Kinetics of step bunching during growth: A minimal model

Slanina, František; Krug, Joachim; Kotrla, Miroslav

doi:10.1103/physreve.71.041605

Cited by 21 publications

(38 citation statements)

References 37 publications

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“…Figure 6(b) shows the further evolution of these bunches during the coarsening regime. A variety of models of step bunching shows that the mean number of steps in a single bunch obeys a power law n(t) ∼ t β [8,11]. In the present case this behavior is expected to be more complex due to the presence of oscillations in the step size.…”

mentioning

confidence: 73%

Kinetic Step Bunching Instability during Surface Growth

Frisch

Verga

2005

Phys. Rev. Lett.

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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].

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confidence: 73%

Kinetic Step Bunching Instability during Surface Growth

Frisch

Verga

2005

Phys. Rev. Lett.

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“…In general the k ± are unequal. The case k + > k − corresponds to the so called Ehrlich-Schwoebel effect [9] while in the converse case we speak about an inverse Ehrlich-Schwoebel effect [12][13][14].…”

Section: Modelmentioning

confidence: 99%

“…The function (14) contains an additional term compared to the potential V 0 (u) considered in [18]. This term causes a maximum of V g (u) to appear at some u * , whereas V 0 (u) grows monotonically for large u.…”

Section: Mechanical Analog For Symmetric Stationary Bunchesmentioning

confidence: 99%

Anticoarsening and complex dynamics of step bunches on vicinal surfaces during sublimation

2010

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A sublimating vicinal crystal surface can undergo a step bunching instability when the attachment-detachment kinetics is asymmetric, in the sense of a normal Ehrlich-Schwoebel effect. Here we investigate this instability in a model that takes into account the subtle interplay between sublimation and step-step interactions, which breaks the volume-conserving character of the dynamics assumed in previous work. On the basis of a systematically derived continuum equation for the surface profile, we argue that the non-conservative terms pose a limitation on the size of emerging step bunches. This conclusion is supported by extensive simulations of the discrete step dynamics, which show breakup of large bunches into smaller ones as well as arrested coarsening and periodic oscillations between states with different numbers of bunches.

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“…Like the argument of Chernov, the ansatz (1.28) is problematic because the bunch spacing is not the only length scale in the system [31,45]; for example, the bunch width W defines a second (time-dependent) scale which cannot obviously be ignored. An explicit counterexample where the existence of an additional length scale leads to coarsening exponents which differ from (1.26) was presented in [49].…”

Section: Coarseningmentioning

confidence: 99%

“…For the relation of this problem to the standard velocity selection problem for traveling waves moving into unstable states see [49]. 7) Note however that traffic jams generally move in the direction opposite to the traffic flow [52,53].…”

Section: )mentioning

confidence: 99%