Universal analytic expression of electric-dipole matrix elements for carbon nanotubes

Zarifi, Abbas; Pedersen, Thomas Garm

doi:10.1103/physrevb.80.195422

Cited by 21 publications

(19 citation statements)

References 36 publications

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“…In this section, we derive selection rules for transitions in armchair carbon nanotubes (ACNTs). In spite of being known for a long time [44,[50][51][52][53][54], they have not been derived from the full tight-binding Hamiltonian. The purpose of this exercise is to provide deeper understanding of the difference in the optical properties of zigzag graphene nanoribbons and ACNTs and also to show their relation to the graphene single layer sheet.…”

Section: Appendix D: Armchair Nanotube Selection Rulesmentioning

confidence: 99%

“…The distinctive selection rules of zigzag graphene nanoribbons were noticed as early as 2000 by Lin and Shyu [9]. This remarkable and counter-intuitive result, especially when compared to the optical selection rules of carbon nanotubes [44,[50][51][52][53][54], was obtained numerically and followed by a few attempts to provide an analytical explanation [22,35].…”

Section: Introductionmentioning

confidence: 97%

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Optical selection rules of zigzag graphene nanoribbons

2017

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We present an analytical tight-binding theory of the optical properties of graphene nanoribbons with zigzag edges. Applying the transfer matrix technique to the nearest-neighbor tight-binding Hamiltonian, we derive analytical expressions for electron wave functions and optical transition matrix elements for incident light polarized along the structure axis. It follows from the obtained results that optical selection rules result from the wave function parity factor (−1) J , where J is the band number. These selection rules are that J is odd for transitions between valence and conduction subbands and that J is even for transitions between only valence (conduction) subbands. Although these selection rules are different from those in armchair carbon nanotubes, there is a hidden correlation between absorption spectra of the two structures that should allow one to use them interchangeably in some applications. The correlation originates from the fact that van Hove singularities in the tubes are centered between those in the ribbons if the ribbon width is about a half of the tubes circumference. The analysis of the matrix elements dependence on the electron wave vector for narrow ribbons shows a smooth nonsingular behavior at the Dirac points and the points where the bulk states meet the edge states.

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Section: Appendix D: Armchair Nanotube Selection Rulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Optical selection rules of zigzag graphene nanoribbons

2017

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“…Meanwhile, the selection rules and expression of dipole matrix elements in different mass were derived (Ajiki and Ando 1994). Moreover, the optical properties and selection rules for cross light polarized and arbitrary directions light polarized with respect to nanotube axis have been analytically studied (Jiang et al 2004;Liu et al 2013;Samsonidze et al 2004;Goupalov 2005;Zarifi and Pedersen 2009;Wang et al 2007;Takagi and Okada 2009). The absorption coefficient of CNTs and the optical cross section modifying with nanotubes chirality for arbitrary directions light polarized have also been calculated (Miyauchi et al 2006;Zhang et al 2010;Battie et al 2012; Barkelid et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Tight-binding description of optoelectronic properties of silicon nanotubes

Shokri

Ahmadi

2014

Opt Quant Electron

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Using a tight-binding model up to the second nearest-neighbor (2NN) interactions, an analytic expression for the selection rule and the optical dipole matrix elements have been derived as a function of optical energy of some single-walled silicon hexagonal nanotubes (Si h-NTs). For this purpose, the energy dispersion, dipole matrix elements and optical absorption obtained up to the 2NN are compared with those obtained for the first nearestneighbors (1NN) for incident light polarized parallel to the tube axis. By concerning more distant-neighbors, in general, the 1NN model can be improved. The results show that there is a shift in the dispersion energy including second neighbors in comparison with first neighbors, which it depends on the subband index. One can also see that the absorption intensity is increased for both metallic and semiconducting nanotubes. The numerical result may be useful in designing nano-optoelectronic devices.

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“…For our simulator we use the Young's modulus of 1 TPa. In addition to the bending beam approach, we consider that semiconducting CNTs can be polarized as described in Fagan et al [2007], Zarifi and Pedersen [2009], and Lu et al [2007]. We express the polarization in terms of the susceptibility χ whereas χ is a tensor between the electric field E and the dielectric response D using the following equation D = (1 + χ )ε 0 E, where ε 0 is the vacuum permittivity.…”

Section: Extraction Of Key Parameters For Cnt Shape Simulatormentioning

confidence: 99%

Effect of the Active Layer on Carbon Nanotube-Based Cells for Yield Analysis

Beste

Tahoori

2014

J. Emerg. Technol. Comput. Syst.

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Carbon Nanotube Field Effect Transistor (CNTFET)-based technologies become more and more a concurrent alternative to Metal Oxide Semiconductor Field Effect Transistors (MOSFET) technologies. In contrast to a MOSFET technology, the active layer of a CNTFET technology is not a regular silicon film with homogeneous doping and rectangular dimensions, but an array of mostly aligned carbon nanotubes (CNTs). The quality of this active layer, which depends on various technology process parameters, is expressed by parameters such as CNT alignment and array density. These parameters affect the electrical properties of the logic cells placed on top of the active layer and hence the overall CNTFET circuit yield. Although not all parameters in CNT fabrication process can be fully controlled, designers still need to assure a very high yield of their cell layouts, that is, a high reproducibility of the electrical characteristics to achieve a reasonable manufacturing yield for the entire chip. In this work we close the gap between CNTFET process fabrication and circuit design by presenting a novel accurate model for active layers in CNTFET-based technologies. Our model enables the designers to obtain technology-dependent driver strength of the custom cell layouts under realistic conditions. The new model can also be used to extract and evaluate CNTFET Design for Manufacturing (DfM) and Design for Robustness (DfR) design rules, and provide feedback to adjust process technology parameters to achieve desirable functional yield. ACM Reference Format:Matthias Beste and Mehdi B. Tahoori. 2014. Effect of the active layer on carbon nanotube-based cells for yield analysis.

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Universal analytic expression of electric-dipole matrix elements for carbon nanotubes

Cited by 21 publications

References 36 publications

Optical selection rules of zigzag graphene nanoribbons

Optical selection rules of zigzag graphene nanoribbons

Tight-binding description of optoelectronic properties of silicon nanotubes

Effect of the Active Layer on Carbon Nanotube-Based Cells for Yield Analysis

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