Journal of Nanoscience and Nanoengineering
Articles Information
Journal of Nanoscience and Nanoengineering, Vol.1, No.2, Aug. 2015, Pub. Date: Aug. 13, 2015
Beyond the Basic Tight Binding Model to Calculate Optical Transition Energies of SWCNT
Pages: 84-95 Views: 4864 Downloads: 1864
Authors
[01] G. R. Ahmed Jamal, Department of Electrical and Electronic Engineering, University of Asia Pacific, Dhaka, Bangladesh.
[02] S. M. Mominuzzaman, Department of Electrical and Electronic Engineering, Bangaldesh University of Engineering and Technology, Dhaka, Bangladesh.
Abstract
The one-dimensionality of the Single Wall Carbon Nanotubes (SWCNT) give rise to 1D sub-bands in nabnotube density of states. The tight-binding (TB) model has been widely used for modeling electronic band structure of SWCNT due to its simplicity. A number of recent optical spectroscopic experiments reveal that TB model fails to give accurate quantitative and qualitative description of different optical transition energies in SWCNTs. Hence, many authors tried to improve this model through different approaches so as to extend the capacity of basic TB model to predict different optical transition energies in SWCNTs. Some tried to calculate the band structure from first principle calculations. Others proposed empirical models to fit the experimental results. This work presents a review of some important previous research works that proposed improved TB models, empirical models or first principle based models to overcome the limitation of basic TB model in calculating different optical transitions of SWCNTs. The advantage and limitation of each of these approaches are also highlighted in this work.
Keywords
SWCNT, Density of State, Optical Transition Energy, Tight Binding Model, Chiral Index
References
[01] V. N. Popov, “Carbon nanotubes: properties and application”, Materials Science and EngineeringR, 43, pp. 61–102, 2004.
[02] T. W. Odom, J. L. Huang, P. Kim, and C. M. Lieber, “Structure and Electronic Properties of Carbon Nanotubes”, J. Phys. Chem. B, 104, pp.2794-2809, 2000.
[03] N. Hamada, S. Sawada, and A. Oshiyama, “New one-dimensional conductors: graphitic microtubules,” Phys. Rev. Lett., Vol.68, No.10, pp.1579-1581, 1992.
[04] J. W. Mintmire and C. T. White, “Universal density of states for carbon nanotubes”, Phys. Rev. Lett., Vol. 81, No.12, 1998.
[05] S. Reich and C. Thomsen, “Chirality dependence of the density-of-states singularities in carbon nanotubes”, Phys. Rev. B, Vol 62, No. 7, 2000.
[06] M.S. Dresselhausa, G. Dresselhausc, A. Jorio, A.G. Souza Filho, R. Saito, “Raman spectroscopy on isolated single wall carbon nanotubes”, Carbon, 40, pp.2043–2061, 2002.
[07] J. D. Correa, A. J. R. da Silva, and M. Pacheco, “Tight-binding model for carbon nanotubes from ab initio calculations,” J. Phys.: Condens. Matter, Vol.22, No.7, 275503, 2010.
[08] R. Kundu, “Tight binding parameters for graphene”, Modern Physics Letters B, Vol. 25, No. 3, pp.163-173, 2011.
[09] S. Reich, J. Maultzsch, and C. Thomsen, “Tight-binding description of graphene,” Phys. Rev. B, Vol.66, No.3, pp.035412, 2002.
[10] Y. Lian, Y. Maeda, T. Wakahara, T. Akasaka, S. Kazaoui, N. Minami, N. Choi and H.Tokumoto, “Assignment of the Fine Structure in the Optical Absorption Spectra of Soluble Single-Walled Carbon Nanotubes”, J. Phys. Chem. B, 107, 12082-12087, 2003.
[11] H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y.Achiba, “Optical properties of single-wall carbon nanotubes,” Synthetic Met., Vol.103, pp.2555, 1999.
[12] R. B. Weisman and S. M. Bachilo, “Dependence of optical transition energies on structure for single-walled carbon nanotubes in aqueous suspension: an empirical kataura plot,” Nano Lett., Vol.3, No.9, pp.1235-1238, 2003.
[13] M. Y Sfeir., T.Beetz, F Wang, L.Huang, X. M. H Huang., M.Huang, J. Hone, S. O’Brien, J. A Misewich, T. F.Heinz, L.Wu, Y.Zhu, L. E. Brus, “Optical Spectroscopy of Individual Single-Walled Carbon Nanotubes of Defined Chiral Structure”, Science, Vol. 312, April 2006.
[14] Bachilo S. M., Strano M. S., Kittrell C.,Hauge R. H., Smalley R. E., Weisman R. B., “Structure-Assigned Optical Spectra of Single-Walled Carbon Nanotubes”, Science, Vol 298 No. 5602, pp.2361, 2002.
[15] V. Zólyomi and J. Kürti, “First-principles calculations for the electronic band structures of small diameter single-wall carbon nanotubes”, Phys. Rev. B70, 085403, 2004.
[16] V. N. Popov,“Curvature effects on the structural, electronic and optical properties of isolated single-walled carbon nanotubes within a symmetry-adapted non-orthogonal tight-binding model”, New Journal of Physics, Vol. 6, 2004.
[17] H. Zeng, H. F. Hu, J. W. Wei, Z. Y. Wang, L. Wang, and P. Peng, “Curvature effects on electronic properties of small radius nanotube,” Appl. Phys. Lett., Vol.91, No.3, pp.033102, 2007.
[18] O. Gulseren, T. Yildirim and S. Ciraci, “A systematic ab-initio study of curvature effects in carbon nanotubes”, Phys. Rev. B 65, 153405, 2002.
[19] J W Ding, X H Yan, J X Cao, “Analytical relation of band gaps toboth chirality and diameter of single-wall carbon nanotubes”,Phys. Rev. B , Vol. 66, Issue 7, Pages: 2-5, 2002.
[20] R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Trigonal warping effect of carbon nanotubes,” Phys. Rev. B, Vol.61, No.4, pp.2981-2990, 2000.
[21] Kane C. L. and Mele E. J., “The Ratio Problem in Single Carbon Nanotube Fluorescence Spectroscopy”,Phys. Rev. Lett. 90, 207401, 2003.
[22] E.J. Mele, C.L. Kane, “Many body effects in carbon nanotube fluorescence spectroscopy”, Solid State Communications 135, pp. 527–531, 2005.
[23] H. Lin, J. Lagoute, V. Repain, C. Chacon, Y. Girard, J.-S. Lauret, F. Ducastelle, A. LoiseauS. Rousset , “Many-body effects in electronic bandgaps of carbon nanotubes measured by scanning tunnelling spectroscopy”, Nature Materials 9, 235–238, 2010.
[24] C. D. Spataru, S. I. Beigi, L. X. Benedict and S. G. Louie,“Excitonic Effects and Optical Spectra of Single-Walled Carbon Nanotubes”, AIP Conf. Proc., vol 772, p. 1061-1062, 2004.
[25] H. Zhao, S. Mazumdar, “Excitons in semiconducting single-walled carbon nanotubes”, Synthetic Metals, 155, p.250–253, 2005.
[26] G. Dukovic, F. Wang, D. Song, M. Y. Sfeir, T. F. Heinz, and L. E. Brus, “Structural dependence of excitonic optical transitions and band-gap energies in carbon nanotubes,” Nano Lett., Vol.5, No.11, pp.2314-2318, 2005.
[27] J. X. Cao, X. H. Yan, J. W. Dingand D. L. Wang, “Band structures of carbon nanotubes: the sp3s*tight-binding model”, J. Phys.: Condens. Matter13, L271–L275, 2001.
[28] A. Hagen and T. Hertel, “Quantitative Analysis of Optical Spectra from Individual Single-Wall Carbon Nanotubes”, Nano letters, Vol. 3, No. 3, pp. 383-388, 2003.
[29] Z. Wang, H. Zhao, and S. Mazumdar, “Quantitative calculations of the excitonic energy spectra of semiconducting single-walled carbon nanotubes within a π-electron model”, Phys. Rev. B 74, 195406, 2006.
[30] J. Maultzsch, H. Telg, S. Reich, and C. Thomsen, “Radial breathing mode of single-walled carbon nanotubes Optical transition energies and chiral-index assignment”, Phys. Rev. B 72, 205438, 2005.
[31] H. Yorikawa, S. Muramatsu, “Electronic structure characteristic of carbon nanotubules”, Z. Phys. B,Condensed Matt., vol. 104, pp. 71–76, 1997.
[32] A. Jorio, C. Fantini, M. A. Pimenta, R. B. Capaz,Ge. G. Samsonidze, G. Dresselhaus, M. S. Dresselhaus, J. Jiang, N. Kobayashi, A. Grüneis and R. Saito, “Resonance Raman spectroscopy (n,m)-dependent effects in small-diameter single-wall carbon nanotubes”, Phys. Rev. B71, 075401, 2005.
[33] J. Lefebvre, S. Maruyama and P. Finnie, “Photoluminescence: science and applications”, Topics in Applied Physics, Vol. 111, pp.287-319, 2008.
[34] P. K. Valavala, D. Banyai, M. Seel, and R. Pati, “Self-consistent calculations of strain-induced band gap changes in semiconducting (n,0) carbon nanotubes,” Phys. Rev. B, Vol.78, No.23, pp.235430, 2008.
[35] A. Jorio, P. Araujo, S. K. Doorn, S. Maruyama, H. Chacham, and M. A. Pimenta, “The Kataura plot over broad energy and diameter ranges,” Phys. Stat. Sol. (b),Vol.243, No.13, pp.3117-3121, 2006.
[36] H. Yorikawa and S. Muramatsu, “Energy gaps of semiconducting nanotubles,” Phys. Rev. B, Vol.52, No.4, pp.2723-2727, 1995.
[37] H. Yorikawa and S. Muramatsu, “Chirality-dependence of energy gaps of semiconducting nanotubules”, Solid State Communications, Vol. 94, Issue 6, Pages 435-437, 1995.
[38] G. Lanzani, L. Luer, “Carbon Nanotubes: Electronic Structure and Spectroscopy”, Comprehensive Nanoscience and Technology,Vol. 1, pp. 23–39, 2011.
[39] Ge. G. Samsonidze, R. Saito, N. Kobayashi, A. Grüneis,J. Jiang, A. Jorio, S. G. Chou, G. Dresselhaus and M. S. Dresselhaus, “Family behavior of the optical transition energies in single-wall carbon nanotubes of smaller diameters,Appl. Phys. Lett., Vol 85, No. 23, 2004.
[40] J. Maultzsch, C. Thomsen, “Characterization of Carbon Nanotubes by Optical Spectroscopy, Advanced Micro and Nanosystems”,Carbon Nanotube Devices,Vol. 8., Edited by Christofer Hierold, Verlag GmbH and Co. KGaA, Weinheim, Berlin, Germany, 2008.
[41] H. Telg, “Raman studies on individual nanotubes and nanotube ensembles –vibrational properties and scattering efficiencies”, Ph.d thesis, Physics, Institute für Festkörperphysik, Berlin, 2009.
[42] G. R. Ahmed Jamal, M. S. Arefinand S. M. Mominuzzaman, “Empirical Prediction of Bandgap in Semiconducting Single-Wall Carbon Nanotubes”. Proceeding 7th International Conference on Electrical and Computer Engineering (ICECE-2012), pp. 221-224, 20-22 December, 2012, Dhaka, Bangladesh.
[43] G. Bertoni, L. Calmels, “First-principles calculation of the electronic structure and energy loss near edge spectra of chiral carbon nanotubes”, Micron 37, pp.486–491, 2006.
[44] M. Machón, S. Reich, C. Thomsen, D. S. Portal and P. Ordejón, “Ab initio calculations of the optical properties of 4-Å-diameter single-walled nanotubes”, Phys. Rev. B 66, 155410, 2002.
[45] X. P. Yang, H. M. Weng and J. Dong, “Optical properties of 4 Å single-walled carbon nanotubes inside the zeolite channels studied from first principles calculations”, The European Physical Journal B - Condensed Matter and Complex Systems,Vol. 32, No. 3, pp.345-350,2003.
[46] W. Z. Liang, G. Chen, Z.Li, Z. K. Tang, “Absorption spectra and chirality of single-walled 4 Å carbon nanotubes”, Applied Physics Letters, vol. 80 no. 18, pp. 3415-3417, 2002.
[47] Liu K, Deslippe J, Xiao F, Capaz RB, Hong X, Aloni S, Zettl A, Wang W, Bai X, Louie SG, Wang E, Wang F., “An atlas of carbon nanotube optical transitions”, Nat. Nanotech. 7, 325–329, 2012.
[48] S. Lebedkin, F. Hennrich, T. Skipa, M. M. Kappes, “Near–infrared photoluminescence of single–walled carbon nanotubes prepared by the laser vaporization method”,J. Phys. Chem. B, 107, p.1949, 2003.
[49] P. T. Araujo, S. K Doorn, S. Kilina, S. Tretiak, E. Einarsson, S. Maruyama, H. Chacham, M. A. Pimenta, A. Jorio, “Third and fourth optical transitions in semiconducting carbon nanotubes”, Phys. Rev. Lett. , 98,067401, 2007.
[50] V. N. Popov, L. Henrard, P. Lambin, “Electron–phonon and Electron–photon interactions and resonant Raman scattering from the radial–breathing mode of single-walled carbon nanotubes”, Phys. Rev. B , 72,035436, 2005.
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