Supported Two-Dimensional Materials under Ion Irradiation : The Substrate Governs Defect Production

Focused ion beams perfectly suit for patterning two-dimensional (2D) materials, but the optimization of irradiation parameters requires full microscopic understanding of defect production mechanisms. In contrast to freestanding 2D systems, the details of damage creation in supported 2D materials are not fully understood, whereas the majority of experiments have been carried out for 2D targets deposited on substrates. Here, we suggest a universal and computationally efficient scheme to model the irradiation of supported 2D materials, which combines analytical potential molecular dynamics with Monte Carlo simulations and makes it possible to independently assess the contributions to the damage from backscattered ions and atoms sputtered from the substrate. Using the scheme, we study the defect production in graphene and MoS2 sheets, which are the two most important and wide-spread 2D materials, deposited on a SiO2 substrate. For helium and neon ions with a wide range of initial ion energies including those used in a commercial helium ion microscope (HIM), we demonstrate that depending on the ion energy and mass, the defect production in 2D systems can be dominated by backscattered ions and sputtered substrate atoms rather than by the direct ion impacts and that the amount of damage in 2D materials heavily depends on whether a substrate is present or not. We also study the factors which limit the spatial resolution of the patterning process. Our results, which agree well with the available experimental data, provide not only insights into defect production but also quantitative information, which can be used for the minimization of damage during imaging in HIM or optimization of the patterning process.


Introduction
Ion irradiation 1,2 is one of the most powerful tools to change the atomic structure and properties of the materials through controllable introduction of impurities and defects. The technique suits particularly well for the processing of two-dimensional (2D) materials, because due to the small thickness of the system a uniform distribution of dopants and defects with regard to their depth is not an issue, as evident from numerous examples for graphene [3][4][5][6][7][8][9] or transition metal dichalcogenides (TMDs). [10][11][12][13][14][15][16] Moreover, exposure to energetic ions can be combined with in-situ or postirradiation chemical treatment of these atomically thin targets 11,[17][18][19][20][21] to incorporate foreign atoms into the atomic network due to chemically reactive vacancies.
Focused ion beams can be used to produce defects with a high spatial resolution. They can also be employed for cutting and patterning 2D materials. 22 In this context, the He-ion microscope (HIM), 23 where He or Ne ion beams have sub-nanometer diameters, have been demonstrated to be a perfect tool for not only getting insights into sample morphology, but also altering its structure and geometry at the nano-scale. Specifically, structural defects were controllably introduced in a few-layer MoS 2 sample 15 so that its stoichiometry and electronic transport properties could be 2 tuned. Nanoribbons with widths as small as 1 nm were reproducibly fabricated in graphene 4,6,9,24 and MoS 2 sheets. 15 An increase in Young's modulus of MoSe 2 samples irradiated in HIM was reported, along with the possibility to tune optical properties of TMDs. 25 Structural changes in free standing graphene and that encapsulated between sheets of hexagonal boron nitride under focused helium ion beam irradiation have been studied 26 in the HIM and showed the benefits of graphene encapsulation for post-synthesis doping and self-healing of the beam-induced lattice damage.  Figure 1: Schematic presentation of the channels for defect production in a supported 2D material under ion irradiation by the example of He ion impacts on a MoS 2 sheet on a SiO 2 substrate. Defects, e.g, S vacancies, can be produced by direct ion impacts, by backscattered ions and atoms sputtered from the substrate.

MoS
In the typical experimental setup used for ion bombardment, the 2D target is placed on a substrate, normally a Si/SiO 2 slab. However, the experimental data is frequently rationalized using atomistic computer simulations carried out for free-standing systems. [27][28][29][30] It is tacitly assumed that most of the defects are produced from direct interaction of the primary beam with the target, which as we show below, is not generally true, especially for the case of light ion irradiation in the HIM.
Indeed, the experiments carried out for supported and free-standing 2D MoS 2 31 and graphene 32 clearly indicate that there are substantial differences in the amount of the beam-induced damage and the properties of the irradiated samples.
3 Contrary to free-standing targets (e.g., graphene 33 or MoS 2 suspended on a TEM grid 15,31 ), where all the defects are created by the impinging ions, the substrate can affect defect production in several ways. Putting aside the case of highly-charged ions 34 and swift heavy ions which literally 'blow-up' the substrate so that the 2D material on top is torn apart by the atoms coming from the substrate, 35 defects in the 2D system can be produced at moderate ion energies by two other mechanisms, in addition to (i) direct ion impacts: (ii) backscattered ions 1 and (iii) atoms sputtered from the substrate, as schematically illustrated in Fig. 1. The latter two mechanisms are indirect defect production channels. Moreover, experimental investigations 9,32,36-38 using state of the art focused ion beam technology indicate that the substrate hinders higher patterning resolutions, so that a detailed microscopic understanding of the role of the substrate and its effects on defect production under ion irradiation is required. The substrate also plays the key role in the evolution and annealing of defects. 39 Several attempts to account for the effects of the substrate have been carried out for high-energy (MeV) heavy ion 40 and 30 keV He 32 ion irradiation of supported graphene, but the trends and physical processes involved were not systematically analyzed.
Computationally, this is a very challenging task, as first-principles approaches cannot be used due to the high computational costs required to collect representative statistics for systems composed from a few thousand atoms. Furthermore, analytical potentials developed for multi-atomic systems are either of limited accuracy or are still computationally too expensive for adequate modeling of the system.
In this work, we suggest an efficient scheme to model the irradiation of supported 2D materials, which combines analytical potential molecular dynamics (MD) simulations for the 2D material, augmented with a universal repulsive potential to account for the effects of the substrate on sputtered atoms and a Monte Carlo (MC) method. This allows to assess independently the contributions to the damage from backscattered ions and atoms sputtered from the substrate and hitting the supported 2D system. Using the scheme, we study defect production in graphene and MoS 2 sheets, which are the two most widely used 2D materials, deposited on a SiO 2 substrate. We pay particular attention to helium and neon ions since they are used in HIMs for material modification, nano-patterning and imaging purposes. 23 While for the patterning processes the controllable production of defects in a narrow region is desirable, minimal defect production should be aimed at for non-destructive imaging. Using our approach, we access defect production rates of He, Ne and Ar ions for a wide range of initial ion energies including the HIM-typical energy interval from 1 keV to 30 keV. Our results indicate that in this energy interval defect production in graphene and

Results and Discussion
He ion irradiation. MD and MC simulations of impacts of the projectiles (He, Ne, Ar ions as well as Si and O atoms) onto 2D materials (graphene and monolayer MoS 2 ) were carried out as described in detail in the Methods section. As we are aiming at assessing the effects of low-dose irradiation, we assumed that the ions always impinge into pristine material. To collect representative statistics for different impact points, an irreducible area was chosen as depicted in Fig. 2(c).
In order to include the effects of the SiO 2 substrate in the MD simulations and at the same time have a computationally efficient scheme, we modelled the substrate as an external potential acting on the atoms in the corresponding region (see Figure 2). The potential has no effect on the impinging ions, while backscattered ions were treated using a statistical approach with the data collected from the MC simulations. Splitting defect production into two different channels is possible due to a very small probability for the backscattered ions and sputtered atoms to hit the area where defects were already produced by that same ion. Due to the geometry of the system, we independently considered defect production by the ions coming from above the 2D target, with ion velocity vectors pointing towards the substrate (direct impacts), and from below, with ion velocity vectors pointing away from the substrate (the case for backscattered ions and sputtered substrate atoms).
The average number of defects produced by impinging and backscattered particles, along with those produced by sputtered substrate atoms, were obtained from MD simulations as functions of ion energy and angle. The results for He ions are presented in Fig. 3. It is evident that the number of sputtered S and C atoms increases with ion energy, then quickly drops due to a decrease in the cross-section to displace an atom from the 2D target. This is in agreement with the results of previous calculations. 27,28 The atoms sputtered from the substrate are more abundant than backscattered ions for typical HIM energies. Detailed statistics data of projectile characteristics obtained from the MC data, such as energy and angle probability distributions, can be found in the supplemental material in Fig. 11. The number of sputtered atoms depends also on the incidence angle, with the maximum in defect production being shifted towards higher ion energies for off-normal incidence. He ions as obtained from molecular dynamic simulation. Impacts of He atoms onto MoS 2 from above (a) and below (b). Impacts of He atoms into graphene from above (c) and below (d).
We performed similar MD calculations for the impacts of O and Si projectiles onto MoS 2 and graphene sheets. Only impacts from 'below' were considered. The results are presented in Fig. 4.
The production of defects shows similar trends as for He ions, but the number of sputtered atoms is considerably higher due to larger atomic masses of O and Si atoms as compared to He. By combining the MD and MC data, the average number of sputtered target atoms N total (Mo, S for MoS 2 and C for graphene) can now be calculated: where N direct (He) is the averaged number of directly sputtered atoms per He-ion and N BS (He) , N SP (Si, O) are the contributions from the backscattered ions and sputtered substrate atoms, respectively. The average number of created S-vacancies from direct impacts is given by N direct = N above (E 0 , θ 0 = 0) , where N above is derived from MD simulations with impacting ion starting in the upper half plane with velocity pointing towards the substrate (see the blue trajectory in Fig. 1).
The average number of S-vacancies created by backscattered ions N BS (E 0 ) in turn is estimated by averaging over all possible trajectories (defined by energies and angles E 1 , θ 1 ) of the backscattered ions. This is realized by performing the probability distribution weighted integration of the average number of defects N below (E 1 , θ 1 ) (see green trajectory in Fig. 1) over the energies and angles of the backscattered particles. The integral is further multiplied by the probability P BS (E 0 ) 9 for the ion to be backscattered and hit the 2D target again and the transmission probability T (E 0 ) to obtain the average number of sputtered S atoms where p BS (θ 1 ) and p BS (E 1 |E 0 ) are the angular and energy probability distribution of the backscattered ions, respectively. The latter depends on the incident ion energy E 0 while the former is universal.
A similar expression can be used to evaluate the effects of sputtered atoms N SP (E 0 ) on vacancy production with the backscattering probability replaced by the average number of sputtered atoms and summing over the contributions from Si and O atoms (grey and red trajectories in Fig. 1).
Sulfur atom yield Y S The results obtained with the combined MD and MC approach are presented in Fig. 6. The data for damage production by direct impacts and the data for free-standing material are obtained directly from MD simulations carried out for the same setup. The results for free-standing systems agree well with the previously published data. 27,28 As for MoS 2 , the average number of sputtered S-atoms for He irradiation without substrate shows two pronounced peaks which can be attributed to the sputtering from the top and bottom sulfur layers. 27 The data for direct He ion impacts also 10 shows two peaks, but the second one is considerably suppressed, meaning that the substrate reduces the forward sputtering for the second layer. This is supported by the averaged number of sulfur vacancies per layer obtained by analyzing the defect density and locations after the ion impact (Wigner-Seitz analysis of the final configurations of the MD data).
As compared to the free-standing system, the direct defect production in supported MoS 2 is smaller in the energy range from 400 eV to 800 eV. This is a consequence of the reduced sputtering from S-layer facing the substrate. S recoils generated there (in forward direction) can not easily leave the sample. Furthermore, for typical HIM energies, see the inset in Fig. 6(a), direct sputtering is almost completely absent, while defect production is still noticeable in the supported system. In this energy range indirect sputtering, more specifically the sputtering by substrate atoms can clearly be identified as the dominant damage mechanism. Oxygen has the largest influence, but Si sputtering appears to be more efficient, as for a smaller number of projectiles a compara-  Fig. 6(b) illustrates defect production in free-standing and supported graphene. It is evident that as in MoS 2 , the substrate impedes the production of defects at very low energies, but the effect is stronger than in MoS 2 , as graphene has only one layer of atoms. At high ion energies more defects are produced in the supported system with a substantial contribution from sputtered O and Si atoms. The birds eyes view on the defect production mechanisms of He irradiated MoS 2 reveals that the substrate has a dramatic influence on the atom sputtering rate. For MoS 2 , the sputtering rate is approximately five times larger than without substrate in the HIM energy interval.
A similar behavior is observed for graphene. Such an increase in the damage rate was also found experimentally for the He ion bombarded of graphene supported by a SiO 2 /Si substrate. 32 Ne ion and Ar ion irradiation. Similar to the modeling of He ion irradiation, we carried out simulations of the impacts of heavier Ne and Ar ions onto a supported MoS 2 sheet. We found that the number of backscattered ions decreases dramatically as compared to helium, while the average number of sputtered substrate atoms increases, see Fig. 7. In particular, the probability for Ne ions to be backscattered from the SiO 2 substrate is less than 1% for all the energies and is zero for Ar. Both observations can be understood within binary collision approximation considering the projectile-to-target mass ratio, as backscattering is more likely for lighter ions and the momentum transfer to secondary projectiles is more efficient for a mass ratio close to unity (m He /m Si = 0.14, m Ne /m Si = 0.71, m Ar /m Si = 1.42). As expected, for increasing ion mass the maximum of the sputtering yield shifts to higher energies.  The results for free-standing monolayers are also presented for the sake of comparison. The data for free-standing monolayers, shown as a reference, agrees well with previously published results for noble gas ion bombarded MoS 2 and graphene. 27,28 As follows from the data on the abundance of the available projectiles, Fig. 7, the contribution to the damage in the 2D target from backscattered particles is negligible, and defect production process is governed by direct impacts of ions and by atoms sputtered from the substrate. A salient feature is the suppression of defect production at low ion energies, as the substrate 'stops' the atoms sputtered away from the target and increases the probability for immediate recombination of the vacancy-interstitial pair. It is also evident from Fig. 8 that while the total sputtering yield increases due to the higher ion mass, the enhancement in the indirect sputtering of target atoms is less pronounced than the boost in direct sputtering. This means that for heavier ions the effect of the substrate on defect production is smaller. Nevertheless, as panels (a-c) in F For both He and Ne ions with energies below 1 keV almost all sulfur vacancies are produced within a 8 nm radius from the impact point. However, for typical HIM energies the defective region is more extended: up to two thirds of defects are produced outside the 8 nm region, as is evident from Fig. 9, panels (a) and (b). Although defect density decays rapidly with increasing distance R from the impact point, defects can be created at typical HIM energies even outside the 10 nm range.
As compared to the free-standing material, where defects are expected only in the close vicinity of 15 the impact point, this result agrees well with the previous experimental observations and indicates that backscattered ions and sputtered substrate atoms are the main reason for resolution limitations in patterning of supported 2D materials. 9,36,38 It is interesting to note that spatial extend of the damage also depends on ion mass. As is evident from our results (see Fig. 9) that higher energies (e.g., 30 keV) would give a better spatial resolution for He, while it is the other way around for Ne.
For the latter, the lowest energies still attainable in HIM (e.g., 5 keV) are preferable. for the sample on a substrate. 15 Our results (Fig. 6) indicate that Y ∼ 0.008 S atoms are sputtered away by 30 keV He ion. A dose of 10 17 He + /cm 2 corresponds to N I ∼ 90 ions hitting the primitive cell area. Correspondingly, the relative number of atoms which should still remain in the system is (2 − Y · N I )/2 ∼ 0.6, which is in a very good agreement with the experimental data.
As for He ion irradiation of graphene, our simulations indicated that the number of defects should be larger in supported samples (as compared to free-standing) by a factor of about three, which qualitatively agrees with the experimental ratio 32 for doses below 10 15 He + /cm 2 . Our results for 500 eV Ar irradiation on MoS 2 were also in order-of-magnitude agreement with the dose (about 5 × 10 15 Ar + /cm 2 ) required to sputter ca. 25% of the S atoms. 19 The agreement with the published experimental values for higher Ar energies is even more striking: while for bilayer graphene on

Conclusions
We suggested a computationally efficient scheme which combines analytical potential MD and MC simulations to model the irradiation of supported 2D materials. The scheme makes it possible to assess independently the contributions to the damage from backscattered ions and atoms sputtered from the substrate. The approach can in principle be applied to any 2D material/substrate combination, provided that the potential for the 2D target exists. The method does not require to explicit account for the interaction of the substrate material with the target, as the substrate is replaced by an effective repulsive potential. Using this scheme, we studied defect production in graphene and MoS 2 sheets on a SiO 2 substrate. Our results, which agree well with the available experimental data, demonstrate that depending on ion mass and energy the number of defects produced in the target by the impinging ions can be smaller or larger than in the free-standing material, that is deposited on top of a trench in the substrate or on a TEM grid. For helium and neon ions with a wide range of initial ion energies including those used in commercial helium ion microscope, we showed that defect production in 2D systems can be dominated by backscattered ions and sputtered substrate atoms rather than by the direct ion impacts. The last statement is especially true for light ions. In particular, this is the case for 30 keV He ions, most widely used for imaging and patterning of 2D targets. We also studied the factors which limit the spatial resolution of the patterning process. Our results provide microscopic insights into defect production mechanism, along with the quantitative information, which can be used for the minimization of damage during imaging or optimization of the patterning process.

Methods
Molecular dynamic (MD) simulations were carried out using the LAMMPS 43 package to extract the statistics of defects produced by impacts of the projectiles (He, Ne, Ar ions and Si O atoms) onto the 2D materials (graphene and monolayer MoS 2 ). The MD calculations of ion impacts onto targets were performed as described previously. 27 At minimum 320 impact points per energy and angle configuration were chosen. A modified Stilinger-Weber (SW) potential 44 with a smooth transition to the Ziegler-Biersack-Littmark (ZBL) potential 45 for small distances was used. For collisions of ions with the target atoms the ZBL part dominates at high energies, so that ZBL potentials were also used to describe impacts of atoms sputtered from the substrate. This approximation is further validated by a rather weak interaction of O and Si adatoms with pristine graphene and MoS 2 : the adatoms are mobile on graphene 46 and MoS 2 47 surfaces, so that they should form compounds and desorb from the system. The MD calculations for ion bombardment of graphene were carried out using the combined Tersoff and ZBL potential.
The effects of the SiO 2 substrate were modelled as an external potential acting on the target atoms (Mo,S or C) in the corresponding region (see Fig. 2). The potential in this approximation can be expressed as where the coefficients are determined by the boundary of the potential region z 0 = 2 Å, the surface approximation energy -the energy required to approach a surface located at d = 3 Å (distance from the monolayer) 48 from infinity U (z = d) = 10 eV, and a defined kinetic energy loss of the incident particle with U (z = 4 Å) = 50 eV. This yields the coefficients A = 10/3 eV ≈ 3.33 eV and β = 2 ln 2 Å −1 ≈ 1.38 Å −1 .
The MD approach was combined with the Monte Carlo method implemented in the SRIM code 49