Properties and dynamic interaction of step density waves at a crystal surface during electromigration affected sublimation

Stoyanov, S.; Tonchev, Vesselin

doi:10.1103/physrevb.58.1590

Cited by 79 publications

(88 citation statements)

References 25 publications

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“…Equation (5) is valid only for a conserved system with negligible desorption, which assumes that the adatom's mean diffusion path λ s tends to infinity. 27 As a result, the critical field tends to zero in accordance with the equation for E cr ,…”

Section: B Experimental Results and Discussionmentioning

confidence: 79%

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

et al. 2012

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In this paper, we investigate the antiband instability on vicinal Si(111) surfaces with different angles of misorientation. It is known that prolonged direct current-annealing of Si(111) results in the formation of antibands; i.e., the step bunches with the opposite slope to the primary bunches. We provide a theoretical description of antiband formation via the evolution of the atomic steps' shape. We also derive a criterion for the onset of the antiband instability under the conditions of sublimation controlled by slow adatom surface diffusion. We examine this criterion experimentally by studying the initial stage of the antiband formation at a constant temperature of 1270 • C while systematically varying the applied electromigration field. The experiment strongly supports the validity of the derived theoretical criterion and indicates the importance of accounting for the factor of critical field in the theoretical modeling of step bunching or antiband instabilities. Deduced from the comparison of theory and experiment, the Si surface atoms' effective charge cannot exceed double the elementary charge, set by the lower limit of kinetic characteristic length d s = 0.3 nm. Using d s = 1.7 − 4.5 nm draws values of the effective charge in line with the values reported in earlier studies.

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Section: B Experimental Results and Discussionmentioning

confidence: 79%

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

et al. 2012

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“…The value of n e s in the vicinity of the i-th step depends on the distances to the neighboring steps i + 1 and i − 1, since n e s (x i ) = n e s exp[∆µ(x i )/k B T ], where 29,30 ∆µ(…”

Section: Discrete Model and Basic Concepts Of Sublimation By Stepmentioning

confidence: 99%

“…Quite recently it was realised that step bunching is a promising way to study the interactions between the steps 29,30,31,32,33,34 . The physical ground is simple: The steps in the bunch keep a certain distance from each other because the step-step repulsion balances the tendency to further compression of the bunch.…”

Section: Introductionmentioning

confidence: 99%

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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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“…In addition, based on recent developments in the study of non-equilibrium bunched steps [49]- [53], the values of the exponents in the profile of a bunched step are related to the force range of the effective step-step interactions on the non-equilibrium vicinal surface. The values of the exponents are thought to be related to the shape exponent θ n on the ECS.…”

Section: Introductionmentioning

confidence: 99%

Non-universal equilibrium crystal shape results from sticky steps

Akutsu¹

2011

J. Phys.: Condens. Matter

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Abstract. The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z = z(x, y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal GruberMullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) n(p) using the Monte Carlo method, where p = (∂z/∂x, ∂z/∂y), and · represents the thermal average. Using the result of the |p| dependence of n(p) , we derive a |p|-expanded expression for the non-universal surface free energy f eff (p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f eff (p).

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Properties and dynamic interaction of step density waves at a crystal surface during electromigration affected sublimation

Cited by 79 publications

References 25 publications

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

Scaling properties of step bunches induced by sublimation and related mechanisms

Non-universal equilibrium crystal shape results from sticky steps

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