Kinetic Step Bunching Instability during Surface Growth

Abstract

We study the step bunching kinetic instability in a growing crystal surface characterized by anisotropic diffusion. The instability is due to the interplay between the elastic interactions and the alternation of step parameters. This instability is predicted to occur on a vicinal semiconductor surface Si(001) or Ge(001) during epitaxial growth. The maximal growth rate of the step bunching increases like F 4 , where F is the deposition flux. Our results are complemented with numerical simulations which reveals a coarsening behavior on the long time for the nonlinear step dynamics. The field of surface growth on semiconductors is very active due to its importance for both technological applications and fundamental science [1,2,3]. Under nonequilibrium growth a variety of experiments reveal rich crystal morphologies resulting from the nonlinear evolution of step flow instabilities [4,5]. The kinetic and elastic effects drive the system towards self-organized states, characterized by the appearance of ordered structures on the vicinal surfaces. This self-organization can be exploited in semiconductor nanotechnology, for the development of devices having interesting quantum properties [6,7]. A basic mechanism for pattern formation in vicinal semiconductor surfaces is the step bunching instability [8, 9, 10] whose origin is commonly attributed to the presence of impurities, to the inverse Ehrlich-Schwoebel effect, or to electro-migration (see [11,12] and references therein). This Letter is motivated by the molecular beam epitaxy (MBE) experiments on Si(001) in which it was observed a new type of kinetic instability leading to the formation of step bunches [13,14,15]. Microscopic kinetic Monte-Carlo simulation showed that in the case of Si(001), step bunching is due to the coupling between diffusion anisotropy and differences in step kinetic parameters [16]. Here we provide a macroscopic instability mechanism for the step bunching instability that does not require any inverse Ehrlich-Schwoebel effect. We show that the interplay between the elastic step interactions and the alternation of kinetic parameters, characteristic of the Si(001) vicinal surface, induces a finite wavelength instability with maximal growth rate increasing as F 4 (F is the deposition flux). Our results are complemented by numerical simulations which reveal a coarsening behavior on the long time for the non-linear step dynamics.The Si(001) vicinal surface consists of a periodic sequence of terraces where rows of 2 × 1 dimerised adatoms (terrace of type a) alternate with 1×2 dimerised adatoms (terrace of type b), see Fig. 1. On the reconstructed surface adatoms diffuse preferentially along dimer rows, giving rise to an anisotropic diffusion. Therefore, the steps separating the terraces are of two kinds. The S a step is rather straight while the S b step is very corrugated [17].

Effect of alternation of kinetic coefficients on step instabilities on Si(001) vicinal face

“…The results of theoretical study [9] agree with the experiments [7,8]. However, the step motion in sublimation at the low temperature has not been observed.…”

“…Frisch and co-workers [9] theoretically studied the step bunching by one-dimensional step flow model. They showed that the alternation of the surface diffusion is not important for the bunching.…”

Effect of step permeability on step instabilities due to alternation of kinetic coefficients on a growing vicinal face

“…When the difference in terrace width is small [20], δV is proportional to F 2 . In the present case, the tight step pairs are formed and the difference in terrace width is large.…”

“…Frisch and co-worker [20] theoretically studied the step bunching. They used a step flow model, in which the anisotropy of the surface diffusion and the kinetic coefficients are changed alternately, and showed that the alternation of the kinetic coefficients causes the step bunching on the growing vicinal face.…”

“…They used a step flow model, in which the anisotropy of the surface diffusion and the kinetic coefficients are changed alternately, and showed that the alternation of the kinetic coefficients causes the step bunching on the growing vicinal face. In the study [20], they assume that the steps are impermeable. Without solidification, surface diffusion between neighboring terraces does not occur.…”