Nano-solenoid: helicoid carbon-boron nitride hetero-nanotube.

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Nanoscale View Article Online

DOI: 10.1039/C3NR02914J

Nano-Solenoid: Helicoid Carbon-Boron Nitride Hetero-Nanotube Zi-Yue Zhang, Chunyang Miao, and Wanlin Guo* State Key Laboratory of Mechanics and Control of Mechanical Structures,

Education and Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China *Corresponding author. E-mail: [email protected]

As a fundamental element of nanoscale passive circuit, a nano-inductor is proposed based on a hetero-nanotube consisting of a spiral carbon strip and a spiral boron nitride strip. It is shown by density functional theory associated with nonequilibrium Green function calculations that the nanotube exhibits attractive transport properties tunable by tube chiral, diameter, component proportion and connection manner between the two strips, with excellent ‘OFF’ state performance and high current on the order of 10-100 µA. All the hetero-nanotubes show negative differential resistance. The transmission peaks of current are absolutely derived from the helicoid carbon strips or C-BN boundaries, giving rise to a spiral current analogous with an energized nano-solenoid. According to Ampere’s Law, the energized nano-solenoid can generate uniform and tremendous magnetic field more than 1 tesla, closing to that generated by the main magnet of medical nuclear magnetic resonance. Moreover, the magnitude of magnetic field can be easily modulated by bias voltage, providing great promise for a nano-inductor to realize electromagnetic conversion at the nanoscale. 1

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Page 2 of 33 View Article Online

DOI: 10.1039/C3NR02914J

1. Introduction Electric circuits are considered to be made up of four fundamental passive circuit elements: the resistor, the capacitor, the memristor and the inductor. With the

expected to break the physical and geometrical limits and generate new device paradigms based on plenty of nanoscale materials. The nano-resistor and nano-capacitor have attracted wide research attention. For example, diamond and cubic BN are proved to be pretty nano-resistors due to well insulating nature as well as high chemical and thermal stabilities.1-3 High capacitance structures using nanowires4,

5

and single- or multi-walled nanotubes6-10 have been investigated

widely. Even the last proposed memristor has been studied11 and realized at the nanoscale.12, 13 However, there are few studies on the nano-inductors independent of existing silicon technology. As a key monolithic passive component, the nano-inductor is especially necessary in order to develop highly integrated circuit. The inductor is usually a coil of wire wrapped around vacuum or some ferromagnetic materials, called solenoid, as shown in Fig. 1a. A nearly uniform magnetic field can be generated with a steady current flowing through the solenoid, while a time-varying current creates a electromotive force opposing the change of current in both the solenoid itself (self-inductance) and in any nearby conductors (mutual inductance). If accomplished the solenoid at the nanoscale, what is the suitable structure? A sort of novel mixed carbon-boron-nitrogen nanotube made up of helicoid carbon (C) and boron nitride (BN) strips entered our 2



continued need of miniaturization in electronic devices, these circuit elements are

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line of sight for its three key advantages. Firstly, advanced technologies allow the fabrication of many mixed C-BN nanotubes with controlled diameter and component14-20. Secondly, carbon and BN strips show huge different properties

hetero-nanotubes with C and BN which is curled from hetero-nanoribbons, the carriers for the nearest states of the Fermi level (Ef) are derived from the C-B and C-N boundaries (armchair tubes) or from the carbon parts (zigzag tubes).26 This indicates the possibility that the carriers can move along the helicoid channels with bias voltage to form a current in helicoid C-BN nanotubes [C-(BN)NTs]. Finally, the hollow cylinder structures can be filled with ferromagnetic materials to improve the magnitude of magnetic field and inductance. Recent experiments have shown that when carbon nanotubes are filled with iron nanowires or particles, their alternating current impedance spectra exhibit an inductive phase.27-30 Although numerous studies have demonstrated nano-devices and applications based on mixed C-BN nanotubes, the helicoid construction of C-BN hetero-nanotube and using it as nano-solenoid to realize electromagnetic conversion is a unique and novel proposal. Our study is based on the architectural designs of nano-solenoid devices built on the helicoid C-(BN)NT, where the helicoid carbon strip is deemed as wrapped metallic wires. We illustrate the intrinsic current-voltage characteristics of four constructions for helicoid C-(BN)NT by the density functional theory and nonequilibrium Green function calculations. The results show that these

3



ranging from small gap semiconductors to wide gap insulators.21-25 Therefore, in

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constructions exhibit versatile transport properties in relation to their electronic properties, which can be varied through modulating the tube diameter and the chemical ratio of carbon and BN strips. Furthermore, all the helicoid C-(BN)NTs

potential device applications.31-33 Importantly, it is found that the transmission peaks of current, especially the two peaks near the Ef, are absolutely derived from the carbon strips or the C-BN boundaries, suggesting the existence of the helicoid channels for current. Altering bias voltage can easily control the change of current in tubes, thereby switch the magnetic field. The largest magnetic field is calculated to be 1.53 T, which is approximately to that generated by the main magnet of medical nuclear magnetic resonance. With the altering of current, the mutative magnetic flux will induce an electromotive force that opposes the change in current, giving rise to a self-inductance. Based on our results, we believe that the helicoid C-(BN)NT is a novel nano-solenoid, filling the blank of the nano-inductor devices and consummating the fundamental elements of the nano-circuit.

2. Methods and models 2.1 Computational details

In this letter, all the first-principles calculations are carried out on the basis of the density functional theory (DFT),34 as implemented in the Vienna ab initio simulation package.35,

36

In our calculations, the generalized gradient 4



show negative differential resistance (NDR) feature, which has a wide range of

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approximation (GGA) is employed to describe the exchange-correlation potential. The energy cutoff is chosen to 435 eV and the Brillouin zone is sampled with 1×1×26 Monkhorst meshes. A unit cell is set up with one-dimensional periodic

adjacent tubes is 1 nm, eliminating the effect of direct tube-tube interaction. The structures were fully relaxed using the conjugate gradient method until the force on each atom is less than 0.1 eV/nm. These parameters have been validated in our previous works.26, 37 For the transmission values, the scattering part and two electrodes are described by single-ζ plus polarization basis sets and the GGA, implemented in the SIESTA package38 at first to get related density matrix elements. The electronic transport properties are studied by the non-equilibrium Green's function (NEGF) techniques within the Keldysh formalism as implemented in the TRANSIESTA package.39 30 points of contour integration on the imaginary plane is used to obtain the density matrix from the Green’s function. A cut off energy of 300 Ry for the grid mesh is employed to have converged transmission values. The current through the contact region is calculated using the Landauer-Buttiker formula,40 µL

I (Vb ) = G0 ∫ T ( E ,Vb )dE , µR

(1)

where G0 = 2(e 2 / h) is the unit of quantum conductance and T ( E , Vb ) is the transmission probability of electrons incident at energy E under potential bias Vb. The electrochemical potential difference between the two electrodes is

5



boundary condition along the tube axis and the vacuum space between two

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eVb = µL − µR .41, 42

2.2 Computational models

and a helicoid BN strip with C-B and C-N bonds. C-BNNTs can be divided into four groups according to the tube chirality and connection manner (Fig. 1b): zigzag tube with zigzag connection between C and BN strips [zzCm-(BN)n-mNT], zigzag tube with armchair connection between C and BN strips [zaCm-(BN)n-mNT], armchair tube with zigzag connection between C and BN strips [azCm-(BN)n-mNT], and armchair tube with armchair connection between C and BN strips [aaCm-(BN)n-mNT]. n and m are integers, where n denotes either the total number of armchair chains in zigzag nanotubes, or hexagon chains in armchair nanotubes, along their respective tube axes, and m denotes the chains that start with carbon dimer from any sections. For example, since there are six armchair chains along the tube axis and three starting with carbon dimmer (circled with dashed lines) in the section of (6, 0) C-(BN)NTs, we marked them as zaC3-(BN)3NT and zzC3-(BN)3NT, which have armchair and zigzag connection manner between C and BN strips, respectively. The super cells for the calculations are shown in rectangular boxes. For zzCm-(BN)n-mNT, azCm-(BN)n-mNT and aaCm-(BN)n-mNT, the super cells contain n, n and 3n unit cells, respectively. The situation is more complex for zaCm-(BN)n-mNT: when n = 3q (q is an integer), the super cell is comprised of n/3 unit cells; when n = 3q-1 and n = 3q-2, the super cells are made

6



The C-BNNT we studied is formed by the connection of a helicoid carbon strip

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up of n unit cells.

3. Results and discussion

known that their WFs have only a slight change in values, as compared to pure carbon nanotubes with the same diameters (see Supporting Information Table S1). This allows us to use metallic carbon nanotubes as electrodes to build a transport system. A common feature of carbon nanotube-based devices fabricated to date has presented a Shottky barrier at the nanotube-metal junctions.43, 44 This energy barrier severely limit transistor conductance in working state, and reduce the current delivery capability. This difficulty may be circumvented by designing and constructing device architectures based on nanotubes absolutely for avoiding a large contact resistance between the metal electrodes and nanotubes induced by a very small contact area. Due to the similar work function of helicoid C-(BN)NT and pure carbon nanotube, the “ON” states of semiconducting helicoid C-(BN)NTs can behave like in ohmical contact with metallic carbon nanotubes. Thus, our investigation focused primarily on four kinds of helicoid C-(BN)NTs coupled to perfect carbon nanotube electrodes with the same diameters. Typically, Fig. 3a is the schematics of helicoid C-(BN)NT-based transport device, made from one aaC2-(BN)2NT channel connected to two (4, 4) armchair metallic CNT leads. The channel lengths for all four kinds of helicoid C-(BN)NTs are at least 2.0 nm, guaranteeing that they are long enough such that the center of the devices has the

7



From the calculation of the work function (WF) of helicoid C-(BN)NTs, it is

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electronic properties of a very long nanotube. And every electrode is made up of four unit cells in most of the calculations. We have studied the current-voltage (I-V) characteristics of zzC3-(BN)3NT,

values of current of the armchair tubes appear basically symmetrical behavior, suggesting that they are excellent ambipolar transistors. However, the symmetry of current in zigzag tubes is relatively worse, where the positive current is clearly greater than the negative current. This difference can be ascribed to unequal work function at both ends of zigzag helicoid C-(BN)NTs. The I-V curve of zzC3-(BN)3NT clearly shows the linear characteristic in the bias window [-8V, 8V], which suggests the system being of the metallic behavior. It is well consistent with the electronic properties calculated by VASP, as shown in Fig. 2a. Comparing with metallic pristine (6, 0) and (4, 4) CNTs, the current of zzC3-(BN)3NT is notably smaller than the former but larger than the latter. To quantitatively describe the current variety of the tubes, we obtained the resistances of them in [-2V, 2V] applied bias voltage by linearly fitting of their I-V curves. The results indicate that the resistance of zzC3-(BN)3NT is 19.46 kΩ, which is 11 kΩ increased and up to 32 kΩ reduced comparing with that of the pristine (6, 0) and (4, 4) CNTs, respectively. To clarify the transport mechanism, the bias dependent transmission curves T(E, Vb) are presented in Fig. 4a. Since zzC3-(BN)3NT is metallic, the peak of T(E, Vb) around Ef is contributed from both the valence band maximum (VBM) states and the conduction band minimum

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zaC3-(BN)3NT, azC2-(BN)2NT and aaC2-(BN)2NT, see Fig. 3. The numerical

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(CBM) states. At zero bias, there are four transmission peaks corresponding to the EVBM-1, EVBM, ECBM and ECBM+1 from left to right, respectively. With the increase of bias, the peaks of EVBM-1, EVBM and ECBM remain in almost the same positions,

transmission peak in the right edge of the bias window. As a consequence, more and more transmissions of zzC3-(BN)3NT come into the bias window, which contributes more and more efficient current channels with linearly increased bias. In sharp contrast to the linear behavior of the metallic zzC3-(BN)3NT, the I-V curves of zaC3-(BN)3NT, azC2-(BN)2NT and aaC2-(BN)2NT are flattened over a small bias range, where the current approaches zero, displaying typical semiconductor I-V characteristics. In fact, our VASP calculation has shown the semiconducting properties of zaC3-(BN)3NT, azC2-(BN)2NT and aaC2-(BN)2NT, which have finite energy gaps of 0.49, 1.04 and 0.67 eV, respectively, as seen in Fig. 2b-d. The threshold voltage of azC2-(BN)2NT with 2 nm channel length is 0.2 V, which is slight smaller than zaC3-(BN)3NT, while the ‘ON’ state of aaC2-(BN)2NT occurs at about 1eV. However, the open current of azC2-(BN)2NT is enlarged twice over that of zaC3-(BN)3NT while the current of aaC2-(BN)2NT is the largest among them. This indicates the independence of threshold voltage and open current on the energy gap for different types of tubes. The performance of the semiconducting C-(BN)NT-based transport devices can be understood in terms of metal-semiconductor tunneling junctions within the semiclassical band-bending model. At zero bias, Ef is considered to be located at the midgap of the

9



while the peak of ECBM+1 shifts left and gradually disappears with merging into the

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semiconducting channel because both the metal leads and the semiconducting channel have similar WFs. Thus，the carriers cannot transport through the channel since they experience an energy barrier at the metal-semiconductor junction at this

channel is raised or lowered resulting in the bending of valance or conduction band, as shown in Fig. 5a. At the same time, the electrostatic potentials of the left and right electrodes (µL and µR) have the following relations: µL = EF + eVb/2, µR = EF - eVb/2.

(2)

For the case of applying positive bias, µL (µR) will be raised (lowered) and the conduction band of channel will bend downwards causing a thinning of barrier at the metal-semiconductor interface. Conversely, with negative bias, µL (µR) is lowered (raised) and the valance band of channel bends upwards. When a large enough bias is applied, electrons (holes) can tunnel from the left electrode into channel and than from channel into the right electrode. In this way, helicoid C-(BN)NTs will stay in the ‘OFF’ state with small bias and will be switched on at a large enough bias. We noticed a common occurrence in the I-V characteristics of all the four kinds of helicoid C-(BN)NTs, as shown in Fig. 2, where the current decreases with increasing bias voltage, inducing nonlinear transport properties in the systems. This is known as the negative differential resistance (NDR) phenomenon. The appearance of NDR under positive and negative voltage is asymmetric, where

10



moment. When a bias voltage Vb is applied, the electrostatic potential in the

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slight higher voltage is needed at positive voltage region. For example, the peak currents are 12.65 µA at 1.0 V, 6.33 µA at -0.6 V and the valley currents are 10.06 µA at 1.2 V, 2.13 µA at -0.8 V in azC2-(BN)2NT. In contrast with the other tubes,

voltage around Vb = 10 V. Interestingly, the I-V curve of zaC3-(BN)3NT exhibits NDR twice with negative bias, with dips in the current occurring between 0.8 to 1.0 V bias and 1.2 to 1.4 V. In order to investigate the physical origin of the NDR and ‘ON/OFF’ trend in the current of these helicoid C-(BN)NTs, we show the bias dependent transmission spectrum in Fig. 4. For simplicity, here we just consider applying positive bias voltage. Taking azC2-(BN)2NT as an example, four peaks are visible in the zero-bias transmission spectrum within a 1.4 eV energy window, in which two peaks near Ef are corresponding to the EVBM and ECBM. The energy gap between EVBM and ECBM is calculated to be 1.0 eV, in good agreement with the result from the calculation by VASP package. When applying bias, the peaks below (above) the Fermi energy will shift right (left). Under small bias, no transmission peaks move into the bias window, leading to ‘OFF’ state of the system. When the bias voltage is enhanced to 0.4 V, the transmission peaks of EVBM and ECBM touch the left and right chemical potential, respectively. The carrier hopping between the electrodes and the scattering region is good for transport, resulting in an initial increase in current. The increase of bias also simultaneously reduces the peak heights and decreases the weight of the

11



the NDR phenomenon of metallic zzC3-(BN)3NT occurs in the region of high

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transmission spectrum in the bias window. However, the shift of transmission peaks with high energy will compensate for the height reduction of low-energy peaks, so that the heights of some transmission peaks seemingly look increasing.

always touch the transmission peaks below 1.0 V bias. At the same time, more and more transmission spectrums move into the bias window with increasing voltage, leading to the durative growth of current within 0.4~1.0 V bias. It is worth noting that µL and µR are both located in the gap of two transmission peaks at 1.2 V bias, where the hopping of carriers becomes difficult. This leads to a net drop in current and the onset of NDR. At a bias of 1.4 V, the transmission peaks touch the chemical potential of electrodes again, giving rise to the end of the NDR phenomenon and the beginning of an increase of the currents from their valley values. A similar explanation holds for other helicoid C-(BN)NTs. In conclusion, if there are energy gaps between two adjacent VBM or CBM states, by which when the chemical potentials of the electrodes touch with non-zero bias voltage, the NDR phenomenon can appear. To identify the nature of states giving rise to the transmission peaks, we analyze the electrons distribution of VBM and CBM states for these tubes by VASP calculation. As shown in Fig. 2, VBM states completely concentrate at C-B boundary and CBM states are mainly located at C-N boundary in zigzag connection tubes. However, the VBM and CBM states are mainly contributed by C-C bonds in armchair connection tubes. This difference can be easily understood

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The shift of transmission peaks and the expanding of bias window make µL and µR

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by treating carbon parts in helicoid C-(BN)NTs as curled graphene nanoribbons, where the ribbons with zigzag edges have localized states at the zigzag edges and uniform distribution of CBM and VBM can be seen in ribbons with armchair

states are consolidated for armchair C-(BN)NTs and weakened for zigzag ones. Owing to the weakened localization of electrons for VBM and CBM states, the energy gaps for zigzag C-(BN)NTs are smaller than armchair ones. Especially in zzC3-(BN)3NT, the valence bands and conduction bands with low energies can easily become half-filled bands that cross over Ef, inducing its metallic properties. Regardless of their origins, the CBM and VBM states are all spirally coiled along the tube axis, giving rise to the transmission peaks. This indicates that carriers will move along the helicoid channels at ‘ON’ state to form current. On the other hand, there is no conduction in BN nanotubes with no more than 10 V bias voltage because of their wide band gaps.45 Thus, it is reasonable to believe that the currents through helicoid C-(BN)NTs are primarily determined by the properties of carbon strips. To further identify the origin of the current, we separated the carbon strip and BN strip, and calculated their transport properties individually. From the I-V characteristics, as shown in Fig. 5b, we find that individual spiral carbon strips all exhibit the nature of the conductor with bias. With exception of the BN strip from zzC3-(BN)3NT generating finite current, the other BN strips demonstrate their insulative properties, suggesting that the transport channels of zaC3-(BN)3NT,

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edges21. With different manners of curliness, the distribution of VBM and CBM

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azC2-(BN)2NT and aaC2-(BN)2NT are helicoid determined by carbon strips. For the particularity of carbon and BN strips from zzC3-(BN)3NT, we have analyzed their origin of transmission peaks. It is found that the transmission peaks in carbon

those in BN strip result from B and N edges. Therefore, the transport channel in integrated zzC3-(BN)3NT is also helicoid rooting in C-N and C-B boundaries with diffusing to the center of carbon strip. On the other hand, it is noticed that the current in carbon strip from zzC3-(BN)3NT is lower than that in integral nanotube, while the currents in the other three carbon strips is much larger compared with their corresponding C-(BN)NTs. Therefore, the high current in zzC3-(BN)3NT can be recognized as the superimposed effect of carbon and BN strips. However, in zaC3-(BN)3NT, azC2-(BN)2NT and aaC2-(BN)2NT, the presence of BN strips suppresses the increase of current with low bias, giving rise to the ‘OFF’ states of nanotubes. When the threshold voltage is arrived, the suppress effect of BN strip can not contend with the increase of current in carbon strip and the tube will display ‘ON’ state. Interestingly, the helicoid currents along the tube axis remind us of solenoids which are familiar in macroscopic physics. As we all known, magnetic field can be generated in energized solenoid, the magnitude of which is determined by Ampere’s law: B = µ 0 nI ，

(3)

where µ0 is the permeability of vacuum, n is the number of coils per unit length

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strip are derived from the two carbon edges with diffusing to the center, while

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and I is the magnitude of current through the solenoid. Analogously, the helicoid C-(BN)NT can be described as a nano-solenoid, the ‘wire’ is carbon strip. With sufficient bias voltage, there will be spiral current passing through the nanotube. If

for magnetic field excitation is born. More importantly, the bias voltage can effectively modulate the ‘OFF/ON’ and magnitude of magnetic field. Fig. 6a shows the calculated magnetic field for the four helicoid C-(BN)NTs as a function of bias voltage. Corresponding to their I-V curves, the magnetic fields for zaC3-(BN)3NT, azC2-(BN)2NT and aaC2-(BN)2NT are nearly zero at low bias but begin to increase with application of a sufficiently high bias voltage. The magnitude of magnetic field will oscillate with the emergence of the NDR phenomenon.

While

for

zzC3-(BN)3NT,

the

magnetic

field

increases

monotonically with the increasing bias in a large voltage region. In the [-2V, 2V] bias window, the magnetic field can reach 250 gauss (=0.025 T) for helicoid C-(BN)NTs, a value 25 times larger than that of a giant horseshoe magnet. The largest magnetic field that we can calculate is 1.53 T for azC2-(BN)2NT at 20 V bias voltage, the value of which is approximately to that generated by the main magnet of medical nuclear magnetic resonance. Other than a magnetic field, any electric current can also produce a total magnetic flux in an energized solenoid. With a change of current, the magnetic flux will change as well, inducing an electromotive force that opposes the change in current. The ratio of the magnetic flux to the current is called the

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the macroscopic Ampere’s law is also applicable here, a novel nano-scale device

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self-inductance, customarily denoted as the symbol L. The quantitative definition of L for a solenoid is:

L = µ 0 n 2lS ,

(4)

self-inductance is independent of current but proportional to the diameter and length of the solenoid. Therefore, the increase of channel length and tube diameter will directly enhance the value of self-inductance in our nano-solenoids that is shown in Fig. 6b, while other structure parameters will not work on the self-inductance value. Due to small size of our calculation model, the self-inductances of helicoid C-(BN)NTs are estimated on the order of 10-15 H. In practice, the length and diameter of the tube is much larger, and some ferromagnetic materials such as iron can be filled in the tube, consumedly enhancing the electromagnetic induction. However, according to formulae (3), the alteration of channel length, C/BN ratio or tube diameter itself cannot change the magnitude of magnetic field by treating helicoid C-(BN)NTs as solenoids. Instead it will cause the movement of current resulting in the variation of the magnetic field. Thus, it is necessary to further investigate the transport performance of helicoid C-(BN)NTs with various lengths, diameters and component proportions. Fig. 3d shows the current in azC2-(BN)2NT with different channel length as a function of bias. Evidently, the growth of channel length does not influence the transport properties of semiconductor, but the threshold voltage is enhanced. For example, the threshold voltage of azC2-(BN)2NT with 3 nm length is enlarged to

16



where l is the length of solenoid and S is the cross sectional area. The

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about 1.0 V, which is 0.6 V larger than with 2 nm length. Similarly, the threshold voltage will be enlarged with the increase of electrode unit length as well, as seen in aaC2-(BN)2NT (Fig. 3e). A similar case also appears for other helicoid

On the other hand, the transport properties of helicoid C-(BN)NTs can be modulated by component proportion and tube diameter as well. As shown in Fig. 3c, the threshold voltage for helicoid zaCm-(BN)6-mNTs will decrease with increasing C/BN ratio. When C:BN = 4:2, the I-V characteristic will even exhibit obvious conductor property. The reason can be traced back to the effect of C/BN ratio on the band gap of helicoid tubes that the band gaps will increase (decrease) with decreasing (increasing) C/BN ratio, as seen in Supporting Information Fig. S1. The tubes may turn from semiconductors to metals with enough wide carbon strips, taking zaC4-(BN)2NTs and azC3-(BN)1NTs for example. On the other hand, the influence of tube diameter on the transport properties of helicoid C-(BN)NTs is illustrated in Fig. 3f-g represented by azC-(BN)NTs and zaC-(BN)NTs. When the diameter increases, the threshold voltage will decrease for zaC-(BN)NTs, while the trend is opposite for azC-(BN)NTs. The different change of threshold voltage is derived from different relationships between band gaps of semiconducting helicoid C-(BN)NTs and tube diameters (see Supporting Information Fig. S1). It is found that the band gaps of zaCm-(BN)n-mNTs (∆n) clearly oscillates with the increase in tube diameters, separated into three groups with a hierarchy of gap size given by ∆3p-1>∆3p+1>∆3p (where p is a positive

17



C-(BN)NTs.

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integer), while the calculated band gaps of azC-(BN)NTs decrease monotonically with the increase of tube diameter. Therefore, an interesting conclusion is produced that the magnitude change of threshold voltage is consistent with

to band gap if the tube size is changed. For example, the energy gap of zaC4-(BN)4NT is 0.67 eV larger than that of zaC3-(BN)3NT, but the threshold voltage for zaC4-(BN)4NT is 0.1 V lower. Differently, zaC2-(BN)4NT has 0.23 eV larger gap compared with zaC3-(BN)3NT, and its threshold voltage is also enlarged to 1.4 V. A few comments are now in order. Firstly, it is fortunate that the NDR phenomenon can still be found in helicoid C-(BN)NTs with altered length of channel or electrode, BN/C ratio and tube diameter, although the increase of these factors will delay the NDR phenomenon to higher bias region. Secondly, the diameter dependent transport properties of helicoid C-(BN)NTs with zigzag chirality can only be investigated qualitatively, because not all the CNTs as electrodes are metallic. The armchair (n, n) CNTs whereas the zigzag (n, 0) tubes

show a metallic behavior,

are semiconductors, except the tube chirality of

n=3k, where k is an integer, which becomes metallic again.46 As a result, the I-V curves of some helicoid C-(BN)NTs like zaC4-(BN)3NT, the chiral of which is (7, 0) cannot accurately and quantitatively be calculated due to the absence of CNT electrode with matching size. Thirdly, the relative stability of helicoid C-(BN)NTs is very important in practice. As these structures have different chemical

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nanotube band gap when the component proportion is altered, while it is contrary

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compositions, the binding energy per atom does not provide a suitable measurement for the comparison of their relative stability. Therefore, we adopt the approach customary used in tertiary phase thermodynamics to account for

helicoid C-(BN)NT, BNNT and CNT are respectively defined as: δG = E(χi) – ∑ χi µi, where E(χi) is the total energy per atom of a nanotube with given i

composition and dimensions, χ i (i = C, BN) is the molar fraction of C atom and BN pair in the nanotube, satisfying the relation

∑

χi = 1, and µi is the chemical

i

potential of the constituent i at a given state. We choose µC and µBN as the total energy per atom (BN pair) of a single infinite graphene and BN sheets, respectively. The results (see Supporting Information Fig. S2) show that the formation energies for helicoid C-(BN)NTs are about 0.3 eV/atom higher than that of CNTs at most, and approximately equal to that of CNTs for tubes with small diameters, suggesting the comparable stability between them. On the other hand, we note that their formation energies are somewhat sensitive to tube chirality: zigzag forms are found to be more stable than armchair ones, and zaC-(BN)NTs are the most favorable configurations compared to the other helicoid nanotubes.

4. Conclusions In conclusion, we have performed density functional theory associated with nonequilibrium Green function calculations to demonstrate the intrinsic current-voltage characteristics of helicoid C-BN hetero-nanotubes. The tubes

19



chemical compositions.47 In this approach the formation energy δG for the

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DOI: 10.1039/C3NR02914J

made from helicoid carbon strips connected with helicoid BN strips can exhibit high current on the order of 10-100 µA, excellent ‘ON/OFF’ conversion performance and tunable transport properties. Moreover, the negative differential

current, it is found the carriers are absolutely derived from the carbon strips or the C-BN boundaries, indicating the existence of the helicoid channels for current. The helicoid current can generate uniform magnetic field, which can be easily controlled by bias voltage. With the altering of current, the mutative magnetic flux will induce an electromotive force that opposes the change in current, giving rise to a self-inductance. Consequently, we believe that helicoid C-BNNTs are architectural designs of novel nano-solenoid, providing great promise of a nano-inductor and supplying a gap of electric circuits at the nanoscale.

Acknowledgments This work was supported by 973 program (2013CB932604, 2012CB933403), the Fundamental Research Funds for the Central Universities and Funding of Jiangsu Innovation Program for Graduate Education (CX09B_072Z).

20



resistance phenomenon is found in all tubes. From the analysis about the cause of

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Figure captions

Fig. 1. (a) The schematic structure of macroscopical energized solenoid. The

models of zaC3-(BN)3NT, zzC3-(BN)3NT, azC3-(BN)3NT and aaC3-(BN)3NT. The unit cells in calculations are denoted by dashed rectangle boxes.

Fig. 2. Band structures and the isosurface plots (0.1 e/Å3) of partial charge densities corresponding to the VBM (below) and CBM (above) of (a) zzC3-(BN)3NT, (b) zaC3-(BN)3NT, (c) azC2-(BN)2NT and (d) aaC2-(BN)2NT.

Fig. 3. (a) Schematic illustration of helicoid C-(BN)NT, which is in contact to its corresponding perfect carbon nanotube electrode on the left and right. I-V characteristics of (b) zzC3-(BN)3NT as well as CNT (4, 4) and (6, 0), (c) zaC-(BN)NTs with different C/BN ratio, (d) azC2-(BN)2NT with different channel

lengths, (e) aaC2-(BN)2NT with different lengths of electrodes and (f) azC-(BN)NTs and (g) zaC-(BN)NTs with different diameters.

Fig. 4. Bias dependent transmission curves of (a) zzC3-(BN)3NT, (b) zaC3-(BN)3NT, (c) azC2-(BN)2NT and (d) aaC2-(BN)2NT as a function of energy.

The circles point out the positions of the left and right chemical potentials (µL and µR, respectively). The peaks EVBM-1, EVBM, ECBM and ECBM+1 which are mentioned

in text are marked in the figure.

Fig. 5. (a) Schematic illustration of flatband under equilibrium state (upper panel), 25



generated magnetic field is labeled by orange arrow. (b) Typical ball-and-stick

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as well as band bending under positive (middle panel) and negative (lower panel) bias voltage. (b) I-V characteristics of carbon strip alone (solid) and BN strip alone (open) in zzC3-(BN)3NT, zaC3-(BN)3NT, azC2-(BN)2NT and aaC2-(BN)2NT. The

Fig. 6. (a) Magnetic fields generated by energized helicoid C-(BN)NTs as a function of bias voltage. (b) The self-inductances for C-(BN)NTs with length



inset is the schematic drawings of energized carbon strip.

about 2nm.

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Fig. 1.

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Fig. 4.

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Fig. 6.

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Energized nano-solenoid made from helicoid carbon-boron nitride hetero-nanotube can generate tunable tremendous magnetic field by bias voltage.



DOI: 10.1039/C3NR02914J

Helicoid peripapillary chorioretinal degeneration.

[Goldmann-Witmer, definitive diagnosis in unifocal helicoid choroiditis].

Shell colouration and parasite tolerance in two helicoid snail species.

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Direct access to macroporous chromium nitride and chromium titanium nitride with inverse opal structure.

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PMMA functionalized boron nitride sheets as nanofillers.

Polymeric photocatalysts based on graphitic carbon nitride.

Quantum electromechanics on silicon nitride nanomembranes.

Electrochemical ammonia production on molybdenum nitride nanoclusters.

Stable boron nitride diamondoids as nanoscale materials.

Self-assembled Cubic Boron Nitride Nanodots.

Boron nitride nanomaterials for thermal management applications.

Electronic Biosensors Based on III-Nitride Semiconductors.

Rebar graphene from functionalized boron nitride nanotubes.

Experimental observation of boron nitride chains.

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Novel nanoscroll structures from carbon nitride layers.

Inter-layer potential for hexagonal boron nitride.