Kinetic Roughening of Ion-Sputtered Pd(001) Surface: Beyond the Kuramoto-Sivashinsky Model

We investigate the kinetic roughening of ${\mathrm{Ar}}^{+}$ ion-sputtered Pd(001) surface both experimentally and theoretically. In situ real-time x-ray reflectivity and in situ scanning tunneling microscopy show that nanoscale adatom islands form and grow with increasing sputter time $t$. Surface roughness $W(t)$ and lateral correlation length $\xi (t)$ follow the scaling laws $W(t)\sim t^{\beta }$ and $\xi (t)\sim t^{1/z}$ with the exponents $\beta \simeq 0.20$ and $1/z\simeq 0.20$, for an ion beam energy $\epsilon =0.5\mathrm{keV}$, which is inconsistent with the prediction of the Kuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying the coarse-grained continuum approach of the Sigmund theory to the order of $\mathcal{O}({\nabla }^4,h^2)$, where $h$ is the surface height, and derive a new term of the form ${\nabla }^2(\nabla h{)}^2$ which plays a decisive role in describing the observed morphological evolution of the sputtered surface.

Figure 1

Specular x-ray reflectivity (symbols) as a function of the momentum transfer, $q_z$, for increasing sputter times with $\epsilon =0.5\mathrm{keV}$ and $f=2.0\times {10}^{13}\mathrm{ions}/{\mathrm{cm}}^2/\mathrm{s}$. The solid lines are the theoretical prediction by the Parratt formula.

Figure 2

The surface roughness $W$ as a function of sputter time $t$ for different ion energies, $\epsilon =0.5$ (○), 1.5 (□), and 2.0 (△) keV, but with a fixed ionic flux, $f=2.0\times {10}^{13}\mathrm{ions}/{\mathrm{cm}}^2/\mathrm{s}$. The inset shows that the roughness evolution for a given $\epsilon$ follows the same fluence dependence, irrespective of $f$.

Figure 3

X-ray diffraction intensity along $[110]$ for different $q_z$. The positions of satellite peaks shift to the larger $q_{\parallel }$ for the larger $q_z$, with a fixed angle to the surface normal, indicating that the spots originate from a facet formed by sputtering. Inset: Positions of satellite peaks, $q_{\parallel }$, as a function of $q_z$.

Figure 4

STM images, $200\times 200{\mathrm{nm}}^2$ in size, according to time evolution. The insets at right bottom of each image show the height-height correlation function obtained from the corresponding surface profile.

Figure 5

Plot of the lateral correlation length $\xi$ (□) and the surface roughness $W$ (●) for $\epsilon =0.5\mathrm{keV}$ obtained from the STM images as a function of sputter time $t$.

Figure 6

Comparison of the KPZ and the CKPZ terms for a prototypical profile of eroded surface.