Tuning Electronic Structures of BN and C Double-Wall Hetero-Nanotubes

First principle calculations based on density functional theory with the generalized gradient approximation were carried out to investigate the energetic and electronic properties of carbon and boron nitride double-wall hetero-nanotubes (C/BN-DWHNTs) with different chirality and size, including an armchair (n, n) carbon nanotube (CNT) enclosed in (m, m) boron nitride nanotube (BNNT) and a zigzag (n, 0) CNT enclosed in (m, 0) BNNT.The electronic structure of these DWHNTs under a transverse electric field was also investigated. The ability to tune the band gap with changing the intertube distance (d i ) and imposing an external electric field (F) of zigzag DWHNTs provides the possibility for future electronic and electrooptic nanodevice applications.


Introduction
Carbon nanotubes (CNTs) play a very important role in nanodevice applications due to their novel properties.by comparison with CNTs, boron nitride nanotubes (BNNTs) are formed with similar structures, however, of very distinctive properties [1].Of similar crystalline structure, hexagonal boron nitride (h-BN) has been considered as a potential substrate material for graphene [1,2].Recently, the structures of bilayer and trilayer graphene/h-BN have been reported with tunable band gaps for electronic device applications [3][4][5].
Hexagonal boron nitride shares similar crystalline structure with graphene, and it is slightly lattice-mismatched from graphene by about 1.5%, which implies that it is possible to form hetero-nanostructures. BNNTs' growth on CNT has successfully been applied to nanowires [6].Several studies have also been conducted on BN-coated CNTs [7,8].The BNNT around the CNTs effectively helps to protect them and makes them more stable; for example, oxidation degradation of CNTs is reduced by coating with BNNTs, and the thermal stability of CNT@BNNTs is far superior to CNTs [9].
An efficient way to modify the band gap of nanotubes is to apply an external electric field  [10].The response of the nanotube to  is of interest for studying its future application, such as that in logic gates, static memory cells, and sensor devices [11][12][13].Ab initio calculation showed that band gaps of both CNTs and BNNTs can be greatly reduced by a transverse electric filed [14,15].An intriguing question to answer is whether external electric fields can also be an efficient way to modulate the electronic properties of C/BN-DWHNTs.
However, a first-principles study on the stability as well as the electronic properties modulated with   and  of C/BN-DWHNTs is not available.To fill the deficiency, in this work, we performed a series of first-principles calculations to study the coaxial CNT@BNNT and to examine the electric field shielding effect of BNNT on the inside CNT.We calculated the band structures of coaxial CNT@BNNT consisting of armchair and zigzag CNT cores and BNNT sheaths, focusing on the band structure variations with   and .The relative insensitivity of armchair CNT@BNNT to , at least for the few cases considered here, suggests that zigzag CNT@BNNT would be a suitable candidate for double-wall hetero-nanotubes devices.

Calculation Methods
The geometric structure optimization and calculation of the related electrical properties of the CNT@BNNT with no  were conducted using SIESTA [16,17] and adopted normconserving nonlocal pseudopotentials for the atomic core.The Perdew, Burke, and Ernzerhof (PBE) form generalized gradient approximation (GGA) corrections were employed for the exchange-correlation potential energy [18].The atomic orbital basis set employed throughout was double- plus polarization functions (DZP).Periodic boundary condition along the axis was employed for nanotubes.Brillouin zones were sampled by a set of -points grid (1 × 1 × 8) according to the Monkhorst-Pack approximation [19].
When electric field was imposed, the calculation was using density functional theory available in DMol3 code [20,21].The PBE function [22] of GGA was used to calculate the exchange-correlation potential energy, the all electron approach was used, and the orbit population parameter smearing was set at 0.0005 a.u.
Our models were constructed within a tetragonal super cell with lattice constants of  and  equaling 40 Å to avoid the interaction between two adjacent nanotubes and , the lattice constant in  direction along the tube axis, equaling one-dimensional (1D) lattice parameter of the nanotubes.
The tube was taken along the  direction and the circular cross section was lying in the (, ) plane.Both the CNT and BNNTs structures were fully optimized until the force on each atom was less than 0.005 eV Å−1 during relaxation.The van der Waals interactions are very important in twodimensional materials [23], especially in layered structures.The van der Waals force has obvious effect on the adsorption energy and adsorption position and height [24][25][26].In this paper, the distances of the CNT and BNNT are fixed, and the optimization does not change the C/BN-DWHNTs structures.The van der Waals interactions could increase the value of   , but they should not affect the electronic properties of C/BN-DWHNTs [10].
The calculated covalent bond lengths of the various C/BN-DWHNTs in the fully optimized structures are listed in Table 1.For any C/BN-DWHNTs, we define the binding energy per atom as   = [ @  −  C − ( B +  N )]/( + ), where  C ,  B , and  N are the energy of isolated carbon, boron, and nitride atoms, respectively. @  is the total energy of a C/BN-DWHNT,  is the number of C atoms, and  is the number of B and N atoms.The formation energy   (  =  @  −  C  −  BN  ) of each C/BN-DWHNT is also calculated, in which the  C  and  BN  are the binding energy of free standing CNT and BNNT, respectively.
The stability of C/BN-DWHNTs is determined by the interaction force between the inner and outer nanotubes, as shown in Table 1.The formation energy   varying with   was plotted in Figure 1(b).When   = ∼2.60Å,   is positive, which means the free standing CNT and BNNT are favorite in energy.When   = ∼3.5 Å, the armchair C/BN-DWHNTs have the lowest binding energy and formation energy, meaning that the armchair C/BN-DWHNTs at   = ∼3.5 Å are more possible to exist.This result is in agreement with the literature [27], in which Yuan and Liew have studied the coaxial CNT@BNNT nanocables and found that the optimal intertube distances between inner C tube and the outer BN are about 3.5 Å for armchair nanocables.
The calculated band structures of C/BN-DWHNTs are shown in Figure 2. The armchair C/BN-DWHNTs are metallic, with the lowest conduction band and the highest valence band crossing over the Fermi level at ∼2/3 along Γ- direction in reciprocal space.The electric band structure near the Femi level is very similar to the CNTs because the lowest conduction band and the highest valence band are determined by the carbon atoms.We also found that changing   cannot be an efficient way to open the band gap for armchair C/BN-DWHNTs.
The calculated band gaps are listed in Table 1(b).All the zigzag CNT(7, 0)@BNNT structures are found to be direct gap semiconductors with both the valence band top and conduction band bottom at the Γ point.In Figure 3(a), analysis of the PDOS of CNT(7, 0)@BNNT indicated that p orbitals of the carbon atoms dominate the band near Femi level.However, for CNT(7, 0)@BNNT(14, 0), the p orbitals of the nitrogen atoms have a contribution to the bands near the Femi level, which also proved the stronger interaction when the   strayed from ∼3.6 Å. Figure 3(b) shows the DOS of CNT(7, 0)@BNNT(14, 0) and CNT(7, 0)@BNNT(16, 0) DWHNTs.The band gap of CNT(7, 0)@BNNT(14, 0) became small when comparing with the CNT(7, 0)@BNNT(16, 0) during the stronger intertube interactions.After the CNTs were encapsulated into the BNNT, for the stable structure such as CNT(5, 5)@BNNT(10, 10), their geometries changed little.To study the effect of the transverse electric field on the electronic structure of the nanotubes, F along y direction (perpendicular to the tube axis) was imposed.We first examined the electronic properties of Table 1: (a) Calculated bond lengths ( C-C and  B-N ) in the direction of the tube axis () and in the perpendicular direction (), intertube spacing (  ), the unit being Å, the binding energy (  ), and the forming energy (  ) in kJ/mol of different geometrically optimized armchair double-wall hetero-nanotube optimizations.(b) Calculated bond lengths ( C-C and  B-N ) in the perpendicular direction (), intertube spacing (  ), the unit being Å, the binding energy (  kJ/mol) and the forming energy (  kJ/mol) kJmol −1 , and GGA band gap (  eV) of different geometrically optimized zigzag double-wall hetero-nanotube optimizations.(c) The calculated bond lengths ( C-C and  B-N ) of various doublewall hetero-nanotubes, in the direction of the tube axis () and in the perpendicular direction (), and intertube spacing (  ) of different geometrically optimized double-wall hetero-nanotube optimizations; the unit is Å.   the CNT(5, 5) under an electronic field (see Figure 4(a)).The CNT(5, 5) remains semimetallic with an enhancement of density of states around the Fermi level with increasing the eternal electrical field.Two linear bands became flat (localized) around the Femi level in CNT(5, 5) with increasing field strengths.It can therefore be inferred that the conductance will be greatly enhanced.And the results were well consistent with the literature [29].The calculated values of the band structures for the armchair CNT(5, 5)@BNNT(10, 10) at  = 0, 0.1 and 0.15 V/ Å are presented in Figure 4(b).There is no distinct difference between the electronic structures of the CNT(5, 5)@BNNT(10, 10) under different transverse electric fields.It shows that the transverse field does not affect the electric structures evidently.Whereas the band structures for CNT (5,5) under  = 0 and  = 0.25 V/ Å show a striking contrast, the band structures for the CNT(5, 5)@BNNT(10, 10) under  = 0 and  = 0.25 V/ Å are quite similar.The same phenomenon has been found for CNT (6,6)@BNNT(10, 10) and CNT (7, 7)@BNNT (12,12) DWHNTs when  is smaller than critical   (here   is a boundary when  >   , the band structure of armchair CNT@BNNT would change abruptly, when  <   , and the band structure of armchair CNT@BNNT would keep original shape).See the results in Table 1(c); both CNT and BNNT single-walled nanotubes experience large structural changes after geometric optimization with increasing .When  = 0.25 V/ Å, optimized CNT(5, 5) was distortion.
However, with increasing , the DOS of the CNT@BNNT is not a simple superposition of the DOS for the individual CNT and pristine BNNT under .The peak heights for several particular states on the DOS are moderately strengthened or weakened due to the tube-tube interaction.To explore the origin of this phenomenon, the PDOS for C, B, and N in pristine CNT (5,5), BNNT (10,10), and CNT(5, 5)@BNNT(10, 10) under electric fields  = 0 and 0.25 V/ Å was plotted, respectively, as shown in Figure 5.The calculated PDOS indicates that the -states of carbon atoms contribute mainly to the energy levels near the Femi level.The -states of boron and nitrogen in pristine BNNT are very sensitive to the .However, the change is not obvious in the heterostructure, which maybe caused by the effect of the tube-tube interaction.

Figure 1 :
Figure 1: Structure of the optimized CNT(5, 5)@BNNT(10, 10): (a) top view (A) and side view (B).(b) The formation energy   variation versus intertube distance   .I and ◻ are the formation energy of calculated armchair and zigzag DWHNTs, respectively.The solid line was plotted in eyes.