J. Phys. Chem. B 2008, 112, 16891–16894
16891
Large Negative Differential Resistance in a Molecular Junction of Carbon Nanotube and Anthracene Ying Xu,†,‡ Gang Zhang,*,§ and Baowen Li†,| Department of Physics and Centre for Computational Science and Engineering, National UniVersity of Singapore, 117542 Singapore, Department of Physics, Jiangxi Normal UniVersity, Nanchang 330022, People’s Republic of China, Institute of Microelectronics, 11 Science Park Road, Singapore Science Park II, 117685, Singapore, and NUS Graduate School of IntegratiVe Science and Engineering, 117597 Singapore ReceiVed: August 11, 2008; ReVised Manuscript ReceiVed: October 17, 2008
We propose a novel molecular junction with single walled carbon nanotube (SWNT) as electrodes bridged by an anthracene molecule. It is found that when the coupling between the molecule and the SWNT is noncovalent, the current-voltage (I-V) curve shows a striking nonlinear feature and a large negative differential resistance (NDR) at small bias. While in covalent adsorption site, the I-V curve behaves nearly linear. Theoretical studies based on the nonequilibrium Green’s function method demonstrate that mechanism of the NDR is due to the narrow features of the local density of states (LDOS) of the SWNT as well as the alignment between the peak of LDOS of the electrodes and the molecular energy levels. Single-molecular devices have been demonstrated to be promising in the nano electronics.1 Traditionally, metallic electrodes are used in molecular electronics with gold being the most common substrate. However, metals also bring undesirable effects such as gap states and weak ionic bonds.2 Recently nonmetallic electrodes have attracted a tremendous amount of attention because of the work on silicon-based molecular junctions3-6and carbon nanotube-based molecular junctions.7-11 Experimental and theoretical studies demonstrate that nonmetallic contact provides a lot of desirable advantages over its metallic counterpart. Room temperature negative differential resistance (NDR) has been observed in silicon-based molecular junctions.3 Devices with NDR character are important elements with a wide variety of circuit applications such as logic cell and memory. A possible scenario that NDR is likely to occur is in a weak link between two parts of the conducting system, each of which has relatively narrow features of density of states (DOS) in the energy range of interest.12,13 In this case, narrow peaks in the local density of states (LDOS) of an atomic scale tip sweep past the LDOS of an adsorbed molecule as the increasing of applied bias voltage. This has been widely recognized in the scanning tunneling microscope study.3,14 NDR behavior has also been found in some other molecular junctions experimentally and theoretically, and different mechanisms have been proposed. For instance, charging of the molecule followed by the localization/delocalization of molecular orbitals was the possible mechanism of NDR in the trimer substituted by nitro and amino groups.15,16 In double quantum dots resonance system, electron tunneling is resonantly enhanced when two discrete levels become aligned, and the current drops as the two levels fall out of alignment upon increase of the applied bias, thus causing NDR.17,18 Also, NDR mechanisms such as rotation of * To whom correspondence should be addressed. E-mail: zhangg@ ime.a-star.edu.sg. † National University of Singapore. ‡ Jiangxi Normal University. § Singapore Science Park II. | NUS Graduate School of Integrative Science and Engineering.
the molecular conformation19-21 and donor-acceptor model1,22,23 are also proposed. The NDR behavior observed in silicon-based molecular junction3-6 is delineated by a resonant tunneling model and opens new possibilities for silicon-based molecular electronic devices. Theoretical studies based on nonequilibrium Green’s function (NEGF) method have shown that the presence of a semiconducting band-edge can lead to a novel molecular resonant tunneling diode when the molecular levels are driven into the semiconductor band gap.4 In addition to silicon electrodes, single-walled carbon nanotubes (SWNTs) are among the most promising candidates for the construction of nanoscale electronic devices due to their unique properties and potential applications in many fields.7-11 However, contrast to the silicon-molecule junctions, so far no NDR phenomenon has been observed in any two-terminal SWNT-molecule junctions.7-11 In this work, we demonstrate that noncovalent coupling between the molecule and SWNT can induce NDR, and the NDR peak position is determined by the molecular energy level and 1D LDOS of the SWNT. The system we consider consists of three parts, left electrode, right electrode, and scattering region. In our calculations, metallic (4, 4) SWNT is taken as electrodes. For the scattering region, we choose the aromatic organic molecule anthracene (C14H10) to bridge the two ends of the SWNT as shown in Scheme 1. The sidewall functionalization of organic molecules on SWNT has been studied extensively.24-31 It has been found that aromatic molecule can be adsorbed on SWNT surface by noncovalent adsorption26-28 with bridge-site is demonstrated to be the most favorable adsorption site.26 The equilibrium tubearomatic molecule distance changes from 3.2 to 3.7 Å26-28 and depends on the tube diameters and calculation methods. In our calculations, we focus on the noncovalent bridge-site adsorption, and the aromatic molecule-tube distance is set to be 3.4 Å. In addition to noncovalent sidewall functionalization, the covalent sidewall functionalizations of SWNT with aromatic molecules have been reported recently.29-31 Here, we also study the transport property of covalent bridge-site adsorption, where the aromatic molecule-tube distance is set to be 1.4 Å, to compare
10.1021/jp807175n CCC: $40.75 2008 American Chemical Society Published on Web 12/03/2008
16892 J. Phys. Chem. B, Vol. 112, No. 51, 2008
Xu et al.
SCHEME 1: Schematic Drawing of the SWNT-Anthracene Molecular Junctiona
a
C and H atoms are represented in gray and white, respectively.
with the transport property of noncovalent adsorption. The transport properties are calculated by using a recently developed first-principles package Atomistix Toolkit 2.0,32,33 which is based on the combination of density function theory as implemented in the well-tested SIESTA34 method with the NEGF technique. The current through this atomic scale system is described by the quantum-mechanical probability for electrons to tunnel from one electrode to the other, and is calculated from Landauer-Bu¨ttiker formula35
I)
2e h
∫ dET(E, V)[fl(E - µL) - fr(E - µR)]
(1)
where µL and µR are the electrochemical potentials of the left and right electrodes, respectively, and fl and fr are the corresponding electron distribution of the two electrodes. T(E,V) is the transmission coefficient at energy E and bias voltage V. The total transmission T(E) can be decomposed into nonmixing eigenchannels Tn(E)35,36 as
T(E) )
∑ Tn(E)
(2)
n
For the system at equilibrium, the conductance G is evaluated by the transmission coefficients T(E) at the Fermi energy Ef of the system
G)
2e2 T(Ef) h
Figure 1. Current-Voltage curve for the SWNT-anthracene molecular junction with different contact distances. Left labels correspond to the covalent adsorption and right labels correspond to the noncovalent adsorption.
(3)
In our calculations, the local-density approximation as parametrized by Perdew and Zunger37 to the exchange-correlation potential is used. The wave functions are expanded by localized numerical atom orbitals38 (double-ζ basis plus polarization for C and double-ζ for H). The atomic cores are described by normconserving pseudopotentials.39 The convergence criterion for the Hamiltonian, charge density, and bandstructure energy is 10-5 via the mixture of the Hamiltonian. The I-V curves for noncovalent and covalent adsorption are shown in Figure 1. It is interesting to see that the I-V curve of the noncovalent case illustrates a significant nonlinear behavior. A large NDR is observed at about 1.05 V bias voltage. However, when the molecule is covalently adsorbed, the I-V curve shows nearly linear behavior. Although the current in noncovalent adsorption site is much lower than that in covalent adsorption site, it is in the same order of magnitude with that in silicon based molecular junctions.4
Figure 2. Transmission spectra of the 2-terminal system with SWNTs as electrodes bridged by an anthracene molecule. Channel T1 is represented by blue solid line and channel T2 is represented by red dash line. (a) Covalent adsorption (b) noncovalent adsorption.
To understand the underlying mechanism of different transport characteristics, we plot the eigenchannels decomposed transmission spectra in Figure 2. For clarity, the Fermi level has been shifted to zero. In both adsorption sites, there are two eigenchannels (T1 and T2) contributing to the total transmission. The number of eigenchannels is determined by the number of energy bands running across the Fermi level of SWNT.40 In metallic armchair SWNTs, this number is two.41 Obviously, the equilibrium conductance (at E ) 0) is dominated by the transmission from T1. For covalent adsorption (Figure 2a), channel T1 has broad characteristic and provides significant contribution to the total equilibrium conductance, about 0.73 G0. Channel T2 provides nearly zero contribution to the equilibrium conductance although it also has broad characteristic. As it is known, in the covalent adsorption there exists strong coupling between the central molecule and SWNT electrodes, which results in large broadening and shift in the discrete energy levels of the central molecule, thus leading to a quasi-continuous states distribution between the left/right electrodes.42 Consequently, electrons can transport from one electrode to the other via such quasi-continuous energy states and the transmission spectra do not exist evident tunneling peaks. Thus the broad distribution of eigenchannels prevents the occurrence of resonant tunneling and NDR phenomenon. In contrast, in the noncovalent adsorption site, the coupling between the electrodes and central molecule is very weak. The energy levels of the central molecular remain discrete, and the electrons
Molecular Junction of Carbon Nanotube and Anthracene
Figure 3. The renormalized LDOS of the SWNT and the energy levels of the central molecule. The orange solid lines represent the positions of the MPSH molecular energy levels. The red dot line represents the Fermi level. The pink arrows indicate the LDOS peaks which correspond to NDR.
transport in principle via resonant tunneling.43 Therefore obvious tunneling peaks are observed in the transmission spectrum (Figure 2b). The NDR observed in the noncovalent adsorption is consistent with the NDR mechanism proposed by Lang.12 From LandauerBu¨ttiker formula,35 the transmission coefficient T(E,V) is given by the product of the LDOS of the left and right electrodes by the off-diagonal matrix elements of the Green’s function connecting the left electrode to the right one. Therefore, a lowering in the product LDOS within the energy integration window will result in a reduction in the current. In the noncovalent adsorption, the link between carbon atoms of electrodes and central molecule is weak. We can think of changing the bias in the full system as sweeping DOS of the two electrodes past each other. Since there are sharp DOS peaks, NDR behavior is expected. However, in covalent adsorption, as the strong link between the two electrodes, it is no longer possible to speak of sweeping DOS of the two electrodes past each other, and NDR disappears. This is very similar to the NDR behavior observed in the strong/weak link atomic chains.12 For further discussion, the appearing of NDR at 1.05 V can be analyzed from the alignment of the peak of LDOS of the electrodes and molecular energy level. The LDOS of the SWNT as well as the molecular energy levels of the central molecule are shown in Figure 3. Here the vacuum region is infinite far away from the SWNT, and the vacuum level is the selfconsistent potential at the vacuum region and is set to zero. To involve the interaction of the central molecule and the electrodes, the molecular energy levels here are from the renormalized molecular energy level based on the results of molecular projected self-consistent Hamiltonian (MPSH).27 These energy levels are the molecular orbitals renormalized by the moleculeelectrode couplings. Also, the LDOS of the SWNT is the renormalized one. The renormalized highest occupied molecular orbital is at about -7.5 eV. The nearest two LDOS peaks of the SWNT locate at -7.0 and -8.1 eV, respectively. With applied bias, it causes the molecular level to move. When the level eventually aligns with the LDOS peak, resonant tunneling through the molecular state occurs, resulting in an increase in current. A further increase in bias lifts the level away from the LDOS peak, which prohibits carrier flow through the molecular junction, resulting in a drop in current and NDR. Similar NDR behavior has been observed in a donor-acceptor molecular complex sandwiched between two electrodes.23 Because of the
J. Phys. Chem. B, Vol. 112, No. 51, 2008 16893 simplified NEGF-derived NDR position equation, the NDR peak position relative to the molecular energy level E is roughly 2|E - E0|/e, where E0 is the electrode band edge and e is the elementary charge.4 From this equation, the NDR peaks will appear at 1.0 and 1.2 V, respectively. While these two peaks are very close, they are combined to form one large NDR peak at around 1.05 V, which is in good agreement with the direct calculated I-V curve. This behavior is consistent with the resonant tunneling mechanism in the silicon-based semiconductor-molecule-metal junction.4 In summary, we have performed first-principles based NEGF calculations on the transport properties of the 2-terminal system with metallic (4, 4) SWNT as electrodes and bridged by an anthracene molecule. The calculated I-V curves are strongly dependent on the molecule-SWNT coupling. Large NDR is observed at small bias when the interaction between the central molecule and the SWNT is noncovalent. In noncovalent adsorption, coupling between the electrodes and the central molecule is quite weak, and the transmission spectra show very narrow peaks near the Fermi level, which provides the possibility for resonant tunneling. The mechanism of the NDR is due to the narrow features of the LDOS of the SWNT as well as the alignment between the peak of LDOS of the electrodes and the molecular energy levels. The large numbers of electronic states in narrow energy ranges, known as van Hove singularities, can lead to strong resonant tunneling and large NDR. Our results indicate that it is possible to fabricate molecular device to obtain large NDR with SWNT as the electrodes. Acknowledgment. The work is supported in part by an Academic Research Fund Grant, R-144-000-203-112, from Ministry of Education of Republic of Singapore. References and Notes (1) Aviram, A.; Ratner, M. A. Chem. Phys. Lett. 1974, 29, 277. (2) Damle, P.; Rakshit, T.; Paulsson, M.; Datta, S. IEEE Trans. Nanotechnol. 2002, 1, 145. (3) Guisinger, N. P.; Greene, M. E.; Basu, R.; Baluch, A. S.; Hersam, M. C. Nano Lett. 2004, 4, 55. (4) Rakshit, T.; Liang, G-C; Ghosh, A. W.; Datta, S. Nano Lett. 2004, 4, 1803. (5) Lu, W. C.; Meunier, V.; Bernholc, J. Phys. ReV. Lett. 2005, 95, 206805. (6) Quek, S. Y.; Neaton, J. B.; Hybertsen, M. S.; Kaxiras, E.; Louie, S. G. Phys. ReV. Lett. 2007, 98, 066807. (7) Qi, P. F.; Javey, A.; Rolandi, M.; Wang, Q.; Yenilmez, E.; Dai, H. J. J. Am. Chem. Soc. 2004, 126, 11774. (8) Guo, X. F.; Small, J. P.; Klare, J. E.; Wang, Y.; Purewal, M. S.; Tam, I. W.; Hong, B. H.; Caldwell, R.; Huang, L.; O’Brien, S.; Yan, J.; Breslow, R.; Wind, S. J.; Hone, J.; Kim, P.; Nuckolls, C. Science 2006, 311, 356. (9) Tang, Q.; Moon, H. K.; Lee, Y.; Yoon, S. M.; Song, H. J.; Lim, H.; Choi, H. C. J. Am. Chem. Soc. 2007, 129, 11018. (10) Wei, Z.; Kondratenko, M. M.; Dao, L. H.; Perepichka, D. F. J. Am. Chem. Soc. 2006, 128, 3134. (11) Chen, Y.-R.; Zhang, L.; Hybertsen, M. S. Phys. ReV. B 2007, 76, 115408. (12) Lang, N. D. Phys. ReV. B 1997, 55, 9364. (13) Lyo, I.-W.; Avouris, Ph. Science 1989, 245, 1369. (14) Xue, Y.; Data, S.; Hong, S. H.; Reifenberger, R.; Henderson, J. I.; Kubiak, C. P. Phys. ReV. B 1999, 7852 (R), 59. (15) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550. (16) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015. (17) Liu, R.; Ke, S. H.; Baranger, H. U.; Yang, W. T. J. Am. Chem. Soc. 2006, 128, 6274. (18) van der Wiel, W. G.; De Franceschi, S.; Elzerman, J. M.; Fujisawa, T.; Tarucha, S.; Kouwenhoven, L. P. ReV. Mod. Phys. 2003, 75, 1. (19) Di, M.; Kim, S. G.; Pantelides, S. T.; Lang, N. D. Phys. ReV. Lett. 2001, 86, 288. (20) Taylor, J.; Brandbyge, M.; Stokbro, K. Phys. ReV. B 2003, 121101 (R), 68.
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