# Adhesion Behavior between Multilayer Graphene and Semiconductor Substrates
## 3 Results and Discussions  
The exfoliation process of a three-layer system was studied and the results are discussed below. At first, a V\({}_{\text{up}}\) of 5 A/ps was applied to the topmost layer of graphene. Due to the force induced by the velocity, the topmost layer of graphene started to move up. The topmost graphene was also subjected to the force from the Si substrate and underlying layers of graphene. Because the velocity was too low to create enough force, the topmost graphene was pulled back to the substrate after reaching the farthest distance of 10.86 A from the substrate surface at timestep 1422. In other words, if the external vertical constant velocity applied to the topmost layer is too low, the produced kinetic energy cannot exceed the adhesion energy, and thus graphene cannot move far away from the Si surface. This is similar to the experimental phenomenon in which a small speed excitation cannot produce any effective response. The external force created by the V\({}_{\mathrm{up}}\) was applied continuously to the topmost layer, and the distance between the topmost layer and the Si substrate surface peaked once again at timestep 5558. This peak value was 10.21 A less than the first peak value, as shown in the black curve in Figure 2a. Due to the constraint of the Si substrate and underlying layers, the external force created by the V\({}_{\mathrm{up}}\) was gradually balanced, and the topmost layer was located around 9.46 A from the Si surface. From the displacement curve and graphene atomic trajectory shown in Figure 2, it can be seen that the topmost layer cannot be exfoliated if the external V\({}_{\mathrm{up}}\) is 5 A/ps. Due to the van der Waals forces between the graphene layers, the three-layer graphene acted like a spring with a fixed bottom. The second and bottom layers of graphene moved up with the topmost layer at the beginning; their movement trends were in sync with the topmost layer and were almost identical. The second layer reached as far as 7.30 A from the Si surface at timestep 1382, and the second peak was 6.70 A at timestep 5743; meanwhile, the bottom layer reached only as far as 3.88 A from the Si surface at timestep 1134, and the second peak occurred at timestep 5806 with a value of 3.25 A. Like the topmost layer, the second layer and bottom layer were finally maintained at around 6 A and 2.55 A from the Si surface, respectively. According to the results shown in Figure 7, when the V\({}_{\mathrm{up}}\) was 5 A/ps, the gap between the topmost layer and the second layer of graphene was no more than 3.87 A. The largest gap occurred at timestep 170 when the topmost layer started to move up, and the gap varied slightly up and down. The external force and the internal interactions gradually reached a dynamic equilibrium, and finally the gaps between the topmost and second layers and between the  
Figure 2: Adhesion behavior in a three-layer graphene system, where the vertical upward velocity is 5 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. second and bottom layers were stable at around 3.45 A (as shown in Figures 7 and 8). The gaps were larger than the natural value of 3.35 A. During the movements, the three graphene layers exhibited regular wavy fluctuations, and the fluctuation states of the three layers were consistent, as shown in Figure 2b. It was found that, at a lower Vup, the three layers moved consistently because of the interlayer interactions of the graphene. Once the Vup increased to 6.98 A/ps, the external force induced by velocity was greater than the forces exerted by the Si substrate and underlying layers. The topmost layer of graphene was exfoliated, moving away from the Si surface gradually. The distance between the topmost layer and the Si surface increased with the timestep in a nonlinear fashion at the beginning.