Effect of the External Velocity on the Exfoliation Properties of Graphene from Amorphous SiO₂ Surface

Abstract

External action has a significant influence on the formation of high-quality graphene and the adhesion of graphene on the surface of the MEMS/NEMS device. The atomic-scale simulation and calculation can further study the exfoliation process of graphene by external actions. In multilayer graphene systems where graphene layers were simulated weakly contacted with SiO₂ substrate, a constant vertical upward velocity (V_up) was applied to the topmost layer. Then two critical velocities were found, and three kinds of distinct exfoliation processes determined by critical upward velocities were observed in multilayer graphene systems. The first critical velocities are in the range of 0.5 Å/ps–3.18 Å/ps, and the second critical velocities are in the range of 9.5 Å/ps–12.1 Å/ps. When the V_up is less than the first critical velocity, all graphene layers will not be exfoliated. When V_up is between the first and second critical V_up, all layers can be exfoliated almost synchronously at last. When V_up is larger than the second critical V_up, the topmost layer can be exfoliated alone, transferring energy to the underlying layers, and the underlying layers are slowly exfoliated. The maximum exfoliation force to exfoliate the topmost layer of graphene is 3200 times larger than that of all graphene layers. Moreover, it is required 149.26 mJ/m² to get monolayer graphene from multilayers, while peeling off all layers without effort. This study explains the difficulty to get monolayer graphene and why graphene falls off easily during the transfer process.

1. Introduction

Since monolayer graphene was successfully produced by mechanical exfoliation [1], its excellent properties have attracted extensive research attention, such as low mass with atomic thickness [2], high Young’s modulus [3], excellent thermal and electrical properties [4,5]. Due to specific advantages, many high-performance graphene-based MEMS/NEMS devices have been developed [6,7,8,9,10]. In most MEMS/NEMS devices, graphene cannot be directly synthesized on a semiconductor substrate, it is usually firstly fabricated on a specific substrate by epitaxial growth [11] or exfoliation techniques [12], and then transferred to the aimed surface [6,7,8,9,10]. Because the specific surface area of 2D nanostructure graphene is super large, many unexpected issues may happen during the graphene-based MEMS/NEMS fabrication process. The quality of produced graphene is critical, and weak adhesion, ripple, wrinkles that may be arisen during decoupling graphene from the original substrate to the target surface also influence the performance of MEMS/NEMS devices, all these imply that the fabrication process is still elegant work.

Mechanical exfoliation is one of the most commonly used methods [12,13], which can produce high-quality graphene sheets. Using sticky tape to produce large force to exfoliate graphene one layer by one layer was the first and simplest method to produce graphene. The elastomeric polymer was also used to isolate graphene layers [14]. By inserting nano ball into interfaces, an axisymmetric blister was formed and graphene was exfoliated [15]. Manipulating AFM cantilever to pick up one end of graphene or scratch graphene, the monolayer was exfoliated by shearing away from neighbor layers normal or parallel to the substrate [16,17]. Additionally, the wedge crack technique was reported [18,19]. Understanding the basic exfoliation process at the molecular scale is crucial to give insights into producing high-quality graphene sheets.

When transferring graphene to target surfaces, the original substrates have to be removed, and many processes like graphic lithography are inevitable in MEMS/NEMS technology, ultrasonic cleaning treatment and various solvents are also usually used. According to our experimental work, graphene layers were easily detached when the PMMA layer was removed away. Other researchers also found that graphene was cracked easily during the transfer process, and this was because graphene had not been fully contacted with the target substrate [20,21]. To get an integrated transferred structure, plenty of attempts should be taken [22,23].

The external actions have a great influence both on exfoliation and transfer processes. By intercalating inert gas atoms between graphene sheets or adjusting the ambient pressure, the shape and heights of the graphene blisters were different and can be measured at the atomic scale, the adhesion energy was then analyzed and calculated to determine the graphite adhesion energy of 221 ± 11 mJ/m² [24,25]. Nanoparticles also can be inserted into the graphene-SiO₂ interface, and adhesion energy was measured to be 151 ± 28 mJ/m² through raised supported axisymmetric blisters [15,26]. AFM cantilever was used to induce graphene nanoribbon detachments from the gold surface, during the process stick–slip and stop-and-go motion were accompanied [27]. By wedge crack force, the adhesion energy between graphene and Si was 357 ± 16 mJ/m² [18].

Generally, the external actions to exfoliate graphene layer by layer are greater than that of delamination from a weak bonding surface. It is very difficult to reveal the action mechanism of the external parameters on graphene by experiments, in this paper we turn to molecular dynamics simulations as an effective means [28,29,30,31]. Different external vertical upward velocities were applied to the topmost layer to exfoliate one to ten layers of graphene directly, and the physical molecular exfoliation process was observed. The influence of exfoliating velocity on the exfoliation phenomena of graphene was clarified. Critical velocities, critical peeling forces, and adhesion energies were obtained. This research can support insights into further study of graphene-based MEMS/NEMS devices.

2. Method

The molecular dynamics (MD) exfoliation model of a four-layer graphene system on a-SiO₂ substrate as a representative is shown in Figure 1. Each graphene layer contains 3608 C atoms with a size of 97 Å × 97 Å. The a-SiO₂ substrate contains 34,116 Si and O atoms with a size of 168 Å × 168 Å × 17 Å. The SiO₂ substrate surface is numbered 0, the bottom layer is numbered 1, the second layer is numbered 2, the third layer is numbered 3, and the topmost layer is numbered 4, as shown in Figure 1. The fact that graphene has not been fully contacted with the target substrate could induce all graphene layers delamination from the substrate or formation of crack [20]. A series of constant vertical upward velocities are applied to graphene to give different external actions. Ten different models with one to ten layers of graphene are set up to clarify the comprehensive exfoliation mechanism.

In the simulation, to calculate the carbon atoms interaction of graphene, Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential [31] is used. The AIREBO potential can well calculate the interlayer interaction of graphene because of the inclusion of the long-range Lennard–Jones (LJ) potential [32]. The AIREBO potential has been widely used for graphene in MD simulations [33]. The formation is similar to a pairwise dispersion–repulsion potential.

$$E=\frac{1}{2}{\displaystyle \sum _i}{\displaystyle \sum _{j\ne i}\left[E_{ij}^{REBO}+E_{ij}^{LJ}+{\displaystyle \sum _{k\ne i}}{\displaystyle \sum _{l\ne i,j,k}{E}_{kijl}^{TORSION}}\right]}$$

(1)

$E_{ij}^{REBO}$ is the REBO potential [34], describing the intralayer atom interactions of graphene, and its formulation is:

$$E_{ij}^{REBO}={\displaystyle \sum _i}{\displaystyle \sum _{j(>i)}\left[V_{ij}^{\mathrm{R}}\left(r_{ij})-b_{ij}{V}_{ij}^{\mathrm{A}}\right(r_{ij})\right]}$$

(2)

$V_{ij}^{\mathrm{R}}\left(r_{ij}\right)$ represents all repulsive interatomic interactions while $V_{ij}^{\mathrm{A}}\left(r_{ij}\right)$ is the attractive interactions. r_ij is the distance between pairs of nearest-neighbor atoms i and j. The bond-order function b_ij can deal with many-body effects and is capable of calculating the formation and breaking of covalent bonds. Because the bond-order function b_ij contains both dihedral angle interaction weighing the bond strength and radicals and conjugate or non-conjugate structure of carbon, as well as rotation barrier which prevents the unrealistic bond rotation from occurring. The long-range interactions between graphene atoms are determined by the LJ potential described in $E_{ij}^{LJ}$. $E_{kijl}^{TORSION}$ depends on the four-body potential torsion terms of the dihedral angle. The interactions among SiO₂ atoms is described by Tersoff potential [35]. The Van der Waals interaction between the SiO₂ substrate and graphene was described by LJ potential function [36].

The MD simulation was carried by open-source LAMMPS [37]. The system is set NVE microcanonical ensemble. N is the number of atoms, V is the system volume, and E is the energy. The total energy was constant in the NVE ensemble. The equations of the motion of the particles are solved by the Verlet algorithm, and the simulation time step is 0.001 fs [38], which is adequate for system relaxation by examining the stability through the root mean square deviations of the atoms. All the simulations were performed at 300 K. After a long time of relaxation, the equilibrium distance between the bottom layer and substrate surface is about 3 Å in one-layer to ten-layer graphene systems respectively.

3. Results and Discussions

According to the different features of exfoliation phenomena, two critical velocities to exfoliate graphene from the SiO₂ surface exist in each one to ten layers of graphene systems. Here, the exfoliation process of the four-layer graphene system is shown as a representation. In a four-layer system, three kinds of distinct exfoliation processes take place determined by critical upward velocities, and the critical upward velocities are 0.9 Å/ps and 10.23 Å/ps. As shown in Figure 2, V_up 0.4 Å/ps, which is less than the critical V_up 0.9 Å/ps, is applied to the topmost layer of graphene. The V_up is too slow to generate enough kinetic energy, and four layers can not be exfoliated, fluctuating on the surface of SiO₂. The SiO₂ substrate and neighbor layers have interactions on graphene layers, and the Z-direction force (Fz) of each layer is complicated (Figure 3), which varies irregularly with time. At last, the steady distance between the bottom layer and the substrate surface is 2.74 Å. The movements of four graphene layers keep consistent. Due to the peeling force on the topmost layer, the average gap between graphene layers is about 3.40 Å, a little bigger than the natural value 3.35 Å.

Once V_up increases to 0.9 Å/ps, the peeling force induced by velocity is larger than the forces from the SiO₂ substrate and underlying layers. The topmost layer of graphene moves away from the SiO₂ surface, and is exfoliated finally, as shown in Figure 4. The distance between the topmost layer and the SiO₂ surface increases linearly with time. The third layer of graphene goes upward with the topmost layer because the upward force from the topmost layer graphene is greater than the downward force from the SiO₂ substrate and the underlying layers. The same phenomenon occurs to the bottom and second layer, which move upward together with the top two layers. Four layers go up at the same rate, and the curves of movement are parallel. From the movement snapshots of the atomic trajectory, relative slipping occurs between the neighbor layers. The SiO₂ surface atoms which close to the edge of graphene dislocate, because the interaction between graphene and SiO₂ substrate is much larger, Graphene fluctuates a lot, but the trajectories of the three layers are similar.

Figure 5 shows the Z-direction forces of four layers at 0.9 Å/ps. The initial distance between the SiO₂ surface and neighbor layer graphene is small. At this time, a repulsive force exists, and the external Fz is negative decreasing with time. With time increasing, the topmost layer is forced by the SiO₂ by adhesion forces, and the peeling force becomes larger than 0 nN. At 209 ps, the force exerts on each layer reaches the first maximum value of 44.92 nN, but the Fz of all four layers are still about 0 nN. Although the Fz of each layer fluctuates violently and irregularly, the amplitude reduces.

Exfoliation processes at different upward velocities between critical V_up 0.9 Å/ps and 10.23 Å/ps were simulated, and 10 Å/ps was shown to illustrate the situation (the trajectory and force of graphene is shown in Figure 6 and Figure 7 respectively). V_up higher than critical velocities 0.9 Å/ps created large enough kinetic energy, the topmost layer is forced to leave the neighbor layers and the distance between the topmost layer and third layer (D₃₄) reaches a maximum of 7.87 Å at 3380 ps, while the topmost layer wound up around the X-axis. Figure 6 shows the variations of morphologies of the topmost layer over time. When the velocity is 10 Å/ps, the front and back ends of the topmost layer are curled symmetrically on the X-axis. As the topmost layer gets further away from the surface of the substrate, the distance between the topmost layer and its neighbor layer becomes larger, the angle of the front and back atomic layer also increases. When D₃₄ gets a maximum value of 7.87 Å, the curled angle is 33.37° (shown in Figure 8a). Because of the interaction between graphene layers, the topmost layer is drawn back to the neighbor layer, and the middle part of the topmost layer gets close to the bottom layer fastest, causing the angle of the curled ends of graphene to increase more. As shown in Figure 8, when D₃₄ is shortened to 5.77 Å, the curled angle reaches a maximum of 48.03°. The end of graphene has no visible curl as D₃₄ recovers to near natural value 3.63 Å. At the same time, the length of the curled ends gradually becomes shorter.

The bottom three layers keep consistent movements during the exfoliation process, the relative balance D₁₂ (the distance between the bottom and second layer), D₂₃ (the distance between the second and third layer) are both 3.46 Å larger than the natural graphene interlayer gap 3.35 Å. While the topmost layer is pulled back to the neighbor layer after 13,869 ps, the relative balance gap of D₃₄ is also 3.46 Å. From the atomic trajectories, as shown in Figure 6, the four layers keep consistent regular waves at last.

The force of all four graphene layers becomes zero when the distance between the bottom layer and SiO₂ substrate is larger than 8.94 Å. Graphene layers interact with each other, and the amplitudes of Z-direction forces of graphene layers decrease when the topmost layer was pulled back to neighbor ones. For example, from Figure 7, the maximum Fz peak of the bottom layer is 136.03 nN, it gradually decreases five times to 31.72 nN at 5556 ps when the D₃₄ is 6.57 Å, and D₀₁ (the distance between the bottom layer and substrate surface) is 14.06 Å. From the Fz peak values of four layers, it can be seen that the maximum Fz of the topmost layer is the largest among the four layers. Although the curves of Fz are complicated, the general rule is: Fz peak of the topmost layer > Fz peak of the bottom layer > Fz peak of the third layer > Fz peak of the second layer. The reason is that the topmost layer and the bottom layer do not just withstand forces from graphene, the topmost layer is applied by the peeling force and Van der Waals’ force from the underlying layers, the bottom layer receives the forces from the SiO₂ substrate and neighbor layers.

With V_up 10.23 Å/ps, the topmost layer can be unbound to the SiO₂ substrate and moved far away from the underlying graphene and Si surface, as if the spring between the topmost layer and neighbor layer graphene is broken. The movement curve of the topmost layer is nonlinear at the beginning, as shown in Figure 9. Before 7281 ps, when the distance between the topmost layer and SiO₂ surface is less than 34.32 Å, the SiO₂ substrate and underlying layers still exert forces on the topmost layer graphene. D₀₁ is 14.89 Å, and D₃₄ is 11.45 Å at 7281 ps. The maximum Fz of the topmost layer is 158.68 nN at 106 ps as shown in Figure 10. Without the forces from the neighbor layers, the topmost can get rid of all the constraints, moving up linearly.

The second layer is pulled up by the topmost layer, and because the atoms of graphene edge have unsaturated bonds, the interaction between the SiO₂ substrate and the edge of graphene is intense, causing a bulge at the center. The underlying three layers are driven by the topmost layer and moved up linearly with time. Fz of the second layer and third layer varies periodically with time, the maximum Fz of the bottom layer and the third layer is 139.41 nN and 85.33 nN, respectively. The second layer is sandwiched between the bottom layer and third layer, and Fz of the second layer is irregular. The peak values of the Z-direction forces of the underlying three layers decrease gradually, and after 7281 ps, the resultant Fz of all the underlying three layers becomes zero.

When the velocity is faster than 10.23 Å/ps (15 Å/ps as an example), the displacement curve of four-layer graphene and the atomic trajectory is obtained as shown in Figure 11. The phenomena are similar to that when the upward exfoliation velocity is 10.23 Å/ps. The topmost graphene layer gets rid of the constraints from the SiO₂ substrate and underlying layers much more quickly. At 68 ps, Fz of the topmost layer is maximum 158.68 nN as shown in Figure 12, then it decreases to zero after 870 ps, and D₃₄ increases from 3.76 Å to 6.04 Å. The underlying three layers are driven by the topmost layer and move up linearly with time at slow speed, and relative slip occurs between the underlying three layers.

The Fz curves of the second layer and third layer were periodic, the maximum Fz of the bottom layer and the third layer was 138.33 nN at 1014 ps and 86.11 nN at 1612 ps respectively. Fz of the second layer was irregular because it was sandwiched between the bottom layer and the third layer. As a whole, the Fz of the underlying three layers decreased gradually. After 870 ps, the resultant Fz of all the underlying three layers becomes zero, indicating that all these three underlying layers escape from the substrate.

The critical velocities to exfoliate all graphene layers are much lower than that of the topmost layer which are summarized in Figure 13. The critical exfoliate velocity increases with the increasing graphene layers to pull up all the layers. In contrast, the critical exfoliate velocity decreases with the increasing graphene layers to strip the topmost layer. For the one-layer graphene system, the critical V_up is 0.21 Å/ps. While in the two-layer graphene system, the critical V_up to exfoliate the entire two layers and the topmost layer is 0.5 Å/ps and 12.1 Å/ps, respectively. In the three-layer graphene system, the critical V_up to exfoliate the entire three layers increases to 0.81 Å/ps, and the critical exfoliation velocity of the topmost layer is 10.8 Å/ps. In four layers to ten layers graphene systems, the exfoliation critical V_up to exfoliate all graphene layers is in the range of 0.8 Å/ps–3.18 Å/ps, while exfoliation critical V_up to exfoliate the topmost layer is 9.5 Å/ps–10.23 Å/ps.

The force to exfoliate graphene is minimum in the one-layer graphene system, the value is 0.0067 nN, and the SiO₂ substrate almost does not influence one-layer graphene. In one to four layers graphene systems, with the increasing of graphene layers, it needs larger force to exfoliate all the graphene. However, the maximum force does not increase very much (from 0.0067 nN to 0.046 nN). It suddenly increases to 0.13 nN in the five-layer graphene system, then reaches a maximum of 0.24 nN in the six-layer graphene system. This is because the more layers the peeling force pulled on, the higher Van der Waals force, the greater the force requires. In seven or eight layers graphene systems, pushing inertia forces may be generated, and the maximum pulling force occurs. However, it increases in nine- and ten-layer graphene systems because there are too many graphene layers.

The work carried out by the peeling force is discussed and is shown in Equation (3), and the maximum work is also adhesion energy.

W = F ∗ S

(3)

W—the work carried out by the peeling force, F—the peeling force, S—the absolute displacement of graphene.

The maximum work which is also adhesion energy in one to ten layers graphene system is 0.64 mJ/m² (occurs in the ten-layer graphene system). In one to five layers graphene systems, with graphene layers increasing, the work to exfoliate all the graphene layers increases. It is 0.33 mJ/m² in the five-layer graphene system and decreases to 0.31 mJ/m² in the six-layer graphene system, then the maximum work in the seven-layer system increases to 0.38 mJ/m². On the whole, the principle is messy, but it could be concluded that the necessary work to exfoliate all the graphene layers was very small, in the range of 0.01 mJ/m²–0.64 mJ/m²(shown in Figure 14 and Figure 15).

The maximum force and maximum work to exfoliate all the graphene are very small. During fabricating graphene-based devices, the frequently used process is the graphene transfer process. This simulation explained that if the binding of graphene and substrate is not unreliable during the transfer process, all graphene layers may fall off.

Exfoliating the topmost layer of graphene requires a much larger force, as shown in Figure 16. Because the bottom layer of graphene is far from the surface of the SiO₂ substrate, the influence of the substrate is ignored, so it needs to overcome the Van der Waals forces of the underlying layers to exfoliate the topmost layer. The distance between the topmost layer and the neighbor layer is within the range of Van der Waals forces, the maximum force to exfoliate the topmost layer in the two-layer graphene system is 149.7 nN. The distance between the topmost and the third layer from the top is almost twice more than 3.35 Å, and Van der Waals forces are weakened, so that the maximum force is increased slightly to 158.75 nN. As the number of graphene layers increasing, the distance between the topmost layer and the bottom layer from the top is almost three times larger, which already exceeds the interaction threshold. Therefore, the maximum forces to exfoliate the topmost layer in four to ten layers graphene systems are almost the same as that of the three-layer graphene system. In three to ten layers graphene systems, the average maximum force to exfoliate the topmost layer is 158.63 nN.

The work to exfoliate the topmost layer graphene in two to ten layers systems increases 10³ to 10⁴ times than that to exfoliate all layers. In the two-layer graphene system, the work to exfoliate the topmost layer is 136.79 mJ/m² shown in Figure 17, the average adhesion energy in three to ten layers graphene systems is 149.26 mJ/m², consistent with the results in the literature [24]. Because of Van der Waals, it is difficult to exfoliate the topmost layers of graphene, reflecting the difficulty of fabricating monolayer graphene.

In addition, the graphene edges are sometimes passivated by hydrogen, oxygen or nitrogen atoms. In this paper, in order to explore the influence of the edge termination on the exfoliation property, the edge of graphene is passivated by hydrogen in the two-layer graphene system. The critical velocity to exfoliate the topmost layer is higher in the hydrogen-terminated graphene system (13 Å/ps) than that in the unsaturated graphene system (12.1 Å/ps). This is because the hydrogen-terminated graphene system is more stable, it can be seen that the total energy is −56,067 eV, which is lower than that in unsaturated graphene system (−53,541 eV) as shown in Figure 18c.

4. Conclusions

The exfoliation process of graphene was observed by applying a constant vertical upward velocity to the topmost graphene layer when weakly contacted with SiO₂ substrate. In the multilayer graphene system, two critical velocities to exfoliate graphene from the SiO₂ surface were found, and three kinds of distinct exfoliation processes took place determined by critical upward velocities. In the four-layer graphene system, the critical upward velocities were 0.9 Å/ps and 10.23 Å/ps. When V_up was smaller than 0.9 Å/ps, it was too slow to generate enough kinetic energy, and four layers can not be exfoliated. By the adhesion from SiO₂, graphene layers began to sink to the substrate surface. When V_up was in the range of 0.9 Å/ps and 10.23 Å/ps, all graphene layers can be exfoliated, four layers went up at the same rate, and the movement curves were parallel. With a V_up of more than 10.23 Å/ps, the topmost layer was unbound to the SiO₂ substrate. In two to ten layers graphene systems, the critical velocities to exfoliate all graphene layers (0.5 Å/ps–3.18 Å/ps) were much lower than that of the topmost layer (9.5 Å/ps–12.1 Å/ps). The critical exfoliate velocity increased with the increasing graphene layers to pull up all the layers. In contrast, the critical exfoliate velocity decreased with the increasing graphene layers to strip the topmost layer. The adhesion force to exfoliate all the graphene layers was 0.0067 nN–0.24 nN in one to ten layers graphene systems. When exfoliating the topmost layer, under Van der Waals forces between the topmost layer and the neighbor layer, the average maximum force required to exfoliate the topmost layer was 158.75 nN in two to ten layers graphene systems. The maximum work to exfoliate all layers in one to ten layers graphene systems was 0.64 mJ/m², while the average maximum work to exfoliate the topmost layer in three to ten layers graphene systems was 149.26 mJ/m², consistent with the results in the literature.