Coarsening of ion-beam-induced surface ripple in Si: Nonlinear effect vs. geometrical shadowing

The temporal evolution of a periodic ripple pattern on a silicon surface undergoing erosion by $30\mathrm{keV}$ argon ion bombardment has been studied for two angles of ion incidence of 60° and 70° using ex situ atomic force microscopy (AFM) in ambient condition. The roughness amplitude $\left(w\right)$ grows exponentially with sputtering time for both the angle of ion incidence followed by a slow growth process that saturates eventually with almost constant amplitude. Within the exponential growth regime of amplitude, however, ripple wavelength $\left(l\right)$ remains constant initially and increases subsequently as a power law fashion $l\propto t^n$, where $n=0.47\pm 0.02$ for a 60° angle of ion incidence followed by a saturation. Wavelength coarsening was also observed for 70° but ordering in the periodic ripple pattern is destroyed quickly for 70° as compared to 60°. The ripple orientation, average ripple wavelength at the initial stage of ripple evolution, and the exponential growth of ripple amplitude can be described by a linear continuum model. While the wavelength coarsening could possibly be explained in the light of recent hydrodynamic model based continuum theory, the subsequent saturation of wavelength and amplitude was attributed to the effect of geometrical shadowing. This is an experimental result that probably gives a hint about the upper limit of the energy of ion beam rippling for applying the recently developed type of nonlinear continuum model.

Figure 1

AFM images of ${\mathrm{Ar}}^{+}$ beam-sputtered Si surfaces (ion $\text{fluence}=1\times {10}^{18}\text{ions}{\mathrm{cm}}^{-2}$, ion $\text{flux}=18\mu \mathrm{A}{\mathrm{cm}}^{-2}$, and $E_{\mathit{\text{ion}}}=30\mathrm{keV}$) at different ion incidence angles $\left(\theta \right)$: (a) 0°, (b) 50°, (c) 55°, (d) 60°, (e) 65°, (f) 70°, (g) 75°, and (h) 80°. No ripple features at $\theta =0°$ (a) and 50° (b); a ripple appears in the angular range 55°–70° (c)–(f) and disappears beyond that (g) and (h). The arrow marks denote the direction of the projection of ion beam on to surfaces.

Figure 2

Plot of the experimentally determined wavelength as well as theoretically calculated wavelength (normalized with respect to the wavelength at 55°) as a function of ion incidence angle (covering the angle window within which ripples are observed) for a fluence of $1\times {10}^{18}\text{ions}{\mathrm{cm}}^{-2}$.

Figure 3

AFM images of Si surfaces sputtered with ${\mathrm{Ar}}^{+}$ for different sputtering times (a) $5700\mathrm{s}$, (b) $10700\mathrm{s}$, and (c) $26600\mathrm{s}$ at $E_{\mathit{\text{ion}}}=30\mathrm{keV}$, $\theta =60°$ (upper panel) and (d) $7500\mathrm{s}$, (e) $11300\mathrm{s}$, and (f) $28200\mathrm{s}$ at 70° (lower panel). The height profiles shown under each of the AFM images are taken along the line indicated in the images.

Figure 4

The ripple wavelength $l$ and the surface roughness amplitude $w$ as a function of bombardment time for ion incidence angles 60° (upper figure) and 70° (lower figure).

Figure 5

Cross-sectional TEM (XTEM) image of the Si surface sputtered with $30\mathrm{keV}$ ${\mathrm{Ar}}^{+}$ for a fluence of $9\times {10}^{17}\text{ions}{\mathrm{cm}}^{-2}$ at 60° angle of ion incidence. (a) Low magnification image and (b) high magnification image.

Figure 6

Depth distribution of deposited energy simulated with the SRIM code for $30\mathrm{keV}$ ${\mathrm{Ar}}^{+}$ on Si at normal incidence. The solid line presents a fit using Eq. (1).