Understanding the interaction between energetic ions and freestanding graphene towards practical 2D perforation

We report experimentally and theoretically the behavior of freestanding graphene subject to bombardment of energetic ions, investigating the ability of large-scale patterning of freestanding graphene with nanometer sized features by focused ion beam technology. A precise control over the He+ and Ga+ irradiation offered by focused ion beam techniques enables to investigate the interaction of the energetic particles and graphene suspended with no support and allows determining sputter yields of the 2D lattice. We find strong dependency of the 2D sputter yield on the species and kinetic energy of the incident ion beams. Freestanding graphene shows material semi-transparency to He+ at high energies (10-30 keV) allowing the passage of>97% He+ particles without creating destructive lattice vacancy. Large Ga+ ions (5-30 keV), in contrast, collide far more often with the graphene lattice to impart significantly higher sputter yield of ~50%. Binary collision theory applied to monolayer and few-layer graphene can successfully elucidate this collision mechanism, in great agreement with experiments. Raman spectroscopy analysis corroborates the passage of a large fraction of He+ ions across graphene without much damaging the lattice whereas several colliding ions create single vacancy defects. Physical understanding of the interaction between energetic particles and suspended graphene can practically lead to reproducible and efficient pattern generation of unprecedentedly small features on 2D materials by design, manifested by our perforation of sub-5-nm pore arrays. This capability of nanometer scale precision patterning of freestanding 2D lattices shows practical applicability of the focused ion beam technology to 2D material processing for device fabrication and integration.

Discovery of isolated and stable graphene has launched a new research field to explore a variety of unforeseen properties of this two-dimensional (2D) material. 1 In particular graphene has drawn significant attention by showing extraordinary mechanical strength, 2 great electrical 3 and thermal conductivities, 4 and virtually uninhibited transmission of light 5 yet hermetic sealing against material permeation. 6 Potential graphene-based technology is proposed for various applications including ultimately permeable membranes 7 and flexible electronics, 8 of which embodiment can be propelled by large-scale synthesis capabilities such as chemical vapor deposition (CVD). 9,10 Device integration of graphene to exploit its unique properties, on the other hand, will require selective patterning via etching or crystallographic modification through exposure to plasma 11 or energetic ions. 12 The evolution of the electrical properties and quality of supported or sandwiched graphene subject to ion irradiation has been investigated, [13][14][15][16][17][18] all assuring that graphene can be patterned by energetic ion irradiation. Nevertheless, it is the presence of a support structure that obscures a mechanistic understanding of the effects of ion bombardment on a 2D lattice of graphene because the bulk sputtering mechanism of the support 19 perplexes the otherwise clearly observable 2D sputtering mechanism. For example, effects of the secondary cascade interaction of bombarding particles with the support layer, such as ion implantation and substrate swelling, 13,15,20 can influence experimental results significantly, eventually hampering the extraction of 2D sputtering mechanism. Freestanding graphene has been patterned using transmission electron microscopy where pores 21 and vacancies 22 can be created with very high precision but limited in scale due to immense irradiation dose required. Nanometer-sized feature formation in graphene has been enabled by block-copolymer self-assembly 23 as well as by strain assisted metal intercalcination, 24 both limited to feature sizes of ~20 nm. In the pattern-size regime other than 20 nm, a focused ion beam milling (FIB) process of freestanding graphene can be a promising technology for practical applications at intermediate scales. Recently, the possibility of pattern generation in freestanding graphene by ion irradiation has been demonstrated by the formation of nanoscale pores, 7, 25 nanoribbons 26 or other geometries, 27 though these studies lack a mechanistic understanding of the energetic-ion-graphene interaction. More insight about the interaction has been obtained by a few theoretical investigations using Monte Carlo simulation. 17,18,28 Despite a growing understanding of the 2D sputtering mechanism including graphene amorphization upon Ga + irradiation, 29 there is few report of combined experimental and theoretical investigation about the fate of freestanding graphene layers subject to ion bombardment of various ion species and energies, hampering exploitation of the advanced manufacturing capability of the ion bombardment on freestanding graphene.
Here, we investigate experimentally and theoretically the perforation physics of unsupported, freestanding graphene by energetic ion bombardment. We differentiate the interaction schemes between energetic ions and graphene layers. Depending on the physical dimension and kinetic energy, incident accelerated ions can either penetrate the freestanding graphene or collide with the atoms of the 2D crystal to produce various vacancies for sputtering. We rationalize these interactions by assuming a binary collision process between incident ion and the graphene lattice.
In great agreement with experimental results, our model successfully elucidates the ion interaction mechanism with freestanding graphene. According to the results, it is the graphene lattice spacing that can, on a certain condition, render this 2D material semi-transparent to incident energetic ions.
Our understanding of the ion-carbon interaction enables to create vacancies and patterns on freestanding graphene by design, leading to an establishment of the reproducible and scalable perforation method for graphene membranes such as sub-3-nm and sub-4-nm pore arrays using He + and Ga + FIB, respectively.

RESULTS AND DISCUSSION:
High degree of control of three synthesis steps for graphene device fabrication (CVD graphene growth, transfer, and subsequent annealing process) yielded ultraclean, freestanding graphene samples (Figure 1a) showing very few graphene wrinkles and sparse contamination sites. These samples transferred to the FIB chamber were irradiated with energetic ions. When exposed to He + irradiation, graphene was resistant to a high dose of ions bombarding the monolayer. We could take images of freestanding monolayer graphene repeatedly at a standard imaging dose (σHe+ ≈ 10 18 m -2 ) of helium ion microscope (HIM) without significant damage to samples, in agreement with pervious findings. 30,31 The power of HIM and the cleanliness of the graphene samples allow to clearly distinguish the layer numbers of freestanding multilayer graphene (Figure 1b).
However, in the same experiment on a FIB system using Ga + ions, we found out that the freestanding graphene quickly deteriorated and was etched away. These findings indicate that the interaction between Ga + and carbon in the graphene lattice is more destructive than that between He + and graphene; namely, a Ga + ion has higher probability to chop off carbon atoms from the 2D lattice than the a He + ion does. To precisely quantify the difference in C atom removal, the sputter yield is determined by patterning 200 nm circular features into monolayer graphene. The average number of vacancies produced per ion bombardment, or a sputter yield γ, shows significantly higher value for Ga + (Figure 2a). For instance, the sputter yield of freestanding graphene upon 30-keV Ga + bombardment is about 47% (γGa+ ≈ 47%), which confirms qualitative findings of previous reports for Ga + -based graphene sputtering. 27,32 This corresponds to a total ion dose necessary to create a pattern in monolayer graphene by 30-keV Ga + ions of ~8.1 × 10 19 m -2 ( Figure   2b) which is very much in line with a recent report 29 of 9.5 × 10 19 m -2 for Ga + at 35-keV.
Furthermore, in our experiments γ of freestanding monolayer graphene showed clear dependency on the energy of the incident particles. For Ga + the reduction of the accelerating voltage from 30 kV to 5 kV increases the sputter yield from γGa+ ≈ 47% to 81% (Figure 2a), in line with predictions of Monte Carlo molecular dynamics simulations. 17,18 Interestingly, these γGa+ values of monolayer graphene are significantly smaller than those of its 3D counterpart: reportedly 120-270% depending on carbon allotropes. 32,33 Figure 1. (a) SEM micrograph of freestanding clean monolayer CVD graphene after transfer on porous SiNx substrate. Brighter lines show graphene wrinkles (double layer) and small bright dots are sparse contaminates of the graphene. (b) Helium ion micrograph of He + patterned freestanding double layer graphene membrane. Local number variation of graphene layers can be clearly distinguished by pronounced brightness changes. (c) Binary collision model illustrated in a centerof-mass reference frame moving at a speed of vc, where collision parameters p and θ are the shortest projected distance and the scattering angle between two colliding particles, respectively (following reference 19 ). (d) Schematic of an ion bombardment process of freestanding monolayer graphene. A red dashed box illustrates a unit cell of graphene. (e) A contour of superimposed energy from 15-keV Ga + to carbon atoms in a graphene unit cell, calculated from the binary collision model. Red shaded area depicts area of double vacancy production.
For He + FIB the sputtering yield is about two-order-of-magnitude lower (γHe+ ≈ 0.7%) than for Ga + FIB. Therefore, pattern generation with 30-keV He + ions requires significantly higher dose of ~5.7 × 10 21 m -2 (Figure 2b). Reaffirming the mechanism of HIM imaging, 30, 31 our finding sheds a renewed light on the possibility that, not only to proton, 34,35 graphene can be nearly transparent to energetic He + ions as shown theoretically. 17 For example, at a kinetic energy of 30 keV approximately 99% of He + ions can penetrate through the monolayer graphene with statistically sputtering little or no carbon atom from the lattice, reminiscent of the photon and proton transmission. The material transparency of graphene is slightly reduced at lower He + acceleration voltages (γHe+, 10 keV ≈ 2.4%, Figure 2a) yet only to ~97.6%. Both observations of the material transmission of H + 34, 35 and He + through the defect-free graphene lattice offers a new insight on the ability of graphene as the barrier material. In the case of increased particle energy or commensurable particle size, graphene crystals in their freestanding state (let alone crystallographic defects) indeed allow the permeation of small atoms through the lattice.
The interaction between energetic ions and carbon atoms in the graphene lattice can be elucidated further by considering the classic binary collision theory. 19,36 This theory assumes an interception of two particle trajectories where the energetic ion at velocity v0 is colliding with a carbon atom at velocity vc (Figure 1c). Depending on the minimum projected distance between two particle trajectories, p, the nuclei start to repel each other to avoid the overlap of the coulombic potential of the nuclei. The scatter angle, θ, can be calculated using eq. (1): where EC = E0 M2 / (M1 + M2) denotes the collision energy with E0 being the acceleration energy of the ion, r the ion-to-atom center-of-mass distance, and V(r) the Ziegler-Biersack-Littmark interatomic potential between ion and atom (Figure 1c). A good approximation for the interatomic  19 It is valid for collisions with kinetic energies higher than a few 100 eV, where interatomic interactions are governed primarily by repulsive nuclei such that the Born-Oppenheimer approximation can be omitted. 37 For each scattering angle, θ, one can calculate the energy transferred, T, from the ion to the atom: A carbon atom is removed from the graphene lattice if the transferred energy T (EC, p) exceeds the lattice displacement energy, EL. Previously reported EL values for graphene range from experimentally determined 22 eV 38 to density-functional-theory predicted 23 eV. 39, 40 We use this energy cut-off to calculate a theoretical sputter yield for ion bombardment of graphene. Defining a graphene unit cell (Figure 1d) with the superimposed transferred energy landscape around each carbon atom we calculated the area fraction corresponding to T(EC,p) ≥ EL (yellow area) in which incident ions transfer energy higher than EL to one carbon atom (Figure 1e) for creating single vacancies, γs. Moreover, an impact of an ion could produce a double vacancy, if the ion hits the unit cell in the area fraction, γd, where the transferred energy to dual carbon atoms is higher than EL (red area Figure 1e). The upper bound of the theoretical sputter yield, γU, of a defect-free, relaxed graphene lattice can be calculated by γU = γs + 2γd. Therefore, γU corresponds to the expectation value out of the discrete probability distribution of the following three events: ion passing without sputtering; producing a single vacancy defect; and producing a double vacancy defect. The calculated upper bound corresponds therefore to the chance of C atom removal from a pristine monolayer graphene target and is necessarily higher than the experimental sputter yield which is an average removal rate in the course of graphene etching (Figure 2a). Continued exposure to ions removes carbon atoms from the lattice, leading to lowered probability of bombarding carbon atoms by the next ion incidence, whose effect is manifested by a decrease in the sputter yield. Therefore, it is reasonable to define a lower bound of the theoretical sputter yield, Since the Ga + ions carries more charges in the nucleus than He + , V(r) with a carbon atom can be stronger and extend wider in space. From eq. (1) and (2), this strongly repelling interatomic potential leads to large scattering angles close to the backscatter condition, θ = π, likely transferring a substantial amount of energy to an atom in the target lattice to chop it off. Besides capturing the different aspects of He + and Ga + sputtering, our model provides an accurate description about decreasing sputter yield of monolayer graphene with increasing kinetic energy of incident energetic ions (Figure 2a), in good agreement with previous predictions. 17,18 At lower kinetic energies the approaching ions get slower, interaction time prolongs, and the resultant scatteringangle distribution would become wider. Specifically, the interaction cross section extends wider in space, and since the average kinetic energy of the ions is still at least two-order-of-magnitude higher than EL, the bombarded atom in the lattice could possibly be removed upon, the results indicate that the repulsive interaction of the defect-free monolayer graphene becomes very strong when the energy of the colliding particle is comparable to or lower than the lattice displacement energy, corroborating the barrier property of monolayer graphene previously reported. 6 The good model fit, indicates that indeed the interactions between the ion and the graphene can be modeled as binary collisions where single C atoms are removed from the lattice when hit by the incoming ion. Therefore, previous theoretical findings are confirmed which show that in the energy range studied the indeed create only single or double vacancy defects. 18 Only significantly lower energies <200 eV or >50 keV would lead to other effects like C atom substitution / ion implantation 28   to γN = γion (N + 1)/2. Using this assumption, we calculated an increase in sputter yields with layer number for both He + and Ga + FIB processes (Figure 2b). For freestanding multilayer graphene, the experimentally observed sputter yield for Ga + ions increases from ~0.5 for monolayer graphene to ~1.3 for quadruple layer samples matching nicely the theoretically prediction (Figure 2b). The consistency between experiment and theoretical prediction shows that interestingly the overall escape of the C atom from the multilayer graphene samples is not inhibited. C atom removal in multilayer graphene could follow the route of a cascading collision of equal collision partners.
Once a C atom in the first layers is hit it recoils and collides with a C atom in the lower layers from where the cascade continues until a C atom in the last graphene layer is removed by forward sputtering or even more complicated effects like catalytic etching in the presence of an underlying graphene layer 38 may cause this counterintuitive finding. For He + ion the observed increase in sputter yield is less than the model prediction (Figure 2b), possibly attributed to a less efficient vibrational cascade since the average transferred energy to the target atom is significantly lower than in the case of Ga + ion sputtering (see Supporting Information). Both results show that in contrast to monolayer graphene ion interaction the presence of additional graphene layers require more extensive modeling attempts.
Vacancy generation mechanism in graphene under energetic ion bombardment can be further elucidated by Raman spectroscopic monitoring of the evolution of pristine freestanding graphene subject to various ion irradiation doses. 2D Raman maps are used to acquire a representative Raman signal from the pristine and irradiated graphene (Figure 3a). The Raman spectrum of pristine graphene verifies high quality monolayer with a sharp G peak of FWHM 23.5 cm -1 at ~1587 cm -1 (Figure 3b), indicative of abundance of sp 2 -hybridized carbon atoms rather than sp 3 . 41 A sharp second harmonic benzene breathing mode commonly named a G' peak around ~2679 cm -1 shows a single peak of twice the intensity of the G peak (Figure 3b), indicative of defect-free monolayer graphene. 42 Defects in the graphene lattice can affect the intensity of the D band (at ~1340 cm -1 ) in the Raman spectrum. This first harmonic or the radial breathing peak of the benzene ring unit activated in the case of asymmetry in a sp 2 -hybridized lattice 41 can originate largely from the vicinity of grain boundaries or vacancy sites and serves as a convenient measure of defect densities of any kind. In particular, the intensity ratio of the D and G peaks, I(D)/I(G), has been shown to follow a characteristic dependency on the defect density. 43 Using the experimentally  (Figure 3c, II). In the third regime in the bonding structure therefore the I(D)/I(G) remains constant around the unity with total peak intensities vanishing slowly until nearly all the atoms are removed (Figure 3c, III). Analysis of the Raman spectrum of ion-irradiated freestanding graphene elucidates the pattern formation on freestanding graphene via FIB (Figure 4). It follows the route of gradual vacancy formation at the initial step ensued by defect agglomeration that ends up amorphizing on the ionbeam irradiated area of the graphene lattice as recently proposed by TEM study of irradiated graphene. 29 At the last step of patterning the amorphous yet sp 2 -hybridized carbon layer is etched away.
Using these insights we could, for the first time, achieve the smallest pore-array patterns on graphene perforated by FIB. The 2D nature of graphene prefers forward sputtering such that each particle removal from the graphene lattice is caused by the particle collision with an incident energetic ion. On freestanding double layer graphene we cut holes with ultimate precision and repeatability at relatively high rates allowing an efficient large scale pattern formation. With ~10 4 Ga + ions per pore at 30 keV in a single-pixel exposure experiment, we could drill into double layer graphene an array of holes smaller than 9 nm (with a mean diameter of 5.8 nm) at the average spacing of 50 nm (Figure 4a). Reducing the Ga + ion dose on monolayer graphene to 2500 Ga + ions per pore we obtained pore sizes of 3.5 nm (Figure 4c), which is significantly smaller than previously reported results of sub-10-nm pores on graphene. 25 The tight control of the exposed ions does not only allow to pattern at the resolution limit of the Ga FIB system, which is defined by the beam size (~4 nm). The low dose guaranties an exceptional short process time of few us per pattern, enabling even large scale patterning of graphene for device integration. Note that these top-down-drilled pore sizes are significantly smaller than sputtering of bulk material could produce. In 3D sputtering process, an incident ion collides with multiple target atoms to initiate a collision cascade within the target material. Recoiling target atoms can induce a momentum inversion of certain atoms close to the surface, resulting in an escape from the bulk phase. 19 These secondary events occur in the vicinity of the incident ion spot called an interaction diameter of which reported values are around 20-30 nm. 47,48 For ion exposure of graphene in HIM we achieved even smaller feature sizes. Here again we could overcome the previously reported interaction diameter limit of 5 nm 47 and repeatedly patterned pore arrays into freestanding double layer graphene with mean diameter of 3.4 nm at 25nm-wide spacing using 30-keV He + ions at 4.4×10 5 per pore (Figure 4b). The effect of total ion dose on the pore size can be observed by exposing a freestanding monolayer graphene with 3.9×10 5 to 6.2×10 5 He + ions (Figure 4d). Despite the single-pixel exposure we see a pore size increase from 4.9 to 7.1 nm caused by the imperfect spot shape of the irradiating beam. By decreasing the number of He + hitting the monolayer graphene to 2.7×10 5 we were able to produce holes with 2.6-nm-wide diameter (Figure 4e), comparable to pore sizes drilled in graphene using TEM systems. 21, 49 Our results show a significant advancement in graphene patterning via FIB milling in terms of feature size and array dimension, enabled by detailed knowledge of the interaction mechanisms involved and the 2D nature of our target material. Use of freestanding graphene allowed us to create patterns while avoiding undesirable secondary effects during FIB milling (e.g., ion implanting and substrate swelling), unlike frequently reported for the supported graphene samples. 13,15,32,50 CONCLUSION: Experimental and theoretical investigations of the interaction between freestanding graphene layers and energetic ion irradiation confirm that pristine graphene could be transparent to material at elevated kinetic energy suggested by previous theoretical investigations. 17 For instance, graphene is highly transparent to 30-keV-accelerated He + particles, only ~1% of which collide with the graphene lattice and sputter carbon atoms as compared with 47% for Ga + (30 keV). Both binary collision theory and experimental characterizations point out the uniqueness of the 2D material sputtering in that the major sputtering mechanism would be a simple binary collision After the patterning we acquire SEM micrographs and measure the resulting pattern area Ap using an image analysis program (ImageJ). The lower bound number of removed carbon atoms N C = σ C ApN can be easily calculated by using the areal density of carbon in graphene σ C (m -2 ) and the number of graphene layers, N. The sputter yield is defined as γion = N C /Nion, where Nion = σion An is the total number of ions irradiating the graphene layer.
Graphene pore characterization: Sizes of pore arrays in double layer graphene were determined using high-resolution SEM images obtained on a FEI Helios 450 at 5 keV, 13pA probe current collecting secondary electrons.
The micrograph was analyzed (ImageJ) with identifying the circular pore area by the dark regions (no secondary electrons generated), from which the diameter or the pore dimension was calculated.
Electron micrographs of the smallest pores created in monolayer graphene were obtained using Hitachi SU8230 SEM at 30 keV and 55 pA probe current and equipped with an SEM detector for a bright-field transmission electron mode (aperture size: 1 mm). Pore area appears as bright area where electrons pass the sample without being scattered. The micrographs were analyzed using the Gatan Digital Micrograph image analysis software.

Author Contributions
JB, IS and HGP conceived the study and designed the experiment. RW provided the freestanding graphene samples. JB and IS performed the experiments. JB analyzed the data. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Transferred Energy
The transferred energy to the target atom in the graphene strongly depends on the collision parameter p. Therefore, one can calculate the amount of energy transferred to the C atom depending on the area fraction = 2 ℎ � of the graphene unit cell covered by p ( Figure   S1). Since energetic ions hit the graphene unit cell at a random location, the area fraction can be identified with the fraction of C atoms hit the graphene target. As a result, one can estimate the percentage of C atoms gaining a certain transferred energy T. As an example ~50% of Ga + ions gaining more than the lattice displacement energy have energies higher than ~200eV compared to only ~15% in the case of He + (Figure S1). Figure S1. Transferred energy for Ga + and He + ion irradiation versus area fraction of the graphene unit covered by collision parameter p. Energy of incident ions given in eV. Two cutoff energies are displaced: black line corresponds to lattice displacement threshold of 23eV necessary to remove a C atom form the graphene lattice whereas the red solid line depicts the threshold line of 200 eV indicating the fraction of hit C atoms having significant recoiling energy.

Lower Bound of Theoretical Sputter Yield
The lower bound of the sputter yield can be derived by the following consideration. Initially the graphene sheet contains total number of carbon atoms, C . Each carbon atom has a scattering cross section area of AC defined by the area in which the transferred energy of the ion hitting carbon atoms exceeds the lattice displacement energy EL (see main text Figure 1e yellow area). The total scattering-cross-section area occupied by the carbon atoms meeting the sputtering condition equals to C C . Initially the probability of hitting a carbon atom, 1 , equals to the ratio of the total scattering-cross-section area to the total defined pattern area, , yielding 1 = � . Once sputtering occurs in this event the number of carbon atoms is reduced by one, giving a new probability, 2 = ( − 1) � , to the next carbon atom to be removed from the 2D lattice. By continuing this argument all the way to the rest of carbon atoms in the lattice, an average sputtering probability is obtained: Now noticing that C � is constant and that At can be expressed in number of initial carbon atoms n C and unit cell area Au ( = 1 2 � C ), one sees that � = 1 � contains the upper bound of sputter yield, . Therefore the mean probability can be rewritten as ̅ = Noticing the summation over , one immediately arrives at = +1 2 .

Limiting Ion Beam induced deposition
On the He + FIB we used relatively high probe currents of 5-17 pA. These values are significantly higher than the standard imaging conditions and previously reported patterning currents of 0.5-1 pA. 15 However, we found the high probe currents to be necessary for large-scale graphene patterning because they enable to pattern 10 6 pores of sub-5 nm in size within 2 hours. For low currents we found out that dose required for the patterning increases substantially (by factor of 10-50). We attribute this increase to the deposition of amorphous carbon material around the patterned area, which prevents readily removing of carbon atoms from the graphene lattice ( Figure S2a).