 3.11: O-K EELS map from Sample #324 showing roughness of Ga2O3/SiO2
interface following 1000 ?C PDA. The roughness amplitude of approximately 3 nm is
visible in the HAADF-STEM signal (periodic bright bands) as well as the Ga and Si
EELS component maps.
vs. Si in SiO2 (105 eV). The NMF algorithm made it possible to distinguish these
components. Two principal components were sufficient to fully describe the core-
loss spectrum image in Fig. 3.10, corresponding to the sample treated by 1000 ?C
PDA. In this region the interface showed minimal roughness (Fig. 3.10(b)) and was
1.8 ? 0.4 nm wide. Inspection of another SI from a different area along the same
interface shown in Fig. 3.11 revealed similar roughness features as shown in the
HRTEM image, with an amplitude of about 3 nm.
60
Al2O3 gate oxides
Crystallization of the Al2O3 gate layer under the electron beam
During HRTEM imaging of the devices with amorphous, ALD-grown Al2O3
gate oxides, it became apparent that the gate layer crystallizes under the electron
beam in TEM. Two HRTEM images of one Ga2O3/Al2O3 interface (Sample #454)
are shown in Fig. 3.12. The first (Fig. 3.12(a)), taken after only a few seconds of
TEM beam exposure, shows a 1.5 nm crystalline layer adjacent to the substrate.
After additional exposure on the order of tens of seconds, the crystalline region had
propagated outward from the interface, and the Al2O3 film had fully crystallized
under the beam (Fig. 3.12(b)). This crystallization phenomenon was confirmed
multiple times by watching the Fast Fourier Transform signal of the Al2O3 film
(Fig. 3.12, upper-right insets) evolve from amorphous halo rings to crystalline spots
at different points along the TEM specimen, as well as by the HRTEM and electron
diffraction imaging of the fully crystallized film. In total, of the three Ga2O3/Al2O3
samples studied in this work, all exhibited a qualitatively similar crystallization ef-
fect, including the sample that was annealed at 500 ?C?meaning that the annealing
did not by itself cause crystallization.
Since crystallization proceeded quickly to completion in under 60 seconds, it
was not immediately apparent whether the initial image in Fig. 3.12a is representa-
tive of the sample as fabricated, or simply showing the initial stages of crystallization
under the electron beam used to image the sample. The observation of a narrow
61
Ga2O3 interface Al2O3
(a)
t < 3 s ~1.5 nm
5 1/nm
5 nm
(b) (b)
t > 60 s
Figure 3.12: HRTEM images of the Ga2O3/Al2O3 interface. (a) After minimal electron
beam exposure of a few seconds, a 1.5 nm-wide crystalline layer of Al2O3 was visible at
the interface between the substrate and amorphous Al2O3. Inset: Fast Fourier Transform
(FFT) of Al2O3 layer in the region displayed. The absence of spots or rings in the pattern is
indicative of the layer?s amorphous character. (b) Further tens of seconds? exposure led to
the complete crystallization of the Al2O3 layer in the region under the beam. Inset, right:
Discrete spots in the FFT of Al2O3 demonstrate the formation of a complete crystalline
layer in the region shown. Inset, left: FFT corresponding to the [102] zone axis of the
Ga2O3 substrate.
62
band of crystalline Al2O3 is similar to that observed by Kamimura et al. on (010)-,
but not (2?01)-oriented Ga2O3 substrates [112]. In that work, no crystallization due
to TEM electron-beam exposure was reported for any sample or imaging conditions,
suggesting that the influence of the electron beam was greater in this work and that
the initial crystallization shown in Fig. 3.12a was caused by the beam. Quantitative
investigation of this crystallization phenomenon is discussed in Sec. 3.2.2.
Interdiffusion between Ga and Al
Several EEL spectrum images were collected in STEM mode from another
Ga2O3/Al2O3 sample (#24) prepared under the same conditions. Multivariate sta-
tistical analysis (MSA) of EELS data was performed using the NMF and MCR-LLM
algorithms as detailed in Sec. 2.1.2.2. NMF decomposition of one spectrum image in
the range of the Al-L2,3 and Ga-M2,3 edges is presented in Fig. 3.13. Two NMF com-
ponents were sufficient to fully describe the data, as with the Ga2O3/SiO2 interface.
However, unlike the systems containing SiO2, which exhibited somewhat abrupt
transitions at the interface, the relative intensity of the Ga signal declined gradu-
ally with distance up to 3.2 nm into the Al2O3 layer. Such a profile indicates some
interdiffusion between Ga and Al, most likely occurring during the ALD process.
Similar interdiffusion has been reported in metal-organic CVD-grown GaN films
on sapphire substrates [113] as well as with pulsed-laser deposited (PLD) ?-Ga2O3
films on sapphire substrates above 600 ?C [114]. The region of Ga interdiffusion
was significantly wider on the device that was subjected to a 500 ?C, 2-min. post-
63
Figure 3.13: Decomposition of the core-loss EELS spectrum image from a Ga2O3/Al2O3
MOS device without post-deposition anneal (PDA). (a) From top to bottom: Relative in-
tensities of the enhanced STEM (Z-contrast) signal, Al2O3 and Ga2O3 NMF components,
respectively. (b) Line-profile averages showing the gradual decrease in Ga intensity across
the interface. (c) NMF component spectra corresponding to the elemental maps in (a).
64
(a) Al2O3 Ga2O3
10 nm
(b) (c)
Ga-M2,3
Ga2O3
Al-L2,3
5.6 nm
Al2O3
? Interface 
Figure 3.14: EELS spectrum image from a Ga2O3/Al2O3 MOS sample treated by 500 ?C
PDA. (a) Relative intensity maps of the principal NMF components belonging to Al2O3
(left) and Ga2O3 (right), respectively. (b) Line profile of the gradual tail-off in Ga intensity
extending 5.6 nm into the Al2O3 layer. (c) NMF component spectra corresponding to Ga-
M2,3 and Al-L2,3 EELS edges.
deposition anneal (Sample #25) as indicated by NMF analysis of interfacial EELS
data presented in Fig. 3.14. The Ga signal in this device extended about 5.6 nm
into the Al2O3 gate layer before leveling off.
This result was validated with higher confidence using the MCR-LLM algo-
rithm which has been recently demonstrated to identify strongly overlapping, low
signal-to-noise ratio EELS components as detailed in Sec. 2.1.2.2. A spatial integra-
tion of each column in the spectrum image (parallel to the interface) was performed
prior to MCR-LLM decomposition in order to satisfy the constraint of the algo-
rithm to 1 spatial dimension, as well as to enhance the strength of the raw EEL
65
Figure 3.15: Comparison of line profiles generated by MCR-LLM from the Ga2O3/Al2O3
interface, (a) without PDA and (b) following 500 ?C PDA. The width of the 95?5% drop
in intensity of the Ga-M component (solid green line) across the interface nearly doubled
from 2.5 nm without PDA to 4.7 nm following the PDA process, clearly demonstrating the
role of PDA in promoting interdiffusion between Ga and Al. Dashed green and blue lines
represent the abundance of O-K signals originating with Ga2O3 and Al2O3, respectively.
signal. MCR-LLM-generated line profiles of Ga and Al relative abundance across
the interfaces are shown by the solid lines in Fig. 3.15a (corresponding to the NMF
plot in Fig. 3.13b) and Fig. 3.15b (corresponding to Fig. 3.14b). Additionally,
the abundance of O-K EELS edges are indicated for the Ga and Al components by
dashed green and blue lines, respectively. The line profiles are qualitatively similar
to those produced by NMF, but with significantly less noise, which facilitates un-
derstanding of the effects PDA has on the Ga2O3/Al2O3 interface. The width of the
interdiffusion region was represented by the 95?5% intensity drop across the inter-
66
face. Following PDA the width of this region nearly doubled from 2.5 nm to 4.7 nm,
indicating the pronounced diffusion effect promoted by PDA. MCR-LLM profiles
also more clearly reveal the asymmetric nature of the diffusion, with Ga penetrating
more deeply into the Al2O3 gate layer than Al into the Ga2O3 substrate.
An anomalous Ga feature appears within the un-annealed Al2O3 region, several
nm away from the interface. This feature does not appear to be a non-physical
?artifact? of the multivariate analysis, as it appeared in multiple Al-L + Ga-M
spectrum images from the specimen (Sample # 24). Furthermore, a noisy but
perceptible rise in Ga-M signal is also visible in the NMF decomposition (Fig. 3.13b)
a few nm into the Al2O3 layer, around x = 40?50 nm. This feature was not expected
to arise during ALD growth of the gate layer, nor was it seen in other samples
prepared under the conditions in Table 3.1. By elimination of other possibilities,
the most likely explanation for the anomaly is Ga+ ion implantation during final
FIB preparation of the lamella. Ga FIB preparation has been known to induce
ion-implantation damage in metallic Al foils up to 20 nm deep for a 30-kV Ga+
beam [115].
Relationship between interface structure and electrical peoperties
These results indicate that structural changes at the ?-Ga2O3/Al2O3 interface
indeed contribute to the increased density of interface traps measured by Jayawar-
dena in these Ga2O3/Al2O3 devices subjected to post-deposition annealing [23].
Potential mechanisms for this increase include different interface trap profiles in the
67
mixed phase (AlGa)2O3 transition region [116] and the formation of O vacancy or
interstitial defects depending on whether the ambient process condition is O-poor
or O-rich, respectively [117]. Annealing in this work was conducted in an O-poor
forming gas environment and therefore expected to contribute O vacancies to the
system, which tended to act as electron traps at the interface [118]. This dependence
raises the possibility of controlling the defect structure at the Al2O3/?-Ga2O3 in-
terface via the annealing environment as reported by Zhou et al., who compensated
for O vacancies by annealing in O2 [119].
This set of experiments sheds light on the structural features responsible for
undesirable increases in interface trap density and interfacial roughness in Ga2O3
MOS capacitors with CVD-deposited SiO2 and ALD Al2O3 gate oxides. Inspection
of Ga2O3/SiO2 interfaces by HRTEM imaging reveals that post-deposition anneal-
ing parameters affect the interface roughness, with greater roughness attributed
to higher PDA temperatures. At the Ga2O3/Al2O3 interfaces, EELS line profiles
show interdiffusion between the Ga2O3 substrates and Al2O3 films. This effect was
amplified by post-deposition annealing and indicates mechanisms for the increased
interface trap density associated with the mixed-phase region.
3.2.2 Electron beam-induced crystallization of Al2O3 gate oxides
Rapid crystallization of the initially amorphous ALD-grown Al2O3 gate lay-
ers in TEM lamellas was an unexpected finding from the work in Sec. 3.2.1, given
the chemical stability of the materials in question and the unremarkable doses of
68
electron irradiation used for TEM imaging. This phenomenon was consistently re-
producible, and warranted further investigation from a purely fundamental materials
science standpoint. Furthermore, while it is not obvious from microscopy alone what
the performance and reliability implications may be for MOS devices subjected to
electron irradiation and/or complete crystallization of the gate oxide layer, recent
reports indicate that they may be substantial. This section of the thesis describes
quantitative investigation of the electron beam-induced crystallization phenomenon,
further research possibilities and the potential implications for Al2O3-gated MOS
devices based on ?-Ga2O3.
3.2.2.1 Experimental methods
Sample preparation
The same set of TEM specimens prepared by Auburn University for the ex-
periments in Sec. 3.2.1 were used to investigate the gate oxide crystallization, albeit
with pristine regions of the interface not previously used for STEM/EELS spectrum
imaging or HRTEM. Refer to Sec. 3.2.1 for fabrication conditions. All four samples
with Al2O3 gate oxides were inspected qualitatively for crystallization phenomena,
and one (#454) was investigated quantitatively in detail.
Electron microscopy imaging and spectroscopy
In addition to high-resolution images, diffraction patterns and Fast Fourier
Transform patterns (FFTs) provided evidence of the crystal structures and orien-
69
220 311
111
Ga O Al contact2 3 Al2O3
220 311
111
Figure 3.16: Lower-magnification TEM image of the interface near the area shown in
Fig. 3.12(b) illustrating the lateral extent of crystallite formation along the interface. The
crystallized region ultimately extended through the entire depth of the Al2O3 gate oxide
layer up to the Al contact. Insets: FFT patterns indicate the high degree of crystalline
orientation within the gate oxide.
tations at the interfaces studied. The lower-magnification image with associated
FFTs in Fig. 3.16 illustrates the spatial extent and degree of crystalline ordering. A
major challenge in studying this system was capturing images, diffraction and FFT
patterns frequently enough to show the evolution of the amorphous?crystalline tran-
sition. Ideally each would be captured every second or even more frequently, which
was not feasible manually or through the automatic capture functionality of Digi-
tal Micrograph. A successful workaround was to record a video screen capture of
the live image and FFT together while translating along the interface and exposing
different regions of the specimen to the electron beam. EELS spectrum images col-
lected for Sec. 3.2.1 were also used in this section to identify features relevant to the
crystallization phenomenon; analyses using the NMF and MCR-LLM algorithms
70
Beam Beam Current Crystallization Time to Corresponding
energy diameter density front rate crystallize dose
(keV) (nm) (A/cm2) (nm/s) (s) (e nm?2)
200 168 ? 8 23.5 ? 2.0 2.3 ? 0.4 18 6.8? 107
200 360 +30 5 +5 0.5 ? 0.2 60 5 +5 7?100 ?1 ?1 ? 10
100 450 ? 24 5.0 ? 0.5 3.4 ? 0.4 13 1.4? 107
100 813 ? 43 1.5 ? 0.2 0.5 ? 0.2 55 1.3? 107
Table 3.2: Electron beam conditions (accelerating voltage and current density) and re-
sulting crystallization effects on the Al2O3 gate oxide layer. At each of the 2 voltage
conditions, the rate of crystallization corresponded to the electron dose rate and required
similar overall doses to achieve complete crystallization, independent of the beam current
density. Lowering the beam energy from 200 to 100 keV resulted in a factor of 4 drop in
the necessary overall dose to complete crystallization.
were performed in order to clarify whether structural and compositional features
originated with processing steps or were due to electron irradiation.
3.2.2.2 Quantification of the crystalline transformation
The crystallization phenomenon seen in all Al2O3 gate-oxide samples was qual-
itatively detailed in Sec. 3.2.1. A quantitative analysis of the crystalline transforma-
tion and its relationship to beam energies and intensities follows here. Measurements
to determine electron-beam currents, current densities and dose rates imparted to
the TEM specimens were performed in a separate session using a picoammeter in
conjunction with the drift tube of the EEL spectrometer. The approach and results
of these measurements are described in Appendix A.
71
Electron dose-rate dependence of crystallization front propagation
The electron beam conditions and corresponding crystallization phenomena in
this work are summarized in Table 3.2. Crystallization was first observed under a
200 kV electron beam with a current density of 23.5 ? 2.0 A/cm2, corresponding to
an electron dose rate of 3.8? 106 e nm?2 s?1. The crystallization front propagated
in a direction parallel to the interface at a rate of 2.3 ? 0.4 nm/s. When the
beam diameter was enlarged by a factor of 2, the current density was reduced to
approximately 5 A/cm2, and the same process was repeated in a pristine amorphous
region where the crystallization propagated at the slower rate of 0.5 ? 0.2 nm/s.
The roughly linear dependence of crystallization front speed on electron dose rate
is suggestive of an electronic interaction mechanism. The overall dose required to
locally achieve complete crystallization was independent of the beam convergence
(current density).
About 18 seconds of exposure were required to completely crystallize the oxide
layer under the 23.5 A/cm2 condition, for a total dose of 6.8?107 e nm?2. This value
is comparable to the 4.5 ? 107 e nm?2 at 200 kV required by Nakamura et al. to
obtain full transformation from amorphous to polycrystalline ?-Al2O3, as indicated
by appearance of the (440) Debye-Scherrer ring [120]. In contrast, Murray et al.
required a total of 2.0? 109 e nm?2 (16 min. under 13 A/cm2) to observe discrete
diffraction spots with an Al2O3 film sandwiched between a sputtered Pt and Al film
in a metal-insulator-metal capacitor structure [121].
72
Increased rate of crystallization at reduced beam energy
After observing crystallization under a 200 keV beam, pristine regions of the
same sample were exposed to the same electron beam operating at 100 keV to
provide insight into the nature of the electronic interaction process. Lower current
densities were required to propagate crystallization at similar rates as with 200
keV electrons. Ultimately a factor of 4 lower electron dose was necessary to fully
crystallize the gate oxide film under the 100?keV beam.
Two main types of electron beam?induced atomic displacement interactions
occur in TEM: elastic scattering of electrons with atomic nuclei (knock-on displace-
ment), and inelastic scattering of incident electrons with atomic electrons and subse-
quent bond-breaking (excitation and radiolysis, respectively). In general, knock-on
effects are dominant for higher incident electron energies, which must be above a
threshold energy E0 (typically greater than 100 keV) in order to displace bulk atomic
nuclei [122]. Radiolytic damage, by contrast, is more pronounced at lower energies
because the inelastic scattering cross section is inversely related to the incident en-
ergy [123]. Inelastic scattering events are more likely with 100 keV electrons than
200 keV. Thus, the crystalline transformation observed may be attributed to an
inelastic scattering process as reported by Nakamura et al. [120].
73
3.2.2.3 Factors contributing to crystallization of the Al2O3 gate layer
Negligible effect of beam-induced heating
High temperatures on the order of hundreds of degrees above ambient are nor-
mally needed to induce crystallization of amorphous ALD-deposited Al2O3 [124].
Two models of beam-induced heating independently show that beam-induced heat-
ing could not have played a meaningful role in the crystalline transformation de-
scribed in this work.
The magnitude of beam-induced heating was first approximated using a simple
heat-transfer model put forth by Egerton [122],
4??t(T ? T0)
I < E >= , (3.1)
0.58 + 2ln(2R0/d)
where I = 5 nA is the TEM beam current as measured using the GIF and picoam-
meter, < E >= 45.1 eV is the average energy loss within the gate oxide as measured
by EELS (described in Fig. 3.17), i.e., the maximum energy per electron potentially
lost to sample heating, ? = 1.8 W/(m K) is the thermal conductivity of Al2O3,
the specimen thickness t ? 100 nm, and the length scale R of the specimen is the
10-?m width of the lamella. Under these conditions the temperature rise T ? T0
was only 0.2 K. This calculation suggests that beam-induced heating was negligible.
However, this approach is limited by the assumption that the specimen has a single,
isotropic value for thermal conductivity, which is not valid for a lamella comprising
74
105
<E> = 45.1 eV
104
103
102
0 50 100 150 200 250 300 350 400
Energy loss (eV)
Figure 3.17: The average electron energy loss was identified by performing a weighted
average of the complete EEL spectrum over the Al2O3 gate oxide layer shown above;
< E >= 45.1 eV. If it is assumed that all energy lost to the specimen via inelastic
scattering is converted to heat, the maximum temperature increase of the specimen is
given by Eq. 3.1. Note the use of a semi-log scale.
mostly Ga2O3 (whose conductivity is strongly anisotropic) and capped by an Al
contact with good thermal conductivity.
To obtain a more complete understanding of thermal effects, a finite element
model was constructed of the entire TEM lamella and Cu grid post to estimate
the distribution of temperature rise due to beam-induced heating. The equilibrium
temperature distribution of the lamella was simulated using the known specimen
dimensions, material properties and electron beam current, and is illustrated in
Fig. 3.18. The Al2O3 EEL spectrum in Fig. 3.17 indicated that an average of 45.1
eV of thermal energy was deposited into the lamella by each incident electron, at
a rate corresponding to the electron-beam current of I = 5 nA. Using a simulated
beam of diameter d = 300 nm, the maximum temperature rise was less than 0.2 K
in all areas of the lamella.
75
Counts
electron beam Al contact (150 nm)
100 nm
Al2O3
Ga O 293.36 K2 3
1 ?m
Cu TEM grid 293.15
Figure 3.18: Finite-element model of the lamella temperature during exposure to a simu-
lated 5-nA electron beam. The lamella consisted of the 100 nm thick, 10-?m-wide Ga2O3
substrate with a 100 nm-thick Al2O3 gate layer, capped by a 150-nm-thick Al contact pad
and mounted on one side to a standard Cu grid post. Despite the relatively low thermal
conductivities of both oxide materials, the maximum temperature rise was on the order
of 0.2 K, far from sufficient to crystallize amorphous ALD-deposited Al2O3.
Epitaxial relationship between ?-Al2O3 and (2?01) ?-Ga2O3
The comparatively fast formation of a fully crystalline Al2O3 layer with pre-
ferred orientation in this work is attributed to the crystallinity of the ?-Ga2O3 sub-
strate, facilitated by the relatively good lattice mismatch between the two layers.
This is supported by the observation that crystallites of Al2O3 did not homoge-
neously nucleate within the bulk of the gate layer, nor did crystallization propagate
from the interface of the gate layer with the top Al contact for any beam conditions
or samples used in these experiments.
Examination of the film and substrate orientation provides insight into the
heteroepitaxy of ?-Al2O3 on (2?01)-oriented ?-Ga2O3. The diffraction pattern of the
fully crystallized Al2O3 (Fig. 3.19) corresponds to a < 112 > zone axis, parallel to
the [102] direction of Ga2O3. In the plane of the film, therefore, ?-Ga2O3 [102] ||
76
? [112] {111} Al
220 311
58.5?
111 222
Figure 3.19: Electron diffraction pattern of the Al2O3 layer after crystallization. The
magnitudes of the indicated diffraction peaks (g220 = 3.54 1/nm, g111 = 2.12 1/nm and
g311 = 4.15 1/nm) as well as the angle between g111 and g311 match closely with the
expected values for the idealized cubic ?-Al2O3 spinel structure [125].
?-Al2O3 [112?]. Parallel to the interface and normal to the electron beam, the in-
plane epitaxial relationship observed is ?-Ga2O3 [010] || ?-Al2O3 [1?10]. Inspection of
the oxygen sub-lattice of (2?01) ?-Ga2O3 shows that it has approximately hexagonal
symmetry, similar to that of (111) ?-Al2O3 as depicted in Fig. 3.20. The average
oxygen sub-lattice mismatch in each direction is calculated using the lattice con-
stants for cubic ?-Al2O3 (denoted a
? = 0.79 nm) [125,126] and monoclinic ?-Ga2O3
(a = 1.2214, b = 0.3037, c = 0.5798 nm, ? = 103.83?) [127]. Along the [010] direction
of Ga2O3:
dAl2O3 Ga2O3 ?
f = 110
? d010 (a /4)|[110]| ? b
010 = = ?0.080 (3.2)
dGa2O3010 b
and, using the empirically determined atomic structure of ?-Ga2O3 [127?129] to find
the average separation of O atoms along the [102] direction, dGa2O3102 = 0.490 nm:
dAl2O3112 ? dGa2O3 ?102 (a /4)|[112]| ? dGa2O3f = = 102102 Ga O = ?0.013. (3.3)d 2 3 dGa2O3102 102
77
0.490 nm 0.484 nm
[010] [110]
[102] [112]
[201] [111]
(201) ?-Ga2O3 (111) ?-Al2O3
Figure 3.20: Oxygen sub-lattices of the (2?01) ?-Ga2O3 (red, at left) and (111) ?-Al2O3
planes (gray, at right) showing the in-plane epitaxial relationship observed. The (2?01) ?-
Ga2O3 surface has approximately hexagonal symmetry, corresponding to the (111) surface
of ?-Al2O3. The in-plane lattice mismatch of the Al2O3 film along the [1?10] direction of
Al2O3 and the [010] direction of Ga2O3 was approximately ?0.080, and about ?0.013
along the [112?] direction of Al2O3 and the [102] direction of Ga2O3.
As discussed in prior works [112, 129] involving Al2O3 films on (010)-oriented
?-Ga2O3, an epitaxial relationship between these two systems is made possible by
the similarity of their oxygen sub-lattices, which are both hexagonal in the plane of
the film. The relatively small mismatch values, especially along the [102] direction
of ?-Ga2O3, allow for preferential orientation of the Al2O3 upon crystallization. The
fact that both structures are well-matched is also consistent with the observation
that the Al2O3 films only crystallized into the ?-phase in this work, not for example
?-Al2O3.
It is actually the ?-Al2O3 phase, and not ?-Al2O3, which is monoclinic and
isomorphic with the ?-Ga2O3 substrate [126]. As such it is not intuitive that ?-
Al2O3 will be the result of crystalline transformation. Nevertheless, the electron
diffraction pattern of the fully crystallized Al2O3 (Fig. 3.19) is a better match to
78
0.304  nm
0.279  nm
?-Al2O3 than to ?-Al2O3 in terms of the magnitudes and ratios of its g-vectors.
Furthermore, the lattice mismatch between ?-Ga2O3 and either phase of Al2O3 is
such that the Al2O3 film must be under tensile strain, due to the lattice constant
b = 0.304 nm of Ga2O3 being larger than the corresponding b = 0.291 nm of ?-Al2O3
?
or d220 = 2/4a = 0.28 nm of ?-Al2O3. If the diffraction pattern were from ?-Al2O3,
its g220 magnitude would imply that the film were under significant compressive
strain of (1/3.44)?(1/3.54) = 2.8%. On the other hand, if the film were ?-Al2O3 as we1/3.44
assert, it would be under a more reasonable tensile strain of (1/3.57)?(1/3.54) = ?0.8%.
1/3.57
The density of amorphous alumina varies over a wide range, from 2.1?3.6
g/cm3 depending on deposition parameters, with typical values for low-temperature
ALD ranging from 2.5?3.0 g/cm3 [130,131]?all lower than the 3.65 g/cm3 density for
?-Al2O3. In the course of accommodating this difference the crystallization process
must therefore give rise to densification of the gate oxide layer. Tensile strain at
the interface implies a local density reduction for crystallites that are coherently
matched to the substrate, which should lower the energy barrier to initial formation
of Al2O3 crystallites on the ?-Ga2O3 substrate (as compared to e.g. a sapphire
substrate).
Atomic rearrangement during post-deposition annealing
Consideration of the sample subjected to 500 ?C, 2-min. post-deposition an-
nealing (PDA) provides additional evidence of the negligible role of thermal effects
on crystallization in this system. Despite annealing at elevated temperature, TEM
79
(a) (b)
Ga-M2,3
Al-L2,3
with PDA
no PDA
80 100 120 140 80 100 120 140
Energy loss (eV) Energy loss (eV)
(c)
5 nm
Figure 3.21: (a) Raw EELS spectra obtained as line scans from the bulk of the ?-Ga2O3
substrates in the non-annealed (red) and annealed (black) samples. The weak, gradual
onset of the Ga-M2,3 EELS edge at 105 eV is indicated. (b) Corresponding EELS line-scan
spectra from within the bulk of the Al2O3 gate layers (> 5 nm from the interface) after
crystallization. The Al-L2,3 edge is denoted at 77 eV. Signals from Si or other unintentional
dopants were not observed. (c) HAADF-STEM image and normalized intensity line profile
from the un-annealed sample collected simultaneously with the EELS data of the Ga-M2,3
edge presented in the red curves of (a-b) and in Fig. 3.22.
imaging showed that the annealed gate oxide was initially amorphous, and became
crystalline in the same way as the un-annealed samples following exposure to the
electron beam. Furthermore, there is evidence that atomic rearrangement alone
is not a sufficient condition for crystallization in the gate oxide layer, even at el-
evated temperatures. STEM-EELS spectrum imaging performed on samples with
and without the PDA treatment (Fig. 3.21) revealed interdiffusion between Ga and
Al in both cases. During the ALD process, interdiffusion led to a gradual drop-off
in Ga intensity about 2.5 nm wide into the gate layer of the device not subjected
to PDA, as shown in Fig. 3.22. In the annealed device, the width of this region had
nearly doubled to 4.7 nm, indicating significant atomic rearrangement?but still
with no observable crystallization of the amorphous Al2O3 prior to electron-beam
80
Ga O interface2 3 Al2O3
1 no PDA
with PDA
4.7 nm
2.5 nm
0
-6 -4 -2 0 2 4 6
Distance from interface (nm)
Figure 3.22: Line-profile average of the relative Ga-M2,3 EELS edge signal identified
by MCR-LLM in samples subjected to 500 ?C post-deposition anneal (PDA) (solid black
line; 5?95% intensity transition width 4.7 nm) and without post-deposition anneal (dashed
red; transition width 2.5 nm). Despite the high temperature and atomic motion indicated
by the broadening of the Ga signal tail-off following PDA, no crystalline interlayer was
observed until the specimen was exposed to the electron beam.
irradiation in the TEM. This finding is consistent with recent work that subjected
the (010) ?-Ga2O3/Al2O3 interface to 5-min. PDA treatments at a range of tem-
peratures and found that crystallization began between 600?700 ?C [132].
3.2.2.4 Device performance implications and recommendations for
future work
From a device applications perspective, the most natural questions relate to the
stability and performance of MOS devices based on ?-Ga2O3 with amorphous Al2O3
gate oxide layers. For instance, one of the desired use cases for WBG semiconductor
electronics is high-radiation environments. Will the amorphous oxide remain stable
under ionizing radiation? Recent work indicates that interface charge trapping and
damage to the dielectric layer, not the intrinsic radiation hardness of the substrate,
are the limiting factors for the robustness of a ?-Ga2O3 device against gamma
81
Relative abundance
radiation [133]. If an Al2O3 gate oxide crystallizes during the service lifetime of a
device, this structural change will most likely be accompanied by changes in the
device performance or reliability. The topics of radiation resistance and the effects
of crystallization on the device behavior will require further investigation.
In summary, amorphous Al2O3 gate oxide layers grown by ALD on (2?01) ?-
Ga2O3 substrates were found to become fully crystalline under electron irradiation
in TEM. This phenomenon was observed reproducibly on samples both with and
without PDA treatment at 500 ?C. Estimates of the local temperature rise induced
by the electron beam, on the order of 0.2 K, mean that thermal effects alone are
far too small to induce crystallization in the amorphous gate layer. The roughly
linear dependence of crystallization front propagation rate on electron dose rate, in
combination with faster crystallization at lower beam energy, indicates that crystal-
lization occurs via an electronic excitation process. Crystal growth is aided by the
favorable lattice matching between ?-Ga2O3 and ?-Al2O3.
These findings raise several possible topics for further investigation. From an
applications perspective, these include measuring the robustness (in terms of peak
performance as well as long-term reliability) of ?-Ga2O3/amorphous Al2O3 devices
during exposure to electron-beam or ionizing radiation, the electrical properties of
devices after crystallization of the gate layer, and whether ALD process temperature
plays a role in the early stages of the crystallization process.
82
Chapter 4: Modeling and characterization of nanocarbon-metal com-
posites
Metal alloys are ubiquitous in modern life. From microscopic electromechan-
ics to aircraft bodies, and from integrated circuits up to transcontinental electric
grids?the engineering of metal alloys provides finely tuned combinations of cost-
effectiveness, performance, and longevity in myriad applications. Copper and alu-
minum alloys have been the prevailing choice owing to their good combinations of
electrical conductivity, mechanical strength, and low cost. Continued improvement
in these properties is desirable, but difficult. Avenues for conductivity enhancement
by traditional metallurgy techniques, such as striving for extremely high purity or
designing single-crystal parts, are cost-prohibitive and offer limited benefits. As
some nanostructured forms of carbon such as graphene [27] and carbon nanotubes
(CNTs) [28] have exceptionally high mechanical strength and charge carrier mo-
bility, the broad objective of this research is to investigate ways of incorporating
carbon nanostructures into metal-matrix composites such that some combination of
their bulk mechanical, electrical, or thermal properties are enhanced. The resultant
nanocarbon-metal composites are known as covetics. This chapter describes a range
of experiments to elucidate the structures responsible for these enhanced properties
83
using Raman spectroscopy, analytical electron microscopy, and modeling based on
first-principles.
4.1 Analysis of C distribution and structure by Raman spectroscopy
Raman spectroscopy is an established technique that is well-suited to the char-
acterization of carbon materials. Sec. 2.3 provides an introduction to the relevant
literature regarding the characteristic modes of ordered and disordered carbon ma-
terials and the details of the curve-fitting routines used in this work. In Subsec-
tion 4.1.1, Raman spectroscopy has been used to provide new insights regarding
the distribution of nano-graphitic crystallite sizes La, and in Subsection 4.1.2, to
estimate the number of graphitic layers stacked in a typical cluster of GNRs.
4.1.1 Distribution of the nano-graphite crystallite size, La
Prior to the covetics reaction process
Raman spectrum imaging indicates that the activated carbon source material
in this work was nanocrystalline, with an average crystallite size of 8.7 ? 1.8 nm
calculated via Eq. 2.4. The uncertainty was estimated to be twice the standard
deviation of a distribution containing 211 individual spectra from 4 separate areas
of the activated C powder. Fig. 4.1 shows the average of all Raman spectra (left)
and distribution of the associated La values from the individual spectra (right).
It is important to distinguish between the measurement error of the technique
and the true width of the distribution, which is naturally greater than zero because
84
(a) (b)
Figure 4.1: (a) The average Raman spectrum from activated C source material used in
Al covetics qualitatively shows a low degree of ordering due to the broad D and G bands
and low I(G)/I(D) ratio. (b) Distribution of nano-graphite crystallite size La calculated
from 211 individual spectra via Eq. 2.4. The average crystallite size was 8.7 ? 1.8 nm,
with the uncertainty defined as 2?.
the graphitic crystallites do not all have exactly the same size. The width of the
distribution measured from the 211 spectra shown in Fig. 4.1(b) is the result of both
of these sources of spreading. The narrow spread of La values is indicative of the
low measurement error inherent in the Raman spectrum-imaging approach, as long
as the signals are moderately strong; the absolute uncertainty in the measurement
in any calculation of La via the I(G)/I(D) ratio should not be greater than 1.8 nm.
After the covetics reaction
The threshold for distinguishing between converted and unconverted carbon
in covetics is inevitably somewhat arbitrary, as the degrees of graphitic ordering lie
on a spectrum, e.g. from fully amorphous to fully crystalline, and from small to
large crystallites. The presence of a 2D peak, narrowing of the G and D peaks, and
increase in the I(G)/I(D) ratio are each indications of this transition which extend
across a range, with fully ?converted? and fully ?unconverted? at either extreme.
85
It is nevertheless useful to define a threshold for conversion in order to make the
analysis more quantitative. In the case of activated C powder, this threshold was
defined as 2 standard deviations above the mean crystallite size, or 10.5 nm. On
account of the normal distribution of the data, there is a less than 5% chance
that any Raman spectrum would give an La value greater than this threshold in
the as-received material (without having undergone transformation by the applied
current).
4.1.1.1 Characteristic long-tailed distribution of La after conversion
Unlike the distribution of La for unconverted activated C, as shown in Fig. 4.1,
distributions of La in covetics exhibited a distinct positive skewness. This asym-
metry can be seen in datasets taken from 4 distinct covetic samples, each of which
contains at least 1000 measurements from Raman maps collected in different regions
of polished cross-sections. These data are presented in Fig. 4.2. The asymmetry was
persistent across samples manufactured using different reaction times and different
electrode geometries (therefore, different current densities), which suggests that it
is characteristic of a sizable range of the covetics-fabrication parameter space. Each
distribution is composed of a large number N > 1000 of La measurements from
different parts of the specimen, and is therefore statistically meaningful.
In addition to the characteristic positive skewness, each of the distributions
in Fig. 4.2 is bi-modal. As a consequence, it was necessary to fit each dataset to a
86
unconverted ? ? converted unconverted ? ? converted
16% 21%
(a) (b)
cv20190408 cv20190702
N = 1070 N = 1630
unconverted ? ? converted unconverted ? ? converted
19% (c) 5% (d)
cv20190716 cv20190731
N = 1381 N = 2267
Figure 4.2: Distributions of carbon crystallite size La were consistently asymmetric across
a range of covetics fabricated using different applied current densities and durations. The
features of each distribution were enhanced by the use of a large number N of Raman
spectra, each of which provides one measurement of La. Many of the distributions were
bi-modal, which indicates that a fraction of the original carbon material remained un-
converted (La below the cutoff of 10.5 nm, as indicated by the dashed vertical lines).
A superposition of a normal distribution and a gamma distribution was chosen for the
histogram fit in order to account for this feature. Each sample was identified by a number
(cv2019xxxx) corresponding to its fabrication date. N is the total number of spectra used
in the analysis of each sample.
87
superposition of a normal or Gaussian distribution and a gamma distribution:
[ ] [ ]
? ?1
2
(1 p) e?
1 x??
2( ? ) 1+ p xa?1e?x/b (4.1)
? 2? ba?(a)
where p is the fraction of converted carbon represented by the gamma distribution,
(1? p) is the fraction of unconverted carbon represented by the Gaussian distribu-
tion, and the other symbols take their usual meanings in the context of probability
distributions. Note that p was only used to determine the best fit for Eq. 4.1; a
fixed cutoff of La = 10.5 nm was used to distinguish between the two regimes for
all other purposes.
Physical meaning of bi-modality
When a prominent small-La peak was present, as in Fig. 4.2(a?c), it was
narrow and symmetrical with a position of around 8 nm. This corresponds well
with the distribution of La in the activated-carbon source material. As such, this
peak can be attributed to un-reacted activated carbon. When the peak was small,
as in Fig. 4.2(d), it is an indication that the graphitic conversion had proceeded
more completely. In this case it is illustrative to note that sample #cv20190731 in
Fig. 4.2(d) was fabricated for twice the duration of applied current, but otherwise
under the same conditions as sample #cv20190716 in Fig. 4.2(c). This trend is
supported more broadly by samples fabricated across a range of reaction residence
times (i.e., the duration of applied current) as indicated by Fig. 4.3.
88
1.0
0.9
0.8
0.7
0.6
0.5  100 A around electrode
 100 A far from electrode
0.4  150 A around electrode
0.3  150 A away from electrode
0.2
0.1
0.0
0 5 10 15 20 25 30
Residence Time (min)
Figure 4.3: The fraction of carbon source material converted to larger graphitic crystal-
lites, as defined by La > 10.5 nm, increased monotonically with residence time (the total
exposure time of the melt to direct current), but only in regions within ? 5 mm of the
electrode where the current density was above a critical value. Adapted from Ref. [134].
Physical meaning of positive skewness
The presence of positive skewness in the crystallite size distributions following
the application of current is a clear indication of a physical transformation. No
such feature was ever observed in the distribution of La in the as-received activated
carbon material. In the midst of the large spread in the distribution, the mean of La
values also increased monotonically with residence time. Representative distribu-
tions of samples fabricated using 100 A current over different durations are plotted
in Fig. 4.4.
89
Fraction of Converted C
150 A
Figure 4.4: The mean La increased linearly with residence time ranging from 0 to 30 min.
All reactions were conducted with an applied current of 100 A except for the single point
and distribution indicated by arrows (light blue) for which the current was 150 A.
4.1.2 Estimating the thickness of embedded GNRs
It is not trivial to estimate the thickness (i.e., the number of layers) of the
GNRs embedded in a covetic. Unlike the case of a wide and thin graphene sheet
resting on a substrate, where the thickness can be obtained from visible light absorp-
tion of 2.3% per layer [135], optical thickness determination is not possible through
the metal matrix (and furthermore, the GNRs are narrower than the wavelength
of visible light). Conventional TEM imaging gives a projection through the whole
specimen, and does not readily permit visualization of structures along the beam
axis.
Inspection of the 2D Raman peak shape provides additional insight regarding
the number of graphene layers. Experimental and theoretical studies show that the
2D band is described by a single Lorentzian peak for single-layer graphene, while
the bilayer-graphene 2D band exhibits a pronounced shift, to 3 [136] or 4 peaks [83].
90
unconverted ? ? converted
With 10 layers or more, a distinct asymmetry is present in the 2D band. (It is not
possible to distinguish the number of layers when there are more than 10, because
at that stage the 2D band begins to appear skewed positive, the same as it appears
in bulk graphite [83,137].) Qualitative inspection of 11 2D peaks distributed on the
polished surface of a well-characterized covetic (cv20190408, Fig. 4.5) suggests that
the typical number of layers is probably between 3 and 10. The 2D bands are broad,
with maxima around 2700 cm?1. These features are not consistent with single-layer
graphene, which has a single Lorentzian peak around 2680 cm?1 [136]. Some of the
bands are asymmetric, especially at spots 2, 9 and 11, as in bulk graphite with 10 or
more layers; others appear more similar to spectra reported for structures with 2?6
layers [136, 137]. Overall, the GNRs contained approximately between 3?10 layers
of graphene in this specimen.
It is important to bear in mind the limitations inherent in collecting Raman
spectra from randomly distributed GNRs which have varying degrees of graphitic
ordering. Since the Raman excitation-laser spot size is on the order of 1 ?m in
diameter?between one and two orders of magnitude greater than the width of
GNRs?many GNRs will likely contribute to each Raman spectrum. The graphi-
tization of the carbon precursor is not uniform for several reasons, including the
non-uniformity of the current density distribution and/or mechanical stirring of the
melt. Because of these uncertainties, the Raman-based interpretation of the number
of graphene layers in GNRs remains an order-of-magnitude estimate.
91
(a) G
D 2D (b)
11
10
9
8
7
6
5
4
3
2
1
2700
Figure 4.5: (a) Raman spectra from 11 points on the covetic sample cv20190408 with
clearly defined 2D bands, plotted on a linear intensity scale of arbitrary magnitude. (b)
Detail box of the 2D peak decomposition at point #11. The 2D bands do not appear as
they would for either single-layer graphene (a single Lorentzian peak around 2680 cm?1)
or bulk graphite, which suggests qualitatively that the GNRs contained between 3?10
layers of graphene in the regions probed.
92
4.2 TEM investigation of metal-carbon interface structures
A wide range of TEM-based techniques were used to explore processing-structure-
property relationships in Al covetics produced under different conditions, as well as
several reference specimens for comparison. The general approach was to evaluate
structures over a broad range of length scales, from micron to sub-nanometer, to
adapt to the many length scales across which the structure of a composite can vary.
4.2.1 Specimen preparation and experimental approach
As described in the preceding section, Raman spectroscopy was generally the
first characterization step following fabrication, cutting and polishing. The optical-
and spectrum-imaging length scale of tens of microns was well suited to positively
identifying carbon-containing regions. These regions typically displayed darker con-
trast relative to the matrix, and often?but not always?exhibited strong Raman
signals. Occasionally clusters of unconverted activated C were observed, physically
trapped in the matrix. Being unique to covetics, the ordered regions were prime
candidates for further characterization, and their positions were recorded relative to
a corner or other distinct feature of the sample surface so that they could be located
later in SEM. An illustration of this approach is shown in Fig. 4.6.
Conversely, Raman spectra of carbon in any form were almost never observed
in parts of the matrix that appeared optically like pure metal alloy. This limitation
is due to the shallow penetration depth of visible light into metals; for example in
Al, 90% of incident 532 nm light is attenuated within the top 15 nm, decaying expo-
93
-300
Sum of 121 Raman spectra
-250
-200
-150
-100
-50
0
50
100
150
200 100 ?m
250
20 ?m
300
-300 -200 -100 0 100 200 300
X (?m)
-55
-50
-45
-40
-35
-30
-25
-20
-15 20 ?m
-10
-5
0
5
10
15
20
25
30
35
40
45
50
4 ?m
55
-60 -40 -20 0 20 40 60
X (?m)
Figure 4.6: Simultaneously-collected optical image and average Raman spectrum of a
polished covetic cross-section (Sample #cv20190408). The Raman spectra were collected
from the region highlighted in the 20-?m ? 20-?m white box (lower left detail box).
According to the Raman spectra, the bright regions of optical images were exclusively
metal matrix with no C signal, while the dark regions indicate graphitic or disordered
carbon, grain boundaries, scratches, or voids.
nentially [138]. Essentially, only the surface of the cross section could be inspected
for carbon of any degree of ordering; everything greater than a few nm below the
surface was rendered invisible by the metal above it.
Several cross-sectional TEM specimens were prepared from regions similar
to that shown in Fig. 4.6. EDS mapping prior to milling confirmed the presence
and distribution of C; for instance, in the map in Fig. 4.7, which corresponds to
the graphitic feature in Fig. 4.6. The approximately 1-?m depth of the volume of
interaction in SEM at a beam energy of 20 keV [139] implies that these carbon
structures extended on the order of 1 ?m below the sample surface.
94
Y (?m) Y (?m)
(a) Lamella (b)
20 ?m
Figure 4.7: SEM-EDS mapping of the graphitic C feature shown in Fig. 4.6 prior to
lamella extraction from the region indicated, using a beam energy of 20 keV.
4.2.2 Large-scale graphitic carbon structures in Al covetics
TEM revealed that the nano- to micro-structure of covetics was highly variable,
even within the same sample. The most common feature was graphitized carbon on
length scales of microns to tens of microns. A less common microstructure, aligned
graphitic fibers and ribbons on a width scale of under one micron, is relatively
more homogeneous and therefore offers potentially more benefits for the resultant
composite, as previously identified by Jaim et al. [56] and explored theoretically in
Sec. 4.3.
Samples were numbered by their date of fabrication. The sample numbered
cv20190408 was ultimately found to exhibit both strongly graphitic Raman sig-
nals (Fig. 4.6) and a significant 5.7 ? 1.5% increase in conductivity relative to a
carbon-free control subjected to the same metallurgical process [140]. As such, it
was analyzed by a range of TEM-based techniques including bright-field (BF) and
95
(a) In-beam BSE (b)
~100 nm 1 Bright-field 
TEM
Carbon
SiO2  
protective cap
Carbon
Al
2
5 ?m
Al
Figure 4.8: (a) In-beam backscattered electron (BSE) SEM image of the cv20190408
lamella after final thinning to approximately 100 nm with a 5-keV Ga+ ion beam (Inset:
SEM view down the lamella top edge). Higher-Z atoms produce stronger signals in the
BSE detector, allowing the Al, C and protective SiO2 regions to be distinguished. (b) 2 kx-
magnification composite TEM image with two regions of interest highlighted: 1. Locally
thinner area from the bulk of the graphitic inclusion; 2. The Al-C interface region.
dark-field (DF) imaging, diffraction pattern analysis, and scanning TEM (STEM)
spectrum imaging. SEM and TEM images of the cv20190408 lamella are shown in
Fig. 4.8.
Fig. 4.9(a) shows that the graphitic structures are uniform over several mi-
crons in some areas, while others are locally thinner or thicker, or appear as small
grains. Higher-resolution inspection of region 1 indicated that the bulk of the carbon
inclusion is graphitic. The electron diffraction pattern from this region (Fig. 4.9(b))
indicates a lattice spacing of 0.353 nm, which is about 4% larger than the c-axis
interplanar spacing of graphite. The locally thin structure visible in Fig. 4.9(c?d)
shows lattice fringes of C parallel to the longer dimension of the thin area. This
96
 
SSiiOO22    pprrootteeccttiivvee  ccaapp
(a) (b)
2.83 1/nm ? 
0.353 nm
(c) (d)
Figure 4.9: TEM images of region 1 from Fig. 4.8(b) at progressively increasing resolution.
(a) 8 kx image of graphitic structures which are uniform over several microns in some
areas, while other areas are locally thinner, thicker, or comprise small grains. (b) Electron
diffraction pattern corresponding to (a) indicating an interplanar spacing corresponding to
that of layered graphene. (c?d) Detailed view of a locally thin area at 100 kx and 500 kx,
respectively, with the latter showing lattice fringes of C with small-scale undulations along
the longer dimension of the thin area.
97
 
structure is substantially more ordered than the activated carbon source material,
however it retains some disorder at the atomic scale.
Composition analysis of this specimen was primarily done via energy-filtered
TEM (EFTEM), which makes use of the filtering capabilities of the electron energy-
loss spectrometer to form images using only the chosen energy-loss signals (Sec.
2.1.2). It provides a fast, qualitative picture of composition over a large length
scale, complementary to e.g. STEM-EELS spectrum imaging. EFTEM images
from the bulk of the graphitic region 1 are shown in Fig. 4.10. They reveal that C is
the predominant element in this region, with trace presence of O around the edges
of the thin regions in the specimen (which appear brighter in the bright-field and
zero-loss images). No meaningful signals were seen in energy ranges corresponding
to Si-L and Fe-L, which are trace elements in Al 1350 (the parent alloy for this
specimen) and other 1000- and 6000-series alloys [141].
The region containing the Al-C interface (ROI 2 in Fig. 4.8(b)) was also imaged
by EFTEM; these composition maps are shown in Fig. 4.11. Carbon is predominant
on the left side of the interface in the EFTEM images, while Al is present only on
the right. Some oxygen was present everywhere, generally overlapping with the Al.
This overlap suggests that an the graphitic carbon was in contact with an aluminum
oxide phase and not pure metal. A color-enhanced superposition of the C, Al, and
O EFTEM maps shows this structure more clearly in Fig. 4.12.
A second TEM specimen was prepared from the same bulk sample of cv20190408
by ion milling in order to explore a larger electron-transparent area with similar in-
terface features. The regions of interest indicated in Fig. 4.13 were investigated by
98
Bright-field TEM
Zero-loss EFTEM
C-K O-K Al-L
Figure 4.10: Energy-filtered TEM images captured from the graphitic bulk in the region
highlighted, revealing predominantly C with weak traces of other elements. The zero-loss
EFTEM image is composed of electrons with energy losses less than 10 eV (the slit width),
while the core-loss edges used a slit width of 30 eV. Black and white arrows indicate a
common feature of reference (point of elongated thin feature) and direction between the
BF and EFTEM images to assist with the viewer?s orientation.
99
Bright-field 
TEM
Zero-loss EFTEM
C-K O-K Al-L
Figure 4.11: EFTEM composition mapping captured from the graphitic carbon/Al in-
terface of cv20190408 over the region highlighted in green in the bright-field TEM image.
Arrows face in the same direction towards a common feature in all images. Overlap in
the Al- and O-rich regions at the right of the EFTEM images suggest the presence of an
aluminum oxide phase next to the carbon.
Zero-loss C (green) Al (blue) C + Al + O (red)
Figure 4.12: Color-enhanced superposition of EFTEM images from the C/Al interface in
Fig. 4.11. Center image: superposition of C (green, left side) and Al signals (blue, right
side) reveals minimal overlap between the two phases. Right image: All three concentra-
tion maps (C, Al, and O, red) superimposed. O and Al coincide, suggesting an aluminum
oxide phase instead of pure Al alloy.
100
5 1/nm
EDS 2
EDS 1
Figure 4.13: Survey of cv20190408 TEM specimen prepared by ion milling. Top: The
Al/C interface structure shown is representative of others seen around the electron-
transparent perimeter of the hole in the ion-milled specimen. Inset: Multiple diffrac-
tion spots originating from Al indicate slight misorientations of Al crystallites around a
< 110 > zone axis. Bottom: Detail view of the interface structure with two regions of
interest marked for STEM-EDS analysis.
STEM-EDS to provide a more quantitative composition analysis. The specimen was
oriented such that it was imaged down a < 110 > zone axis. Multiple diffraction
spots originating from Al indicate slight rotations of Al crystallites with respect to
each other; this grain structure was frequently seen in covetics. STEM and EDS
data from the thinner region of interest denoted EDS 1, near the bottom of Fig. 4.13,
are shown in Fig. 4.14. In the HAADF-STEM image in Fig. 4.14(a), bright regions
101
(a) HAADF-STEM (b) STEM-EDS
C O Fe Al
Al
C
Figure 4.14: (a) High-angle annular dark field (HAADF)-STEM image from the region
of EDS 1 in Fig. 4.13; the red arrow indicates the position of the EDS line scan. Stronger
(i.e. brighter) high-angle scattering signals originate with higher atomic-mass species,
indicating that such species were present in a band between C and Al. (b) EDS line-scan
signals plotted from points 100 nm apart, moving from C into Al in the direction of the
arrow. The EDS signals indicate that the bright band between C and Al was an Fe-, Al-
and O-rich secondary phase. The C phase (dark blue EDS spectrum) also contained O
and Al, while the concentration of other elements in the Al region was below detection
limits.
correspond to higher atomic-mass species. The bright band in the center of the
structure thus appears to be a secondary phase of the Al 1350 alloy used in the
composite, such as one rich in Fe, which is the highest-concentration constituent
of Al 1350 after Al (up to 0.4% [141]). Indeed, the EDS line scan in Fig. 4.14(b)
(purple spectrum) confirmed that the bright band was both Fe- and Al-rich.
EDS signals collected from the second region of interest were subjected to the
MCR-LLM algorithm to enhance the low signal-to-noise ratio of the raw spectra
and to identify unique phases. Fig. 4.15 presents the HAADF-STEM and TEM
structure images (a?b, respectively) and EDS components and relative intensities
along the line scan (c?d). Three constituent EDS signals were identified in the
line scan. Each phase contained a strong Al-K? signal around 1.5 keV. The C-rich
102
(a) (b)
SI integrated 
to line scan
(c) (d) C-rich C-rich Al Fe-rich Al
pure Al MCR-LLM
 decomp.
C-
rich
O Fe-rich
Figure 4.15: Structure and composition of the second EDS region of interest along the
interface. (a) HAADF-STEM and (b) bright-field TEM images showed similar contrast
features as EDS 1 (Figs. 4.13 and 4.14). A narrow spectrum image (SI) was collected from
the green box and summed along the short dimension to improve signal-to-noise ratio.
(c) EDS spectra of 3 phases identified in the SI by the MCR-LLM decomposition. Each
contained a strong Al-K? signal. The C-rich phase displayed C-K? and O-K? signals in
addition to Al. The other two phases displayed no evidence of C and only weak O signals
(in the case of Al, likely from an oxide passivation layer). (d) Normalized intensity profile
of the three phases along the SI. Al and C overlap only in the thinner region to the left of
the Fe-rich intermetallic band.
103
phase displayed prominent C-K? and O-K? signals in addition to Al, while neither
of the other two displayed evidence of C; the Fe-rich phase was predominantly Fe
and Al, and the ?pure Al? phase contained only a weak O signal in addition to
Al?which is to be expected, given the rapid formation of an oxide passivation layer
on Al exposed to air and the small thickness of the specimen. The normalized
intensity profile (Fig. 4.15(d)) shows some overlap between C and Al signals to the
left of the Al/Fe secondary phase. This region therefore could contain the sort of
Al/C interface structures expected to give rise to enhanced conduction properties.
However, the uniformly ? 200 nm-thick band of Al/Fe intermetallic appears to have
blocked longer-range interaction between the C and Al.
A subsequent covetic sample exhibited similar intermetallic and oxide features.
The cross-sectional TEM specimen was prepared by FIB from a region displaying
strong graphitic Raman spectra. A composite low-magnification TEM image shows
the entire lamella in Fig. 4.16. The lamella comprised distinct C and Al phases
separated by an interfacial band in the center. Close inspection of the carbon phase
indicated that it is graphitic. Selected-area electron diffraction from region of inter-
est 1 and HRTEM imaging (with corresponding Fast Fourier Transform) of region 2
indicated that the lattice spacing was in the range of 0.337?0.339 nm, which corre-
sponds to the (0001) interplanar spacing of graphite (Fig. 4.17). Graphitic ordering
was again strongest in the (0001) out-of-plane direction, as with the previous covetic
structure shown in Fig. 4.9. The aligned contrast features visible on the left-hand
side of the TEM image in Region 1 indicate that the atomic planes of carbon were
104
Interfacial 
111 022
layer 200
Protective cap
5 1/nm
1
2
C Al Cu grid
2 ?m
Figure 4.16: Composite bright-field TEM image of cross-sectional TEM specimen
cv20190502, which consisted of distinct Al and C phases separated by an interfacial band.
A protective tungsten cap was deposited before lamella extraction in order to limit amor-
phization damage effects from the ion beam. The two regions of interest marked 1 and
2 were investigated in further detail. The selected-area diffraction pattern was captured
from the Al phase only.
well-aligned on a length scale of up to a micron, but nevertheless exhibited consistent
small-scale undulations as seen in the HRTEM image of Region 2.
EDS composition analysis (Fig. 4.18) was performed on the interfacial band
separating the C and Al phases shown in Fig. 4.16. The EDS data indicated that
the C phase was pure and contained minimal O and Al signals, as was the Al phase,
which exhibited only a weak O-K? peak in addition to Al. The interfacial band
visible in the STEM image was approximately 0.25 ?m wide. Correspondingly, the
full width at half-maximum (FWHM) of the O-K? signal from the same region
was 0.2 ?m. As with the two specimens of cv20190408, this interfacial oxide layer
appears to have blocked the C phase from coming into contact with the Al matrix
in the region of the sample from which the lamella was taken.
A portion of the Al matrix near to the interface was also imaged at high
resolution, shown in Fig. 4.19, in an effort to identify any nanostructured C that
105
1
C
Cu 
grid
2.97 1/nm ? 
0.337 nm
Al
0.5 ?m
2
2.95 1/nm ? 
0.339 nm
Figure 4.17: Closer inspection of the 2 regions of interest indicated in Fig. 4.16. Region
1: The selected-area diffraction pattern (left) was collected approximately from the left
side of the image (right), in the area where banded contrast features are visible in the
carbon phase. The reciprocal of the g-vector magnitude between primary diffraction
peaks matches the interplanar spacing of graphite at 0.34 nm. Region 2: The HRTEM
image and associated Fast Fourier Transform pattern (left) generated from the white box
confirms the presence of graphitic ordering.
106
  
C-K
O-K Al-K
FWHM of O-K signal ~0.2 ?m
Al-K
Figure 4.18: STEM-EDS line scan across the Al/C interface region. Left: Bright-field
STEM image with the red arrow indicating the line-scan direction across the interface.
The dark interfacial band was approximately 0.25 ?m wide. Right: Selected EDS spectra
from representative areas of the scan within the C- (red outline), O- (green), and Al-rich
phases (blue). The full width at half-maximum (FWHM) of the O-K? signal was about
0.2 ?m, corresponding to the width of the dark band in the STEM image.
might have been incorporated in it. The Al was locally thinner in this region, and
therefore was affected proportionally worse by FIB amorphization damage (mostly
confined to the top quarter of the image). The interplanar spacing in the most
ordered crystalline direction was 0.231 nm, which matches the < 111 > direction
in FCC Al. The crystallites were oriented on a < 110 > zone axis but with many
slight rotations off-axis, which gave rise to additional spots in the FFT pattern and
to defects indicated by the inverse FFT. Two weak spots in the FFT indicated
similar distance in real space to the interplanar spacing of graphene; however this
was not captured on a larger scale by an electron diffraction pattern such as the inset
to Fig. 4.16, indicating that C incorporation within the Al lattice was either limited
to a short distance from the interface or that the concentration of C in question was
too low to produce noticeable diffraction peaks.
107
0.25 ?m
3.08 1/nm 200
Al 0.325 nm 111
(amorphous)
111
Al 
(crystalline)
1 n
m
.230
Figure 4.19: HRTEM of the Al structure near the interface with C (out of frame, to the
top and left). The thinnest part of the Al was amorphous in that region, most likely due
to FIB damage and not the covetics reaction. Within the crystalline Al, the zone axis
was < 110 > as indicated on the FFT pattern on the top right (generated from the white
box). Several additional weak spots were also visible, including one pair marked by arrows
that matched the interplanar spacing of graphite. Local mis-orientation and texturing was
visible in the inverse FFT image generated using the 111 spots of Al.
4.2.3 Well-integrated carbon nanostructures in Al covetics: Analyt-
ical TEM-EELS
Analysis of the carbon structures described in the previous section raises as
many new questions as it answers. On the one hand it is apparent that graphitic or-
dering takes place during the covetics fabrication process, because the carbon source
material is disordered and amorphous before the reaction, and no graphitic struc-
tures were found by Raman spectroscopy or TEM in the reference samples from the
original alloy material. Furthermore, variable but persistent gains in bulk electrical
conductivity have been reported in Al covetics [140]; these are not explained by
micron-scale inclusions of graphite, whose bulk conductivity (2 ? 106 S/m [32]) is
108
 
lower than that of pure Al (3.5? 107 S/m). The main question is, therefore: What
forms of nanostructured carbon are responsible for the bulk properties observed?
One early covetic Al 6061 alloy sample, known by its manufacturer-assigned
reference number H49, has outperformed nearly all other covetics in terms of relative
conductivity enhancement?from 15% after heat treatment up to over 40% in the
as-extruded condition [57]. This sample also exhibited significant integration and
epitaxy of graphitic nanoribbons in the Al lattice, on a length scale of over 1 ?m [56].
Such structures are the best explanation of its conductivity properties especially in
light of the conductivity modeling described in Sec. 4.3 of this work. In this section,
new HRTEM and EELS results from sample H49 are presented and contrasted with
more recent covetics structure findings.
Several TEM specimens of H49 had been previously prepared by electropolish-
ing prior to this work. One of these (known to the research group as ?#3?, reflecting
the original sequence of preparation) was re-visited using analytical TEM and EELS
in order to identify new features of interest using more precise data-analysis methods
such as NMF. Fig. 4.20 presents a visual summary of the results. At low magnifica-
tion in Fig. 4.20(a), several rod-like structures over 1 ?m long are visible connecting
2 distinct Al grains. Inspection at higher resolution in Fig. 4.20(b) shows that these
are about 20 nm wide, and exhibit spots and rings in the diffraction pattern match-
ing the < 1010 > and < 1120 > interplanar spacings in graphite (Fig. 4.20(d)).
Crucially, EELS spectrum imaging indicated that the structure exhibited 2 prin-
cipal components of the C-K EELS edge (Fig. 4.20(e?f)). ?? and ?? peaks were
present in both components.
109
(a) 1 (b)
2
3
sion
Fiber inclu
(c) (d)
220 Al 220
311
[112] 5.07 1/nm
111
Al matrix
(e) (f)
?* ?*
284 eV
5 nm
Figure 4.20: TEM and EELS of rod-like graphitic structures in electropolished Al 6061
covetic #3. (a) Bright-field TEM image of a gap between 2 Al grains bridged by 3 rod-
like structures (numbered and indicated by arrows). (b) HRTEM reveals a crystalline Al
matrix closely integrated with the fiber structure. (c) Electron diffraction pattern from
the Al matrix, oriented such that the electron beam imaged along a [112] zone axis. (d)
Diffraction pattern from the region of the fiber inclusion. Spots corresponding to the Al
< 220 > directions are visible. The inner and outer rings correspond to distances of 0.197
and 0.121 nm, respectively matching the < 1010 > and < 1120 > interplanar spacings in
graphite. (e) NMF decomposition identified two significant components with intensities
distributed as shown. (f) The corresponding components of the C-K EELS edge each
displayed a ?? peak associated with sp2 bonding character.
110
Inspection of the C-K edges? energy loss near-edge structure (ELNES) provides
further insight into the bonding character of atomic C. sp2 hybridization contributes
a characteristic ?? peak around 284 eV, whereas both sp2 and sp3 bonding gives
rise to the edge onset around 290 eV (??) [142]. Intensity ratios of these peaks can
be used to estimate the degree of sp2 character in a particular region, relative to a
reference such as highly oriented pyrolytic graphite (HOPG) [142,143]. Qualitative
inspection of the blue curve in Fig. 4.20(f) therefore indicates that the center of
the fiber, as shown in the lower map in (e), has a stronger sp2 character than the
periphery (upper map; green curve). This observation is consistent with the concept
that graphitic (i.e., sp2) ordering took place during the covetics fabrication process,
with the later addition of a hydrocarbon contamination layer or other source of C
with a weaker sp2 character.
TEM imaging of the specimen was also performed along a < 111 > zone axis
of Al near the rod-like features. Diffraction patterns and conventional dark-field
imaging indicate that ordered graphitic ribbons were present, similar to those previ-
ously reported by Jaim et al. [56]. These data are shown in Fig. 4.21. In addition to
the {220} spots of Al, distinct secondary peaks are visible in the diffraction patterns
throughout the specimen (insets of (a) and (b)). These correspond to d = 0.204 nm
and d = 0.211 nm respectively, which match the < 1010 > spacing in the basal plane
of graphite. Conventional TEM dark-field imaging (Fig. 4.21(c)) was also performed
using the signal from one of these diffraction spots, circled in (b). This image showed
a series of parallel graphitic ribbons roughly 20 nm wide and hundreds of nm long
linking 2 adjacent Al grains. Such structures were visible throughout the electron-
111
(a) 3
2
1
220 202
022
2 ?m
(b) (c)
220 202
DF
d = 0.211 nm 022
5 1/nm
Figure 4.21: TEM imaging of aligned GNRs near the C fiber structures along a < 111 >
zone axis of Al. (a) Composite bright-field image showing the thin perimeter of the elec-
tropolished specimen. The C fiber structures introduced in Fig. 4.20 are visible on the
right, labeled 1, 2, and 3. (Inset: corresponding Al diffraction pattern with additional weak
spots marked by arrows, indicating an interplanar distance of 0.204 nm.) (b) Bright-field
TEM image showing banded features across 2 Al grains. Inset: Al < 111 > electron
diffraction pattern with 4 secondary spots corresponding to d = 0.211 nm, which matches
the < 1010 > spacing in graphite. (c) Dark-field TEM imaging using the graphitic diffrac-
tion spot indicated ?DF? in (b) revealed a series of aligned ribbons about 20 nm wide and
several hundred nm long.
112
transparent regions of the specimen and?to the extent that graphene nanoribbons
provide enhanced electrical conduction pathways in the composite?give the best
explanation for this sample?s exceptional conductivity properties.
4.2.4 Dislocation structure, microstructure, and mechanical proper-
ties of covetics
Dislocation structure and microstructure are known to significantly influence
both mechanical and electrical behavior of Al alloys [144]. These aspects of covetics
were investigated using TEM and other methods through collaboration between
UMD and the U.S. Army Research Laboratory (ARL). A series of covetic samples
prepared by UMD were subjected at ARL to micro- and nanomechanical testing
to determine hardness, ultimate tensile strength, and local contact resistance; after
these tests a subset of the samples were characterized using the TEM techniques
featured in this thesis, including energy-filtered TEM and dark-field imaging, to
explore the defect structures of covetics.
Al 1350 covetic samples were subjected to nano-indentation with the goal of
validating molecular dynamics simulations of graphitic C structures embedded in
Al [145]. The inclusion of graphene nanoribbons in a metal matrix was expected
to influence the composite?s mechanical properties (e.g. tensile or yield strength).
Rectangular arrays of spherical nano-indents on the order of 100 nm deep were im-
posed across a grain boundary on a polished surface of the covetic sample known
as ?29A.? This array is shown in Fig. 4.22(a). A cross-sectional TEM specimen
113
Nano-indents (a) (b)
Protective Pt
Grain 
boundary
5 ?m 5 ?m
200 (c) (d) (e)
111
022 IND
[110] ENT
0.2 ?m 0.2 ?m
Figure 4.22: Characterization of the covetic sample 29A after nano-indentation. (a?b)
The cross-sectional lamella was extracted from the region highlighted in the white box
in (a), after deposition of a protective Pt capping layer, and thinned to ? 90 nm thick.
(c) High-contrast image of one Al grain revealed that it was composed of several smaller,
closely-oriented ? 1-?m grains. (d) Energy-filtered TEM image of the grain boundary
region generated using electrons from the energy loss range matching the C-K EELS
edge. C signals were visible in the grain boundary region as shown and not elsewhere in
the specimen. (e) Zero-loss EFTEM image corresponding to (d).
(Fig. 4.22(b)) was prepared by FIB from the indicated region in order to capture
the area under the indent array from both sides of the grain boundary. Each of the
two grains exhibited a single unique electron-diffraction pattern, corresponding to
(111) and (011) on the left and right sides of the grain boundary in Fig. 4.23(a),
respectively. As seen in the bright-field image in Fig. 4.22(c), however, these grains
were highly textured and ultimately composed of several smaller, highly-oriented
grains. Inspection of multiple electron diffraction patterns within the (011)-oriented
grain revealed sub-grain misorientations of typically 2?3?. This fine-grained struc-
114
ture matches the report of paracrystalline behavior previously observed via electron
backscatter diffraction (EBSD) which is often correlated with large dislocation den-
sities [145]. Similar fine-grained features were also observed in a TEM specimen
extracted far away from the indent array, indicating that these features were a prod-
uct of the bulk process and not mechanical testing. Energy-filtered TEM indicated
the distribution of C around the grain boundary region in Fig. 4.22(d). Meaningful
concentrations of C were not observed outside of this region.
Conventional TEM dark-field (DF) two-beam condition was used to enhance
contrast between grains and dislocation features, and is summarized in Fig. 4.23(b).
The DF image was generated from the (111)-oriented grain using the g = (022)
diffraction spot. A high concentration of dislocations and low-angle grain bound-
aries are visible near the surface of indentation. The dislocation density under
the indent region was estimated to be 2.3? 1014 m?2 in the highest-density region
bounded by the dashed blue box, roughly 2 orders of magnitude greater than in
a typical sample of pure unstressed Al [146]. In comparison, the dislocation den-
sities simulated by Shumeyko et al. were on the order of 1016 m?2. The main
reason for this discrepancy is the significantly smaller length scale of the molecular
dynamics simulation (angstroms) compared to TEM (hundreds of nanometers to
microns). Experimental limitations such as differences in FIB milling rates also led
to uncertainty in the exact position of the final lamella relative to the indents?i.e.,
the lamella plane could correspond to the top or bottom edge of the white box
in Fig. 4.22, not directly under indents, and represent a less-strained area. Fur-
thermore, ? 50 nm of the lamella top surface?expected to be the most defective
115
(a)
Grain 200
boundary 
200 region 111 (b)
111
5 1/nm 022 5 1/nm
022
Direction 
of Indents
5 ?m
2 ?m
Figure 4.23: (a) Bright-field TEM image showing differently-rotated < 011 > grains on
the left and right sides of the grain boundary, respectively. Indentation was performed
in the direction indicated; the inset shows the TEM lamella with an arrow specifying the
direction of naoindentation. (b) TEM dark-field image from the outlined region in (a)
using the g = (022) diffraction spot. Several low-angle grain boundaries were visible and
the dislocation density was estimated to be 2.3 ? 1014 m?2 in the area outlined in the
dashed blue box.
area after indentation?was damaged or removed during the final FIB milling step.
For this reason the dislocation density values reported from experiments should be
considered low-range estimates.
It is encouraging for the concept of mechanical-property enhancement that
GNR distribution in simulated Al covetics is correlated with different dislocation
density and propagation behavior, which lends credence to the principle that GNRs
block dislocation motion within the metal matrix and lead to increased strength
and hardness [145]. TEM dislocation-density estimates support this concept, as
the dislocation density away from the indents in the covetic 29A was about 1.3 ?
1014 m?2, lower than the 1.7 ? 1014 m?2 seen in an Al 1350 control subjected to
the same metallurgical treatment. This implies that the propagation of dislocations
away from the indent region may have been blocked more effectively in the covetic
116
than in the control, and is a promising first step towards a larger body of results
to corroborate models; however, this difference is not itself statistically significant,
and further work is needed in this area.
Similar defect structures between covetics and controls
Further characterization of mechanical properties was conducted at larger
scales to assess whether these differed between covetic composites and reference
Al alloys (i.e. controls?without the addition of C but otherwise subjected to the
same melt/cool cycle and treatment). The importance of this topic was twofold:
First, since graphitic structures are known for their high tensile strength and other
mechanical properties, the inclusion of these materials could provide a pathway to
enhanced strength of the composite. Second, even if a certain application calls only
for high electrical conductivity, with no particular concern for mechanical behavior,
it is important to understand the effect of microstructural features such as grain
size on the conductivity of covetics, in order to separate it from enhancements due
to the introduced carbon.
Previous research on traditional (non-covetic) Al6061 alloys shows a clear re-
lationship between increased annealing temperature, decreasing yield strength, and
increasing electrical conductivity (Zhang et al. 2018, Fig. 9 [144]), a straightforward
demonstration of the concept that a higher density of structural defects (e.g. grain
boundaries and dislocations) increases the difficulty to propagate both dislocations
and electrons through the metal structure. By contrast, ?traditional? metallurgical
117
(a) (b)
63 230
61 210 Baselines
59 190
Baselines
57
0 30 60 90 120 1700 30 60 90 120
Charge (kC) Charge (kC)
Figure 4.24: Trends in covetics? (a) electrical conductivity and (b) ultimate tensile
strength as functions of total charge applied through the melt during fabrication (i.e.,
current ? reaction time, in kilo-Coulomb (kC) units). While the conductivity tended to
increase with total charge, no corresponding decrease in UTS was discerned, suggesting
that the conductivity increases were not simply due to reduction in dislocation density or
other changes in defect structure. Original data were collected by S. Zhang of General
Cable [140].
structure interpretations do not explain the increased electrical conductivity in cov-
etics. A side-by-side comparison of the electrical- and mechanical-property trends
in several covetic samples, Fig. 4.24, shows how the conductivity tended to increase
with total charge applied during the fabrication process, but no corresponding de-
crease in UTS was observed, as one would expect if the conductivity increase had
been due solely to reduced density of microstructural defects. Furthermore, the
typical grain size of Al 1350 covetics as determined by optical micrographs of etched
surfaces were similar to an Al 1350 control (Fig. 4.25.) Taken all together, bulk
mechanical property characterization shows that Al 1350 covetics? hardness, ulti-
mate tensile strength, and grain size distributions do not differ significantly from
the parent alloys subjected to the same processes. Because the inclusion of C does
not alter the bulk Al microstructure, direct comparison of electrical conductivity
between covetic samples and parent-alloy control samples is permissible.
118
Conductivity (% IACS)
UTS (MPa)
Covetic (a) Reference (b)
Avg. grain 100 ?m Avg. grain 128 ?m
400 ?m 100 ?m
Figure 4.25: Optical micrographs indicated that the typical grain sizes of (a) the Al 1350
covetic and (b) the control were not substantially different. A direct comparison of electri-
cal properties is therefore reasonable, because resistance due to electron grain-boundary
scattering will be comparable in both materials.
4.3 Effective medium model of electrical conductivity
A simple model of NCMC conductivity based on fundamental principles will
be important to fill gaps in understanding regarding conductivity enhancement in
covetics?especially considering the many different forms and structures that carbon
can take when embedded in a metal matrix. Significant uncertainties have persisted
regarding the magnitude of conductivity enhancement in NCMCs such as the Al
covetics characterized in this work. Early reports on a 3 wt.% C-Al6061 covetic
suggested conductivity enhancement of 43% and 15% above the reference Al6061
in the as-extruded condition and following T6 heat treatment, respectively [57].
In contrast, investigations of covetics based on other metals such as Cu and Ag
have shown much less or no improvement [147], and extensive measurements of as-
cast Al 1350 covetics have produced increases in conductivity in only the 0?5 %
range [140]. Furthermore, large variations and uncertainties in the measurement
119
also arise depending on the specimen aspect ratio and surface treatment [57]. As
such, there remains a great deal of uncertainty regarding electrical conductivity
enhancement in covetics: the magnitude of increase in bulk samples, the fabrication
and metallurgical processing treatments which affect it, the nature of the nanoscale
structures which enhance or inhibit conductivity, and what the maximum increase
in conductivity might be under ideal conditions.
4.3.1 The need for a new model
The rule of mixtures provides a simple starting point to understand the con-
ductivity of an Al-matrix composite with embedded graphitic inclusions. Provided
that the inclusions are uniaxial and aligned, this model approximates the effective
conductivity of a composite, ?e, as a volume-weighted average of the conductivities
of the matrix (?m) and inclusions (?f ). The conductivity is bounded by the mini-
mum, set by the case of a load (i.e., a voltage) applied transverse to the inclusions
(Reuss model, [148]) and the maximum set by the case of a load along the inclusion
axis (Voigt model, [149]):
( )?1
f 1? f
+ ? ?e ? f?f + (1? f)?m (4.2)
?f ?m
where f is the inclusion volume fraction.
The electrical conductivity of Al 1350 and similar alloys is about 3.5?107 S/m.
This value is larger than conductivities reported for graphitic structures such as ideal
pure graphite (? 2?106 S/m, [32]) or even suspended graphene (? = ne? = 2.2?107
120
Graphene ribbons 
parallel (upper curve) and 
? (S/m) perpendicular (lower curve)e
Graphite rods parallel 
to the current
Graphite rods 
perpendicular to the 
current
Graphitic vol. frac. f
~4 wt.% C
Figure 4.26: The projected conductivity ?e of nanocarbon-Al composites following the
rule of mixtures decreases monotonically, whether the inclusions are graphite (? bounded
by the lower 2 curves) and suspended or non-interacting graphene (? bounded by the
upper 2 curves). This simple model is contradicted by measurements showing conductivity
increases in covetics, indicating that a more sophisticated model is needed.
S/m, [34]). Therefore, ?e will always be smaller than ?m for any volume fraction of
carbon f greater than zero, as shown in Fig. 4.26, as long as the assumptions implied
by the rule of mixtures are valid?namely, that the inclusions and the matrix are
non-interacting. This assumption appears not to be valid for covetics because many
samples have shown conductivity enhancement. These samples serve as evidence
that metal-carbon interaction such as charge transfer is present in covetics, and
that this interaction serves to enhance their conductivity. A more sophisticated
model is needed to accurately represent the effective conductivity of covetics.
A 2004 theoretical study by Hjortsam and co-workers sought to demonstrate
the high-conductivity potential of carbon-metal composites [150]. Their effective
medium model suggested that the effective conductivity of an aligned single-wall
121
CNT (SW-CNT)-Cu system could be a factor of 2 greater than the International
Annealed Copper Standard (IACS) conductivity, with a volume fraction of 30?40%
SW-CNT. Such a large magnitude of projected conductivity enhancement is promis-
ing. However, obtaining this result required simplifications that are not physically
realistic. Hjortsam et al. neglected the existence of a percolation threshold, the
critical volume fraction above which inclusions are likely to form long-range inter-
actions. The percolation threshold is substantially lower than 40% for elongated
inclusions: it drops below 1% for aspect ratios between 50 and 100 [151]. Secondly,
metal-carbon interfaces were treated as ideal and non-interacting, which is not likely
for a moderately reactive metal such as Al.
4.3.2 Structural inputs to the model
The effective medium approximation (EMA), introduced in Sec. 2.4, forms
the basis for the model developed in this section. Previous studies have utilized
EMA to estimate the effective properties of composites containing nanostructured
C [152]. A number of experimental reports relate to an insulating matrix such as a
polymer with embedded CNTs, showing enhancement of thermal conductivity and
hardness [153,154].
The effective-medium approach in the present work incorporates several key
modifications to that of Hjortsam, in order to reflect the structure of covetics as it
is understood thus far, and to bridge the remaining knowledge gaps in a rigorous
122
way using theoretical and computational approaches. Two key assumptions were as
follows:
1. Graphitic structures are randomly oriented
Previous TEM investigations of covetics at the nanoscale, such as the work
by Jaim [56] and in Sec. 4.2.3 of this thesis, suggest local orientation of GNRs on
the Al (111) crystallographic planes. However, the casting and/or furnace cooling
process produces a polycrystalline metal matrix. A macroscopic piece of covetic
composite will therefore have randomly aligned grains, unless it has undergone a
process that imparts directionality, such as extrusion. This randomness implies that
embedded graphitic structures will also be randomly oriented on a macroscopic scale,
independent of the carbon structures? degree of alignment within individual grains.
A schematic illustrating the orientation of GNRs in two adjacent metal grains is
shown in Fig. 4.27. Some experiments have even found significantly smaller average
grain sizes in covetics than in parent 6000-series Al alloys [155, 156], which would
contribute further to the random orientation of carbon structures within the bulk
composite.
2. Graphitic carbon takes the form of multi-layer graphene ribbons
The multi-layer nature of GNRs in covetics was identified using Raman spec-
troscopy as discussed in Sec. 4.1.2. Most GNRs appeared to contain between 3 and
10 layers. The thickness of the embedded graphene nanoribbons will have a substan-
tial negative effect on their ability to provide a composite with enhanced electrical
123
Metal matrix
 
rai
n ry
G aun
d
Bo
GNR
Figure 4.27: Schematic representation of GNRs embedded in a polycrystalline metal
matrix. Even while the nanoribbons are locally aligned within one grain or across a grain
boundary, they are treated as randomly oriented across macroscopic length scales as a
consequence of the metal grains? random orientations with respect to one another. This
assumption is valid as long as orientation is not introduced in a subsequent processing
step, e.g. extrusion.
properties. Fundamentally, thick graphene is analogous to graphite, whose electrical
conductivity is worse than many transition metals [157]. The c-axis electrical [158]
and thermal [159] conductivities of graphite are lower than their corresponding in-
plane values owing to weak van der Waals bonding between the layers. Furthermore,
when graphene is doped by interaction with a substrate leading to a shift in the Fermi
level, as described in Sec. 1.2.1, this interaction only affects the layer next to the
substrate [160]. It is therefore desirable that GNRs be as thin as possible (single-
or bilayer). This effect is addressed in the present work by introducing an effective
volume fraction parameter to consider only the top and bottom monolayers of GNRs
as contributing to enhanced conductivity.
124
4.3.3 Electronic inputs to the model
The Cu-CNT model put forth by Hjortsam et al. [150] rests upon the assump-
tion that the matrix and inclusions each retain their original electronic properties
when formed into a composite. Experimental findings and calculations indicate that
this is not the case in a metal-GNR system, where electronic interactions between
the metal matrix and graphitic inclusions lead to enhanced conductivity at these
interfaces. In addition, quantization of electron energies in narrow graphene ribbons
leads to a conductivity that is dependent on the GNR width, which must be taken
into account in order to build a representative model.
4.3.3.1 Charge transfer at the metal?graphene interface
In the work of Cao et al., first introduced in Sec. 1.2, conductive atomic force
microscopy (c-AFM) measurements were taken from metal-graphene layered struc-
tures with varying numbers of graphene layers from 1 to 20 [44,45]. It was demon-
strated that the conductivity of graphene embedded in Cu was up to 3 orders of
magnitude greater than the matrix, up to 7.1?1010 S/m [44], but only for single- or
bilayer graphene. Increasing the number of layers caused the peak current measure-
ment to drop precipitously, which suggested that the conductivity enhancement was
closely confined to the interface. The authors attributed this trend to the mecha-
nism of charge carrier transfer from metal to graphene, which has been theoretically
predicted in Cu, Al, and other metals [42,43,161]. Follow-up density-functional the-
ory (DFT) calculations by Cao et al. support this mechanism, predicting electron
125
?3 ?1 
Al C Al
Figure 4.28: Structure of the simulated Al?GNR?Al interface with a single-layer graphene
ribbon (gray) bounded on both sides by Al(111) oriented crystals (brown), used for carrier
density calculation and the estimate of out-of-plane vs. in-plane GNR conductivity ?1/?3.
densities on the order of 1014 cm?2 in bilayer graphene embedded in either Cu [44]
or Al [45].
In collaboration with Andrew Palughi of Texas A&M University, first-principles
DFT calculations were used to estimate the charge carrier concentration n of a
graphene sheet embedded in Al, as well as the ratio of the electrical conductivity
normal to the plane of the GNR relative to in-plane, ?1/?3. All calculations were
performed using the Vienna Ab Initio Simulation Package (VASP) [162, 163]. The
system consisted of a single layer of graphene placed on the (111) crystallographic
plane of FCC aluminum, with 17 Al layers in total, as illustrated in Fig. 4.28. The
magnitude of charge transfer was obtained via electronic structure calculations. On
average, 0.045e per 2-atom graphene unit cell were transferred from the metal to
the GNR, which translated to a carrier density n of 1.7 ? 1014 cm?2. The ratio
of out-of-plane to in-plane GNR electrical conductivity, ?1/?3, was obtained using
the implementation of the Boltzmann transport equations in the BoltzTrap2 pack-
age [164]. This ratio was on the order of 10?5, so the conductance normal to the
plane of graphene is negligible.
126
4.3.3.2 Width dependence of GNR conductivity due to quantum con-
finement
Some of the unique electronic properties of graphene are attributed to its con-
strained geometries. In addition to the characteristic two-dimensional electron gas
behavior, conductance in graphene nanoribbons is subject to quantum confinement;
due to their narrow width, the ribbons act as electron waveguides and propagating
electrons? energies are quantized. This phenomenon has been explored experimen-
tally [160] as well as theoretically [165, 166]. Wider GNRs are ultimately able to
support more electron-wavefunction states and therefore exhibit higher conductivity
than narrow ribbons. This conclusion is supported by the following two cases of a
quantum-conductance model.
Simplified case: An isolated GNR as an infinite potential well
The analysis of Naeemi et al. in Ref. [165] serves as a starting point for
the present work. In the language of quantum mechanics, an isolated nanoribbon
(for instance, suspended in vacuum) may be treated as an infinite potential well.
Outside of the ribbon the electron wave function must be equal to zero, implying the
transverse boundary condition sin(k?W ) = 0, where W is the width of the ribbon.
The corresponding allowed wavevectors are
n?
k? = (4.3)
W
127
where n is an integer. The approximate dispersion relation is given by [35]:
E(~k) = ?h??F |~k|, (4.4)
where h? is the Planck constant h divided by 2? and ?F is the Fermi velocity of
graphene. This leads to the allowed energies En,
( )
n?
En = h??F = n?E. (4.5)
W
The energy level spacing ?E = h?F/2W is an inverse function of the GNR width
[165]. This result shows the plausibility that a wider GNR is more conductive,
because it allows a greater number of electronic wavefunctions.
The scattering behavior of different propagating electron modes is another way
in which conductance depends on W . As discussed by Berger [160] and Naeemi [165],
the mean free path of the nth mode ln is also a function of W . Assuming that
scattering at the edges is diffusive (corresponding to edge roughness greater than
? 1 nm [160,165]), ln is a function of the ratio between longitudinal and transverse
wavevectors, k|| and k? respectively. Adapting Eq. 3 from Ref. [165]:
????( )2k|| EF/?Eln = W = W ? 1, (4.6)
k? n
where EF is the Fermi energy. In other words, as k? increases with n, electrons
propagate progressively shorter distances ln before scattering at the edges. The W
dependence can be seen qualitatively in the illustration in Fig. 4.29. An expression
128
ln
W
ln
W
Figure 4.29: The electron mean free path due to edge scattering ln is finite for all n 6= 0
as a consequence of the transverse wavevector k?, which is non-zero except for n = 0. A
wider graphene ribbon (top) is therefore able to accommodate a longer path length in the
longitudinal direction than a narrow ribbon (bottom).
for the total conductance G is obtained by applying Matthiessen?s rule, given by
Ref. [165], Eq. 4 :
2e2 ? 1
G = (4.7)
h n 1 + L(1/lD + 1/ln)
where 2e2/h is the quantum conductance (hereafter defined as G0), L is the GNR
length, and lD is the mean free path corresponding to defect and phonon scattering,
independent of the edge scattering effects. Reported values of lD range from 600
nm [160] to tens of microns in special cases, such as for 40 nm-wide GNRs epitaxially
grown on SiC (16 ?m, [49]) or graphene sheets encapsulated in hexagonal boron
nitride (28 ?m, [167]). lD was assumed to be 1 ?m for the purpose of this model [165].
The trends of Eq. 4.7 are illustrated in Fig. 4.30 for various n, W , and EF .
Having identified a model for G in isolated GNRs, it is possible to estimate
G for GNRs embedded in a metal matrix using a known value of the Fermi energy
129
(a)
W = 100 nm
EF = 0.4 eV
W = 50 nm
EF = 0.4 eV
n
(b)
EF = 1.0 eV
EF = 0.4 eV
W (nm)
(c)
EF = 0.4 eV
EF = 1.0 eV
W (nm)
Figure 4.30: The effects of W and EF on the conductance G of GNRs with L = lD =
1 ?m. (a) For a given EF = 0.4 eV, G increases step-wise with the number of quantum
modes n. Both the number of allowed modes and the magnitude of increase in G per
additional mode increases with W , as illustrated by the stepped curves for W = 50 and
W = 100 nm, respectively. The dashed gray line indicates the envelope of G(W ). (b?c)
The increase of G with W is more pronounced with larger EF ; the log-log plot in (c)
presents the same curves in (b) in terms of the equivalent resistance per unit length, r.
130
r (?/m)m)
G / G G / G0 0
EF , which is related to the carrier density n via the 2D density of states function for
graphene, as introduced in Sec. 1.2.1. Applying the D2D(E) expression in Eq. 1.2
to the definition of n:
?
n = ? f(E)D(E)dEEF
n ? D2D(E)dE
0
E2
n = F
?h?2
(4.8)
?2F
Plugging in the carrier density n = 1014 cm?2 for the graphene/Al system estimated
via DFT by Cao et al. [45], a value of EF = 1.2 eV is obtained. This value is larger
than those presumed by Naeemi et al. [165], however it is not beyond the realm of
possibility; Fermi energies on the order of 1 eV have been experimentally observed in
systems with ?ultrahigh? carrier densities of around 1014 cm?2 [38,168], which would
be expected to produce conductivities increasing with W similar to that illustrated
in Fig. 4.30.
Modeling the metal-graphene interface as a finite potential barrier
Although it is a helpful starting point, the infinite potential well is a better
approximation of an isolated or suspended GNR than one embedded in a metal
matrix. Electrons in the embedded GNR will experience a finite energy barrier,
V0, which is determined by factors such as the work functions of the metal (?M)
and of graphene (?G), as well as the nature of the bonding interaction at the inter-
face [43, 169, 170]. One interpretation for the magnitude of V0 is the difference in
131
(a) Before contact
Evac
?M ?G
EF
E
Al D
(b) After contact
Evac
? ? ?GM
E
E ?V FF ?EF
Al
Figure 4.31: (a) Work functions of the isolated metal and graphene surfaces with respect
to the vacuum level, Evac. (b) Band bending at the Al-GNR interface. ?M is the work
function of the metal (4.24 eV for Al), ?G =4.6 eV for pure graphene, and ? = 4.04 eV
for graphene adsorbed on Al. ?V is a potential barrier at the metal-graphene interface
defined by ?M ? ? [43]. Adapted from Refs. [43, 161,171].
work functions, V0 = ?M ? ?G, i.e., about 4.6 ? 4.24 = 0.36 eV, as illustrated in
Fig. 4.31 [43,170]. The height of the potential energy barrier between the metal and
graphene?through which electrons must tunnel to enter and exit the graphene?
can also be considerable. Using DFT, the height of this barrier has been estimated
at 1.2 eV for Al with a corresponding transmission probability of 35% [172].
Consider a graphene nanoribbon as a finite potential well of width W = 2a, as
in Fig. 4.32. The following solution is based on the standard approach employed in
132
Graphene
Graphene
V(x)
-a a
x
-V0
Figure 4.32: A finite potential well representing a GNR of width W = 2a.
many quantum mechanics texts [173]. The Schro?dinger equation within the region
V = ?V0 is given by
? h?
2 d2? ??V0? = E? , or (4.9)2m dx2
d2? 2m(E + V0)
= ?l2? , where l ? .
dx2 h?
V0 is positive and E < 0 for bound states; a finite number of bound states are allowed
for electrons with E < V0, which take the form ?(x) = C sin(lx) +D cos(lx) within
the well. Outside of the well, ?(x) takes the form of decaying exponential functions
of the form Be?x, where x < 0, and Fe??x where x > 0. ?(x) is subject to the
typical constraints that ?(x) and d?/dx are continuous at the barrier walls, which
gives rise to the condition that ? = l tan(la). Defining a change of variables where
?
z ? la and z0 = (a/h?) 2mV0, one obtains the transcendental equation
?
tan(z) = (z0/z)2 ? 1, (4.10)
133
z = l a
Figure 4.33: Graphical solution for electrons confined to a GNR of width W = 50 nm and
potential well depth V0 = 0.4 eV. The thick black line is the right-hand side of Eq. 4.10.
Its intersections with the left-hand side, tan(z) and cot(z), provide the even and odd
solutions, respectively. The vertical axis is dimensionless.
which may be solved numerically or graphically for the allowed values of z (and
therefore the allowed wavevectors l). At this stage the dispersion relation E(l) for
graphene given in Eq. 4.4,
E + V0 = h??F l, (4.11)
is reintroduced. For the case where the well is ?large? in terms of a and V0, the
allowed wavevectors ln and the bound-state energies are approximately as follows:
? n?zn lna ?
2
E + V0 ?
h??Fn?
, (4.12)
2a
where n is an integer. The graphical solution to this system shown in Fig. 4.33
indicates that this approximation is reasonable for W = 50 nm and V0 = 0.4 eV
(and therefore all larger W and V0 [173]). The number of allowed states, 10, is
134
tan z
cot z
the same as for the simplified infinite-potential well case shown in Fig. 4.30(a) (the
orange stepped curve with W = 50 nm and EF = 0.4 eV). In terms of the number
of allowed states and their contributions to the GNR conductance, therefore, the
infinite-well case produces reasonable results. The principal difference in the finite-
energy barrier case from the infinite-well case is that it is not possible to create an
arbitrarily large number of states given an arbitrarily large Fermi level energy: If
V0 is an intrinsic parameter of the material system, it will impose a limit on the
effect of EF , because states where E > V0 are scattering (continuum) states, not
bound (quantized) states. Based on this result, a maximum Fermi energy of the
tunneling barrier height for Al contacting graphene, 1.2 eV [172], will be considered
the most reasonable within the context of the effective-medium model for the overall
conductivity of Al-graphene composites developed in the following section.
4.3.4 The effective conductivity of a composite with randomly-oriented
inclusions
An analytical expression for conductivity in such a system containing randomly-
oriented rod-like inclusions is given by Ref. [91]:
[ ]
?e f 1 2
= 1 + ? + , (4.13)? 3m 3 ( ? 1)?1 +H ( ?1 ? 1)?1 + (1?H)/2?m ?m
where f is the inclusion volume fraction, ?m denotes the conductivity of the metal
matrix, ?3 and ?1 are the in- and out-of-plane conductivities of the graphitic struc-
tures, respectively, and H represents the influence of the GNR aspect ratio p = L/W
135
via the expression
[ ( ? ) ]1 p
H(p) = ? ln p+ p2 ? 1 ? 1 (4.14)
p2 ? 1 p2 ? 1
where L is the ribbon length and W is the width. As p becomes larger (more
needle-like), H(p) rapidly becomes small; H ? 0.002 for p = 40.
It follows from the c-AFM measurements of Cao et al. [44] that, due to the
low carrier density within a sheet of many-layer graphene, the bulk of the graphene
does not contribute to enhanced conductivity of the overall composite. Therefore,
in this work, the relevant volume fraction is only the outermost atomic layers of
graphene which are in direct contact with the metal. It now becomes necessary to
replace the overall C volume fraction f in Eq. 4.13 with an effective volume fraction,
feff , representing only the volume of the top and bottom monolayers of graphene
in a many-layer graphene nanoribbon:
( ) ( )
VGNR,surface 2
feff = f = f , (4.15)
VGNR,total N of GNR layers
such that Eq. 4.13 becomes
[ ]
?e feff 1 2
= 1 + ? + . (4.16)? 3 ( 3m ? 1)?1 +H ( ?1 ? 1)?1 + (1?H)/2?m ?m
Note that feff depends only on the thickness of the graphene; it is independent
of both L and W . Therefore, for needle-like inclusions with p large and H(p)
136
Metal matrix
GNR
n 
Gr
ai da
ry
n
Bo
u
Few-layer 
graphene
Metal?GNR 
interfaces
Figure 4.34: Enhanced detail of the metal matrix and embedded few-layer graphene. Only
the outer monolayers of graphene (metal-GNR interfaces, highlighted in blue) are treated
as having enhanced conductivity; the interior of the GNRs and the matrix properties are
identical to their respective bulk values.
small, the thickness of the nanoribbons is overwhelmingly the dominant dimensional
variable in this model.
The present work assumes that the bulk properties of carbon (i.e. graphite)
and metal are unchanged in covetics with the exception of the doped metal/graphene
interface. Thus, the inclusion of a single GNR in the metal matrix is treated as
illustrated in the detail box on the right-hand side of Fig. 4.34, with distinct edge
regions (blue; top and bottom) and bulk regions (gray; interior). The model assumes
ideal electrical contact at interfaces and neglects percolation effects, as the total
volume fractions f under consideration are small, under 5%.
4.3.5 Results
The effective medium model was first validated using the experimental results
of Cao et al. [44]. The operative principle was that if the model is accurate, it should
137
be able to take the theoretical calculation of carrier density and graphene dimensions
as inputs, and generate the experimentally-measured conductivity increase as the
output. Using the reported values of ?3 = 7.1?1010 S/m at the Cu?graphene inter-
face, graphene bilayer thickness of 0.7 nm, width and length of 30 ?m, and fill factor
f = 0.008%, an effective relative conductivity of ?e/?m = 103.5% is predicted. This
3.5% increase compares favorably with the 5.2% enhancement measured by c-AFM
and attributed to the presence of graphene by Cao et al., indicating that the model
should produce adequate predictions for systems yet to be realized. The following
models predict the bulk conductivity of covetics using doped-graphene conductivities
that were respectively measured and reported in literature (Case 1), and predicted
using the quantum conductance model introduced in Sec. 4.3.3 (Case 2).
Case 1: Few-layer graphene embedded in Al with ?3 measured at imperfect interfaces
Recent covetics work has focused largely on Al [56,156], which is preferred for
many applications such as grid-scale power transmission due to its favorable combi-
nation of mechanical strength, electrical conductivity, and low density. However, the
formation of an Al-graphene composite presents unique challenges. Ensuring good
graphene-metal contact is more difficult with Al than with Cu as it is not a suitable
substrate for CVD growth of graphene, and additionally forms an oxide passivation
layer rapidly upon contact with air or other source of oxygen [45]. Using the effective
medium model to predict the properties of a ?real world? Al-GNR system requires
an estimate of the impact of this oxide layer on the metal?graphene charge transfer
responsible for bulk conductivity enhancement. Reasonable values were provided by
138
25 nm Al2O3
Interfacial monolayer
GNR interior
Al matrix
25 nm Al2O3
GNR Interfacial 
interior monolayer
Al matrix
GNR vol. frac. f
Figure 4.35: Estimated effective conductivity of Al-matrix covetics with randomly aligned
GNRs of the cross-sections shown (insets; not to scale), 1-?m long, as a function of GNR
volume fraction f . Thicker GNRs have a smaller fraction of their volume exposed to the
metal surface, so the effective conductivity is correspondingly lower. ?e was calculated
using Eq. 4.16 via a measurement of conductivity at a real Al/graphene interface [45].
conductive AFM measurements of the Al-bilayer graphene system reported by Cao
et al. in Ref. [45]; in that case, ?3 was 2.55?109 S/m. This measurement accounted
for the few-nm thick aluminum oxide passivation layer which was observed in that
system. The projected conductivity enhancement as a function of GNR vol. fraction
is illustrated in Fig. 4.35 for this value of ?3, with ?1 = 10
?5 ? ?3, GNRs 25 nm
wide ? 1 ?m long, with thicknesses of 3 and 12 layers (respectively 1 and 4 nm)
and a nominally 60% IACS Al matrix.
For a GNR volume fraction of 5% (equivalent to ? 4 wt.% C), the effective
conductivity of the bulk covetic with 12-layer GNRs would be 19% greater than
the matrix, which corresponds to an absolute conductivity of about 71% IACS.
The enhancement is significantly greater in the 3-layer system, where 2/3 of the
carbon volume supports enhanced conductivity, as opposed to 1/6 of the volume
139
Effective conductivity ?e / ?m 
1 nm
4 nm
in the 12-layer GNRs. The direct measurement of in-plane conductivity ?3 used in
this calculation took into account the detrimental effect of interfacial Al2O3 (red
in Fig. 4.35) on the conductivity enhancement as described in Ref. [45]. Since the
interfacial conductivity ?3 was provided by measurement of a real system, this model
accounts for the presence of interfacial oxide impurities, as long as the dimensions
assumed for graphene ribbons can be ensured throughout the composite.
Case 2: Few-layer graphene embedded in Al with ?3 corresponding to the ideal quan-
tum conductance
To complement the measurement-based model, one can also build a model on
the conductivity values determined from first principles within the framework of
quantum mechanics. The preceding effective-medium case uses a direct measure-
ment of conductivity from a specific geometry of Al-graphene system, which brings
with it some inherent limitations. The most significant of these is that the mea-
surement was based on a carefully built-up stack of metal foils and graphene sheets
which extended laterally for tens of microns in both in-plane directions [45]; how-
ever, the conductance will be different for different graphene geometries, as explored
in Sec. 4.3.3.2. From the plot of resistance per unit length, r, in Fig. 4.30, the axial
conductivity of graphene nanoribbons is readily obtained via
GL
?GNR = , (4.17)
A
140
where A is the ribbon cross section taken to be W ? 0.34 nm. The conductivity
?GNR relative to aluminum is shown in Fig. 4.36(a).
Using these values as inputs to the effective-medium model of Eq. 4.16, Fig.
4.36(b) shows the effective conductivity increase for bulk Al-GNR composites as a
function of carbon volume fraction f , in conjunction with the geometry depicted in
the inset: W = 120 nm, L = 1000 nm, and t = 3 layers. The most obvious difference
between this case and Case 1 (shown again on Fig. 4.36(b) as ?Cao reference?) is
the significantly lower projected conductivity increases. In the case of EF = 0.4
eV, where the conductivity of the 120 nm-wide GNR is very close to that of Al,
the conductivity of the resultant composite actually decreases with f , due to the
low out-of-plane conductivity term (?1 = 10
?5??3) and insufficiently high in-plane
conductivity to compensate for it. Larger EF yields small improvements in the
conductivity of the bulk composite, roughly on the order of what has been recently
reported in Al covetics: A 3.6 wt.% graphitic C concentration was correlated with
an increase in bulk conductivity ?e from 58.5 ? 0.7% to 61.8 ? 0.7% IACS, for a
fractional improvement of 5.7? 1.7% on a length scale of roughly 1 cm [140].
4.3.6 Discussion
The results of the effective-medium models in the preceding section illuminate
several concepts that are significant for covetics development. Comparison of the
two model cases?the first based on a conductivity measurement from a carefully
engineered stack of Al foils alternated with CVD-grown bilayer graphene sheets, and
141
(a) EF = 2.0 eV
EF = 1.0 eV
E  = 0.4 eV
1 F
W (nm) W = 120 nm
(b)
t = 3 layers
Cao measurement
?3 = 73 ?Al 
EF = 2.0 eV
EF = 1.0 eV
EF = 0.4 eV
GNR vol. frac. f
Figure 4.36: (a) Ideal GNR conductivities relative to pure Al, taken from the calculated
resistances per unit length shown in Fig. 4.30(c). For each value of EF , the conductivity
of the GNR transitions to being greater than the metal at a critical width, indicated by
intersection with the dashed gray line. (b) Effective conductivity of composites made
from GNRs with the indicated dimensions. The effective-medium approximations were
calculated using Eq. 4.16 and the ?GNR values given in (a) at W = 120 nm as the in-plane
conductivities, ?3.
142
Effective conductivity ?e / ?Al Relative conductivity ?GNR / ?Al 
L = 1000 nm
the second grounded more firmly in the fundamental physics?helps to elucidate
these concepts.
The fundamental point to establish is that the potential exists to enhance
the bulk conductivity of Al alloys by incorporation of small volume fractions of
graphitic nanostructures. This is the same conclusion reached by Hjortsam et al.
in 2004 regarding carbon nanotubes embedded in copper [150], however the present
work builds upon that of Hjortsam in important ways. First, the present model is
better adapted to a realistic composite system in terms of the low carbon loading:
5 vol.% or lower vs. over 40% in Hjortsam. Such a large C volume fraction would
likely compromise the structural integrity of the composite as a whole, especially
given the potential for structural weakness and oxidation at metal-carbon interfaces.
The Hjortsam model additionally did not account for scattering within or between
graphitic structures, whereas both model cases in the present work incorporate the
effects of scattering (either by reference to direct measurement or by theory). Even
the more conservative Case 2, based on the quantum confinement of electrons in a
narrow GNR, suggests a modest conductivity enhancement in the bulk Al covetic
of between 2?10% for Fermi energies between 1?2 eV and a carbon volume fraction
of 5% (i.e., 4 wt.%). The recently reported 5.7% relative conductivity enhancement
for a 3.6 wt.% C-Al covetic falls neatly within this range [140].
Furthermore, it is clear that the geometry of the graphitic carbon has a large
influence on the conductivity of the final composite, based on the roughly 10-fold
difference in measured in-plane conductivity for wide graphene sheets embedded
in Al (?3 = 2.55 ? 109 S/m, [45]) relative to the projections based on quantum
143
confinement. The different dimensions of graphene between the two cases may ac-
count for most if not all of this difference. A larger width/length dimension (the
two can be considered equivalent for the case of randomly oriented inclusions) ap-
pears to lead to greater conductivity in the graphitic inclusions, and thus the overall
composite, due to the greater number of quantum-mechanical modes allowed for a
particular Fermi energy. On the other hand, larger thickness is always detrimental
to conductivity because only a small fraction of the total carbon present is doped
by contact with the metal; the interior layers of graphene are analogous to graphite,
which results in diminished conductivity as illustrated by the simple Rule of Mix-
tures model in Fig. 4.26. In spite of the broad applicability of the effective-medium
approach, uncertainty surrounding the dimensions of graphene ribbons and sheets
embedded in metals leads to a wide range of projected conductivity changes in the
bulk composite, ranging from trivial to remarkable.
It was not feasible to directly calculate the carrier mobility of the Al-GNR
interface due to the long relaxation time of phononic interactions. An order-of-
magnitude estimate for the conductivity of this region may be obtained via mobility
measurements from similar systems, such as graphene-based field effect transistors
(FETs). These systems yield mobilities on the order of 104 cm2/Vs [174, 175],
including in the regime of large carrier densities above 1014 cm?2 facilitated by
interfaces such as ionic gates [40]. Given ? = 104 cm2/Vs and n = 1.7 ? 1014
cm?2 (i.e. 5.1? 1021 cm?3), the doped GNR conductivity would be on the order of
8? 108 S/m. This value is not far off from the measurement of ?3 = 2.55? 109 S/m
used for the effective medium approximation, which indicates that the model is,
144
generally speaking, reasonable. Nevertheless, the measured conductivity was higher
by a factor of 3, even though it represented a reduction from the ideal (due to the
interfacial aluminum oxide). This implies that electrons may behave differently in
graphene embedded in metals compared to graphene that is suspended [34] or on a
non-metallic substrate, which tend to show a ? ? 1/n dependence [37,48] that was
not observed in the work of Cao et al. [44, 45].
A further constraint on the domain of the model is that it is not valid for high
concentrations of inclusions. When the volume fraction f is sufficiently large that
the inclusions are able to interact directly with each other over a long range, the
assumption inherent in the model?that inclusions are dilute and non-interacting?
no longer applies. At this stage the system has reached the percolation threshold
where transport can proceed through chains of inclusions rather than the matrix
[87]. If the inclusions are more conductive than the matrix, the overall conductivity
proceeds to rise sharply above the effective medium prediction with increasing f over
a small transition region [176]. The specific volume-fraction value of the percolation
threshold is a strong function of the inclusions? aspect ratio of length to width;
for instance, needle-like inclusions can connect end-to-end with less material than
required for spheres or plates. This dependence is reflected in numerical [151] and
analytical estimates [176] showing threshold volume fractions of randomly-oriented
ellipsoids ranging from 0.29 for spheres to below 0.01 for aspect ratios greater than
100 [151].
145
4.4 Summary
A broad range of qualitative and quantitative measurements were performed on
a series of covetic and reference specimens in the course of this work. By identifying
graphitic regions of interest using Raman spectroscopy, it was possible to prepare
TEM specimens corresponding to specific graphitic features and orientations within
the samples. Distributions of graphitic crystallite size, La, estimated from Raman
spectroscopy were positively-skewed after the covetics reactions, which suggested
non-uniform rates of graphitic ordering. Inspection of the Raman 2D peaks indicated
that graphitic carbon generally took the form of few-layer graphene comprising 3?10
layers.
Large and thick ordered carbon structures on length scales of microns to tens
of microns were observed by TEM in a majority of samples. Electron diffraction
and HRTEM imaging confirmed that these were graphitic, but also exhibited small-
scale undulations. Al and C phases also tended to remain separate in these regions,
with minimal penetration of C structures into Al. STEM-EDS mapping of these
interface regions indicated that an aluminum oxide layer of up to 250 nm thick was
often present between C and Al. This interfacial layer and the large-scale nature of
these thick graphitic structures suggest that they will not contribute to enhanced
electrical conductivity and could be actively detrimental. On the other hand, a cov-
etic specimen with a reported conductivity enhancement of over 15% shows unique
nanostructured forms of graphitic carbon, including long narrow fibers and ribbons
spanning across Al grain boundaries. In contrast to the larger inclusions, these
146
structures appeared well-ordered and well-integrated in the metal matrix and did
not show evidence of oxidation. Investigation of the samples? mechanical properties
indicates that observed increases in electrical conductivity were independent of mi-
crostructural defects such as grain boundaries. Graphitic nanoribbon structures are
therefore the most likely origin of electrical conductivity enhancement in covetics.
A simple effective medium approximation was used to model the conductivity
of Al-based nanocarbon-metal composites with varying graphitic inclusion dimen-
sions and concentrations. Conductivity enhancements on the order of 10% relative
to the matrix are projected on the basis of localized conductivity measurements
reported in literature as well as first-principles DFT calculations, which indicate
doping of graphene layers via electron transfer in the presence of metals. Two
model cases were used to project the conductivity of bulk composites based on re-
ported measurement and on quantum confinement of propagating electrons, with
the latter providing a conductivity value closely aligned with recent experimental
work. Graphene nanoribbons will ideally be wide, long, and thin (mono- or bi-layer)
in order to fully exploit the localized charge transfer at the metal-graphene interface.
Future computational research in this area may explore first-principles methods to
determine the transport properties?in particular, carrier mobility?of the doped Al-
graphene interface, which in conjunction with the calculated carrier density would
provide a complete theoretical prediction of conductivity enhancement in covetics.
147
Chapter 5: Conclusions
5.1 Summary of research
Through the analytical framework of electron microscopy, this work brings
together two seemingly unrelated material systems?wide-bandgap semiconductors
and nanocarbon-metal composites. Both of these systems have the potential to
support more efficient and sustainable energy transfer technologies such as lighter-
weight vehicles which will be essential to confront global challenges such as climate
change. They also present materials-characterization challenges, which must first
be understood in order to realize that vision.
5.1.1 Wide-bandgap MOS interfaces
Silicon carbide represents a success story in the realm of wide-bandgap tech-
nologies, as the last 20 years have seen it transition from the laboratory into commer-
cial applications. The potential for continued improvement nevertheless remains, in
the form of novel annealing treatments that may exceed the performance enhance-
ment imparted by the present NO anneal. This thesis has explored the structural
and composition characteristics of SiC MOS structures with boron-doped SiO2 ox-
148
ide (BSG) and Sb ion-implanted SiC in conjunction with NO post-oxidation anneal
(Sb+NO). In the SiC/BSG system, EELS spectrum imaging in conjunction with
multivariate statistical analysis indicated a narrow pile-up of B less than 3 nm wide
immediately at the interface, with a uniform lower concentration throughout the
bulk of the BSG layer. The fine structure of the B-K edge indicated sp2 hybridiza-
tion, which is predicted to relieve interfacial stresses and thus can act as a mechanism
for the reduction in Dit previously observed in B-doped SiC MOS devices. This sys-
tem also provided an opportunity to explore and validate the MCR-LLM algorithm
for hyperspectral decomposition of EELS data in a doped wide-bandgap MOS struc-
ture. In the Sb+NO system, this algorithm was used to identify a weak Sb EELS
edge that could not be identified by NMF. The relatively smaller interface transition
width in this device and overall abrupt, stable structure suggest that Sb counter-
doping is a viable method to improve channel mobility from a structural quality
perspective, independently from and in addition to post-oxidation annealing.
Gallium oxide device technology is significantly less mature but presents sig-
nificant advantages over SiC and other wide-bandgap systems for very high-power
and high-voltage applications. This thesis investigated the structure of ?-Ga2O3 in-
terfaces with SiO2 and Al2O3 gate oxide layers prepared under a range of deposition
and post-deposition anneal (PDA) conditions. Elevated PDA temperature was cor-
related with a larger amplitude of interfacial roughening likely to be detrimental to
the long-term reliability of the gate oxide. In the case of Al2O3 gate oxides produced
by atomic layer deposition, an interdiffusion region containing both Ga and Al was
found to extend several nm wide across the interface, with the use of a PDA step
149
correlated with the wider transition regions. TEM characterization of Ga2O3/Al2O3
specimens also led to the unexpected finding that the initially amorphous Al2O3 be-
came crystalline upon exposure to the electron beam. The phenomenon resulted
in a highly-oriented, fully-crystalline gate oxide layer after tens of seconds? expo-
sure. Faster rates of crystallization using a 100-keV electron beam indicated that an
ionization-induced atomic rearrangement mechanism is the probable origin of this
phenomenon, which is likely to alter the electronic properties of the device.
5.1.2 Nanocarbon-metal composites (Covetics)
The goal of covetics development is to utilize the superior properties of nanos-
tructured carbon to enhance the bulk properties of widely used metals such as alu-
minum alloys, ultimately leading to industrial efficiency gains in terms of reduced
resistive losses and lower material usage. This thesis has sought to explore covetic
Al composites from both experimental and theoretical angles in order to capture the
full range of possibilities presented by a technology which remains far from maturity.
Structure-property relationships in covetics were investigated experimentally
using progressively smaller-scale spectroscopy methods. Raman spectroscopy was
used to determine the carbon distribution and degree of ordering on length scales of
microns to millimeters. Raman spectrum images comprising hundreds to thousands
of individual spectra indicated that graphitic ordering consistently occurred after
exposures to concentrated direct current above critical thresholds of current density
and duration. Graphitic crystallite size, La, was estimated from the integrated
150
intensity ratios of the G (graphitic) to the D (disorder) peaks in the Raman spectra
and compared to the ratio in the activated carbon used as source. The average value
of La was directly related to the duration of applied current. Compilation of over
1000 spectra per sample revealed that the La distribution became asymmetric after
the covetics reaction, which is a clear indication that the applied current had played a
role in the ordering of graphitic crystallites embedded in the Al matrix. Inspection of
the Raman 2D peak strongly associated with layered graphitic structures indicated
that between 3?10 layers of graphene were typically stacked together.
TEM investigation of several Al covetic samples in Sec. 4.2 revealed significant
variability in the structure and distribution of carbon within the metal matrix. Two
main types of structure were identified: graphitic inclusions on the length scale of
microns to tens of microns, and thin, narrow aligned graphene ribbons tens of nm
wide and several microns in length. The thicker inclusions generally exhibited an
interfacial oxide region between C and Al on the order of 100 nm wide, which would
be detrimental for bulk conductivity and tensile strength and most likely prevented
the carbon from extending into the Al matrix surrounding these areas. Conversely,
graphitic ribbons were well integrated in the metal matrix, spanning between grains
with minimal separation or oxidation, and are the most likely to lead to enhanced
bulk conductivity in these structures.
The magnitude of property enhancement that a covetic composite may provide
constituted an important knowledge gap at the start of this work. This thesis sought
to develop more quantitative modeling approaches for the prediction and engineer-
ing of electrical conductivity in nanocarbon-metal composites. Using a quantum
151
mechanical model, graphene nanoribbons embedded in Al were estimated to con-
tribute a locally enhanced conductivity at the Al/C interface. An effective-medium
model was used to predict the effect of this enhancement on a bulk Al composite
with randomly oriented graphene nanoribbons as a function of the ribbon geome-
try and the C volume fraction. Wide, thin ribbons contribute most efficiently to
the conductivity enhancement, up to several percent relative increase per volume
percent of C.
5.2 Recommendations for future work
5.2.1 Wide-bandgap MOS interfaces
Further investigation will be necessary to image the nanostructure of the ?-
Ga2O3/amorphous Al2O3 system prior to initial crystallization, because even the
moderate electron doses and accelerating voltages used for structure determination
in this work were sufficient to initiate the crystalline transformation. The tech-
niques of high-speed electron microscopy will be useful for this purpose. There are
broadly two categories of high-speed techniques, each facilitated by laser-induced
photoemission: single-shot or dynamic TEM (DTEM) and stroboscopic or ultrafast
TEM (UTEM) [177]. The former generates an intense pulse of ? 109 electrons on a
timescale of nanoseconds, which is suitable to capture irreversible processes such as
microstructure evolution or crystallization in conjunction with a fast image-capture
system. In the case of beam-induced crystallization the primary advantage is that,
unlike conventional in-situ imaging, the illumination does not need to be continu-
152
ous and the total electron exposure necessary to capture an image may be reduced.
High-speed EM techniques offer a potential solution to the difficulties encountered
in this work of imaging the interface structure as-fabricated, without altering it
through excessive exposure to the electron beam.
5.2.2 Nanocarbon-metal composites
A range of different covetic micro- and nanostructures were observed in the
course of this work. Uncertainty remains regarding when and how certain features
emerge, and the ability to control the composite structure will be essential to cov-
etics? commercialization. With regard to fabrication, it would be worthwhile to
investigate ways to eliminate the interfacial aluminum oxide between C and Al,
for instance by preparing samples in an oxygen-free environment. Greater control
over the graphitic nanostructure will also be desirable in order to increase the con-
centration of graphene nanoribbons and sheets, and avoid trapping large graphitic
clusters in the matrix. Potential for improvement exists with regard to more uni-
form, higher-speed mixing of the melt and bubbling of inert gas to remove oxygen
and eliminate void formation; these are topics of active research at the time of this
writing. Additionally, the wetting behavior between molten Al and graphitic C is
known to be poor [178, 179]; the potential for alloy-compatible additives such as
Cu or Ni to increase contact between the matrix and inclusions in covetics would
be worthy of further investigation. There are several broader directions in which
covetics research and development may be extended. Other metals? potential as
153
covetics have not been studied as thoroughly as Al; elemental Cu and Ag are better
electrical conductors which have also been demonstrated as covetics. It would be
worthwhile to investigate the processing, structure and performance of Cu- and Ag-
carbon composites in order to validate and build upon the findings in this project.
Furthermore, Cu is of particular importance for microelectronic interconnects, where
continual reductions in component size?without loss of performance?are essential
to facilitate continued development of advanced semiconductor technologies.
154
Appendix A: Measurement of electron-beam currents in the field-
emission TEM
In order to quantify the effect of the electron beam on the crystallization of the
gate oxide, it was necessary to estimate the total current imparted by the beam to the
specimen, including backscattered electrons and accounting for any systematic error
in the current density reported from the fluorescent screen. Neither the TEM nor
the specimen holder in this work were equipped with a Faraday cup to measure the
current directly. However, it was possible to make a series of accurate beam current
measurements using the drift tube of the Gatan Imaging Filter (GIF) in conjunction
with an external picoammeter, as described by Mitchell and Nancarrow [180].
A.1 Approach
Following this method, the magnetic prism was switched off so that electrons
reaching the bottom of the TEM column, which would strike the screen or CCD
to form images, instead struck the wall of the drift tube. The resulting electric
current was captured by a safe high voltage (SHV) cable ordinarily leading from
the drift tube to the GIF power supply. For these measurements, the SHV cable
from the GIF was connected directly to a Keithley electrometer (Model 617) with
155
Figure A.1: The safe high voltage (SHV) cable leading from the EEL spectrometer drift
tube, originally connected to the GIF power supply (left), was connected to a Keithley
electrometer (right) to measure the total electron beam current incident on the wall of the
drift tube with pA sensitivity.
pA resolution by means of a custom-built SHV-BNC adapter. A photograph of the
equipment used appears in Fig. A.1.
Electron beam currents were measured for a range of conventional TEM-mode
conditions. The variables most commonly used to change the beam current are the
choice of condenser lens aperture (CLA), from 1 (largest) to 3 (the smallest typically
used; CLA 4 is the smallest available), and spot size (?Spot?), ranging from 1 (larger
fully-converged spot) to 5 (smaller) [181]. Magnification was not expected to affect
the total current, and measurements were taken at 40 kx and 200 kx to confirm that
this was in fact the case.
For each condition, measurements were first taken at the drift tube by the
electrometer, with the beam fully converged, after allowing a few seconds for the
reading to stabilize (a precaution to minimize the influence of the drift tube capaci-
tance [180]). The beam was then spread to about 60 % of the screen diameter, and
156
Figure A.2: Measurements of total TEM beam current collected using the EELS drift
tube and picoammeter for a range of conventional TEM-mode conditions (CLA 1?3, Spot
size 1?5, and Mag. 40 and 200 kx.) Systematically lower current readings using CLA 1
at 200 kx are attributed to the 5-mm GIF entrance aperture blocking part of the beam
at the higher magnification. Good agreement between the 40- and 200-kx measurements
using the smaller CL apertures 2 and 3 means that the magnification had no meaningful
influence on the total beam current.
the screen current density was recorded from the JEOL operation software. Data
from these measurements are shown in Fig. A.2 and Fig. A.3, respectively.
The 5-mm diameter of the GIF entrance aperture was a known limitation,
which in certain cases led to discrepancies; notably, current readings using CLA 1
at 200 kx were systematically lower than those taken at 40 kx, a deviation which
did not occur for the smaller CL apertures. It was found during the experiment
that the beam would not converge to as small a physical spot at 200 kx than at 40
kx, so the 200-kx values are systematically low, probably due to some blocking of
the beam by the GIF aperture. Therefore, the 40-kx measurements are considered
more accurate. Using CLA 2 and 3, 40- and 200-kx measurements agreed very
well, so the magnification did not appear to affect the total current, as expected.
157
Figure A.3: Beam current densities reported by the phosphorescent large screen, when
the beam was spread to about 12 cm diameter. Readings at 200 kx (upper red curve)
were systematically higher than at 40 kx (lower blue curve), typically by a magnitude
comparable to the precision of the measurement (i.e. the margin of error, ?0.1 pA/cm2).
158
Measurements of the screen current density (Fig. A.3) showed slightly larger values
at 200 kx than at 40 kx, but the magnitude of deviation was comparable to or less
than the precision of the measurement (i.e. the margin of error, ?0.1 pA/cm2).
For the purpose of the beam-induced crystallization experiments described
in Sec. 3.2.2, direct measurements of the current density at the EELS drift tube
were the most useful thanks to the high precision of the picoammeter, once it was
confirmed that magnification did not affect the total current. These measurements
were repeated for both 100 kV and 200 kV conditions.
A.2 Estimating the electron dose rate on the specimen
Total current measurements were used to estimate specimen current densities
on ?-Ga2O3/Al2O3 lamellas introduced in Sec. 3.2.2. This was done by relating
the known width of the deposited gate oxide layer, which was consistent within
each sample, to the diameter of the beam on the phosphor screen. The approach
is demonstrated in Fig. A.4 for the lower-intensity 100-keV case. In general it was
not possible to see the extent of the beam on TEM images, due to magnification
inherent in the CCD image-capture optics (this condition is suitable for imaging in
conventional TEM mode where a broad parallel beam is desired). In order to obtain
the beam diameter and convert the drift-tube current measurements to an incident
current density on the specimen, the beam was converged so that its diameter would
match that of the large phosphor screen (Fig. A.4(b)). After optically photographing
the beam on the screen?off-axis, due to the angle of the viewing window?and
159
(b)
Al2O3
Ga2O3 Al Protective W cap
(a) m813 n
Ga2O3 Al2O3 Al
38 nm 38 nm
Figure A.4: (a) In the TEM image the CCD viewing range is significantly smaller than
the beam diameter under typical intensities and exposures, which is normally desirable
to provide uniform illumination, however the beam size is not apparent. (b) Comparison
of the gate oxide width (38 ? 2 nm) in the TEM image with the image on the phosphor
screen provided an estimate of the beam diameter (813 ? 43 nm) once the beam was
converged to exactly fill the screen. The thin vertical white lines defining the width of the
gate oxide film served as guides for the eye during image post-processing while adjusting
the image perspective to be in parallel with the beam, normal to the screen.
adjusting the perspective of the image to make the beam circular via digital post-
processing, it was simple to measure the beam diameter as a multiple of the width
of the gate oxide (38 nm). Due to the diffusion which occurred between Ga and Al
from the substrate and gate oxide, respectively, the interface had a transition width
of some 3?5 nm as discussed in Sec. 3.2.1, which translated to an uncertainty in the
width of the gate oxide imaged by HRTEM of about 2 nm, a relative uncertainty of
5.3 %. Therefore, a best estimate of the beam diameter in Fig. A.4 was 813?43 nm.
160
Appendix B: Publications and presentations related to this work
Publications
1. C. Shumeyko, X. Ge, C. Klingshirn, L. Salamanca-Riba, D. Cole, ?Tun-
able mechanical behavior of graphene nanoribbon-metal composites fabricated
through an electrocharge-assisted process,? Materials Science & Engineering
A 800, 140289 (2021) [145]
2. C. Klingshirn, A. Jayawardena, S. Dhar, R. Ramamurthy, D. Morisette, Z.
Warecki, J. Cumings, T. Zheleva, A. Lelis, L. Salamanca-Riba, ?Electron
beam-induced crystallization of Al2O3 gate oxide on ?-Ga2O3,? Micron 140,
102954 (2021) [182]
3. X. Ge, C. Klingshirn, M. Morales, M. Wuttig, O. Rabin, C.M. Shumeyko, D.P.
Cole, S. Zhang, and L.G. Salamanca-Riba, ?High Electrical Conductivity of
Nano-Carbon-Aluminum Composites,? Carbon, Carbon 173, 115 (2021) [140]
4. C. Klingshirn, A. Jayawardena, S. Dhar, R. Ramamurthy, D. Morisette, T.
Zheleva, A. Lelis, L. Salamanca-Riba, ?Analytical Electron Microscopy of
Ga2O3/SiO2 and Ga2O3/Al2O3 Interface Structures in MOS Devices,? in prepa-
ration (2020)
161
5. X. Ge, C. Klingshirn, M. Wuttig, K. Gaskell, P.Y. Zavalij, Y. Liang, C.M.
Shumeyko, D.P. Cole, and L.G. Salamanca-Riba, ?Mechanism studies and fab-
rication for the incorporation of carbon into Al alloys by the electro-charging
assisted process,? Carbon 149, 203 (2019) [156]
6. U. Balachandran, S. Dorris, B. Ma, T. Lee, D. Forrest, and C. Klingshirn.
Electrodes for making nanocarbon-infused metals and alloys. Provisional US
Patent No. US20200176573A1 (2018)
7. J.A. Taillon, C.J. Klingshirn, C. Jiao, Y. Zheng, S. Dhar, T.S. Zheleva, A.J.
Lelis, and L.G. Salamanca-Riba, ?Analysis of the electronic and chemical
structure in, boron and phosphorus passivated 4H-SiC/SiO2 interfaces using
HRTEM and EELS,? Applied Physics Letters 113 (2018) [99]
Conference presentations
1. ?Modeling the Effective Electrical Conductivity of Nanocarbon-Metal Com-
posites Made by the Electrocharging Assisted Process, accepted to the Mate-
rials Research Society Joint Spring/Fall Meeting, Virtual, Nov. 2020
2. ?Effective electrical conductivity of nanocarbon-metal composites made by the
electrocharging assisted process,? accepted to the American Physical Society
March Meeting, Denver, USA, Mar. 2020.
162
3. ?TEM Investigation of Local Mechanical Behavior in Nanocarbon-Aluminum
Composites Made by the Electrocharging Assisted Process,? Materials Re-
search Society Fall Meeting, Boston, USA, Dec. 2019 (Poster)
4. ?Analytical TEM-EELS and Raman Spectroscopy of Nanocarbon-Al Com-
posites Made by the Electrocharging Assisted Process,? Materials Research
Society Fall Meeting, Boston, USA, Nov. 2018 (Poster)
5. ?TEM-EELS Analysis of Ga2O3/SiO2 and Ga2O3/Al2O3 Interface Structures
with Electron Beam Induced Crystallization of Al2O3 Gate Layer,? Materials
Research Society Fall Meeting, Boston, USA, Nov. 2018
6. ?Analytical Electron Microscopy of Antimony Doped 4H-SiC/SiO2 and 4H-
SiC/Boron and Phosphorus Doped SiO2 Interface Structures in MOS Devices,?
American Physical Society March Meeting, Los Angeles, USA, Mar. 2018.
7. ?Sub-Nanometer Mapping of Boron-Passivated 4H-SiC/SiO2 Interfaces by An-
alytical Electron Microscopy,? Infineon Winter School, Villach, Austria, Feb.
2018.
8. ?Analytical Electron Microscopy of Ga2O3/SiO2 and Ga2O3/Al2O3 Interface
Structures in MOS Devices,? Materials Research Society Fall Meeting, Boston,
USA, Dec. 2017.
9. ?EELS Characterization of 4H-SiC/Oxide Interfaces,? SiC MOS Program Re-
view, College Park, USA, Aug. 2017.
163
10. ?In-situ analysis of catalyst nanoparticle growth using hot-stage transmission
electron microscopy,? DAAD Research Internships in Science & Engineering
(RISE) Scholars? Meeting, Heidelberg, Germany, Jul. 2017.
11. ?TEM-EELS Investigation of Boron and Phosphorus Passivated 4H-SiC/SiO2
Interface Structures,? American Physical Society March Meeting, New Or-
leans, USA, Mar. 2017.
12. ?Raman Spectroscopy of High-Carbon Al Covetic Alloys,? Materials Research
Society Fall Meeting, Boston, USA, Nov. 2016 (Poster)
164
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