1. Introduction
CNT has attracted broad attention in fields such as physics,chemistry,and materials science. Lots of research on CNT,the new one-dimensional molecular material,has been conducted in terms of its unique properties in electronics and mechanics,and its potential application prospects in molecular devices and composite materials. In addition,researchers and experts have also conducted extensive researches on CNT preparation,structure,properties,its optical and electric properties,and its mechanical properties under loading,for example: Faria[1] conducted research on CNT anisotropic behaviors,stiffness and strength under stretching or loading conditions (6,3); Tada[2] studied the mechanical properties of SWNT,such as stretch,contraction and torsion; Jeong[3] studied the mechanical properties of hollow or filled SWNT in the molecular dynamics simulation test; Wu[4] studied the optical properties of primitive and doped nanotube,for example,Raman spectrum; and,Karimov[5] found that CNT facilitates the production of novel pressure and displacement transducers. Most researchers have conducted their research based on ideally perfect structures,while in fact the CNT produced through physicochemical methods almost unavoidably has defects in the modular structures,such as carbon atom vacancy,absence of carbon-carbon covalent bond and topological defects. Zhang[6] revealed the influence law on SWNT mechanical properties caused by different SWNT defects,defect quantities,and arrangement by conducting axial tension and pure twisting to SWNT with defects. Zhang[7] found that CNT is much more stable when the vacancy defect is lower than 6.25%,and not stable when the vacancy defect is within 6.25%-12.50%. Zhang Lijuan found the total energy of the SWNT system with nitrogen topological defects decreases while the bond becomes more stable; in addition,half-full impurity band appears nearby the Fermi level. Sharma[8] studied the influence of defects on CNT mechanical properties. Partovi-Azar{ [9],Zhou[10] found that different CNT defects lead to various electronic properties. Since deformations and defects have significantly different influence on the electrical properties of CNT,the research on the difference of influence of tension-twisting deformation and different types of defects on optical and electrical properties of CNT help develop CNT photoelectronic primitives,which have potential application value in semiconductor devices,probes,internal contacts of electronic devices and other fields[11, 12]. Although the above experts have conducted broad researches on CNT,few of them are related to the optical and electronic properties of doped CNT,or CNT with tension-twisting deformations or defects. It is well-known that most armchair carbon nanotube superlattices doped with B and N in a cyclic alternative way are metallic,indicating that their band gap is zero. Nevertheless, CNT will become a semiconductor with non-zero band gap if it is doped with B and N in an alternative and cyclic manner. In order to further transform optical and electrical properties of such semiconductor,this paper has investigated the optical and electrical properties of B,N doped CNT to see if it suffers from any tension-twisting deformation or defects. Considering its large surface area and good conductivity,CNT might be developed into a kind of ideal electrode material offering electrical double-layer capacitor. This means that the capacitor will have higher energy and higher power density. The research on the energy gap of materials in this paper is only related to CNT conductivity. In addition,carbon nanotube film is expected to replace common conducting metallic oxide film in the production of flexible organic solar cells or organic light-emitting devices. In this paper,dielectric function real part and refractivity are calculated to interpret its relevant optical properties and provide reference for its application in photoelectronic devices. Our calculations show that carbon nanotube film can be used as an optical transparent electrode.
2. Calculation method
This paper has optimized and simulated B,N doped carbon nanotube superlattices with tension-twisting,or defects,or mixed type based on the Perdew-Burke-Ernzerhof (PBE) functional in generalized gradient approximation (GGA) of density functional theory (DFT) by means of CASTEP quantum mechanics program module in MS6.0. Ultrasoft pseudopotential{ [13, 14] } is used to deal with the interactions between the ion core and the electron in the process of module optimization. In reciprocal lattice space,the cut-off energy of plane wave is set as 380 eV,and K-point lattices as specially high-symmetry brillouin zone integral in 1 × 1 × 10 Monkhorst-Pack; convergency of iteration precision refers to the total energy of an atom,which is smaller than 1.0-6 eV/atom and the total atomic power smaller than 0.01 eV/Å and 0.1 GPa. Before calculation of relevant electronic structures and optical properties of the model,geometric optimization should first be done to the model.
3. Discussions about calculation results
3.1 Structural models and its stability
A system optimization model is established as shown in Figure 1. First,replace the carbon atoms in the first sphere of (5,5) armchair carbon nanotubes,and then dope it with B and N atoms in a cyclic and alternative way. In the module,each sphere contains 10 atoms,in which the blue ones are N atoms,the pink ones B atoms,and the gray ones C atoms. In other words,5 N atoms and 5 B atoms are alternatively doped into the end of finite-length (5,5) armchair carbon nanotubes,the scenes of twisting deformation,axial tension deformation and three defects are simulated,and this model is optimized according to the relevant parameters specified in the calculation method. Figures 1(a)-1(f) demonstrates twisting-tension deformation to the B and N doped carbon nanotube. Specifically speaking,twist the model to the angle of 0°,3°,6°,9°,12°,and 15° and then stretch 5% in the axial direction. Figures 1(g)-1(i) separately show C atom absence (atomic defect),C-C bond absence (bond defect),and topological defect (STW defect) of the B and N doped carbon nanotube. Figures 1(j)-1(l) show the B and N doped carbon nanotube with mixed type; that is,with the combination of tension-twisting deformation (stretch 5% and twisting 15°) and atomic defect,bond defect,and STW defect. In this paper,the model is optimized with CASTEP module in MS6.0,only to find that there is no significant change to the structure of optimized model with combined deformations and that the models with other two kinds of defects maintain their tubular structures,except the topological defect,which shows mild depression.

In this paper,the bond length of each model is further calculated. In terms of tension deformation,5% stretch is exerted to all the simulated models while the twisting angles are set as 3°,6°,9°,12° and 15°. As shown in Table 1,compared with the common B,N doped carbon nanotubes,the minimal bond length of those with tension-twisting deformations,defects,and mixed type decreases and the maximal bond length of those increases,except for the model with an atomic defect,whose maximal bond length otherwise increases. The bond length range of the model with bond defects sharply declines compared with the models with other defects. Its maximal bond length is the smallest and the minimal bond length is the largest. Therefore,the system structure with such a defect will suffer the slightest deformation because its structure nearly experiences no change. In addition,the system with STW defects has depressions in its structure but its general bond length does not change very much; therefore,its overall stability is still acceptable.
Twisting angle | 0° | 3° | 6° | 9° | 12° | 15° |
Maximum | 2.989 | 2.914 | 2.914 | 2.918 | 2.915 | 2.915 |
Minimum | 1.406 | 1.403 | 1.403 | 1.402 | 1.403 | 1.403 |
Defects and mixed type | Atom | STW | Bond | 15°+Atom | 15°+Bond | 15°+STW |
Maximum | 2.997 | 2.954 | 2.891 | 2.92297 | 2.91448 | 2.91558 |
Minimum | 1.395 | 1.315 | 1.395 | 1.38397 | 1.40281 | 1.40211 |
In order to study the structural stability of B,N doped carbon nanotube,the binding energy of the system with tension-twisting deformations,defects,and mixed types are respectively calculated. The binding energy is defined as follows:
Ebind=Estru−Eatom. |
(1) |
In the formula,Ebind is the binding energy of the nanotube; Estru the total energy; Eatom the total energy calculated when each atom of the nanotube gets discrete. From the point of view of energy: the lower the binding energy is,the higher the structural stability is. Table 2 demonstrates that bind energy is in different negative values. The binding energy of the system with tension-twisting deformation increases in line with the angle of the twisting angle; that is to say: the greater the deformation is,the lower the stability is. Compared with intrinsic carbon nanotubes,the stability of B,N doped carbon nanotubes decreases but it can still maintain stability because its structure suffers no significant changes. The B,N doped carbon nanotube with tension-twisting deformation is more stable than those without such deformation but their stability experiences no significant changes. Among the system with the three kinds of defects and mixed types,the stability in sequence from high to low is: bond defect,STW defect and atomic defect,indicating that defects play a more significant role than tension-twisting deformation in system stability.
Intrinsic | Doped | Twisting angle | |||||
0° | 3° | 6° | 9° | 12° | 15° | ||
–364.278 | –348.284 | –350.68 | –350.66 | –350.60 | –350.58 | –350.53 | –350.68 |
Defect types | Mixed types | ||||||
Atom | STW | Bond | 15+CAtom | 15+CBond | 15+CSTW | ||
–512.75 | –521.97 | –526.68 | –342.836 | –356.652 | –356.593 |
3.2 Electronic structures of B,N doped carbon nanotube
3.2.1 Influence of tension-twisting deformations and defects on the band gap of B,N doped carbon nanotubes
The energy gap plays an essential role in the electronic structure of materials. In order to further analyze the electronic structure of the system,this paper has calculated the energy gap of the system with tension-twisting deformations and defects. As shown in Table 3,on the premise that the system suffers a stretch of 5%,if the twisting angles smaller than 12° are exerted to the system,its energy gap is smaller compared with the B,N doped carbon nanotubes without deformations; however,if the twisting angle is 12° or 15°,then the energy gap of the system increases. If there is another kind of defect in the system,then the energy gap decreases about 0.6 eV in comparison with the B,N doped carbon nanotubes without deformations,indicating that the defect damages the system symmetry and the structural asymmetry will further lead to unsymmetrical charge distribution. Because of this defect,the bonding structure is changed and electric charge reallocated. Therefore,the electronic transport properties of the system increases,and so does the conductivity; while the semi-conductivity declines,and its metallicity increases. In this paper,further research on the system with both tension-twisting deformations and defects (i.e. stretch of 5% and twisting angle of 15°,together with separately atomic defect,bond defect,STW defect or mixed types) found that the system with the twisting angle of 15° and atomic defect has a much larger energy gap than the system with single tension-twisting deformation or defect,providing an effective way to improve the semi-conductivity of B,N doped carbon nanotubes.
Twisting angle | |||||
0° | 3° | 6° | 9° | 12° | 15° |
0.987 | 0.943 | 0.952 | 0.948 | 1.001 | 1.015 |
Defect types | Mixed types | ||||
STW | Atom | Bond | 15+CAtom | 15+CBond | 15+CSTW |
0.246 | 0.319 | 0.349 | 1.402 | 1.000 | 0.984 |
3.2.2 Influence of tension-twisting deformations on the density of states (DOS) and Fermi level of B,N doped carbon nanotubes
The electronic structure is necessary to be interpreted by the density of state at the micro level,which can bring forth visible results to the electronic structure. Figure 2 shows the impurity band appearing at the Fermi level Ef by calculating the density of state of parts of the B,N doped carbon nanotubes with tension-twisting deformations. Due to the electron gain or loss of B,N atoms,donor level and acceptor level are shaped and then an impurity band is formed by their combined actions. From Figure 2,it is seen that different twisting angles make the electronic density of state at the Fermi level of the system diversified. When the twisting angle ranges from 0° to 9°,there is little difference. When the twisting angle is 0°,the density of state is 2.083 eV-1; when the twisting angle is 3°- 9°,the density of state is 2.403 eV-1; while when the twisting angle is 12° and 15°,the density of state at the Fermi level is 1.556,1.458 eV-1 respectively. From the above data,it can be concluded that tension-twisting deformations increase the electron barrier of the surface of the B,N doped carbon nanotubes and constrain more electrons in the system from migration. This way,the conductivity of B,N doped carbon nanotubes is decreased to make it easier to demonstrate the properties of a semiconductor. This conclusion is consistent with the calculated energy gap of the system with the twisting angles of 12° and 15°.
3.3 Influences of tension-twisting deformations and defects on the optical properties of B,N doped carbon nanotubes
This paper further calculated the optical properties of the system with tension-twisting deformations,defects and mixed types. Figure 3 shows the real part of dielectric function and refractivity of the system. From the dielectric function graph [Figures 3(a) and 3(b)],it is seen that all the real parts of NBCNT dielectric functions are larger than zero. The formula of dielectric function and refractivity, ε=(n+ik)2 in which ε is dielectric function,n the real part of the refractivity,i the imaginary unit,and k the imaginary part of the refractivity,demonstrates the semiconductor properties of the system. The real and imaginary parts of the refractivity of the system with tension-twisting deformation are shown in Figures 3(d)-3(g),from which it is seen that the scope of real part is 0-2.5 and that of the imaginary part is 0-1.4,which is larger than the refractivity of corresponding wave length within 320 nm. The real part is larger than the imaginary part in value,which indicates that the system suffering tension-twisting deformation still mainly demonstrates the properties of a semiconductor. In addition,this paper calculates the real part of the dielectric function and refractivity of the system with defects and mixed types. The conclusion is that same as above,that is to say: the real part of the refractivity is larger than the imaginary part,the real part of dielectric function is always positive and the system demonstrates the properties of a semiconductor in general,as shown in Figures 3(e),3(h) and 3(f),3(i). In addition,the electronic structure of the system is the same as that mentioned above. What is interesting is that when the incident wavelength is short (i.e. the incident photon energy is high,for example,the wave length is within 160-320 nm shown in Figures 3(a) and 3(b) below),the system with tension-twisting deformation (except the twisting angle of 15°) and defects has a negative real part of dielectric function,and the real part is smaller than imaginary part in refractivity,while the system will demonstrate metallicity. In other words,the electron can be energized to leap into another conduction band by absorbing enough energy offered by incident photons with different energies so as to enhance the electronic transport properties and electric conductivity and change the system property from semi conductivity to metallicity.
4. Conclusions
In this paper,analog calculation is conducted to the B,N doped nanotubes with tension-twisting deformations,defects,and mixed types by means of CASTEP module of density functional method and MS6.0 to analyze the relationship between binding energy,bond length,energy gap,density of state,dielectric function,and refractivity of the system and its stability,bonding nature and electronic transportation properties. Our research has found that tension-twisting deformations,defects,and mixed types make an insignificant difference to the geometrical structure of carbon nanotubes. When the system contains STW defects,a depression appears in its geometrical structure. Nevertheless,tension-twisting deformations,defects,and mixed type change the stability of B,N doped carbon nanotube superlattices. The larger tension and twisting angle are exerted,the lower the system stability is. B,N doped carbon nanotube superlattices with tension-twisting deformation,defects and mixed type still demonstrate semi conductivity. The optical properties of the system with tension-twisting deformation and defects show that the semi-conductivity of the system can be transformed into metallicity by adjusting the optical wave energy.