Emergence and detailed structure of terraced surfaces produced by oblique-incidence ion sputtering

Abstract

We study the nanoscale terraced topographies that arise when a solid surface is bombarded with a broad ion beam that has a relatively high angle of incidence θ. We find that the surface is not completely flat between the regions in which the surface slope changes rapidly with position: Instead, small-amplitude ripples propagate along the surface. Our analytical work on these ripples yields their propagation velocity as well as the scaling behavior of their amplitude. Our simulations establish that the surfaces exhibit interrupted coarsening, i.e., the characteristic width and height of the surface disturbance grow for a time but ultimately asymptote to finite values as the fully terraced state develops. In addition, as θ is reduced, the surface can undergo a transition from a terraced morphology that changes little with time as it propagates over the surface to an unterraced state that appears to exhibit spatiotemporal chaos. For different ranges of the parameters, our equation of motion produces unterraced topographies that are remarkably similar to those seen in various experiments, including pyramidal structures that are elongated along the projected beam direction and isolated lenticular depressions.

Ion-induced nanopatterning of silicon: Toward a predictive model

“…As the focus here is on linear theories, we refer readers to two other reviews that cover this specific line of inquiry, 32,72 as well as more recent work specifically exploring the behavior of nearly vertical, shock-like features on otherwise flat surfaces, 5,[73][74][75] and sawtooth-like structures featuring alternating facets of different slopes. [76][77][78][79] Of particular interest in our context, however, we note that this approach also yielded additional linear terms at third and fourth orders. As noted in the original work of Bradley and Harper, 16 thermally activated Mullins surface diffusion is unlikely to be very strong at room temperature, and an alternate regularization mechanism should be identified for low temperature irradiation.…”

“…81 (Indeed, without any changes, the Sigmund model can also be applied in the fully nonlinear case of large amplitudes and slopes, leading to work on the behavior of steep-walled shock fronts 5,73-75 and on the behavior of alternating sawtooth-like structures. [76][77][78][79] In contrast, the CV model does not give a spatially resolved picture of atomic redistribution in 3D. Instead, it represents a hypothesized behavior of an average quantity-the net atomic displacement vector.…”

AFM and Raman study of graphene deposited on silicon surfaces nanostructured by ion beam irradiation

“…In Figure 1(B), the morphology of the silicon substrate S2 has transformed from parallel‐mode ripples of S1 into parallel‐mode terraces. This is a well‐known evolution, which can be observed by increasing the ion irradiation time –– and therefore the fluence (Harrison et al ., 2017), and/or by increasing the ion incidence angle (Castro et al ., 2012; Dell'Anna et al ., 2018). From an analytical point of view, the terraced topographies develop on the irradiated surfaces when nonlinear contributions cannot be ignored anymore in the equation for the surface height evolution in time (Harrison et al ., 2017).…”

“…This is a well‐known evolution, which can be observed by increasing the ion irradiation time –– and therefore the fluence (Harrison et al ., 2017), and/or by increasing the ion incidence angle (Castro et al ., 2012; Dell'Anna et al ., 2018). From an analytical point of view, the terraced topographies develop on the irradiated surfaces when nonlinear contributions cannot be ignored anymore in the equation for the surface height evolution in time (Harrison et al ., 2017). In the x ‐ACF of S2 in Figure 2(B), the previous very regular spatial correlation of S1 along the x direction is lost, whereas the shortest correlation length l = 673.1 nm is now much larger than the fundamental ripple wavelength in S1, λ = 42.2 nm (Table 2).…”

Stress-driven nonlinear dynamics of ion-induced surface nanopatterns

“…[25] for a recent review. Indeed, nonlinear descriptions of IBS surface nanopatterning are available [26][27][28][29][30], but they assume erosion (sputtering) as the main cause for the surface instability, which implies for instance that pattern formation can occur for any value of the incidence angle including θ = 0 • , contradicting recent experimental observations [25]. The limitations to the predictive power of such nonlinear descriptions are underscored by yet more recent experiments on Si with Ar + ions for very low E at which the sputtering yield is negligible [31], which find a pattern formation process just like the one seen at higher E and erosion rates [24,25,32].…”