Conductance Superposition Rule in Carbon Nanowire Junctions with

Article pubs.acs.org/JPCC

Conductance Superposition Rule in Carbon Nanowire Junctions with Parallel Paths Kun Peng Dou† and Chao-Cheng Kaun*,†,‡ †

Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan Department of Physics, National Tsing-Hua University, Hsinchu 30013, Taiwan

‡

ABSTRACT: Using first-principles calculations, we investigate conductance of molecular junctions consisted of single and double polyacene (PA) molecules bridging different carbon nanowire electrodes, including armchair carbon nanotubes (CNT) and zigzag graphene nanoribbons (GNR). Doubling the PA molecule enhances the junction conductance, except in the junction where a molecule contacts armchair CNT with nonvertical edges. Elongating the PA molecules change junction conductance. The different conductance scaling behaviors among various junctions are governed by the interface between the molecule and the electrode, the molecular length, and the edge states of zigzag GNR.

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INTRODUCTION Understanding charge transport through multiply molecules is imperative to build efficient electronic devices. Conductance of an ensemble of molecules may not be the conductance sum of individual molecules, as the collective1/cooperative2,3 effects can arise from adjacent molecules at the nanometer scale. Although the linear conductance scaling is observed in both saturated σ-bonded molecules4,5 and π-conjugated molecules,6 due to the weak intermolecular coupling (the π−π interaction),7 however, such coupling can exist but be screened by the substrate-mediated interactions2,3 in these metal− molecule−metal (MMM) junctions. In addition, the mismatch of orbital symmetries among the metal electrode, anchor atom, and the molecule gives rise to the complexity in conductance scaling rules for MMM junctions.8,9 Carbon nanowires, such as carbon nanotube (CNT) and graphene nanoribbon (GNR), offer seamless coupling to molecules10−12 and circumvent the significant effects from metallic contacts,13−15 giving alternating opportunities to probe collective1/cooperative2,3 and contact effects in molecular junctions. Nonlinear conduction scaling laws thus have been detected for polyene12 and π-cruciform molecule in CNT junctions.16 However, the interfacial problems15 arising from the complex topology of the all-carbon π system and the special edge state of zigzag graphene nanoribbon (ZGNR)17 occur, which is relatively unexplored. Polyacene (PA) molecules represent a fragment of the πbonded carbon network of the electrode and can form seamless junctions. However, the length-dependent conduction of PA molecules is still an open issue experimentally and theoretically. Evidence of exponential conductance drop with PA length increasing is demonstrated in conducting probe atomic force microscopy18,19 and STM break junction measurements,20 © 2016 American Chemical Society

while conductance does not exponentially depend on PA length in other STM experiments.21 The theoretical conductance value of PA molecule is reported to oscillate with length by several groups.11,22−25 For example, the length-dependent conductance of PA molecules follows the exponential law in the low bias region but oscillates in the high bias region.23 Moreover, in a tight binding study, by tuning the third neighbor coupling parameter across each ring parallel to the vertical rungs of PA molecules, three conductance trends are obtained: oscillating, exponential, and nonexponential decrease with PA length increasing.11 This behavior is similar to that observed in structureless molecular wires, where the length-dependent conductance is determined by the overlap between the energy bands of the wire and the Fermi level of reservoir.26 In this work, we investigate the dependence of conductance superposition rule on the molecular conduction channels, the carbon nanowire electrodes, and the interface of the molecule with the electrode from first-principles calculations. In particular, the junctions consist of single and double PA molecules contacting armchair CNT or ZGNR electrodes. As the molecular length increases, conductance of the junction changes, depending on the interfaces and the electrodes. The corresponding transmission spectra and density of states are addressed to gain insight into these systems.

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METHODS Each junction was optimized by using density functional theory (DFT) implemented in the SIESTA package,27 within the local density approximation. An energy cutoff of 200 Ry was used. Received: June 24, 2016 Revised: August 5, 2016 Published: August 8, 2016 18939

DOI: 10.1021/acs.jpcc.6b06399 J. Phys. Chem. C 2016, 120, 18939−18944

Article

The Journal of Physical Chemistry C

Figure 1. Length-dependent conductance of single and double polyacene molecules bridging (a) CNT (6, 6) with vertical edges, (b) CNT (5, 5) with vertical and nonvertical edges, (c) 10-ZGNR with vertical edges, and (d) 9-ZGNR with vertical and nonvertical edges. Red circles: double molecules; black triangles: a single molecule with vertical edges; green triangles: a single molecule with nonvertical edges.

Figure 2. (a) Transmission spectra and (c) PDOS of single (black) and double (red) PA7 molecules bridging CNT (6, 6). (b) Transmission spectra and (d) PDOS of single (black), single nonvertical-edge (green), and double (red) PA7 molecules bridging CNT (5, 5). Bottom panels: LDOS at different energies of the PA7 molecules.

Valence electrons were expanded in a double-ζ plus polarization basis set. Structural relaxations were allowed until the force acting on each atom was less than 0.01 eV/Å. Then transport calculations were performed with Nanodcal package,28 based on DFT and the nonequilibrium Green’s function formalism. Three primitive layers of each electrode were

included as buffer layers in the scattering region. The transmission spectra were sampled by 100 k-points. The conductance value G = T(Ef)G0, where T(E) is the transmission spectrum, Ef is the Fermi energy, and G0 = 2e2/ℏ is the conductance quantum. 18940


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Figure 3. Energy positions (a, b) and widths (c, d) of the transmission peaks in CNT (6, 6) (left panels) and CNT (5, 5) (right panels) junctions. The colors of energy positions correlate with those of transmission spectra in Figure 2. Black triangles (circles): L0 (H0) of a single molecule with vertical edges; red triangles (circles): L0 (H0) of double molecules; green triangles (circles): L0 (H0) of a single molecule with nonvertical edges.

Figure 4. (a) Schematic illustration of the interfaces (in red dashed boxes) of the double PA with CNT (6, 6) junction. (b) Contour plots of the LDOS along the black dashed line shown in (a) for double PA3 and PA7 junctions. (c) Conductance ratio of double and single PA molecules comparing with PDOS over interfaces of double PA junctions. The horizontal dashed line corresponds to twice the conductance of a single PA molecule.

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RESULTS AND DISCUSSION

configuration of the two molecules, which is energetically favorable.16,29 Hereafter, G1, G1′ and G2 refer to the junction conductance containing single PA molecule with vertical edges, single PA molecule with nonvertical edges, and double PA molecules, respectively. Figure 1 also shows junction conductance, presenting three superposition trends. First, for CNT (6, 6)-based junctions, G2 is more than twice of G1, where the conductance ratio of G2/G1 is 4.02, 3.72, 3.34, 2.91, and 2.58 for PA3 to PA7, respectively, decreasing with molecular length increase. Second, for CNT (5, 5)-based junctions, G1 > G2 > G1′. The nonvertical edges of CNT strongly mask the electronic signature of the molecule

CNT (6, 6), CNT (5, 5), 10-ZGNR (ten zigzag C chains), and 9-ZGNR (nine zigzag C chains) are adopted as electrodes. The junction structures used in our calculations are shown in Figure 1, where the PA molecule length is three (PA3). The structures in the first row show the molecules contacting with CNT (6, 6) [CNT (5, 5)] electrode with vertical [vertical and nonvertical] edges. Those in the second row indicate the molecules bridging the 10-ZGNR (9-ZGNR) electrodes with vertical (vertical and nonvertical) edges. All double PA molecules in CNT junctions are in parallel, corresponding to the maximally separated 18941


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Figure 5. Transmission spectra of single and double PA5 molecules bridging 10-ZGNR and 9- ZGNR electrodes. The insets show the LDOS at Ef on the structures of these junctions.

and reduce its conductance (G1′). Third, for the PA molecules bridging ZGNR along the top and bottom edges, nearly linear superposition presents, G2 ≈ 2*G1. To analyze conductance scaling rules in CNT junctions, the transmission spectra of PA7 molecules are calculated and shown in Figure 2a,b. The tails of transmission peaks overlap with each other at Ef and give the off-resonance conductance of each junction. The corresponding projected density of states (PDOS) shown in Figure 2c,d indicate that these peaks resonate with the molecular states. The orbital channels supporting these peaks are represented by the local density of states (LDOS) of double PA molecular junctions at the corresponding energy levels, shown in lower panels of Figure 2. The LDOS distributes on both PA molecules equally in CNT (6, 6)-based junctions, indicating that two PA molecules have degenerate molecular levels, while such degeneracy is broken in CNT (5, 5)-based junctions. The resonance peaks in Figure 2b come from levels of PA molecules with vertical and nonvertical edges. Hybridization of electrode and molecular states leads to resonance peaks and the conduction channels. The LDOS at Ef distributes only on the vertical-edge PA molecule in the junction pointing the dominant conduction channel in CNT (5, 5)-based junctions. The energy positions of the transmission peaks in the CNT (6, 6)-based junction, shown in Figure 2a, with those of other length molecules are plotted in Figure 3a. The peak positions approach to Ef as the molecular length increases. The widths (Γ) of the peaks are shown in Figure 3c, estimated from the Lorentzian fit.30 H0 and L0 peaks have the similar widths, while the L0 peak is closer to Ef than the H0 peak is. Thus, the tail of L0 produces larger transmission at Ef.2 Although L0 of single PA molecule is closer to Ef than that of double PA one, its width is smaller than that of the latter. The level alignment competes with the level broadening, giving G/G0 ≈ Γ2/(L02 + Γ2) and resulting in G2 lager than G1 in these junctions. In addition, the conductance ratio of G2/G1 is more than twice, which reflects the constructive crosstalk between the two PA molecules. Especially, for PA3, the ratio of 4.02 agrees with an earlier report.31 The strain effect by elongating the junction of 0.1 Å is also considered and no apparent deviation is found. The conductance ratio decreasing with molecular length increasing is associated with the length-dependent variation in crosstalk between molecules, due to the direct interwire coupling (π−π interactions) and the interfacial coupling. In previous theoretical studies, the vertical distance between the two molecular backbones is shorter than 5 Å.32,33 Here, the separation between two PA molecules is more than 8.06 Å in

CNT (6, 6)-based junctions, so that the direct interwire coupling is weak enough to be omitted and the crosstalk comes from the interfacial coupling between electrodes and molecules. To estimate this coupling, PDOS of interfacial atoms at Ef for double PA molecular junctions are shown in Figure 4c. Correlation is observed when compare the variation of this term with that of the conductance ratio, where both decrease with the molecular length increasing. Contour plots of the LDOS (Figure 4b) at the interfaces (Figure 4a) also display this trend. LDOS is denser in double PA3 junction than that in the double PA7 one. The change of molecular length impacts on the crosstalk between two PA molecules mediated by the interfacial atoms, leading to the length-dependent conductance scaling rules. Moreover, decreasing the distance between the two molecules (from cofacial to noncofacial) in the junction can even increase the conductance ratio. However, the destructive interference can be observed in the CNT(6, 6) junction, as a nonvertical edge is adopted. For example, such a PA5 junction provides that G1 (0.0122G0) > G2 (0.0064G0) > G1′ (0.0007G0). Figures 3b and 3d show the energy positions and widths of the transmission peaks of CNT (5, 5)-based junctions, respectively. The resonances of the single PA molecule with nonvertical edges are appreciably narrower and further away from Ef than those of the single and double PA molecules, resulting in the extreme low conductance of the former. A near perfect (poor) contact could be achieved by connecting the organic molecule to a five-member (six-member) ring on the edge of CNT34 due to that the molecular plane is nearly perpendicular to the tube wall in the six-member configuration, breaking the conjugation across the junction. Here, although PA molecules with both types of edges are nearly parallel to the tube wall, the nonvertical edges of CNT are apparently poor contacts to incorporate PA molecules into the junction for conduction. In the double PA molecules with CNT (5, 5) junctions, their conductance are dominated by the PA molecule with vertical edges, as shown in the bottom panels of Figure 2. In particular, their H0 and L0 have the similar widths while L0 is closer to Ef than H0 is so that L0 contributes more to the conductance. The L0 of the double-PA junction is further away from Ef than that of the single-PA-vertical-edge junction. As shown in Figure 3b,d, when nonvertical edges are involved in the junction, the peak becomes narrower and shifts further from Ef than that of the single-PA-vertical-edge junction does, leading to G1′ < G2 < G1. 18942


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(3) Reuter, M. G.; Seideman, T.; Ratner, M. A. Molecular Conduction through Adlayers: Cooperative Effects Can Help or Hamper Electron Transport. Nano Lett. 2011, 11, 4693−4696. (4) Xu, B. Q.; Tao, N. J. Measurement of Single-Molecule Resistance by Repeated Formation of Molecular Junctions. Science 2003, 301, 1221−1223. (5) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Reproducible Measurement of Single-Molecule Conductivity. Science 2001, 294, 571−574. (6) Kushmerick, J. G.; Naciri, J.; Yang, J. C.; Shashidhar, R. Conductance Scaling of Molecular Wires in Parallel. Nano Lett. 2003, 3, 897−900. (7) Yaliraki, S. N.; Ratner, M. A. Molecule-interface coupling effects on electronic transport in molecular wires. J. Chem. Phys. 1998, 109, 5036−5043. (8) Kaun, C.-C.; Larade, B.; Guo, H. Electrical transport through oligophenylene molecules: A first-principles study of the length dependence. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 121411. (9) Kaun, C.-C.; Guo, H.; Grütter, P.; Lennox, R. B. Momentum filtering effect in molecular wires. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 195309. (10) Agapito, L. A.; Kioussis, N. ″Seamless” Graphene Interconnects for the Prospect of All-Carbon Spin-Polarized Field-Effect Transistors. J. Phys. Chem. C 2011, 115, 2874−2879. (11) Chen, Y.-R.; Zhang, L.; Hybertsen, M. S. Theoretical study of trends in conductance for molecular junctions formed with armchair carbon nanotube electrodes. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 115408. (12) Chen, Y.-R.; Chen, K.-Y.; Dou, K.-P.; Tai, J.-S.; Lee, H.-H.; Kaun, C.-C. Electron Transport through Polyene Junctions in between Carbon Nanotubes: An Ab Initio Realization. Carbon 2015, 94, 548− 553. (13) Sen, A.; Kaun, C.-C. Effect of Electrode Orientations on Charge Transport in Alkanedithiol Single-Molecule Junctions. ACS Nano 2010, 4, 6404−6408. (14) Sen, A.; Lin, C.-J.; Kaun, C.-C. Single-Molecule Conductance through Chiral Gold Nanotubes. J. Phys. Chem. C 2013, 117, 13676− 13680. (15) Wang, J.; Prodan, E.; Car, R.; Selloni, A. Band alignment in molecular devices: Influence of anchoring group and metal work function. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 245443. (16) Bruque, N. A.; Ashraf, M. K.; Beran, G. J. O.; Helander, T. R.; Lake, R. K. Conductance of a Conjugated Molecule with Carbon Nanotube Contacts. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 155455. (17) Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. Peculiar Localized State at Zigzag Graphite Edge. J. Phys. Soc. Jpn. 1996, 65, 1920−1923. (18) Kim, B.-S.; Beebe, J. M.; Jun, Y.; Zhu, X.-Y.; Frisbie, C. D. Correlation between HOMO Alignment and Contact Resistance in Molecular Junctions: Aromatic Thiols versus Aromatic Isocyanides. J. Am. Chem. Soc. 2006, 128, 4970−4971. (19) Kim, B.; Choi, S. H.; Zhu, X. Y.; Frisbie, C. D. Molecular Tunnel Junctions Based on π-Conjugated Oligoacene Thiols and ithiols between Ag, Au, and Pt Contacts: Effect of Surface Linking Group and Metal Work Function. J. Am. Chem. Soc. 2011, 133, 19864−19877. (20) Kaliginedi, V.; Moreno-García, P.; Valkenier, H.; Hong, W.; García-Suárez, V. M.; Buiter, P.; Otten, J. L. H.; Hummelen, J. C.; Lambert, C. J.; Wandlowski, T. Correlations between Molecular Structure and Single-Junction Conductance: A Case Study with Oligo (phenylene-ethynylene)-Type Wires. J. Am. Chem. Soc. 2012, 134, 5262−5275. (21) Quinn, J. R.; Foss, F. W.; Venkataraman, L.; Hybertsen, M. S.; Breslow, R. Single-Molecule Junction Conductance through Diaminoacenes. J. Am. Chem. Soc. 2007, 129, 6714−6715.

Figure 5 shows transmission spectra of single and double PA5 molecules bridging 10-ZGNR and 9- ZGNR electrodes. The transmission peak at Ef gives rise to the on-resonance for these junctions. LDOS at Ef, shown in the insets, possess significant weight only on the outmost edges of the molecule and the edges of the ZGNR electrodes across the whole junction, indicating that the transmission peak at Ef originates from the electrode edge states rather than the molecular one. In first-principles studies35,36 and tight-binding approach including second-nearest-neighbor interaction,37 transmission peaks are observed at Ef, where the flat bands at Ef are slightly bent and more than one band across Ef contribute to different conducting channels. Here, the scaling rule of G2 ≈ 2G1 is the evaluation of decaying behavior of the electrode edge states across the junction rather than the intrinsic conduction nature of PA molecules. From single molecule with vertical edges to double PA5 molecules, the resonant peaks around 0.6 and −0.6 eV shift away from Ef (do not move) in 10-ZGNR (9-ZGNR)-based junctions. However, from single molecule with vertical edges to that with nonvertical edges in 9-ZGNR-based junctions, these two peaks reduce to one peak at −0.8 eV. Therefore, although the contacts do not change the conductance, they still alter the conduction characters in these ZGNR-based junctions.

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CONCLUSIONS Our results obtained from these all-carbon junctions show that electron transport follows distinct superposition rules depending on the molecular length, the interface between the molecules and the electrodes, and the edge states of ZNGR electrodes. Doubling the PA molecule increases the conductance of junctions, except in CNT (5,5)-based junctions where nonvertical edges occur. Elongating the PA molecules change junction conductance and in particular reduce the conductance ratio of double and single PA molecules in CNT (6, 6)-based junctions. The conductance scaling rule is related to the crosstalk due to the interfacial coupling between electrodes and molecules. While etching techniques hold promise to tailor the junctions,38−40 our results provide an understanding on full π-systems for designing efficient nanoelectronic devices.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; phone 886-2-2787-3178 (C.-C.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by the Ministry of Science and Technology, Taiwan, through No. 104-2112-M-001-008MY3 and the National Center for Theoretical Sciences, Taiwan.

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Conductance Superposition Rule in Carbon Nanowire Junctions with

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