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Journal ArticleDOI

Equilibrium shapes of polycrystalline silicon nanodots

19 Feb 2014-Journal of Applied Physics (American Institute of Physics)-Vol. 115, Iss: 7, pp 074304
TL;DR: In this article, a numerical minimization formulation for the surface energy density and transitions of energy density states at grain boundaries of polycrystalline nanodots has been proposed, which allows to account for adhesion energy from an underlying substrate.
Abstract: This study is concerned with the topography of nanostructures consisting of arrays of polycrystalline nanodots. Guided by transmission electron microscopy (TEM) measurements of crystalline Si (c-Si) nanodots that evolved from a “dewetting” process of an amorphous Si (a-Si) layer from a SiO2 coated substrate, we investigate appropriate formulations for the surface energy density and transitions of energy density states at grain boundaries. We introduce a new numerical minimization formulation that allows to account for adhesion energy from an underlying substrate. We demonstrate our approach first for the free standing case, where the solutions can be compared to well-known Wulff constructions, before we treat the general case for interfacial energy settings that support “partial wetting” and grain boundaries for the polycrystalline case. We then use our method to predict the morphologies of silicon nanodots.
Citations
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Journal ArticleDOI
TL;DR: In this paper, theoretical and experimental evidence of an alternative semiconductor material, SiGe alloys, for dielectric Mie resonator applications is provided. But, the practical implementation of technological products is still elusive, one of the important limits is the absence of a highperforming material and a fabrication method that can be easily integrated into modern microelectronic devices at affordable costs.
Abstract: Dielectric Mie resonators have attracted a great deal of attention over the past few years thanks to their remarkable capabilities in manipulating light propagation at the nanoscale. However, the practical implementation of technological products is still elusive. One of the important limits is the absence of a high-performing material and a fabrication method that can be easily integrated into modern microelectronic devices at affordable costs. Here, we provide theoretical and experimental evidence of an alternative semiconductor material, SiGe alloys, for dielectric Mie resonator applications. As a material compatible with the processing requirements of the semiconductor industry, it possesses comparable optical properties to its conventional Si-based counterpart at visible frequencies in spite of its higher optical losses. These dielectric resonant particles can be obtained over very large surfaces on arbitrary silica substrates via spontaneous solid state dewetting of ultrathin (<100 nm) SiGe amorphou...

76 citations

Journal ArticleDOI
TL;DR: In this article, a sharp-interface continuum model based on a thermodynamic variational approach is proposed to investigate the strong anisotropic effect on solid-state dewetting including contact line dynamics.

40 citations

Journal ArticleDOI
TL;DR: The fabrication of Si-based dielectric Mie resonators via a low cost process based on solid-state dewetting of ultra-thin amorphous Si on SiO2 and Morphological and structural characterization reveal the polycrystalline nature of the semiconductor matrix as well as rather irregular morphologies of the dewetted islands.
Abstract: We report the fabrication of Si-based dielectric Mie resonators via a low cost process based on solid-state dewetting of ultra-thin amorphous Si on SiO2. We investigate the dewetting dynamics of a few nanometer sized layers annealed at high temperature to form submicrometric Si-particles. Morphological and structural characterization reveal the polycrystalline nature of the semiconductor matrix as well as rather irregular morphologies of the dewetted islands. Optical dark field imaging and spectroscopy measurements of the single islands reveal pronounced resonant scattering at visible frequencies. The linewidth of the low-order modes can be ∼20 nm in full width at half maximum, leading to a quality factor Q exceeding 25. These values reach the state-of-the-art ones obtained for monocrystalline Mie resonators. The simplicity of the dewetting process and its cost-effectiveness opens the route to exploiting it over large scales for applications in silicon-based photonics.

33 citations

Journal ArticleDOI
01 Nov 2016-Small
TL;DR: This study reports on the deterministic nucleation and precise positioning of Si- and SiGe-based nanocrystals by templated solid-state dewetting of thin silicon films.
Abstract: Thin film dewetting can be efficiently exploited for the implementation of functionalized surfaces over very large scales. Although the formation of sub-micrometer sized crystals via solid-state dewetting represents a viable method for the fabrication of quantum dots and optical meta-surfaces, there are several limitations related to the intrinsic features of dewetting in a crystalline medium. Disordered spatial organization, size, and shape fluctuations are relevant issues not properly addressed so far. This study reports on the deterministic nucleation and precise positioning of Si-and SiGe-based nanocrystals by templated solid-state dewetting of thin silicon films. The dewetting dynamics is guided by pattern size and shape taking full control over number, size, shape, and relative position of the particles (islands dimensions and relative distances are in the hundreds nm range and fluctuate approximate to 11% for the volumes and approximate to 5% for the positioning).

33 citations

Journal ArticleDOI
TL;DR: In this paper, a two-dimensional phase field model for solid state dewetting where the surface energy is weakly anisotropic is proposed, and the corresponding sharp interface limit is derived via matched asymptotic analysis involving multiple inner layers.
Abstract: We propose a two-dimensional phase field model for solid state dewetting where the surface energy is weakly anisotropic. The evolution is described by the Cahn–Hilliard equation with a bi-quadratic degenerate mobility together with a bulk free energy based on a double-well potential and a free boundary condition at the film-substrate contact line. We derive the corresponding sharp interface limit via matched asymptotic analysis involving multiple inner layers. We show that in contrast to the frequently used quadratic degenerate mobility, the resulting sharp interface model for the bi-quatratic mobility is consistent with the pure surface diffusion model. In addition, we show that natural boundary conditions at the substrate obtained from the first variation of the total free energy including contributions at the substrate imply a contact angle condition in the sharp-interface limit which recovers the Young–Herring equation in the anisotropic and Young's equation in the isotropic case, as well as a balance of fluxes at the contact line (or contact point).

30 citations


Cites background from "Equilibrium shapes of polycrystalli..."

  • ...For the equilibrium state the equations governing the shape of a nano- or micro crystal in contact with a substrate has been systematically derived as well as experimentally validated in [31, 59]....

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References
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Journal ArticleDOI
TL;DR: In this paper, the authors present an attempt towards a unified picture with special emphasis on certain features of "dry spreading": (a) the final state of a spreading droplet need not be a monomolecular film; (b) the spreading drop is surrounded by a precursor film, where most of the available free energy is spent; and (c) polymer melts may slip on the solid and belong to a separate dynamical class, conceptually related to the spreading of superfluids.
Abstract: The wetting of solids by liquids is connected to physical chemistry (wettability), to statistical physics (pinning of the contact line, wetting transitions, etc.), to long-range forces (van der Waals, double layers), and to fluid dynamics. The present review represents an attempt towards a unified picture with special emphasis on certain features of "dry spreading": (a) the final state of a spreading droplet need not be a monomolecular film; (b) the spreading drop is surrounded by a precursor film, where most of the available free energy is spent; and (c) polymer melts may slip on the solid and belong to a separate dynamical class, conceptually related to the spreading of superfluids.

6,042 citations

Journal ArticleDOI
TL;DR: The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints that is represented as a simplicial complex.
Abstract: The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints. The surface is represented as a simplicial complex. The energy can include surface tension, gravity and other forms. Constraints can be geometrical constraints on vertex positions or constraints on integrated quantities such as body volumes. The minimization is done by evolving the surface down the energy gradient. This paper describes the mathematical model used and the operations available to interactively modify the surface.

2,241 citations


"Equilibrium shapes of polycrystalli..." refers methods in this paper

  • ...We also note that, based on minimization methods for anisotropic crystals in an unbounded domain, as well as attached to an isotropic surface have been discussed in (17) and (18), using software based on (19)....

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Journal ArticleDOI
TL;DR: In der krystallographischen Literatur der letzten Zeit erscheinen mehr und mehr Arbeiten, welche dem gegenseitigen Verhältnisse des Krystalles and des Mediums, in welchem er sich bildet, gewidmet sind.
Abstract: In der krystallographischen Literatur der letzten Zeit erscheinen mehr und mehr Arbeiten, welche dem gegenseitigen Verhältnisse des Krystalles und des Mediums, in welchem er sich bildet, gewidmet sind. Besonders erfolgreich sind in dieser Hinsicht die Arbeiten von B e c k e gewesen. Seine Abhandlung über die Aetzflguren und die Auflösung des Fluorits veranlasste mich, die vorliegende Untersuchung zu beginnen. Das Verhältniss des Krystalles zu seiner Mutterlauge ist dreierlei Art. Der Krystall kann in ihr wachsen oder sich auflösen oder unverändert bleiben, je nach dem Grade der Sättigung der Lösung. Die Fähigkeit des Wachsens unterscheidet wesentlich die Krystalle von den amorphen Körpern. Dabei versteht man unter dem Wachsthume eine solche Vergrösserung des Volums, welche weder von einer Veränderung

1,803 citations


"Equilibrium shapes of polycrystalli..." refers methods in this paper

  • ...We begin with the discussion on results obtained with a well-established geometrical procedure, the Wulff construction (9)....

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  • ...Free surface energy minimizers are typically obtained by application of the geometrical Wulff construction (9; 10), the geometrical plot of the Cahn-Hoffmann vector, see for example (11), or numerically in terms of gradient flows that evolve with time to the equilibrium setting, for example using a level-set method (12)....

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Journal ArticleDOI
Conyers Herring1
TL;DR: In this article, the Wulff construction for the equilibrium shape of a small particle and the relations between atomic models of crystal surfaces and the surface free energy function used in this construction are discussed.
Abstract: Although the interpretation of experiments in such fields as the shapes of small particles and the thermal etching of surfaces usually involves problems of kinetics rather than mere equilibrium considerations, it is suggested that a knowledge of the relative free energies of different shapes or surface configurations may provide a useful perspective. This paper presents some theorems on these relative free energies which follow from the Wulff construction for the equilibrium shape of a small particle, and some relations between atomic models of crystal surfaces and the surface free energy function used in this construction. Equilibrium shapes of crystals and of noncrystalline anisotropic media are classified, and it is pointed out that the possibilities for crystals include smoothly rounded as well as sharp-cornered forms. The condition is formulated for thermodynamic stability of a flat crystal face with respect to formation of a hill-and-valley structure. A discussion is presented of the limitations on the applicability of the results imposed by the dependence of surface free energy on curvature; and it is concluded that these limitations are not likely to be serious for most real substances, though they are serious for certain idealized theoretical models.

1,208 citations


"Equilibrium shapes of polycrystalli..." refers background or methods in this paper

  • ...Free surface energy minimizers are typically obtained by application of the geometrical Wulff construction (9; 10), the geometrical plot of the Cahn-Hoffmann vector, see for example (11), or numerically in terms of gradient flows that evolve with time to the equilibrium setting, for example using a level-set method (12)....

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  • ...Wulff’s construction relies on a surface energy density that is continuous (10)....

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Journal ArticleDOI
TL;DR: The large exciton binding energy in Si and Ge quantum dots suggests that the photoluminescence from these nanostructures is of excitonic origin even at room temperature.
Abstract: The quantum confinement effect on excitons in quantum dots of indirect-gap materials is investigated and a mechanism that induces an indirect-to-direct conversion of the character of the optical transition is clarified. The exciton transition energy and the exciton binding energy are calculated and found to be in good agreement with experimental results on Si and Ge nanostructures. The large exciton binding energy in Si and Ge quantum dots suggests that the photoluminescence from these nanostructures is of excitonic origin even at room temperature. The estimated radiative lifetime of excitons is strongly size dependent and varies from nanosecond to millisecond corresponding to the diameter from \ensuremath{\sim}10 to \ensuremath{\sim}30 \AA{}. These theoretical results suggest strongly the importance of the quantum confinement effect in the luminescence processes of porous Si.

956 citations


"Equilibrium shapes of polycrystalli..." refers background in this paper

  • ...Such systems are of interest for investigating quantum confinement effects in general and in particular by exploiting size dependent band gap engineering for silicon material (6)....

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