Fluctuations and instabilities of steps in the growth and sublimation of crystals

Abstract

Asymmetry in step kinetics (Schwoebel effect) has drastic effects on the motion of steps, and we study them theoretically and by simulation. With asymmetric step kinetics a step becomes smooth when it melts, whereas it becomes increasingly rough when it grows. When the Mullins-Sekerka type of instability takes place, the step does not form any stable pattern but shows a chaotic behavior although the crystal anisotropy influences the morphology. For a vicinal face consisting of equidistant steps, a similar enhancement of the step fluctuation in growth occurs while the fluctuation of step separation (terrace width) is suppressed because of the interference of the diffusion field. In sublimation, on the other hand, the step width is reduced but the fluctuation of the terrace width is enhanced. This leads to a bunching instability of steps. With one-sided step kinetics, steps always form pairwise bound states which have a hierarchical structure. In general various types of bound states appear, some of which lead to a morphological instability of the vicinal face.