NANO LETTERS
First-Principles Study of Electrochemical Gate-Controlled Conductance in Molecular Junctions
2006 Vol. 6, No. 9 2091-2094
Wenyong Su,†,‡ Jun Jiang,†,§ Wei Lu,§ and Yi Luo*,† Department of Theoretical Chemistry, Royal Institute of Technology, AlbaNoVa, S-106 91 Stockholm, Sweden, Department of Physics, Beijing Institute of Technology, Beijing 100081, China, and National Key Lab for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, China Received June 15, 2006; Revised Manuscript Received August 16, 2006
ABSTRACT A first-principles computational method is developed to study the electrochemical gate-controlled conductance in molecular junctions. It has been applied to a single molecular field-effect transistor made by a perylene tetracaboxylic diimide molecule connected to gold electrodes and has successfully reproduced the experimentally observed huge gate voltage effect on the current. It is found that such a significant gain is a result of the large polarization of the molecule induced by the huge local electrical field generated by the electrochemical gate. The resonant electron tunneling through unoccupied molecular orbitals is shown to be the dominant transport process.
Various functions of single molecular devices have been verified in the past decade. The electron-transport properties of two-terminal molecular junctions are by far the most studied systems, both theoretically and experimentally. A detailed understanding of molecular junctions has emerged, although some outstanding issues still remain.1 For making large-scale integrated circuits, the three-terminal field-effect transistor (FET) is an essential device that provides the muchneeded power gain and has been fabricated recently.2,3 Both theory and experiment reveal a weak gate effect on the phenylene-based conjugated molecular devices with conventional silicon-oxides gates.2,5 In a recent study, Ghosh, Rakshit, and Datta have discussed different field-effect mechanisms in molecular transistors involving both electrostatic and conformation changes.6 But in general the standard semiconductor-like gate configuration cannot lead to large gain in current for a single molecular transistor. Tao and co-workers3,4 have developed a new approach by using an electrochemical gate to control the conductance of a single molecular transistor. They have demonstrated that the current through the molecule can be reversibly controlled with a gate electrode over nearly 3 orders of magnitude at room temperature. Such a large gain is obviously interesting for future applications. But, it is not a behavior that is expected from conventional theoretical models for molecular FET devices.5,6 In this letter, we report a theoretical model * Corresponding author. E-mail:
[email protected]. † Royal Institute of Technology. ‡ Beijing Institute of Technology. § Shanghai Institute of Technical Physics. 10.1021/nl061376z CCC: $33.50 Published on Web 08/29/2006
© 2006 American Chemical Society
that takes into account the electrochemical gate field effects on conductance in molecular junctions and its application to the FET device of Xu et al.3 We have found that the electrochemical gate produces a strong electric field that acts on the molecule, and leads to large polarization and the change of electronic structures. It is also found that the gating effects are strongly dependent on the direction of the field. The perylene tetracaboxylic diimide (PTCDI) molecule used in the device of Xu et al.3 is connected to two gold electrodes (source and drain) via gold-thiol bonds with the central perylene lying in the xy plan, as shown in Figure 1. The line between the two anchor sulfur atoms coincides with the x axis. A molecule-gold complex, consisting of the PTCDI molecule and two triangle gold clusters attached on each sides of the PTCDI, is treated quantum mechanically. The sulfur atom is located about 2.32 Å above the center of the gold triangle. The complex is in equilibrium with the source and the drain, which are described by an effective mass approximation (EMA), through the line up of their effective Fermi levels. Geometry optimization and electronic structure calculations are carried out using the hybrid density functional theory with B3LYP functional and the Lanl2dz basis set as implemented in the Gaussian 03 package.7 The electron-transport properties are calculated using the QCME program,8,9 which is based on a generalized quantum chemical approach in combination with the scattering theory that has been developed by our group in the past few years. The QCME program has been applied to different molecular junctions for both elastic10,12 and inelastic9,11 scattering
Figure 1. (a) Schematic drawing of the single PTCDI molecular field-effect transistor. The central phenyl rings are placed in the xy plane with the molecular main axis along the x direction. (b) Calculated and (c) experimental3 source-drain current (Isd) as a function of sourcedrain bias voltage (Vsd) under various gate voltages (Vg). (d) Calculated and (e) experimental3 source-drain current (Isd) vs gate voltage (Vg) when the source-drain voltage is 0.1 V.
processes. The calculated results are often in very good agreement with the experiments. The molecular approach used in the QCME program is flexible in order to deal with the gate effects. In this case, the interacting Hamiltonian (Hint) caused by the external fields is treated as the interaction between the electrons and the external electric field (Ei) (including both source-drain and gate fields), that is, Hint ) ΣieriEi , (i ) x, y, z and r is the coordination of the electron). The modified total Hamiltonian is then used to calculate the field-dependent eigenstates and eigenfunctions of the device. A similar approach was adopted before treating the solvent effect on the optical and nonlinear optical properties of molecules.13 It was shown that more than 90% of the total solvent effects on the electronic structures and optical properties of molecules could be recovered by this approach.13 A large gate field, around 1 V/Å, was addeed to the device in the experiment3 by using an electrochemical gate. In this case, the gate electrodes surround the entire molecule and have the same shape as the molecule. The gate voltage is added between the electrodes and the gate electrolytes around the molecules. In our simulations, we have assumed that the gate is about 1.2 Å away from the molecular surface in order to fit the experimental gate voltage. This distance also corresponds to the averaged van der Waals radii of the atoms in the molecule. By inspecting the molecular structure shown in Figure 1a, one can immediately notice that the closest contact between gate and molecule can be reached when the gate is placed along the z axis, that is, normal to the central perylene. The distance between gate electrolytes and electrodes is much larger along the y axis, around 5 Å. This implies that the gate electric field along the z direction can be 4 times larger than that along the y direction. It is also noted that the permanent dipole moment of the molecule is quite small. The 2092
three components of the permanent dipole moment of the molecule-gold complex, µx, µy, and µz, are found to be 0.01, 0.14, and 0.03 D, respectively, which are smaller than the permanent dipole moment of the original molecule in the gas phase. It should be mentioned that two phenyl rings are twisted with respect to the central perylene and the symmetry of the molecule is broken. The presence of metal-molecule bonds has actually reduced the polarity of the system slightly. The simplest approach that one can think of is to consider the external gate field as a perturbation. In this case, the effect of the external gate is simply to shift up/down of the molecular orbitals. Calculations show that this approach can only produce a very small gate effect because of the small dipole moment of the molecule and weak gate voltage. The largest current gain is less than 1 order of magnitude, consistent with previous theoretical findings.5,6 A more realistic approach is to treat the interaction between electrons and external fields precisely and to solve the Schro¨dinger equation nonperturbatively. Here the interaction energy is represented as a three-dimensional potential in the real space and is sensitive to the direction of the external gate field. One of the important features of the nonpertubative approach is the ability to include the polarizabilities of the molecules. The PTCDI molecule has a small dipole moment but very large polarizability because of its strong conjugation. The orbital energy, as well as orbital properties, can be largely perturbed by the external electric field13 through the polarization, as shown clearly by the following simple energy expression, a ) a0 - µai Ei - 1/2Rai EiEj.... Here a0 and a are the energy of orbital a without and with electric field Ei, respectively, and µia and Riia are the dipole moment and polarizability of orbital a, respectively. When the external electric field and polarizability of the molecule are large, a Nano Lett., Vol. 6, No. 9, 2006
small dipole moment cannot prevent a large gate effect. From this expression, one can also conclude that the orbital energy shifting is not linearly dependent on the external electric field. Our calculations have shown that the polarizability of the PTCDI molecule has three big diagonal components with values of 1072, 388, and 223 au for Rxx, Ryy, and Rzz, respectively. In the experiment of Xu et al.,3 the distribution of external field in the space cannot be determined experimentally because the shape of the electrochemical cell around the molecule is unknown. We would like to demonstrate that theoretical simulations can provide useful information about the effect of different gate configurations on the performance of the device. It should be mentioned that the effect of molecular dipole moment on the performance of the FET device was discussed by Ghosh et al.6 We present here an alternative computational approach and numerical solutions for a real device containing molecules with small dipole moments but large polarizabilities. We have tested many different configurations. The results that fit the best with the experiment are presented in Figure 1. They are obtained from one particular device configuration, where the source-drain field is oriented 150° with respect to the x axis in the x-z plane and can be described by a vector (-0.87,0,0.5). The gate field follows the vector of (-0.5,0,-0.87), perpendicular to the source-drain field. As one can see from Figure 1, the agreement between theory and experiment is very good for both absolute current and relative changes induced by the gate voltage. The experimental source-drain current (Isd) shows a nonmonotonic dependence on the gate voltage (Ig) when the source-drain voltage (Vsd) is set to 0.1 V, see Figure 1e. The experimentally observed plateau between gate voltages of 0.7 and 0.8 V is also largely reproduced by the calculations. To understand this behavior, we have plotted the transmission spectra of the device under the gate voltage of -0.1, -0.6, -0.8, and -0.9 V, respectively, with Vsd ) 0.1 V in Figure 2. It should be noted that the current flow at Vsd ) 0.1 V is determined by the tail of the conducting bands, consisting of a group of delocalized conjugated orbitals. When gate voltage Vg ) -0.1 V, the first conducting band is located about 3.8 eV above the Fermi level. The transmission intensity at 0.1 eV is thus very weak. At Vg ) -0.6 V, the first conducting band has shifted down to 2.2 eV and becomes much broader. The transmission intensity at 0.1 eV has increased by 3 orders of magnitude in comparison with the case of gate voltage Vg ) -0.1 V. This explains the large gate effects shown in Figure 1. It is noted that between these two gate voltages the orbital energy shifting, 1.6 eV, is much larger than the increase of the gate voltage, 0.5 V, indicating that the molecular orbitals are largely affected by the strength of the electric field, rather than by the voltage itself. By increasing the gate voltage Vg to -0.8 V, the transmission intensity at 0.1 eV is actually dropped to below the corresponding value for Vg ) -0.6 V and it explains the formation of the plateau in the Isd-Vg curve. The transmission intensity under a gate voltage of -0.9 V is enhanced because of the near-resonance effect. The molecular orbitals are not shifted linearly with respect to the Nano Lett., Vol. 6, No. 9, 2006
Figure 2. Transmission spectra of the single PTCDI FET above Fermi level under different gate voltages (Vg) with Vsd at 0.1 V. *: the spectrum for Vsd ) -0.1 V has been multiplied by a factor of 100 for a better presentation. The inset shows that the small peak in the transmission spectra corresponds to the real molecular orbitals.
Figure 3. Calculated Isd-Vg relations at Vsd ) 0.1 V under four different gate configurations, with the gate field vector along (-0.5,-0.87,0), (0,-1,0), (-0.5,0,-0.87), and (0,0,-1) directions, respectively.
increase of the gate voltage. Theoretical calculations thus become very important for understanding the microscopic processes of the device. In the setup described above, the source-drain electric field has its component along the gate direction. We have also lined up the source-drain field to be parallel with the x axis, along the (1,0,0) direction. The calculated current of the device at Vsd ) 0.1 V in different gate configurations is presented in Figure 3. When the gate field is along either the z axis or the y axis, the Isd shows almost no gate-voltage dependence. The permanent dipole moment of the moleculemetal complex has its maximum component along the y direction. However, the distance between the gate and the source becomes much larger because of the size of the molecule along this direction, which in turn leads to a smaller gate electric field and smaller gate effects. When the gate field is in the xz plane and forms an angle of 240° with the molecular axis x, a large gain of current is observed, although it behaves slightly different from the experimental results. In summary, we have carried out first-principle simulations for a single molecular FET device in order to understand 2093
the underlying electron-transport mechanism. Our calculations have reproduced the experimental results nicely and shown that the resonant electron tunneling through unoccupied molecular orbitals is the dominant transport process. We have also demonstrated that the direction of the gate field has a strong impact on the performance of the devices and theoretical modeling can provide guidelines for the design of single molecular FET devices. Acknowledgment. This work was supported by the Swedish Research Council (VR) and the Carl Trygger Foundation (CTS.). W.S. acknowledges the support of the China Scholarship Council. References (1) (a) Ratner, M. A.; Joachim, C. PNAS 2005, 102, 8801. (b) Molecular Nanoelectronics; Reed, M. A., Lee, T. T., Eds.; Am. Sci.: Stevenson Ranch, CA, 2003. (2) Lee, J.-O.; Lientschnig, G.; Wiertz, F.; Struijk, M.; Jamssen, R. A. J.; Egberink, R.; Reinhoudt, D. N.; Hadley, P.; Dekker, C. Nano Lett. 2003, 3, 113. (3) Xu, B. Q.; Xiao, X. Y.; Yang, X. M.; Zang, L.; Tao, N. J. J. Am. Chem. Soc. 2005, 127, 2386. (4) Xiao, X.; Nagahara, L. A.; Rawlett, A. M.; Tao, N. J. J. Am. Chem. Soc. 2005, 127, 9235. (5) (a) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Appl. Phys. Lett. 2000, 76, 3448. (b) Emberly, E. G.; Kirczenow, G. Phys. ReV. B 2000, 62, 10451. (c) Damle, P.; Rakshit, T.; Paulsson, M.; Darra, S. IEEE Trans. Nanotechnol. 2002, 1, 145. (d) Bratkovsky, A. M.; Kornilovitch, P. E. Phys. ReV. B 2003, 67, 115307.
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