# Adhesion Behavior between Multilayer Graphene and Semiconductor Substrates
## 3 Results and Discussions
At timestep 403, the maximum Fz of all three layers was 26.73 nN. At this time, the distance between the bottom layer of graphene and the Si surface was 3.13 A. When the three layers were exfoliated entirely, at about timestep 2800, the force gradually reduced to zero. Meanwhile, the bottom layer was 6.16 A from the Si surface. The Fz of all three layers on each layer of graphene fluctuated violently at the beginning. The Fz variation of the bottom layer started to become harmonic at timestep 3200, and the amplitude range was between \(-33\) nN and 45 nN. The top graphene started the harmonic change at 3700 with an amplitude of \(-42\) nN-35 nN. The Fz curve of the second layer of graphene was more disordered. When the V\({}_{\text{up}}\) exceeded the first critical of V\({}_{\text{up}}\) 6.98 A/ps, the variation curve of the Fz applied to the three-layer graphene system over time was relatively smooth at 9 A/ps. At timestep 434, the maximum force was 23.67 nN. After plenty of calculations, it was found that when the top layer of graphene was between 6.98 A/ps and 10.16 A/ps, the strongest force for stripping off the three layers of graphene was 26.73 nN, representing the adhesion force required for the exfoliation of all three layers of graphene. Only the topmost layer of graphene was exfoliated at the critical V\({}_{\text{up}}\) of 10.16 A/ps, so the force of the three-layer graphene as a whole cannot be counted. As can be seen from Figure 10, at timestep 64, the topmost layer was subjected to the maximum force of 74.75 nN, and this was the adhesion force required for the exfoliation of the topmost layer of graphene. The Fz of the topmost layer of graphene was almost zero after timestep 1500, when it moved to a distance of 16.78 A away from the Si surface. When the topmost layer was completely exfoliated, the Fz forces applied to the second and bottom layers of graphene gradually decreased to zero. Figure 9: Fz to exfoliate the total number of layers of graphene varying with timestep. Figure 11: Fz of the second layer of graphene varying with timestep. Figure 3:0 Fz of the bottom layer of graphene varying with timestep. Figure 3:1 Fz to exfoliate the topmost layer of graphene varying with timestep. In order to obtain the adhesion energy between graphene and the Si substrate, the work done (W) by Fz was calculated, which was defined as the direction force (Fz) applied to graphene multiplied by the average distance the graphene layer moved (S):  
Figure 3:2  
The work done by the external force to all three layers was negative before timestep 234 (shown in Figure 13). This is because when the three-layer graphene was exfoliated entirely at a velocity of 6.98 A/ps, the effect of the negative direction of the Fz on all graphene layers was caused by the existence of the repulsive force between graphene and the Si surface. Under the critical Vup of 6.98 A/ps, the work curve of the Fz showed a certain fluctuation due to the variations of the external force, and finally was reduced to zero due to the disappearance of the external force. The maximum work done to exfoliate the three layers was 68.51 mJ/m\({}^{2}\), which was equal to the adhesive energy of the entire three-layer graphene. When the critical velocity was 10.16 A/ps, only the topmost layer was exfoliated, and the work curve of the topmost layer by the external force is shown in Figure 3:3 The maximum work value of the external force was 148.31 mJ/m\({}^{2}\), which was equal to the adhesive energy of the topmost layer in the three-layer graphene system. Figure 3:4 The work of Fz to exfoliate the topmost layer of graphene when the upward velocity is 10.16 Å/ps. Figure 3:5 The work of the Fz to exfoliate all three layers of graphene when the upward velocity is 6.98 Å/ps. The exfoliation processes of one- to ten-layer graphene systems were calculated. Additionally, the critical velocities, the maximum exfoliation forces, and the adhesion energies were calculated and are summarized in Figures 15-17, respectively.