Theory of equilibrium shape of an anisotropically strained island: Thermodynamic limits for growth of nanowires

Pradhan, Amit Kumar; Ma, Naiyang; Liu, Feng

doi:10.1103/physrevb.70.193405

Cited by 31 publications

(24 citation statements)

References 15 publications

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“…For the rare-earth elements, this produces a close lattice match along the silicide's [1120] direction (< 2%), whereas the typical lattice mismatch along the orthogonal [0001] direction is ~ 4-9%. This anisotropic strain is likely responsible for the strongly anisotropic silicide growth, producing long nanowires that extend along the Si< 110 > directions (14). The present case of yttrium is unique, however, in that the misfit along the wire direction vanishes almost completely (< 0.07% at 300 K).…”

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confidence: 73%

Charge-order fluctuations in one-dimensional silicides

et al. 2008

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Metallic nanowires are of great interest as interconnects in future nanoelectronic circuits. They also represent important systems for understanding the complexity of electronic interactions and conductivity in one-dimension. We have fabricated exceptionally long and uniform YSi 2 nanowires via self-assembly of yttrium atoms on Si(001). The thinnest wires represent one of the closest realizations of the isolated Peierls chain, exhibiting van-Hove type singularities in the onedimensional density of states and charge order fluctuations below 150 K. The structure of the wire was determined though a detailed comparison of scanning tunneling microscopy data and firstprinciples calculations. Sporadic broadenings of the wires' cross section imply the existence of a novel metal-semiconductor junction whose electronic properties are governed by the finite-sizeand temperature-scaling of the charge ordering correlation.One-dimensional (1D) conductors have always captured the imagination of physicists. While a strictly 1D material remains a theoretical construct, a vast number of materials can be viewed as quasi 1D, making them interesting test cases for theoretical predictions and nanoscale applications. Classic examples include charge transfer complexes such as TTF-TCNQ and the Bechgaard salts, which have been studied extensively because of their unusual electrical properties and potential applications as organic conductors (1). These compounds can be viewed as macroscopic ensembles of weakly-coupled quantum chains. They are also textbook illustrations of the venerable Peierls theorem, which states that a 1D metallic chain should be unstable with respect to a symmetry-lowering modulation of the atomic coordinates and valence-charge density (2). The mechanism driving this instability entails the strong coupling between the vibrational modes of the lattice and electrons near the Fermi level. The ground state of a Peierls chain is insulating but the band gap decreases with increasing temperature and metallicity is ultimately restored via a second order phase transition.This simple picture contains some interesting caveats. First of all, the Peierls theory ignores thermodynamic fluctuations. In the 1D limit, thermal fluctuations always destroy long-range order so in principle there is no phase transition (3). Paradoxically, 2D or 3D interchain coupling appears essential for observing the Peierls phase transition in real systems (3). Secondly, the Peierls theory completely ignores electron-electron correlations. Depending on the various interaction parameters, the Peierls transition may be preempted by a competing 'many-body' ground state such as a spin density wave state or Luttinger liquid (1-3). To date, the closest experimental realization of a 1D model system is, arguably, the single-wall carbon nanotube (4-7). Yet, there is no experimental evidence of a Peierls distortion in nanotubes, possibly because the tube diameters are not small enough for observing the transition (5-7). Some experiments even suggest the ex...

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confidence: 73%

Charge-order fluctuations in one-dimensional silicides

et al. 2008

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“…In addition, other authors report wires in anisotropically strained systems [12,21,22]. In order to account for the shape evolution in such systems, Pradhan et al [14] developed a general approach to island shape evolution dealing with both isotropically and anisotropically strained islands. Their model predicts that there is no shape instability as the nucleated islands are anisotropic in morphology.…”

Section: Introductionmentioning

confidence: 98%

“…In order to control nanostrutures shape and spatial distribution (i.e. for self-organization), it is necessary to develop a detailed understanding of the mechanism for heteroepitaxial nanostructures growth [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Endoepitaxial growth of hexagonal-Fe13Ge8 islands on Cubic-Ge(001)

Tok

Foo

2012

Journal of Physics and Chemistry of Solids

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“…[5][6][7][8][9] For example, the understanding of ͑1D͒ onedimensional wire formation during epitaxial growth has attracted intense interests in recent years. Most theoretical/ experimental reports only focus on the equilibrium growth at high temperature, [10][11][12] which differs from conditions used in industry where deposition temperatures are typically lower, thus leaning more toward the kinetically constrained growth regime. 13 Therefore, factors and conditions that could affect or control island formation during growth, especially in the regime far from equilibrium, are still not well understood.…”

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confidence: 97%

Kinetically constraint zero- and one-dimensional heteroepitaxial island growth

Singh

Tok

et al. 2007

Applied Physics Letters

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Direct observation of the dynamics, formation, and selective growth of low dimensional epitaxial Fe13Ge8 structures [zero-dimensional (0D) compact islands or one-dimensional (1D) wires of different aspect ratios] was conducted in real time using in situ ultra high vacuum transmission electron microscopy at 350, 430, 480, and 510°C. Both types of island (0D/1D) share the same epitaxial relation to the underlying Ge substrate. The compact islands are formed preferentially at lower deposition temperature while wires, which are kinetically constrained, at higher temperature. The effective Ea for growth along two orthogonal azimuths of an Fe13Ge8 island are 0.17 and 0.95eV. The temperature dependence in morphological evolution is due to anisotropy in corner barriers and ledge diffusion on orthogonal azimuths during growth.

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Theory of equilibrium shape of an anisotropically strained island: Thermodynamic limits for growth of nanowires

Cited by 31 publications

References 15 publications

Charge-order fluctuations in one-dimensional silicides

Charge-order fluctuations in one-dimensional silicides

Endoepitaxial growth of hexagonal-Fe13Ge8 islands on Cubic-Ge(001)

Kinetically constraint zero- and one-dimensional heteroepitaxial island growth

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