Determination of Ge(001) step free energies

Zandvliet, Henricus J.W.

doi:10.1103/physrevb.61.9972

Cited by 36 publications

(48 citation statements)

References 22 publications

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“…The roughening transition occurs when the step free energy goes to zero so that steps spontaneously form. 39,40 It is impossible that the mean energy u of a step becomes negative before the step free energy. Thus, if the antifaceting model (III) applies at all, there must also be some conditions under which the ATG model (II) applies.…”

Section: Theoretical Evidencementioning

confidence: 99%

Surface energy effects on the self-assembly of epitaxial quantum dots

Friedman

2009

SPIE Proceedings

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Epitaxial self-assembled quantum dots (SAQDs) result from Stranski-Krastanow growth whereby epitaxial 3D islands form spontaneously on a planar thin film. Common systems are Ge x Si 1−x /Si and In x Ga 1−x As/GaAs. SAQDs are typically grown on a (001) surface. The formation and evolution of SAQDs is governed in large part by the interaction of surface energy and elastic strain; however, the surface energy density is quite complicated and not well understood. Many growth processes take place at high temperature where stress and entropy effects can have a profound effect on the surface free energy. There are three competing theories of the nature of the planar (001) surface: I. It is a stable crystal facet. II. It is a stable non-faceted surface. III. It is an unstable crystal antifacet. Each leads to a different theory of the SAQD formation process. The first theory appears most often in modeling literature, but the second two theories take explicit account of the discrete nature of a crystal surface. Existing observational and theoretical evidence in support of and against these theories is reviewed. Then a simple statistical mechanics model is presented that yields a phase-diagram depicting when each of the three theories is valid. Finally, the Solid-on-Solid model of crystal surfaces is used to validate the proposed phase diagram and to calculate the orientation and height dependence of the surface free energy that is expressed as a wetting chemical potential, a wetting modulus and surface tilt moduli.

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Section: Theoretical Evidencementioning

confidence: 99%

Surface energy effects on the self-assembly of epitaxial quantum dots

Friedman

2009

SPIE Proceedings

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“…Because the roughness of the steps is frozen in at an elevated temperature and T F ϭ575Ϯ75 K. 16 In order to find the step free energy of a 100% kinked step oriented along the ͗010͘ direction we consider the case of an isotropic NN interaction (ϭ ʈ /2ϩ Ќ /2) and an attractive NNN interaction (␦у0). We only take into account the two energetically most favorable pathways, because all the other pathways involve significantly more step edge length and are therefore much higher in energy ͑see Fig.…”

Section: Step Free Energiesmentioning

confidence: 99%

Faceting of 〈010〉 steps on Si(001) and Ge(001) surfaces

et al. 2004

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We have used scanning tunneling microscopy to study the faceting of ͗010͘ oriented steps on Si͑001͒ and Ge͑001͒ surfaces. The ͗010͘ oriented steps on Si͑001͒ tend to facet into local S A and S B step segments, whereas ͗010͘ oriented steps on Ge͑001͒ meander along the mean ͗010͘ direction. We show that the step faceting behavior of the Si and Ge͑001͒ surfaces is fully governed by the next-nearest-neighbor ͑NNN͒ interaction between the substrate dimers. Only in the case of a repulsive NNN interaction, as for Si͑001͒, faceting occurs.

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“…Thus, if one can measure the equilibrium shape of an (vacancy) island and if one knows the values of the step-free energies, one can, in principle, determine the strain energy (and hence the surface stress anisotropy). By analyzing the kink distributions we have recently extracted the step-free energies of both types of monatomic steps on Ge(001) [27]. Using these values and the equilibrium shape of a vacancy island we have for the first time determined the surface stress anisotropy of the dimer-reconstructed Ge(001) surface.…”

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“…where g A 17 meV͞a (a is the surface lattice constant, i.e., 4 Å) and g B 43 meV͞a are the step edge formation energies, and´A 43 meV͞a and´B 17 meV͞a [27] are the kink creation energies (here we have used a step edge edge freeze in temperature of 500 K rather than the 575 K used in Ref. [27]).…”

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Surface Stress Anisotropy of Ge(001)

2002

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By analyzing the equilibrium shape of vacancy islands on the Ge(001) surface we have determined the surface stress anisotropy, i.e., the difference between the compressive stress component along the substrate dimer rows and the tensile stress component perpendicular to the substrate dimer rows. In order to extract the surface stress anisotropy we have used a model recently put forward by Li et al. [Phys. Rev. Lett. 85, 1922]. The surface stress anisotropy of the clean Ge(001) surface is found to be 80 6 30 meV͞Å 2 . This value is comparable to the surface stress anisotropy of the closely related Si(001) surface. DOI: 10.1103/PhysRevLett.88.196105 PACS numbers: 68.35.Md, 68.37.Ef Among the most intriguing and frequently studied surfaces belong to the semiconductor group-IV (001) surfaces [1,2]. Because of its technological importance, the majority of studies have been devoted to the Si(001) surface rather than to the closely related Ge(001) surface. In many aspects the Ge(001) surface is very similar to the Si(001) surface. Both surfaces reconstruct to form rows of dimerized atoms, yielding a ͑2 3 1͒ surface unit mesh. The surface dimers can buckle with respect to the surface plane leading to higher-order reconstructions, such as c͑4 3 2͒ and p͑2 3 2͒. The dimerization of these surfaces in the ͑2 3 1͒, p͑2 3 2͒, or c͑4 3 2͒ reconstruction induces an anisotropic surface stress tensor: the surface is under a compressive stress along the substrate dimer row direction and under a tensile stress in a direction perpendicular to the substrate dimer rows. If the surface exhibits a slight miscut with respect to the [001] direction, single layer steps are found. The monatomic steps separate terraces with alternating ͑2 3 1͒ and ͑1 3 2͒ reconstruction. After cleaning, Ge(001) exhibits a well-ordered domain pattern consisting of ͑2 3 1͒ and c͑4 3 2͒ stripes and almost no missing dimer defects [3].The missing dimer concentration on Si(001) can be increased by ion bombardment with noble gases [4][5][6][7][8], etching [9 -13] (O 2 , H 2 , Br 2 , I 2 , etc.), or metal contamination [14-18] (Ni, Cu, Co, Ag, etc.). For sufficiently high temperatures those missing dimers order into vacancy islands. The equilibrium shape at low vacancy concentrations (,0.2 0.3 monolayers) [19] of these vacancy islands is elongated in a direction perpendicular to the substrate dimer rows. At vacancy concentrations above 0.2 0.3 monolayers the vacancy islands rotate shape and are aligned parallel to the substrate dimer rows [8]. The absence of dimerization at the bottom of the narrow vacancy islands in combination with the specific rebonding at the island edges is believed to be responsible for this shape transformation [19][20][21][22][23][24]. Ab initio calculations [20] and tight-binding total-energy calculations [21] are in perfect agreement with the experimental observations of the shape transformation. Such a shape transformation has not been observed for the Ge(001) surface. Experiments performed on Ge(001) so far have revealed that the bo...

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Determination of Ge(001) step free energies

Cited by 36 publications

References 22 publications

Surface energy effects on the self-assembly of epitaxial quantum dots

Surface energy effects on the self-assembly of epitaxial quantum dots

Faceting of 〈010〉 steps on Si(001) and Ge(001) surfaces

Surface Stress Anisotropy of Ge(001)

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