# Adhesion Behavior between Multilayer Graphene and Semiconductor Substrates
## 3 Results and Discussions
After timestep 2584, when the topmost layer of graphene was 13 A away from the Si surface, the displacement curve (the black curve in Figure 3a) became almost linear. The second layer of graphene was forced upward with the topmost layer, since the pulling up force from the topmost layer of graphene was greater than the pulling down force from the Si substrate and bottom layer of graphene. The same condition occurred for the bottom layer, which moved upward together with the top two layers. At the beginning, the ascending rates of the three layers were different, leading to the maximum spacing of the topmost and second layers being 4.2 A (shown in Figure 7), and the maximum spacing of the second and bottom layers being 3.92 A (shown in Figure 8). After timestep 2584, when the effect of the substrate disappeared, the three layers went up at the same rate, and the three motion curves were parallel, as shown in Figure 3a. Figure 3b depicts one movement snapshot of the atomic trajectory. Because the interaction between graphene and the Si substrate was much more significant, the dislocation phenomena of Si surface atoms close to the edge  
Figure 3: Adhesion behavior in a three-layer graphene system, when the vertical upward velocity is 6.98 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. of the graphene occurred. Graphene fluctuated wildly, but the atomic motion morphologies of the three layers were identical. When a V\({}_{\text{up}}\) of 9 A/ps was applied to the topmost layer, the topmost layer of graphene could pull the second and bottom layers up, according to the observation of the atomic trajectories. The topmost layer completely eradicated the bandage of the Si substrate, and the three layers went up at the same rate after 1357 timesteps, when the distance between the topmost layer and the Si substrate was larger than 13 A. A faster V\({}_{\text{up}}\) created more momentum and caused the three layers to leave the Si surface more quickly, in addition to resulting in a larger maximum gap of 5.1 A between the topmost and second layers (shown in Figure 7). The relative balance gap between the topmost and second layers was 3.44 A larger than the natural graphene interlayer gap of 3.35 A. From the atomic trajectories, shown in Figure 4b, the three layers maintained consistent, huge waves. With a V\({}_{\text{up}}\) of 10.16 A/ps, only the top can be unbound from the Si substrate and move far away from the underlying graphene and Si surface, as if the springs between the graphene layers were suddenly broken. Before timestep 2347, when the distance between the topmost layer and Si surface was less than 19.59 A, the Si substrate and underlying layers still exerted forces on the topmost layer of graphene, and the movement curve of the topmost layer was nonlinear at the beginning, as shown in Figure 5a. Once the distance between the topmost layer and the Si substrate was larger than 19.59 A, the topmost layer could eliminate all constraints and move up linearly. Figure 4: Adhesion behavior in a three-layer graphene system, when the vertical upward velocity is 9 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. The second layer was pulled up by the topmost layer with a bulge at the centre, as a result of the strong interaction between the Si substrate and the edge of the graphene, which was caused by the unsaturated bonds of graphene edge atoms. The topmost layer attempted to pull the underlying layers up before 13,926 timesteps. However, after this time, the bulge slowly flattened. The red and blue curves in Figure 5a show the displacement of the second and bottom layers of graphene, respectively, and the maximum average distance between the second layer and Si surface was 14.6 A. Meanwhile, the maximum average distance between the bottom layer and Si surface was 10.9 A.