Shape universality of equilibrated silicon crystals

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

doi:10.1016/s0039-6028(98)00599-8

Cited by 36 publications

(17 citation statements)

References 37 publications

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“…16 However, there is still clearly a significant disagreement between the magnitudes of our results and those reported earlier. 19,24 Our result is about 40% higher.…”

Section: A Step Line Tensioncontrasting

confidence: 49%

“…17 Stiffness values of 69 and 38 meV/ Å were determined from the fluctuation behavior of two different steps at 1173 K. 17 These values were later revised upward by a factor of 2, 18 and finally a single lower value of 46 meV/ Å was settled on after further corrections were made to the analysis. 19 This is a little larger than the stiffness of 30 meV/ Å that was determined earlier at 1173 K from an evaluation of the time correlation functions for the different Fourier modes of equilibrium step fluctuations. 20 The stiffness was determined from the mean-square fluctuation displacement at 1323 K to be 3.2 meV/ Å.…”

Section: Introductionmentioning

confidence: 73%

“…Steps on the Si͑111͒ ͑1 ϫ 1͒ surface, which are the subject of the investigations described here, have been studied widely 3,8,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] due to their intriguing phenomenology. The Si͑111͒ surface undergoes a structural phase transition between ͑7 ϫ 7͒ and ͑1 ϫ 1͒ configurations at a transition temperature of T c = 1133 K. The step line tension is expected to be nearly isotropic on the Si͑111͒ ͑1 ϫ 1͒ surface above T c .…”

Section: Introductionmentioning

confidence: 99%

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Step line tension and step morphological evolution on the Si(111)(1×1)surface

et al. 2008

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The temperature dependence of the step line tension on the Si͑111͒ ͑1 ϫ 1͒ surface is determined from a capillary wave analysis of two-dimensional island edge fluctuations and straight step fluctuations that are observed with low energy electron microscopy. The line tension decreases by nearly 20% with a linear temperature coefficient of −0.14 meV/ Å K between 1145 and 1233 K. Temporal correlations of step fluctuations exhibit the distinctive signature in the wavelength dependence of the relaxation time of a terrace diffusion-limited mechanism for step motion. We also find that the role of desorption in island decay increases dramatically in the temperature range ͑1145-1380 K͒ that island decay is studied. Consequently, we generalize the current quasistatic model of island decay to take account of desorption. The evaluation of the island decay time with this model referenced to the temperature-dependent line tension accurately determines activation energies that are relevant to mass transport and sublimation.

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“…16 However, there is still clearly a significant disagreement between the magnitudes of our results and those reported earlier. 19,24 Our result is about 40% higher.…”

Section: A Step Line Tensioncontrasting

confidence: 49%

Section: Introductionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Step line tension and step morphological evolution on the Si(111)(1×1)surface

et al. 2008

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“…The formation of facets below the roughening temperature, and the Pakrovsky-Talapov predictions [26] for the edge shape (z(x)) of crystals have been demonstrated in a number of clean systems [27][28][29][30][31][32][33][34]. In addition to studies on 3D crystals, there has been substantial work on the 2D ECS of islands [15,[35][36][37][38][39]] to obtain the edge free energy, equilibrium edge fluctuations and decay kinetics.…”

Section: Introductionmentioning

confidence: 99%

Nano-scale equilibrium crystal shapes

Degawa¹,

Szalma²,

Williams³

2005

Surface Science

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The finite size and interface effects on equilibrium crystal shape (ECS) have been investigated for the case of a surface free energy density including step stiffness and inverse-square step-step interactions. Explicitly including the curvature of a crystallite leads to an extra boundary condition in the solution of the crystal shape, yielding a family of crystal shapes, governed by a shape parameter c. The total crystallite free energy, including interface energy, is minimized for c=0, yielding in all cases the traditional PT shape (z~x 3/2 ). Solutions of the crystal shape for c≠0 are presented and discussed in the context of meta-stable states due to the energy barrier for nucleation. Explicit scaled relationships for the ECS and meta-stable states in terms of the measurable step parameters and the interfacial energy are presented.

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“…In three-dimensional crystals, this construction leads to faceted shapes, with the size and the number of facets decreasing when the temperature increases. Such shapes were observed by scanning electron microscopy in micron-sized crystals of ordinary metals such as lead [3], silicon [4], or silver [5]. Large He 4 crystals (i.e., of centimetric size) are also faceted, with the advantage of equilibrating much faster than the former due to their quantum nature (atoms can go through energy barriers by tunneling effect) [6].…”

Section: Introductionmentioning

confidence: 99%

Faceting and stability of smectic A droplets on a solid substrate

Oswald

Lejček

2006

Eur. Phys. J. E

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Abstract. It is shown that a smectic A droplet deposited on a solid substrate treated for strong homeotropic anchoring is faceted at the top in spite of the fact that there are no steps at the free surface, but instead edge dislocations in the bulk. The radius of the facet and the full profile of the curved part of the droplet are determined as a function of the temperature in the vicinity of a nematic-smectic A phase transition. It is shown that the observed profiles do not correspond to the actual equilibrium shape, but to metastable configurations close to their point of marginal stability. In addition, we predict that the profiles must be different for a given temperature depending on whether the droplet has been heated or cooled down to reach this temperature. Finally, we discuss the problem of the formation of giant dislocations in big droplets (Grandjean terraces).

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Shape universality of equilibrated silicon crystals

Cited by 36 publications

References 37 publications

Step line tension and step morphological evolution on the Si(111)(1×1)surface

Step line tension and step morphological evolution on the Si(111)(1×1)surface

Nano-scale equilibrium crystal shapes

Faceting and stability of smectic A droplets on a solid substrate

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