# Surface Ripple Formation by Bombardment with Clusters: Influence of Mass
## 4 Conclusions  
In this work, a Co(110) metal surface is bombarded with clusters of small dimensions (six atoms) and different angles of incidence. This study focuses on analyzing the effect of the mass of the cluster atoms on the process of surface ripple formation. For this, five types of atoms were used: He, Ne, Ar, Kr, and Xe. In all cases, the bombardment energy was 0.25 eV/atom, and the same fluence was used. Furthermore, diffusive effects have been ruled out, which would require considerably longer simulation times, since the surface temperature was not excessively high.  
The bombardment is concentrated on a surface in the form of a longitudinal strip to accelerate surface processes. Bombardment with heavy species accentuates the effects of surface ripple formation. For this type of species, it is verified that in collisional processes, the transfer of energy to the solid is greater; therefore, the surface energy deposited is also greater. However, it is also true that the energy is deposited deeper for intermediate angles, so the sputter yield is lower. Only for grazing angles does the sputter yield for heavy atoms become greater than that for light species because the energy deposited superficially is greater. Therefore, sputtering can be the cause of surface pattern formation only for these angles.  
Displacements generally increase with the mass of the cluster species. The horizontal displacement has a clearly defined maximum at 50\({}^{\circ}\), which shifts towards 60\({}^{\circ}\) for heavy atoms, such as Xe. This fact points to redistribution as a predominant effect for these angles. It also means that, according to certain experimental results, the critical angle is greater for heavy atoms. This displacement is very small for light ions and grazing incidence, a fact that would rule out the redistribution effect as a cause of the appearance of surface ripples. For its part, the vertical displacement only has a maximum for heavy atoms around 50\({}^{\circ}\), while for light ions, it decreases monotonically.  
Figure 6: Redistribution factor \(f_{rd}\) as a function of the angle of incidence for bombardment with different clusters.  
Finally, the redistribution factor confirms the importance of sputtering in the ripple formation process for the grazing angles, and close to the grazing angles if the projectile atoms are light, and of redistribution for all the other cases. The weight of redistribution decreases linearly in an approximate fashion as the angle of incidence increases. The redistribution effect increases with the mass of the projectile. In the case of He, the vertical displacements due to the formation of defects would justify the formation of small ripples for intermediate angles. In fact, sputter yields are very small due to channeling phenomena. For grazing angles, no surface patterns are observed.  
Conceptualization, J.C.J.-S., S.M. and P.P.; methodology, J.C.J.-S. and P.P.; software, J.C.J.-S.; validation, J.C.J.-S. and S.M.; formal analysis, J.C.J.-S. and P.P.; investigation, J.C.J.-S.; resources, J.C.J.-S. and P.P.; data curation, J.C.J.-S., S.M. and P.P.; writing--original draft preparation, J.C.J.-S., S.M. and P.P.; writing--review and editing, J.C.J.-S., S.M. and P.P.; visualization, J.C.J.-S. and S.M.; supervision, J.C.J.-S. and P.P.; project administration, J.C.J.-S. and S.M.; funding acquisition, S.M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The volume of data handled is such that it will only be available upon request to the authors.  
This work was supported by the Universidad Complutense of Madrid under the Project for Research Groups (Bioelectromagnetism Research Group 910305).  
The authors declare no conflicts of interest.