Article pubs.acs.org/JPCC
Drilling Nanopores in Graphene with Clusters: A Molecular Dynamics Study Shijun Zhao,† Jianming Xue,*,†,‡ Li Liang,† Yugang Wang,†,‡ and Sha Yan† †
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, P. R. China Center for Applied Physics and Technology, Peking University, Beijing 100871, P. R. China
‡
S Supporting Information *
ABSTRACT: Using molecular dynamics simulation with empirical potentials, we show that energetic cluster ion beam is a powerful tool to drill nanopores in graphene, which have been proved to possess the potential applications in nanoporebased single-molecule detection and analysis such as DNA sequencing. Two types of clusters are considered, and different cluster size and incident energies are used to simulate the impact events. Our results demonstrate that by choosing suitable cluster species and controlling its energy, a nanopore with expected size and quality could be created in a graphene sheet. Furthermore, suspended carbon chains could be formed at the edge of the nanopore via adjusting the ion energy, which provided a feasible way to decorate the nanopore with chemical methods such as adsorption of large molecules or foreign atoms for biosensing applications.
1. INTRODUCTION Graphene has wide applications due to its excellent twodimensional property. Recently, graphene with nanopores has been proved to be enormously useful in nanopore sensors. It is ascertained that a single nanopore in graphene is the most prospective candidate for nanopore-based DNA sequencing with current-blocking method because of its ultrathin thickness which enables it to distinguish single base.1−8 The potential applications of graphene with multinanopores have also been demonstrated, such as seawater desalination, biosensors, ionic sieves of high selectivity and transparency, etc.9−12 Consequently, the approach for drilling nanopores in graphene has aroused much attention. Subnanometer pores could be generated in graphene by using a focused electron beam.1,2,4,13 However, it is not feasible to use this approach widely because of its low efficiency and high cost.14 In this sense, heavy ions are more effective to manipulate the morphology of graphene because of their much larger masses compared with electrons, which means more kinetic energy could be transferred to the target atoms. Energetic ions have been used widespread to tailor the structure and properties of nanostructured carbon materials with high precision, and it has been successfully used to tune the structure of carbon nanotube as well as graphene.15−18 It has been demonstrated that spatially localized ion irradiation could lead to modifications of graphene in a controllable manner, such as cutting or doping graphene.19−22 While ion irradiation is routinely used nowadays to achieve the manipulation of graphene in a controllable manner, one can expect that graphene subjected to the impact of energetic ions will be an appropriate method to create nanopores with desired parameters. © 2012 American Chemical Society
In order to drill a nanopore in graphene with ion beams, one possible way is to use the ion track lithography method,23 which allows the energetic ions to bombard the graphene through the predefined nanopores in a mask. Nevertheless, the predefined pore should not be too small so that plenty of incident ions could pass through it. Besides, it is of low efficiency for processing large and multiple nanopores. In this regard, the most effective way is to take advantage of cluster ion beam which contain thousands of atoms. Cluster is an aggregate of ions which has characteristic properties compared with single ion from the viewpoint of not only material science but also ion beam engineering. The collisional process of cluster and solid target is termed the “nonlinear” effect,24 which gives a very high efficiency in damaging materials. Previous works about the ion beam processing with graphene were mainly concentrated on cutting or doping graphene with energetic ions.20,21,25 Only simple defects induced in graphene such as single vacancy and double vacancies were investigated in these studies. Both simulation and experiment shows that large area damage in a graphene sheet could appear when bombarded with a cluster.26,27 Therefore, by carefully choosing the parameters of the incident cluster, it is possible to fabricate a nanopore of high qualities in a graphene sheet. In this paper, we present our systematic molecular dynamics investigation on the nanopore formation in graphene induced by energetic clusters, which are different not only in mass but also in the cluster size. The dimension and quality of the pores produced in graphene are analyzed in details as a function of Received: March 10, 2012 Revised: May 1, 2012 Published: May 9, 2012 11776
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Figure 1. The characteristics of the nanopore created by the impact of energetic clusters are dependent on its incident
the parameters of incident clusters. Our results indicate that cluster ion beam is a powerful tool to fabricate nanopores in graphene, and the diameters of the nanopores can be controlled by changing the energy and diameter of the cluster.
2. METHODS Empirical molecular dynamics was performed to simulate the impact of cluster on the graphene. The large scale atomic/ molecular massively parallel simulator (LAMMPS) code28 is used in our simulations. We only considered the energy loss originated from elastic collisions between the cluster and the graphene because nuclear stopping prevails during the ion− graphene interaction process. The electronic stopping such as ionization and excitation was not taken into account in the calculations since it is not important owing to the excellent charge and heat conductance of graphene. C60 and Aun clusters (n = 249, 887, 3925) were used in this simulation. The incident Aun clusters had spherical shape and fcc structure. The interaction between Au atoms were described with an embedded-atom-method (EAM) potential,29 and the Aun clusters were fully relaxed using this potential before the impact simulations. To model the C−C interatomic interaction in the graphene, we used the adaptive intermolecular reactive empirical bond order (AIREBO) potential.30 This potential allows for covalent bond breaking and creation and has been successfully applied to study the properties of carbon-based nanomaterials such as condensed-phase hydrocarbon molecules,31 nanotubes,32,33 and graphene.34−36 The Aun cluster− graphene interatomic interactions were calculated with only the Ziegler−Biersack−Littmark (ZBL) universal repulsive potential.37 This simplification was based on the fact the binding energy of Au−C was very weak compared with that of C−C. The interactions between C60 and graphene were modeled by Tersoff-like potentials.38 This potential was smoothly splined to the ZBL potential at short interatomic distances, which included a short-range repulsive force between all pairs of atoms to better describe the collisions. The graphene target consisted of 36 864 atoms, and its dimension was 30.67 × 31.49 nm. Periodic boundary conditions were applied on the two lateral directions. The initial configuration was fully relaxed before the impact simulations, and the target temperature was maintained at 300 K with a Nosé−Hoover thermostat39,40 in a canonical ensemble. The graphene was then bombarded at normal incident angle with clusters which are placed 60 Å above the surface. This relative large separation precluded any interaction between the cluster and graphene before the incidence. During the collision phase, a Berendsen thermal bath41 was introduced at the borders of the graphene. The thermal bath was governed by the Berendsen algorithm to keep the temperature at 300 K, which absorbed excess kinetic energy given by the cluster impact in order to prevent waves induced by the bombardment to return back to the impact region over periodic boundaries. The system was allowed to relax for 10−15 ps after the ion impact depending on impact energy. Test simulations with longer time showed that the damage area did not change after that at the energies used in the simulations.
Figure 1. Ball-and-stick schematic presentation of the simulation setup. The incident clusters are represented by yellow spheres. A thermostat is applied to the borders of graphene, which is emphasized by the red area.
energy, configuration, and size of the cluster as well as the impact point in graphene. Therefore, we investigated the pore formation process, removed atoms, and the size of the pore created when the energy per cluster atom varied from 0.5 eV/ atom to 500 keV/atom. For each incident energy and cluster, 10 independent runs were carried out by randomly choosing the impact point and orientation to obtain the statistical value. To illustrate how the nanopore is created, we first show in Figure 2 the formation process of a nanopore in graphene due
Figure 2. Several snapshots of the nanopore formation in graphene resulted from the impact with Au887 with an energy of 50 keV/atom. The snapshot (a) is taken when the cluster just penetrated through the graphene. The subsequent evolution of the nanopore is shown at times of (b) 0.15, (c) 1.15, and (d) 30.15 ps. Only the carbon atoms are displayed with green spheres for clarity. The ripples induced by the incident cluster with hexagon shape can be seen as a result of the fcc structure of Aun cluster. The removed carbon atoms get far away from the graphene plane with an increase in time. The carbon chains at the edge of the nanopore are formed self-organized.
to the impact of 50 keV/atom Au887 cluster in details. The carbon atoms which directly interacted with incident Au are all removed as indicated by Figure 2a. These carbon atoms are then moving far away from the graphene sheet with an increase of time. As a consequence, a nanopore is created in graphene. A hexagonal ripple is observed in Figure 2c owing to the fcc structure of Au887 cluster, and it is obviously dependent on the
3. RESULTS AND DISCUSSION 3.1. Nanopore Formation Process. In present work, four different clusters (C60, Au249, Au887, Au3925) are considered. A schematic illustration of the simulation setup is presented in 11777
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observed that C60 disintegrates in the collision with the graphene, and all of its constituent carbon atoms collapsed in it. As a consequence, the number of removed atoms is limited to a small area and leads to a relatively small nanopore. On the other hand, when the full Aun cluster interact with graphene, the carbon atoms within the footprint area of the cluster are all displaced. Second, due to the large mass of Au, the primary knock-on atoms still have enough energy to induce the secondary displaced atoms at the edge of the pore, which leads to the bigger area of the nanopore formed in graphene. Examination of the atomic structure during the impacts revealed that the damaged zone in graphene is much bigger than the cross-section clusters. This observation accounts for the very large area created for incident Aun clusters. 3.3. Threshold Energy for Nanopore Formation. We can see from Figure 3 that the nanopore can only be formed when the energy of the incident cluster is within a certain range. Accordingly, it is necessary to introduce the concept of lower and upper threshold energy for the incident cluster to form a nanopore in graphene. Here, the threshold energy is defined as the energy of cluster which leads to the rupture of graphene sheet and results in a nonzero area of the nanopore. Only the incident cluster with energy above the lower threshold and below the upper threshold can give rise to the formation of nanopore. The lower threshold energy for the incident C60 and Aun to create a nanopore in graphene were calculated, and the results are summarized in Table 1.
orientation of incident clusters. Some carbon atomic chains are formed self-organized at the edge of the nanopore finally (Figure 2d), which suggests that a line of carbon atoms are energy favorable structures, as will be discussed in more detail later in this paper. 3.2. Size of Nanopores. We then calculated the size of the nanopore formed in graphene resulted from one cluster collision as a function of incident energy. The area of the nanopore is obtained by comparing the atomic structure before and after the incidence of cluster. If no atom exists in the lattice position defined by the carbon atoms in intact graphene, a hole with the radius r is regarded to be created at the lattice site, where r is the average bond length between carbon atoms in graphene. The total area of these holes is taken as the size of the nanopore formed in graphene.26 The area of the nanopore created depends on the position where the collision between incident cluster and graphene occurs as well as the orientation of the incident cluster. Consequently, different impact points and orientations were selected within a square region in the middle of graphene in our simulations, and the results of 10 independent runs were averaged to obtain the statistical value. The results are shown in Figure 3.
Table 1. Lower Threshold Energy (in eV/atom) for Different Clusters To Create a Nanopore in Graphenea clusters
lower threshold energy per atom
lower threshold energy per unit area
C60 Au249 Au887 Au3925
11.4 18.3 15.6 9.8
17.3 14.5 19.5 19.6
a
These energies are averaged from 10 independent runs. The total energy per square angstrom of the cross section (in eV/Å2) for each cluster are also presented in the third column.
Figure 3. Dependence of the area of nanopore created in graphene caused by the impact of energetic clusters on the collision energy. The red lines in these figures denote the cross-section area of incident clusters.
When the energy of C60 was less than lower threshold, the incident C60 first collapsed on the graphene and spread in the lateral direction along the surface. All of the carbon atoms in C60 adsorbed on the graphene and formed strong bonds with graphene owing to the chemical properties between carbon atoms. As a result, a C60−graphene composite was produced by the impact without any pore formation in graphene (see movie S1 in Supporting Information). When the energy was increased to the lower threshold, the collision of C60 with graphene could give rise to the formation of pores. In this case, most of the incoming carbon atoms passed through the graphene which resulted in the creation of nanopore, although a small part of C60 still adsorbed on the edge of the pore and became indistinguishable from those carbon atoms in graphene (movie S2 in Supporting Information). It is worth mentioning that these adsorbed carbon atoms, either with or without pore formation, are very interesting because they can be functionalized chemically.43 For Aun clusters, when the energy is below the lower threshold, the incident cluster could not traverse the graphene. The cluster was just reflected back due to the strong repulsive interactions between the Au and C atoms. The graphene acted
It is demonstrated in Figure 3 that the curve of the nanopore area resulted from the bombardment of high-energy C60 intersects with the line of the cross-section area of C60. It is clear that the total damaged area increases with ion energy first and then decreases at high energies. The reason for such behavior is that at low energies the damage production grows with ion energy since there is more energy available for the displacement of atoms, while the cross section for defect production drops at high ion energies.42 As a result, highenergy carbon atoms can hardly damage graphene sheet as most of the carbon atoms could travel through it without any damage production attributed to the low cross section for defect production at high energies.20,25 However, the areas of pores induced by the collision of Aun clusters are all much bigger than the cross-section area of these clusters. There are several reasons for this fact. First, the C60 is an empty shell while Aun cluster is a full sphere. Upon C60 bombardment, it is 11778
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as a flexible membrane and the impact just caused some ripples and no damaged region was formed (movie S3 in Supporting Information). To create a hole in graphene sheet, the energy of Aun cluster must exceed the lower threshold as shown in Table 1, which resulted in the rupture of the graphene and all the Au atoms could move through the graphene (movie S4 in Supporting Information). It is observed that the lower threshold energy of Aun is decreasing as the size of the cluster increases. This implies that a big size Aun cluster is easier to rupture the graphene sheet when the energy per cluster atom is the same. This is related to the energy density of clusters. The collision area when incident clusters interact with graphene sheet is approximately the cross section area of the cluster. The total energy per cross section area of the Au3925 cluster is the biggest (19.6 eV/Å2) as indicated in the Table 1, which renders graphene the most vulnerable to rupture when bombarded with Au3925 cluster and leads to the smallest lower threshold energy (9.8 eV/atom). This conclusion is in line with the damage formation in Si surface impacted with Ar clusters, in which the threshold energy to cause displacement decreases with increasing cluster size due to high-energy density irradiation effect induced by cluster bombardment.44 Not only there is a lower threshold of the ion energy to create nanopores in graphene, but also there is an upper threshold. As indicated in Figure 3, the pore area decreases with increasing cluster energy when the incident energy is above 100 keV/atom. It could be expected that the nanopore could not be formed when the energy is high enough. For C60, nearly no atom could be knocked out when the cluster energy is higher than 300 keV/atom. However, this upper limit should be higher for Aun clusters due to its larger mass. 3.4. Distribution of Nanopore Size. The error bars presented in Figure 3 for the incident Aun clusters are bigger than those for C60 due to the fact that the fcc structure of Aun clusters makes them not strictly spherical in shape while the C60 is close to the perfect spherical appearance. As a consequence, the area of nanopore created in graphene is more dependent on the cluster orientation and impact point for the incident Aun clusters. To illustrate how sensitive the area of nanopore is to characteristic of incident clusters, we have made a histogram graph of the minimum values (Smin) and maximum values (Smax) of the area created, as shown in Figure 4. It is observed that the variation trend of Smax/Smin is similar to that of the mean area of nanopore shown in Figure 3, which has a maximum at certain energy in accordance with the peak in the area of nanopore owing to the maximal displacement cross section in this energy. Closer examination of Figure 4 reveals that the area created by collision of C60 has a larger deviation with the largest Smax/Smin ratio of 8.5. However, the largest ratio is only 2.0 for incident Aun clusters. For this reason, Aun cluster is more suitable to fabricate nanopores in graphene with a homogeneous size distribution. 3.5. Efficiency of Cluster Impacts. To get deeper insight into the efficiency of cluster impact on the nanopore formation, we calculated the number of removed atoms resulted from impact of different clusters, which is the number of target carbon atoms removed from the graphene with one cluster impact. It is determined as the number of carbon atoms kicked out of graphene plane after the incidence of clusters. Those carbon atoms with vertical distance beyond zcut value above or below graphene are viewed as removed atoms. In this simulation, we first calculated the number of removed atoms
Figure 4. Histogram illustration of the area of nanopore created in graphene due to the impact of energetic clusters.
as a function of zcut which represented the total number of atoms that crossed the planes at the height (+zcut) and (−zcut) beyond the graphene plane. A large quantity of atoms could cross the planes when zcut was small, but this number decreases gradually to a stable value as the zcut increased. By comparing these curves obtained at different time elapsed after a cluster impact, the value of zcut that led to the stable number of removed atoms is determined to be 8 Å.45 Thus, the planes at ±8 Å above or below the graphene plane are taken as the criteria, and those atoms crossing these two planes are regarded as removed atoms, as it indicates that these atoms are well beyond the interaction distance with the graphene. With this approach, the number of removed atoms caused by the impact of different clusters as a function of cluster energy is provided in Figure 5. We can see from Figure 5 that the number of removed atoms is corresponding to the area of nanopore in graphene induced by the collision of clusters in Figure 3. Because of a large quantity of carbon chains connected to the edge of pores, the displaced atoms counted as area are more than the number of removed atoms.
Figure 5. Number of removed atoms resulted from the impact of different clusters as a function of incident energy. 11779
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It is shown in Figure 5 that the number of removed atoms increased with the increasing cluster size. However, these numbers are all smaller than the number of constitute atoms of cluster because of the existence of carbon chains in the edge of the nanopore. The dangling carbon chains with an end attached to the graphene are not included in the removed atoms. Upon closer inspection, we find that for the incident C60 the number of removed atoms first increases with energy when the incident energy is below 1 keV/atom, then it decreases, and finally saturates for high energies. The maximum of the number of removed atoms can be interpreted by the peak in the displacement cross section for defect production.42 In general, the variation trend of the removed atom numbers resulted from the impact of Aun clusters with energy is similar to that of C60. When the incident energy is below 30 keV/atom, the removed atom numbers increase quickly with energy, and then they decrease and finally achieve a stable value for high cluster energies. This is ascribed to the movement of the maximum of the displacement cross section to higher energies due to the large mass of Au. The number of removed carbon atoms because of the impact of energetic clusters finally tends to a steady value even if the kinetic energy of the cluster increases. The interaction time between the clusters and graphene is very short when the incident energy is high. Because of the planar structure of graphene, the incident cluster can interact with graphene only once. For this reason, the removed atoms are mainly those displaced atoms directly by the collision. 3.6. Morphology of Nanopores. The morphologies of the nanopores formed resulted from the impact of C60 and Au249 clusters with the energy of 0.5, 50, and 500 keV/atom are shown in Figure 6. As discussed above, we can see that the area of nanopore created depends on the size of incident clusters. For the relative smaller C60, the removed carbon atoms are limited. As a consequence, the nanopore produced in graphene is rather small compared to those created by the incidence of Au249. Furthermore, the nanopores created by energetic Aun clusters are closer to circular pores. As can be seen in Figure 6, the morphologies of nanopores are dependent on the energy of the clusters. For the C60 cluster, more carbon chains are observed at the edge of the nanopores when its incident energy is 50 keV/atom (Figure 6b) compared to that of 0.5 keV/atom (Figure 6a). There is no evidence of nanopore formation when the energy of C60 is increased to 500 keV/atom (Figure 6c), which suggests that the graphene sheet is transparent to the C60 cluster. This is because the irradiation induced changes in graphene are dominated by knock-on atom displacements and electronic excitation and ionization effects are less important as graphene is excellent heat and charge conductor.46 When the C60 cluster with the energy of 500 keV/ atom penetrated the graphene, the graphene cannot be damaged by the cluster ascribe to the lower cross section for defect production. In fact, most energy is dissipated into the whole membrane via heat and electric conduction with few elastic collisions in this energy. The resulted defects are typically Stone−Wales (SW) type47 as emphasized by red pentagons and heptagons in Figure 6c, which is an important topological defect in sp2-bonded carbon materials. When the Au249 cluster interacts with graphene, all the carbon atoms in the collision area are removed and subsequently leads to the formation of nanopore. There are increasing carbon chains observed with increasing energy of Au249 cluster which is attributed to the big displacement cross
Figure 6. Final atomic configurations resulted from the incidence of C60 and Au249 clusters with the energy of 0.5, 50, and 500 keV/atom, where the carbon atoms are indicated by green spheres. The red ball and stick representation emphasized in (c) is Stone−Wales defects dominated by carbon pentagons and heptagons.
section of Au particles. According to the binary collision (BC) theory, the maximum of the displacement cross section moves to higher energies with increasing ion mass.42 Because of the large mass of Au, the displacement cross section dominates over a wide energy range from a few eV to several hundred keV, so that the irradiation damage induced by 500 keV/atom Au249 cluster (Figure 6f) is more severely than that of 0.5 keV/atom (Figure 6e). There are two kinds of carbon chains found in the edge of nanopores formed in graphene by the impact of energetic clusters. One is the suspended free-hanging monatomic carbon chains with its end point attached to the edge of nanopore, and the other is the carbon chain loops along the pore edges. This is in accordance with the stable chains formed in graphene exposed to electron irradiation, in which the carbon chains were found to be stable under intense electron beam.48−50 However, the chain loops is more abundant than others observed in our simulations. By a close examination of the trajectory of the nanopore formation, we found that the carbon chains came mostly from the incorporation with pentagons, heptagons, and other multiple polygons resulted from the bombardment of incident clusters. As discussed in previous literatures, this transformation is energetically favorable because of the presence of edge stress.51,52 The edge reconstruction was followed by the atomic rearrangement along with the removal of carbon atoms caused by incident clusters. The atomic carbon chains with unsaturated 11780
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Notes
bonds thus provide a feasible method for the achievement of adsorption of large molecules or foreign atoms in graphene, which paves the way for controllable modification of its physical properties as demonstrated43 lately. Our results indicate that it is a very effective method to generate nanopores in graphene with the impact of energetic clusters. Compared to the electron beam nanosculpting technique, the energetic cluster irradiation is more efficient for the fabrication of nanometer-scale pores in graphene. In experiment, the clusters consisting of up to thousands of atoms including C, Au, and other species could be produced with accelerator. Therefore, it is possible to deposit locally a large amount of mass and energy into graphene and drill nanopores with cluster ion beam. Recent experimental evidence about the creation of nanopores in graphene by bombardment with highenergetic Au clusters,27 further confirms that it is a feasible and promising way to achieve graphene-nanopore-based applications. Our simulations also demonstrate that when the nanopore is created, the rest of the graphene can still keep intact. For this reason, it is very suitable for the fabrication of nanopore arrays or nanomesh in graphene, which is shown to result in band-gap opening and magnetism in graphene and increase the transconductance of the graphene transistors.53−56 As the shape of nanopores could be modulated by the incident clusters, this method provides a way toward realization of nanopore arrays in graphene in a controlled manner, which has been proved recently to be a promising prospect for the application of novel spintronic devices. 57 In addition, suspended carbon chains created at the edge of the nanopore afford chemically active sites to bind foreign atoms or large molecules and thus offer a method to achieve functionalized graphene nanopores in a graphene sheet.43,58
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is financially supported by NSFC (Grant No. 10975009) and by the Ministry of Science and Technology of China (Grant No. 2010CB832904).
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4. CONCLUSIONS In summary, we have demonstrate that the creation of a nanopore in a graphene sheet induced by the bombardment of energetic clusters using the classical molecular dynamics. Four types of incident clusters were considered, which were different not only in mass but also in cluster size. Our results demonstrate that the nanopore could be created in graphene with collision of energetic clusters. The nanopore may take many shapes depending on the configuration of the incident cluster. However, a large quantity of carbon chains are observed at the edges of the pores, which are formed self-organized during the removal of carbon atoms. This suggests that the carbon chain is a preferential and stable configuration at a low density of carbon atoms. The area of nanopore can be controlled by varying the incident energy of clusters. Our results showed that energetic clusters are effective tools to fabricate nanopores in graphene and the properties of nanopore formed can be tailored by varying the incident clusters.
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ASSOCIATED CONTENT
S Supporting Information *
Movies about the trajectory of C60 and Au3925 which impact with graphene sheet at lower threshold energy. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. 11781
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The Journal of Physical Chemistry C
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