Fluctuation and instability of steps in a diffusion field

Fluctuation and morphology of steps growing in a surface diffusion field are studied theoretically and by the Monte Carlo simulation. Owing to the asymmetry in step kinetics (Schwoebel effect), a morphological instability takes place for advancing steps at a critical impingement rate ${\mathit{f}}_{\mathit{c}}$ of gas atoms. The fluctuation of a step is reduced for receding steps with f${\mathit{f}}_{\mathrm{eq}}$, and enhanced for advancing steps with f>${\mathit{f}}_{\mathrm{eq}}$. The width of a single step shows critical divergence at ${\mathit{f}}_{\mathit{c}}$. Above the instability f>${\mathit{f}}_{\mathit{c}}$, the step motion exhibits spatiotemporal chaos, in which the crystal anisotropy influences the morphology. For a vicinal face, when the step advancement rate increases, the motion of consecutive steps is strongly correlated and the terrace width becomes stable although the fluctuation of each step is enhanced. When steps recede in sublimation, bunching of the steps is observed, which is analyzed as an instability of antiphase oscillation.