Transformations on clean Si(111) stepped surface during sublimation

Латышев, А. В.; Aseev, A. L.; Krasilnikov, A.B.; Stenin, S. I.

doi:10.1016/0039-6028(89)90256-2

Cited by 439 publications

(210 citation statements)

References 12 publications

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“…We noted already in Sect.V D that the equations of step motion (10,15,16) are mathematically equivalent to appropriate limiting cases of those obtained for step bunching instabilities induced by electromigration and growth in the presence of inverse Ehrlich-Schwoebel barriers. Here we elaborate on that observation and translate the results derived from the continuum theory to the different physical contexts.…”

Section: Equivalent Problemsmentioning

confidence: 95%

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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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Section: Equivalent Problemsmentioning

confidence: 95%

“…Mechanisms causing step bunching instabilities include strain effects 1,2,7,8 , sublimation under conditions of asymmetric detachment kinetics known as the Ehrlich-Schwoebel (ES) effect 9,10,11 , growth with an inverse ES effect 9,12,13,14 , and surface electromigration 15,16,17,18,19,20,21,22,23,24,25,26,27,28 .…”

Section: Introductionmentioning

confidence: 99%

Scaling properties of step bunches induced by sublimation and related mechanisms

et al. 2005

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“…[1][2][3][4][5][6][7][8][9][10] When Si(111) is annealed by direct current (dc) driven along the miscut direction, adatom surface electromigration causes the atomic steps to gather together and creates step bunches separated by wide terraces. These step bunches grow with time and reach tens to hundreds of nanometers in height, while the terraces between them can grow to several micrometers in width.…”

Section: Introductionmentioning

confidence: 99%

“…These step bunches grow with time and reach tens to hundreds of nanometers in height, while the terraces between them can grow to several micrometers in width. 1,2,10 Soon after the discovery of step bunching, it was found that prolonged dc annealing of Si(111) allows the surface morphology to further develop, giving rise to new morphologies such as antibands, which can be described as step bunches with slopes of the opposite sign as compared to the primary bunches. 11 Antibands are primarily formed via the shape evolution of atomic steps crossing the wide terraces between step bunches.…”

Section: Introductionmentioning

confidence: 99%

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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“…With a weak ES effect [14], the fluctuation of step density occurs and the large bunches are formed. With the drift of adatoms [15], the step bunching occurs if the kinetic coefficients are finite [16][17][18][19]. In a conserved system, bunches grows by coalescence of bunches.…”

Section: Introductionmentioning

confidence: 99%

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

Sato

Deura

2008

Journal of Crystal Growth

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With taking account of alternation of kinetic coefficients, we study the possibility of step instabilities on a Si(001) vicinal face. In sublimation, a step with large kinetic coefficient recedes faster than that with small kinetic coefficient, and step pairs are formed. The upper side step in the step pair is the step with large kinetic coefficient. An equidistant array of the pairs is unstable against bunching. Number of steps N max in bunches increases with time as N max ∼ t β . The exponent β = 0.5 when the bunch grows via successive collisions of step pairs, and β ≈ 1.2 when the bunch grows via coalescence of bunches.

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Transformations on clean Si(111) stepped surface during sublimation

Cited by 439 publications

References 12 publications

Scaling properties of step bunches induced by sublimation and related mechanisms

Scaling properties of step bunches induced by sublimation and related mechanisms

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

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

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