Surface diffusion currents and the universality classes of growth

Krug, Joachim; Plischke, Michael; Siegert, Martin

doi:10.1103/physrevlett.70.3271

Cited by 226 publications

(155 citation statements)

References 22 publications

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“…The physical meaning of this current is clear in the context of surface electromigration -it is simply the current of adatoms driven across the terrace by the combined action of the electromigration force and the chemical potential gradient. The notion of a surface current induced by attachment asymmetry is also well established in the context of epitaxial growth 40,42,49,50,51 . It is less evident that the concept can be extended to sublimation, where the atoms detached from the steps do not necessarily remain on the terrace.…”

Section: The Mean Surface Currentmentioning

confidence: 99%

Scaling properties of step bunches induced by sublimation and related mechanisms

et al. 2005

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This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length d d = Ds/K d is larger than the average distance l between the steps on the vicinal surface; here Ds is the surface diffusion coefficient and K d is the step kinetic coefficient. In the opposite limit d d ≪ l the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the form L ∼ H α , lmin ∼ H −γ between the width L, the height H, and the minimum interstep distance lmin of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for the case d d ≫ l. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through comparison with numerical simulations of the discrete step equations, we establish the value γ = 2/(n + 1) for the scaling exponent of lmin in terms of the exponent n of the repulsive step-step interaction, and provide an exact expression for the prefactor in terms of the energetic and kinetic parameters of the system. For the bunch width L we observe significant deviations from the expected scaling with exponent γ = 1 − 1/α, which are attributed to the pronounced asymmetry between the leading and the trailing edges of the bunch, and the fact that bunches move. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.

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Section: The Mean Surface Currentmentioning

confidence: 99%

Scaling properties of step bunches induced by sublimation and related mechanisms

et al. 2005

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“…A zero in j ES is extremely important [10], because the other terms in j will be seen to depend on higher order derivatives of z(x, t). So, a constant slope m 0 may be a stationary slope if and only if j ES (m 0 ) = 0.…”

Section: A Ehrlich-schwoebel Currentmentioning

confidence: 99%

“…So, a constant slope m 0 may be a stationary slope if and only if j ES (m 0 ) = 0. An extra-zero m 0 may have different origins: the symmetry of the crystal lattice [10,11], nonthermal relaxation mechanisms [12], or a transient mobility of the adatom just after the deposition [13]. For example, the slope at 45 degrees corresponds in a cubic lattice to the high-symmetry orientation (11): we expect that j ES vanishes on it, as it vanishes on the (10) (m = 0) and (01) (m = ∞) orientations.…”

Section: A Ehrlich-schwoebel Currentmentioning

confidence: 99%

Kink dynamics in a one-dimensional growing surface

Politi

1998

Phys. Rev. E

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A high-symmetry crystal surface may undergo a kinetic instability during the growth, such that its late stage evolution resembles a phase separation process. This parallel is rigorous in one dimension, if the conserved surface current is derivable from a free energy. We study the problem in presence of a physically relevant term breaking the up-down symmetry of the surface and which can not be derived from a free energy. Following the treatment introduced by Kawasaki and Ohta [Physica 116A, 573 (1982)] for the symmetric case, we are able to translate the problem of the surface evolution into a problem of nonlinear dynamics of kinks (domain walls). Because of the break of symmetry, two different classes (A and B) of kinks appear and their analytical form is derived. The effect of the adding term is to shrink a kink A and to widen the neighbouring kink B, in such a way that the product of their widths keeps constant. Concerning the dynamics, this implies that kinks A move much faster than kinks B. Since the kink profiles approach exponentially the asymptotical values, the time dependence of the average distance L(t) between kinks does not change: L(t) ∼ ln t in absence of noise, and L(t) ∼ t 1/3 in presence of (shot) noise. However, the cross-over time between the first and the second regime may increase even of some orders of magnitude. Finally, our results show that kinks A may be so narrow that their width is comparable to the lattice constant: in this case, they indeed represent a discontinuity of the surface slope, that is an angular point, and a different approach to coarsening should be used.

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“…Diffusion bias refers to such generic non-equilibrium currents that are proportional to the local surface slope [18]. One possible origin of such currents is in the Schwoebel barriers [19]:…”

Section: Conservative "Mbe" Modelsmentioning

confidence: 99%

Dynamic scaling phenomena in growth processes

Kardar

1996

Physica B: Condensed Matter

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Inhomogeneities in a deposition process may lead to formation of rough surfaces. Fluctuations in the height h(x, t), of the surface (at location x and time t) can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest that, quite generally, the height fluctuations have a self-similar character; their average correlations exhibiting a dynamic scaling form,. The roughness and dynamic exponents, α and z, are expected to be universal; depending only on the underlying mechanism that generates self-similar scaling. Despite its ubiquitous occurrence in theory and simulations, experimental confirmation of dynamic scaling has been scarce. In some cases where such scaling has been observed, the exponents are different from those expected on the basis of analysis or numerics. I shall briefly review the theoretical foundations of dynamic scaling, and suggest possible reasons for discrepancies with experimental results.

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Surface diffusion currents and the universality classes of growth

Cited by 226 publications

References 22 publications

Scaling properties of step bunches induced by sublimation and related mechanisms

Scaling properties of step bunches induced by sublimation and related mechanisms

Kink dynamics in a one-dimensional growing surface

Dynamic scaling phenomena in growth processes

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