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

We investigate the kinetic roughening of Ar$^+$ ion-sputtered Pd(001) surface both experimentally and theoretically. \textit{In situ} real-time x-ray reflectivity and \textit{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, $\xi(t)$, follows 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 ion beam energy $\epsilon=0.5$ keV, which is inconsistent with the prediction of the Kuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying the Sigmund theory of sputter erosion to the higher order, ${\cal O}(\nabla^4, h^2)$, where $h$ is surface height, and derive a new term of the form $\nabla^2(\nabla h)^2$ which plays an indispensable role in describing the observed morphological evolution of the sputtered surface.