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First-principles study of the electronic transport properties of the anthraquinone-based molecular switch
Physica B 406 (2011) 895–898
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
First-principles study of the electronic transport properties of the anthraquinone-based molecular switch P. Zhao a,n, D.S. Liu b,c, P.J. Wang a, Z. Zhang a, C.F. Fang b, G.M. Ji b a
School of Science, University of Jinan, Jinan 250022, China School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China c Department of Physics, Jining University, Qufu 273155, China b
a r t i c l e in f o
abstract
Article history: Received 17 September 2010 Received in revised form 13 November 2010 Accepted 7 December 2010 Available online 15 December 2010
By applying non-equilibrium Green’s function (NEGF) formalism combined with first-principles density functional theory (DFT), we have investigated the electronic transport properties of the anthraquinonebased molecular switch. The molecule that comprises the switch can be converted between the hydroquinone (HQ) and anthraquinone (AQ) forms via redox reactions. The transmission spectra of these two forms are remarkably distinctive. Our results show that the current through the HQ form is significantly larger than that through the AQ form, which suggests that this system has attractive potential application in future molecular switch technology. & 2010 Elsevier B.V. All rights reserved.
Keywords: Molecular switch Anthraquinone Non-equilibrium Green’s function Electronic transport
1. Introduction Because of rapid progress in microscale fabrication technology, molecular electronics has attracted increasingly much attention recently. A critical mission of the molecular electronics is to develop novel devices at single molecular level. In the last several years, many molecular electronic devices with different functionalities have been designed and analyzed [1–10]. Among these, a single molecular switch holds great promise since it is critical to the ability to store digital information and route signals in future molecular electronic logic circuits. The basic requirement for a molecular switch is bistability, which is the occurrence of two different forms of a molecule that can be selectively and reversibly converted into each other in response to an external trigger such as light [6,7], electric field [9], redox process [10], and so on. Recently, van Dijk et al. [11] synthesized a kind of anthraquinone-based molecular wire, which can be reversibly switched electrochemically between the reduced hydroquinone (HQ) and oxidized anthraquinone (AQ) states via redox reactions. Drawing from the chemical intuition, one can see that the p-conjugation extends over the entire HQ form, whereas it is cut in the AQ form because of the p-benzoquinone (p-bq) unit. As a consequence, the HQ form is expected to exhibit better conductance than the AQ form. Especially, this redox-controlled molecular switch has the advantage that the overall length and
n
Corresponding author. Tel.: + 86 53182765976. E-mail address: [email protected] (P. Zhao).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.12.023
thus the molecule–electrode binding geometry of the switch is not changed significantly. It is well known that the conductive properties are of crucial importance in any device application. Very recently, Markussen et al. [12] analyzed the zero-bias transmission properties of the anthraquinone-based molecular switch. In this paper, we investigated the electronic transport properties of the anthraquinonebased molecular switch at finite bias by a theoretical simulation that combines both first-principles density functional theory (DFT) and non-equilibrium Green’s function (NEGF) method.
2. Model and method Detailed knowledge of the geometrical properties of materials is a necessary requirement for understanding their electronic transport properties. Thus, we first optimize the geometries of free thiol (SH) groups capped molecule with the above-mentioned two forms. Next, we construct a two-probe system to resemble a mechanically controlled break junction (MCBJ) experimental situation as follows. Based on the experimental issues about selfassembled monolayers (SAMs), it is generally accepted that hydrogen atoms are dissociated on adsorption to metal surfaces [13,14]. So the two terminal hydrogen atoms bonded to the sulfur atom are eliminated from the optimized structure, and the remained part is sandwiched between two parallel Au(1 1 1) surfaces that correspond to the surfaces of the gold electrodes, which have a face-centered cubic (f.c.c.) structure. There are three possible adsorption sites of a sulfur atom on the Au(1 1 1) surfaces, i.e., top, bridge, and hollow sites [15–18]. Most of the studies
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P. Zhao et al. / Physica B 406 (2011) 895–898
predicted that the top and the hollow adsorption sites are more favorable in energy. Since our main purpose in this work is to determine the conductivity of the switch through a redox reaction, the nature of Au–S interaction is not investigated here. We choose the sulfur atom to locate at the hollow site of each gold surface [18]. ˚ is chosen to fit The distance between two gold electrodes, 28.42 A, best the length of the optimized HQ/AQ molecule [19]. Each layer of the gold electrodes is represented by a (3 3) supercell with the periodic boundary conditions so that it imitates bulk metal structures. As shown in Fig. 1, the entire molecular switch is divided into three regions: a left electrode (L), a central scattering region (C), and a right electrode (R). The semi-infinite electrodes are calculated separately to obtain the bulk self-energy. The central scattering region includes the HQ/AQ molecule and two layers of gold slab from each electrode to screen the perturbation effect from the central region and they are denoted as surface-atomic layers. The geometry of the central extended molecule is fully optimized by minimizing the atomic forces on the HQ/AQ molecule to be ˚ while keeping all the gold atoms fixed. All smaller than 0.05 eV/A, the geometrical optimizations have been carried out by using the Spanish initiative for electronic simulations with thousands of atoms (SIESTA) package [20]. The electronic transport properties of the molecular switch is calculated by a fully self-consistent NEGF formalism combined with the first-principles DFT, which is implemented in Atomistix ToolKit (ATK) package [21,22]. This methodology has been adopted to explain various experimental results successfully [23,24]. In our calculations, the exchange–correlation potential is described by the gradient generalized approximation with the Perdew, Burke, and Ernzerhof parameterization (GGA.PBE) [25]. Core electrons are modeled with Troullier–Martins non-local pseudopotential [26], and valence electrons are expanded in a SIESTA localized basis set [20]. A single-zeta plus polarization (SZP) basis set for gold atoms and a double-zeta plus polarization (DZP) basis set for the organic molecule are adopted. An energy cutoff of 150 Ry for the grid integration is set to present the accurate charge density. In NEGF theory, the transmission function T(E,V) of the system is a sum of transmission probabilities of all channels available at energy E under external bias voltage V [27]: TðE,VÞ ¼ Tr½GL ðVÞGR ðE,VÞGR ðVÞGA ðE,VÞ
ð1Þ
Then, the current (I)–voltage (V) characteristics are obtained ¨ from the Landauer–Butiker formulism [27]: Z 2e IðVÞ ¼ ½ f ðEmL Þf ðEmR ÞTðE,VÞdE: ð2Þ h where h is Planck’s constant, e the electron charge, f the Fermi function, mL,R the electrochemical potential of the left and right electrodes, and the difference in the electrochemical potentials is given in eV with the applied bias voltage V, i.e.mL=R ðVÞ ¼ EF 8 eV=2, EF is the Fermi level of the system.
3. Results and discussion In Fig. 2, we describe the self-consistently calculated I–V characteristic curves of the molecular switch with two forms at bias up to 1.5 V, which is reasonable in practical experimental measurements. Obvious switching behavior can be seen from Fig. 2. Although the two forms differ only by two hydrogen atoms, their conductance properties are drastically different. The current through the AQ form is strongly suppressed over the entire bias range, while the current through the HQ form is evidently larger than that through the AQ form. Thus, when HQ is oxidized to AQ by application of an electrochemical potential to the electrode, the switch is predicted to switch from the on state (high conductance) to the off state (low conductance), and vice versa. As a figure of merit, the on–off ratio of currents, R(V)¼IHQ/IAQ, versus bias V is plotted in the inset of Fig. 2. At the zero bias when both currents vanish, we calculate the on–off ratio using the zero-bias conductance. From the inset of Fig. 2, we can see that R varies from around 37 to 1480 in the bias range under investigation. Such a significant on–off ratio can be easily measured and desirable for the real application. To understand the dramatic difference in conductance appearing in the HQ and AQ forms, we calculated the energy dependence of zerobias transmission spectra. As shown in Fig. 3, the transmission spectra display extraordinarily different characteristics. The system with the HQ form has a strong transmission peak at 1.17 and 0.33 eV above and below the EF, respectively. Obviously, the transport properties are predominated by the tail of the peak located at 0.33 eV below the EF at small bias voltage. However, the nearest transmission peak is at 0.81 eV above the EF and no obvious transmission peak below the EF in
where GR,A is the retarded and advanced Green’s function, coupling function GL,R are the imaginary parts of the left and right selfenergies, respectively.
Fig. 1. Schematic illustration of the molecular switch with two forms. The white, gray, red, yellow, and golden spheres represent H, C, O, S, and Au atoms, respectively. The vertical black line denotes the interface between the central scattering region and the left or right gold electrode. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Calculated current–voltage characteristic curves of the molecular switch with two forms. The squares linking with black solid lines are for the switch with the HQ form, while the circles linking with short red dotted lines stand for the switch with the AQ form. The inset is the on–off ratio of currents as a function of the applied bias. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
P. Zhao et al. / Physica B 406 (2011) 895–898
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Fig. 3. Zero-bias transmission spectra of the molecular switch with the HQ and AQ forms. The positions of MPSH eigenvalues are marked with squares for the HQ form and with circles for the AQ one, respectively. In our calculations, we set the energy origin as the Fermi level EF.
the system with the AQ form. The calculated zero-bias conductance is 1.8 10 2G0 for the HQ form. In contrast, the zero-bias conductance for the AQ form is about 300 times smaller than that of the former one. It is clear that the lack of any significant peak in between 1.5 and 0.7 eV accounts for the low conductance in the AQ form. The sharp contrast between transmission spectra of these two forms reflects the vital significance of structure effects on transport properties in the HQ/AQ molecule. It should be pointed out that our zero-bias transmission spectra are in qualitative agreement with the results obtained by Markussen et al. [12]. However, both the transmission peaks and tip are shifted toward higher energies in our case, which may be attributed to the different electrode coupling [12]. To further elucidate the origins of the peaks in the transmission spectra and of the different transmission characteristics for these two forms, we analyze the molecular projected self-consistent Hamiltonian (MPSH) [28], which can be obtained by projecting the selfconsistent Hamiltonian of the molecular switch onto the Hilbert space spanned by the basis functions of the molecule (includes HQ/AQ and anchoring sulfur atoms). The MPSH is then the self-consistent Hamiltonian of the molecule in the presence of gold electrodes. In Fig. 3, for clarity, we mark the positions of MPSH eigenvalues relative to the EF with squares for the HQ form and with circles for the AQ one. Note the positions of MPSH eigenvalues correspond nicely with the transmission peaks. The spatial distribution and energy values of the lowest unoccupied MPSH orbital (LUMO), the highest occupied MPSH orbital (HOMO), HOMO-1, and HOMO-2 of two forms are shown in Fig. 4. For a free sulfured HQ/AQ molecule, there are 160/158 valence electrons. Thus the MPSH orbital 80/79 is the HOMO and 81/80 is the LUMO for the free sulfured HQ/AQ molecule, respectively. In the switch with HQ form, both the HOMO and LUMO are delocalized orbitals leading to low barrier for electron transport. These delocalized orbitals provide good transport channels, electrons that enter the molecule at the energy of these orbitals have high probability of reaching the other end, which contribute to the strong transmission peak above and below the EF in Fig. 3(HQ form). The spatial profiles of HOMO-1 and HOMO-2 are localized at the left and right parts of the HQ molecule, respectively, which lead to high barrier for electron transport and have no contribution to the transmission. In the AQ case, the delocalized LUMO is responsible for the significant transmission peak at 0.81 eV above the EF in Fig. 3(AQ form). However, this LUMO transmission peak is located far away from the EF to contribute the total current at small bias voltage (for example,
Fig. 4. Spatial distribution of the MPSH orbitals including the molecule–electrode interaction. Right hand side figure stands for the HQ form, and left hand side figure for the AQ one, where the small balls indicate the atomic sites. Numbers inside parentheses are the orbital numerical index, those outside are the eigenvalues in eV by setting the EF to zero.
Fig. 5. Bias dependence of the transmission spectra at biases 0, 1.0 and 1.5 V for the HQ (a) and AQ (b) forms.
less than 1.0 V). The spatial profiles of HOMO and HOMO-1 are cut in the middle of the AQ molecule, while the spatial profile of HOMO-2 is strongly localized at the central unit, all of which have no contribution to the transmission. In fact, the zero-bias transmission spectra are not sufficient to completely describe the electronic transport properties of the molecular junction. It is necessary to investigate the changes in the transmission characteristics under the applied bias voltage. The bias dependence of the transmission characteristics at biases 0, 1.0, and 1.5 V of the HQ/AQ forms are presented in Fig. 5. From Fig. 5, we can see that the deviation in both the magnitude and the peak position of transmission becomes significant at a large bias.
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P. Zhao et al. / Physica B 406 (2011) 895–898
which indicates that the large switching feature of the HQ/AQ molecule is insensitive to the interface coupling.
4. Summary In summary, we have investigated the electronic transport properties of the anthraquinone-based molecular switch by applying NEGF formalism combined with first-principles DFT. The dramatic difference in conductance appearing in the HQ and AQ forms is interpreted by means of transmission spectra and spatial distribution of MPSH orbitals. Our results show that the current through the HQ form is significantly larger than that through the AQ form, and a large on–off ratio of currents from around 37 to 1480 is obtained. Furthermore, the large switching feature of the HQ/AQ molecule is insensitive to the interface coupling. This suggests that this kind of anthraquinone-based molecule is usable as one of the good candidates for redox-controlled molecular switches and may have some future applications in the molecular circuit. Fig. 6. Zero-bias transmission spectra of the molecular switch in the STM setup with the HQ (a) and AQ (b) forms. The inset is the corresponding atomic structures.
Acknowledgments This work was jointly supported by the National Natural Science Foundation of China (Grant no. 11074146), the Natural Science Foundation of Shandong Province, China (Grant no. ZR2009AL004), the Doctoral Foundation of University of Jinan, China (Grant no. XBS1004), and the Science and Development Project Program of Shandong Province, China (Grant no. 2009GG20003028). References
Fig. 7. Calculated current–voltage characteristic curves of the molecular switch in the STM setup. The inset is the corresponding on–off ratio of currents as a function of applied bias.
However, the HQ form always exhibit better transmission properties than the AQ form around the EF. It is well known that the interface plays a significant role in electronic transport in molecular junctions [29]. Then, next, we investigate the effect of interface coupling on the switching behavior. Namely, we construct a two-probe system to resemble the scanning tunneling microscope (STM) experimental situation, where the molecule is bound only to one Au surface. In Fig. 6, we plot the zero-bias transmission spectra of the STM setup. It can be seen clearly that the transmission values are dramatically reduced compared to the case of MCBJ setup. This is due to the weak coupling between the molecule and the right electrode in the STM setup [12]. The corresponding I–V characteristic curves along with the on–off ratio are plotted in Fig. 7. As we can see that the on–off ratio is nearly unchanged compared to the case of MCBJ setup,
[1] C. Joachim, J.K. Gimzewski, R.R. Schlittler, C. Chavy, Phys. Rev. Lett. 74 (1995) 2102. [2] M.A. Reed, C. Zhou, C.J. Muller, T.P. Burgin, J.M. Tour, Science 278 (1997) 252. [3] J. Reichert, R. Ochs, D. Beckman, H.B. Weber, M. Mayor, H.v. Lohneysen, Phys. Rev. Lett. 88 (2002) 176804. [4] R.H.M. Smit, Y. Noat, C. Untiedt, N.D. Lang, M.C. van Hemert, J.M. van Ruitenbeek, Nature 419 (2002) 906. [5] G.V. Nazin, X.H. Qiu, W. Ho, Science 302 (2003) 77. [6] P. Zhao, C.F. Fang, C.J. Xia, Y.M. Wang, D.S. Liu, S.J. Xie, Appl. Phys. Lett. 93 (2008) 013113. [7] P. Zhao, C.F. Fang, C.J. Xia, D.S. Liu, S.J. Xie, Chem. Phys. Lett. 453 (2008) 62. [8] P. Zhao, P.J. Wang, Z. Zhang, D.S. Liu, Phys. Lett. A 374 (2010) 1167. [9] R. Pati, S.P. Karna, Phys. Rev. B 69 (2004) 155419. [10] F. Chen, J. He, C. Nuckolls, T. Roberts, J.E. Klare, S. Lindsay, Nano Lett. 5 (2005) 503. [11] E.H. van Dijk, D.J.T. Myles, M.H. van der Veen, J.C. Hummelen, Org. Lett. 8 (2006) 2333. ¨ [12] T. Markussen, J. Schiotz, K.S. Thygesen, J. Chem. Phys. 132 (2010) 224104. [13] T. Vondrak, J.C. Cramer, X.Y. Zhu, J. Phys. Chem. B 103 (1999) 8915. [14] H. Gronbeck, A. Curioni, W. Andreoni, J. Am. Chem. Soc. 122 (2000) 3839. [15] S.H. Ke, H.U. Baranger, W. Yang, J. Chem. Phys. 123 (2005) 114701. [16] J. Nara, S. Higai, Y. Morikawa, T. Ohno, J. Chem. Phys. 120 (2004) 6705. [17] J. Gottschalck, B.A. Hammer, J. Chem. Phys. 116 (2002) 784. [18] Y. Cao, Q. Ge, D. Dyer, L. Wang, J. Phys. Chem. B 107 (2003) 3803. [19] H. Sellers, A. Ulman, Y. Shnidman, J.E. Eilers, J. Am. Chem. Soc. 115 (1993) 9389. [20] J.M. Soler, E. Artacho, J.D. Gale, A. Garcia, J. Junquera, P. Ordejon, D.S. Portal, J. Phys.: Condens. Matter 14 (2002) 2745. [21] J. Taylor, H. Guo, J. Wang, Phys. Rev. B 63 (2001) 245407. [22] M. Brandbyge, J.L. Mozos, P. Ordejon, J. Taylor, J.K. Stokbro, Phys. Rev. B 65 (2002) 165401. [23] S.O. Koswatta, M.S. Lundstrom, D.E. Nikonov, Nano Lett. 7 (2007) 1160. [24] S.M. Lindsay, M.A. Ratner, Adv. Mater. 19 (2007) 23. [25] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [26] N. Troullier, J. Martins, Phys. Rev. B 43 (1991) 1993. [27] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, New York, 1995. [28] K. Stokbro, J. Taylor, M. Brandbyge., J.-L. Mozos, P. Ordejon, Comput. Mater. Sci. 27 (2003) 151. [29] J. Taylor, M. Brandbyge, K. Stokbro, Phys. Rev. Lett. 89 (2002) 138301.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
First-principles study of the electronic transport properties of the anthraquinone-based molecular switch P. Zhao a,n, D.S. Liu b,c, P.J. Wang a, Z. Zhang a, C.F. Fang b, G.M. Ji b a
School of Science, University of Jinan, Jinan 250022, China School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China c Department of Physics, Jining University, Qufu 273155, China b
a r t i c l e in f o
abstract
Article history: Received 17 September 2010 Received in revised form 13 November 2010 Accepted 7 December 2010 Available online 15 December 2010
By applying non-equilibrium Green’s function (NEGF) formalism combined with first-principles density functional theory (DFT), we have investigated the electronic transport properties of the anthraquinonebased molecular switch. The molecule that comprises the switch can be converted between the hydroquinone (HQ) and anthraquinone (AQ) forms via redox reactions. The transmission spectra of these two forms are remarkably distinctive. Our results show that the current through the HQ form is significantly larger than that through the AQ form, which suggests that this system has attractive potential application in future molecular switch technology. & 2010 Elsevier B.V. All rights reserved.
Keywords: Molecular switch Anthraquinone Non-equilibrium Green’s function Electronic transport
1. Introduction Because of rapid progress in microscale fabrication technology, molecular electronics has attracted increasingly much attention recently. A critical mission of the molecular electronics is to develop novel devices at single molecular level. In the last several years, many molecular electronic devices with different functionalities have been designed and analyzed [1–10]. Among these, a single molecular switch holds great promise since it is critical to the ability to store digital information and route signals in future molecular electronic logic circuits. The basic requirement for a molecular switch is bistability, which is the occurrence of two different forms of a molecule that can be selectively and reversibly converted into each other in response to an external trigger such as light [6,7], electric field [9], redox process [10], and so on. Recently, van Dijk et al. [11] synthesized a kind of anthraquinone-based molecular wire, which can be reversibly switched electrochemically between the reduced hydroquinone (HQ) and oxidized anthraquinone (AQ) states via redox reactions. Drawing from the chemical intuition, one can see that the p-conjugation extends over the entire HQ form, whereas it is cut in the AQ form because of the p-benzoquinone (p-bq) unit. As a consequence, the HQ form is expected to exhibit better conductance than the AQ form. Especially, this redox-controlled molecular switch has the advantage that the overall length and
n
Corresponding author. Tel.: + 86 53182765976. E-mail address: [email protected] (P. Zhao).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.12.023
thus the molecule–electrode binding geometry of the switch is not changed significantly. It is well known that the conductive properties are of crucial importance in any device application. Very recently, Markussen et al. [12] analyzed the zero-bias transmission properties of the anthraquinone-based molecular switch. In this paper, we investigated the electronic transport properties of the anthraquinonebased molecular switch at finite bias by a theoretical simulation that combines both first-principles density functional theory (DFT) and non-equilibrium Green’s function (NEGF) method.
2. Model and method Detailed knowledge of the geometrical properties of materials is a necessary requirement for understanding their electronic transport properties. Thus, we first optimize the geometries of free thiol (SH) groups capped molecule with the above-mentioned two forms. Next, we construct a two-probe system to resemble a mechanically controlled break junction (MCBJ) experimental situation as follows. Based on the experimental issues about selfassembled monolayers (SAMs), it is generally accepted that hydrogen atoms are dissociated on adsorption to metal surfaces [13,14]. So the two terminal hydrogen atoms bonded to the sulfur atom are eliminated from the optimized structure, and the remained part is sandwiched between two parallel Au(1 1 1) surfaces that correspond to the surfaces of the gold electrodes, which have a face-centered cubic (f.c.c.) structure. There are three possible adsorption sites of a sulfur atom on the Au(1 1 1) surfaces, i.e., top, bridge, and hollow sites [15–18]. Most of the studies
896
P. Zhao et al. / Physica B 406 (2011) 895–898
predicted that the top and the hollow adsorption sites are more favorable in energy. Since our main purpose in this work is to determine the conductivity of the switch through a redox reaction, the nature of Au–S interaction is not investigated here. We choose the sulfur atom to locate at the hollow site of each gold surface [18]. ˚ is chosen to fit The distance between two gold electrodes, 28.42 A, best the length of the optimized HQ/AQ molecule [19]. Each layer of the gold electrodes is represented by a (3 3) supercell with the periodic boundary conditions so that it imitates bulk metal structures. As shown in Fig. 1, the entire molecular switch is divided into three regions: a left electrode (L), a central scattering region (C), and a right electrode (R). The semi-infinite electrodes are calculated separately to obtain the bulk self-energy. The central scattering region includes the HQ/AQ molecule and two layers of gold slab from each electrode to screen the perturbation effect from the central region and they are denoted as surface-atomic layers. The geometry of the central extended molecule is fully optimized by minimizing the atomic forces on the HQ/AQ molecule to be ˚ while keeping all the gold atoms fixed. All smaller than 0.05 eV/A, the geometrical optimizations have been carried out by using the Spanish initiative for electronic simulations with thousands of atoms (SIESTA) package [20]. The electronic transport properties of the molecular switch is calculated by a fully self-consistent NEGF formalism combined with the first-principles DFT, which is implemented in Atomistix ToolKit (ATK) package [21,22]. This methodology has been adopted to explain various experimental results successfully [23,24]. In our calculations, the exchange–correlation potential is described by the gradient generalized approximation with the Perdew, Burke, and Ernzerhof parameterization (GGA.PBE) [25]. Core electrons are modeled with Troullier–Martins non-local pseudopotential [26], and valence electrons are expanded in a SIESTA localized basis set [20]. A single-zeta plus polarization (SZP) basis set for gold atoms and a double-zeta plus polarization (DZP) basis set for the organic molecule are adopted. An energy cutoff of 150 Ry for the grid integration is set to present the accurate charge density. In NEGF theory, the transmission function T(E,V) of the system is a sum of transmission probabilities of all channels available at energy E under external bias voltage V [27]: TðE,VÞ ¼ Tr½GL ðVÞGR ðE,VÞGR ðVÞGA ðE,VÞ
ð1Þ
Then, the current (I)–voltage (V) characteristics are obtained ¨ from the Landauer–Butiker formulism [27]: Z 2e IðVÞ ¼ ½ f ðEmL Þf ðEmR ÞTðE,VÞdE: ð2Þ h where h is Planck’s constant, e the electron charge, f the Fermi function, mL,R the electrochemical potential of the left and right electrodes, and the difference in the electrochemical potentials is given in eV with the applied bias voltage V, i.e.mL=R ðVÞ ¼ EF 8 eV=2, EF is the Fermi level of the system.
3. Results and discussion In Fig. 2, we describe the self-consistently calculated I–V characteristic curves of the molecular switch with two forms at bias up to 1.5 V, which is reasonable in practical experimental measurements. Obvious switching behavior can be seen from Fig. 2. Although the two forms differ only by two hydrogen atoms, their conductance properties are drastically different. The current through the AQ form is strongly suppressed over the entire bias range, while the current through the HQ form is evidently larger than that through the AQ form. Thus, when HQ is oxidized to AQ by application of an electrochemical potential to the electrode, the switch is predicted to switch from the on state (high conductance) to the off state (low conductance), and vice versa. As a figure of merit, the on–off ratio of currents, R(V)¼IHQ/IAQ, versus bias V is plotted in the inset of Fig. 2. At the zero bias when both currents vanish, we calculate the on–off ratio using the zero-bias conductance. From the inset of Fig. 2, we can see that R varies from around 37 to 1480 in the bias range under investigation. Such a significant on–off ratio can be easily measured and desirable for the real application. To understand the dramatic difference in conductance appearing in the HQ and AQ forms, we calculated the energy dependence of zerobias transmission spectra. As shown in Fig. 3, the transmission spectra display extraordinarily different characteristics. The system with the HQ form has a strong transmission peak at 1.17 and 0.33 eV above and below the EF, respectively. Obviously, the transport properties are predominated by the tail of the peak located at 0.33 eV below the EF at small bias voltage. However, the nearest transmission peak is at 0.81 eV above the EF and no obvious transmission peak below the EF in
where GR,A is the retarded and advanced Green’s function, coupling function GL,R are the imaginary parts of the left and right selfenergies, respectively.
Fig. 1. Schematic illustration of the molecular switch with two forms. The white, gray, red, yellow, and golden spheres represent H, C, O, S, and Au atoms, respectively. The vertical black line denotes the interface between the central scattering region and the left or right gold electrode. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Calculated current–voltage characteristic curves of the molecular switch with two forms. The squares linking with black solid lines are for the switch with the HQ form, while the circles linking with short red dotted lines stand for the switch with the AQ form. The inset is the on–off ratio of currents as a function of the applied bias. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
P. Zhao et al. / Physica B 406 (2011) 895–898
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Fig. 3. Zero-bias transmission spectra of the molecular switch with the HQ and AQ forms. The positions of MPSH eigenvalues are marked with squares for the HQ form and with circles for the AQ one, respectively. In our calculations, we set the energy origin as the Fermi level EF.
the system with the AQ form. The calculated zero-bias conductance is 1.8 10 2G0 for the HQ form. In contrast, the zero-bias conductance for the AQ form is about 300 times smaller than that of the former one. It is clear that the lack of any significant peak in between 1.5 and 0.7 eV accounts for the low conductance in the AQ form. The sharp contrast between transmission spectra of these two forms reflects the vital significance of structure effects on transport properties in the HQ/AQ molecule. It should be pointed out that our zero-bias transmission spectra are in qualitative agreement with the results obtained by Markussen et al. [12]. However, both the transmission peaks and tip are shifted toward higher energies in our case, which may be attributed to the different electrode coupling [12]. To further elucidate the origins of the peaks in the transmission spectra and of the different transmission characteristics for these two forms, we analyze the molecular projected self-consistent Hamiltonian (MPSH) [28], which can be obtained by projecting the selfconsistent Hamiltonian of the molecular switch onto the Hilbert space spanned by the basis functions of the molecule (includes HQ/AQ and anchoring sulfur atoms). The MPSH is then the self-consistent Hamiltonian of the molecule in the presence of gold electrodes. In Fig. 3, for clarity, we mark the positions of MPSH eigenvalues relative to the EF with squares for the HQ form and with circles for the AQ one. Note the positions of MPSH eigenvalues correspond nicely with the transmission peaks. The spatial distribution and energy values of the lowest unoccupied MPSH orbital (LUMO), the highest occupied MPSH orbital (HOMO), HOMO-1, and HOMO-2 of two forms are shown in Fig. 4. For a free sulfured HQ/AQ molecule, there are 160/158 valence electrons. Thus the MPSH orbital 80/79 is the HOMO and 81/80 is the LUMO for the free sulfured HQ/AQ molecule, respectively. In the switch with HQ form, both the HOMO and LUMO are delocalized orbitals leading to low barrier for electron transport. These delocalized orbitals provide good transport channels, electrons that enter the molecule at the energy of these orbitals have high probability of reaching the other end, which contribute to the strong transmission peak above and below the EF in Fig. 3(HQ form). The spatial profiles of HOMO-1 and HOMO-2 are localized at the left and right parts of the HQ molecule, respectively, which lead to high barrier for electron transport and have no contribution to the transmission. In the AQ case, the delocalized LUMO is responsible for the significant transmission peak at 0.81 eV above the EF in Fig. 3(AQ form). However, this LUMO transmission peak is located far away from the EF to contribute the total current at small bias voltage (for example,
Fig. 4. Spatial distribution of the MPSH orbitals including the molecule–electrode interaction. Right hand side figure stands for the HQ form, and left hand side figure for the AQ one, where the small balls indicate the atomic sites. Numbers inside parentheses are the orbital numerical index, those outside are the eigenvalues in eV by setting the EF to zero.
Fig. 5. Bias dependence of the transmission spectra at biases 0, 1.0 and 1.5 V for the HQ (a) and AQ (b) forms.
less than 1.0 V). The spatial profiles of HOMO and HOMO-1 are cut in the middle of the AQ molecule, while the spatial profile of HOMO-2 is strongly localized at the central unit, all of which have no contribution to the transmission. In fact, the zero-bias transmission spectra are not sufficient to completely describe the electronic transport properties of the molecular junction. It is necessary to investigate the changes in the transmission characteristics under the applied bias voltage. The bias dependence of the transmission characteristics at biases 0, 1.0, and 1.5 V of the HQ/AQ forms are presented in Fig. 5. From Fig. 5, we can see that the deviation in both the magnitude and the peak position of transmission becomes significant at a large bias.
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which indicates that the large switching feature of the HQ/AQ molecule is insensitive to the interface coupling.
4. Summary In summary, we have investigated the electronic transport properties of the anthraquinone-based molecular switch by applying NEGF formalism combined with first-principles DFT. The dramatic difference in conductance appearing in the HQ and AQ forms is interpreted by means of transmission spectra and spatial distribution of MPSH orbitals. Our results show that the current through the HQ form is significantly larger than that through the AQ form, and a large on–off ratio of currents from around 37 to 1480 is obtained. Furthermore, the large switching feature of the HQ/AQ molecule is insensitive to the interface coupling. This suggests that this kind of anthraquinone-based molecule is usable as one of the good candidates for redox-controlled molecular switches and may have some future applications in the molecular circuit. Fig. 6. Zero-bias transmission spectra of the molecular switch in the STM setup with the HQ (a) and AQ (b) forms. The inset is the corresponding atomic structures.
Acknowledgments This work was jointly supported by the National Natural Science Foundation of China (Grant no. 11074146), the Natural Science Foundation of Shandong Province, China (Grant no. ZR2009AL004), the Doctoral Foundation of University of Jinan, China (Grant no. XBS1004), and the Science and Development Project Program of Shandong Province, China (Grant no. 2009GG20003028). References
Fig. 7. Calculated current–voltage characteristic curves of the molecular switch in the STM setup. The inset is the corresponding on–off ratio of currents as a function of applied bias.
However, the HQ form always exhibit better transmission properties than the AQ form around the EF. It is well known that the interface plays a significant role in electronic transport in molecular junctions [29]. Then, next, we investigate the effect of interface coupling on the switching behavior. Namely, we construct a two-probe system to resemble the scanning tunneling microscope (STM) experimental situation, where the molecule is bound only to one Au surface. In Fig. 6, we plot the zero-bias transmission spectra of the STM setup. It can be seen clearly that the transmission values are dramatically reduced compared to the case of MCBJ setup. This is due to the weak coupling between the molecule and the right electrode in the STM setup [12]. The corresponding I–V characteristic curves along with the on–off ratio are plotted in Fig. 7. As we can see that the on–off ratio is nearly unchanged compared to the case of MCBJ setup,
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