Journal of Nanoscience and Nanoengineering

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Limitations of Tight Binding Model in Describing Electronic Properties of Single Wall Carbon Nanotubes

Pages: 96-106 Views: 2041 Downloads: 734

[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.

Carbon nanotubes are one of the most intensively studied materials in recent decades. The tight-binding (TB) model of π-bands of graphene using the zone-folding approximation has been widely used for modeling electronic band structure of single-wall carbon nanotube (SWCNT) due to its simplicity and low computational cost. However, thorough investigation and detailed comparison of the result from this theoretical model with various recent optical spectroscopic experiments reveals that TB models fails quantitatively and in some cases qualitatively to predict different optical transition energies in SWCNTs. Many authors discussed this issue through theoretical and experimental results and showed the limitation of TB model in describing SWCNTs. The purpose of this work is to discuss various limitations of TB model of SWCNTs along with main theoretical factors that limit this model. This work will presents a summary and review of some important previous research works by different authors highlighting the limitations of Tight-binding (TB) model, especially its nearest-neighbor approximation. This work will also focus on findings by various researchers regarding the main factors that cause the tight binding model given electronic band structure and corresponding transition energies to deviate from experimental results. This review work concludes that the TB model greatly fails in describing SWCNTs.

Carbon Nanotube, SWCNT, Tight Binding Model, Optical Transition Energy, Chiral Index

[01]
S. Iijima, “Helical microtubules of graphitic carbon”, Nature 354, pp.56 – 58, 1991.
[02]
S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1-nm diameter”, Nature 363, pp.603 – 605, 1993.
[03]
A. P. Graham, G.S. Duesberg, W. Hoenlein, F. Kreupl, M. Liebau, R. martin, B. Rajasekharan, W. Pamler, R. Seidel, W. Steinhoegl, E. Unger, “How Do Carbon Nanotubes Fit into the Semiconductor Roadmap?”, Appl. Phys. A, 80, pp.1141–1151, 2005.
[04]
Kahng, B. Andrew , “Scaling: More than Moore's law”, Design and Test of Computers, IEEE, Vol. 27 , Issue 3 , pp.86 – 87, 2010.V. N. Popov, “Carbon nanotubes : properties and application”, Materials Science and Engineering R, 43, pp. 61–102, 2004.
[05]
V. N. Popov, “Carbon nanotubes: properties and application”, Materials Science and Engineering R, 43, pp. 61–102, 2004.
[06]
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.
[07]
N. Hamada, S. Sawada, and A. Oshiyama, “New one-dimensional conductors: graphitic microtubules,” Phys. Rev. Lett., Vol.68, No.10, pp.1579-1581, 1992.
[08]
J. W. Mintmire and C. T. White, “Universal density of states for carbon nanotubes”, Phys. Rev. Lett., Vol. 81, No.12, 1998.
[09]
S. Reich and C. Thomsen, “Chirality dependence of the density-of-states singularities in carbon nanotubes”, Phys. Rev. B, Vol 62, No. 7, 2000.
[10]
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.
[11]
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.
[12]
R. Kundu, “Tight binding parameters for graphene”, Modern Physics Letters B, Vol. 25, No. 3, pp.163-173, 2011.
[13]
S. Reich, J. Maultzsch, and C. Thomsen, “Tight-binding description of graphene,” Phys. Rev. B, Vol.66, No.3, pp.035412, 2002.
[14]
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.
[15]
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.
[16]
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.
[17]
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.
[18]
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.
[19]
V. Zólyomi and J. Kürti, “First-principles calculations for the electronic band structures of small diameter single-wall carbon nanotubes”, Phys. Rev. B 70, 085403, 2004.
[20]
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.
[21]
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.
[22]
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.
[23]
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.
[24]
S. Okada, S. Ogawa, and S. Maruyama, “Curvature Effects on Electron States of Semiconducting Nanotubes”, Materials Science, Feb 20, 2004.
[25]
Kane C. L. and Mele E. J., “The Ratio Problem in Single Carbon Nanotube Fluorescence Spectroscopy”, Phys. Rev. Lett. 90, 207401, 2003.
[26]
E. J. Mele, C.L. Kane, “Many body effects in carbon nanotube fluorescence spectroscopy”, Solid State Communications 135, pp. 527–531, 2005.
[27]
H. Lin, J. Lagoute, V. Repain, C. Chacon, Y. Girard, J.-S. Lauret, F. Ducastelle, A. Loiseau S. Rousset , “Many-body effects in electronic bandgaps of carbon nanotubes measured by scanning tunnelling spectroscopy”, Nature Materials 9, 235–238, 2010.
[28]
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.
[29]
H. Zhao, S. Mazumdar, “Excitons in semiconducting single-walled carbon nanotubes”, Synthetic Metals, 155, p.250–253, 2005.
[30]
M. J. O'Connell, S.M. Bachilo, C.B. Huffman, V.C. Moore, M.S. Strano, E.H. Haroz, K.L. Rialon, P.J. Boul, W.H. Noon, C. Kittrell, J. Ma, R.H. Hauge, R.B. Weisman, and R.E. Smalley, “Band Gap Fluorescence from Individual Single-Walled Carbon Nanotubes”, Science 297, pp.5581-5593, 2002.
[31]
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.
[32]
O. Gulseren, T. Yildirim and S. Ciraci, “A systematic ab-initio study of curvature effects in carbon nanotubes”, Phys. Rev. B 65, 153405, 2002.
[33]
J W Ding, X H Yan, J X Cao, “Analytical relation of band gaps to both chirality and diameter of single-wall carbon nanotubes”, Phys. Rev. B , Vol. 66, Issue 7, Pages: 2-5, 2002.
[34]
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.
[35]
H. Telg, “Raman studies on individual nanotubes and nanotube ensembles –vibrational properties and scattering efficiencies”, Ph.d thesis, Physics, Institute für Festkörperphysik, Berlin, 2009.
[36]
A. Javey, J. Kong, Editors: “Carbon Nanotube Electronics”, pp. 16, 35, Springer Science and Business Media, LLC, 2009.
[37]
Ana Dergan, “Electronic and transport properties of carbon nanotubes”, seminar paper, Department of physics, University of Ljubljana, October 2010.
[38]
Francois Leonard, “The physics of carbon nanotube devices”, Ed: Jeremy Ramsden, William Andrew Inc. Norwich, New York. 2009.
[39]
C. L. Kane and E. J. Mele, “Size, shape, and low energy electronic structure of carbon nanotubes,” Phys. Rev. Lett., vol. 78, pp. 1932–1935, 1997.
[40]
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.
[41]
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.
[42]
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.
[43]
G.D. Li, Z.K. Tang, N. Wang, J.S. Chen, “Structural study of the 0.4-nm single-walled carbon nanotubes aligned in channels of AlPO4-5 crystal”, Carbon, 40, pp.917–921, 2002.
[44]
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.
[45]
P. Lambin, F. Troizon and V. Meunier, “Electronic Transport in Nanotubes and Through Junctions of Nanotubes”, Carbon Nanotubes:NATO Science Series, Volume 222, III, pp. 123-142, 2006.
[46]
R. Saito and H. Kataura, “Optical Properties and Raman Spectroscopy of Carbon Nanotubes”, Carbon Nanotubes, Edited by M. S. Dresselhaus, G. Dresselhaus, Ph. Avouris,Topics in Applied Physics, Vol. 80, pp.213-247, Springer-Verlag Berlin Heidelberg, 2001.
[47]
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.
[48]
H. Yorikawa, S. Muramatsu, “Electronic structure characteristic of carbon nanotubules”, Z. Phys. B, Condensed Matt., vol. 104, pp. 71–76, 1997.
[49]
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. B 71, 075401, 2005.
[50]
J. Lefebvre, S. Maruyama and P. Finnie, “Photoluminescence: science and applications”, Topics in Applied Physics, Vol. 111, pp.287-319, 2008.
[51]
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.
[52]
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.
[53]
H. Yorikawa and S. Muramatsu, “Energy gaps of semiconducting nanotubles,” Phys. Rev. B, Vol.52, No.4, pp.2723-2727, 1995.
[54]
H. Yorikawa and S. Muramatsu , “Chirality-dependence of energy gaps of semiconducting nanotubules” , Solid State Communications, Vol. 94, Issue 6, Pages 435-437, 1995.
[55]
G. Lanzani, L. Luer, “Carbon Nanotubes: Electronic Structure and Spectroscopy”, Comprehensive Nanoscience and Technology, Vol. 1, pp. 23–39, 2011.
[56]
J. Jiang, R. Saito, Ge. G. Samsonidze, A. Jorio, S. G. Chou, G. Dresselhaus and M. S. Dresselhaus, “Chirality dependence of exciton effects in single-wall carbon nanotubes: Tight-binding model”, Phys. Rev. B 75, 035407, 2007.
[57]
K. Sato a R. Saito, J. Jiang, G. Dresselhaus, M.S. Dresselhaus, “Chirality dependence of many body effects of single wall carbon nanotubes”, Vibrational Spectroscopy: Elsevier, Vol. 45, Issue 2, pp.89–94, 2007.
[58]
T. Ando, “Family Effects on Excitons in Semiconducting Carbon Nanotubes” Journal of the Physical Society of Japan, Vol. 78, No. 10, 104703, 2009.
[59]
T. G. Pedersen, “Exciton effects in carbon nanotubes”, Carbon 42, pp.1007–1010, 2004.
[60]
C. D. Spataru, S. I. Beigi, R. B. Capaz, and S. G. Louie, “Theory and ab initio calculation of radiative lifetime of excitons in semiconducting carbon nanotubes”, Phys. Rev. Lett., vol. 95, Issue 24, 247402, 2005.

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