NANO LETTERS
Interface Sensitivity in Quantum Transport through Single Molecules
2004 Vol. 4, No. 2 209-212
Katsunori Tagami,* Liguang Wang,† and Masaru Tsukada‡ Department of Physics, Graduate School of Science, UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Received October 13, 2003; Revised Manuscript Received November 26, 2003
ABSTRACT By the density-functional-derived tight-binding model, the quantum transport properties of single phenalenyl-based molecules are investigated. We find that the transport character of the system can be tuned from the semiconductive to the metallic just by changing the sites connected to the electrodes or by substituting the central atom of the phenalenyl with the boron atom. This shows that designing not only molecules but also interface structures is highly important in single molecular electronic devices.
In the research field of single molecular devices, moleculedependent quantum transport properties have been a hot scientific issue. Thus far, the transport properties of various molecules have been studied (e.g., benzene,1,2 fullerene,3 oligoporphyrin molecules,4-7 benzothiophene-based molecular solenoids,8 and phenylenevinylene-based molecular magnets9). In addition, the effects of chemical doping on the single molecular devices have been clarified.8,10 However, most of these works have focused on exploring the target molecules. It should be noted that the molecule/electrode interface structures are also significant for quantum transport through single molecular devices.7 In this work, we will demonstrate how the molecule/ electrode interface structure affects the transmission probabilities of the molecular bridge system in the coherent transport regime. As an example, we adopt the phenalenyl (C13H9) molecule (see Figure 1a). Here, XdC˙ indicates that the unpaired electron exists in the molecule, but it does not mean that this electron is localized on the central site. Measured from the central site, the second- and third-nearest sites are labeled R and β, respectively. There are six R sites and three β sites in the molecule. The β sites lie on the σV mirror plane of the D3h point group. The phenalenyl itself is one of the relatively stable neutral radicals, and many derivative molecules have been synthesized.11-15 Furthermore, by the crystallization of this molecule and its complexes, bulk properties such as magnetism and conductivity have been studied.16,17 Their higher conductivities have attracted considerable attention compared to those of the other neutral radical crystals.16 In this paper, we concentrate on clarifying two points: the * Corresponding author. E-mail:
[email protected]. † College of Science, Southern Yangtze University, Wuxi 214064, China. ‡ University of Tokyo. 10.1021/nl0348894 CCC: $27.50 Published on Web 01/13/2004
© 2004 American Chemical Society
Figure 1. Structures of phenalenyl-based molecules. (a) Phenalenyl (XdC˙ ), (b) 9b-azaphenalene (XdN), and (c) 9b-boraphenalene (Xd B) molecules. The second- and third-nearest sites from the center are labeled as R and β sites.
dependence of the conductance (1) on the atomic sites (R, β) connected to the electrodes and (2) on the substitution of the central carbon atom (9b site) with the nitrogen/boron atom (see Figure 1b and c). The latter point is intended to reveal the effects of the arrangement of the resonant molecular levels caused by adding/extracting an electron to/ from the molecule. (These atomic substitutions have been extensively studied for nanotubes18-22 and fullerenes.23-26) Thus, whereas the ground state of the phenalenyl molecule is a spin-polarized monoradical, the other two molecules are spin-unpolarized. We consider the molecular bridge structures where these molecules are bridged between the two gold electrodes through the mercapto-vinyl groups, as schematically illustrated in Figure 2. In this example, the two mercaptovinyl groups are attached to the left and right R atomic sites. The configurations of these electrode-molecule-electrode systems are prepared in the following way. First, the atomic coordinates of these three types of molecules, including two mercapto-vinyl groups at their ends, are determined by ab initio calculations using the B3LYP exchange-correlation functional27,28 with the LANL2DZ bases. Then, these molecules are located between two semi-infinitely long gold electrodes.8 In making contact with the electrodes, H atoms in S-H bonds are assumed to be removed, and thiolate (S-
Figure 2. Structure of the phenalenyl-based molecular bridge. The label X is defined in Figure 1. The molecule is connected to the electrodes (shaded) through the mercapto-vinyl groups.
Figure 4. Transmission spectra of (a) type-C, (b) type-N, and (c) type-B molecular bridges. The R sites are connected to the electrodes through the mercapto-vinyl groups.
Figure 3. Schematic energy diagram and wave functions of isolated molecule. The e′′ molecular orbitals are doubly degenerate.
Au) bonds are assumed to be formed instead. The length of the S-Au bonds is set to about 2.55 Å. The details of the calculation technique have been published elsewhere.8,9 Briefly speaking, the electronic states of the metal-molecule-metal system are described by the spin-polarized density-functional-derived tight-binding model.29 This tight-binding formalism has been established well and has been successfully applied to research on various materials4-9,30-35 The infinite size of the extended system is treated by the extended-molecule approach2,36 coupled with the Green functions method. The transmission spectra are evaluated by the Landauer formula.36 Before discussing the transmission spectra, we will show the electronic states of the isolated molecules, which are necessary to comprehend the transmission spectra of the molecular bridges. Figure 3 illustrates several molecular orbitals of the isolated molecules shown in Figure 1, which lie around the Fermi level. The radius of the circle on each atomic site denotes the amplitude of the corresponding molecular orbital (MO). White and black denote the positive and negative phases of the MO, respectively. The a1′′ orbital is the nonbonding orbital12 and has amplitude only on the R atomic sites. One of the doubly degenerate e′′ orbitals is symmetric with respect to a σV mirror plane, and the other orbital is antisymmetric with respect to the same plane. Hereafter, we will call the former and latter orbitals φs and φa, respectively. Because the a2′′ orbital has a large amplitude on the central atom site, its energy level is considerably affected by the atomic species X. In the case of XdC˙ , the a1′′ state is the singly occupied molecular orbital (SOMO), and the a2′′ level is close to the 210
e′′ level. In the case of XdN, the a1′′ state is doubly occupied and is the highest occupied molecular orbital (HOMO). The a2′′ level is 0.83 eV lower than the e′′ level. In the case of XdB, the a1′′ state is the lowest unoccupied molecular orbital (LUMO). In addition, the order of the occupied a2′′ and e′′ levels is changed. Namely, the a2′′ level is now 1.00 eV higher than the e′′ level. These features reflect the fact that the on-site p-orbital level gets deeper in the order of B, C, N. Then, we will discuss how the transmission spectra are affected by the positions of the atomic sites connected to the electrodes and by the substitution of the central atom with the other atoms. For simplicity, in the following discussion we will refer to the molecular bridges with XdC˙ , N, and B as type-C, type-N, and type-B molecular bridges, respectively. In the case when the two R sites are connected to the left and right electrodes through the mercapto-vinyl groups, the transmission spectra of the type-C and type-N molecular bridges are illustrated in Figure 4a and b. The lateral variable is the electron energy E incident from the electrode, whose origin is set to the Fermi level of the gold electrodes. The transmission peaks are found in the very vicinity of the Fermi level (i.e., at E ) 0.08 and -0.02 eV for the corresponding cases). These peaks are found to originate from the nonbonding a1′′ orbital. Note here that transmission through the a1′′ orbital is allowed because this orbital has amplitude on the R sites (see Figure 3). Because the resonant peaks between the interval [EF - eV/2, EF + eV/2] contribute to the current under the bias voltage V, both molecular bridges are expected to conduct well even at lower bias voltages. Here we should comment on two points in the spectra. First, the achieved electronic states of the type-C bridge are spin-unpolarized, although the isolated phenalenyl molecule is spin-polarized. One of the reasons is considered in the following way. In the phenalenyl molecule, the majority (up) spin density is distributed on the R sites as illustrated in Figure 5 because the singly occupied a1′′ orbital has a density only on the R sites (see Figure 3). Once the electrode is Nano Lett., Vol. 4, No. 2, 2004
Figure 5. Spin-density distribution of the isolated phanelenyl molecule. Orange and Blue correspond to the up (majority) and down (minority) spin densities, respectively.
connected to this site through the mercapto-vinyl group, the large spin density around it is remarkably disturbed by the electrode wave function, which may lead to the disappearance of the spin polarization. In contrast, as will be discussed later, the spin density on this R site is maintained when the electrode is connected to the β site. However, to achieve a clear understanding of this difference, more accurate calculations are necessary. Second, the peak position in the type-C molecular bridge lies above the Fermi level, but the peak position in the type-N bridge lies slightly below it. This can be explained as follows. If a resonant peak is found just at the Fermi level, then the corresponding molecular level is 50% occupied. Taking into account the spin degeneracy, this orbital is considered to be singly occupied. Thus, the upward peak shift in the type-C bridge means that the occupation number of the a1′′ orbital is less than 1.0. In fact, the molecule (the area enclosed by the dotted lines in Figure 2) is found to be positively charged by 0.27e. The downward peak shift in the type-N bridge means that the occupation number of the a1′′ orbital is more than 1.0 but less than 2.0. In a similar manner, the molecule is positively charged by 0.34e. In contrast, for the type-B molecular bridge, three transmission peaks are observed between -1.0 < E < 0.0 eV, as illustrated in Figure 4c. The peaks at E ) -0.78, -0.58, and -0.14 eV are found to originate from the e ′′(φa) orbital, the mixture of the e′′(φs) and a2′′ orbitals, and the a2′′ orbital, respectively. Because these orbitals have large amplitudes on the R sites, the system is expected to conduct well. As for the charge distribution, the molecule (the area enclosed by the dotted lines in Figure 2) is negatively charged by 0.15e. The charge transfer in the opposite direction compared to the other two molecular bridges brings about the upward shift of the molecular level. For example, the transmission peak that corresponds to the a1′′ orbital appears at around E ) 1.5 eV, which is beyond the energy range in the Figure. In the case when the left and right β sites are connected to the electrodes, the corresponding transmission specta are shown in Figures 6a-c. The green and red lines in the spectra Nano Lett., Vol. 4, No. 2, 2004
Figure 6. Transmission spectra of (a) type-C, (b) type-N, and (c) type-B molecular bridges. The β sites are connected to the electrodes through the mercapto-vinyl groups. In the topmost plot, the green and red lines correspond to the up and down spin components, respectively.
of the type-C bridge (Figure 6a) correspond to the majority (up) and minority (down) spins of the electron incident from the electrodes, respectively. Note here that the transmission spectra are spin-dependent because the corresponding electronic states are converged to the spin-polarized state even after the molecule is connected to the electrodes. However, the peak positions for both spins are found to differ only slightly (i.e., E ) -0.69 eV for the up spin and E ) -0.67 eV for the down spin). In a similar manner, the transmission peak in the type-N molecular bridge is found at E ) -0.79 eV (see Figure 6b). These three resonant peaks are found to originate from the mixture of the two e′′ orbitals and the a2′′ orbital. Their peak heights take small values of 0.13 and 0.49 for the type-C and type-N bridges, respectively, because the corresponding charge densities on the molecules are smaller than those on the electrodes. Note here that the reason for the disappearance of the transmission peak around the Fermi level is that the a1′′ orbital has no amplitude on the β sites. As a result, these two molecular bridges are semiconductive at best with a threshold bias of 1.3 V. Here we assumed that under the bias voltage V the peaks between the interval [EF - eV/2, EF + eV/2] contribute to the current. In contrast, as illustrated in Figure 6c, the transmission spectrum of the type-B bridge shows a totally different feature. The peaks are found at the positions closer to the Fermi level (i.e., E ) -0.52 and -0.17 eV). These two peaks are found to originate from the e′′(φa) orbital and the mixture of e′′(φs) and a2′′ orbitals, respectively. Their peak heights amount to 0.99, which reflects the delocalized charge density along the bridge. Thus, only in this type of molecular bridge, the system is expected to conduct well even at lower bias voltages. In conclusion, we have shown that the quantum transport properties of the phenalenyl-based molecular bridges are highly sensitive to the positions of the atomic sites connected to the electrodes. Namely, when the R sites are connected 211
to the electrodes, the molecular bridge is conductive even at lower bias voltages. In contrast, when the β sites are connected to the electrodes, the system is semiconductive. Such a dramatic change in the transport features is found to originate from the spatial distribution of the nonbonding a1′′ orbital, which has amplitude only on the R sites. These features do not change if the central atom of the phenalenyl is substituted with the nitrogen atom. However, if it is substituted with the boron atom, then the transport now occurs through the orbitals that have amplitude both on the R and β atomic sites. Thus, the system is conductive irrespective of the sites connected to the electrodes. These findings indicate that designing a whole system that includes not only molecules but also interfaces is highly important in fabricating molecular electronic devices. Acknowledgment. This work was supported in part by the Ministry of Education, Culture, Sports, Science and Technology through a Grant-in-Aid for Creative Scientific Research on “Devices on Molecular and DNA Levels”. The numerical calculations were performed on the SR8000 at the ISSP. References (1) Ventra, M. D.; Pantelides, S. T.; Lang. N. D. Phys. ReV. Lett. 2000, 84, 979. (2) Xue, Y.; Datta, S.; Ratner, M. A. J. Chem. Phys. 2001, 115, 4292. (3) Taylor, J.; Guo, H.; Wang, J. Phys. ReV. B 2001, 63, 121104. (4) Tagami, K.; Tsukada, M.; Matsumoto, T.; Kawai, T. Phys. ReV. B 2003, 67, 245324. (5) Tagami, K.; Tsukada, M. Curr. Appl. Phys. 2003, 3, 439. (6) Tagami, K.; Tsukada, M. Jpn. J. Appl. Phys. 2003, 42, 3606. (7) Tagami, K.; Tsukada, M. e-J. Surf. Sci. Nanotech. 2003, 1, 45. (8) Tagami, K.; Tsukada, M.; Wada, Y.; Iwasaki, T.; Nishide, H. J. Chem. Phys. 2003, 119, 7941. (9) Tagami, K.; Tsukada, M. J. Phys. Chem. B, submitted for publication. (10) Lang, N. D.; Avouris, P. Nano Lett. 2002, 2, 1047. (11) Zheng, S.; Lan, J.; Khan, I.; Rubin, Y. J. Am. Chem. Soc. 2003, 125, 5786. (12) Koutentis, P. A.; Chen, Y.; Cao, Y.; Best, T. P.; Itkis, M. E.; Beer. L.; Oakley, R. T.; Cordes, A. W.; Brock, C. P.; Haddon, R. C. J. Am. Chem. Soc. 2001, 123, 3864. (13) Goto, K.; Kubo, T.; Yamamoto, K.; Nakasuji, K.; Sato, K.; Shiomi, D.; Takui, T.; Kubota, M.; Kobayashi, T.; Yakushi, K.; Ouyang, J. J. Am. Chem. Soc. 1999, 121, 1619.
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NL0348894
Nano Lett., Vol. 4, No. 2, 2004
