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A Theoretical Study of Raman Spectroscopy of Carbon Nanotubes and Evaluation of Energy Separation as a Function of Nanotube Diameter

Krishna Prasad Singh1, Uday Narain Singh2 and L. K. Mishra3

1S/o Sri R. R. Singh, Department of Physics, K. S. College, Barun, Aurangabad, Bihar, INDIA. 2Associate Professor, Department of Physics, K. S. M. College, Aurangabad, Bihar, INDIA. 3Department of Physics, Magadh University, Bodh Gaya-824234, Bihar, INDIA.

ABSTRACT

Using the theoretical formalism of P T Araujo et al. [Physica E, 42, 1251 (2010)] and M S Dresselhaus et al. {Phys. Rep. 409, 47 (2009)], we have theoretically studied the Raman spectroscopy of carbon nanotubes. We have evaluated separation energy between valence band and conduction band of both semiconducting and metallic nanotubes as a function of nanotube diameter. Our theoretically obtained results show that separation energy decrease with increase of diameter for both the systems. We have compared our evaluated results with the results of other theoretical workers and found that the agreement between our results with other workers are good so far trend of the results concerned. However the magnitude of our values is less than their values. We have also reported an experimental result of Raman radial breathing mode frequency as a function of reciprocal of the nanotube diameter. The measured frequency increases with reciprocal diameter. The observation is consistent with the two laser source 635nm and 785nm lasers. We have also reported an experimental result and theoretical result34 of transition energy Eii as a function of nanotube chiral number (n, m) for the isolated semiconducting SWNT for two laser source 635nm and 785nm. The reported both measured and evaluated are in good agreement to each other.

Keywords : Raman spectroscopy of carbon nanotube, Raman radial breathing mode frequency, Single Wall carbon nanotubes (SWNTs), Multiwall carbon nanotubes (MWNTs), Laser sources, separation energy, transition energy, Reciprocal of nanotube diameter, G-band.