Abstract
Carbon nanotubes (CNTs) are basically graphene roll-up in cylindrical form that can have large value of length-to-diameter ratio. In this paper electrical property such as band-gap, density of states, and energy-dependent conductance of single walled carbon nanotubes is quantumly calculated using density functional theory (DFT). It can be seen that band-gap of different SWCNTs changes with the change in diameter. Density of states and energy dependent conductance is also calculated for different single walled CNTs. It is observed that armchair carbon nanotube band gap remain constant irrespective of the diametric size.
Access provided by Autonomous University of Puebla. Download conference paper PDF
Similar content being viewed by others
1 Introduction
In more recent history the discovery of CNTs is attributed to Iijima as the first scientist who described the multiwalled carbon nanotubes (MWCNTs) preparation process after a random event during the test of a new arc evaporation method for C60 carbon molecule fabrication in 1991 [1,2,3]. Structurally, SWCNTs can be described as a ‘‘rolled up’’ one-atom-thick sheets of graphene (Fig. 11.1). The way in which the graphene sheet is wrapped gives different structures of carbon nanotubes describe by chiral vector C which is a result of a pair (n,m) of integers that correspond to graphene vectors ~a1 and ~a2 [4, 5]. The principle of SWCNT construction from a graphene sheet along the chiral vector C = na1 + ma2 is shown in Fig. 11.1. Depending on the values of n and m three types of carbon nanotubes are formed [6,7,8]. When n has any integer values and value of m is zero the nanotube structure thus formed is called ‘‘zigzag’’. When values of n = m the nanostructure thus formed is called ‘‘armchair’’. The third type of CNTs construction, for which n > m > 0, is called as ‘‘chiral’’ nanotubes [9].
2 Method
The most common and simplest method used for determining the electronic structure of SWCNTs is the density functional theory (DFT). This model is best for the case of weak overlap of atomic wave functions in an insulating crystal and widely used in solid-state physics. According to the density functional theory (DFT), the conducting properties of different carbon nanotube structure will depend on the relationship between the coefficient n and m of the vector C = na1 + ma2, which relates two crystallographic equivalent sites as shown in Fig. 11.1. It is observed that if mod(n − m,3) = 0, 1, 2, then mod1 and mod2 are semiconducting in nature and mod0 SWCNTs are metallic in nature at room temperature and exhibit a small chirality dependent energy-gap. The small energy-gap corresponds to quasi-metallic conduction at lower temperature. The energy gap has a minimum value of zero corresponding to p = 2n/3. If n is not an integer multiple of three then minimum value of p − 2n/3 is equal to 1/3. This suggests that the minimum energy gap is then given by
The impact of B doping in pristine and doped CNT(8,0) is analysed using density functional theory (DFT) along with non-equilibrium green function (NEGF).
3 Results
The nanotube diameter, dictated through Ch, also affects the electron dispersion and it was derived in a semiconducting nanotube, \( E_{{\text{g}}} = \frac{{4\hbar v_{{\text{F}}} }}{{3d_{{\text{t}}} }} \). The above translates numerically to \( E_{\text{g}} = \frac{0.9}{{d_{\text{t}} }}\,{\text{eV}} \), with a \( v_{\text{F}} = 10^{6} \,{\text{m/s}} \) (Figs. 11.2 11.3 and 11.4).
-
Effect of Boron doping concentration on electronic properties
In this section the CNTs are doped with boron atoms. With variation in the number of doped atoms, there band structures are analyzed. For this work CNT(8,0) is taken and doped with one, two and four atoms of boron. The band structure of the undoped CNT(8,0) is compared with that of doped nanotubes.
Our results clearly indicates that CNT(8,0) is semimetallic in nature (Fig. 11.5a1). The corresponding density of states (DOS) plot shown in Fig. 11.5a2 completely agrees with the band structure of CNT(8,0). There is a band gap of 0.6 eV between the valence and conduction band. Carbon nanotubes electronic properties can be altered by doping with various impurities. In this work, boron is taken for doping of CNT. It was clearly observed from Fig. 11.5 that Fermi level of doped CNT(8,0) shifts downward resulting in p-type semiconducting behavior. The energy band gap is decreased with the increase in doping atoms as evident from band structure of undoped and doped CNT(8,0). The incorporation of boron atoms adds additional electronic states around the Fermi level, EF. With the increase in doping concentration number of electronic states near the Fermi level increases.
4 Conclusion
It was observed that the density of states near the Fermi level EF increases with the increase in doping concentration. CNTs shows potential as future material for the development of next generation devices. The study about band gap and electronic properties of CNTs will help in the development of high speed devices and transistors.
References
S. Iijima, T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter. Nature 363(6430), 603–605 (1993)
S. Iijima, M. Yudasaka, R. Yamada, S. Bandow et al., Nano-aggregates of single-walled graphitic carbon nanohorns. Chem. Phys. Lett. 309, 165–167 (1999)
T.W. Odom, J.L. Huang, P. Kim, C.M. Lieber, Atomic structure and electronic properties of single-walled carbon nanotubes. Nature 391, 62–64 (1998)
Mark C. Hersam, Progress towards monodisperse single-walled carbon nanotubes. Nat. Nanotechnol. 3(7), 387–394 (2008)
K.I. Tserpes, P. Papanikos, Finite element modeling of single-walled carbon nanotubes. Compos. Part B Eng. 36(5), 468–477 (2005)
M.S. Dresselhaus, G. Dresselhaus, R. Saito, A. Jorio, Raman spectroscopy of carbon nanotubes. Phys. Rep. 409(2), 47–99 (2005)
S. Benguediab, A. Tounsi, M. Zidour, A. Semmah, Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes. Compos. B Eng. 57, 21–24 (2014)
N.T. Hung, A.R. Nugraha, E.H. Hasdeo, M.S. Dresselhaus, R. Saito, Diameter dependence of thermoelectric power of semiconducting carbon nanotubes. Phys. Rev. B 92(16), 165426 (2015)
R.N. Gontijo, G.A. Sáfar, A. Righi, R.M. Jain, M.S. Strano, C. Fantini, Quantifying (n, m) species in single-wall carbon nanotubes dispersions by combining Raman and optical absorption spectroscopies. Carbon 115, 681–687 (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Sharma, A.K., Sharma, S. (2019). Effect of Diameter and Doping on Electronic Band Structure of Single-Walled Carbon Nanotubes. In: Sharma, R., Rawal, D. (eds) The Physics of Semiconductor Devices. IWPSD 2017. Springer Proceedings in Physics, vol 215. Springer, Cham. https://doi.org/10.1007/978-3-319-97604-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-97604-4_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97603-7
Online ISBN: 978-3-319-97604-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)