Anisotropy Effect on Step Morphology Described by Kuramoto-Sivashinsky Equation

A step growing in a diffusion field is unstable due to the Schwoebel effect when it advances too fast. A continuum model equation is derived for morphological evolution of the unstable step by taking account of the anisotropy effect in the stiffness. The anisotropy brings up an additional term (∂ H /∂ X ) 2 ∂ 2 H /∂ X 2 in the Kuramoto-Sivashinsky equation that describes an isotropic step. Unless direction of the growth corresponds to the one with the stiffness minimum, the morphology is chaotic in space and time. When the step advances in the direction of the stiffness minimum and the anisotropy is sufficiently strong, the step takes a periodic structure.