# Hydrogenation and etching of single-layer graphene during exposure to atomic hydrogen

Tom Fournier, Samir El Masaoudi, Iann C Gerber, Benjamin Lassagne, Cedric Crespos, Jean-Marc Leyssale, Kelvin Cruz, Germercy Paredes, Felana Andriambelaza, Marc Monthoux, et al.

► To cite this version:

Tom Fournier, Samir El Masaoudi, Iann C Gerber, Benjamin Lassagne, Cedric Crespos, et al. Hydrogenation and etching of single-layer graphene during exposure to atomic hydrogen. Carbon Trends, 2025, 20, pp.100553. 10.1016/j.cartre.2025.100553. hal-05250930

HAL Id: hal-05250930

https://hal.science/hal-05250930v1

Submitted on 11 Sep 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Hydrogenation and etching of single-layer graphene during exposure to atomic hydrogen

Tom Fournier<sup>a, ID</sup>, Samir El Masaoudi<sup>b</sup>, Iann C. Gerber<sup>b, ID</sup>, Benjamin Lassagne<sup>b, ID</sup>, Cedric Crespos<sup>c</sup>, Jean-Marc Leyssale<sup>c, ID</sup>, Kelvin Cruz<sup>d</sup>, Germercy Paredes<sup>d, ID</sup>, Felana Andriambelaza<sup>c, ID</sup>, Marc Monthioux<sup>a, ID</sup>, Pascal Puech<sup>a, *, ID</sup>, Fabrice Piazza<sup>d, *, ID</sup>

## ARTICLE INFO

### Keywords:

- Graphene
- Hydrogenation
- Dehydrogenation
- Etching
- Raman
- Band gap

## ABSTRACT

Opening a band gap in graphene is essential for its integration into electronic devices, but remains a major challenge. Hydrogenation offers a promising route, though the process is complicated by competing mechanisms such as hydrogen desorption and unwanted etching. Here, we investigate one-sided hydrogenation of monolayer graphene on SiO₂/Si substrates at temperatures below ~100 °C, using a hot-filament-assisted method compatible with semiconductor processing. Our results reveal a regime where hydrogen chemisorption and hole formation (etching) coexist. Dehydrogenation experiments and first-principles calculations indicate that hydrogen atoms preferentially cluster on neighboring carbon sites, potentially leading to dome-like lattice distortions. While hydrogen incorporation is favored at these sites, our simulations suggest that the resulting stresses alone are insufficient to cause carbon-carbon bond breakage. Instead, etching likely requires the presence of energetic atomic hydrogen. These findings help clarify the interplay between hydrogenation and etching and provide guidance for controlled graphene functionalization in device applications.

## 1. Introduction

The hydrogenation of single-layer graphene (1LG) on insulating substrates such as SiO₂ is of great interest for nanoelectronics, as it offers a route to band gap engineering [1–3]. Hydrogenated graphene also holds potential for reversible hydrogen storage, with desorption yielding molecular H₂. Beyond device applications, understanding hydrogenation contributes to the chemistry of large polycyclic aromatic hydrocarbons relevant to interstellar environments [4,5].

Hydrogenation of graphene can result in diverse outcomes—chemisorption of hydrogen [1], hole formation (etching) [6], or minimal surface modification [7]—depending on experimental conditions. This complexity has been extensively explored through theoretical approaches such as first-principles calculations and molecular dynamics simulations. Most studies focus on ideal, defect-free graphene [8], examining phase stability [9], edge reactions [10], and the impact of hydrogen kinetic energy [11]. At low coverage, spin-polarized DFT

calculations have shown that hydrogen tends to cluster into ortho- and para-dimer configurations, creating local lattice distortions [5]. This was confirmed by scanning tunneling microscopy measurements [12].

Experimental progress, however, remains limited. While partial hydrogenation has been demonstrated [1,13,14], full hydrogenation to form graphane—where all sp²-carbon atoms convert to sp³ [1]—has not yet been achieved [2,15]. Raman spectroscopy often reveals residual sp²-carbon peaks, even in claims of highly hydrogenated graphene [1, 16]. One-sided full hydrogenation is predicted to be thermodynamically unstable [17,18], and adsorption competes with hydrogen desorption via the Eley–Rideal mechanism [19–21]. Other factors such as substrate interaction [21,22], curvature [23,24], and defects further influence hydrogenation and etching behavior.

Despite these insights, the underlying mechanisms of hydrogen-induced etching and chemisorption remain unclear. For instance, remote hydrogen plasma treatments of graphene on SiO₂ have produced circular pits consistent with isotropic etching, without signs of

<footnote><sup>a</sup> Centre d'Elaboration des Matériaux et d'Etudes Structurales (CEMES), UPR8011 CNRS, Université de Toulouse III, 29 Rue Jeanne Marvig, Toulouse 31055, France</footnote>

<footnote><sup>b</sup> Laboratoire de Physico-Chimie des Nano-objets (LPCNO), UMR5215 CNRS, INSA, Université de Toulouse III, 135 avenue de Rangueil, Toulouse 31077, France</footnote>

<footnote><sup>c</sup> Institut des Sciences Moléculaires (ISM), UMR 5255 CNRS, Bordeaux INP, Université de Bordeaux, Talence 33400, France</footnote>

<footnote><sup>d</sup> Lab. Nanociencia, Pontificia Universidad Católica Madre y Maestra, Autopista Duarte km 1 ½, Apartado Postal 822, Santiago de los Caballeros, Dominican Republic</footnote>

<footnote>* Corresponding authors.
E-mail addresses: pascal.puech@cemes.fr (P. Puech), fpiazza@pucmm.edu.do (F. Piazza).</footnote>
hydrogenation in the unetched regions [25]. The pits appear to nucleate during exposure, rather than originating from defects. Similar behavior on smooth mica suggests that substrate polarity or charge impurities, rather than surface roughness, drive this reactivity. In contrast, other studies using similar conditions report hydrogenation without etching [1], underscoring inconsistencies that may relate to substrate properties, local curvature, or plasma parameters. While curvature-driven adsorption has been observed on SiC and copper substrates [23,24], its general applicability remains uncertain.

In this work, we investigate the hydrogenation of monolayer graphene transferred onto SiO₂/Si substrates at temperatures below ~100 °C, using a hot-filament-assisted hydrogenation process compatible with semiconductor manufacturing. Through combined experimental analysis and spin-polarized DFT calculations, we explore a regime where hydrogen chemisorption and hole formation coexist. Our results offer new insights into the interplay between adsorption and etching processes during low-temperature hydrogenation.

## 2. Materials and method

### 2.1. Single-layer graphene sample preparation

Graphene flakes were obtained in air at 50 % relative humidity and room temperature by mechanical exfoliation of highly-orientated pyrolytic graphite (HOPG) (purchased from HQ Graphene) using the adhesive-tape method [26]. The flakes were then transferred onto a 285 nm-thick SiO₂/Si substrate, which had previously been patterned with gold markers. This SiO₂/Si interferential substrate was selected to enhance the optical contrast of the single-layer graphene (1LG) flakes, allowing for easy detection via optical microscopy [26]. To ensure efficient transfer, the substrates were first cleaned in acetone and in propan-2-ol in an ultrasound bath for 3 min each, followed by exposure to an O₂ plasma for 300 s (RF power of 5 W; O₂ flow rate of 25 sccm). Once the 1LG flakes were optically identified based on their characteristic light-absorption contrast, micro-Raman spectroscopy (using a 488 nm excitation wavelength) was employed to confirm the number of layers. The full width at half maximum (FWHM) of the 2D peak at approximately 2700 cm⁻¹ was measured (< 30 cm⁻¹ for 1LG, ~60 cm⁻¹ for 2LG [27]).

### 2.2. Hydrogenation process

Graphene was hydrogenated using a commercial hot filament reactor (BWI 1000 from Blue Wave Semiconductors) as described in detail previously [28] and frequently used for the synthesis of 2D-diamond materials, including diamane [15,29–31]. In this setup, molecular hydrogen (H₂) was dissociated onto two resistively-heated, surface-carburized tungsten filaments, positioned 4.4 cm from the substrate holder [15]. The carburization step was necessary to prevent incidental deposition of tungsten (W) nanoparticles onto the specimen. The filaments were conditioned in an ultra-high purity (UHP) mixture of 10 % CH₄ in H₂ before introducing the graphene samples into the reactor. The samples were placed on a fluid-cooled, 5 cm-diameter stainless-steel stage. A molybdenum shutter, positioned 3 cm above the substrate holder, shielded the graphene sample from direct exposure to the filament's thermal radiation, ensuring the substrate remained at low temperatures (typically < 100 °C, as measured by a K-type thermocouple with sheathed wires, placed on the substrate holder's surface). Before the hydrogenation, the reactor was evacuated to a residual pressure of 6 × 10⁻⁴ torr using a turbo pump (HiPace 80 from Pfeiffer Vacuum), backed with a hydrocarbon oil pump (DUO 20 M from Pfeiffer Vacuum). During hydrogenation, UHP H₂ gas (approximately 99.999 % pure) was introduced into the chamber through a stainless-steel tube located on top of the chamber. The gas flow was controlled by a mass flow controller (from MKS), and the pressure was maintained via an automatic valve (from MKS) located beneath the substrate holder. The

operating pressure and gas flow were 4 Torr and 10 sccm, respectively. Once steady-state conditions were achieved with H₂ in the chamber, the current through both filaments was increased to raise their temperature to 2100 °C, as monitored by a two-color pyrometer (iR2P-1000-53-C24 from Omega Engineering). At this temperature, the filament catalytically dissociate the H₂ molecules, generating atomic hydrogen (H). Two samples were prepared under these conditions with hydrogen exposure durations of 10 min and 20 min, respectively.

Some experiments were conducted by applying a thermal pretreatment before exposure to hydrogen to investigate the potential effect of water molecules adsorbed on the sample surface. In these experiments, the sample was heated to 120 °C for 60 min in an N₂ atmosphere (50 Torr; heating rate of 50 °C/min). No changes were observed in the results, regardless of whether the pretreatment was applied. This indicates that the formation of holes, as discussed later, was observed even when the thermal pretreatment was applied.

For simplicity, the term "hydrogenated graphene" will be used throughout this work, even in cases where full hydrogenation is considered in our DFT calculations (i.e., when all sp²-carbon atoms are converted to sp³-carbon, resulting in a material that is no longer strictly graphene). It is important to note that there is currently no method to quantify the hydrogenation rate in monolayer graphene flakes deposited on SiO₂. For this reason, throughout this work, we will use qualitative descriptors such as "moderate" or "low" to characterize the hydrogenation rate, based on a comparison of our Raman spectra with those reported in Ref [1], where the highest hydrogenation rate from a gas phas method, estimated to be around 10 at. % in Ref [2], was reported [1].

Dehydrogenation was performed by thermal annealing at 400 °C under an Ar/H₂ atmosphere (95/5 vol. %) for 1 hour. The Ar/H₂ flow was maintained at 500 sccm until the temperature dropped down to 100 °C.

### 2.3. Characterization

Raman spectroscopy was employed to examine the material structure before and after the hydrogenation process. Spectra were acquired in the air using an x100 magnification objective lens (numerical aperture of 0.9, spot size of around 1 µm²) with 633 nm excitation wavelength. The effect of the laser power on the structure was investigated at 0.3, 0.6, 1.2, 4.5, 7.2, and 10 mW, with an acquisition time of 200 s for all cases. For characterisation, a laser power of 0.5 mW was used. Raman parameters such as band shifts, band widths, and intensity ratios were extensively used in this study. Specifically, the intensity ratio of two Raman bands activated by a double resonance process (D over D'), *I*<sub>D</sub>/<sub>*I*<sub>D</sub></sub>, based on the interpretations by Eckmann et al [32], was employed. Despite the lack of theoretical confirmation, the interpretations are supported by reproducible experimental trends and consistency across multiple datasets. Due to the low Raman signal intensity and the use of long acquisition times (200 s per point) to minimize laser-induced damage, spatial Raman mapping was not feasible, as extended measurements are prone to sample and stage drift.

Due to the very low hydrogen coverage achieved in our samples, the C–H signal in X-ray photoelectron spectroscopy (XPS) falls below the detection threshold, making this technique unsuitable for reliably distinguishing sp²- and sp³-carbon in our case.

Atomic force microscopy (AFM, NanoObserver from CSI) was utilized to investigate the topography post-hydrogenation in tapping mode, using SPM-probe model cantilevers from App Nano (resonance frequency: 43–81 kHz, spring constant: 0.6–3.7 N/m).

### 2.4. Calculations

The spin-polarized electronic structures were obtained from DFT calculations with the VASP package [33,34] which employs the plane-augmented wave (PAW) method [35,36] to treat core electrons.
The Perdew-Burke-Ernzerhof (PBE) functional [37] was used as an approximation for the exchange-correlation electronic term in all the geometry optimization steps. A cut-off energy of 400 eV was applied, with a Gaussian smearing of 0.05 eV for partial occupancies. During geometry optimization, all atoms were allowed to relax, with a force convergence criterion set to below 0.005 eV/Å. The van der Waals-corrected scheme of Grimme et al [38] was used for the calculations.

Born-Oppenheimer molecular dynamics (MD) simulations were performed to investigate the stability of hydrogenated graphene structures, starting from a (10 × 10) primitive graphene cell. Simulations were carried out in the canonical NVT ensemble using the Nosé thermostat. Following structural optimization at 0 K, the system was gradually heated to 298 K over 5 ps, followed by a 20 ps simulation with a time step of 0.5 fs to integrate the atomic equations of motion. The computational settings matched those described earlier, with a reduced k-point sampling at the Γ-point.

To examine the effect of hydrogen coverage on the electronic band structure, a series of (n × n) graphene supercells were constructed, each unit cell containing two carbon atoms. Single-sided hydrogen adsorption was modeled in configurations ranging from (1 × 1) to (2 × 2), (4 × 4), and (5 × 5) supercells, each with a single adsorbed hydrogen atom. The corresponding k-point meshes used were (15 × 15 × 1), (9 × 9 × 1), (5 × 5 × 1), and (5 × 5 × 1), respectively. Additionally, three (7 × 7) supercells with two hydrogen atoms in para, meta, and ortho positions were simulated using a (5 × 5 × 1) grid. Electronic band structures were computed along the high-symmetry path Γ → M → K → Γ using the band-unfolding method [39] implemented via the vaspkit code [40], and compared with pristine single-layer graphene.

Optical indices were then estimated from these band structures using density functional perturbation theory (DFPT) [41], employing fine k-point meshes: (38 × 38 × 1) for pristine graphene, and (25 × 25 × 1) for H@(5 × 5) and semi-hydrogenated (5 × 5) configurations.

Transition states were identified using the climbing-image nudged elastic band (CI-NEB) method [42,43], with three intermediate images optimized via a quasi-Newton algorithm on a (3 × 3 × 1) k-point grid. To confirm these correspond to true transition states, the numerical Hessian matrix was diagonalized, and a single imaginary frequency was verified. Displacing each relevant atom by ±0.015 Å along the normal mode recovered the initial and final states, further validating the transition paths.

The NEB-calculated energies represent potential energy surfaces only. Thermal and vibrational corrections were estimated at 298 K by considering five selected atoms, neglecting translational, rotational, and electronic contributions. These corrections typically shifted the relative energies (reactant/transition state/product) by ~0.1-0.3 eV compared to the static DFT values.

Phonon spectra were not computed due to the large size of the simulation cells (>300 atoms), which makes full vibrational analysis computationally demanding. We note, however, that such calculations would be valuable for future work aimed at direct comparison with experimental Raman data.

In our model, we did not include any SiO₂ substrate, as it has been shown that, for a fully passivated SiO₂ surface (either by silanol or hydroxyl groups), the interaction between a graphene monolayer and the SiO₂ substrate is purely physisorption, i.e., of the weak van der Waals type. The electronic structure of the graphene layer on a passivated SiO₂ substrate has been shown to be very similar to that of the pristine graphene, and therefore, it is unlikely to influence the reactivity of the graphene layer [44]. This finding was confirmed by MD simulations [11].

# 3. Results and discussion

## 3.1. Sample exposed to H for 10 min

Fig. 1b presents an optical microscopy image of a typical exfoliated graphene sample transferred onto a SiO₂ substrate, as previously described. The corresponding Raman spectrum is characteristic of 1LG (Fig. 1a), featuring a 2D peak with a FWHM of 26 cm⁻¹. The absence of a D peak indicates that the sample has a very low concentration of defects, typical of exfoliated graphene. A close-up of the D band region is included in the Supplementary Information (Fig. S1a). After exposure to hydrogen for 10 min, only minor changes in the contrast are observed in the optical microscopy images (compare the framed areas in Fig. 1b and 1c).

In contrast, topographic AFM images reveal significant changes in the specimen following hydrogenation (Fig. 2a). This image shows a high density of sub-micrometer-sized holes on the surface, which appear as circular dark contrasts. The dimensions of these holes differ from those of the lighter-optical contrast areas observed in Fig. 1c, which are on a different size scale. The hole size distribution, shown in Fig. 2b, provides insight into the dynamics of hole formation. The polymodal distribution suggests the involvement of various formation mechanisms, consistent with the observation of varying hole shapes (roughly round or roughly hexagonal) and/or different stages of hole formation. The broad nature of the distribution indicates considerable variation in the formation process, suggesting that some local configurations are more conducive to hole formation than others. The longer tail of the distribution, extending toward larger sizes, indicates the "coalescence" of holes.

Numerical simulations are essential for understanding the underlying physical mechanisms behind hole formation and expansion, as discussed further below. To the best of our knowledge, apart in Ref [25], the occurrence of holes has rarely been reported in the context of hydrogenation of monolayer graphene deposited on a SiO₂ substrate. Specifically, earlier studies on electronic devices did not include nanoscale topographic images to confirm the potential presence of such holes [1–3]. This omission raises some uncertainty regarding the interpretation of results in the existing literature.

After exposure to hydrogen for 10 min, the Raman spectra reveal the D, G, D', and 2D bands (Fig. 3) [1]. The intensity ratio of the D and G bands $I_D/I_G$ is 0.6 while the $I_D/I_D$ ratio is 10.6, which is close to 13. This suggests that the defect-activated D and D' bands [1] are primarily influenced by the presence of sp³-C atoms, affecting the sp²-C response [32]. These Raman spectra remain consistent even with increasing laser power (up to 7.2 mW). Given the moderate hydrogen coverage (as indicated by the relatively low $I_D/I_G$ ratio), the thermal conductivity of the material is sufficient to prevent hydrogen desorption from laser irradiation at 633 nm. Even with power up to 10 mW, the G band only down-shifted by −2 cm⁻¹, corresponding to a temperature increase of about 86 K [45]. However, when the sample is annealed at 400 °C in H₂/Ar atmosphere, the intensity of both the D band and 2D bands relative to the G band decreases (Fig. 3). Simultaneously, both the G and 2D bands shift, with $\Delta\omega_G = +12$ cm⁻¹ and $\Delta\omega_{2D} = +9$ cm⁻¹, respectively. This results in a $\Delta\omega_{2D}/\Delta\omega_G$ ratio of 0.75, characteristic of hole-doping according to Ref [46]. $I_D/I_G$ decreases from 0.6 to 0.3, and $I_D/I_D$ drops from 10.6 to 5.4. This doping effect indicates that the Dirac cone is restored at the K point. No changes were observed in the AFM image after thermal treatment. These results suggest that a significant portion of hydrogen was removed during annealing, allowing some of the sp³-C atoms to recover their sp² hybridization. This reveals that the hydrogenated material is heterogeneous, with a relatively low overall hydrogen coverage. The optical contrast change observed in Fig. 1c (after 10 min of hydrogenation and before annealing at 400 °C) is thus attributed to the local absence of material (holes), possibly combined with altered photon adsorption properties induced by local hydrogenation and changes in the electronic structure (see Section 3.3.1).
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Left column: 10 min hydrogenation experiment. (a) Raman spectrum. (b) Optical microscopy image of the 1LG sample exfoliated onto a SiO₂ substrate before hydrogenation. (c) Optical microscopy image of the same sample after hydrogenation. Right column: 20-minute hydrogenation experiment. (d) Raman spectrum. (e) Optical microscopy image before hydrogenation. (f) Optical microscopy image after hydrogenation. In both columns, areas of higher contrast indicate multi-layer regions. Insets show close-up views of the framed areas.</figcaption></figure>

However, the significant photon absorption observed overall confirms that the hydrogen coverage before annealing remained moderate.

Raman spectroscopy can be used to estimate hydrogen coverage by evaluating the mean distance between defects. The phenomenological model for the *I*<sub>D</sub>/<sub>I*<sub>G</sub></sub> ratio, originally proposed by Lucchese et al. for ion-bombarded graphene samples [47], may also be applicable to the system shown in Fig. 2a, specifically in the regime where the distance between defects, *L*<sub>D</sub>, is large enough that the nature of the defects does not significantly affect the *I*<sub>D</sub>/<sub>I*<sub>G</sub></sub> ratio [48]. By analogy, we can consider that

a chemisorbed hydrogen induced modifications on two length scales, $r_A$ and $r_S$ (with $r_A > r_S$). These correspond to the radii of two circular areas centered around the chemisorbed hydrogen atom. Within the circular area defined by $r_S$, structural disorder occurs, which is analogous to the “structurally disordered” or “S region” defined in Ref [47]. For distances larger than $r_S$ but shorter than $r_A$, the lattice structure remains intact, but the proximity to the chemisorbed hydrogen breaks the selection rules, enhancing the D band. This is equivalent to the “activated” or “A-region” described in Ref [47]. Areas outside the A-region contribute only to the
<figure><img src="image_3.png" /><figcaption>Fig. 2. (a) Topographic AFM image of the 1LG sample exposed to hydrogen, showing holes (dark contrasts), corresponding to Fig. 1c (10-minute exposure). (b) Distribution of hole sizes in (a). (c) Similar to (a), but corresponding to Fig. 1f (20-minute exposure), showing that the holes have expanded across almost the entire 1LG. Simulated evolution of the graphene surface (yellow) during etching at different time intervals: (d) 10 min, and (e) 20 min. Colored images are available in the electronic version of this article.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Raman spectra of the 1LG sample after 10 min of hydrogenation (red), corresponding to moderate hydrogen coverage, and after exposure to a thermal treatment of 400 °C (blue), corresponding to low hydrogen coverage (see text for details).</figcaption></figure>

G band. Given that the values of rS and rA proposed in Ref [47] are 1 nm and 3.1 nm, respectively [47], the I<sub>D</sub>/I<sub>G</sub> ratio can be expressed as:

$$ \frac{I_D}{I_G} (L_D) = C_A f_A(L_D) + C_S f_S(L_D) \quad (1) $$

In this model, fA and fS represent the fractions of the A and S areas in the graphene sheet, respectively, relative to the total area [47]. C_A and C_S are fitting parameters that account for the contributions of these regions to the Raman spectra. The A-regions, where the lattice structure is disturbed but not fully disordered, contribute most strongly to the D band, while the S-regions, which correspond to areas of significant

structural disorder, contribute less to the D band. In ref [47], C_S = 0.86 and C_A = 4.56 for a 515 nm excitation wavelength. Given that the excitation wavelength in this study is 633 nm and assuming a fourth power dependence of the excitation energy [49], the parameters are adjusted to C_A = 10.74 and C_S = 2.03 at 633 nm. This same approach (Eq. (1)) was applied by AlSalem et al [50], though with different values for rS and rA (0.07 and 1 nm, respectively). The model was also applied by Wang et al [51] in the case of hydrogenation, building on the work of Niyogi et al [52], who proposed a relationship between I<sub>D</sub>/I<sub>G</sub> and L<sub>D</sub>. According to their model, the expression I<sub>D</sub>/I<sub>G</sub> = 25 L<sub>D</sub><sup>2</sup> holds for small L<sub>D</sub>, while for larger L<sub>D</sub>, the relationship becomes I<sub>D</sub>/I<sub>G</sub> = 11/L<sub>D</sub><sup>2</sup> at 532 nm. In our case, the thermal desorption is limited as the layer coverage is low, meaning that the high thermal conductivity of graphene is largely preserved. The final value of hydrogen coverage is governed by the heat induced by the laser beam and the thermal conduction of the defected layer (where defects = edges and chemisorbed hydrogens). Assuming that full deshydrogenation was achieved by the thermal treatment, the reduction in the I<sub>D</sub>/I<sub>G</sub> ratio from 0.6 to 0.3 upon treatment suggests that the minimum value of 0.3 corresponds to the contribution of the sp<sup>3</sup>-C-H bonding to the D band. Using Eq. (1), we calculate L<sub>D</sub> = 29 nm. Alternatively, following the method in Ref [52], L<sub>D</sub> is 8.7 nm, and using the approach in Ref [50], L<sub>D</sub> is 10.4 nm. A L<sub>D</sub> value of 10 nm corresponds to a hydrogen coverage of 0.05 at. %. After thermal treatment, the remaining D band is primarily attributed to the presence of holes, which are associated with edge sites (carbon atoms with dangling bonds) and carbon vacancies. This is supported by the I<sub>D</sub>/I<sub>D'</sub> ratio of 5.6, which contrasts with the expected value of 7 for defects consisting solely of vacancies [32].

## 3.2. Sample exposed to H for 20 min

Fig. 1e shows an optical microscopy image of the graphene sample before exposure to the hydrogenation for 20 min. As with the previous sample, the corresponding Raman spectrum (Fig. 1d) is typical of 1LG,
displaying a 2D peak with a FWHM of 26 cm⁻¹, and no D peak is detected. A close-up of the D band region is included in the Supplementary Information (Fig. S1b). After exposure to hydrogen for 20 min, a significant decrease in contrast is observed, making the flake barely visible (Fig. 1f). The topographic AFM image reveals that a large fraction of the layer has been etched, leaving only some areas intact (Fig. 2c). From the size of the largest circular holes observed in Fig. 2a (0.27 µm), which are presumably the first to have been created at *t* = 0 min and subsequently expanded without merging with others, we estimate that the hole radius increased at an average rate of 13 nm/min during the first 10 min. The linearity of hole expansion—and hence the etching process—was maintained over the following 10 min, as shown in Fig. 2c. This is supported by the results (Fig. 2d-e, and movie S1 in the supplementary information) of a linear model (see Fig. S2 in the supplementary information), which assumes random pit creation at a rate of 40 pits/min over a 5 µm × 5 µm surface (as deduced from Fig. 2b), and a linear etching speed of 13 nm/min. The etching rate observed here at a substrate temperature below 100 °C can be compared to the extrapolated rate of 10 nm/min at 100 °C for 1LG, as reported in Ref [25], confirming previous observations. No features are detected in the Raman spectra at low laser power (below 1.2 mW), suggesting that the remaining material is highly hydrogenated. If this is the case, it may be possible to recover a graphene spectrum by increasing the laser power [53]. Fig. 4 displays the spectra obtained by exposing the sample to increasing power during Raman measurements. The spectra are normalized per laser power for direct intensity comparison. The data show that some graphene Raman signal is gradually recovered starting at a 1.2 mW laser power, although the relative intensity of the 2D band remains low. This recovery is not due to a lack of material or detector non-linearity, as evidenced by the minimal increase in the Si support signal (3T0 peak) with increasing laser power, while the D band intensity increases significantly. At 7.2 mW, the *I*<sub>D</sub>/<i>I</i><sub>G</sub> ratio is approximately 3 (±30 % standard deviation), a value that is rarely reported in the literature but is consistent with the large number of domain edges present, considering the extent of etching observed (Fig. 2c). This suggests that increasing the laser power during Raman measurements can recover the graphene Raman signal and promote dehydrogenation. The thermal desorption is favored by the significantly reduced thermal conductivity, indicating that this situation differs from that of the 10-minute hydrogenated graphene, where the coverage is much lower. As in the 10-minute case, the final hydrogen coverage is governed by both the heat induced by the laser beam and the thermal conductivity of the defected layer. However, the *I*<sub>D</sub>/<i>I</i><sub>D</sub> ratio at 7.2 mW stabilizes around

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Raman spectra of the 1LG sample after 20 min of hydrogenation, followed by exposure to increasing laser power during Raman measurements. The spectra are normalized by laser power for direct intensity comparison.</figcaption></figure>

7, indicating that either the graphene surface was not fully dehydro-
genated or the defect concentration is too high. If the latter is the case,
applying the “stage 2" model, where I<sub>D</sub>/I<sub>G</sub> ≈ 1/L<sub>D</sub>² [32], we obtain L<sub>D</sub> ≈
0.6 nm. As noted by Ref [32], in this scenario, it becomes difficult to
distinguish between different types of defects. It is important to note that
the hydrogenation rate is not linear over time. The adsorption energy for
the first hydrogen chemisorption on a graphene layer has been calcu-
lated to be approximately −0.85 eV. For a second hydrogen atom
adsorbed in the ortho or para position relative to the first, the adsorption
energy becomes even more favorable, reaching around −2.0 eV, while
adsorption in the meta position is less favorable, with an adsorption
energy of about −0.77 eV [5,12], as confirmed by our own calculations.
Other processes, such as the Eley–Rideal mechanism (e.g., H₂ desorp-
tion), also influence the final hydrogen coverage, making it a complex
function of exposure time and experimental conditions.

3.3. Modelling

The hydrogen coverage for the sample exposed to hydrogen for 20 min is significantly higher than that of the 10-minute sample. As previously discussed, the hydrogenation process is not linear: subsequent hydrogen adsorption events are energetically more favorable, particularly in the ortho and para positions relative to pre-adsorbed atoms. For this reason, we focus on the coverage value of the 20-minute sample in the following discussion, which is approximatively 3.5 at. % based on the analysis presented in Ref [50].

3.3.1. Electronic band structure

The contrast variations observed in optical microscopy images
following hydrogenation (Fig. 1), as well as those reported in earlier
work [45], can be attributed to local changes in the optical absorption of
the graphene layer, potentially combined with a reduction in material
surface. DFT calculations of the electronic band structure at increasing
hydrogen coverage (Fig. 5a-c) reveal a progressive alteration of the
Dirac cone, which significantly impacts the optical indices (Fig. 5d-f)
and absorption behavior (Fig. S3). At low hydrogen coverage (~2 at.
%), a bandgap begins to open, consistent with previous studies [22,54],
while portions of the Dirac cone remain intact. At 12.5 at. % coverage,
the Dirac cone disappears entirely, and the band structure exhibits
localized, low-dispersion states near the K point. These changes lower
the real part of the refractive index (n) in highly hydrogenated regions
(Fig. 5d-f), resulting in decreased absorption (Fig. S3) and reduced
optical contrast. As the number of states available for vertical electronic
transitions diminishes, the material becomes more transparent at the
corresponding photon energies. This trend aligns with our optical ob-
servations (Fig. 1 and [53]) and is in agreement with prior theoretical
and experimental studies [55–58]. Thus, increasing hydrogen coverage
leads to bandgap opening, suppression of the Dirac cone, and enhanced
optical transparency.

At 12.5 at. % coverage, the average distance between hydrogen-
defect sites is <2 nm, consistent with the observed decrease in the I<sub>D</sub/
I<sub>G</sub> ratio typically seen in highly disordered graphenic systems when L<sub>a</sub> <
2 nm [59]. Based on the present data, a direct correlation between the
localized, low-dispersion states near the K point and the suppression of
the Raman D and D' peaks cannot be conclusively established. A more
detailed investigation involving phonon dispersion and electro-
n-phonon coupling would be required to assess their influence on
Raman activity, which lies beyond the scope of this study.

Further electronic band structure calculations were performed
considering the same coverage of ~2 at. % with four different config-
urations among which the first three were previously observed in STM
experiments [12]: (i) monomer, (ii) ortho-dimer, (iii) para-dimer, and
(iv) meta-dimer (Fig. S4). The distance between H atoms in the case of
the 1H@(5 × 5) (Fig. S4a) is about 1.2 nm, meaning that they can be
considered isolated. Figs. S4a-d show that, in all cases, a gap opens in
the K-valley, which is responsible for the absence of the Raman G-peak
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Electronic band structure of 1LG at three different hydrogen coverages: (a) 3.1 at. %, (b) 12.5 at. % and (c) 50 at. %. Blue dots represent spin-up electronic states, while red dots represent spin-down states. The band structure of pristine graphene is shown for reference as black lines. Optical indices for (d) pristine graphene, (e) single hydrogen adsorption on a (5 × 5) supercell [1H@(5 × 5)], and (f) single hydrogen adsorption on a (1 × 1) unit cell [1H@(1 × 1)].</figcaption></figure>

shift induced by doping.

As already reported, the isolated-monomer configuration induces a local magnetic moment [60]. The ortho-dimer and para-dimer configurations are the most energetically stable [12], and there is no magnetic moment in their cases (Figs. S4b and S4d in the SI) but there is one in the unfavorable case of meta-dimer configuration (Fig. S4c), as expected from the Lieb theorem and the detailed analysis by Ferro et al [61].

### 3.3.2. Hole formation and growth

We have investigated the initial stage of hole formation, focusing on the first C—C bond breakage, through DFT calculations. This analysis considers the interaction between atomic hydrogen (reactive species) and various models of partially-hydrogenated 1LG. It is known that the adsorption of a single atomic hydrogen on a pristine graphene surface results in an energy gain of approximately 0.8 eV (±0.2 eV, depending on computational settings), with an energy barrier of around 0.2 eV [22, 62]. While H₂ molecules can be formed via the Eley-Rideal mechanism [19], we assume that the formation of hydrogenated "clusters" on the graphene surface (regions where chemisorbed H atoms concentrate) is possible since the next preferred chemisorption site after one H bonds to a C atom is in close proximity to that atom, in ortho or para positions (meta positions are excluded), as reported experimentally [12] and by simulation [5,61]. As a result, the binding energy per H atom [24,54] increases, as the energy barrier for H-adsorption near such H-clusters is reduced [63]. To explore C—C bond breaking, we considered a

one-sided hydrogenated model with high hydrogen coverage, based on boat-like carbon cycles [64], as shown in Fig. 6. In this model, half of the carbon atoms (the protruding ones) are hydrogenated in para positions, with 7 additional H chemically bound to free carbon atoms, as displayed in Fig. 6. To accommodate the induced strain in this high H-coverage configuration, a dome-like structure forms upon geometry optimization, with C atoms exhibiting various intermediate sp²-sp³ hybridization characteristics.

Interestingly, MD calculations for durations exceeding 20 ps indicate that the structural model remains stable at room temperature, without the spontaneous release of H species. To date, direct experimental observation of dome-like structure formation under the specific conditions investigated in this work has not been reported. Our theoretical results therefore provide a novel prediction of such phenomena, offering detailed insight into the size and structure of the domes formed. According to our simulations, the characteristic dome diameter falls within the nanometric range. We hope that these findings will motivate future experimental efforts to detect and characterize dome formation in similar systems.

To identify rate-limiting steps in plausible reaction mechanisms leading to a C—C bond cleavage, several energy barriers must be estimated. These barriers correspond to three steps: (i) the adsorption of an additional H, (ii) the actual C—C bond cleavage to form a -CH₂ (methylene) group with an incoming H, and (iii) further hydrogenation of the methylene group into a -CH₃ group, followed by the formation of molecular CH₄. Step (iii) is not the rate-limiting step, as the release of CH₄
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Side and top views of a largely hydrogenated sp³-C layer with 7 additional chemisorbed H (high-coverage model). The side-view illustrates the boat-like shape of the carbon rings, with the red circle highlighting one C atom free of hydrogen. The adsorption and activation energies for this atom are estimated (see text). The colored figure is available in the electronic version of this article.</figcaption></figure>

(or more complex species) from hydrogenated polyaromatic molecules interacting with H species is nearly barrierless [65–67]. Therefore, our study focuses on the first two steps. First, additional H must be chemisorbed to further destabilize the electronic structure. We assume that

the upper limit of the activation energy required for chemisorbing an additional H on the high H-coverage structure from Fig. 6 is given by NEB calculation, where the initial state involves an incoming free H positioned 0.2 nm above a hydrogen-free carbon atom of the

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** (a) Side view of the initial and final atomic configurations for the reaction of a H-saturated site (red circle as in Fig. 6) peripheral to the dome with an incoming hydrogen (high H-coverage model). (b) Reaction mechanism profile, showing top views of the initial, transition, and final states. In the starting structural state, the red-circled carbon atom is the same as in Fig. 6, after the first H is chemisorbed.</figcaption></figure>
non-distorted one-side hydrogenated structure, at the periphery of the
dome (red circle in Fig. 6). Indeed, we can consider that clustering en-
hances the adsorption energy while simultaneously lowering the energy
barrier, as previously shown in graphene [60,62]. The adsorption re-
action for Step (i) is thermodynamically favorable (ΔE = -0.3 eV) with
an energy barrier of 1.3 eV. This suggests that the formation of the
dome-like structure is feasible within the temperature range typically
used in experiments, and that over-hydrogenation of the sample (i.e.,
hydrogenation of all carbon atoms locally) is also plausible. For
instance, our calculations show that this zone remains favorable for
further adsorption, with local H-saturation being possible. Indeed, an
additional H species can still be adsorbed onto the closest
non-hydrogenated carbon adjacent to the one outlined in red in Fig. 6,
resulting in a decrease in energy by 0.5 eV, while the corresponding
activation energy is 0.9 eV. Subsequently, when an additional H ap-
proaches this site, C—C bond breaking occurs, leading to the formation
of a -CH₂ group adjacent to a -CH group, provided an energy barrier of
1.57 eV is overcome (see state 2 in Fig. 7, which shows for the atomic
configurations of the initial, transition, and final states of this
rate-limiting step). This step is slightly endothermic, as the final state
(state 3) is about 0.3 eV higher than the initial configuration. However
in a second step, with an energy barrier of 0.8 eV (state 4), the -CH group
can then point down so that the final state (state 5) is largely lower (–2.0
eV) in energy than the initial state, making the global process
exothermic. We agree that the activation energy obtained from NEB
calculations for the rate-limiting step, which is C—C bond cleavage, is
probably too large to be considered accessible at the experimentally
measured temperatures. Low energy H (about 0.2 eV for a filament
temperature of 2000 °C) alone cannot be solely responsible for the
creation of holes. An additional agent or process is required to lower the
activation energy. It has been suggested that the substrate polarity or the
presence of charged impurities within the substrate could be responsible
for the observed phenomena [25]. However, we also observed the for-
mation of holes in 1LG deposited on BN flakes, where the charged im-
purity density is extremely low (Fig. S5). This suggests that the etching
process is not driven by charged impurities. The process could involve
residual water or other molecules trapped between the graphene flake
and SiO₂ during the transfer. However, the formation of holes was also
observed in 1LG membranes (Fig. S6), ruling out this interpretation as
well. Additionally, the effect of H₂O molecules on the sample surface is
unlikely, as holes were still observed even after applying a thermal
pretreatment (Section 2.2). A hypothetical hydrocarbon contamination
effect (from the backing pump) is also ruled out, as etching was not
consistently observed [53]. These observations suggest the likely
involvement of energetic hydrogen species, such as ions or atomic
hydrogen, with energies around 2 eV [11]. The hot-filament process is
not expected to generate hydrogen ions [68]. Even if some hydrogen
ions were produced, they could not be accelerated toward the substrate,
as ions cannot be accelerated in the absence of a plasma sheath or
external bias. Therefore, the potential effects of hydrogen ions on the
specimen can be ruled out. However, these ions may be involved if a
plasma is used [25,69,70]. In the hot-filament process, most atomic
hydrogen impinging on the specimen will have thermalized to the local
gas temperature, meaning their energy is well below 0.5 eV [71]. This
energy is insufficient for thermal atomic hydrogen to bind with the basal
plane, as supported by MD calculations [11]. Upon dissociation of H₂
molecules, some atomic hydrogen may leave the filament with kinetic
energy approximately half of the bond dissociation energy (i.e., 4.52 eV
/ 2). If these atoms reach the graphene surface without collisions, their
kinetic energy would be around 2.25 eV. MD simulations have shown
that nanopores in the graphene basal plane can be formed when the ion
energy is approximately 2 eV for circular holes [11]. Electronically
excited atomic hydrogen is not expected to be present near the specimen
under the current experimental conditions due to the large W-fila-
ment/graphene distance and the interposition of a shutter, which
together create a relatively long path, allowing H atoms in excited states

ample time to return to their ground state [71].

Once a hole is formed and remains exposed to hydrogen, hydrogen chemisorption can occur at the edges. Subsequently, when an additional H interacts with the chemisorbed hydrogen, etching can occur, as observed in long-term experiments. This is because, as mentioned above, the release of CH₄ (or more complex species) from hydrogenated polyaromatic molecules interacting with H species is nearly barrierless [65-67].

It is important to note that a low-coverage model, where the dome-
like structure deformation is surrounded by non-hydrogenated carbon
atoms across the graphene layer, leads to similar observations and
conclusions.

The possibility that dome-like features act as Raman hotspots is an
interesting prospect. However, establishing a direct link between these
features and Raman activity would require detailed calculations of
electron–phonon coupling and optical transition matrix elements. While
electronic densities of individual Bloch states can be visualized, this
alone does not allow unambiguous identification of the states involved
in Raman-active transitions. Such an analysis lies beyond the scope of
the present study but represents a valuable direction for future work.

3.3.3. Further discussion on experimental hydrogenation

Hydrogenation on one side is less favorable than on both sides. In the
case of both-side hydrogenation, the lattice deformation caused by one
chemisorbed hydrogen atom is compensated by the deformation
induced by a neighboring hydrogen atom chemisorbed on the opposite
side. As a result, hydrogenation on both sides is more favorable and can
withstand a wider range of hydrogenation conditions. This explains why
genuine diamane can be formed from bilayer graphene [29]. However,
one-side hydrogenation remains the preferred option for fabricating
electronic devices, as it eliminates the need for subsequent transfer on
wafers. In that case, however, the hydrogenation process parameters (i.
e., temperature, flux, and residual pressure) and the sample preparation
are critical. To prevent the formation of holes, it is necessary to employ
rather a low filament temperature (2000 °C) and short exposure time (a
few minutes) [53]. In this work, we have addressed the issue of etching,
which may go undetected when characterization techniques with
insufficient nanometric resolution are employed. For example, X-ray
photoelectron spectroscopy cannot distinguish whether hydrogenation
affects only the edges or also the graphene surface. In contrast, Raman
scattering is more effective for this purpose. A high *I*<sub>D</sub>*I*<sub>D</sub>*ratio* (*> ~10*)
indicates a high H-coverage, where the inner C atoms of the 1LG are
hydrogenated. A low *I*<sub>D</sub>*I*<sub>D</sub>*ratio* (*< ~5*), suggests the presence of edges,
which are likely to host most of the chemisorbed hydrogen. If a shift in
the G band is observed, indicating doping, it means the Dirac cone re-
mains intact. However, if no G band shift is observed, this suggests that
hydrogenation has created a gap.

**5. Conclusion**

The operating conditions for hydrogenation and hydrogen etching
are closely related and may overlap under certain experimental condi-
tions. We analyzed the hydrogenation of 1LG on a SiO₂/Si interferential
substrate at two different exposure times. The optical contrast was
observed to decrease with increasing hydrogenation, most likely due to
heterogeneous local coverage and, in all cases, as a result of both hole
formation in the carbon layer (as revealed by AFM images) and the
consequent modification of graphene's electronic and structural prop-
erties. In the most exposed sample, which was both highly hydrogenated
and highly etched, the Raman signal could be recovered by increasing
the excitation laser power, thereby promoting dehydrogenation. The
complexity and variety of processes involved in graphene hydrogenation
necessitate caution in drawing conclusions; a combination of techniques
with nanoscale resolution is essential for accurately analyzing the effects
and mechanisms of hydrogenation. Our calculations, suggest that the
creation of holes in monolayer graphene is unlikely to be solely caused
by the reaction of incoming low-energy (a few tenths of eV) atomic
hydrogen with carbon atoms from the graphene lattice. The observed
hole formation in 1LG, even on BN flakes with low charged impurity
density, rules out the involvement of substrate polarity, charged impu-
rities, or residual water during transfer. Various experiments have ruled
out the effect of hypothetical hydrocarbon contamination and H₂O
molecules on the graphene surface. These findings suggest the likely
involvement of energetic atomic hydrogen with an energy of approxi-
mately 2 eV. Further modeling and experiments, including gas-phase
characterization, would help clarify this.

CRediT authorship contribution statement

**Tom Fournier:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Samir El Masaoudi:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Iann C. Gerber:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Benjamin Lassagne:** Writing – review & editing, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Jean-Marc Leyssale:** Writing – review & editing, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Kelvin Cruz:** Writing – review & editing, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. **Germercy Paredes:** Writing – review & editing, Validation, Investigation, Funding acquisition, Formal analysis, Data curation. **Felana Andriambelaza:** Writing – review & editing, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Marc Monthioux:** Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Pascal Puech:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Fabrice Piazza:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

Acknowledgments

This research is supported by ANR-21-CE09-0003 GLADIATOR
project and received exchange funding from CNRS (France) through the
French-Dominican International Research Project NEWCA. T.F. thanks
NanoX ANR-17-EURE-0009 in the framework of the "Programme des
Investissements d'Avenir" for the mobility scholarship. This research
was partially funded by the Presidency of the Dominican Republic, by
the Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico
(FONDOCyT), Dominican Republic, grants #2018-2019-1A2-087,

#2020-2021-1A1-066 and #2022-1A1-095, and by the U.S. Office of
Naval Research Global and the Southern Office of Aerospace Research &
Development, grant #N62909-24-1-2000. F.P. would like to thank
Prof. Paul W. May of the University of Bristol for fruitful discussions. S.
E. M. acknowledges EUR grant NanoX no. ANR-17-EURE-0009 in the
framework of the "Programme des Investissements d'Avenir" for
financial support. S. E. M. and I. C. G. thankfully acknowledge the
computer resources through CALMIP initiative (project p0812), and
CINES, IDRIS, and TGCC under the allocation 2024-A0160906649 made
by GENCI.

Declaration of generative AI and AI-assisted technologies in the writing
process

During the preparation of this work the authors used ChatGPT in
order to improve language and readability. After using this tool/service,
the authors reviewed and edited the content as needed and take full
responsibility for the content of the publication.

**Supplementary materials**

Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.cartre.2025.100553.

Data availability

Data will be made available on request.

**References**

[1] D.C. Elias, R.R. Nair, T.M.G. Mohiuddin, S.V. Morozov, P. Blake, M.P. Halsall, et al., Control of graphene's properties by reversible hydrogenation: evidence for graphane, Science 323 (2009) 610-613, https://doi.org/10.1126/science.1167130.

[2] M. Pumera, An Won, graphane and hydrogenated graphene, Chem. Soc. Rev. 42 (2013) 5987-5995, https://doi.org/10.1039/C3CS60132C.

[3] Z. Sun, C.L. Pint, D.C. Marcano, C. Zhang, J. Yao, G. Ruan, et al., Towards hybrid superlattices in graphene, Nat. Commun. 2 (2011) 559, https://doi.org/10.1038/ncomms1577.

[4] R. Martinazzo, S. Casolo, L.H. Hornekær, Hydrogen recombination on graphitic surfaces, in: R. Díez Muiño, H. Busnengo (Eds.), Dynamics of Gas-Surface Interactions. Springer Series in Surface Sciences, Vol 50, Springer, Berlin, Heidelberg, 2013, https://doi.org/10.1007/978-3-642-32955-5_7.

[5] L. Hornekær, Z. Sljivančanin, W. Xu, R. Otero, E. Rauls, I. Stensgaard, et al., Metastable structures and recombination pathways for atomic hydrogen on the graphite (0001). Surface, Phys. Rev. Lett. 96 (2006) 156104, https://doi.org/10.1103/PhysRevLett.96.156104.

[6] L. Xie, L. Jiao, H. Dai, Selective etching of graphene edges by hydrogen plasma, J. Am. Chem. Soc. 132 (2010) 14751-14753, https://doi.org/10.1021/ja107071g.

[7] L.-W. Huang, C.-K. Chang, F.-C. Chien, K.-H. Chen, P. Chen, F.-R. Chen, et al., Characterization of the cleaning process on a transferred graphene, J. Vac. Sci. Technol. A 32 (2014) 050601, https://doi.org/10.1116/1.4886735.

[8] L.A. Chernozatonskii, P.B. Sorokin, A.G. Kvashnin, D.G. Kvashnin, Diamond-like C₂H nanolayer, diamane: simulation of the structure and properties, JETP Letters 90 (2009) 134-138, https://doi.org/10.1134/S0021364009140112.

[9] O. Leenaerts, B. Partoens, F.M. Peeters, Hydrogenation of bilayer graphene and the formation of bilayer graphane from first principles, Phys, Rev. B 80 (2009) 245422, https://doi.org/10.1103/PhysRevB.80.245422.

[10] J.I. Martínez, J.A. Martín-Gago, J. Cernicharo, P.L. de Andres, Etching of graphene in a hydrogen-rich atmosphere toward the formation of hydrocarbons in circumstellar clouds, J. Phys. Chem. C 118 (2014) 26882-26886, https://doi.org/10.1021/jp509195d.

[11] A. Harpale, M. Panesi, H.B. Chew, Plasma-graphene interaction and its effects on nanoscale patterning, Phys. Rev. B – Condens. Matter. Mater. Phys. 93 (2016) 035416.

[12] R. Balog, B. Jørgensen, J. Wells, E. Lægsgaard, P. Hofmann, F. Besenbacher, et al., Atomic hydrogen adsorbate structures on graphene, J. Am. Chem. Soc. 131 (2009) 8744-8745, https://doi.org/10.1021/ja902714h.

[13] J. Liu, S. Chen, R. Papadakis, H. Li, Nanoresolution patterning of hydrogenated graphene by electron beam induced C-H dissociation, Nanotechnology 29 (41) (2018) 415304.

[14] Z. Luo, T. Yu, K. Kim, Z. Ni, Y. You, S. Lim, et al., Thickness-dependent reversible hydrogenation of graphene layers, ACS Nano 7 (2009) 1781-1788, https://doi.org/10.1021/nn900371t.

[15] F. Piazza, K. Gough, M. Monthioux, P. Puech, I. Gerber, R. Wiens, et al., Low temperature, pressureless sp² to sp³ transformation of ultrathin, crystalline carbon
films, Carbon N Y 145 (2019) 10–22, https://doi.org/10.1016/j.carbon.2019.01.017.

[16] F. Delfino, C. Ros, S.M. Palardonio, N.M. Carretero, S. Murcia-López, J.R. Morante, et al., Multi-methodological analysis of hydrogen desorption from graphene, Carbon. N Y 227 (2024) 119211, https://doi.org/10.1016/j.carbon.2024.119211.

[17] J.O. Sofo, A.S. Chaudhari, G.D. Barber, Graphene: a two-dimensional hydrocarbon, Phys. Rev. B 75 (2007) 153401, https://doi.org/10.1103/PhysRevB.75.153401.

[18] D.W. Boukhvalov, M.I. Katsnelson, A.I. Lichtenstein, Hydrogen on graphene: electronic structure, total energy, structural distortions and magnetism from first-principles calculations, Phys. Rev. B 77 (2008) 035427, https://doi.org/10.1103/PhysRevB.77.035427.

[19] D. Eley, E. Rideal, Parahydrogen conversion on tungsten, Nature 146 (1940) 401–402, https://doi.org/10.1038/146401d0.

[20] T. Zecho, A. Güttler, X. Sha, B. Jackson, J. Küppers, Adsorption of hydrogen and deuterium atoms on the (0001) graphite surface, J. Chem. Phys. 117 (2002) 8486–8492, https://doi.org/10.1063/1.1511729.

[21] R. Balog, B. Jørgensen, J. Wells, E. Lægsgaard, P. Hofmann, F. Besenbacher, et al., Atomic hydrogen adsorbate structures on graphene, J. Am. Chem. Soc. 131 (2009) 8744–8745, https://doi.org/10.1021/ja902714h.

[22] R. Balog, B. Jørgensen, L. Nilsson, M. Andersen, E. Rienks, M. Bianchi, et al., Bandgap opening in graphene induced by patterned hydrogen adsorption, Nature Mater. 9 (2010) 315–319, https://doi.org/10.1038/nmat2710.

[23] S. Goler, C. Coletti, V. Tozzini, V. Piazza, T. Mashoff, et al., Influence of graphene curvature on hydrogen adsorption: toward hydrogen storage devices, J. Phys. Chem. C 117 (2013) 11506–11513, https://doi.org/10.1021/jp4017536.

[24] Q. Li, F. Li, Y. Li, Y. Du, T.-M. Shih, E. Kan, Hydrogen induced etching features of wrinkled graphene domains, Nanomaterials 9 (2019) 930, https://doi.org/10.3390/nano9070930.

[25] G. Diankov, M. Neumann, D. Goldhaber-Gordon, Extreme monolayer selectivity of hydrogen-plasma reactions with graphene, ACS Nano. 7 (2013) 1324–1332, https://doi.org/10.1021/nn304903m.

[26] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, et al., Electric field effect in atomically thin carbon films, Science 306 (5696) (2004) 666–669, https://doi.org/10.1126/science.110289.

[27] A.C. Ferrari, J.C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, et al., Raman spectrum of graphene and graphene layers, Phys. Rev. Lett. 97 (2006) 187401, https://doi.org/10.1103/PhysRevLett.97.187401.

[28] F. Piazza, G. Morell, J. Beltran-Huarac, G. Paredes, M. Ahmadi, M. Guinel, Carbon nanotubes coated with diamond nanocubes and silicon carbide by hot-fluor chemical vapor deposition below 200°C substrate temperature, Carbon. N Y 75 (2014) 113–123, https://doi.org/10.1016/j.carbon.2014.03.043.

[29] F. Piazza, K. Cruz, M. Monthoux, P. Puech, I. Gerber, Raman evidence for the successful synthesis of diamane, Carbon. N Y 169 (2020) 129–133, https://doi.org/10.1016/j.carbon.2020.07.068.

[30] F. Piazza, M. Monthoux, P. Puech, I.C. Gerber, Towards a better understanding of the structure of diamanoïds and diamanoid/graphene hybrids, Carbon. N Y 156 (2020) 234–241.

[31] F. Piazza, M. Monthoux, P. Puech, I.C. Gerber, K. Gough, Progress on diamane and diamanoid thin film pressureless synthesis, C 7 (2021) 9. https://doi.org/10.3390/c7010009.

[32] A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K.S. Novoselov, et al., Probing the nature of defects in graphene by raman spectroscopy, Nano Lett. 12 (2012) 3925–3930, https://doi.org/10.1021/nl300801a.

[33] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558–561, https://doi.org/10.1016/0022-3093(95)00355-X.

[34] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186, https://doi.org/10.1103/PhysRevB.54.11169.

[35] P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994) 17953–17979, https://doi.org/10.1103/PhysRevB.50.17953.

[36] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999) 1758–1775, https://doi.org/10.1103/PhysRevB.59.1758.

[37] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996), https://doi.org/10.1103/PhysRevLett.77.3865, 3865–3668.

[38] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132 (2010) 154104, https://doi.org/10.1063/1.3382344.

[39] V. Popescu, A. Zunger, Extracting *E versus k* effective band structure from supercell calculations on alloys and impurities, Phys. Rev. B 85 (2012) 085201, https://doi.org/10.1103/PhysRevB.85.085201.

[40] V. Wang, N. Xu, J.C. Liu, G. Tang, W.T. Geng, VASPKIT: a user-friendly interface facilitating high-throughput computing and analysis using VASP code, Comput Phys Commun 267 (2021) 108033, https://doi.org/10.1016/j.cpc.2021.108033.

[41] M. Gajdos, K. Hummer, G. Kresse, J. Furthmüller, F. Bechstedt, Linear optical properties in the projector-augmented wave methodology, Physic. Rev. B 73 (2006) 045112, https://doi.org/10.1103/PhysRevB.73.045112.

[42] G. Henkelman, H. Jónsson, Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points, J. Chem. Phys. 113 (22) (2000) 9978–9985, https://doi.org/10.1063/1.1323224.

[43] G. Henkelman, B.P. Uberuaga, H.A. Jónsson, Climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113 (22) (2000) 9901–9904, https://doi.org/10.1063/1.1329672.

[44] C. Li, X. Yang, Y. Guo, DFT simulation of interfacial interaction of graphene/SiO₂ composites, Mater. Sci. Semicond. Process. 150 (2022) 106964, https://doi.org/10.1016/j.mssp.2022.106964.

[45] S. Linas, Y. Magnin, B. Poinsot, O. Boisron, G.D. Förster, V. Martinez, et al., Interplay between Raman shift and thermal expansion in graphene: temperature-dependent measurements and analysis of substrate corrections, Phys. Rev. B 91 (2015) 075426, https://doi.org/10.1080/05704928.2010.483886.

[46] J. Lee, G. Ahn, J. Shim, Y.S. Lee, S. Ryu, Optical separation of mechanical strain from charge doping in graphene, Nat. Comm. 3 (2012) 1024, https://doi.org/10.1038/ncomms2022.

[47] M.M. Lucchese, F. Stavale, E.H. Martins Ferreira, C. Vilani, M.V.O. Moutinho, R. B. Capaz, et al., Quantifying ion-induced defects and Raman relaxation length in graphene, Carbon. N Y 48 (2010) 1592–1597, https://doi.org/10.1016/j.carbon.2009.12.057.

[48] L.G. Cançado, A. Jorio, E.H. Martins Ferreira, F. Stavale, C.A. Achete, R.B. Capaz, et al., Quantifying defects in graphene via Raman spectroscopy at different excitation energies, Nano Lett. 11 (2011) 3190–3196, https://doi.org/10.1021/nl201432g.

[49] L.G. Cançado, A. Jorio, M.A. Pimenta, Measuring the absolute Raman cross section of nanographites as a function of laser energy and crystallite size, Phys. Rev. B 76 (2007) 064304, https://doi.org/10.1103/PhysRevB.76.064304.

[50] H. Alsalem, X. Just-Baringo, I. Larrosa, U. Monteverde, X. Jiang, Y. Feng, S. P. Koehler, Evidence for site-specific reversible hydrogen adsorption on graphene by sum-frequency generation spectroscopy and density functional theory, J. Physic. Chem. C 123 (42) (2019) 25883–25889.

[51] Q.H. Wang, Z. Jin, K.K. Kim, A.J. Hilmer, G.L. Paulus, C.J. Shih, M.S. Strano, Understanding and controlling the substrate effect on graphene electron-transfer chemistry via reactivity imprint lithography, Nat. Chem. 4 (9) (2012) 724–732.

[52] S. Niyogi, E. Bekyarova, M.E. Itkis, H. Zhang, K. Shepperd, J. Hicks, R.C. Haddon, Spectroscopy of covalently functionalized graphene, Nano Lett. 10 (10) (2010) 4061–4066.

[53] T. Fournier, K. Cruz, M. Monthoux, B. Lassagne, L. Petit, S. Moyano, et al., Raman analysis of the dehydrogenation process of hydrogenated monolayer graphene, Mat. Chem. Phys. 321 (2024) 129490, https://doi.org/10.1016/j.matchemphys.2024.129490.

[54] Gao, et al., Band gap tuning of hydrogenated graphene: h coverage and configuration dependence, J. Phys. Chem. C 115 (2011) 3236–3242.

[55] M. Mirzadeh, Mani Farjam, First-principles study of bandgap effects in graphene due to hydrogen adsorption, Condens. Matter. 24 (2012) 235304, https://doi.org/10.1088/0953-8984/24/23/235304.

[56] S. Putz, M. Gmitra, J. Fabian, Optical conductivity of hydrogenated graphene from first principles, Phys. Rev. B 89 (2014) 035437, https://doi.org/10.1103/PhysRevB.89.035437.

[57] M. Bruna, S.J.A.P.L. Borini, Optical constants of graphene layers in the visible range, Appl. Phys. Lett. 94 (3) (2009).

[58] R. Santosh, V. Kumar, The effect of pressure on the electronic and optical properties of hydrogenated graphene: a first-principles study, J. Comput. Electron. 18 (2019) 770–778.

[59] A.C. Ferrari, J. Robertson, Interpretation of Raman spectra of disordered and amorphous carbon, Phys. Rev. B 61 (20) (2000) 14095.

[60] D. Soriano, D. Van Tuan, S.M.-M. Dubois, M. Gmitra, A.W. Cummings, D. Kochan, et al., Spin transport in hydrogenated graphene, 2D Mater. 2 (2015) 022002, https://doi.org/10.1088/2053-1583/2/2/022002.

[61] Y. Ferro, D. Teillet-Billy, N. Rougeau, V. Sidis, S. Morisset, A. Allouche, Stability and magnetism of hydrogen dimers on graphene, Phys. Rev. B 78 (8) (2008) 085417, https://doi.org/10.1103/PhysRevB.78.085417.

[62] M. Bonfanti, S. Achilli, R. Martinazzo, Sticking of atomic hydrogen on graphene, Condens. Matter 30 (2018) 283002, https://doi.org/10.1088/1361-648X/aac89f.

[63] M. Casolo, O.M. Løvvik, R. Martinazzo, G.F. Tantardini, Understanding adsorption of hydrogen atoms on graphene, J. Chem. Phys. 130 (2009) 054704, https://doi.org/10.1063/1.3072333.

[64] J. Zhou, Q. Wang, Q. Sun, X.S. Chen, Y. Kawazoe, P. Jena, Ferromagnetism in semihydrogenated graphene sheet, Nano Lett. 9 (11) (2009) 3867–3870, https://doi.org/10.1021/nl9020733.

[65] C. Kanai, K. Watanabe, Y. Takakuwa, Ab initio calculations on etching of graphite and diamond surfaces by atomic hydrogen, Phys. Rev. B 63 (2001) 235311, https://doi.org/10.1103/PhysRevB.63.235311.

[66] D.U.B. Aussems, K.M. Bal, T.W. Morgan, M.C.M. van de Sandenac, E.C. Neyts, Atomistic simulations of graphite etching at realistic time scales, Chem. Sci. 8 (2017) 7160.

[67] D.U.B. Aussems, K.M. Bal, T.W. Morgan, M.C.M. van de Sanden, E.C. Neyts, Mechanisms of elementary hydrogen ion-surface interactions during multilayer graphene etching at high surface temperature as a function of flux, Carbon N Y 137 (2018) 527–532.

[68] P.W. May, J.N. Harvey, J.A. Smith, Reevaluation of the mechanism for ultrananocrystalline diamond deposition from Ar/CH₄/H₂ gas mixtures, J. Appl. Phys. 99 (2006) 104907, https://doi.org/10.1063/1.2195347.

[69] J.D. Jones, W.D. Hoffmann, A.V. Jesseph, C.J. Morris, G.F. Verbeck, J.M. Perez, On the mechanism for plasma hydrogenation of graphene, Appl. Phys. Lett. 97 (2010) 233104.

[70] A. Felten, D. McManus, C. Rice, L. Nittler, J.-J. Pireaux, C. Casiraghi, Insight into hydrogenation of graphene: effect of hydrogen plasma chemistry, Appl. Phys. Lett. 105 (2014) 183104.

[71] N.M.R. Ashfold, P.W. May, J.R. Petherbridge, K.N. Rosser, J.A. Smith, Y. A. Mankelevich, et al., Unravelling aspects of the gas phase chemistry involved in
diamond chemical vapour deposition, Phys. Chem. Chem. Phys. 3 (2001) 3471–3485, https://doi.org/10.1039/b104265n.