Stabilization of graphene nanopore

Significance

The key driving force for nanopore research has been the prospect of DNA sequencing, which requires small, thin pores for highest resolution. The length of the pore channel can be reduced to a single layer of atoms through the use of graphene. However, it is known that tiny holes in graphene are unstable against filling by carbon adatoms. Thus, the stabilization of such holes is a critical issue to be resolved to enable applications. We demonstrate the existence of stabilized holes in graphene and theoretical understanding of why they are stable. Our discoveries are a major step toward the development of robust and reliable graphene-based molecular translocation devices.

Abstract

Graphene is an ultrathin, impervious membrane. The controlled introduction of nanoscale pores in graphene would lead to applications that involve water purification, chemical separation, and DNA sequencing. However, graphene nanopores are unstable against filling by carbon adatoms. Here, using aberration-corrected scanning transmission electron microscopy and density-functional calculations, we report that Si atoms stabilize graphene nanopores by bridging the dangling bonds around the perimeter of the hole. Si‐passivated pores remain intact even under intense electron beam irradiation, and they were observed several months after the sample fabrication, demonstrating that these structures are intrinsically robust and stable against carbon filling. Theoretical calculations reveal the underlying mechanism for this stabilization effect: Si atoms bond strongly to the graphene edge, and their preference for tetrahedral coordination forces C adatoms to form dendrites sticking out of the graphene plane, instead of filling the nanopore. Our results provide a novel way to develop stable nanopores, which is a major step toward reliable graphene-based molecular translocation devices.

Extensive experimental and theoretical work has been done on vacancy clusters and nanopores in graphene (1–6). In particular, nanopore technology has emerged as a powerful tool for single-ion channels, single-molecule detection, and liquid purification. A monolayer graphene nanopore (7–9) compared with a typical solid-state nanopore of a 30-nm thickness (10–14) provides an optimal approach for very high-resolution, high-throughput, rapid DNA sequencing.

Rapid progress has been made in experimental studies exploring a wide variety of methods for introducing nanopores in graphene. The most recent methods have used diblock copolymer templating, helium-ion beam drilling, and chemical etching to achieve both higher porosity and a more precise pore size control (15–18). However, it is observed that small holes in graphene are subject to reconstruction and partial or total filling by diffusing carbon or other adatoms (known as the self-healing process) (19–21). Stabilization of pores for extended periods of time has not been achieved so far.

Here, we report that Si atoms stabilize graphene nanopores by bridging the dangling bonds around the perimeter of the hole. Without passivation, we find that small pores in graphene fill within hours even under ultrahigh-vacuum conditions. This pore stabilization is understood in terms of the fact that Si atoms prefer tetrahedral coordination so that C adatoms that might bond to them would not lie in the graphene plane (22, 23). Our molecular-dynamics (MD) simulations show that the C adatoms would form dendrites sticking out of the graphene plane, instead of filling the nanopore, suggesting that Si passivation is indeed effective in preventing the self-healing process. Furthermore, experimental and theoretical evidence suggests that Si-stabilized nanopores are stable in ambient atmosphere and liquids.

Results

Hydrogen may be expected to stabilize pores in graphene by passivating dangling bonds at the pore rim. It has been reported that graphene edges can be terminated by mono- and di-hydrogen (24). Recent muon spectroscopy investigations have confirmed the existence of C—H bonds at graphene defects (25). There is no report, however, of intentional hydrogenation of nanopores in graphene to determine whether hydrogen passivation prevents filling. To explore how hydrogen passivation affects carbon filling, Born–Oppenheimer MD simulations were done in the microcanonical ensemble (NVE), where the number of particles (N), the volume (V), and the energy are conserved. (Details of the MD simulations are provided in Methods.) The MD simulations show that carbon adatoms interact strongly with H-passivated nanopores and form a planar network that fills the nanopore (Fig. 1 A–D and Movie S1). Thus, hydrogen passivation of the carbon edge atoms is not expected to prevent filling of graphene nanopores by carbon.

Fig. 1.

Intermediate snapshots of ab initio MD simulations of H- and Si-passivated nanopores. (A–D) Snapshots of MD simulations of a H-passivated nanopore at varying transient states at 0, 0.1, 0.2, and 0.3 ps. C dangling bonds around the pore rim are initially terminated by 12 monohydrogen atoms (green color). Thirty-four C atoms (orange color) are inserted near the pore, and their coordinates are randomly chosen. Carbon adatoms interact strongly with the H-passivated nanopore, filling it with a planar network. (E–H) Snapshots of MD simulations of a Si-passivated nanopore at the same times. Si dangling bonds around the pore rim are initially terminated by six di-hydrogens. Twelve C atoms are inserted near the pore and their coordinates are again randomly chosen. The preference of Si atoms for tetrahedral coordination prevents the formation of a planar C network inside the nanopore. Instead, C atoms form dendrites sticking out of the graphene plane.

Our experimental data and density-functional calculations both demonstrate that Si atoms can passivate nanopore rims very effectively. Silicon is one of the most common impurities in graphene grown by chemical vapor deposition (CVD). During the high-temperature CVD growth process, it is most likely that Si impurities are introduced into the graphene layer due to the presence of a Si source (the quartz tube) (26, 27).

Fig. 2 A–C shows annular dark-field (ADF) Z-contrast images of Si atoms decorating graphene multivacancies. For a hexavacancy, the addition of three Si atoms can effectively stabilize the defect structure by bridging the dangling bonds on neighboring perimeter C atoms, forming characteristic five-member rings (4 C + 1 Si). Precisely the same arrangement occurs naturally in a decavacancy where just four Si atoms provide optimal passivation. Calculated lowest-energy atomic configurations are overlaid on the observed images (Fig. 2 D–F). The relaxed structural models of V₆-Si₃ and V₁₀-Si₄, where V indicates the number of carbon vacancies, are depicted in Fig. 2 G and H. Small pores with diameters of ∼0.2 and ∼0.4 nm are formed with curved armchair-type edges (indicated in red) passivated by Si atoms.

Fig. 2.

Atomic structures for Si atoms decorating graphene multivacancies. (A–C) Experimental STEM-ADF Z-contrast images of Si atoms (2, 3, and 4, respectively) in graphene multivacancies (4, 6, and 10, respectively). (D–F) Schematics of the structure models, overlaid on the corresponding ADF images, for the defect structures shown in A–C, respectively. (G and H) Detailed schematics of the structure models of V₆-Si₃ and V₁₀-Si₄, where V denotes the number of C vacancies. Each armchair edge is indicated in red. (Scale bar: 0.2 nm.)

The binding energy of Si atoms is calculated to be larger than 8 eV. This large binding energy is consistent with the experimental fact that the V₆-Si₃ structure is stable under prolonged exposure for 169 s to the high-energy (60-keV) electron beam in the electron microscope (Fig. 3). ADF Z-contrast images of the V₆-Si₃ structure shows that the Si atoms around the perimeter spin without enlarging the hole, forming defects or ripping off atoms under the long consecutive electron beam irradiation (Fig. 3) (28, 29). We find that the energy barrier for the rotation is about 2.0 eV. Under the 60-keV electron beam irradiation, the maximum energy transfer to a Si atom is 4.67 eV (30), which is lower than the binding energy of Si atoms, but higher than the energy for rotation. That is why we observed only the rotation instead of ejection of Si atoms from the V₆-Si₃ structure.

Fig. 3.

STEM-ADF Z-contrast images of the V₆-Si₃ structure. Forty-eight consecutive Z-contrast images of the V₆-Si₃ while being irradiated by the electron beam for 169 s. The Si atoms move around the perimeter of the hole without enlarging it, or forming defects. The white arrow represents the rotation of Si atoms.

Fig. 4A shows a larger pore passivated by 17 Si atoms. A total of 68 carbon atoms are missing. From the lowest-energy atomic configurations (Fig. 4B), we see that all carbon dangling bonds at the pore rim are completely passivated by Si atoms. Although there is a variety of bonding configurations, all Si atoms have binding energies larger than 5 eV as shown in Fig. 4C.

Fig. 4.

Atomic structure of the V₆₈-Si₁₇ structure and the binding energy of the Si atoms. (A) STEM-ADF Z-contrast image of a graphene nanopore passivated by 17 Si atoms. (B) Structure model for the Si-passivated nanopore. (C) Binding energy distributions of the 17 Si atoms.

The observation of a large Si-passivated pore several months after the sample was fabricated suggests that such structures are intrinsically stable against carbon filling [carbon adatoms usually fill pores within several hours even under ultrahigh vacuum (19)]. This stability can be understood in terms of the fact that Si atoms prefer tetrahedral coordination so that C adatoms that might bond to them would not lie in the graphene plane (22, 23). To further confirm this conjecture, we performed MD simulations by adding C adatoms to a Si-passivated 24-vacancy nanopore. We find that the C adatoms tend to form dendrites sticking out of the graphene plane, instead of filling into the nanopore (Fig. 1 E–H and Movie S2), suggesting that Si passivation is very effective in preventing the self-healing process.

Translocation of molecules through nanopores for various applications would require the deliberate fabrication of holes of specific sizes and shapes. We, therefore, explored two types of nanopores that are larger versions of those observed in Fig. 2 (V₆-Si₃ and V₁₀-Si₄). Round pores are shown in Fig. 5A. Their rims could contain both armchair and zigzag edge portions, and the number of Si atoms obeys the formula V_(6m²₎ -Si_max{6m-6,3} (m ≥ 1) (Fig. S1). In contrast, pores constituted of purely curved armchair edges would have rectangular shapes as shown in Fig. 5B. These rectangular-shaped pores can be described as V_(14n-18)-Si_2n (n ≥ 2) (Fig. S2). In the round pores, some Si atoms form single bonds with C atoms (zigzag sites) from V₅₄-Si₁₂, whereas in the rectangular pores all Si atoms bridge pairs of C atoms (armchair sites) at the perimeter.

Fig. 5.

Calculated sequence of stable nanopores and the binding energy for the Si passivating atoms. (A) Calculated sequence of round pores. (B) Calculated sequence of rectangular-shaped pores. (C) Binding energy of bridge-bonded Si atoms (armchair sites). Additionally, the binding energy of a Si atom bonded to a single C atom (zigzag site) in a round pore (V₅₄-Si₁₂) is indicated by the orange square.

Calculated binding energies of bridge-bonded Si atoms in different pores are shown in Fig. 5C. These binding energies are all larger than 8 eV, which appears to be a saturation value for large pores. In contrast, the binding energy of the Si atoms bonded to a single C atom in a round pore (e.g., V₅₄-Si₁₂, rectangular orange) is 5.5 eV, which is still large enough for a robust passivation. Therefore, we expect that fabricated pores with jagged edges can still be robustly passivated by Si atoms.

Discussion

We have shown that it is possible to passivate the chemical bonds around the perimeter of pores in graphene. However, our results have shown that not all elements are effective in this role. For example, hydrogen bonds at pore edges, but it does not stop carbon adatoms from filling small holes in graphene. Our experimental and theoretical investigations demonstrate that Si is particularly effective in this role. This stability can be understood in terms of the fact that Si atoms strongly prefer tetrahedral coordination so that C adatoms that might bond to them would not lie in the graphene plane.

Si atoms at the pore edges are reactive because of the presence of Si dangling bonds pointing out of the graphene plane. However, hydrogen can passivate these dangling bonds (Fig. S3). The calculated H binding energy is ∼3.0 eV, which means that H passivation of the Si-terminated edges is also robust, leading to highly inert and stable nanopores in graphene. Finally, Si passivation of the pore rim is stable against ambient atmosphere as the samples were stored in air for months before the present investigation. In addition, the Si-terminated pores remained intact during the removal of monolayer graphene from the Cu substrate when they are bathed in liquid FeCl₃, i.e., exposed to water and Cl ions, which are very reactive. To explore stability against oxygen, Si dangling bonds around the pore rim were terminated by oxygen atoms, as shown in Fig. S4, and then MD simulations were carried out in the canonical ensemble at 300 K. C adatoms were inserted near the pore and their initial coordinates were chosen randomly. The MD results confirm that Si passivation of the rim still remains stable, whereas volatile CO and CO₂ molecules are generated from reactions between C adatoms and oxygen. This phenomenon can be explained by the fact that the reactions between that C adatoms and oxygen have significantly higher energy gain than oxygen reactions with Si atoms. These results are consistent with a previous study on the oxidation resistance of bonded Si atoms in a graphene lattice (31). The net conclusion is that the Si-passivated graphene pores are stable in ambient condition.

We propose that a technology can be developed for the fabrication of stable nanopores in graphene. Pores of desirable size, shape, and pattern can be fabricated by focused electron or ion beams (18) or by chemical etching using masks. Subsequent supply of Si atoms would naturally passivate the rims of the as-fabricated nanopores. If the graphene layers can be kept clean, the resulting stabilized pores would be suitable for a wide range of applications. In particular, robust graphene nanopores of specific size and shape (Fig. S5) can provide an “optimal” approach for very high-resolution, high-throughput, single‐molecule detection and rapid DNA sequencing. This discovery is a major step toward the development of stable and reliable graphene-based molecular translocation devices (32–35).

Methods

Sample Preparation.

The graphene material was grown on a copper film following a CVD method reported in the literature (36). Cu foil of 100-μm thickness was used as the growth substrate and was placed directly in the quartz tube. During the growth, the temperature was first raised to 950 °C under 10 torr Ar/H₂ gas flow. Once the temperature reached 950 °C, the Ar/H₂ gas was cut off and 4 s.c.c.m. CH₄ was introduced into quartz tube for graphene growth. The reaction time is typically 10 min. The system was then cooled down at a rate of 50 °C/min under the protection of a 500 mtorr Ar/H₂ atmosphere. The graphene layers were then extracted from the copper film via chemical etching by FeCl₃ and deposited onto a 2,000-mesh copper grid. The sample contained both monolayer and multilayer graphene.

Scanning Transmission Electron Microscopy ADF Z-Contrast Imaging Experiments and Impurity Identification.

Aberration-corrected scanning transmission electron microscopy (STEM) ADF imaging was performed with a Nion UltraSTEM-100. The microscope was operated at 60-kV accelerating voltage, which is below the knock-on radiation damage threshold of graphene. The convergence semiangle of the incident probe was set to ∼30 mrad, and the ADF images were collected using a ∼54- to 200-mrad detector half-angle. The probe current was set to ∼100 pA, contained in a probe of 1.3 Å in diameter. The ADF images shown in the manuscript have been deconvolved following the method described in ref. 30, which allows atom-by-atom chemical analysis based on quantitative image intensity analysis (37). The intensity from the impurity atoms is about 3.83 times the intensity obtained from the carbon atoms, which is close to the Z^1.6 ratio of 1:3.87 for Z = 6 (C) and Z = 14 (Si), respectively. Furthermore, electron energy-loss spectroscopy analysis from a substitutional impurity atom with the same ADF image intensity ratio confirms that the impurities seen passivating the pores in graphene are Si atoms (Fig. S6). The contrast variation within the graphene lattice in Fig. 4A is due to residual aberration and astigmatism during the acquisition of this image.

First-Principles Calculations and MD Simulations.

First-principles calculations, based on density-functional theory (DFT) (38, 39), were performed using the Vienna ab initio simulation package (VASP) (40). The projector augmented wave (PAW) method was used to mimic the ionic cores (41), whereas the generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) parameterization was used for the exchange and correlation functional (42). Atomic positions, as well as lattice parameters, were optimized using a conjugate gradient algorithm. Ionic and electronic relaxations were performed by applying a convergence criterion of 5 × 10⁻² eV/Å per ion and 10⁻⁴ eV per electronic step, respectively. The size of the graphene supercell is 2.47 × 2.57 nm for the binding energy calculations and ab initio MD simulations. A rectangular graphene nanopore containing 250 C atoms (graphene pore consists of 216 C atoms and 34 C adatoms) and 12 H atoms was considered to conduct the MD simulation for the H-passivated pore at 300 K. Another rectangular graphene nanopore containing 228 C atoms (graphene pore consists of 216 C atoms and 12 C adatoms), 6 Si, and 12 H atoms was considered to conduct the MD simulation for the Si-passivated pore at 300 K. The Born–Oppenheimer MD simulations were done in the NVE, where the number of particles (N), the volume (V), and the energy (E) are conserved. The NVE ensemble is suitable for simulating the self-healing phenomenon because it is experimentally observed in an isolated ultrahigh vacuum where the total energy of system is assumed to be constant. Initially, C adatoms are randomly distributed around the pore. To avoid the short-range repulsive interactions, C adatoms are separated by, at least, 1.7 Å (distance between each C atom in graphene is about 1.43 Å). We intentionally place C adatoms within 2 Å out of plane to expedite reaction near the graphene pore. Two different initial configurations are simulated, but they did not change our main results. Time step of 0.5 fs is taken to track the positions of all of the atoms as precise as possible including hydrogen (the lightest element on the periodic table). Increasing the time step (1 or 2 fs) does not change our main results but hides the details of dynamics. The temperature was initialized at 300 K (temperature in NVE ensemble is defined by the equipartition theorem). After an equilibration time (of ∼150 fs), the temperature is stabilized at ∼824.4 K for the H-passivated pore (Fig. S7) and 1,071.9 K for the Si-passivated pore (Fig. S8). Even though they are around the stable temperature, the temperature is clearly stabilized within 800 steps (0.4 ps) for both cases (Figs. S7 and S8). There are no significant changes in temperature when a planar network consisting of carbon adatoms is formed in the graphene nanopore for a H-passivated pore (Movie S1), or when dendrites are formed out of graphene plane (Movie S2). The total simulation time spans are about 0.5 ps.