Precise determination of the conductivity exponent of 3D percolation using exact numerical renormalization

Clerc, Jean-Pierre; Podolskiy, Viktor A.; Sarychev, Andrey K.

doi:10.1007/s100510051153

Cited by 56 publications

(36 citation statements)

References 5 publications

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“…Both processes may contribute; then the process is called tunneling-percolation. According to many proposed theories of transport in isotropic percolating materials [36][37][38][39][40] the dc bulk conductivity of a metal/insulator composite, near the critical conductor/ insulator transition, is given by the power law, Ϸ 0 ͑x − x c ͒ t , where 0 is a proportionality constant, x the normalized metal atom concentration of the conducting phase, x c the critical concentration or percolation threshold, below which the composite has zero conductivity, and t is the "critical exponent." There are three conduction regimes: ͑1͒ metallic or conductor ͑x Ͼ x c ͒, ͑2͒ transition ͑x Ϸ x c ͒, and ͑3͒ insulator or dielectric ͑x Ͻ x c ͒.…”

Section: Resultsmentioning

confidence: 99%

Gold-implanted shallow conducting layers in polymethylmethacrylate

Teixeira

Salvadori

Cattani

et al. 2009

Journal of Applied Physics

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Characterization of bias stress induced electrical instability in liquid-crystalline semiconducting polymer thin-film transistors J. Appl. Phys. 110, 084511 (2011) Influence of crystallization-induced amorphous phase confinement on -and -relaxation molecular mobility in parylene F J. Appl. Phys. 110, 063703 (2011) Variability of physical characteristics of electro-sprayed poly(3-hexylthiophene) thin films J. Appl. Phys. 110, 054515 (2011) Metallic-like conduction in Co-phthalocyanine/Fe-phthalocyanine composite films grown on sapphire substrates Appl. Phys. Lett. 99, 112102 (2011) Theoretical study of substitution effects on molecular reorganization energy in organic semiconductors J. Chem. Phys. 135, 104703 (2011) Additional information on J. Appl. Phys. PMMA ͑polymethylmethacrylate͒ was ion implanted with gold at very low energy and over a range of different doses using a filtered cathodic arc metal plasma system. A nanometer scale conducting layer was formed, fully buried below the polymer surface at low implantation dose, and evolving to include a gold surface layer as the dose was increased. Depth profiles of the implanted material were calculated using the Dynamic TRIM computer simulation program. The electrical conductivity of the gold-implanted PMMA was measured in situ as a function of dose. Samples formed at a number of different doses were subsequently characterized by Rutherford backscattering spectrometry, and test patterns were formed on the polymer by electron beam lithography. Lithographic patterns were imaged by atomic force microscopy and demonstrated that the contrast properties of the lithography were well maintained in the surface-modified PMMA.

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Section: Resultsmentioning

confidence: 99%

Gold-implanted shallow conducting layers in polymethylmethacrylate

Teixeira

Salvadori

Cattani

et al. 2009

Journal of Applied Physics

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“…The conductivity mechanism in this regime can be described in the frame of percolation theory. 25,26 Briefly, electron transport through granular materials consisting of small conducting regions embedded in an insulating medium can occur through either of two possible processes or their combination. When the conducting elements are in geometric contact, the process is called percolation; 27 percolation refers to the flow of current through random resistor networks.…”

Section: Introductionmentioning

confidence: 99%

“…For our system of PMMA implanted with low energy gold ions, the conductivity process is due only to percolation and the contribution from tunneling conduction is negligible. 26,27 In the metallic regime, the gold clusters contact each other and the composite behaves like a dirty metal; the resistivity is relatively low. It was shown 24 that for our system the critical dose c for percolation is c = 1.0ϫ 10 16 cm −2 and the maximum dose ͑saturation dose͒ is about 2.5ϫ 10 16 cm −2 when a coalesced gold film begins to evolve.…”

Section: Introductionmentioning

confidence: 99%

Surface plasmon resonance of gold nanoparticles formed by cathodic arc plasma ion implantation into polymer

Teixeira¹,

Salvadori²,

Cattani³

et al. 2009

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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Shallow subsurface layers of gold nanoclusters were formed in polymethylmethacrylate ͑PMMA͒ polymer by very low energy ͑49 eV͒ gold ion implantation. The ion implantation process was modeled by computer simulation and accurately predicted the layer depth and width. Transmission electron microscopy ͑TEM͒ was used to image the buried layer and individual nanoclusters; the layer width was ϳ6-8 nm and the cluster diameter was ϳ5-6 nm. Surface plasmon resonance ͑SPR͒ absorption effects were observed by UV-visible spectroscopy. The TEM and SPR results were related to prior measurements of electrical conductivity of Au-doped PMMA, and excellent consistency was found with a model of electrical conductivity in which either at low implantation dose the individual nanoclusters are separated and do not physically touch each other, or at higher implantation dose the nanoclusters touch each other to form a random resistor network ͑percolation model͒.

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“…In spite of this, some phenomena still remain incompletely understood. 29 According to many proposed theories of transport in isotropic percolating materials, [29][30][31][32][33] the dc bulk conductivity of a metal/insulator composite, near the critical conductor/insulator transition, is given by the power law…”

mentioning

confidence: 99%

“…These composites include carbon-black/polymer systems, oxide-based thick film resistors, and other metal/inorganic insulator composites and metal/organic insulator composites. Many theoretical approaches 23,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] have been proposed to explain the experimental results.…”

mentioning

confidence: 99%

Conducting polymer formed by low energy gold ion implantation

Salvadori

Cattani

Teixeira

et al. 2008

Applied Physics Letters

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A buried conducting layer of metal/polymer nanocomposite was formed by very low energy gold ion implantation into polymethylmethacrylate. The conducting layer is ∼3 nm deep and of width ∼1 nm. In situ resistivity measurements were performed as the implantation proceeded, and the conductivity thus obtained as a function of buried gold concentration. The measured conductivity obeys the behavior well established for composites in the percolation regime. The critical concentration, below which the polymer remains an insulator, is attained at a dose ∼1.0×1016 atoms/cm2 of implanted gold ions.

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Precise determination of the conductivity exponent of 3D percolation using exact numerical renormalization

Abstract: PACS. 05.50.+q Lattice theory and statistics (Ising, Potts, etc.) - 05.70.-a Thermodynamics,

Cited by 56 publications

References 5 publications

Gold-implanted shallow conducting layers in polymethylmethacrylate

Gold-implanted shallow conducting layers in polymethylmethacrylate

Surface plasmon resonance of gold nanoparticles formed by cathodic arc plasma ion implantation into polymer

Conducting polymer formed by low energy gold ion implantation

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