# Adhesion Behavior between Multilayer Graphene and Semiconductor Substrates
## 3 Results and Discussions
Finally, due to van der Waals forces from the Si substrate, the second and bottom layers were pulled back to the Si surface. During the central uplifting process of the underlying layers, the left and right edges of the second and bottom layers moved toward the center of the Si substrate, so that a more serious slip dislocation of Si surface atoms occurred (shown in Figure 5b). When the velocity was faster than 10.16 A/ps--for example, 12 A/ps--the displacement curve of three-layer graphene and the atomic trajectory were obtained as shown in Figure 6. Graphene shed the constraints from the Si substrate and underlying layers much more quickly. Moreover, the second and the bottom layers were pulled up only a very short distance (with maximum distances of 7.03 A and 3.5 A, respectively) by the topmost layer at timestep 998, following with the tension of the topmost layer disappearing, and the underlying two layers were balanced at 6.11 A and 2.69 A, respectively, on the Si surface. Figure 5: Adhesion behavior in a three-layer graphene system, when the vertical upward velocity is 10.16 Å/ps: (**a**) The variation of distance between graphene and the Si substrate surface with timestep; (**b**) atomic trajectory of the three-layer graphene system. It can be seen from Figures 7 and 8 that, when the V\({}_{\rm up}\) was 6.98 A/ps or 9 A/ps, the topmost layer of graphene pulled the second and the bottom layers up, and all three layers were able to separate from the Si substrate together. When the velocity was 10.16 A/ps or 12 A/ps, the topmost layer was exfoliated alone. By massive calculations, it can be concluded that, if the V\({}_{\rm up}\) is less than 6.98 A/ps, graphene cannot be exfoliated; if the V\({}_{\rm up}\) is in the range of 6.98 A /ps-10.16 A/ps, three-layer graphene can be exfoliated entirely; if the V\({}_{\rm up}\) is faster than 10.16 A/ps, only the topmost layer can be exfoliated. As a result, velocities of 6.98 A/ps and 10.16 A/ps were determined to be the critical exfoliation velocities for three-layer graphene systems. Figure 6: Adhesion behavior in a three-layer graphene system, when the vertical upward velocity is 12 Å/ps: (**a**) The variation of distance between graphene and the Si substrate surface with timestep; (**b**) atomic trajectory of the three-layer graphene system. Figure 9 summarizes the Z direction forces of all three layers of graphene at 5 A/ps, the first critical V\({}_{\rm up}\) of 6.98 A/ps, 9 A/ps and the second critical V\({}_{\rm up}\) of 10.16 A/ps. Figures 10-12 show the Fz of the upmost layer, the second layer, and the bottom layer of graphene at 5 A/ps, the first critical V\({}_{\rm up}\) of 6.98 A/ps, and the second critical V\({}_{\rm up}\) of 10.16 A/ps, respectively. The initial distance between the Si surface and the bottom layer of graphene was small and there was a repulsive force, so the external Fz was a negative value that was reduced with timestep. At timestep 238, the spacing between the graphene bottom and the substrate was 2.6 A, and the interaction between the graphene and substrate reached 0 nN. At timestep 417, the force exerted on all three layers reached 23.96 nN. In the process of balancing the external forces and the internal forces, the Fz fluctuated violently and erratically until timestep 2800, after which the fluctuation amplitude of the force was somewhat stable. Following the changes of the distance between the upmost layer of graphene and the Si surface, the Fz fluctuated  
Figure 8: Variation of distance between the second and bottom layers of graphene versus timestep. Figure 7: Variation of distance between the topmost and second layers of graphene versus timestep. between \(-26\) nN and \(20\) nN, with a trend of decreasing amplitude. In comparison, the Z direction forces on the second layer of graphene were more complex, and the force curve was more disordered. At 6.98 A/ps, according to the displacement and motion trajectory, the top layer of graphene was exfoliated together with the underlying two layers.