_{3}and B

_{3}C Systems by Density Functional Theory

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The optical properties of (8,0) BC_{3} and B_{3}C single-wall carbon nanotubes (SWCNTs) are computed using _{3}C system is reduced compared to BC_{3}. The static dielectric constant in the long wavelength limit for B_{3}C system is 9 times larger than that of BC_{3} in unpolarized electromagnetic field. Within 10 eV frequency (energy) range, the absorption coefficient of B_{3}C is higher compared to BC_{3}, while, above 10 eV, it is less than that of BC_{3}. In parallel polarization, the peak of the loss function for B_{3}C is shifted to higher frequency (energy) region with significantly six orders of magnitude compared to BC_{3} system. The analysis of this study indicates that the optical anisotropies can be gained easily in these boron-doped systems by appropriately choosing the direction of the polarization of the electromagnetic field. Besides, the results of the loss functions may throw some light on the nature of collective excitations of these two systems.

From its very discovery in 1991, carbon nanotubes (CNTs), both single wall as well as multiwall, have attracted the attention of theoretical and experimental research groups [

The electronic properties of single-wall carbon nanotubes (SWCNTs) can be tailored [_{x}_{y}_{z}_{2}O_{3} with CNTs under an Ar atmosphere [^{2} configuration [_{x}_{y}_{3} SWNTs have been interpreted in terms of

With this motivation, we are interested in computing the optical properties of these two boron-doped systems in different polarizations of the electromagnetic field. In particular, in this paper, we study the optical response of (8,0) BC_{3} and B_{3}C SWCNTs under the action of a uniform electric field with various polarizations direction through relaxed C-C bond length

The numerical methods are employed using first-principles (DFT) with Generalized Gradient Approximation (GGA) as implemented in CASTEP code [

The optical properties of any system are generally studied by the complex dielectric function defined by

The matrix element described in (

The typical computational supercell used here is the 3D triclinic crystal (

Before we discuss the optical properties, we show in Figure _{3} and B_{3}C systems.

Ball and stick model of (8,0) (a) BC_{3} and (b) B_{3}C tube in 3D triclinic structure.

All the results presented in this paper have the same set of parameters as indicated in earlier section. For pure (8,0) we find the Fermi energy 6.028 eV with band gap at _{3} system, the Fermi energy reduces to 4.256 eV. With increasing more number of boron atoms in SWNTs, we find, for (8,0) B_{3}C nanotubes, a further reduction of the Fermi energy to 3.614 eV. More interestingly, we note a significant increase of the overlapping of valence and conduction band compared to pure as well as BC_{3} SWNT. This is understood simply from the fact that the electronic configuration of B atom is 1s^{2} 2s^{2}2p^{1}.

Therefore, doping by B atom always reduces the total number of electrons _{3}C system.

Typical energy change per atom of B_{3}C system. The convergence of the energy is noticed in the inset.

In Figure _{3}C system, respectively. All the energies shown in the diagram have been measured with respect to the Fermi energy (shown as the dashed line in the band diagram). The most symmetric point _{3} system turns out as 0.43 eV at

Typical band structure of B_{3}C systems. The dashed line indicates the position of the Fermi energy level.

However, for B_{3}C system, the band gap turns out as 0.58 eV at

Apart from the difference of the Fermi energy in the two cases (see Table _{3} system while those are absent in the energy spectra in the VB for all values of _{3} compared to B_{3}C one.

Comparison of electronic and optical properties of BC_{3} and B_{3}C systems.

Physical properties | BC_{3} | B_{3}C | Pristine |
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Fermi energy | 4.25 eV | 3.61 eV | 6.03 eV |

Static real dielectric constant | 38.45 (Un) | 346.58 (Un) | 19.82 (Un) |

21.71 (Perp) | 76.80 (Perp) | 11.66 (Perp) | |

33.26 (Para) | 396.71 (Para) | 30.98 (Para) | |

Absorption coefficient | Lower | Higher | Highest |

Loss function | Lower (7–12 eV) (Un) | Higher in the same Range (Un) | Higher than BC_{3} but lower than B_{3}C (Un) |

Reflectivity | Smaller (Para) | Larger (Para) | Higher than BC_{3} but very close to B_{3}C (Para) |

(Un: unpolarized, Perp: perpendicular, Para: parallel).

Typical band structure of BC_{3} system.

The partial density of states (PDOS) of B atoms of (8,0) BC_{3} and B_{3}C carbon nanotubes shown in Figure _{3}C case, the contribution of p electrons at the Fermi level have been increased substantially compared to pure case. In fact, the higher value of DOS at the Fermi level signifies the metallicity character of B_{3}C. The DOS at the Fermi level is a measure of available free charge carriers. Thus, the increase of the DOS at the Fermi levels is a signature of more metallic character of B_{3}C system compared to BC_{3} one.

Partial density of states (PDOS) of B atoms of (8,0) (a) BC_{3} and (b) B_{3}C systems.

The direction with relatively flat dispersionless bands at various

We compute the imaginary part of the dielectric constant within the specified frequency range. The polarizations of the electromagnetic field play an important role in computing the imaginary part of the dielectric constant. We compute the dielectric constant for parallel, perpendicular polarization and unpolarized one with normal incidence (1,0,0). The parallel polarization refers here to the direction of light parallel to the axis of respective SWCNTs. In Figure _{3}- and B_{3}C-doped systems as a function of frequency for unpolarized scheme. It is seen in the numerical computation (not shown in the figure) that, in both cases, the imaginary part of the dielectric constant is always positive throughout the range of frequency. This can be understood very simply from (

However, as evident from the figure itself, such a restriction is not obeyed by the real part of the dielectric constant _{3} system is higher compared to pure one. It has been observed that the static dielectric constant of B_{3}C is higher than that of BC_{3} for any type of polarizations (see Table

Variation of dielectric constants of pristine (8,0), BC_{3} and B_{3}C under unpolarized scheme. Inset: the variation is shown up to 5 eV.

In case of semiconducting SWCNT, an _{3}C compared to BC_{3} one. In particular, the static dielectric constant in the long wave length limit for B_{3}C system is 9 times larger than that of BC_{3} in unpolarized electromagnetic field with normal incidence (1,0,0).

The absorption coefficient

The existence of peaks in the spectra indicates the maximum absorption at that particular energy. With doping by B atom(s), both the magnitude of the peaks and its position change significantly. We depict, in Figure _{3} and B_{3}C systems as a function of frequency in the unpolarized case with normal incidence (1,0,0). We notice that in contrast to B_{3}C, there exist several peaks in the absorption spectra. The existence of these rich absorption peaks in the overall frequency range is consistent with the theoretical tight-binding calculations made on (3,3) and (6,0) BC_{3} nanotubes [_{3}C is always higher than that of BC_{3}. However, above 10 eV, the reverse is true.

Variation of absorption coefficient (computed in unit of cm^{−1}) with frequency (calculated in energy unit of eV) of BC_{3} (shaded) and B_{3}C.

The reflectivity _{3} and B_{3}C systems for parallel polarization as a function of frequency. It is clear from the figure that the reflectivity of B_{3}C system is always higher than that of BC_{3} in the whole range of frequency. This could be helpful in designing optical devices involving B-doped SWCNT.

Variation of reflectivity at normal incidence for BC_{3} (shaded one) and B_{3}C for parallel polarization as a function of frequency.

In this time-dependent calculation of the ground state electronic states, the interaction is between the photon and electrons. The transitions between the occupied and unoccupied states are caused by the electric field of the photon. When these excitations are collective in nature, they are termed as plasmons. The loss function, which is a direct measure of the collective excitations of the systems, is defined as

In Figures _{3} and B_{3}C systems for unpolarized case and parallel polarization, respectively. For unpolarized case, we notice that within the range of frequency (7–12 eV), the loss function of BC_{3} is smaller than that of B_{3}C. However, above 12 eV, the loss function of BC_{3} is higher than that of B_{3}C. Besides, the main peak of BC_{3} at 7.24 eV is seen to shift to 9.89 eV with significantly higher magnitude. While in parallel polarization as evident from Figure _{3}C at 8.39 eV is shifted to 8.81 eV for BC_{3} system with significantly six orders of magnitude. In Table

Loss function for BC_{3} (shaded) B_{3}C one for unpolarized case.

Loss function for BC_{3} and B_{3}C (shaded) for parallel polarization.

From the first-principles relaxed C–C bond length DFT calculation of the optical property of BC_{3} and B_{3}C (8,0) SWNT systems, we have observed significant changes in the optical behavior for different polarizations. The behavior of the static dielectric constant of B-doped system depends on the flavor (nature) of the CNTs. The anisotropy signatures of the dielectric constants noticed in these systems are due to the confined geometry of the CNTs. The electronic band structure reveals that the Fermi energy of B_{3}C system is reduced compared to BC_{3}. The static dielectric constant in the long wavelength limit for B_{3}C system is 9 times larger than that of BC_{3} in unpolarized electromagnetic field with normal incidence (1,0,0). Within 10 eV frequency (energy) range, the absorption coefficient of B_{3}C is higher compared to BC_{3}, while, above 10 eV, it is less than that of BC_{3}. In parallel polarization, the peak of the loss function for B_{3}C is shifted to higher-frequency (energy) region with significantly six orders of magnitude compared to BC_{3} system. All these facts about these two systems may throw some light on the nature of collective excitations and nanoscale optical devices.

One of the authors (D. Jana) would like to thank the National Science Council (NSC) of Republic of China (R.O.C) for financially supporting him as a visiting researcher under Contract no. NSC 099-2912-I-002-160.

_{x}C

_{y}N

_{z}nanotubules

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_{z}z nanotubes by a substitution-reaction route

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_{3}single-wall nanotubes upon boron substitution of carbon nanotubes

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_{y}single wall nanotubes

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_{y}nano-composite system

_{x}C

_{y}single wall nanotubes: a first principles approach

_{3}nanotubes