The roughening transition of the Si{113} and Si{110} surfaces – an in situ, real time observation

Heyraud, J.C.; Métois, J.J.; Bermond, J.M.

doi:10.1016/s0039-6028(99)00183-1

Cited by 31 publications

(26 citation statements)

References 11 publications

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“…Since F͑͒ can be viewed as the radius of curvature of the equilibrium crystal surface, L is therefore the radius of curvature of the facet planes, and R is that of the corners of the equilibrium crystal, all made dimensionless by H. 21 As the sharpness of corners on an equilibrium crystal depends on temperature, [28][29][30] R can be used to study the effect of temperature. This periodic function has spikes centered at = i ͑ i are the orientations of facet planes on the equilibrium crystal͒.…”

Section: A Surface-energy Anisotropymentioning

confidence: 99%

Grain-boundary grooving by surface diffusion with asymmetric and strongly anisotropic surface energies

Min

Wong

2006

Journal of Applied Physics

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Dirichlet extremum problem associated with the asymmetric grain-boundary thermal grooving under the Dirac δtype anisotropic surface stiffness in bicrystal thin solid films Grain-boundary migration controls grain growth, which is important in material processing and synthesis. When a vertical grain boundary ends at a horizontal free surface, a groove forms at the tip to reduce the combined grain-boundary and surface energies. The groove affects the migration of the grain boundary, and its effect must be understood. This work studies grain-boundary grooving by capillarity-driven surface diffusion with asymmetric and strongly anisotropic surface energies. The surface energies are described by the delta-function facet model that holds for temperatures above the roughening temperature of the bicrystal. Since the asymmetric anisotropy does not introduce a length scale, the asymmetric groove still grows with time t as t 1/4 . Thus, the nonlinear partial differential equation that governs grooving is reduced by a self-similar transformation to an ordinary differential equation, which is then solved numerically by shooting methods. We vary systematically the crystallographic orientations of the bicrystal and the normalized grain-boundary energy. We find that the self-similar groove profile is faceted and asymmetric for most bicrystals. However, a few asymmetric bicrystals can also yield smooth and symmetric grooves. Some bicrystals may even form ridges instead of grooves. We also find that the asymmetric surface energies tilt the grain-boundary tip sideways, which induces the grain boundary to migrate. We show that anisotropic groove profiles measured in SrTiO 3 and Ni can be well fitted by our model.

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Section: A Surface-energy Anisotropymentioning

confidence: 99%

Grain-boundary grooving by surface diffusion with asymmetric and strongly anisotropic surface energies

Min

Wong

2006

Journal of Applied Physics

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“…The simultaneous use of these three experimental data leads to the experimental determination of the absolute surface free energy c i . From the experimental point of view one has just to be able to perform true equilibrium experiments that means (at last at high temperature) to be able to compensate the desorbing flux by an impinging one as described by Heyraud et al [28].…”

Section: Experimental Determination Of Surface Energy: the Principlementioning

confidence: 99%

“…The procedure is thus quite general and can be applied each time (i) the 2D and 3D equilibrium shapes (with all orientations present) are available, (ii) the geometrical properties of the 2D and 3D equilibrium shapes as well as the thermal fluctuations of an isolated step can be measured with a sufficient accuracy, (iii) the flat surface is characterised by an isotropic stress so that the 2D equilibrium shape is not modified by surface stress (as clearly shown in [36] for Ge(0 0 1) surface). It is the case of Si(1 1 1) surface above the (7 · 7) $ (1 · 1) transition, for which (1) the recovered threefold symmetry provides an isotropic surface stress and (2) all data are available from previous studies [16,17,28,34].…”

Section: Partial Conclusionmentioning

confidence: 99%

Absolute surface energy determination

Métois¹,

Müller²

2004

Surface Science

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Experimental determination of absolute surface energies remains a challenge. We propose a simple method based on two independent measurements on 3D and 2D equilibrium shapes completed by the analysis of the thermal fluctuation of an isolated step. Using then basic equations (Wulff' theorem, Gibbs-Thomson equation, thermodynamics fluctuation of an isolated step) allows us to extract the absolute surface free energy of a singular face. The so-proposed method can be applied when (i) all orientations exists on the equilibrium shape, (ii) the surface stress is isotropic. This procedure is applied to the case of Si(111) where we find a value between 0.59 Jm-2 and 0.83 Jm-2 at 1373 K.Comment: 13 pages, 7 figure

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“…On Si͑113͒, Si͑110͒, and Si͑001͒ at TϾ1100°C, the 2D-island nucleation can be easily observed. 14,15 These surfaces exhibit a roughening transition at about 1340°C ͑Ref. 14͒, 1370°C ͑Ref.…”

Section: Island Diffusion On Si"111…mentioning

confidence: 99%

Experimental evidence for an Ehrlich-Schwoebel effect on Si(111)

2002

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We have used reflection electron microscopy to study ͑1͒ the drift velocity of positive monolayer islands on Si͑111͒ under near equilibrium conditions and direct current ͑dc͒ heating and ͑2͒ the difference between the velocity of monoatomic steps heated by direct current in the step-up and step-down direction under free sublimation. Our results obtained at around 1200°C show that the islands move in the opposite direction of the dc and the step velocity for ascending steps with respect to the dc direction is smaller than the velocity for opposite steps with the same interstep distance. These two experimental results are a clear qualitative prove of the existence of an Ehrlich-Schwoebel effect on Si͑111͒. We analyze the experimental results for the step dynamics within a modified Burton, Cabrera, and Frank model. We find that a quantitative agreement between the model and the experimental results needs an enhanced effect of the electric field on the diffusion species.

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The roughening transition of the Si{113} and Si{110} surfaces – an in situ, real time observation

Cited by 31 publications

References 11 publications

Grain-boundary grooving by surface diffusion with asymmetric and strongly anisotropic surface energies

Grain-boundary grooving by surface diffusion with asymmetric and strongly anisotropic surface energies

Absolute surface energy determination

Experimental evidence for an Ehrlich-Schwoebel effect on Si(111)

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