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A supercell of a nanotube formed by a carbon nanotube (CNT) and a silicon nanotube (SiNT) is established. The electronic structure and optical properties are implemented through the first-principles method based on the density functional theory (DFT) with the generalized gradient approximation (GGA). The calculated results show that (6, 6) - (6, 6) silicon/carbon nanotubes (Si/CNTs) presented a direct band gap of 0.093 eV, (4, 4) - (6, 6) silicon/carbon nanotubes presented a direct band gap of 0.563 eV. The top of valence band was fundamentally determined by the Si-3p states and C-2p states, and the bottom of conduction band was primarily occupied by the C-2p states and Si-3p states in the Si/CNTs. It was found that (6, 6) - (6, 6) Si/CNTs have smaller energy band gap and better conductivity. Besides, Si/CNTs have satisfactory absorption characteristics and luminous efficiency in ultraviolet band.

The discovery of CNTs since 1991 [

In the present work, the electronic properties of Si/CNTs formed by a CNT and a SiNT are investigated with the method of the first-principles density functional theory. In the following, we first investigated electronic properties of Si/CNTs in terms of energy band and density of states (DOS). And then the simulation results of optical properties of Si/CNTs are studied in Section 3. Finally, we conclude in Section 4. This work provided a theoretical basis for the application of SiNTs in photoelectric device.

To study the structural feature and the electronic property of (6, 6) - (6, 6) Si/CNTs and (4, 4) - (6, 6) Si/CNTs, supercell are established. Periodic armchair nanotubes which both ends were not closed and infinitely long were adopted. Calculation was conducted on a × a × c orthogonal supercell, and nanotubes infinitely extended along the repeating units of heterostructure at the direction c. In Si/CNTs structure, SiNTs and CNTs occupied half in the heterostructure along the axial direction. Parameter and constant of supercell are set as 1 × 1 × 4, α = β = 90˚, γ = 120˚, respectively. (6, 6) - (6, 6) Si/CNTs include 48 Si atoms and 48 C atoms. (4, 4) - (6, 6) Si/CNTs include 32 Si atoms and 48 C atoms (ref.

In this work, the first principles calculations for the computational method were carried out using CASTEP package to perform geometry optimization and the specific properties such as band energy and density of states (DOS). All the relaxation and electronic calculations were performed based on the DFT, within the Perdew-Burke-Ernzerhof (PBE) formulation of the generalized gradient approximation [^{−6} eV and 400 eV. Integration on the Brillouin zone is performed using special k points generated by the Monkhorst-Pack [^{2}2p^{2}, Si3s^{2}3p^{2}.

In order to make the model energy tend to be stable, and more close to the real material, and ensure that parameters used in the simulation get accurate results, the initial model was first optimized. The geometry of the (6, 6) SiNTs, (6, 6) - (6, 6) Si/CNTs and (4, 4) - (6, 6) Si/CNTs are optimized by using a Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimizer [

Type | optimized | a/Å | b/Å | c/Å | d_{Si}_{-Si}/Å | d_{C}_{-C}/Å | d_{C}_{-Si}/Å |
---|---|---|---|---|---|---|---|

(6, 6) SiNT | before | 16.7542 | 16.7542 | 16.2120 | 2.34 | - | - |

after | 15.7315 | 15.2161 | 15.6251 | 2.261 | - | - | |

(6, 6) - (6, 6) Si/CNT | before | 16.4104 | 16.4104 | 15.7963 | 2.34 | 1.42 | - |

after | 12.3433 | 12.3375 | 13.7579 | 2.362 | 1.431 | 1.895 | |

(4, 4) - (6, 6) Si/CNT | before | 12.0560 | 12.0560 | 15.7963 | 2.34 | 1.42 | - |

after | 11.3745 | 12.3977 | 12.4007 | 2.370 | 1.421 | 1.882 |

In the process of optimization, the change of internal bond length and bond angle of nanotubes changed the cell volume, but the optimized Si/CNTs crystal cell parameters were close. Si-Si bond in SiNTs has bigger length fluctuation and lower chemical displacement degree. Compared with the smooth structure of CNTs surface, the surface of SiNTs appeared folding structure, and Si/CNTs surface presented some deformation. By comparing with the model in

To have a understanding of the electronic properties of Si/CNTs, the band structure and DOS for the single-walled armchair (6, 6) SiNTs, (4, 4) - (6, 6) Si/CNTs and (6, 6) - (6, 6) Si/CNTs were calculated and presented in Figures 3-5.

The valence band of (6, 6) SiNTs mainly comprises the lower valence band of −12 eV - 5 eV and upper valence band of −5 eV - 0 eV. The top of valence band was fundamentally determined by the Si-3p states and the bottom of conduction band was primarily occupied by the Si-3s states and Si-3p states, showing that

the bonding is mainly formed by sp hybridization. In distant region far from Fermi level, the sp hybridization of s electrons and p electrons for SiNTs relatively remains obvious. The lower valence band is mainly formed from Si-3s states, in which the Si-3p states exert a weak influence. Besides, the upper valence band mainly originates from Si-3p states.

To make further study on the electronic structure of Si/CNTs, the partial density of states (PDOS) of C atoms and Si atoms in the nanotube section are investigated (in

According to the law of electron transition and Krames-Kronig dispersion relation [

ε ( ω ) = ε 1 ( ω ) + i ε 2 ( ω ) (1)

The real part of the dielectric function follows from the relation:

ε 1 ( ω ) = 1 + 8 π 2 e 2 m 2 ⋅ ∑ V , C ∫ B Z d 3 K 2 ( 2 π ) × | e ⋅ M C V ( K ) | 2 [ E C ( K ) − E V ( K ) ] (2)

The imaginary part ε 2 ( ω ) , in the long wavelength limit, has been obtained directly from the electronic structure calculation:

ε 2 ( ω ) = 4 π 2 m 2 ω 2 ⋅ ∑ V , C ∫ B Z d 3 K 2 ( 2 π ) × | e ⋅ M C V ( K ) | 2 × δ [ E C ( K ) − E V ( K ) − ℏ ω ] (3)

M C V ( K ) are the transition moments elements.

The absorption coefficient is given by the following relation:

α ( ω ) = 2 ω [ ε 1 2 ( ω ) + ε 2 2 ( ω ) − ε 1 ( ω ) ] 1 / 2 (4)

ℏ , ω , K are Planck constant, the angular frequency and reciprocal vector, respectively. Subscript C and V represent the conduction band and the valence band of nanotubes, and BZ is the first Brillouin zone. E C ( K ) and E V ( K ) represent the intrinsic level of the conduction band and the valence band. | e ⋅ M C V ( K ) | 2 is Momentum transition matrix element of Transition electrons.

To further analyze the optical properties for the two types of Si/CNTs,

The calculate absorption coefficient of SiNTs and Si/CNTs are provided in ^{5} cm^{−1}, proving SiNTs have good absorption characteristics in far ultraviolet band and near ultraviolet band. In addition, the figure also shows that the absorption spectrums for (6, 6) - (6, 6) Si/CNTs and (4, 4) - (6, 6) Si/CNTs all have strong absorption peak at 100 nm - 200 nm and 200 nm - 400 nm, indicative of good absorption characteristics of Si/CNTs in the ultraviolet band, and the optical absorption band width of Si/CNTs is large in the high energy region near 70 nm - 120 nm, photoabsorption characteristics of far ultraviolet band is satisfactory. Besides, within 120 nm - 300 nm, the absorption coefficients of Si/CNTs all declines compared with (6, 6) silicon nanotube. However, absorption coefficient represents the attenuation percentage of light intensity in unit propagation length in nanotubes, so luminous efficiency of the Si/CNTs increases.

To conclude, in this paper, we perform first-principles calculations in the framework of density-functional theory to determine the electronic structure and optical properties of single-walled armchair (6, 6) SiNTs, (6, 6) - (6, 6) Si/CNTs and (4, 4) - (6, 6) Si/CNTs. The calculated results indicate that (6, 6) SiNTs is an indirect band gap of 0.314 eV. The (6, 6) - (6, 6) Si/CNT is a direct-gap semiconductor with band gap of 0.093 eV, and (4, 4) - (6, 6) Si/CNT is a direct-gap semiconductor with energy gap of 0.563 eV. The top of valence band of Si/CNTs is mainly determined by Si-3p and C-2p electrons, and the bottom of conduction band is occupied by the C-2p electrons, Si-3p electrons and a small amount of Si-3s electrons. It shows that the (6, 6) - (6, 6) Si/CNTs has smaller band gap and higher conductibility, and (6, 6) - (6, 6) Si/CNTs and (4, 4) - (6, 6) Si/CNTs have satisfactory absorption characteristics in ultraviolet band. Moreover, the results also provide instructive theoretical guidance for the applications of silicon nanotubes in optical detectors.

Wang, W.Y., Xu, J.G., Zhang, Y.G. and Li, G.X (2017) First-Principles Study of Electronic Structure and Optical Properties of Silicon/Carbon Nanotube. Computational Chemistry, 5, 159-171. https://doi.org/10.4236/cc.2017.54013