Article pubs.acs.org/JPCC
Vacancy-Induced Intramolecular Junctions and Quantum Transport in Metallic Carbon Nanotubes Hui Zeng,†,∥ Jun Zhao,*,†,∥ Jean-Pierre Leburton,‡ and Jianwei Wei§ †
School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou, Hubei 434023, China Beckman Institute for Advanced Science and Technology, Department of Electrical and Computer Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States § College of Optoelectronic Information, Chongqing University of Technology, Chongqing 400054, China ‡
ABSTRACT: First-principles calculations are carried out to study atomic reconstruction and the electronic structures of metallic armchair and zigzag single-walled carbon nanotubes (SWCNT) in the presence of hexa-vacancy defects. The introduction of hexa-vacancy defects can effectively give rise to the formation of intramolecular junctions in both armchairand zigzag-type SWCNTs. Two kinds of vacancy distribution, six atoms removed along the zigzag chain and a pristine hexagonal lattice, lead to asymmetric and symmetric intramolecular junctions with respect to the axis of the SWCNT after reconstruction, respectively. It is found that the (7,7) symmetric intramolecular junction exhibits more favorable electronic transport compared to the corresponding asymmetric intramolecular junction, whereas the (12,0) symmetric exhibits smaller current in contrast to the asymmetric configuration. This unexpected behavior is attributed to a competition between a widening of the transmission windows that opens additional transmission channels and transport quenching due to orbital misalignment induced by the applied bias.
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INTRODUCTION Owing to their unique electronic and transport properties, single-walled carbon nanotubes (SWCNTs) are promising candidates for the ultimate miniaturization of nanoelectronic integrated circuits.1,2 These quasi-one-dimensional (1D) nanomaterials exhibit either metallic or semiconducting properties depending on their diameter and chirality.3 For this reason, they have stimulated intensive research in a large number of scientific areas,4 which along with their synthesis and characterization, include technological developments with their applications in novel nanoscale devices. Moreover, it has been demonstrated that two SWCNT segments of different diameters and chiralities can be seamlessly joined together to form intramolecular metal−metal, semiconductor−metal, and semiconductor−semiconductor junctions around local defects in the nanostructures.5,6 These remarkable 1D nanostructures anticipate exciting new phenomena with potential applications in nanoelectronics,7,8 such as intramolecular junctions with rectifying properties9 and negative differential resistance behaviors.10 Consequently, SWCNT intramolecular junctions could be functional building blocks in carbon-based nanoelectronic circuits.11 Experimentally, the use of energetic particles irradiation is a powerful technique to create point defects such as pentagon or heptagon in two-dimensional graphene and 1D carbon nanotube (CNT) materials. Recently, Rodriguez-Manzo et al. have demonstrated the possibility of introducing vacancies in CNTs with high precision by controlling the electron beam.12 © 2014 American Chemical Society
Although it was suspected that the presence of vacancy defects introducing lattice disorder deteriorates the performance of carbon-based devices, experimental observations have shown that the various defects could, on the contrary, have beneficial influences in practical applications. This is due to the ability of electron and ion irradiation technology to tailor the atomic structure of CNTs. For instance, it has been shown that the formation of intramolecular junction originates from the reconstruction of vacancy clusters through a series of structural transformations.13 In this context, energetic particle irradiation can be utilized to artificially generate intramolecular junctions in SWCNTs by engineering their atomic structure for controlling their transport properties.14,15 On the theoretical side, first-principles calculations have concluded that the formation of hole-like defects is more favorable for electronic transport compared to the pentagon−heptagon (5−7) pair defects,16 whereas two 5−7 defects separated by a perfect hexagon in hexa-vacancy defected CNT is the most stable configuration in armchair CNTs.17,18 Because the formation of intramolecular junctions is related to the presence of defects in SWCNTs,2 it is crucial to understand the nature of the vacancy defects and their influences on the SWCNTs’ electronic and transport properties. In this article, we conduct a density functional theory (DFT) study on the electronic and transport properties of intraReceived: September 8, 2014 Published: September 9, 2014 22984
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Figure 1. Schematic representation of various intramolecular junction nanostructures after atomic reconstruction. The (7,7) armchair (top panel) and the (12,0) zigzag (bottom panel) asymmetric intramolecular junctions consisting of 5−7−6−7−5 defects (left column of (a) and (c)) are identified as (7,7) 6Va and (12,0) 6Va configurations. The symmetric intramolecular junction consisting of 4−8−8−4 defects (right column of (b)) in armchair tubes and 5−7−7−5 defects (right column of (d)) in zigzag tubes are identified as (7,7) 6Vb and (12,0) 6Vb configurations, respectively. Top, side, and front sectional views of the optimized nanostructures illustrate the changes in the nanotube lattice. The defect areas are highlighted by yellow color online, and the blue bars in Figures (b) and (d) correspond to the newly formed (6,6) and (11,0) SWCNT segments, respectively. The atomic lattice of the removed atoms (close-up image and denoted by green color online) in the pristine CNT is shown in the hollow area of the front sectional view of the tube.
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COMPUTATIONAL METHODS AND MODELS The atomically reconstructed process for defective CNTs is implemented by using density functional theory in the framework of the SIESTA code.20,21 The interaction between valence electrons and the atomic core is computed within the standard norm-conserving Troullier−Martins pseudopotential.22 The numerical double-ζ plus polarization (DZP) parametrization is chosen as basis set, and the kinetic cutoff energy is set to 200 Ry. The generalized gradient approximation (GGA) in the form of Perdew−Burke−Ernzerhof is used for the exchange-correlation functional.23 All nanostructure geometries converged until forces acting on all atoms dropped below 0.01 eV/Å. The calculations are performed at electronic temperature T = 300 K. The defective nanostructures were fully relaxed in terms of 17 unit cells for (7,7) nanotube (associated with 476 atoms) and 10 unit cells for (12,0) nanotube (associated with 480 atoms), respectively. Hence, we used a vacuum space of 30Å as the distance of directions perpendicular to the tube axis, which is sufficient to avoid the tube−tube interaction. According to the previous reports carried out by dynamic simulations and ab initio total energy calculations, the generation of hexa-vacancy along the zigzag chain and one pristine hexagonal lattice would result in the formation of asymmetric and symmetric intramolecular junctions after reconstruction.17,18 In order to obtain the intramolecular
molecular junctions formed in defective zigzag and armchair SWCNTs by introducing hexa-vacancy defects. We focus on the (7,7) and (12,0) nanostructures of approximately 10 Å in diameter, because both are metallic with different chiralities, where the latter (zigzag) is known to develop a small band gap, in contrast to the former (armchair) that has no gap around the Fermi level.19 Structure stability is evaluated by using firstprinciples calculation, and the four lowest-energy structures or metastable configurations are obtained after atomistic reconstruction. In both armchair and zigzag SWCNTs, the formation of tilted 5−7−6−7−5 defects makes the tube twist, and thus asymmetric intramolecular junctions are produced. In contrast, a symmetric intramolecular junction made up of 4−8−8−4 defects is shown to be stable in armchair tubes, whereas in zigzag tubes, the symmetric junction is made up of 5−7−7−5 defects. It is found that the (7,7) symmetric intramolecular junction exhibits better electronic transport than the corresponding twisted nanostructure, whereas the (12,0) symmetric intramolecular junction exhibits smaller current compared to its corresponding asymmetric configuration. To understand this unexpected result, we investigate quantum transport through these intramolecular junctions and provide a detailed analysis below. 22985
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minimum (maximum) electrochemical potential μ of the electrodes. Moreover, the detailed methodology and practical implementation of the nonequilibrium Green’s function approach (NEGF) is available in ref 26.
junctions with different symmetry, we initially remove six atoms along the zigzag chain and one hexagonal lattice in the atomic network of both armchair and zigzag pristine CNTs. Therefore, we consider four defective nanostructures, two asymmetric ((7,7) 6Va and (12,0) 6Va) and two symmetric ((7,7) 6Vb and (12,0) 6Vb) configurations according to structural symmetry, as shown in Figure 1. With the corresponding transformation energies of all nanostructures listed in Table 1 , the asymmetric
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RESULTS AND DISCUSSION As for the (7,7) 6Va intramolecular junction shown in Figure 1a, the 5−7−6−7−5 defect makes the tube twist around the defect area, which locally increases the diameter of the SWCNT at the location of the two pentagons. One notices that the orientations of the 5−7−6−7−5 defect in (7,7) and (12,0) SWCNTs are different. In this context, we define the defect orientation as the angle made by the axis of the defect (indicated by the angle φ and ϕ in Figure 1a,c, respectively) with the horizontal direction. Hence, the 5−7−6−7−5 defect in the (7,7) SWCNT is tilted at φ = 22° with respect to the horizontal axis, while the orientation of such defect in the (12,0) SWCNT is ϕ = 73°, as a result of the differences in SWCNTs chirality. In addition, this configuration is the most energetically favorable nanostructure among hexa-vacancies with the armchair chirality.17 As shown in Figure 1b, the defective area comprising the symmetric 4−8−8−4 defects (parallel to the axial direction), named (7,7) 6Vb, is predicted to be another metastable configuration compared with previous reports.18,27 Unlike the 6Va configuration, the defects in this intramolecular junction manifest a remarkable indentation in the tube, which is clearly evidenced by the front view. The symmetric tetragons lead to spherical bulge along radial direction, while the bond that connected two adjacent octagons causes prominent shrinkage at this location, and eventually gives rise to the formation of a (6,6) segment, which is visualized by the side view in Figure 1b. The presence of this symmetric intramolecular junction is accompanied by largescale deformation around the vacancy defects. Hence, the 4− 8−8−4 defects are not only subject to comparable stress, but also result in the largest transformation energy among hexavacancy configurations, which is consistent with previous work.17 The (12,0) 6Va intramolecular junction configuration, containing the laterally oriented 5−7−6−7−5 defects, is found to be a metastable configuration.28 In this asymmetric configuration, the major changes caused by the lateral hexavacancy manifest also as a twisting-type deformation after atomic rearrangement, which resembles that of the (7,7) 6Va configuration. The intramolecular junction formed by the 5− 7−7−5 defects (parallel to the axial direction) is the minimumenergy configuration among hexa-vacancy defective nanostructures in zigzag SWCNT,13 as opposed to the case of (7,7) nanostructures. The conjugation of the 5−7 pairs constitutes the architecture of the (11,0) CNT, leading to remarkable shrinkage at the defective area and the formation of the metal− semiconductor−metal (M−S−M) junction. The opposite side of the defective area of this symmetric intramolecular junction configuration, however, undergoes insignificant changes. The structural formation of this intramolecular junction agrees well with previous DFT results for semiconductor−metal−semiconductor (S−M−S) junction in the (16,0) SWCNT,13 validating the reliability of our simulated results. The electronic band structures of the defective SWCNTs are shown in Figure 2. The pristine (7,7) tube is of strongly metallic type because of its gapless electronic band (Figure 2a).15,19 In the (7,7) 6Va configuration, it is noted that the lowest unoccupied band above the Fermi level, marked as γ-
Table 1. Transformation Energy configurations
transformation energy (eV)
(7,7) 6Va (7,7) 6Vb (12,0) 6Va (12,0) 6Vb
6.97 10.69 14.61 5.42
intramolecular junctions (6Va) consisting of the 5−7−6−7−5 defect are present in both armchair and zigzag tubes, as shown in Figure 1a,c. (Note: The transformation energy Et is defined as Et = Ed − Nd/Np × Ep, where Ed is the total energy of the defective tube, Ep is the total energy of the pristine tube, Nd and Np are the number of the atoms in the defective tube and pristine tube, respectively.) In contrast, the symmetric intramolecular junctions (6Vb) consist of the 4−8−8−4 defects in the armchair and the 5−7−7−5 defects in the zigzag SWCNTs. Meanwhile, the symmetric intramolecular junctions in both armchair and zigzag SWCNTs shown in Figure 1b,d are found to be energetically favorable (see Table 1). Specifically, removing a hexagonal lattice from pristine CNT could result in the formation of symmetric intramolecular junctions in the nanostructures, which is in good agreement with the dynamic analysis reported previously.13 To validate our structures of the defective SWCNTs after reconstruction, we have compared our reconstructed nanostructures with previous works in the literature and found excellent agreement.13,17 After performing geometry optimization, accurate electronic band structures were calculated. By using a different number of cells (12, 14 unit cells for the (7,7) tube and 6, 8 unit cells for the (12,0) tube), we found no qualitative change among them except for the γ-state becoming flat with increasing CNT length, ensuring the reliability of the electronic structure calculation. In order to simulate the electronic transport properties of the defective SWCNTs, a two-probe computational approach is implemented.24−26 The theoretical model is built in such a way that the central region consists of an optimized supercell with the hexa-vacancy defects, which is surrounded by two semi-infinite leads made up of one pristine primitive cell on each side. The 3 × 3 × 60 Monkhorst−Pack kpoint sampling is employed for these two leads during quantum transport calculation. The conductance as a function of electron energy and the I−V characteristics are calculated in the framework of Laudauer formalism: l
r
T (E , Vb) = 4Tr[Im(∑ GR ∑ G A )]
I=
2e h
∫μ
μmax
min
dE(fl − fr )T (E , Vb)
(1)
(2)
where Σ (Σ ) represents the self-energies of the left (right) electrode, GR (GA) is retarded (advanced) Green’s function, f l (f r) is the corresponding electron distribution function of the electron eigenstates of the left (right) electrode. Furthermore, μmin = min(μ + Vb, μ) (μmax = max(μ + Vb, μ)) denotes the l
r
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defects, it is concluded that the tilted 5−7−6−7−5 defects yield more pronounced variations than symmetric intramolecular junction configuration. Hence, these modifications correspond to various effects on the CNT conductance, which are analyzed below. The conductance spectra of the defective SWCNTs are shown in Figure 3. The quantized conductances of the pristine
Figure 2. Band structures of the armchair (top panel) and the zigzag (bottom panel) CNT consisting of hexa-vacancy defects: (a) (7,7) pristine CNT; (b) and (c) (7,7) 6Va and (7,7) 6Vb configurations shown in Figure 1a,b, respectively; (d) (12,0) pristine CNT; (e) and (f) (12,0) 6Va and (12,0) 6Vb configurations shown in Figure 1c,d, respectively. The Fermi level is indicated by the dotted line (red online); the coupling misalignments due to band alterations are denoted by the gray shadows, which correspond to the suppression of quantum conductance.
Figure 3. Conductance vs electron energy for the (a) (7,7) and (b) (12,0) SWCNTs consisting of hexa-vacancy defects. The Fermi level is set to be zero. The quasibond states, as denoted by the arrows, are associated with their respective band structures, shown in the insets.
band, derives from a defect state due to the presence of the 5− 7−6−7−5 configuration. Moreover, the bands near the Fermi level are significantly shifted with respect to the Fermi level, which opens a band gap of 0.33 eV. Conversely, the (7,7) 6Vb configuration remains metallic owing to the crossing of two defect states, that is, the γ-band and the δ-band located above and below the Fermi level, respectively. The emergence of the symmetric intramolecular junction in this nanostructure not only gives rise to a band shift but also lifts the band degeneracy. In general, the large-scale deformation (4−8−8−4 defects) dominates the electronic structure of this symmetric configuration. In the pristine (12,0) nanotube, one should point out that the α- and the α′-bands are doubly degenerate (Figure 2d). Owing to the curvature CNT effect,29 they do not merge at the Γ-point, which produces a tiny band gap of approximately 0.08 eV. In the (12,0) 6Va configuration, the α- and α′-bands evolve into the modified β- and β′-bands, respectively. Both of them are pronouncedly shifted away from the Fermi level, generating a direct band gap of 0.38 eV and an indirect band gap of 0.28 eV. In the (12,0) 6Vb configuration, the γ-state created by the defects is the lowest unoccupied band with dispersionless tail extending to the X-point. The occurrence of the defect state effectively reduces the direct band gap to about 0.06 eV by anticrossing with the β-band. Compared with the modifications on electronic bands arising from the various hexa-vacancy
SWCNTs, including both armchair and zigzag types, manifest ballistic transport in the low-dimensional system, and the sharp dip located at the Fermi level in the (12,0) pristine tube derives from curvature effects. 8 For the defective tubes, the conductances are expected to dramatically reduce due to the defect-induced symmetry breaking in the reconstructed nanostructures.30 For the (7,7) 6Va configuration with the presence of the 5−7−6−7−5 defect (Figure 3a), the conductance reduction at the Fermi level originates from coupling mismatch between its highest occupied subband and lowest unoccupied subband. The variations in conductance are featured by a first plateau at about 1G0 around the Fermi level, indicating roughly 50% suppression of the double available electron transmission channels.31 This can be explained by its modified electronic bands as its σ band is lifted and its σ* band is downward shifted, as shown in Figure 2b, which results in transmission channel breaking. In addition, a smooth dip located at about −0.88 eV is the signature of resonant scattering by quasibound state induced by the defect. On the opposite, the 4−8−8−4 defects in the (7,7) 6Vb configuration give rise to less modifications on the conductance at the Fermi level than that in the (7,7) 6Va configuration, which finds their origin in the band structure. As in the (7,7) 6Va configuration, the most noticeable features of the conductance changes in the (7,7) 6Vb nanostructure are concentrated around the Fermi level. Hence, the conductance behavior in the conduction band is analogous to the former configuration, whereas its 22987
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Figure 4. I−V characteristics of the (a) armchair- (left column) and (b) zigzag-defective SWCNTs (right column) , with the corresponding pristine results. The conductance at EF as a function of applied bias is shown in the insets. The colors in the I−V curves identify the nanostructures.
Figure 5. Color plot of the transmission spectrum as a function of electron energy E (horizontal direction) and applied bias (vertical direction). The color scale on the right indicates the conductance values. The top panel and bottom panel correspond to the armchair- and the zigzag-defected CNTs, respectively: (a), (b), (c) are for the pristine, the 6Va, and the 6Vb configurations of the (7,7) nanostructure; (d), (e), (f) are for the pristine, the 6Va, and the 6Vb configurations of the (12,0) nanostructure. The transmission suppression region referred to the critical energy window is indicted by bright (white color online) solid line.
conductance behavior below EF resembles that of the pristine CNT, due to the preservation of band overlap. In addition, a conductance dip at 0.56 eV below EF can be attributed to a transmission resonance through a quasibound state. As shown in Figure 3b, the 5−7−6−7−5 defects in the (12,0) 6Va nanostructure open a 0.24 eV conductance gap, resulting in full suppression of the transmission channel at the Fermi level. Except for the conductance gap, there are no appreciable changes in conductance around EF compared to that of the pristine. For the (12,0) 6Vb configuration, the conductance spectrum around EF is similar to the pristine SWCNT, despite the quantitative difference on the first plateau. Noticeably, the resonant backscattering associated with the quasibound states is created below the Fermi level, indicating that one of the transmission channels is suppressed. The I−V curves of the defective SWCNTs are shown in Figure 4. Clearly, atomic vacancy defects in the nanostructures induce nonlinear I−V characteristics compared to the pristine situation. It is interesting to notice that Figure 4 displays chirality-dependent differences in the I−V characteristics. The
(7,7) 6Vb configuration exhibits more favorable electronic transport compared with the twisted nanostructure of the (7,7) 6Va configuration, whereas the analogous (12,0) 6Vb nanostructure manifests unexpected smaller current in contrast to the case of (12,0) 6Va configuration. Generally, the distinct I−V behaviors of the two chiral tubes rely on their band structure and transmission spectra at equilibrium. Paradoxically, as shown in Figure 2e,f, band structure simulations imply that the symmetric intramolecular junction exhibits smaller band gap than that of the asymmetric intramolecular junction, which is consistent with the conductance spectra shown in Figure 3. However, the differences in the conductance spectra of the two configurations at EF are found, as illustrated in the inset of Figure 4. Indeed, the conductance at EF is mainly dependent on whether π electrons can overlap with and hop to π★ orbitals. Consequently, the conductance decrease shown in Figure 4a is attributed to misaligned coupling between the π and π★ induced by external bias, which is consistent with the I−V curves. 22988
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rearrangements. The stability of all defective configurations is assessed in terms of transformation energy. The I−V characteristics of symmetric configurations in the armchair and zigzag SWCNTs are found to exhibit different behaviors compared with those of the corresponding asymmetric nanostructures, although the asymmetric and symmetric defects induced similar band-structure modifications on the two chiral SWCNTs, respectively. This unexpected behavior is attributed to a competition between a widening of the transmission windows that opens new transmission channels and current suppression due to orbital mismatch under applied bias, which is confirmed not only by the variation of the conductance amplitude at the Fermi level but also by the whole transmission spectra as a function of the electron energy for different applied biases. Our calculation provides insight into the formation of intramolecular junctions in SWCNTs and their influences on electron transport in defective SWCNT materials, which are relevant for practical applications in SWCNT-based nanoelectronics.
In order to understand in detail the influences of chirality and symmetry of the defects on the I−V behaviors of defective SWCNTs, the transmission spectra as a function of electron energy and bias are plotted in Figure 5. The (7,7) pristine nanostructure is featured by considerable transmission coefficients under various biases. The presence of the 5−7− 6−7−5 defect in the (7,7) 6Va nanostructure gives rise to a large region of transmission suppression around the Fermi level, as displayed in Figure 5b. This means that only few electrons can travel from one end of the CNT to the other end, provided that the bias voltage does not exceed the energy range bordered by the bright line (Figure 5b). There also exists a region of moderate transport quenching caused by the 4−8− 8−4 defect in the (7,7) 6Vb nanostructure. However, for the transmission displayed in Figure 5c, it is observed that the quenching region does not cross the Fermi level and this region is remarkably narrowed. As a result, electron transport in the (7,7) 6Vb nanostructure is much more prominent than that in the (7,7) 6Va nanostructure, which is also consistent with the I−V characteristics displayed in Figure 4. For the (12,0) pristine nanostructure at zero bias, a sharp transmission gap is found at the Fermi level, which under bias, shifts away from it. Such transmission gap at the Fermi level evolves into two discrete transmission quenching regions located symmetrically with respect to the Fermi level and moving apart with increasing bias. Comparison with Figure 5e and 5f,d shows significant differences in the transmission coefficients between the pristine CNT and the defective nanostructure in the energy window considered. It should be pointed out that the pristine nanostructure has fairly large transmission coefficient within the critical energy window, and thus, considerable current flowing through the system can be achieved once a small bias is applied, as shown in Figure 4b. In sharp contrast, for the (12,0) 6Va configuration, not only is the transmission quenching region broadened but the transmission coefficient within the critical energy window becomes smaller. Therefore, the current of the (12,0) 6Va configuration is much smaller than that of the pristine CNT under the same bias. As shown in Figure 5f, the transmission coefficient of the (12,0) 6Vb configuration is characterized by a large quenching window spreading over a continuous region indicated by blue color online. Furthermore, the transport quenching region is found to broaden with the applied bias. By comparing Figure 5e with Figure 5f, we find a difference in the size of the transport quenching area; that is, the suppression of electron transmission in Figure 5f is much more pronounced than that in Figure 5e under the same bias. Therefore, the current of the (12,0) 6Va nanostructure is superior to that of the (12,0) 6Vb nanostructure, which can be understood in terms of these two effects: (1) electron transport channels are available in the former; (2) the states far from the Fermi level provide considerable contributions to the current caused by the widening of the transmission windows in the former with increasing bias. The transmission spectra under different bias thus are virtually responsible for the differences of the I−V curves.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Fax: +86 (0)716 8060942. Tel: +86 (0)716 8060942. Author Contributions ∥
H.Z. and J.Z. contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge Prof. K.-L. Yao for fruitful discussions and Dr. Z.-Q. Fan, J.-W. Liang for technical assistance on performing transport properties and relax calculation. This work is financially supported by Natural Science Foundation of China (Grant Nos. 11304022, 11347010, 11404037, and 11204391), the Research Foundation of Education Bureau of Hubei Province of China (Grant Nos. Q20131208 and XD2014069), and the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ130831).
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REFERENCES
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CONCLUSIONS In summary, we have performed first-principles calculations to investigate spontaneous reconstructions in defective (7,7) and (12,0) SWCNTs. Two types of defect distributions, asymmetric and symmetric intramolecular junction configurations, are studied in both armchair and zigzag SWCNTs after atomic 22989
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The Journal of Physical Chemistry C
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dx.doi.org/10.1021/jp508159x | J. Phys. Chem. C 2014, 118, 22984−22990
