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Applied Surface Science
journal homepage: www.elsevier.com/locate/apsusc
Full length article
Fluence and thermal threshold for an effective self-healing in
high-energy-neutron-irradiated Al2O3/QFS-graphene/6H-SiC(0001) system
Semir El-Ahmar a,∗, Jakub Jagiełło b, Maciej J. Szary a, Wiktoria Reddig a, Artur Dobrowolski b,
Rafał Prokopowicz c, Maciej Ziemba c, Tymoteusz Ciuk b
aInstitute of Physics, Poznan University of Technology, Piotrowo 3, 61-138 Poznan, Poland
bŁukasiewicz Research Network - Institute of Microelectronics and Photonics, Aleja Lotników 32/46, 02-668 Warsaw, Poland
cNational Centre for Nuclear Research, 05-400 Otwock, Poland
ARTICLE INFO
Keywords:
Graphene
Epitaxy
Silicon carbide
Hydrogen intercalation
Quasi-free-standing
Neutron irradiation
Radiation-resistant materials
Self-healing effects
ABSTRACT
This article reveals a unique self-healing ability of the amorphous-aluminum-oxide-passivated p-type hydrogen-
intercalated quasi-free-standing epitaxial Chemical Vapor Deposition graphene on semi-insulating vanadium-
compensated nominally on-axis 6H-SiC(0001) system, exposed for 166 h to a destructive flux of 3.3 ×
1011 cm−2s−1of mostly fast-neutrons (1–2 MeV), resulting in an accumulated fluence of 2.0 ×1017 cm−2. Post-
irradiation room-temperature Hall effect characterization proves that the a-Al2O3/QFS-graphene/6H-SiC(0001)
is n-type, which implies the loss of the quasi-free-standing character of graphene and likely damage to
the SiC(0001)-saturating hydrogen layer. Micro-Raman spectroscopy suggests an average defect density in
graphene of 𝑛𝐷= 3.1 ×1010 cm−2with an 𝐿𝐷= 32-nm inter-defect distance. Yet, a thermal treatment up to
623 K eliminates defect-related Raman peaks and restores the original p-type conductance. At the same time,
623 K is not enough to recover the initial transport properties in a sample irradiated for 245 h with a total
fluence of 2.0 ×1018 cm−2. A Density Functional Theory model explains the self-healing phenomenon and
restoration of the quasi-free-standing properties through thermally-activated lateral diffusion of the remaining
population of hydrogen atoms and re-decoupling of the graphene sheet from the SiC(0001) surface. The thermal
regime of 623 K fits perfectly into the operational limits of the a-Al2O3/QFS-graphene/6H-SiC(0001) system,
defined as 300 K to 770 K. The finding constitutes a milestone for two-dimensional, graphene-based diagnostic
and control systems designed for operation in extreme environments.
1. Introduction
The two-dimensional (2D) crystal structure of graphene underlies
its unique functional properties. A carbon allotrope with a monoatomic
thickness, recognized by many as one of the most promising materials
for high-mobility electronics [1–3], has qualities enabling it to operate
in harsh environments [4–8]. Literature reports on the irradiation of
graphene with ions, protons, or electrons [9–11], as well as on theoret-
ical [12] and experimental [13] investigations into the generation of
defects in graphene through neutron radiation (NR).
Graphene may be an excellent active material for high-temperature
magnetic diagnostics [14] in future nuclear energy facilities. A revo-
lutionary step will be to launch the first thermonuclear reactor and
answer humanity’s quest for affordable and clean energy. Over time,
it may contribute to solving the energetic crisis on a global scale [15].
New materials that meet the emerging requirements of plasma
control in tokamak-type fusion reactors are increasingly desirable, as
∗Corresponding author.
E-mail address: semir.el-ahmar@put.poznan.pl (S. El-Ahmar).
changes in the toroidal magnetic field in DEMO-class reactors [16,17]
are about to be monitored with Hall effect sensors operating at 473 K
(ex-vessel position) and up to 773 K (in-vessel position). The temper-
ature hazard comes with exposure to fast-neutron radiation [18] with
a total accumulated dose of 1016 - 1018 cm-2 in ex-vessel zones, 1020 -
1022 cm-2 in intermediate locations, and 1021 - 1022 cm-2 in zones of
maximum fluence. Specifically, 80% of D–T (deuterium–tritium) fusion
energy radiates as neutrons [19]. They are the energy carriers and the
main threat to functional materials. The latest developments in that
field focus mainly on thin layers and nanofilms of metals, semi-metals,
or compound semiconductors [20–23].
The extraordinary resistance of graphene to a stream of electrons,
protons, ions, or neutrons originates from the low probability of colli-
sions of the bombarding particles with atoms of its 2D structure [12].
However, experimental research on the impact of NR on graphene
is scarce due to the necessity of carrying out an extremely invasive
https://doi.org/10.1016/j.apsusc.2024.161953
Received 7 October 2024; Received in revised form 18 November 2024; Accepted 26 November 2024
Applied Surface Science 685 (2025) 161953
Available online 3 December 2024
0169-4332/© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (
http://creativecommons.org/licenses/by/4.0/ ).
S. El-Ahmar et al.
procedure requiring a nuclear reactor as the neutron generator and
prolonged exposures (hundreds and thousands of hours) to emulate the
fusional doses. Nevertheless, the limited susceptibility of graphene to
NR has already been pointed out [13,24,25].
Over the last decade, technology for the epitaxy of graphene has
intensively developed, clarifying two competing trends. These are epi-
taxy by sublimation of the top-most silicon atoms from the SiC(0001)
surface [26–28] and epitaxy through Chemical Vapor Deposition (CVD)
from a gaseous carbon source under conditions inhibiting sublimation
from SiC(0001) [29–32]. In the context of practical verification in the
detection of magnetic fields [33], novel amorphous-Al2O3-passivated
(a-Al2O3) structures made of fully-hydrogen-intercalated quasi-free-
standing (QFS) CVD graphene on a semi-insulating SiC(0001) sub-
strate (QFS-GR@SiC) have demonstrated remarkable thermal stability
assessed from room temperature (RT) up to 770 K [6,7,14,34,35].
Various substrates and techniques for producing graphene-based
structures herald its promising resistance to neutron radiation [36–38].
Yet, no reports indicate a complete radiation resistance of graphene,
regardless of the system in which it operates. Still, the low suscep-
tibility of 2D materials to harmful radiation does not necessarily de-
fine their most critical feature from the perspective of extreme envi-
ronments. Radiation-damaged graphene systems exhibit reconstructive
abilities, which grant them the next level of functionality, significantly
increasing their application potential.
The self-healing of graphene due to the recombination of mobile
carbon adatoms with vacancies is already a known phenomenon [39].
Self-healing is regularly discussed for various graphene-based materi-
als, mainly composites [40], including electronic applications [41–43].
What has not yet been demonstrated experimentally is that radiation
damage caused by high-energy neutrons can also be self-healed by a
relatively low-temperature thermal factor. However, this ability is not
unlimited and requires a precise definition of the conditions for its
occurrence.
This work reveals the self-repair abilities of a-Al2O3/QFS-GR@SiC ,
which we shall denote as effective self-healing. We attribute this term to
the unique property of restoring the QFS properties of the system ex-
posed to high-energy neutrons with a total fluence (dose) of 2.0 ×1017
cm-2, followed by a sequential temperature treatment in the 423 K -
623 K range. The post-NR investigations of the system are performed
for the first time using a semi-insulating vanadium-compensated nom-
inally on-axis 6H-SiC(0001) substrate, previously suggested for appli-
cation in high-temperature Hall effect sensors with a record-breaking
current-mode sensitivity as compared to its metallic counterparts [34].
The analysis enables one to determine a temperature threshold for
effective self-healing in a-Al2O3/QFS-GR@SiC , also from the stand-
point of the received radiation. The MARIA research nuclear reactor
provided the destructive high-energy neutrons. The structural and elec-
tronic properties of the system are investigated ex-situ using micro-
Raman spectroscopy in combination with variable-temperature (VT)
Hall effect investigation. Finally, density functional theory computa-
tions (DFT) are applied to explain the phenomenon by temperature-
triggered lateral diffusion of the remaining population of hydrogen
atoms.
2. Materials and methods
2.1. Fabrication of the a-Al2O3/QFS-GR@SiC structures
The test elements were manufactured using graphene-on-SiC tech-
nology [32] under the geometry and type available with the GET®
platform [44]. Each of the structures was a 1.4 mm ×1.4 mm four-
terminal van der Pauw device [34] featuring an oxygen-plasma-etched,
equal-arm, cross-shaped 100-μm ×300-μm QFS graphene mesa [45],
electron-beam-deposited Ti/Au (10 nm/110 nm) current feed and
voltage readout contacts, and a 100-nm-thick, atomic-layer-deposited,
Fig. 1. (a) Top-view Nomarski interference contrast optical image of the a-Al2O3/QFS-
GR@SiC element implementation. (b) Schematic of pre-irradiation fully hydrogen-
intercalated quasi-free-standing graphene on on-axis 6H-SiC(0001). (c) Schematic of the
high-energy neutron irradiation experiment. (d) Schematic of post-irradiation epitaxial
graphene on on-axis 6H-SiC(0001).
amorphous, non-stoichiometric, oxygen-deficient [46] Al2O3encap-
sulation [47,48]. The graphene was transfer-free, in-situ fully [49]
hydrogen-intercalated [50,51] at 1273 K (therefore quasi-free-standing
and p-type), and epitaxial Chemical Vapor Deposition [30,31]. It was
grown on an as-purchased, non-modified [7] semi-insulating, vanadium-
compensated, nominally on-axis 6H-SiC(0001) (II-VI, Inc.), using ther-
mally decomposed propane as the carbon-sourcing gas [29,52]. An
optical top-view of the structure, along with a schematic of the irra-
diation experiment and its effect on the QFS graphene structure along
with the hydrogen layer (Si-H bond [32]), is presented in Fig. 1.
2.2. Fast-neutron irradiation experiment
Neutron irradiation was carried out in the MARIA research-grade
nuclear reactor operated by the Polish National Centre for Nuclear
Research. The reactor’s capabilities are described in Ref. [53]. The a-
Al2O3/QFS-GR@SiC test elements intended for irradiation were placed
in a container in one of the channels of the MARIA reactor. Since
fusion neutrons from D-D (deuterium atoms) or D–T (deuterium and
tritium) reactions are fast neutrons, i.e., 2.5 MeV and 14.1 MeV, respec-
tively [18], the original reactor spectrum was high-pass-filtered [38] so
that the maximum of the neutron flux was at 1–2 MeV and most reliably
emulated the target operational conditions. An appropriate location
near the reactor core guaranteed the samples were exposed to a fluence
of 2.0 ×1017 cm-2 and 2.0 ×1018 cm-2.
The irradiation process lasted 166 h and 245 h to achieve the
fluences of 2.0 ×1017 cm-2 and 2.0 ×1018 cm-2, respectively. The
reactor was operating at 20.8 MW and 18.9 MW. Fig. 1(c) and (d)
show the idea of irradiating the a-Al2O3/QFS-GR@SiC structure and the
possible radiation disruption of its interface. After the experiment, the
irradiated material was held outside the reactor core for several months
to allow deactivation, after which the a-Al2O3/QFS-GR@SiC elements
were safely recovered and ex-situ investigated.
2.3. Framework of the experiment
For the experiment, four a-Al2O3/QFS-GR@SiC elements were pre-
pared according to the procedure described in Section 2.1.Table 1
summarizes the assignment of the samples to the planned activities.
The samples were labeled REF, F01, F02, and F03. The REF sample
is a reference for the Raman analysis. Samples F01 and F02 were
subject to a fast-neutron fluence of 2.0 ×1017 cm-2, of which F01 was
investigated only at room temperature (micro-Raman), while the F02
underwent a complete thermal treatment with simultaneous measure-
ment of the Hall effect. The F03 sample was irradiated with a fluence of
2.0 ×1018 cm-2 and then underwent the complete thermal procedure
with a simultaneous Hall effect measurement but without a subsequent
Raman analysis.
Applied Surface Science 685 (2025) 161953
2
S. El-Ahmar et al.
Table 1
Sample allocation schedule for the individual experiments.
Sample Neutron irradiation Variable-temp. Hall Micro-Raman
REF × × ✓
F01 2.0 ×1017 cm−2×✓
F02 2.0 ×1017 cm−2RT - 623 K✓
F03 2.0 ×1018 cm−2RT - 623 K×
Fig. 2. Schematic visualization of the symptoms of effective self-healing (orange dashed
line) of initially p-type hydrogen-intercalated quasi-free-standing graphene, turned n-
type after high-energy neutron irradiation, and recovered p-type through thermal
treatment. The vertical asymptote defines the characteristic temperature at which
densities of opposite charge carriers equalize, thus minimizing the Hall voltage and
maximizing the calculated charge carrier concentration, all within the constraints of a
single-carrier model.
2.3.1. Variable-temperature hall effect characterization
The pre-irradiation room-temperature (RT) characterization and the
post-irradiation variable-temperature (VT) characterization of the a-
Al2O3/QFS-GR@SiC elements were carried out under 𝐼= 1 mA direct
current bias in an 0.65 T LINSEIS HCS-1 automated Hall effect mea-
surement system operating van der Pauw formulae and a single-carrier
transport model.
VT measurements were performed according to a strictly adopted
procedure, which we developed and used when discussing the first
experimental results [13], as well as during pre-NR high-temperature
measurements [35]. The post-NR temperature procedure is divided into
five subsequent cycles, each combined with annealing at the indicated
maximum temperature. The maximum temperature of each subsequent
temperature cycle is 50 K higher than the previous one, starting from
423 K and up to 623 K.
Since it was anticipated that the neutron irradiation may affect the
QFS character and the charge carrier type of the system and opposite,
the VT treatment may partially restore its original properties, symptoms
of a possible effective self-healing were defined. It was reasoned that
a thermally-triggered shift from one type of conductivity to another
shall be a gradual process, transiting from asingle-carrier model to a
double-carrier one and then back to a single-carrier one but of opposite
sign.
In a single-carrier transport model, like the one implemented in the
LINSEIS HCS-1 system, the transition shall be marked by a vertical
asymptote on the charge carrier density chart indicating a charac-
teristic temperature, at which densities of opposite carriers equalize
and minimize the Hall voltage, thus maximizing the calculated carrier
concentration. For these reasons, the manifestation of an asymptotic
line was arbitrarily chosen as a symptom of an effective self-healing
process (Fig. 2).
2.3.2. Micro-Raman spectroscopy
The pre-irradiation and post-irradiation room-temperature analysis
of the graphene-related D, G, and 2D modes was carried out with a Ren-
ishaw InVia Raman spectrometer equipped with the 532 nm (2.33 eV)
line of an Nd:YAG laser and an Andor Newton detector. The laser beam
was projected onto the test samples through a 100×objective, and the
active modes were fitted with a mixture of Gaussian and Lorentzian line
shapes. To enhance the statistical perspective and form data clouds,
20 μm × 20 μm 0.5-μm-step, 1681-point Raman maps were collected,
each in a corresponding relative location, i.e., in the center of the QFS-
graphene cross-shaped active region, but in consecutive structures. To
separate graphene modes from the second-order SiC modes, 20 μm ×
20 μm 2.0-μm-step, 121-point reference Raman maps were collected
outside the graphene mesa for each sensor. The background subtraction
procedure was carried out individually for each sensor.
2.3.3. Density functional theory calculations
The material modeling of QFS graphene was executed using a two-
dimensional periodic slab model with approximately 20 Å of vacuum
along the [0001] direction. This model featured a 5×5 graphene sheet
positioned atop an eight-layer SiC(0001) slab, resulting in a minimal
lattice constant mismatch of 0.5%. The density functional theory (DFT)
calculations were carried out with plane waves, pseudopotentials, and
the projector-augmented wave (PAW) method, all implemented within
the Quantum ESPRESSO software package [54–56].
Scalar-relativistic pseudopotentials with nonlinear core corrections
were utilized. The cutoff energies for the plane wave basis set were
50 Ry for the wave functions and 400 Ry for the electron density.
The Brillouin zone sampling of the supercell was performed using
a 4×4×1 Monkhorst–Pack grid [57]. Extensive testing was per-
formed to determine the optimal cutoff energies and k-point grids, with
higher values showing negligible effects on the properties of interest.
For the electron exchange–correlation functional, the Perdew–Burke–
Ernzerhof (PBE) approximation was used [58]. Additionally, Grimme’s
D3 method [59] was utilized to treat the vdW contributions to the
total energy. The nudged elastic band (NEB) method with a climbing
image scheme was employed to estimate energy barriers and the lowest
energy pathways for hydrogen diffusion.
3. Results and discussion
The neutron irradiation with a specific spectrum, energy, and flux
can penetrate the a-Al2O3/QFS-GR@SiC , causing graphene to lose its
QFS properties to some extent. To verify its potential to self-heal and
to assess the fluence-related and thermal thresholds, one shall measure
the Hall effect in irradiated test structures under variable temperature
conditions. This method allows us to collect general information on the
impact of NR on the distribution and flow of charge carriers. These, in
turn, identify the deterioration or improvement of the QFS graphene
properties within the a-Al2O3/QFS-GR@SiC system.
Pre-irradiation Hall effect characterization confirmed that the ma-
terial is p-type, with the hole density 𝑝6𝐻
𝑆determined by the double
polarization mechanism [46] of the substrate-related positive polariza-
tion [60], quantified by vector 𝑃6𝐻
0=−1.2 ×10-2 C/m2[61], and
the negative effect of the a-Al2O3passivation [46], fixing the 𝑝6𝐻
𝑆
at approximately +4.6 ×1012 cm-2, in agreement with our historical
experience [34].
Going deeper into the analysis, the micro-Raman investigation per-
formed on samples subjected to a limit fluence allows us to identify
the improvement in the quality of the a-Al2O3/QFS-GR@SiC structure
by comparing the results before and after thermal treatment. Finally,
numerical methods allowed us to attribute the observed changes to
specific physico-chemical effects.
Applied Surface Science 685 (2025) 161953
3
S. El-Ahmar et al.
Fig. 3. Pre-irradiation (star-shaped points) and post-irradiation (triangular points)
room-temperature (light blue) and varying-temperature (purple to red) Hall effect
investigation of the basic transport properties of the a-Al2O3/QFS-GR@SiC system.
3.1. Variable-temperature Hall effect analysis
Fig. 3is a graphical representation of the influence of the neutron
fluence of 2.0 × 1017 cm-2 and 2.0 × 1018 cm-2 , and the temperature
on QFS-graphene-related sheet density of charge carriers (𝑛𝑆), their
mobility (μ), and sheet resistance (𝑅𝑆). The scales of corresponding
parameters were unified to maintain greater transparency of the com-
bined results. Each subplot contains a vertical dashed line pointing to
the moment of irradiation. The points marked with a light blue star
refer to pre-NR properties. The remaining triangular points illustrate
the course of the post-NR temperature treatment.
The determined values of charge carrier densities and their mobili-
ties have conventional positive and negative values and are calculated
assuming a single-carrier model. Their sign stems from the Hall-effect-
based identification of the majority charge carriers that define the type
of conductivity in the system. The change in the electrical parameters of
the F02 and F03 test elements after irradiation, relative to their values
before NR, indicates several regularities and a trend strictly dependent
on the radiation fluence.
The p-type conductance, typical for the a-Al2O3/QFS-GR@SiC ,
shifted to n-type conductance with carrier density of −4×1012 cm-2
and −7×1012 cm-2, respectively, for the 2.0 × 1017 cm−2 and the 2.0 ×
1018 cm−2 doses. The resultant electron mobilities proved −460 cm2/V s
and −185 cm2/V s, respectively. The sheet resistance rose by 88% and
245% for the two fluences, respectively.
Analyzing the neutron dose of 2.0 × 1017 cm−2, the electron den-
sity increases with subsequent steps of temperature cycles, as seen
in Fig. 3(a). After cycles up to the upper limit of 523 K, it reaches
−2×1013 cm−2. Further cycling changed the observed downward
trend. After annealing at 573 K, the value of 𝑛𝑆became positive,
Table 2
Summary of charge carrier density in the a-Al2O3/QFS-GR@SiC system, measured at
room temperature. The sign conventionally denotes holes (+) and electrons (−).
Sample Pre-irradiation (RT) Post-irradiation (RT) After 623 K (RT)
F02 +5.4 ×1012 cm−2−4.0 ×1012 cm−2+1.1 ×1013 cm−2
F03 +5.0 ×1012 cm−2−6.8 ×1012 cm−2−2.4 ×1013 cm−2
which can be associated with a shift from n-type to p-type conduc-
tivity (Fig. 3(a)). After the complete temperature treatment, the hole
concentration in the F02 sample approached +1 ×1013 cm-2. It was
accompanied by an increase in hole mobility, visible in Fig. 3(b), and
the resultant decrease in 𝑅𝑆(Fig. 3(c)). The last temperature cycle
repeated up to 623 K showed saturation of 𝑛𝑆and further improvement
of carrier mobility (with a decrease in 𝑅𝑆) and the maintenance of
the p-type character (Fig. 3(a,b,c)). This empirical observation fol-
lows all the expected symptoms of the n-type to p-type transition,
previously illustrated in Fig. 2. For these reasons, we declare this exper-
iment a full self-healing of the a-Al2O3/QFS-GR@SiC system exposed to
high-energy neutrons with a fluence of 2.0 × 1017 cm−2.
This finding reveals an exceptional property of QFS graphene,
putting it above thin-film/bulk systems in terms of applications in
radiation conditions. For comparison, in InSb thin-film/bulk systems
subjected to a fluence of 0.7 × 1018 cm−2 of high-energy neutrons, a
beneficial effect of temperature on their electrical parameters has been
noticed. Yet, no full self-healing has been recorded [38].
In sample F03 (fast-neutron fluence of 2.0 × 1018 cm−2), the thermal
dependencies look significantly different. Electron density maintains a
rising trend up to −2×1013 cm-2 throughout the entire temperature
procedure (Fig. 3(d)). This goes along with a steady reduction in
electron mobility (Fig. 3(e)) and an increase in 𝑅𝑆by 10 % compared
to the level before the thermal cycling (Fig. 3(f)). Yet, no symptoms of
self-healing occur, at least within the 623-K temperature range.
The variable-temperature Hall effect analysis of samples F02 and
F03 indicates that the fluence threshold for the self-healing effect below
623 K lies in the (0.2 − 2.0) × 1018 cm−2 range. The threshold is unlikely a
strict value; still, we assume it is closer to the lower limit of this range.
In the literature, there is only one investigation into the electrical
response of the a-Al2O3/QFS-GR@SiC system to fast neutrons at an in-
termediate dose between the green and red areas in Fig. 3. In Ref. [13],
El-Ahmar et al. considered the influence of the fluence of 0.7 × 1018 cm−2
on hydrogen-intercalated QFS graphene, epitaxially grown on semi-
insulating high-purity nominally on-axis 4H-SiC(0001) substrate. Hall
effect measurement indicated a drop in 𝜇after the irradiation by 42%.
While performing the HT procedure, it was possible to recover ∼ 10 %of
the initial value of μ, which indicated a tendency for self-regeneration
but not a full recovery of the transport parameters.
The results presented in Ref. [13] refer to test elements fabricated
on 4H-SiC(0001) rather than 6H-SiC(0001) substrates; therefore, they
cannot be directly compared to those presented in this work, as the
hexagonality of the SiC substrate plays a crucial role in determining the
transport parameters of QFS-GR@SiC. However, the results of Ref. [13]
may provide a guide for estimating the self-healing fluence threshold.
The complete recovery of transport parameters can only occur within a
relatively narrow fluence range, which does not significantly exceed
2.0 × 1017 cm−2. Exceeding this value three times causes a drastic
decrease in the effectiveness of self-healing. In turn, increasing the
fluence ten times (red part of Fig. 3) leads to a complete loss of the self-
healing ability of the a-Al2O3/QFS-GR@SiC system. A tabular summary
of the Hall effect analysis is presented in Tables 2and 3.
3.2. Micro-Raman spectroscopic analysis
We have also verified the phenomenon of a-Al2O3/QFS-GR@SiC sys-
tem self-healing presented above by VT Hall effect analysis from the
spectroscopic side. By performing a micro-Raman analysis, we can
Applied Surface Science 685 (2025) 161953
4
S. El-Ahmar et al.
Table 3
Summary of charge carrier mobility in the a-Al2O3/QFS-GR@SiC system, measured at
room temperature. The sign conventionally denotes holes (+) and electrons (-).
Sample Pre-irradiation (RT) Post-irradiation (RT) After 623 K (RT)
F02 +650 cm2/V s−460 cm2/V s+870 cm2/V s
F03 +876 cm2/V s−185 cm2/V s−49 cm2/V s
Fig. 4. (A) Averaged Raman spectra for the REF (referential), F01 (irradiated with
2.0 × 1017 cm−2 of fast-neutrons), and F02 (irradiated with 2.0 × 1017 cm−2 of fast-neutrons
and annealed) samples. (B) Surface defect concentration (black-edged squares) and the
D-to-G Raman mode intensity ratio (color filling of the black-edged squares). The green-
edged square indicates the number of neutrons per defect.
illustrate the direct impact of the temperature procedure on an irradi-
ated system (sample F02) and compare it with two reference systems:
the non-irradiated one (sample REF) and the irradiated one but not
thermally treated (sample F01).
By accurately analyzing the D, G, and 2D Raman modes of the QFS
graphene, we can determine the changes that have occurred during the
post-NR thermal treatment. Fig. 4(a) illustrates the averaged spectra
from the Raman maps. Immediately visible for the F01 sample (irra-
diated with 2.0 × 1017 cm−2 but not thermally cycled) spectrum is the
emergence of the D and D’ modes, which indicates defect formation
in the QFS graphene. The 𝐼𝐷∕𝐼𝐺mode intensity ratio is 0.13, which
suggests an average distance between defects 𝐿𝐷equal 32 nm and a
defect concentration 𝑛𝐷of 3.1 ×1010 cm-2 [62]. It takes approximately
6.5 million neutrons to create one defect in QFS graphene (Fig. 4(b)).
The results are consistent with an earlier experiment [13] where at a
neutron fluence 6.6 × 1017 cm−2 , the 𝐼𝐷∕𝐼𝐺mode intensity ratio was
0.15, and the average 𝐿𝐷equal 31 nm. Interestingly, the averaged
Raman spectrum of the F02 sample (irradiated with 2.0 × 1017 cm−2
and annealed) resembles the reference one (REF), and its defect density
drops to the referential value. Fitting the D mode is impossible as it is
at the noise level. Since the F02 sample had undergone irradiation and
post-irradiation annealing, the lack of the D band indicates that the
system has self-healed during the temperature treatment.
A detailed analysis of the position and Full Width at Half Maximum
(FWHM) of the Raman modes is presented in Fig. 5. As a result of
the fast neutron irradiation, the Raman modes of graphene undergo
broadening (F01 sample) due to the increased number of defects [63].
However, after the post-irradiation thermal treatment, the FWHM of G
and 2D modes are close to the reference value. This trend is also evident
in the position of the G and 2D modes. There is a significant change
after neutron irradiation, but the values come closer to the reference
after the temperature experiment.
The 1681-point 20 μm × 20 μm post-NR Raman map of the 2D
and G mode positions for each sample is presented in Fig. 6. The Lee
Fig. 5. Positions of the G and 2D Raman modes for the REF (referential), F01
(irradiated with 2.0 × 1017 cm−2 of fast-neutrons), and F02 (irradiated with 2.0 × 1017 cm−2
of fast-neutrons and annealed) samples. The filling color of the squares indicates the
corresponding width of the G and 2D Raman modes.
Fig. 6. Data cloud of the G and 2D band positions originating from the 20 μm ×
20 μm 1681-point Raman maps collected from a cross-shaped 100 μm × 300 μm
hydrogen-intercalated QFS epitaxial CVD graphene mesa on semi-insulating vanadium-
compensated on-axis 6H–SiC(0001). The points are plotted against Lee’s half-plane,
defining limits for p-doped single-layer micromechanically exfoliated graphene trans-
ferred onto a SiO2/Si substrate. The gray hexagon represents undoped and unstrained
graphene on SiO2/Si. The samples include the REF (referential), the F01 (irradiated
with 2.0 × 1017 cm−2 of fast-neutrons), and the F02 (irradiated with 2.0 × 1017 cm−2 of
fast-neutrons and annealed).
space was adjusted to the laser wavelength (532 nm) compared to the
original research [64]. Data clouds above the neutrality point indicate
a compressive strain [65]. REF and F02 data points scatter along a line
with a slope of 2.4 and 2.1, respectively. This slope corresponds to the
ratio of strain-induced shifts of the Raman G and 2D modes [64]. For
the F01 sample, there is a slight decrease in biaxial strain; however,
the data point slope of 1.8 suggests that in addition to changes in
strain, there are also changes in carrier concentration. The G mode
is much more sensitive to the changes of charge carrier concentration
than the 2D mode [66]. Therefore, a significant redshift of the G mode
position with a slight change in the 2D mode position and the increased
FWHM of the G and 2D modes after the fast neutron irradiation suggests
reduced hole doping [66,67]. The temperature treatment is followed
by a blueshift of the G and 2D modes towards reference values. The
blueshift and decreased FWHM of G and 2D modes are inconclusive for
the type of charge carriers [66,67]. Yet, juxtaposed with the electrical
results, the Raman analysis proves the self-healing property.
Applied Surface Science 685 (2025) 161953
5
S. El-Ahmar et al.
Fig. 7. (a) Model representation of the initial state of the interface, where, due to the
local loss of hydrogen intercalation, some of the carbon atoms in graphene bond with
the exposed silicon atoms of the SiC surface. (b, c) The model system after the surface
diffusion of hydrogen. (d) Energy barriers for the surface diffusion of a hydrogen atom,
as determined by NEB calculations, for the pathways from a→b and a→c.
3.3. Density functional theory-based explanation of the self-healing phe-
nomenon
High-energy radiation has a destructive impact on the material’s
crystal structure. However, the specific type of damage in a-Al2O3/QFS-
GR@SiC that leads to the changes in its electrical properties, as seen
in Fig. 3, and the subsequent self-healing induced by thermal treatment
remain unclear. There are likely several mechanisms through which
neutron radiation affects a-Al2O3/QFS-GR@SiC . However, a transition
from p-type to n-type doping in QFS graphene, while maintaining a low
defect density in the sheet, is generally associated with a partial loss
of hydrogen intercalation. This loss affects the electron accumulation
in the acceptor layer formed at the interface and exposes parts of the
SiC surface, compromising the chemical decoupling of graphene. This
change allows for the local formation of clusters of C-Si bonds at the
interface, particularly in areas where hydrogen termination is suffi-
ciently depleted. This reasoning agrees well with previous experimental
investigations on H intercalation of graphene in the 6H-SiC(0001)
system [68]. C-Si bonds clusters can be activated at temperatures below
400 K [49], resulting in an elevated electron doping of graphene, which
coincides with the initial effects of thermal treatment.
At higher temperatures, additional processes occur at the interface,
one of which is the surface diffusion of hydrogen atoms. Fig. 7sum-
marizes the results for modeling such a diffusion with a substantially
depleted intercalation. This model represents a good approximation for
effects occurring on parts of the surface with low hydrogen termination.
Fig. 7a illustrates the model representation of the initial state of the
interface, where, due to the local loss of intercalation, some of the
carbon atoms in graphene bond with the exposed silicon atoms of the
SiC surface. These bonds result in electron transfer from the substrate
to the sheet, affecting its carrier concentration. Moreover, they affect
the hybridization in graphene, making it more sp3in some atoms, thus
inducing defects in its structure.
From here, we can distinguish two distinct types of hydrogen dif-
fusion: one that induces chemical decoupling of graphene (compare
Fig. 7(a) and Fig. 7(c)) and one that does not (compare Fig. 7(a) and
Fig. 7(b)). The latter is a relatively simple process where hydrogen
atoms move between neighboring Si sites with little impact on the
interaction between graphene and SiC, resulting in an activation energy
of approximately 1.1 eV (see Fig. 7(d)). In contrast, the former is a
more complex process that, in addition to hydrogen diffusion, involves
breaking the C-Si bond between graphene and SiC and the structural re-
laxation of the sheet, which combined results in an activation energy of
approximately 1.6 eV (1.1 eV for diffusion and 0.5 eV for decoupling).
Given this disparity in energies, the rate of diffusion will vary
substantially between the two cases (see Fig. 8). For instance, at 473 K,
simple diffusion would statistically take about 0.05 s, as of transition
state theory [69–71], meaning one hydrogen atom would, on average,
diffuse between neighboring Si sites 20 times in one second. In contrast,
the examined decoupling would require over 3 h. Consequently, at the
initial stages of thermal treatment, chemical decoupling of graphene
should generally not occur, unlike hydrogen diffusion. Such diffusion
should occasionally enable a local coverage that could facilitate further
coupling of the graphene and SiC, with little potential to decouple.
This would explain the initial increase in electron concentration in the
graphene, coupled with the loss of carrier mobility and an increase in
sheet resistance (see Fig. 3).
However, at higher temperatures, decoupling will become more
effective. For instance, at 623 K, it would statistically take about
0.9 s. Consequently, effective decoupling should be achievable at the
later stages of the thermal treatment. This process, in turn, exposes
previously unavailable parts of the surface to much faster hydrogen
diffusion, taking approximately 100 μs. Thus, the thermal treatment
should result in a more even distribution of hydrogen, which is ener-
getically favorable if total coverage is at least 25% [49]. These suggest
that after irradiation, the carrier concentration returns to its original
value, indicating a limited loss of intercalation [13].
4. Summary and conclusions
This work identified the consequence of exposing the a-Al2O3/QFS-
GR@SiC system to a mainly high-energy (1–2 MeV) fast-neutron flux
of the MARIA research nuclear reactor for a period enabling accumu-
lated neutron dose of 2.0 × 1017 cm−2 (166 h) and 2.0 × 1018 cm−2
(245 h). The system comprises transfer-free, p-type, fully hydrogen-
intercalated, quasi-free-standing, epitaxial Chemical Vapor Deposition
graphene on semi-insulating, vanadium-compensated, nominally on-
axis 6H-SiC(0001) and encapsulated with 100-nm-thick, atomic-layer-
deposited, amorphous Al2O3.
Post-irradiation Hall effect analysis proved that both neutron flu-
ences shift the initial p-type conductance of the graphene to an n-type
one. It suggests the loss of the quasi-free-standing character of graphene
and likely damage to the SiC(0001)-terminating hydrogen layer. A
subsequent annealing of the 2.0 × 1017 −cm−2-irradiated sample up
to 623 K revealed that its initial electrical properties are restorable
through a thermally triggered self-healing effect. In the 2.0 × 1018 −
cm−2-irradiated sample, no recovery occurred within the 623 K range.
Applied Surface Science 685 (2025) 161953
6
S. El-Ahmar et al.
Fig. 8. The average timeframe for hydrogen atom desorption from SiC(0001) (orange
dashed line) and surface diffusion on SiC(0001) along the diffusion paths a→c (blue
solid line) and a→b (green solid line), as shown in Fig. 7. The temperature range
extends from RT to the effective hydrogen desorption temperature. The inset highlights
the average timescales of these processes at temperatures used during the thermal
treatment of the irradiated a-Al2O3/QFS-GR@SiC systems (see Fig. 3).
Micro-Raman analysis of the defect-related D and D’ modes revealed
that the dose 2.0 × 1017 cm−2 of fast neutrons induces defects in the QFS
graphene with an average density 𝑛𝐷= 3.1 ×1010 cm-2 and an 𝐿𝐷=
32 nm inter-defect distance. Yet, post-irradiation thermal treatment up
to 623-K eliminates the D and D’ peaks, suggesting full recovery of the
QFS properties.
Finally, using a Density Functional Theory model, we explained the
observed self-healing phenomenon through thermally-activated lateral
diffusion of the remaining hydrogen atoms combined with the breaking
of the C-Si bonds between graphene and 6H-SiC(0001), structural
relaxation (decoupling) of the graphene sheet and restoration of its QFS
character.
The effective self-healing of the a-Al2O3/QFS-GR@SiC system adds
value to the natural radiation resistance of the graphene sheet itself.
Its fluence-related and temperature threshold, as evaluated in this
experiment, is 2.0 × 1017 cm−2 and 623 K, respectively. Such neutron
dose is still considered high and may correspond to the extreme require-
ments for ex-vessel magnetic diagnostic systems in future magnetic
field confinement fusion reactors. The temperature of 623 K lies within
the standard operational limits of the a-Al2O3/QFS-GR@SiC system,
validated between 300 K and 770 K.
The observed phenomenon may have a direct applied significance
as the a-Al2O3/QFS-GR@SiC is already a technologically advanced sen-
sory platform. One can imagine a highly stable a-Al2O3/QFS-GR@SiC -
based magnetic diagnostic device operating in extreme environments
and real-time-fed with sufficient current to dissipate enough energy to
meet the threshold for a sustained and continuous effective self-healing.
Nonetheless, the concluded fluence and temperature are only a
single pair of data along the hypothetical curve defining limits for
the self-healing effect. Advisably, one should density the fluence steps
within the 1017–1018 cm−2 orders to draw a detailed picture of the
phenomenon.
CRediT authorship contribution statement
Semir El-Ahmar: Writing – review & editing, Writing – origi-
nal draft, Validation, Supervision, Methodology, Investigation, Formal
analysis, Conceptualization. Jakub Jagiełło: Writing – review & edit-
ing, Writing – original draft, Visualization, Methodology, Investigation,
Data curation. Maciej J. Szary: Writing – review & editing, Writ-
ing – original draft, Visualization, Software, Methodology, Investiga-
tion, Formal analysis, Conceptualization. Wiktoria Reddig: Writing
– review & editing, Visualization, Methodology, Investigation. Artur
Dobrowolski: Writing – review & editing, Visualization, Methodol-
ogy, Investigation. Rafał Prokopowicz: Writing – review & editing,
Methodology, Investigation. Maciej Ziemba: Writing – review & edit-
ing, Methodology, Investigation. Tymoteusz Ciuk: Writing – review
& editing, Writing – original draft, Validation, Supervision, Resources,
Methodology, Formal analysis, Conceptualization.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgments
This work was supported by the Ministry of Education and Science
(Poland) within Project No. 0512/SBAD/2420. The research leading to
these results has received funding from the National Science Centre,
Poland, under Grant Agreement No. OPUS 2019/33/B/ST3/02677 for
project ‘‘Influence of the silicon carbide and the dielectric passivation defect
structure on high-temperature electrical properties of epitaxial graphene’’
and the National Centre for Research and Development, Poland, under
Grant Agreement No. M-ERA.NET3/2021/83/I4BAGS/ 2022 for project
‘‘Ion Implantation for Innovative Interface modifications in BAttery and
Graphene-enabled Systems’’. The M-ERA.NET3 has received funding
from the European Union’s Horizon 2020 research and innovation
programme under Grant Agreement No. 958174. Calculations reported
in this work have been performed at the Interdisciplinary Center for
Mathematical and Computational Modeling (ICM) of the University of
Warsaw, Poland under Grant No. GB81-3.
Data availability
The raw/processed data required to reproduce the above findings
cannot be shared at this time as the data also forms part of an ongoing
study.
References
[1] J. Zhao, P. Ji, Y. Li, R. Li, K. Zhang, H. Tian, K. Yu, B. Bian, L. Hao, X.
Xiao, W. Griffin, N. Dudeck, R. Moro, L. Ma, W.A. de Heer, Ultrahigh-mobility
semiconducting epitaxial graphene on silicon carbide, Nature 625 (7993) (2024)
60–65, http://dx.doi.org/10.1038/s41586-023- 06811-0,arXiv:2308.12446.
[2] M.S. Choi, A. Nipane, B.S.Y. Kim, M.E. Ziffer, I. Datta, A. Borah, Y. Jung, B.
Kim, D. Rhodes, A. Jindal, Z.A. Lamport, M. Lee, A. Zangiabadi, M.N. Nair, T.
Taniguchi, K. Watanabe, I. Kymissis, A.N. Pasupathy, M. Lipson, X. Zhu, W.J.
Yoo, J. Hone, J.T. Teherani, High carrier mobility in graphene doped using
a monolayer of Tungsten oxyselenide, Nat. Electron. 4 (10) (2021) 731–739,
http://dx.doi.org/10.1038/s41928-021- 00657-y, URL https://www.nature.com/
articles/s41928-021- 00657-y.
[3] L. Banszerus, M. Schmitz, S. Engels, J. Dauber, M. Oellers, F. Haupt, K. Watanabe,
T. Taniguchi, B. Beschoten, C. Stampfer, Ultrahigh-mobility graphene devices
from chemical vapor deposition on reusable copper, Sci. Adv. 1 (6) (2015)
1–6, http://dx.doi.org/10.1126/sciadv.1500222, URL https://www.science.org/
doi/10.1126/sciadv.1500222.
[4] S.F. Shaikh, M.M. Hussain, Multisensory graphene-skin for harsh-environment
applications, Appl. Phys. Lett. 117 (7) (2020) http://dx.doi.org/10.1063/
5.0017769, URL https://pubs.aip.org/apl/article/117/7/074101/39446/
Multisensory-graphene- skin-for-harsh-environment.
Applied Surface Science 685 (2025) 161953
7
S. El-Ahmar et al.
[5] G. Cao, H. Lin, S. Fraser, X. Zheng, B. Del Rosal, Z. Gan, S. Wei, X. Gan, B. Jia,
Resilient graphene ultrathin flat lens in aerospace, chemical, and biological harsh
environments, ACS Appl. Mater. Interfaces 11 (22) (2019) 20298–20303, http:
//dx.doi.org/10.1021/acsami.9b05109, URL https://pubs.acs.org/doi/10.1021/
acsami.9b05109.
[6] T. Ciuk, B. Stanczyk, K. Przyborowska, D. Czolak, A. Dobrowolski, J. Jagiello,
W. Kaszub, M. Kozubal, R. Kozlowski, P. Kaminski, High-temperature Hall effect
sensor based on epitaxial graphene on high-purity semiinsulating 4H-SiC, IEEE
Trans. Electron Devices 66 (7) (2019) 3134–3138, http://dx.doi.org/10.1109/
TED.2019.2915632.
[7] T. Ciuk, R. Kozłowski, A. Romanowska, A. Zagojski, K. Pie¸tak-Jurczak, B.
Stańczyk, K. Przyborowska, D. Czołak, P. Kamiński, Defect-engineered graphene-
on-silicon-carbide platform for magnetic field sensing at greatly elevated
temperatures, Carbon Trends 13 (October) (2023) 100303, http://dx.doi.org/
10.1016/j.cartre.2023.100303, URL https://linkinghub.elsevier.com/retrieve/pii/
S2667056923000585.
[8] H. Okeil, T. Erlbacher, G. Wachutka, Very high temperature Hall sensors
in a wafer-scale 4H-SiC technology, Adv. Mater. Technol. 2400046 (2024)
1–14, http://dx.doi.org/10.1002/admt.202400046, URL https://onlinelibrary.
wiley.com/doi/10.1002/admt.202400046.
[9] G. Compagnini, F. Giannazzo, S. Sonde, V. Raineri, E. Rimini, Ion irradiation and
defect formation in single layer graphene, Carbon 47 (14) (2009) 3201–3207,
http://dx.doi.org/10.1016/j.carbon.2009.07.033.
[10] O. Lehtinen, J. Kotakoski, A.V. Krasheninnikov, A. Tolvanen, K. Nordlund, J.
Keinonen, Effects of ion bombardment on a two-dimensional target: Atomistic
simulations of graphene irradiation, Phys. Rev. B 81 (15) (2010) 1–4, http:
//dx.doi.org/10.1103/PhysRevB.81.153401.
[11] L. Tapasztó, G. Dobrik, P. Nemes-Incze, G. Vertesy, P. Lambin, L.P. Biró, Tuning
the electronic structure of graphene by ion irradiation, Phys. Rev. B 78 (23)
(2008) 1–4, http://dx.doi.org/10.1103/physrevb.78.233407.
[12] J. Mo, L. Li, X. Li, Q. Feng, X. Xiang, G. Yang, H. Deng, J. Nie, X. Zu,
First-principles study on the effects of fast neutron irradiation and fast neutron
irradiation under the external electric field on carbon-based material AB bilayer
graphene, Diam. Relat. Mater. 144 (February) (2024) 110988, http://dx.doi.org/
10.1016/j.diamond.2024.110988, URL https://linkinghub.elsevier.com/retrieve/
pii/S0925963524002012.
[13] S. El-Ahmar, M.J. Szary, T. Ciuk, R. Prokopowicz, A. Dobrowolski, J. Jagiełło,
M. Ziemba, Graphene on SiC as a promising platform for magnetic field
detection under neutron irradiation, Appl. Surf. Sci. 590 (2022) 152992, http://
dx.doi.org/10.1016/j.apsusc.2022.152992, URL https://linkinghub.elsevier.com/
retrieve/pii/S0169433222005608.
[14] T. Ciuk, C. Nouvellon, F. Monteverde, B. Stańczyk, K. Przyborowska, D. Czołak,
S. El-Ahmar, High-temperature thermal stability of a graphene Hall effect sensor
on defect-engineered 4H-SiC(0001), IEEE Electron Device Lett. 45 (10) (2024)
1957–1960, http://dx.doi.org/10.1109/led.2024.3436050.
[15] J. Ongena, R. Koch, R. Wolf, H. Zohm, Magnetic-confinement fusion, Nat. Phys.
12 (5) (2016) 398–410, http://dx.doi.org/10.1038/NPHYS3745.
[16] W. Biel, R. Albanese, R. Ambrosino, M. Ariola, M.V. Berkel, I. Bolshakova, K.J.
Brunner, R. Cavazzana, M. Cecconello, S. Conroy, A. Dinklage, I. Duran, R.
Dux, T. Eade, S. Entler, G. Ericsson, E. Fable, D. Farina, L. Figini, C. Finotti,
T. Franke, L. Giacomelli, L. Giannone, W. Gonzalez, A. Hjalmarsson, M. Hron,
F. Janky, A. Kallenbach, J. Kogoj, R. König, O. Kudlacek, R. Luis, A. Malaquias,
O. Marchuk, G. Marchiori, M. Mattei, F. Maviglia, G. De Masi, D. Mazon, H.
Meister, K. Meyer, D. Micheletti, S. Nowak, C. Piron, A. Pironti, N. Rispoli, V.
Rohde, G. Sergienko, S. El Shawish, M. Siccinio, A. Silva, F. da Silva, C. Sozzi,
M. Tardocchi, M. Tokar, W. Treutterer, H. Zohm, Diagnostics for plasma control
– From ITER to DEMO, Fusion Eng. Des. 146 (December 2018) (2019) 465–472,
http://dx.doi.org/10.1016/j.fusengdes.2018.12.092.
[17] W. Biel, M. Ariola, I. Bolshakova, K. Brunner, M. Cecconello, I. Duran, T.
Franke, L. Giacomelli, L. Giannone, F. Janky, A. Krimmer, R. Luis, A. Malaquias,
G. Marchiori, O. Marchuk, D. Mazon, A. Pironti, A. Quercia, N. Rispoli, S.E.
Shawish, M. Siccinio, A. Silva, C. Sozzi, G. Tartaglione, T. Todd, W. Treutterer,
H. Zohm, Development of a concept and basis for the DEMO diagnostic and
control system, Fusion Eng. Des. 179 (2022) 113122, http://dx.doi.org/10.1016/
j.fusengdes.2022.113122.
[18] Y. Guoliang, Y. Qingwei, Y. Jinwei, S. Xianying, L. Xu, W. Huajian, W. Zhiqiang,
Fusion neutron flux detector for the ITER, Plasma Sci. Technol. 16 (2) (2014)
168, http://dx.doi.org/10.1088/1009-0630/16/2/14.
[19] M. Rubel, Fusion neutrons: Tritium breeding and impact on wall materials and
components of diagnostic systems, J. Fusion Energy (2019) http://dx.doi.org/10.
1007/s10894-018- 0182-1.
[20] S. Entler, I. Duran, P. Sladek, M. Simonovsky, J. Reboun, P. Turjanica, K. Vy-
borny, P. Ritzinger, Z. Soban, Temperature tests of miniature ceramic/antimony
Hall sensors for ITER and DEMO, IEEE Trans. Plasma Sci. PP (Table I) (2024)
1–5, http://dx.doi.org/10.1109/TPS.2024.3386770, URL https://ieeexplore.ieee.
org/document/10502335/.
[21] S. El-Ahmar, J. Jankowski, P. Czaja, W. Reddig, M. Przychodnia, J. Raczynski,
W. Koczorowski, Magnetic field sensor operating from cryogenics to elevated
temperatures, IEEE Sens. Lett. 7 (8) (2023) 11–14, http://dx.doi.org/10.1109/
LSENS.2023.3294525.
[22] J. Jankowski, R. Prokopowicz, K. Pytel, S. El-Ahmar, Toward the development of
an InSb-based neutron-resistant Hall sensor, IEEE Trans. Nucl. Sci. 66 (6) (2019)
926–931, http://dx.doi.org/10.1109/TNS.2019.2912720, URL https://ieeexplore.
ieee.org/document/8695770/.
[23] I. Bolshakova, M. Bulavin, N. Kargin, Y. Kost, T. Kuech, S. Kulikov, M.
Radishevskiy, F. Shurygin, M. Strikhanov, I. Vasil’Evskii, A. Vasyliev, Metal Hall
sensors for the new generation fusion reactors of DEMO scale, Nucl. Fusion 57
(11) (2017) 116042, http://dx.doi.org/10.1088/1741-4326/aa7867.
[24] I. Bolshakova, D. Dyuzhkov, Y. Kost, M. Radishevskiy, F. Shurigin, A. Vasyliev, Z.
Wang, M. Otto, D. Neumaier, M. Bulavin, A. Kulikov, Graphene and prospects of
radiation-hard hall sensors, in: 2017 IEEE 7th International Conference Nanoma-
terials: Application & Properties, NAP, IEEE, 2017, pp. 03CBN15–1–03CBN15–5,
http://dx.doi.org/10.1109/NAP.2017.8190226, URL http://ieeexplore.ieee.org/
document/8190226/.
[25] I. Bolshakova, D. Dyuzhkov, Y. Kost, M. Radishevskiy, F. Shurigin, A. Vasyliev,
Z. Wang, M. Otto, D. Neumaier, Prospects of graphene use in sensor technology,
in: 2018 14th International Conference on Advanced Trends in Radioelecrtronics,
Telecommunications and Computer Engineering, TCSET, IEEE, 2018, pp. 466–
470, http://dx.doi.org/10.1109/TCSET.2018.8336242, URL https://ieeexplore.
ieee.org/document/8336242/.
[26] C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov,
E.H. Conrad, P.N. First, W.A. de Heer, Ultrathin epitaxial graphite: 2D electron
gas properties and a route toward graphene-based nanoelectronics, J. Phys.
Chem. B 108 (52) (2004) 19912–19916, http://dx.doi.org/10.1021/jp040650f,
arXiv:0410240, URL https://pubs.acs.org/doi/10.1021/jp040650f.
[27] K.V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G.L. Kellogg, L. Ley, J.L. McChesney,
T. Ohta, S.A. Reshanov, J. Röhrl, E. Rotenberg, A.K. Schmid, D. Waldmann, H.B.
Weber, T. Seyller, Towards wafer-size graphene layers by atmospheric pressure
graphitization of silicon carbide, Nature Mater. 8 (3) (2009) 203–207, http://dx.
doi.org/10.1038/nmat2382, URL https://www.nature.com/articles/nmat2382.
[28] J. Zhao, P. Ji, Y. Li, R. Li, K. Zhang, H. Tian, K. Yu, B. Bian, L. Hao,
X. Xiao, W. Griffin, N. Dudeck, R. Moro, L. Ma, W.A. de Heer, Ultrahigh-
mobility semiconducting epitaxial graphene on silicon carbide, Nature (2024)
http://dx.doi.org/10.1038/s41586-023- 06811-0.
[29] W. Strupinski, K. Grodecki, A. Wysmolek, R. Stepniewski, T. Szkopek, P.E.
Gaskell, A. Gruneis, D. Haberer, R. Bozek, J. Krupka, J.M. Baranowski, Graphene
epitaxy by chemical vapor deposition on SiC, Nano Lett. 11 (4) (2011)
1786–1791, http://dx.doi.org/10.1021/nl200390e.
[30] T. Ciuk, W. Strupinski, Statistics of epitaxial graphene for Hall effect sensors,
Carbon 93 (JUNE) (2015) 1042–1049, http://dx.doi.org/10.1016/j.carbon.2015.
06.032, URL http://linkinghub.elsevier.com/retrieve/pii/S0008622315005473.
[31] T. Ciuk, P. Caban, W. Strupinski, Charge carrier concentration and offset voltage
in quasi-free-standing monolayer chemical vapor deposition graphene on SiC,
Carbon 101 (2016) 431–438, http://dx.doi.org/10.1016/j.carbon.2016.01.093.
[32] A. Dobrowolski, J. Jagiełło, K. Pie¸tak-Jurczak, M. Wzorek, D. Czołak, T. Ciuk,
Spectroscopic properties of close-to-perfect-monolayer quasi-free-standing epitax-
ial graphene on 6H SiC(0001), Appl. Surf. Sci. 642 (2024) 158617, http://
dx.doi.org/10.1016/j.apsusc.2023.158617, URL https://linkinghub.elsevier.com/
retrieve/pii/S0169433223022973.
[33] D. Collomb, P. Li, S. Bending, Frontiers of graphene-based Hall-effect sensors,
J. Phys.: Condens. Matter. 33 (24) (2021) 243002, http://dx.doi.org/10.1088/
1361-648x/abf7e2.
[34] T. Ciuk, A. Kozlowski, P. Piotr, W. Kaszub, M. Kozubal, Z. Rekuc, J. Podgorski, B.
Stanczyk, K. Przyborowska, I. Jozwik, A. Kowalik, Thermally activated double-
carrier transport in epitaxial graphene on vanadium-compensated 6H-SiC as
revealed by Hall effect measurements, Carbon 139 (2018) 776–781, http://dx.
doi.org/10.1016/j.carbon.2018.07.049.
[35] W. Reddig, M. Przychodnia, T. Ciuk, S. El-Ahmar, High-temperature stability
of sensor platforms designed to detect magnetic fields in a harmful radiation
environment, IEEE Sens. Lett. 7 (8) (2023) 1–4, http://dx.doi.org/10.1109/
LSENS.2023.3297795.
[36] I.A. Bolshakova, Y.Y. Kost, M.I. Radishevskyi, F.M. Shurygin, O.V. Vasyliev, Z.
Wang, D. Neumaier, M. Otto, M.V. Bulavin, S.A. Kulikov, Resistance of Hall
sensors based on graphene to neutron radiation,