The equilibrium shape of silicon

Bermond, J.M.; Métois, J.J.; Egéa, X.; Floret, F.

doi:10.1016/0039-6028(95)00230-8

Cited by 125 publications

(67 citation statements)

References 38 publications

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“…In figure 7 is reported the surface free energy anisotropy obtained by Wulf inversion of the experimental equilibrium shape (T = 1373 K) [14,42]. This method does not allow obtaining the absolute values of the free surface energies but only the relative ones.…”

Section: Surface Stress Versus Surface Energymentioning

confidence: 99%

Simple views on surface stress and surface energy concepts

Müller

Saúl

Leroy

2013

Adv. Nat. Sci: Nanosci. Nanotechnol.

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Some aspects of the thermodynamics and mechanics of solid surfaces, in particular with respect to surface stress and surface energy, are reviewed. The purpose is to enlighten the deep differences between these two physical quantities. We consider successively the case of atomic flat surfaces and the case of vicinal surfaces characterized by surface stress discontinuities. Finally, experimental examples, concerning Si surfaces, are described.

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Section: Surface Stress Versus Surface Energymentioning

confidence: 99%

Simple views on surface stress and surface energy concepts

Müller

Saúl

Leroy

2013

Adv. Nat. Sci: Nanosci. Nanotechnol.

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“…This is, however, not so. The traditional way to determine the step energy from the equilibrium shape of crystals is barred with many nontrivial experimental difficulties and additionally requires as an input the free energy of the flat surfaces [17,18], which in turn is not known very accurately. The step-free energy derived from the chemical potential of islands as observed in Ostwald ripening of islands appears to be unrealistically high for reasons hitherto not understood [12].…”

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confidence: 99%

Novel Method for the Experimental Determination of Step Energies

1999

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We describe a novel method for the determination of the absolute step energies using the temperature dependence of the equilibrium shape of adatom or vacancy islands. The method is demonstrated with islands on the Cu(111) surface. PACS numbers: 68.35.Md, 05.50. + q, 68.10.Cr, 68.35.Bs The free energy of steps of monatomic height is one of the most important energetic parameters in the physics of crystalline solids. It controls the size of facets in the equilibrium shape of crystals and the curvature of rough surfaces [1]. It is likewise an important parameter in the stability of vicinal surfaces against step bunching transitions [2,3] and transitions involving a reconstruction of the surface [4,5]. Furthermore, the minimization of the step energy is the driving force for coarsening processes on surfaces, e.g., for the growth of larger islands at the expense of smaller ones, the decay of mounds during and after epitaxial growth [6][7][8][9][10][11][12][13], and for the decay of nanostructures in general. Last but not least, the equilibrium shape and the shape fluctuations of monatomic high islands (2D islands) on surfaces, and thereby also the migration of entire islands on surfaces, depend on the step-free energy [14][15][16]. The ubiquity of the step-free energy as the controlling parameter in many phenomena should provide ample means to determine its magnitude. This is, however, not so. The traditional way to determine the step energy from the equilibrium shape of crystals is barred with many nontrivial experimental difficulties and additionally requires as an input the free energy of the flat surfaces [17,18], which in turn is not known very accurately. The step-free energy derived from the chemical potential of islands as observed in Ostwald ripening of islands appears to be unrealistically high for reasons hitherto not understood [12]. An average step energy was recently calculated from the size dependence of the Brownian motion of islands using a continuum model [15] for the step fluctuations [19]. Possible systematic errors of the method are not known presently. Relying entirely on first principles theoretical calculation is likewise not a remedy to the situation as it seems that different respectable approaches [20,21] yield rather different results [0.38 and 0.26 eV͞atom for B steps on Cu(111), respectively]. While the determination of the absolute value of the step-free energy is a problem, the variation of the step energy as a function of the orientation can be measured straightforwardly from the equilibrium shape of 2D islands. Michely et al., e.g., have determined the ratio of the energies of A and B steps on Pt(111) from island equilibrium shapes [22]. Since 2D islands have no facets at finite temperature the complete orientational dependence of the step-free energy is obtained from the equilibrium shape using an "inverse" Wulff plot [1].In this Letter we describe a novel method to determine the absolute value of step energies from experimental data on the equilibrium shape of 2D islands as a fu...

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“…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%

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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The equilibrium shape of silicon

Cited by 125 publications

References 38 publications

Simple views on surface stress and surface energy concepts

Simple views on surface stress and surface energy concepts

Novel Method for the Experimental Determination of Step Energies

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

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