Rectifying behaviors of an Au/(C₂₀)₂/Au molecular device induced by the different positions of gate voltage

Abstract

The electronic transport properties of a gated Au/(C₂₀)₂/Au molecular device are studied using nonequilibrium Green's function in combination with density functional theory. The results show that different applied positions of the external transverse gate voltage can effectively tune the current–voltage (I–V) characteristic of molecular devices. Rectifying behaviors of the device can be realized when the gate voltage is applied asymmetrically on the left C₂₀ molecule, and the rectification directions can also be modulated by the positive or negative value of the gate voltage. These results provide an important theoretical support to experiments and the design of a molecular rectifier.

---

1 Introduction

Due to their peculiar geometric and electronic structures, fullerene molecules are considered promising candidates as one of the basic elements of the next generation of nanoelectronic devices. Therefore, electronic transport in fullerene bridges has received significant attention both experimentally^1–4 and theoretically.^5–8 The fundamental rule and the pivotal point for employing fullerene molecules as molecular devices is based on how to effectively control the electronic transport properties. At present, there are two main approaches to do this.⁹ One is through conformational changes in the fullerene molecules, and the other is through field-effect gating. The former has been paid much attention and much progress has been made in the past few decades.^10–12 Otani et al.¹³ reported that the conductance is quite sensitive to the number of C₂₀ molecules between electrodes using density-functional theory (DFT) based on local density approximation. Yamamoto et al.¹⁴ investigated the inelastic electronic transport properties under low bias voltage assisted by molecular vibrations using the NEGF formalism combined with the tight-binding molecular-dynamics method. Using first-principles density-functional theory and nonequilibrium Green's function formalism for quantum transport calculation, the electronic and transport properties of C₂₀ fullerene molecule were also investigated.¹⁵ However, it is difficult to accurately control the molecular conformation, and the response speed is also slow. Nowadays, people turn to the latter because of its higher operation frequency and lower energy consumption. Many field effect transistor (FET) configurations have been achieved experimentally.^1,16–19 The fabrication of single-molecule transistors based on individual C₆₀ molecules connected to gold electrodes has been reported.¹ Winkelmann et al. demonstrated the realization of superconducting single molecule transistors involving a single C₆₀ fullerene molecule.¹⁶ The effects of the external gate voltage were also investigated theoretically. A theoretical study proposed by Taylor et al.²⁰ presented an ab initio analysis of electron conduction through a C₆₀ molecular device. They found that the I–V characteristics could be changed from metallic behavior to semiconducting by a gate potential, thereby forming a field-effect molecular current switch. Saffarzaden²¹ and Shokri et al.²² respectively investigated electron transport across a carbon molecular junction consisting of a C₆₀ molecule attached to two one-dimensional electrodes and semi-infinite metallic open-end CNT leads. They found that a gate voltage could shift the molecular levels, where the electron conduction could be controlled by adjusting the related parameters. Also, the quantum transport properties of a single C₆₀ sandwiched between Au and nanotube electrode could be modulated by the gate voltage.²³

So far, in all the studies above, the gate voltage is applied on the whole molecule of the scattering region. However, carbon-nanotube filed-effect transistors with multiple, individually addressable gate segments have been fabricated in experiments.²⁴ Therefore, one fundamental and intriguing question arises: is it possible to control the electronic transport properties of fullerene-based devices by changing the positions where the gate voltage is applied? In this study, we explore the position effect of gate voltage on electronic transport properties of an Au/(C₂₀)₂/Au junction using the ab initio quantum transport method which is based on the nonequilibrium Green's function (NEGF) and density functional theory (DFT). We discovered significantly gate-tuned I–V characteristics. Moreover, we found that rectification behaviors appear when the gate voltage is applied asymmetrically on the left C₂₀ molecule and the rectification direction can be modulated by the positive or negative value of the gate voltage. Rationales for these phenomena are revealed in this work.

2 Model and method

As illustrated in the upper inset of Fig. 1, two C₂₀ molecules are chemisorbed to two Au(111)-(3 × 3) electrodes with bond contacts in a FET configuration where the transverse gate voltage (V_g) is applied on the left C₂₀ molecule. First, we set the initial Au–C distance and C₂₀–C₂₀ distance to be 2.185 Å , which is a typical distance for the Au–C system,¹⁵ and the distance between two C₂₀ molecules is 1.6 Å. And then, we optimize the geometry of the systems by fixing distance between left and right electrodes to 13.29 Å as constraint. After the geometry optimization, the Au–C distance and C₂₀–C₂₀ distance are 1.973 Å and 1.5 Å. After the geometry optimization, we study the electron transport properties. The geometrical optimization and the electronic transport property calculations are carried out by an ab initio code package Atomistix ToolKit (ATK).²⁵ In order to save computational efforts and improve calculating precision and reliability, valence electrons are expanded in single zeta plus polarization (SZP) basis sets for Au atoms and double zeta plus polarization (DZP) basis for other atoms. The norm-conserving Troullier–Martins pseudopotentials are used to describe the core electrons for all atoms. The exchange–correlation potential is described by the Perdew–Burke–Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA) functional. The electrode calculations are performed under periodical boundary conditions, with the unit cell being three layers atoms along the transport direction and the Brillouin zone has been sampled with 3 × 3 × 50 points within the Monkhorst–Pack k-point sampling scheme in case of our three dimensional two-probe system. The self-consistent calculations are performed with a mixing rate set to 0.01, and the convergent criterion for total energy is 10⁻⁵ eV. The electrostatic potentials are determined on a real-space grid with a mesh cutoff energy of 110 Ry to achieve a balance between the calculation efficiency and the accuracy. The currents through the system are obtained from the Landauer–Büttiker formulism, , where T(E, V_b) is the transmission function of the system at energy E under external bias voltage V_b. μ_L(R) and f(E − μ_L(R)) are the chemical potential and Fermi function of the left (right) electrode, respectively. The effect of V_g is taken into account by shifting the scattering region part of the Hamiltonian with V_g (converted into an electrostatic potential energy). This corresponds to assuming that the gate voltage induces an external potential localized in the scattering region. For more details, readers are referred to Ref. 26 and 27.

Fig. 1 Calculated currents as a function of the applied bias under the V_g = −3.0, 0.0, and 3.0 V, respectively. Upper inset: Schematic description of the device: (C₂₀)₂ molecules sandwiched between Au electrodes. An additional V_g is applied asymmetrically on the left C₂₀ molecule. The lower right inset shows the change of corresponding rectification ratio against the bias.

3 Results and discussion

The self-consistently calculated I–V characteristics are shown in Fig. 1. V_g is set to three different values (−3.0, 0.0, and 3.0 V), and V_b is in a range from −2.0 to 2.0 V. This molecular junction demonstrates controllable gate–voltage dependence. The I–V curves show obvious asymmetry and nonlinear characteristics. No matter whether in positive or negative V_b regions, when V_b is low, currents increase faster when V_g is zero than when V_g is −3.0 V and 3.0 V . It seems that the transport abilities are suppressed by V_g. As the negative (positive) bias grows, the currents change quickly as the bias changes when V_g = −3.0 V (3.0 V). For the positive (negative) bias, the current values increase slowly and are obvious small. Thus, the devices show significant rectifying performances under the V_g. Moreover, negative differential resistance (NDR) behaviors are observed when V_g = 3.0 V, V_b = 1.0 V and V_g = −3.0 V, V_b = −1.0 V. In order to evaluate the rectification effect under different values of V_g, we calculated the rectification ratio, which is the ratio of currents between the absolute value under negative (positive) and positive (negative), when V_g = −3.0 V (3.0 V). The rectification ratio is shown in the lower right inset of Fig. 1. An I⁺/I⁻ ratio above 1 means a forward rectifying, while an I⁺/I⁻ ratio above 1 means an inverse rectifying. From Fig. 1, we can clearly see that the gated I–V characteristics have distinct features compared with those of V_g = 0.0 V situation. When V_g = −3.0 V, the molecular device reveals a reverse rectifying, with a maximum ratio of 3.4 at 0.6 V. When V_g = 3.0 V, the molecular device reveals forward rectifying, with a maximum ratio of 2.3 at V_b = 0.8 V. Therefore, the application of asymmetric V_g can induce the rectification effect and the positive or negative value of V_g can significantly alter the rectifying direction.

The mechanisms of the changes in the electronic transport properties after applying V_g on the left C₂₀ molecule can be interpreted in terms of the transmission spectra and the corresponding projection of the density of state (PDOS) at zero bias, and molecular projected self-consistent Hamiltonian (MPSH) of frontier molecular orbitals, as shown in Fig. 2. MPSH is the self-consistent Hamiltonian of the isolated molecule in the presence of the electrode, namely, the molecular part extracted from the whole self-consistent Hamiltonian. If an orbital is delocalized across the molecule, an electron that enters the molecule at the energy of the orbital has a high probability of reaching the other end, and thus there is a corresponding peak in the T(E). From Fig. 2, one can clearly see the gated modulation on molecular orbitals. A positive or negative V_g will, respectively, raise or lower the orbital energies in the molecules relative to the Fermi level (E_f). The transmission coefficients at E_f are 0.403, 0.555, 0.351 for V_g = −3.0, 0.0, 3.0 V, respectively. It is notable that when V_g = −3.0 V, LUMO+2 and LUMO+3 are close to E_f, and therefore LUMO+2 and LUMO+3 are the main transmission channels. When V_g = 0.0 V and 3.0 V, the LUMO and LUMO+1 resonances are close to E_f, and therefore LUMO and LUMO+1 are the main transmission channels. From Fig. 2(b), one can see that, LUMO and LUMO+1 for V_g = 0.0 V are delocalized, which result in the big current in the low V_b region. While LUMO+1 and LUMO+2 for V_g = −3.0 V, and LUMO and LUMO+1 for V_g = 3.0 V localize mainly at one side of (C₂₀)₂ molecules, which reduces the molecular conduction. In addition, the transmission coefficients of gated devices are all lower than those under V_g = 0.0 V at E_f, leading to the suppressed I–V curves at low bias in Fig. 1.

Fig. 2 (a)Transmission spectra T(E) and corresponding PDOS at V_b = 0.0 V for different V_g. The dashed vertical lines stand for the molecular orbitals. The Fermi level E_f is set to zero. (b) MPSH of frontier molecular orbitals for different V_g values at V_b = 0.0 V.

Another attractive phenomenon is the presence of rectifying behaviors in the gated I–V curves. In order to explain the origin of the rectification phenomenon, we plot the total transmission coefficients as a function of V_b under V_g = −3.0 V (Fig. 3(a)) and 3.0 V (Fig. 3(b)), respectively. As explained above, V_g can shift the transmission peak and make the transmission coefficients distribute asymmetrically. Fig. 3 shows that the transmission peaks shift to the positive energy direction. When V_g = −3.0 (3.0) V, as shown in Fig. 3(a) and (b), the transmission spectra within the bias window under negative (positive) bias are apparently stronger than those under positive (negative) bias, and therefore the current increases faster under negative (positive) bias than positive (negative) bias, showing evidently reversed (forward) rectification. When V_b increases to −0.6 (0.8) V, the difference of the current between the two bias regions reaches the maximum. Therefore, the rectification ratio can be up to its extreme value. However, another transmission peak appears in the positive (negative) energy region, which leads to a decrease of the difference of the current between the two bias regions and the decrease of the rectification ratio. When V_g = −3.0 (3.0) V, under the negative bias (positive) region, the transmission peaks decrease at bias of less (greater) than −1.0 (1.0) V, and this is responsible for the current drop from V_b = −1.0 (1.0) V. Consequently, the NDR peak appears.

Fig. 3 The total transmission coefficients as a function of the V_b under the V_g = −3.0 and 3.0 V, respectively. The white solid lines indicate the bias windows.

As demonstrated by many investigations,^28,29 the electronic transport properties of molecular wires are strongly dependent on the spatial distribution of the molecular orbitals. One of the key factors affecting the molecular rectification is the asymmetric shift of frontier orbitals under bias.²⁸ As an effort to deeply understand the origin of the positive and negative rectification, we choose the transmission spectra of V_b = −1.0, 1.0 V under V_g = −3.0, 3.0 V and calculate the MPSH to explore the origin of the asymmetric transmission spectra with respect to bias. In the transmission spectra, the position of the transmission peak is generally determined by the energy level of molecular orbital, i. e. the transmission channels, and the delocalization of orbitals affects the height of transmission peak. The isosurfaces of MPSH eigenstates within the bias window for junction of V_g = −3.0 V at V_b = −1.0 and 1.0 V are plotted in parts (a) and (b) of Fig. 4, respectively. In the transmission spectrum of V_b = −1.0 V, there are five molecular orbitals (LUMO+2, LUMO+3, LUMO+4, LUMO+5 and LUMO+6) inside the bias windows. Two (LUMO+2 and LUMO+3) of the five molecular orbitals are spatially delocalized throughout the scattering region, resulting in the big and wide peaks in the transmission spectrum. Therefore, the peaks in the bias window have large contribution to the current. Because the molecular orbitals shift with the applied bias, the transmission spectra show clear bias-dependent. In contrast, at V_b = 1.0 V, the molecular orbitals LUMO+2 and LUMO+6 shift out of the bias windows and there are only three molecular orbital (LUMO+3, LUMO+4 and LUMO+5) inside the bias windows. All of the three molecular orbitals (LUMO+3, LUMO+4 and LUMO+5) are localized in the left C₂₀ region, making a small contribution to the transmission spectrum featured by the small peaks. As a result, the current at V_b = −1.0 V is much higher than that at V_b = 1.0 V. This difference accounts for the negative rectifying properties of the molecular junction of V_g = −3.0 V. The isosurfaces of the MPSH eigenstates within the bias window for junction of V_g = 3.0 V at V_b = −1.0 and 1.0 V are plotted in parts (c) and (d) of Fig. 4, respectively. At V_b = −1.0 V, all the five molecular orbitals (HOMO, LUMO, LUMO+1, LUMO+2 and LUMO+3) inside the bias window are localized in either the left C₂₀ region or the right C₂₀ region. By contrast, two (LUMO and LUMO+1) of the three molecular orbitals inside the bias window at V_b = 1.0 V are delocalized throughout the scattering region, causing the big and wide peaks in the transmission spectrum. As a result, the molecular junction of V_g = 3.0 V shows a positive rectification behavior. The origin of the rectification properties can be understood from the position and intensities of molecular orbitals inside the bias window. We can infer that the V_b and V_g can shift the molecular orbitals and affect the coupling degree between the molecular orbitals and electrodes, which results in the rectification behaviors.

Fig. 4 Transmission spectra (top panel) and isosurfaces (lower panels) of the MPSH eigenstates within the bias window from E_f = −0.5 to 0.5 eV. (a) and (b) for V_g = −3.0 V, (c) and (d) the V_g = 3.0 V.

A concern of gated molecular junctions is whether the rectification behavior depends on different positions of the gate voltage. To address this issue, we calculated the I–V curves in a bias range from −2.0 to 2.0 V under V_g = −3.0, 0.0, and 3.0 V, which are applied on the whole (C₂₀)₂ molecules, The calculated I–V characteristics are shown in Fig. 5. The device does not exhibit the rectification behavior. Therefore, we can conclude that the different positions of V_g can affect the electronic transport properties. The rectification behavior can be induced by applying the V_g under one of the (C₂₀)₂ molecules and the rectification directions can be changed by the positive or negative value of the gate voltage.

Fig. 5 Calculated currents as a function of the applied bias under the V_g = −3.0, 0.0, 3.0 V, respectively. Upper inset: Schematic description of the device: (C₂₀)₂ molecules sandwiched between Au electrodes. An additional V_g is applied on the (C₂₀)₂ molecules.

4 Conclusion

In summary, we performed a first-principle calculation on the electronic transport properties of a gated (C₂₀)₂ based molecular device. Rectification behaviors are found and the rectification directions can be modulated by the positive or negative value of V_g, originated from the asymmetrical shift of molecular orbitals. This rectification is fully rationalized by the calculated transmission spectra and the spatial distribution of the corresponding molecular orbitals. We proposed a new method for designing the molecular rectification device by using different applying positions of gate voltage. The finding can be useful for the development of future nanoelectronic devices.

Acknowledgements

This work was supported by the National Basic Research Program of China (Grant No. 2009CB929204), Natural Science Foundation of China (Grant No. 11074146), the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 200804220005), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2010AM026 and ZR2010AM037), and the Independent Innovation Foundation of Shandong University (Grant No. 2009TS097 and 2012TS025).

References

1. H. Park, J. Park, A. K. L. Lim, E. H. Anderson, A. P. Alivisatos and P. L. McEuen, Nature, 2000, 407, 57.
2. A. N. Pasupathy, J. Park, C. Chang, A. V. Soldatov, S. Lebedkin, R. C. Bialczak, J. E. Grose, L. A. K. Donev, J. P. Sethna, D. C. Ralph and P. L. McEuen, Nano Lett., 2005, 5, 203.
3. C. G. Zeng, H. Q. Wang, B. Wang, J. L. Yang and J. G. Hou, Appl. Phys. Lett., 2000, 77, 3595.
4. J. Zhao, C. G. Zeng, X. Cheng, K. D. Wang, G. W. Wang, J. L. Yang, J. G. Hou and Q. S. Zhu, Phys. Rev. Lett., 2000, 95, 045502.
5. S. Nakanishi and M. Tsukada, Phys. Rev. Lett., 2001, 87, 126801.
6. M. Otani, T. Ono and K. Hirose, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 69, 121408.
7. J. J. Palacios, A. J. Prez-Jimnez, E. Louis and J. A. Vergs, Phys. Rev. B: Condens. Matter, 2001, 64, 115411.
8. T. Yamamoto, K. Watanabe and S. Watanabe, Phys. Rev. Lett., 2005, 95, 065501.
9. F. Jiang, Y. X. Zhou, H. Chen, R. Note, H. Mizuseki and Y. Kawazoe, J. Chem. Phys., 2006, 125, 084710.
10. Z. Q. Fan, K. Q. Chen, Q. Wan, B. S. Zou, W. H. Duan and Z. Shuai, Appl. Phys. Lett., 2009, 92, 263304.
11. C. Roland, B. Larade, J. Taylor and H. Guo, Phys. Rev. B: Condens. Matter, 2001, 65, 041401.
12. R. Gutierrez, G. Fagas, G. Cuniberti, F. Grossmann, R. Schmidt and K. Richter, Phys. Rev. B: Condens. Matter, 2002, 65, 113410.
13. M. Otani, T. Ono and K. Hirose, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 69, 121408.
14. T. Yamamoto, K. Watanabe and S. Watanabe, Phys. Rev. Lett., 2005, 95, 065501.
15. Y. P. An, C. L. Yang, M. S. Wang, X. G. Ma and D. H. Wang, J. Chem. Phys., 2009, 131, 024311.
16. C. B. Winkelmann, N. Roch, W. Wernsdorfer, V. Bouchiat and F. Balestro, Nat. Phys., 2009, 5, 876.
17. T. P. I. Saragia and J. Salbeck, Appl. Phys. Lett., 2006, 89, 253516.
18. T. D. Anthopoulos, B. Singh, N. Marjanovic, N. S. Sariciftci, A. M. Ramil, H. Sitter, M. Colle and D. M. D. Leeuw, Appl. Phys. Lett., 2006, 89, 213504.
19. A. R. Champagne, A. N. Pasupathy and D. C. Ralph, Nano Lett., 2005, 5, 305.
20. J. Taylor, H. Guo and J. Wang, Phys. Rev. B: Condens. Matter, 2001, 63, 121104.
21. A. Saffarzadeh, J. Appl. Phys., 2008, 103, 083705.
22. A. A. Shokri and S. Nikzad, J. Appl. Phys., 2011, 110, 024303.
23. Z. Q. Fan and K. Q. Chen, J. Appl. Phys., 2011, 109, 124505.
24. S. J. Wind, J. Appenzeller and P. Avouris, Phys. Rev. Lett., 2003, 91, 058301.
25. See http://www.quantumwise.com/for for more information about Atomistix ToolKit.
26. J. Taylor, H. Guo and J. Wang, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 245407.
27. M. Brandbyge, J. L. Mozos, P. Ordejon, J. Taylor and K. Stoll, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 65, 165401.
28. Y. Xing, L. Hongmei and Z. Jianwei, J. Chem. Phys., 2006, 125, 094711.
29. A. Staykov, D. Nozaki and K. Yoshizawa, J. Phys. Chem. C, 2007, 111, 11698.

---