# Surface Ripple Formation by Bombardment with Clusters: Influence of Mass
## 3 Results and Discussion  
### Atomic Description  
Firstly, the surface morphology resulting from bombardment is analyzed for angles of incidence for which surface ripples typically form. Surface irregularities are accentuated if a solid is bombarded with clusters instead of atoms. Figure 2a,b show the surface after bombardment with Ne clusters for the fluence of 10\({}^{16}\) atoms\(\cdot\)cm\({}^{-2}\) and two angles of incidence: 70\({}^{\circ}\) and 50\({}^{\circ}\), respectively. The structure induced after the bombardment and without considering diffusion effects is slot shaped. The lack of dependence on the \(y\) coordinate causes the craters produced after impacts to evolve towards this structure. The groove is shallower for the grazing angles (\(\sim\)70\({}^{\circ}\)) as the penetration of the cluster is less in that situation. The displaced atoms accumulate on both sides of the groove, forming adlayers and giving rise to two ridges. The right ridge accumulates many more atoms than the left one due to the initial linear momentum of the cluster in the \(x\) direction, i.e., the cluster atoms collide with the solid atoms and transfer velocities to them, which are directed towards the right ridge. Since the distance traveled by the solid atoms in the cascade is of the order of the size of the groove, these atoms are most likely deposited on the right ridge. Nanopatterns are surface ripples: valleys and ridges whose origins are excitations caused by irradiation. Initially, cluster bombardment erodes the surface locally, whereas surface redistribution acts in the same way, creating adlayers. However, only one of the processes usually dominates and maintains this structure in a stationary manner. Figure 2: (a,b) \(xz\) projections after bombardment with Ne clusters and (c,d) with Xe clusters for two angles of incidence: 70\({}^{\circ}\) (a,c) and 50\({}^{\circ}\) (b,d). The viewing direction is \(<\)100\(>\). The arrow shows the direction of movement of the cluster. Its endpoint is the point of incidence on the surface (in this case, \(x=0\)). The two surface ridges created on either side of the groove appear in blue. These irregularities are only stable for angles of incidence greater than a certain value, normally close to 50\({}^{\circ}\). Diffusion effects are responsible for damping surface morphologies [2] since, for angles close to the normal, the width of the groove becomes small enough to be reabsorbed. Diffusion takes place in longer time intervals than those considered here, which means that molecular dynamics is limited to describing collisional processes. However, let us remember that the result of these simulations becomes a very good approximation to the final result under conditions of high influence and/or low surface temperature [7]. In fact, the theoretical models themselves have encountered problems when predicting the existence of the critical angle. Classical pattern formation theory did not predict the existence of any critical angle [2]. Certain authors [22] solved this problem by introducing a flux of cascade atoms directed toward the surface. The most interesting aspect is how the surface structure is modified when bombardment with a heavier species, such as Xe, occurs. In the case of 50\({}^{\circ}\), the groove becomes deeper and the right ridge higher. However, the widths of both surface structures are smaller, i.e., a heavier atom excites a surface nanostructure in the form of a higher and shorter wave pulse. In turn, in the case of 70\({}^{\circ}\), the pulse amplitude is also accentuated: the groove becomes deeper and the ridge higher. However, the pulse also widens horizontally. The Xe atoms do not penetrate as much into the solid and displace more surface atoms, thus avoiding the creation of the interior cavity. In short, in the case of 50\({}^{\circ}\), it seems to be observed that the solid atoms travel less distance on average with a heavier projectile atom.