First-principles Study of Electron Transport Through Oligoacenes

Transcription

1 CHINESE JOURNAL OF CHEMICAL PHYSICS VOLUME 22, NUMBER 1 FEBRUARY 27, 2009 ARTICLE First-principles Study of Electron Transport Through Oligoacenes Zhen Pan, Qun-xiang Li, Qin-wei Shi, Xiao-ping Wang Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei , China (Dated: Received on September 16, 2008; Accepted on November 4, 2008) The electronic transport properties of oligoacenes sandwiched between two Au(111) surfaces with serial and parrallel configurations were investigeted by using a fully self-consistent nonequilibrium Green s function method combined with density functional calculations. This theoretical results show that the conductivity of oligoacenes with both sandwiched configurations at low bias voltage is mainly determined by the tail of the transmission peak from the perturbed highest occupied molecular orbital. When the molecular length increases, the zero-bias voltage conductance G(0) of oligoacenes with serial configuration neither follows Magoga s exponential law nor displays the even-odd oscillation effect, while the G(0) of the oligoacenes sandwiched with parallel configuration monotonically increases. The reduction of energy gaps, the alignment of the Fermi level, and the spatial distribution of the perturbed molecular orbitals are used to self-consistently explore the transport mechanism through oligoacenes. Key words: Transport property, Oligoacene, Zero-bias voltage conductance, Firstprinciples calculation I. INTRODUCTION Since the first measurement of conductance through single-molecular junction in 1997 [1], much interest has focused on molecular electronics. With the help of rapid development of experimental techniques such as the scanning tunneling microscope (STM) and mechanical break junction [1-3], the transport behaviors of various kinds of molecules including small conjugated molecules [1,2], carbon nanotubes [4], and fullerene [5] have been extensively studied. Recently, much attention has been devoted to the length-dependent conductance of conjugated oligomers (polymers) and molecular wires [6-13]. Several previous experimental and theoretical reports show that Magoga s law [14], G=G 0 e γl, (G 0 denotes the quantum conductance, G 0 =2e 2 /h, L is the chain length of the oligomer, γ is the damping factor), holds for several conjugated oligomers at low bias voltage case, such as oligophenylenes [12,15], and alkanes [11,16]. Because of their novel electronic properties together with a rigid geometric structure, polyacenes and oligoacenes were predicted to behave as one-dimensional organic conductors [17,18] due to the small band gap of polyacene series [17-21]. The electronic transport properties through oligoacene dithiolates (OAnDTs, n is the number of the benzene ring) or diaminoacenes have Author to whom correspondence should be addressed. liqun@ustc.edu.cn been investigated by several groups [7,8,15,22]. However, the length-dependent conductance of oligoacene is still under debate. Kim et al. reported electronic transport measurements on conjugated oligoacenes of increasing length with either thiol ( S) or isocyanide ( CN) linkers [7]. They found that the lengthdependent resistance through oligoacenes (n=1-3) follows the exponential law. Tada et al. observed an even-odd oscillation effect in the zero-bias voltage conductance with respect to n based on their nonself-consistent calculations [15]. Zhou et al. showed that Magoga s exponential law only holds for OAnDTs (n=2-5) under low bias voltage [22]. Recently, using the break junction method via STM, Quinn et al. measured the conductance of three oligoacenes, 1,4-diaminobenzene, 2,6-diaminonaphthalene, and 2,6- diaminoanthracene [8]. These molecules were sandwiched between two gold electrodes with serial and parallel configurations. They found that, with increasing molecular length, the conductance through oligoacenes decreases for serial configurations and increases for parallel configurations. Moreover, their experimental results clearly demonstrate that the trend of lengthdependent conductance for the serial case obviously deviates from Magoga s law [8]. Clearly, further investigation is desirable to explore the electronic transport properties and length-dependent conductance of oligoacenes with different sandwiched configurations. In this work, the electronic transport properties of OAnDTs sandwiched between two Au(111) surfaces with serial (n=1-8) and parallel (n=2-5) configurations are investigated by a fully self-consistent nonequilib- 7

2 8 Chin. J. Chem. Phys., Vol. 22, No. 1 Zhen Pan et al. rium Green s function (NEGF) method combined with density functional theory (DFT) calculations. With the increasing of the number of benzene rings, the calculated zero-bias voltage conductance G(0) through OAnDTs with serial configuration first decreases (n=1-4) and then increases (n=5-8). For parallel case, the reduction of energy gaps induces the monotonic increase of G(0). A detailed analysis of the electronic structures, such as the electrode-molecule coupling, the energy gap, the spatial distribution of the frontier perturbed molecular orbitals, and the alignment of the Fermi level, is carried out to self-consistently explore the transport properties of the oligoacene molecular junctions. II. COMPUTATIONAL METHOD Existing studies of metal-oligoacene-metal junctions have already given a qualitative explanation of the length-dependence conductance using models involving some phenomenological parameters [15,22]. For example, the Fermi level of gold electrodes in (111) direction was set to be 5.1 ev and adjusted around its work function ( 5.31 ev) [22]. In this work, the electronic transport properties are studied by fully self-consistent NEGF-DFT calculations, which are implemented using the ATK package [23,24]. This methodology has been successfully adopted to explain many experimental results or to design model devices [25,26]. Here, the transmission function, which represents the probability for electrons with incident energy E transferring from one electrode to the other electrode, is calculated as: T (E, V ) = T r[γ L (E, V )G(E, V )Γ R (E, V )G + (E, V )] (1) where V is the applied bias voltage, and Γ L (Γ R ) is the left (right) coupling matrix between the central oligoacene molecule and the left (right) electrode. G(E, V ) is the Green s function of the contact region, which is computed self-consistently. The G(0) can be obtained from the transmission probability T (E F,0): G(0)=(2e 2 /h)t (E=E F,V =0), where e is the electron charge, E F is the average Fermi level of two electrodes, and h is the Planck constant. The current is calculated by integrating the transmission function within a given bias voltage window as I(V ) = µr µ L T (E, V ) [f(e µ L ) f(e µ R )]de (2) where f(e) is the Fermi-Dirac function, and µ L (µ R ) is the chemical potential of the left (right) electrode. Under the applied bias voltage, V, the integration window ranges from µ L = ev /2 to µ R =ev /2. In our calculations, Perdew-Zunger local density approximation is used [27]. Core electrons are modeled with Troullier-Matrins nonlocal pseudopotential [28], and valence electrons are expanded in a Spanish initiative for electronic simulations with thousands of atoms (SIESTA) localized basis set [29]. Single-ζ with a polarization basis set is chosen for Au and double-ζ with polarization (DZP) is used for other atoms. An energy cutoff of 150 Ry for the grid integration is set to obtain the accurate charge density. A (2 2) k-grid on the x-y plane is used both for self-consistent calculation and transmission function evaluation. Test calculations show that the use of 3 3 k-point sampling and DZP basis set for all atoms does not affect the main feature of the transmission functions. III. RESULTS AND DISCUSSION A. Serial configuration It is well known that the experimental fabrication details (i.e. the contact geometry) are unknown in molecular electronics [8]. We begin with a model device: a metal-molecule-metal junction, in which the oligoacene molecule is sandwiched between two Au(111) surfaces, as shown in Fig.1(a). The molecular junction is divided into three regions: left electrode, contact region, and right electrode. The contact region includes an oligoacene molecule and two surface layers of Au(111) surfaces, where all the screening effects are included into the contact region, within which the charge-density matrix is solved self-consistently with the NEGF method. The oligoacene molecule connects to Au(111) surfaces with sulfur anchoring atoms at the hollow sites. The Au(111) surface is modeled by a (4 4) cell with periodic boundary conditions. The positions of all atoms of oligoacenes are optimized by using the SIESTA package [29]. The molecule-electrode distance is fixed to be 2.0 Å for all systems we studied. This separation from the sulfur atom to Au(111) surface is a usually acceptable distance in the Refs.[15,22,30]. For the serial configuration, we examine two molecular junctions: (i) the line connecting two anchoring sulfur atoms, which is perpendicular to Au(111) surfaces, (ii) the end C S bonds, which are perpendicular to Au(111) surfaces. These are shown in Fig.1 (a) and (b), respectively. The corresponding zero-bias voltage conductance G(0) of OAnDTs with respect to the number of benzene rings from 1 to 8 is shown in Fig.1(c) with square and filled circle symbols. It is clear that the main feature of two curves is very similar and they neither follow Magoga s exponential law [14] nor display the odd-even oscillation effect [15]. For the short oligoacenes (n<4), G(0) decreases with increasing of n, but it obviously deviates from Magoga s exponential law, as shown in the inset of Fig.1(c). When n changes from 5 to 8, the calculated G(0) increases gradually. It should be pointed out that this observed tendency of G(0) for the short oligoacenes (n=1-3) is consistent with the Quinn et al. s experimental results (OAnDT, n=1-3) [8], but seems to conflict with Kim et al. s experimental observations [7]. Kim et al. observed the length-

3 Chin. J. Chem. Phys., Vol. 22, No. 1 Electron Transport Through Oligoacenes 9 (a) y z (b) y z FIG. 2 The I -V curves of the OAnDTs molecular junctions (n=1-8) with serial configuration. FIG. 1 Schematic illustration of the Au-OAnDTs-Au junction (n=1-8, here, n=5 is taken as an example). (a) and (b) stand for two different sandwiched configurations. The contact region includes the molecule and two surface layers of the left and right electrodes. (c) The length-dependent conductance at zero bias voltage of OAnDTs (n=1-8). The inset illustrates the deviation from Magoga s exponential law. dependent conductance following the exponential law [7]. We think there are two most possible reasons of this discrepancy between our theoretical results and their experiments. One is the limitations of the used computational method, which always overestimates the current through a molecular junction [23,31]. The other is the contact geometry. The oligoacenes symmetrically couple with two Au(111) surfaces in our computational models, but the molecular junctions are builtin asymmetric in the experiments [7]. The oligoacenes were self-assembled on gold substrate with thiol and isocyanide linkers. Then the transport property is directly probed over the oligoacenes by Au-coated atomic force microscopy tip under external bias voltage. Since the calculated transmission is a function of the applied bias voltage (Eq.(1)), it should be pointed out that the observed feature (Fig.1(c)) of G(0) with respect to the number of benzene rings only holds for the small bias voltage case. In what follows, we just focus on the first kind of connection (i) for clarity since these calculated G(0) of two different contact configurations are very close to each other. Figure 2 shows the current-voltage (I-V ) curves of the OAnDTs (n=1-8) junctions with serial configuration. At each bias voltage, the current is determined self-consistently under the nonequilibrium condition. Clearly, the I-V curves display complicated features and the current nonlinearly increases in all junctions studied here. The calculated current depends on not only the applied bias voltage but also the molecular length. For example, the current at 0.6 V is 6.57, 4.81, 3.75, 3.65, 4.38, 6.03, 11.66, and µa for the oligoacene molecule with n changing from 1 to 8, respectively. When the applied bias voltage is 1.4 V, the corresponding current is 28.22, 22.69, 18.52, 17.72, 23.78, 21.48, 20.15, and µa. To understand these complicated features in the zerobias voltage conductance (Fig.1(c)) and the current (Fig.2) curves with respect to the number of benzene rings, we compute the energy dependence of total zerobias voltage transmission functions for these OAnDTs (n=1-8), which are shown in Fig.3. Here, the vertical dashed line stands for the Fermi level (E F ). The following obvious features are observed: (i) There are several transmission peaks in these transmission function curves for all oligoacene molecules. (ii) The Fermi level lies between two significant transmission peaks located on two sides of the Fermi level labeled with A and B in Fig.3. (iii) The transmission peak A is located closer to the Fermi level. This indicates that the conductivity of oligoacenes with serial configuration is mainly determined by the tail of this transmission peak A under low bias voltage. (iv) The separation between the transmission peaks A and B gradually reduces and the transmission peaks obviously become narrow when the number of benzene rings increases. To uncover the transport mechanism of OAnDTs (n=1-8) junctions, we calculate their electronic structures in detail. In general, the coupling between the molecule and electrodes plays an important role on elec-

4 10 Chin. J. Chem. Phys., Vol. 22, No. 1 Zhen Pan et al n=1 HOMO LUMO LUMO+1 FIG. 3 The zero-bias voltage transmission functions of OAnDTs (n=1-8) sandwiched between two Au(111) surface with serial configuration versus the energy. Here, the dashed vertical line stands for the Fermi level (E F), the vertical short lines stand for the energy levels of MPSH HOMO and LUMO. tronic transport. When an oligoacene molecule is connected to gold electrodes, the energy levels and spatial distribution of molecular orbitals (MOs) are modified due to the molecule-electrode interaction. An effective scheme has been proposed to construct this type of perturbed MOs [23]. First, one needs to project the self-consistent Hamiltonian of the molecular junction onto the central oligoacene molecule, then to diagonalize this molecular projected self-consistent Hamiltonian (MPSH) matrix. The eigenstates and energy levels of MPSH can be correlated to the MPSH MOs and energy levels, respectively. The vertical lines in Fig.3 stand for these MSPH energy levels. It is clear that the positions of transmission peaks correspond nicely with the MPSH energy levels. The transmission peaks A and B in Fig.3 come from the MPSH highest occupied molecular orbital (MPSH HOMO) and the lowest unoccupied molecular orbital (MPSH LUMO), respectively. The Fermi level is aligned between the MPSH HOMO and LUMO. However, for all molecular junctions, the MPSH HOMO lies closer to the Fermi level. Therefore, it is safe for us to conclude that the current through oligoacenes with serial configuration under low bias voltage is mainly contributed by the tail of transmission peak coming from the MPSH HOMO. In fact, for the free oligoacenes [15,18-20], when the oligoacene molecular length (n) increases, the gap between the MPSH HOMO and LUMO (H-L gap) reduce, which is the origin of the reduction of the separation between the two transmission peaks A and B. Figure 4 shows the spatial distributions of the MPSH HOMO and LUMO of OAnDTs (n=1-8). Clearly, two FIG. 4 The spatial distribution of the MPSH HOMO and LUMO of OAnDTs (n=1-8) sandwiched with serial configuration. The LUMO+1 of 1,4-dithiolbenzene (OAnDT, n=1) is also shown. For interpretation of the color in this figure legend, the reader can refer to the web version of this article. frontier MPSH HOMO and LUMO are π-type orbitals, which delocalize on the whole molecule. The spatial distributions on sulfur atoms imply the interaction between molecule and electrodes. With increasing of the number of benzene rings, the electrode-electrode distance becomes large, the spatial distribution on sulfur atoms decreases gradually, which results in the narrowing of these transmission peaks, as shown in Fig.3. Note that for OAnDTs (n=1, 1,4-dithiolbenzene) there is almost no spatial distribution on sulfur atoms. The transmission peak B is contributed by MPSH LUMO+1 rather than the MPSH LUMO. Since the MPSH LUMO and LUMO+1 almost degenerate, two vertical short lines almost overlap together at 2.75 ev in Fig.3. As mentioned above, the conductance at zero-bias voltage G(0), depends on the number of benzene rings in a complicated way (Fig.1(c)). This observation can be easily understood by using the calculated results shown in Fig.3 and Fig.4. For the short OAnDTs (i.e. n<5) junctions, when the number of benzene rings in oligoacenes increases, the H-L gap decreases, but two transmission peaks are located far away from the Fermi level. Note that the spatial distribution of MPSH HOMO and LUMO at anchoring sulfur atoms also decreases, which leads to the narrowing of the transmission peaks. Consequently, G(0) decreases with the increasing of n. When the number of benzene rings further increases, i.e. n>5, the reduction of H-L gap turns into a crucial factor although the transmission peaks continuously become narrow. As a result, G(0) of OAnDTs (n>5) molecular junctions increases. Clearly, the reduction of H-L gaps, the alignment of the Fermi level, and the narrowing of transmission peaks are responsible for these observations in Fig.1(c).

5 Chin. J. Chem. Phys., Vol. 22, No. 1 Electron Transport Through Oligoacenes 11 z (a) y FIG. 5 (a) Schematic illustration of the Au-OAnDTs-Au junction (n=3 as an example) with parallel sandwiched configuration. (b) The calculated length-dependent conductance at zero bias voltage G(0). For interpretation of the color in this figure legend, the reader can refer to the web version of this article. B. Parallel configuration In this section, we turn to examine the transport properties through oligoacenes sandwiched between two Au(111) surface with parallel configuration. The computational model for OAnDTs (n=2-5) is shown in Fig.5(a). Here, Au(111) is simulated with a (5 5) supercell with periodic boundary conditions. Figure 5(b) presents the calculated length-dependent G(0), which monotoniclly increases with increasing of n. This theoretical result agrees well with the experimental results for diamioacenes with parallel sandwiched configuration. Note that, compared with the serial case (Fig.1(c)), G(0) of OAnDTs (n=2-5) with parallel configuration depends differently on the number of benzene rings. To explore the transport properties of OAnDTs junctions with parallel sandwiched configuration, we calculate the zero-bias voltage transmission functions T (E), the frontier MPSH MOs and the spatial distributions of the MPSH HOMO and LUMO of OAnDTs (n=25). The corresponding calculated results are shown in Fig.6. It is clear that two frontier MPSH MOs are delocalized π orbitals, which provide a good transmission channel and result in the resonant transmission peaks located at two sides of the Fermi level. In the molecular junctions studied here, the transmission peak of MPSH HOMO is located much closer to the Fermi level. The tail of this peak mainly determines the calculated G(0). When n in OAnDTs increases, the spatial distribution of MPSH HOMO and LUMO on sulfur atoms changes slightly, the H-L gap reduces obviously, and the corresponding MPSH HOMO and LUMO transmission peaks move toward the Fermi level. These observations can be used to understand why G(0) of OAnDTs (n=2-5) sandwiched with parallel configuration monotonically increases with the increasing of n. By comparing the reported experimental results with theoretical ones, we find that the theoretical current (b) LUMO HOMO n= FIG. 6 (a) The zero-bias voltage transmission functions of OAnDTs (n=2-5) sandwiched between two Au(111) surface with parallel configuration versus the energy. Here, the vertical dashed line labels the Fermi level (EF ), and the vertical short lines stand for the energy levels of MPSH HOMO and LUMO. In the right panel, the symbol * denotes the anchoring positions. (b) The spatial distribution of the MPSH HOMO and LUMO of OAnDTs (n=2-5). For interpretation of the color in this figure legend, the reader can refer to the web version of this article. values are larger by about one order of magnitude than the experimental ones. This discrepancy between theory and experiment is a common problem in molecular electronics [31]. The previous theoretical studies used the hybrid exchange-correlation functionals and the energy gap is usually overestimated based on their hybrid DFT calculations [15,22]. In contrast, the energy gap is underestimated at LDA level, so our calculated H-L gaps are less than the previous theoretical results [15,22]. IV. CONCLUSION Based on fully self-consistent NEGF and DFT calculations, we investigate the length-dependent transport properties of OAnDTs sandwiched between two Au(111) surfaces with serial (n=1-8) and parallel (n=25) configurations. For the OAnDTs (n=1-8) sandwiched with the serial configuration, the Fermi level is located within the H-L gap and the conductivity at low bias voltage is mainly determined by the tail of c 2009 Chinese Physical Society

6 12 Chin. J. Chem. Phys., Vol. 22, No. 1 Zhen Pan et al. transmission peak from the MPSH HOMO. When n in OAnDTs (n=1-8) increases, the H-L gap and the spatial distribution of MPSH HOMO and LUMO on the anchoring sulfur atoms decreases gradually, which results in the G(0) first decreasing (n=1-4) and then increasing (n=5-8). For the OAnDTs (n=2-5) with the parallel configuration, the tail of the transmission peak from the MPSH HOMO also mainly determines their conductivities under low bias voltage. The reduction of H-L gaps is responsible for the monotonic increment of G(0) with increasing n. Theoretical results indicate that various factors, such as the electrode-molecule coupling, the H- L gap, the spatial distribution of the frontier MPSH MOs, and the alignment of the Fermi level, should be taken into account to self-consistently explore the transport mechanism of oligoacene junctions. 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