# Ion Beam Nanopatterning of Biomaterial Surfaces
## 2 Nanoscale Pattern Formation on Solid Surfaces during Ion Beam Irradiation
### Roughening vs. Smoothing  
It was already shown by [PERSON] in 1973 that any rough surface is unstable under ion irradiation [80]. This is because the sputtering yield, i.e., the number of target atoms ejected from the target surface per incident ion, depends on the local surface curvature. This is a direct result of the Gaussian distribution of the deposited energy, which is centered at the mean penetration depth of the ion. In particular, a higher sputtering yield is obtained in depressions than at elevations. This means that depressions are eroded faster than elevations, which is equivalent with an amplification of the initial surface roughness. Since sputtering is an intrinsically stochastic process, this micro-roughening instability will occur also when irradiating atomically flat surfaces, because the first few ion impacts result in the local removal of material and, thus, in the formation of a non-flat surface topography. By itself, however, this mechanism will not lead to the formation of ordered nanopatterns but rather in a self-affine random surface roughness. The former requires the presence of an additional, counteracting smoothing mechanism [81]. In this case, a selection of spatial frequencies will occur and result in one spatial frequency being eroded much slower than all the others are. In a co-moving frame of reference, this will be perceived as an exponential growth of the selected frequency and, thus, the development of an ordered pattern with a fixed periodicity.  
Figure 1: Different nanopatterns obtained on different surfaces by ion beam irradiation. **(a)** Nanorripple pattern on a Si surface obtained by irradiation with 500 eV Ar\({}^{+}\) at 67\({}^{\circ}\) incidence with respect to the surface normal. Reproduced from Ref. [78]. Scale bar 200 nm. **(b)** Nanorripple pattern on a fused silica surface obtained by irradiation with 1 keV Ar\({}^{+}\) at 45\({}^{\circ}\) incidence with respect to the surface normal. Scale bar 200 nm. Republished with permission of IOP Publishing, Ltd., from Ref. [52]; permission conveyed through Copyright Clearance Center, Inc. (**c**) Nanorripple pattern on a polyimide surface obtained by focused ion beam irradiation with 30 keV Ga\({}^{+}\) at 45\({}^{\circ}\) incidence with respect to the surface normal. Scale bar 1 μm. Republished with permission of IOP Publishing, Ltd., from Ref. [50]; permission conveyed through Copyright Clearance Center, Inc. (**d**) Nanodot pattern on a GaSb surface obtained by irradiation with 500 eV Ar\({}^{+}\) at normal incidence. Scale bar 200 nm. Reprinted with permission from Ref. [79]. Copyright 2001 by the American Physical Society. **(e)** Nanohole pattern on a Ge surface obtained by broad ion beam irradiation with 5 keV Ga\({}^{+}\) at normal incidence. Scale bar 200 nm. Reprinted from Ref. [55], with the permission of AIP Publishing. **(f)** Inverted nanopyramid pattern on a crystalline Ge(100) surface obtained by irradiation with 1 keV Ar\({}^{+}\) at normal incidence. Scale bar 1 μm. Reprinted with permission from Ref. [56]. Copyright 2013 by the American Physical Society. **(a,b,f)** Atomic force microscopy (AFM) images. **(c–e)** Scanning electron microscopy (SEM) images.  
In their original model, [PERSON] and [PERSON] considered thermally activated surface diffusion of the Herring-Mullins type [82; 83] as the dominant smoothing mechanism [81]. This immediately suggests that pattern formation kinetics and pattern properties should depend on the target temperature during irradiation. While this was indeed observed in some experiments and especially at elevated temperatures, the observations reported in numerous other studies were incompatible with this interpretation [84]. Under such conditions, alternative, ion-induced smoothing mechanisms are believed to dominate, in particular ion-enhanced viscous flow [85] and ion-induced mass redistribution of the Carter-Vishnyakov type [86].