# Formation of Micro- and Nano-Trenches on Epitaxial Graphene
## 3 Results and Discussions  
Figure 1 shows the results of the Ag/EG system observed by SEM and AFM. The formation of trenches is only motivated by sliding of Ag particles during high vacuum annealing. According to the hexagonal structure of the EG substrate, the angle between two armchair/zigzag directions is 60\({}^{\circ}\), and the angle between an armchair and a zigzag is 30\({}^{\circ}\)[35]. Similarly, the slipping of metal particles is strictly along some particular directions, which are 30\({}^{\circ}\) or 60\({}^{\circ}\) with respect to one another. As marked by the green and blue arrows in Figure 1a,b, the slipping directions can be parallel to each other or intersect, and the width is in several microns. As shown in Figure 1a, the white dashed line is marked, from which the green arrow deviates by about \(\sim\)66\({}^{\circ}\). It indicates the directions of these trenches along the green arrow. The intersected trenches with an angle of \(\sim\)127\({}^{\circ}\) from the green arrow are marked by the green arrow. Some trenches are identified with other directions as marked by the blue arrows, which deviate from the green arrows by \(\sim\)36\({}^{\circ}\) and \(\sim\)150\({}^{\circ}\). The angle between the two blue arrows in Figure 1a is \(\sim\)63\({}^{\circ}\). Figure 1b shows another region of the same sample on which the trench directions are parallel to each other. There is an including angle of 35\({}^{\circ}\) between the blue arrow and the white dashed line, and the sliding direction can be swerved (\(\sim\)127\({}^{\circ}\)) into another one across some defects [36]. Apparently, all these micro-trenches are long and straight. Most of these trenches are parallel and stay in one direction when sliding happens, and the sliding directions might correspond to the some crystallographic orientations of graphene [37]. Figure 1c,d show more details of trenches in an enlarged area by SEM images. Some particles can be swerved or branched into two as indicated by the dashed green and white arrows in Figure 1c. The marked angle of 128\({}^{\circ}\) means the diversion of the trenches, and the moving particle can also introduce the parallel sliding of another Ag particle, as shown under the white dashed arrow. Figure 1d displays the head of Ag trench in a magnified area. The large bright particles on the trench is the aggregation of metal particles during sliding, and the wrinkles caused by push and press are clearly evidenced. It rightly demonstrates the sliding direction. That is to say, vacuum annealing can induce the migration of metal particles, because the annealing temperature (~570 K) is much smaller than that of the melting point of Ag (1234 K); it can be deduced that some small Ag particles would be melted partly at such high vacuum annealing [38], and a tiny perturbation would push Ag particles to move forward and form a trench on graphene sheets. Moreover, the small Ag particles would merge into larger ones gradually as a result of a snowballing effect during sliding as shown in Figure 1d. After that, the large particle with wrinkles ahead of the trench can be clearly visible in the SEM images. Figure 1e displays the surface area without trenches, only showing the morphology of Ag thin films on EG after annealing. The sliding of Ag particles breaks the continuity of Ag films. Figure 1f,g show the AFM morphology and corresponding 3D image, from which SiC steps inside the trench is clearly observed. The straight trench is in depth of ~8.0 nm and in width of ~4.0 \(\upmu\)m as marked by the green profile. Even across SiC steps, the vacuum annealing is still enough to make the sliding of Ag particles. Similarly, trenches can be produced by the sliding of In particles, too. Figure 2a,b display the macroscopic morphology of trenches on EG, in which the white dashed lines are also used to denote one direction. Figure 2a shows large numbers of paralleling trenches with an angle of ~7\({}^{\circ}\) from the white dashed line, and the distance between each channel is randomly.