Square and Triangular Nanohole Array Architectures in Anodic Alumina

Masuda, Hideki; Asoh, Hidetaka; Watanabe, Mitsuo; Nishio, Kazuyuki; Nakao, Masashi; Tamamura, Toshiaki

doi:10.1002/1521-4095(200102)13:3<189::aid-adma189>3.0.co;2-z

Cited by 309 publications

(196 citation statements)

References 11 publications

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“…The Schläfli symbols that describe the polygon type and the degeneracy type that meets at an equivalent vertex labels them appropriately. If we further require that the tilings be constructed with regular polygons that are monohedral, i.e., the same size and shape, we have the three regular tilings, 3 6 , 4 4 , and 6 3 .…”

Section: Introductionmentioning

confidence: 80%

“…The (Shannon) entropy [13] of the graphs can then be defined as follows: (5) or if it is rewritten: (6) where β = 1 / (k B T), and k B is the Boltzman constant. We plot the entropy / link vs. the number of links in Fig.…”

Section: Statistical Mechanicsmentioning

confidence: 99%

“…The regular tilings may have applications in the real world, as the coordinates define the locations of pore sites in nanoporous arrays [6]. All three of the regular tilings have been fabricated by nanolithography into (non-ideal) porous arrays for the definition of nanosized material (dots or wires).…”

Section: Introductionmentioning

confidence: 99%

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Statistical mechanics of two dimensional tilings

Kaatz

Estrada²,

Bultheel

et al. 2012

Physica A: Statistical Mechanics and its Applications

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Reduced dimensionality in two dimensions is a topic of current interest. We use model systems to investigate the statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in nanoporous arrays (quantum dots), in the 2D hexagonal structure of graphene, and as adsorbates on quasicrystalline crystal surfaces. We calculate the statistical mechanics of these networks, such as the partition function, free energy, entropy, and enthalpy. The plots of these functions versus the number of links in the finite networks result in power law regression. We also determine the degree distribution, which is a combination of power law and rational function behavior. In the large--scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In comparison, a Penrose tiling has a degree also equal to about 4.

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Section: Introductionmentioning

confidence: 80%

Section: Statistical Mechanicsmentioning

confidence: 99%

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Statistical mechanics of two dimensional tilings

Kaatz

Estrada²,

Bultheel

et al. 2012

Physica A: Statistical Mechanics and its Applications

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“…This means that the pore shape after anodization is independent of pre-pattern shape on the surface. Note that the pore shape can be control by the pre-patterning lattice such as rectangular and honeycomb [12]. …”

Section: Anodization Of Pre-patterned Aluminummentioning

confidence: 99%

Large-area porous alumina photonic crystals via imprint method

et al. 2002

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A perfect 2D porous alumina photonic crystal with 500 nm interpore distance was fabricated on an area of 4 cm 2 via imprint methods and subsequent electrochemical anodization. A 4'' imprint stamp consisting of a convex pyramid array was obtained by modern VLSI processing using DUV-lithography, anisotropic etching, LPCVD Si 3 N 4 deposition and wafer bonding. The optical properties of the porous alumina photonic crystal were measured with an infrared microscope in Γ-M direction. For both polarizations, a bandgap is observed at around 1 µm for r/a = 0.42. A reflectivity of almost unity for E-polarization in the region of the bandgap is a sign of the high quality of the structure, indicating almost no scattering losses. These experimental results could be correlated very well to the bandstructure as well as reflectivity calculations assuming a dielectric constant of ε = 2.0 for the anodized alumina.

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“…[1][2][3][4][5] Intensive efforts were put especially to the generation of nanoscopic templates with cost-efficiency, easy production and high productivity. [6][7][8][9][10][11][12][13][14] In this regard, selfassembly with colloidal nanoparticles, block copolymer (BCP) and anodized aluminum oxide (AAO) have been favored as well as conventional lithographic methods.…”

Section: Introductionmentioning

confidence: 99%

Alumina Templates on Silicon Wafers with Hexagonally or Tetragonally Ordered Nanopore Arrays via Soft Lithography

Park¹,

Yu²,

Shin

2012

Bulletin of the Korean Chemical Society

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Due to the potential importance and usefulness, usage of highly ordered nanoporous anodized aluminum oxide can be broadened in industry, when highly ordered anodized aluminum oxide can be placed on a substrate with controlled thickness. Here we report a facile route to highly ordered nanoporous alumina with the thickness of hundreds-of-nanometer on a silicon wafer substrate. Hexagonally or tetragonally ordered nanoporous alumina could be prepared by way of thermal imprinting, dry etching, and anodization. Adoption of reusable polymer soft molds enabled the control of the thickness of the highly ordered porous alumina. It also increased reproducibility of imprinting process and reduced the expense for mold production and pattern generation. As nanoporous alumina templates are mechanically and thermally stable, we expect that the simple and costeffective fabrication through our method would be highly applicable in electronics industry.

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Square and Triangular Nanohole Array Architectures in Anodic Alumina

Cited by 309 publications

References 11 publications

Statistical mechanics of two dimensional tilings

Statistical mechanics of two dimensional tilings

Large-area porous alumina photonic crystals via imprint method

Alumina Templates on Silicon Wafers with Hexagonally or Tetragonally Ordered Nanopore Arrays via Soft Lithography

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