H⁺ ion-induced damage and etching of multilayer graphene in H₂ plasmas

Despite unique electronic properties arising from its 2D structure,¹ the integration of graphene into future nano-electronic devices still demands considerable efforts.² Multilayer graphene (MLG) has a higher number of conducting channels and a higher band overlap than single layer graphene (SLG). Due to these superior transport properties, MLG is suitable to replace copper in IC circuits' interconnections.^3–5 The possibility of opening a bandgap in bi- and tri- layer graphene, associated with an electron mobility comparable to the reference SLG devices while producing lower noise levels,^9,10 also makes MLG a good candidate to build high-speed transistors.^6–8 However, MLG-based devices and interconnects manufacturing requires to develop efficient MLG-patterning techniques. Since bottom-up methods are not adapted to large-area wafers, top-down approaches combining photolithography and plasma etching steps should be used, as plasma systems can be easily implemented in production lines. Depending on the application, such methods should allow to pattern the entire MLG film, or, for instance, to only etch a precise number of graphene layers (e.g., to produce monolayer graphene samples starting from thicker MLG). Similarly, MLG etching processes could allow to remove, together with the top graphene layers, PMMA or other surface residues (e.g., resulting from the transfer of MLG to suitable substrates), thus providing “clean” graphene samples.

Some experiments report the use of H₂ or O₂ plasma chemistries to thin MLG samples.^11–13 However, Atomic Layer Etching (ALE) of MLG without physical plasma-induced damage still requires considerable efforts. Besides etching applications, chemical modification of graphene by H₂ plasmas can allow to tune its electronic properties from metallic to semi-conducting.^14–16 Hydrogenation of graphene can ultimately lead to graphene-based derivatives such as graphane (the fully saturated hydrocarbon derived from single sheet graphene), which could be used for two-dimensional electronics^17,18 or for hydrogen storage applications.¹⁹ Considerable attention has also been paid to the adsorption behavior of molecular H₂ on graphitic materials (including carbon nanotubes (CNTs), fullerenes, and multilayer graphene), as hydrogen storage is a key challenge for the development of fuel cells technology.^20–23 Finally, interactions between hydrogen plasmas and MLG can also be interesting for nuclear fusion studies and problems of wall erosion in tokamaks.²⁴ 

Although H₂ plasmas seem promising for chemical modification or patterning of multilayer graphene, little is known about the fundamental mechanisms of plasma-MLG interaction. Moreover, the complexity of these interactions makes the empirical search for optimal operating conditions (power, pressure, etc.,) quite challenging. Thus, we develop atomic-scale simulations to investigate the processes governing the interaction between hydrogen plasmas and MLG. By correlating the modifications induced on MLG with the energies and fluxes of plasma particles (thermal radicals and energetic ions), such simulations can assist the development of plasma processes to functionalize, store hydrogen into, or etch graphene layers. To model plasma conditions in high-density H₂ plasmas, the MLG sample should be bombarded by both energetic hydrogen ions and thermal H radicals. However, energy barriers for H adsorption (∼0.2–0.4 eV at 300 K) are known to prevent H radicals to react on the basal plane of graphene in the absence of specific reactivity sites (free edges, ripples, or pre-existing defects).^25–27 Thus, as a first step, we investigate the ion-induced damage and etching of MLG under low-energy (5–25 eV) H⁺ ion bombardment. This range allows to scan values of ion energy typically found in inductively-coupled plasmas (continuous-wave or pulsed) and low-Te plasmas used in the microelectronics industry. The article is organized as follows. Section II describes the important characteristics of the computational method—Classical Molecular Dynamics (MD)—used to study interactions between hydrogen ions and multilayer graphene. Section III presents and discusses results about the effect of ion fluence and ion energy on the modification of successive graphene sheets (hydrogenation, creation of defects and vacancies, and possibility for hydrogen storage). Our conclusions are given in Section IV.

Molecular Dynamics (MD) is a computer simulation method which solves Newton's equations of motion for a system of N interacting particles. Each atom is treated as a classical point and all the underlying physics is embedded in an interatomic potential energy function. In this work, we use the 2nd generation C-H REBO potential from Brenner and co-workers²⁸ to study the interactions between low–energy (5–25 eV) H⁺ ions and ABA-stacked multilayer graphene at 300 K. This potential, successfully tested against DFT calculations to study elementary interactions between monolayer graphene and atomic hydrogen,^25,48 was also used to understand the mechanism governing the anisotropic (lateral) etching of graphene nanoribbons in downstream H₂ plasmas.²⁹ It allows to model short-range forces between atoms and to describe covalent bond breaking/formation with associated changes in atomic hybridization. Long-range van der Walls interactions, important beyond the cut-off of the REBO potential as they hold the graphene sheets stacked together, are also taken into consideration.³⁰ 

In this MD simulation, the MLG sample has a surface area of ∼625 Ų (Lx=Ly=25 Å) and an initial minimum thickness depending on the incident H_x⁺ energy (from 3 graphene layers at 5 eV to 6 graphene layers at 25 eV). As shown in Figure 1, periodic boundary conditions (PBC) are used in the lateral directions to mimic an infinite plane. When using PBC, the Lx and Ly dimensions of the MD box should be large enough to avoid finite size effects but should also be optimized to reduce the computational cost. To determine them, a simulation test case (cumulative H+ bombardment) is initially performed on various surface sizes; the numerical results are then compared to ensure that the chosen lateral size allows to obtain the same MD results as for larger simulation boxes. In the vertical direction, one carbon atom is held fixed at the bottom to anchor the simulation cell. Graphene layers are separated by 3.35 Å and remain stacked together thanks to the long-range Van der Waals interactions. They are stacked with the n + 1 layer in the same position as the n−1, known as ABA or Bernal stacking, which is assumed to be more thermodynamically stable than the ABC (rhombohedral) counterpart.³¹ Since no PBC are imposed in the Lz direction to allow deposition or etching, the thickness of the MLG sample can vary during the simulation due to H implantation or C removal. The distance between the 1st graphene layer and the top of the simulation box is thus not restricted. Exposure of the MLG substrate to hydrogen ions is simulated by impacting the top surface, at random locations, with low-energy H⁺ ions (5, 10, and 25 eV). In practice, energetic incident species like H⁺ ions are not treated as positively charged but interact with the surface as fast neutrals, as it is generally assumed that ions approaching a conductive surface rapidly recombine via Auger neutralization or other processes.⁵³ By experimentally probing the local electronic dynamics of an ultrathin foil impacted by a charged ion, Gruber et al. recently confirmed the ability of graphene to provide tens of electrons for charge neutralization of a highly charged ion within a few femtoseconds.⁵⁴ Each ion trajectory is performed in the microcanonical (NVE) ensemble; atomic positions and velocities are computed using the velocity-Verlet integration scheme with a time step of 0.1 fs. The MLG sample is bombarded anisotropically (at normal incidence) with hydrogen ions; after each impact, the motion of all atoms is simulated during 1–1.5 ps of collision cascade, which allows to capture the physics of the interaction (H reflection, C-H bond formation, etch product formation, etc.). Continuous ion exposure is modelled by performing recursive impact trajectories, where the output configuration for impact i is used as the input configuration for impact i + 1. Since ion fluxes in high-density plasmas are typically <10 mA cm⁻², ions should impact our MD surface (∼625 A²) at approximately once every 10⁻⁴–10⁻³ s. As the kinetic energy from an incoming ion dissipates into the substrate in ∼10⁻¹² s, the recoil atoms in the impact zone should return to the original cell temperature well before the next ion impact. Since simulation of the millisecond interval is not tractable with MD, events occurring in the long times between ion impacts are not directly simulated. Instead, dissipation of excess kinetic energy is treated by applying a Berendsen thermostat at 300 K after each ion trajectory.³³ When long-timescale processes are important (e.g., surface diffusion during material growth), two other types of methods (accelerated MD techniques or hybrid MD-MC simulations) can be used.^34,35 Regarding the simulations performed in this paper, DFT studies have shown that surface diffusion of chemisorbed H on graphene is strongly limited by thermal desorption. Indeed, contrary to carbon nanotubes (CNTs), predicted energy barriers for both processes are very close on graphene (0.94–1.3 eV for diffusion, 1.1 eV for thermal desorption), which rules out long-range diffusion of hydrogen, even at high surface temperatures^50–52 Since H diffusion along the graphene basal plane remains unlikely, as a first approximation, only short-timescale events are considered in this work; simulation results are thus reported in terms of fluence (ions cm⁻²) rather than in flux or time.

The MD package used in this study is an in-house code written in C++, adapted from a pre-existing version developed in UC Berkeley (Graves Lab) in the early 2000s,³² and which was modified along years to study various systems and chemistries. Time requirements to reach steady-state characteristics for simulations of continuous ion bombardment can vary between 4 and 5 days to several weeks on a standard server with 2 six-cores Intel Xeon X5650 processors.

Figure 2 presents the H uptake, defined as the total number of H atoms chemisorbed or trapped in the MLG cell, as a function of the H⁺ fluence for a bombardment at 5 eV. As described in previous studies,^29,49 at low kinetic energy, H⁺ ions can overcome the ∼0.2–0.4 eV surface barrier of the 1st graphene layer and adsorb on its basal plane. However, they do not have sufficient energy to penetrate through the 1st layer, which is why only the upper-side of the top layer is hydrogenated. As shown in the snapshots of Figure 2, H chemisorption occurs preferentially on energetically favorable ortho- and para- positions, as also reported from experimental STM characterizations of hydrogenated graphite surfaces.^36,37 The H uptake rapidly increases with the ion fluence, before saturating at ∼8 × 10¹⁵ ions/cm²; it then oscillates around a steady state value due to competing adsorption/desorption mechanisms. According to MD simulations, once the graphene top layer is H-saturated, 5 eV H⁺ impacts can lead to several surface reactions: 70% H⁺ are reflected, 11% H⁺ recombine with an adsorbed H to form a volatile H₂ molecule (Eley–Rideal mechanism), 8% H⁺ sputter an adsorbed H and are consecutively reflected, and 11% H⁺ chemisorb on new vacant C sites. In this case, the hydrogenation ratio, defined as the number of chemisorbed H atoms divided by the total number of C atoms in the top layer, is equivalent to the H surface coverage. This ratio saturates at 35% because the formation of fully-hydrogenated hexagonal clusters is prevented by the sp²-sp³ surface reconstruction induced by H chemisorption on graphene (all C atoms should move out of the plane to reach a full surface coverage).²⁹ For low H⁺ incident energy, CH bonds are created until the top layer reaches the saturation coverage, with no subsequent modification of the MLG sample. As expected, higher H⁺ ion energies are required to observe H⁺ penetration into multilayer graphene.

Along with the evolution of the H uptake and the number of etched C atoms, Figure 3 presents the dynamics of CH, CH₂, and CH₃ groups formation in the MLG sample, as a function of the H⁺ fluence for a bombardment at 10 eV. The corresponding snapshots of the MD cell are shown for several fluences in Figure 4. We observe two distinct phases: an initial pure-hydrogenation step (I) followed by the beginning of the etch (II). After 5 × 10¹⁶ H⁺/cm², the H uptake saturates and the C etch yield (proportional to the slope of the red curve) becomes constant and equal to ∼0.02 C/ion, which shows that the MLG sample reaches some steady state. As shown in the snapshots, hydrogenation initially takes place on two graphene layers. At 10 eV, H⁺ ions can adsorb directly on the upper-side of the top-layer or penetrate deeper in the sample (∼20% probability). In the latter case, H⁺ ions lose their kinetic energy by collisions with C atoms from the 2nd layer (ABA stacking), which tends to trap them between the 1st and 2nd layers. As shown in Figure 4(a), when the ion fluence is low (<1 × 10¹⁶ H⁺/cm²), hydrogenation occurs on both sides of the upper-layer without creating any physical defects or vacancies. This temporary state is interesting as graphane (the two-dimensional polymer of carbon and hydrogen derived from monolayer graphene) could be a good candidate for hydrogen storage applications or two-dimensional electronics.^18,38 Hydrogenation of the bottom-side of the top graphene layer is facilitated because H adsorption on top-side C atoms leads to sp²-sp³ rehybridization, pulling-up locally C atoms (in a 3D configuration). This facilitates the adsorption of low-energy H atoms (trapped between the 1st and 2nd layer) on the bottom-side of the sp³-hybridized top layer, which brings additional mechanical stress in the graphene sheet. It should be noted that the stress we evoke here is due to a natural strain/deformation of the material appearing due to the sp²-sp³ rehybridization caused by the chemisorption of H atoms on graphene. As detailed in other DFT and experimental studies,²⁵ this deformation of the graphene sample (in terms of 3D geometry and C-C bond elongation) does not depend on PBC or surface temperature/pressure but is intrinsically related to the nature of graphene and the presence of delocalized π-electrons in its sp²-hybridized state. In other terms, the same sp²-sp³ deformations would be observed when no PBC are used or when temperature is increased/decreased, which was verified in a previous MD study of hydrogenated graphene nanoribbons, where no PBC were imposed in the lateral plane (free zigzag edges).²⁹ When the ion dose increases, these strain-induced mechanisms—associated with the kinetic energy locally transferred by ion impacts—result in C-C bond breaking and defects creation in the top layer (Figure 4(b)). Newly-unsaturated C atoms are then rapidly hydrogenated and saturate their dangling bonds by forming CH₂ and CH₃ groups. Under continuous hydrogenation, C-C bond breaking takes place simultaneously in many locations of the top layer, first creating holes/defects and then isolated islands of hydrogenated C atoms, which induces the beginning of C etching (Figure 4(c)). As shown in Figure 5, carbon atoms removal occurs mainly via the formation of CH_x (∼60%) and C₂H_x (∼30%) by-products, a mechanism commonly reported in ion-enhanced chemical etching processes. A large amount of CH₃ is released since CH₃ groups formed on the edge of defects/vacancies can easily be etched by single H impacts (by forming either methane or methyl products). Under continuous H⁺ exposure, the upper-layer of the MLG sample is gradually etched until it is completely removed. Due to the increasing number of etch holes in the top-layer, more H⁺ ions manage to penetrate deeper in the substrate, without losing kinetic energy. They heavily hydrogenate the underneath 2nd and 3rd layers, creating in turn defects in their structure (Figure 4(d)). These observations suggest that layer-by-layer etching of MLG cannot be achieved vertically with 10 eV H⁺ ions without creating damage in the MLG stack. However, chemical functionalization of the underlayers could be less problematic than physical defects (e.g., etch holes), as it may be possible to restore the original graphene lattice by thermal annealing.^13,15

MD simulation of cumulative 25 eV H⁺ ion bombardment shows another possible way to etch MLG, associated with the storage of H₂ molecules between graphene layers. To better understand this specific mechanism, Figure 6 shows the H uptake, the number of etched C atoms, the number of CH_x groups in the sample, and the number of H₂ molecules trapped in the interlayer space as a function of the H⁺ fluence. The corresponding snapshots of the MD cell are shown for several fluences in Figure 7. Initially, H⁺ ions interact mostly with the first three layers of the sample and reach only occasionally the lower ones. They tend to be implanted preferentially between the 1st and 3rd layers. CH bonds are mainly formed on the bottom-side of the top layer, which contrasts with the 2nd layer that is severely hydrogenated on both sides (Figures 7(a) and 7(b)). This is due to the fact that at 25 eV, penetration of H⁺ ions through monolayer graphene is more probable than adsorption.²⁵ Furthermore, the 1st layer shows very few physical damage (creation of vacancies), as H⁺ penetration occurs either through the hollow sites of graphene or by breaking C-C bonds which often reform straight after.²⁵ After passing the 1st layer, H⁺ ions collide and interact with the underneath layers (ABA stacking) at a reduced energy, which allows them to chemisorb on the top-side of the 2nd layer, but also to penetrate and hydrogenate the top- and bottom-sides of the 2nd and 3rd layers. As shown in Figure 6, hydrogenation of MLG also leads to the formation of H₂ molecules in the interlayer space between the 1st and 2nd graphene layers. For fluences <8 × 10¹⁵ H⁺/cm², these H₂ molecules remain trapped in the MLG sample since almost no vacancies (holes to leak through) are present on the 1st layer (Figure 7(b)). Statistics performed on trapped H₂ molecules reveal three possible formation mechanisms: 8% are formed via gaseous recombination (H_(g) + H_(g) -> H₂), 64% via Eley–Rideal recombination (H_(ads) + H_(g) -> H₂), and 28% by recombination from two neighbor C-H bonds (H_(ads) + H_(ads) -> H₂). As shown in Figure 8, the mechanism responsible for H₂ formation changes with the H⁺ fluence and thus with the degree of MLG hydrogenation. Gaseous recombination occurs rarely and only at very low H uptake, as it requires two unbound H_(g) atoms (having too little remaining energy to adsorb on the 1st or 2nd layer) to encounter. Since the density of C-H bonds increases rapidly between the two graphene sheets, the collision frequency of free/gaseous H_(g) with H_(ads) from C-H bonds increases strongly with fluence, making Eley–Rideal recombination more probable. H-H recombination from two neighbor C-H bonds (which vibrate due to thermal motion) occurs mostly at high fluence, when both graphene layers are heavily hydrogenated. Since the interlayer spacing is small (3.35 Å), H₂ molecules interact together and with both hydrogenated graphene sheets. As their number increases, they exert a force that pushes the two layers away from each other, and as a result, the interlayer distance increases (Figure 7(b)). When the cohesive C-C VdW forces holding the graphene layers stacked together become weaker than the repulsive force exerted by the trapped H₂ molecules, the top layer lifts-off in one single piece (Figure 7(c)). Figure 6 shows that this lift-off process (at ∼8.8 × 10¹⁵ H⁺/cm²) is followed by an abrupt drop of the hydrogen uptake in the MLG sample, since H₂ molecules trapped in the interlayer space are released in the gas phase. Furthermore, together with the 238 C atoms suddenly removed, H atoms stored in CH_X groups on the top layer also leave the MLG sample.

At first glance, this process could be considered as a nanoscale version of the well-known Smart-Cut^® technology, in which hydrogen ion implantation at high energy is used to create a fracture (by H₂ gas accumulation) at a precise depth in silicon wafer, allowing to cleave and thus to thin it.^39,40 A similar process has been reported experimentally when studying the cleaning of graphene samples transferred on SiO₂/Si substrates using H₂-based inductively coupled plasma.⁴¹ In some plasma conditions, Ferrah et al. observed a lift-off of the graphene layer before the end of their cleaning procedure, which they attributed to the formation of H₂ gas between the SiO₂ substrate and the graphene layer. For MLG samples, if repeatable, such a process could allow layer-by-layer etching controlled at the atomic scale. However, for such a process to work, the graphene top layer must remain undamaged (no holes or vacancies) to prevent H₂ leaking and allow its accumulation in the interlayer space. For 25 eV H⁺ bombardment, after the lift-off of the 1st layer, the former 2nd layer (now the “new” top layer) contains considerably more defects and holes than the former one (Figure 7(d)). As discussed previously, this is because before the lift-off, the 2nd layer was already hydrogenated on both sides while the 1st layer was not. Due to its graphane-like configuration, the “new” top layer is more sensitive to ion bombardment and C-C bonds rupture from chair conformations in different locations. As presented in Figure 6, for a fluence >9 × 10¹⁵ H⁺/cm², vacancies/holes formation is followed by an increase of CH₂ and CH₃ groups at the surface. It initiates a “regular” ion-enhanced chemical etching process, like the one described for 10 eV H⁺ bombardment. After the first lift-off event, the H uptake and number of C atoms etched increase slowly with fluence, and no more accumulation of H₂ molecules is observed. Instead, Figure 9 shows that C removal occurs mainly via the formation of CH_Y (54%) and C₂H_Y (24%) by-products. Finally, as shown in Figure 7(e), for a fluence >3 × 10¹⁶ H⁺/cm², the MLG surface becomes highly disordered and we observe some mixing between the two top layers. It seems thus impossible to achieve controllable layer-by-layer etching of MLG under pure 25 eV H⁺ bombardment.

One could ask here about the occurrence of rare/long-timescale events (not simulated in this MD work) and their influence on the mechanisms depicted in these simulations. As mentioned in Part II and verified in preliminary tests, short-timescale trajectories (1–1.5 ps of collision cascade) are sufficient to capture the dissipation of the incoming ion energy into the lattice (95% is in fact dissipated in less than 0.5–0.8 ps), as well as the physics of the interaction (H reflection, C-H bond formation, etch product formation, etc.) which generally occurs on a few hundreds of fs. Additional tests were run for the specific bombardment at 25 eV H+, to ensure that the formation/trapping of H₂ molecules followed by the lift-off a full graphene layer was not due to short-timescale effects. For this purpose longer trajectories (up to 50 ps) were simulated, in particular, to verify that H₂ molecules formed were stable and would not leak through the top graphene layer on longer timescales. If H diffusion along the graphene basal plane is unlikely due to energy barriers, more thermal desorption could however occur during the long timescales between impacts.^50–52 Some competition between H adsorption and H desorption was observed when simulating short timescale trajectories (see Figure 2) but this phenomenon could be amplified. In such a case, steady state hydrogenation/etching could be longer to reach (or delayed) compared with our calculations, but we believe this would not change the etching mechanism itself (H adsorption or implantation, formation of CH₂ and CH₃ groups on surface, and C etching). Since our goal here is to understand the etching mechanism at the atomic scale, and not to quantitatively retrieve the fluence or timescales on which it should occur, the main conclusions of the paper thus should not change.

Although only focused on H⁺ bombardment, the mechanisms of ion-induced damage evidenced by this MD study are also supported by other results reported in the literature. Graphite and amorphous carbon sputtering by hydrogen isotopes (mainly mono-energetic ion beams) have been investigated computationally for nuclear fusion related studies.^24,42–45 Using MD simulations, Ito et al. studied the chemical erosion of graphite due to hydrogen isotopes and observed graphite “peeling,” with a flux of detached C atoms increasing linearly with the incident H energy.²⁴ Stuart et al. studied the bombardment of graphite surfaces with 20 eV D atoms and showed that upon bombardment, the surfacemost layers progressively lose their layered structure and become amorphous.⁴² At low fluences (∼1 × 10²⁰ D m⁻²), the outermost layer was shown to become amorphous while the 2nd layer still preserved much of its planar structure; the degradation was shown to continue at higher fluences (1.96 × 10²⁰ D m⁻²) with a 2nd layer soon subsumed into the amorphous outer skin. Although the behaviour of D⁺ and H⁺ ions cannot be strictly compared, these surface evolutions seem consistent with our observations. Focusing on carbon sputtering yields for an amorphous graphite target irradiated with 100 eV D⁺ ions, Marian et al. reported ion-induced release of unsaturated hydrocarbons (IRUH) directly from the bombarded surface, with important quantities of CD, CD₂, CD₃ and C₂D₂ molecules in the by-products distribution.⁴³ The basic mechanism behind IRUH, the so-called swift chemical sputtering, was identified by Salonen and co-workers, who studied the C sputtering yield for an a-C:H cell bombarded by H⁺ ions as a function of the incident ion energy.⁴⁴ They reported C yield values of ∼0.01 C/ion at 10 eV and ∼0.03 C/ion at 25 eV, in reasonable agreement with the values found in our hydrogenated MLG study (0.02 C/ion at 10 eV and 0.05 C/ion at 25 eV). Experimentally, Wojtaszek et al. reported the hydrogenation of single and bilayer graphenes by an Ar/H₂ plasma produced in a reactive ion etching (RIE) system; they showed that under chosen plasma conditions (mostly H₃⁺ ions with E_ion ≤ 5–20 eV and H radicals), the hydrogenation level can be precisely controlled and even reversed.¹⁴ Felten et al. also achieved covalent modification of mono- and bi-layer graphenes using RF hydrogen plasmas.⁴⁵ By studying the evolution of defect density in the sample using Raman spectroscopy, they showed that the hydrogenation rate increases with the exposure time (or ion dose) before saturating. Reporting similar hydrogenation rates for mono- and bi-layer graphenes, they suggested that this could be due to the specific role of energetic positive ions in the functionalization process. In a later study, Felten et al. tested the ability to tune the H ions energy distribution and therefore the degree of functionalization of graphene; by increasing the plasma chamber pressure (and thus reducing the ion energy), they indeed observed a strong decrease in the defect density.⁴⁶ These observations seem to be in global agreement with our MD results and allow to better understand the role of ion energy and ion flux on MLG modification. However, the influence of various H₂-plasma species (energetic ions and reactive neutral species) should be studied to truly compare MD predictions with experimental data. This could be done by bombarding the sample, alternatively and at random locations, with both low-energy H⁺/H₂⁺/H₃⁺ ions and H radicals at 300 K. The impact of additional parameters like the ion composition or the neutral-to-ion flux ratio could be studied. H₂ plasmas are indeed known to contain high concentrations of molecular ions (H₂⁺ or H₃⁺), sometimes in higher proportion than atomic ions (H⁺).^15,46,47 Reactive H atoms, whose density can be 10–100 times higher in the plasma, could enhance the etch rate by reacting chemically on defect-sites produced by ion bombardment (H adsorption and formation of CH_x volatile products). Such simulations are, however, beyond the scope of the present paper.

In this paper, we investigated the ion-induced damage and etching of MLG at 300 K under low-energy (5–25 eV) H⁺ ion bombardment using MD simulations. We more particularly focused on the impact of ion fluence and ion energy on the modification of the successive graphene sheets (hydrogenation, creation of defects and vacancies, and possibility for hydrogen storage). At 5 eV, only the upper-side of the top layer was shown to be hydrogenated as H⁺ ions have enough energy to overcome the hydrogenation barrier but not enough energy to penetrate through the 1st layer. The H coverage was shown to grow with the ion fluence before saturating and oscillating around a value of 35%, due to competing adsorption/desorption mechanisms. At 10 eV, a layer-by-layer peeling/erosion of the MLG sample was observed, associated with damage in the underneath graphene layers. At low fluences (<1 × 10¹⁶ H⁺/cm²), the top layer was almost exempt of defects and hydrogenated from both sides, in a chair or graphane configuration potentially interesting for hydrogen storage applications or two-dimensional electronics. As the H⁺ dose increased, strain-induced mechanisms were found to lead to the creation of defects in the top layer, initiating C etching via the formation of CH_x (∼60%) and C₂H_x (∼30%) by-products. A steady-state was reached after ∼5 × 10¹⁶ H⁺/cm², as evidenced by a constant C etch yield of ∼0.01 C/ion and the saturation of the hydrogenation rate. At this energy, plasma conditions for an ALE process controlled at the atomic scale could be eventually found as hydrogenation of underneath layers can be reversible by thermal annealing; however, the creation of physical defects and vacancies would be more problematic. At 25 eV, an original etching mechanism—associated with the storage of H₂ molecules between graphene layers—was observed. For fluences <8 × 10¹⁵ H⁺/cm², hydrogenation lead to the formation and trapping of H₂ molecules in the interlayer space between the 1st and 2nd graphene layers. As almost no vacancies (holes to leak through) were present on the 1st layer, with increasing H⁺ dose, the H₂ gas accumulation was followed by the lift-off of the entire top layer. This mechanism, similar to a nanoscale version of the Smart-Cut® technology, was not repeated as the underneath layer contained considerably more defects and holes than the former top layer. At higher ion dose, regular ion-enhanced chemical etching of the sample was observed via the formation of CH_x (54%) and C₂H_x (24%) by-products, with a C etch yield of ∼0.05 C/ion and surfacemost layers highly disordered. The mechanisms of ion-induced damage evidenced by this MD study seem to be in reasonable agreement with results reported in the literature and allow to better understand the role of ion energy and ion flux on MLG modification. However, to model plasma conditions found in real high-density H₂ plasmas, the MLG sample should be exposed simultaneously to various hydrogen ions (H⁺, H₂⁺, H₃⁺) and thermal H radicals. For true and more complete comparison with experiments, further investigation of the ion composition and simulations of combined H/H_x⁺ bombardment should be carried out in the future.

We are grateful to the Nanosciences Foundation of Grenoble, for the financial support of this work in the frame of the 2010 Chairs of Excellence Program. The authors also thank the French National Research Agency in the frame of the cleanGRAPH project (ANR-13-BS09-0019-4). D.B.G. acknowledges partial support from the U.S. Department of Energy Office of Fusion Science.