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First-Principles Study on Formation and Electron-Transport Properties of Single Oligothiophene Molecular Junctions Zong-Liang Li,* Guang-Ping Zhang, and Chuan-Kui Wang College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
bS Supporting Information ABSTRACT: In this work, the formation of single oligothiophene molecular junctions was studied using density functional theory. The elastic scattering Green’s function method was applied to investigate the electron-transport properties of the molecular junctions and their conductance switching properties caused by an electrochemical gate. Given four configurations, the optimized structures and breakdown forces of the molecular junctions were obtained. The breakdown of the oligothiophene molecular junctions is likely to occur at the AuS bond as the electrodes are pulled. The simulated results show that the experimental findings that the four-repeating-unit oligothiophene is more conductive than the three-repeating-unit oligothiophene are due to their different configurations. The oligothiophenes’ electronic structures are sensitive to the gate field, and their conductance switching properties are explained when a gate field is applied.
I. INTRODUCTION Applying single molecules to design functional electronic components is an important research area in nanoelectronics.19 Up to now, the general understanding of electron-transport properties of molecular devices is good. On the basis of experimental studies, a series of molecules such as small conjugated molecules,1014 single- and multiple-wall carbon nanotubes,15 and macro-organic molecules16,17 have been found to exhibit functional device characteristics in such applications as molecular switches,8,1820 molecular memory,16 negative differential resistance,17,2123 molecular rectifiers, and single-molecule transistors.1,2,57 The ability to construct molecular functional devices plays a key role in the development of molectronics. The electron-transport properties and functional performance of molecular devices are influenced by many factors,2436 for instance, molecular structure,29 contact configuration,30 positions of terminal atoms on metal surfaces,31 distance between electrodes,32 pressure of scanning tunneling microscope probe,33 and ambient conditions.3436 Thus, many challenges need to be solved for a theoretical understanding of experimental measurements. To obtain the detailed construction of molecular junctions, theoretical methods have been applied to simulate the formation of molecular junctions.28,3739 For instance, Qi et al. presented a theoretical study of the elongation process of octanedithiol molecular junctions and demonstrated probable coupling geometries.37 Paulsson et al. employed density functional theory (DFT) molecular dynamics to study the dynamical formation of goldalkanedithiolgold junctions and used the obtained geometries for a conductance study.38 Xu et al. experimentally investigated the electron-transport and electromechanical properties of single oligothiophenes with three and four thiophene repeating units.8 They found that the four-repeating-unit molecule r 2011 American Chemical Society
is more conductive than the three-repeating-unit molecule and that the conductance of the molecules decreases upon stretching. Furthermore, when an electrochemical gate is applied, the fourrepeating-unit molecule has a more obvious field effect than the three-repeating-unit molecule. Here, we report a theoretical study on the electron-transport properties of single oligothiophenes involving the application of a quantum chemistry approach and generalized Green’s function method. The stretching process of the molecular junction was also simulated. The breakdown forces for the molecular junctions and the optimized molecular junctions were thus obtained.
II. THEORETICAL MODEL AND COMPUTATIONAL DETAILS The molecular systems investigated consisted of two semiinfinite electron reservoirs, namely, the source (S) and the drain (D), connected by a molecule (M). Based on the general Green’s function formalism of Mujica et al.,40 the net current density of molecular junction from source to drain for a three-dimensional electrode can be written as4145 Ef þ eVSD Ez Z 1 þ exp 4emkB T ∞ k T B iSD ¼ ln E Ez p3 f eVSD 1 þ exp kB T jζðEz , VSD Þj2 nS ðEz Þ nD ðEz Þ dEz
ð1Þ
Received: January 1, 2011 Revised: June 21, 2011 Published: June 23, 2011 15586
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where VSD is the external bias; m* is the effective mass of an electron; e is the charge of an electron; Ef is the Fermi level energy; nS and nD are the densities of states of the source and drain, respectively; p is Planck's constant; kB is the Boltzmann constant; and T is the temperature, which was set as 300 K in the calculations. The transition matrix element from the source to the drain is ζðEz , VSD Þ ¼
ÆJjnæÆnjKæ
∑J ∑K UJSðVSD Þ UKDðVSD Þ ∑n ½Ez En ðVSD Þ þ iΓn ð2Þ
where |næ is an eigenstate of the Hamiltonian (H) of a finite system that consists of the molecule sandwiched between two clusters of metal atoms. The summation of n runs over the eigenstates whose energies are higher than the Fermi level. J and K run over all atomic sites, which are denoted as 1, 2, ..., N, where sites 1 and N are the two end sites of the molecule that connect with two electron reservoirs. Γn is the energy broadening. The coupling energy UJS (or UKD) between an atomic site J (or K) and a reservoir S (or D) is written as UJS ðVSD Þ ¼ ÆJjHjSæ ¼
∑ CJnR ÆJR jHjSi æCSni
n, R, i
UKD ðVSD Þ ¼ ÆKjHjDæ ¼
CKnβ ÆKβ jHjDj æCDnj ∑ n, β, j
ð3Þ
where CJnR (or CKnβ) is an expansion coefficient of a molecular orbital |næ on an atomic basis function |Ræ (or |βæ) at an atomic site J (or K) of the bare molecule and CSni (or CD nj) is an expansion coefficient of the molecular orbital |næ on an atomic basis function |iæ (or |jæ) of a gold atom cluster at the source (or drain) side. Then, the current is obtained as ISD = AiSD, where A is the effective injection area25 and the conductance is G = ∂ISD/∂VSD. When an electrochemical gate is used, the Hamiltonian of the system is expressed as H = H0 + eVg(r), where H0 is the Hamiltonian of the molecular system without the electrochemical gate and Vg(r) is the potential induced by the gate field.5 The electronic structures of the molecular systems are self-consistently calculated at each gate field. Considered experimental circumstance that the molecule is surrounded by the gate electrolytes, the gate voltage can be calculated by taking the difference of boundary potentials of the molecule with and without a gate field. The geometric optimizations and electronic structure determinations were performed using hybrid density functional theory (DFT) at the B3LYP level in the Gaussian 03 package.46 The electron-transport properties were carried out using QCME codes47 based on the generalized quantum chemical Green’s function theory.5,4145
III. RESULTS AND DISCUSSION Two typical configurations for the oligothiophenes with three thiophene units (denoted as 3T1DT) and four thiophene units (denoted as 4T1DT) anchored on the gold electrodes are shown in Figure 1a. The corresponding extended molecular systems shown in Figure 1b are denoted as Conf1, Conf2, Conf3, and Conf4. Each of the molecular systems consists of an oligothiophene molecule and two triangular gold clusters, with the terminal sulfur atoms anchor above the hollow position of the
Figure 1. Schematic structures of (a) oligothiophene molecular junctions and (b) extended oligothiophene molecules with different geometric configurations. The oligothiophene with three thiophene units is denoted as 3T1DT, and that with four thiophene units is denoted as 4T1DT.
gold triangles. For Conf1 and Conf3, the two triangular gold clusters are parallel and face each other, whereas for Conf2 and Conf4, the terminal CS bonds are approximately perpendicular to the triangle surfaces. The formation of molecular junctions was simulated by adjusting the distances of two electrodes. Given one distance, we optimized the molecular structures using the Lanl2TZ basis set for the Au atoms and the 6-311G basis set for the C, H, and S atoms. The interaction force between the molecule and the electrode is defined as F = ∂E/∂D, where E is the ground-state energy and D is the distance between the two electrodes.28,48,49 Plots of the ground-state energy, force, and molecular length as functions of the distance are shown in Figure 2. From Figure 2, one can see that the minimum energies for configurations Conf1, Conf2, Conf3, and Conf4 occur at D = 2.11, 1.96, 2.50, and 2.42 nm, respectively. The minimum energy of Conf2 (Conf4) is about 0.52 eV lower than that of the Conf1 (Conf3), which seems to indicate that the terminal CS bonds are likely to be vertically anchored on the Au(111) surface. Furthermore, for the junctions with the minimum energies, the distances between the end sulfur atoms and the gold triangles are 0.230, 0.223, 0.230, and 0.225 nm, respectively, which are close to the widely used values.50 It should be noted that Conf2 is special because the molecule is adsorbed on gold at the side position. When the distance between the two gold clusters was 1.96 nm, the tip radius of the electrode was estimated to be less than 3 nm. If the tip radius of the electrode were larger than 3 nm, the two gold tips would be in contact with each other, which makes the molecular junction invalid. Considering the experimental technique, we thus predict that the configuration Conf2 is difficult to form. The positive force between the molecule and the electrode represents a pressure, where a negative value means a stretching force. When the distance was increased from the equilibrium 15587
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Table 1. Typical Geometric Parameters (nm) of Optimized Molecular Junctions with Electrodes at Different Distances (D), where L is the Molecular Length
Conf1
Conf2
Conf3
Figure 2. Ground-state energies (E) and forces (F) as functions of the distance between two electrodes. A schematic view of the variations of the oligothiophene molecular lengths (L) (dashed lines) is also included. (a) Conf1, (b) Conf2, (c) Conf3, (d) Conf4.
distance for each of the configurations shown in Figure 2, both the stretching force and the molecular length first increased and then began to decrease at the electrode distance that corresponds to the breakdown of the molecular junction. The breakdown forces for Conf1, -2, -3, and -4 were determined to be about 1.53, 1.43, 1.56, and 1.48 nN, respectively, which are consistent with the experimental result of 1.5 ( 0.2 nN measured by Xu et al.8 Typical geometric parameters for the optimized extended molecular systems are listed in Table 1. It is observed that, when the electrode distance increased, the terminal SAu bond lengths exhibited an obvious change, whereas the other bond lengths in the molecule exhibited only a slight change; that is, the molecular length changed slightly. Taking Conf1 as an example, we found that the SAu bond length increased from 0.23 to about 0.29 nm as the electrode distance stretched from 2.11 to 2.28 nm, whereas the variation of the other bond lengths was less than 0.003 nm. When the electrode distance reached a value of 2.30 nm, the left SAu bond length decreased to 0.25 nm, whereas the right SAu bond length increased to 0.38 nm. At the same time, the 3T1DT molecular length decreased to 1.67 nm. This indicates that the molecular junction was then broken. According to the above discussion, one can conclude that the breakdown of the molecular junction occurs at the SAu bond. To further verify whether the molecular junction breaks down between the terminal sulfur atom and the gold cluster under the stretching of the electrodes, we also calculated the breakdown force for a gold nanowire. The results show that the breakdown force for a gold nanowire, that is, for the last AuAu bond being broken, is 1.21.8 nN, which is consistent with the measurements of Rubio et al.51,52 and Frei et al.53 However, when a gold atom is pulled out from a bulk gold sample, a stretching force of more than 2.8 nN is needed.54,55 We estimate that the breakdown of the oligothiophene molecular junctions is likely to occur at the AuS bond as the electrodes are pulled. It is noted that the electronic contribution to the total energy was calculated only when the molecular junctions were elongated.
Conf4
D
L
SAu (left)
SAu (right)
2.11
1.65
0.23
0.23
2.18
1.68
0.23
0.23
2.24
1.70
0.27
0.27
2.28
1.70
0.29
0.29
2.30 1.96
1.67 1.61
0.25 0.22
0.38 0.22
2.04
1.65
0.24
0.24
2.14
1.68
0.27
0.27
2.22
1.69
0.30
0.30
2.24
1.65
0.24
0.41
2.50
2.04
0.23
0.23
2.56
2.07
0.24
0.24
2.64 2.68
2.10 2.10
0.27 0.29
0.27 0.29
2.70
2.07
0.25
0.39
2.42
2.02
0.23
0.23
2.53
2.07
0.26
0.26
2.65
2.10
0.30
0.30
2.67
2.10
0.30
0.31
2.69
2.04
0.24
0.46
Nevertheless, the zero-point vibrational energy exhibited a close relationship with the molecular structures. Thus, the effect of the zero-point vibrational energy on the elongation process of the molecular junction needs to be investigated. When the zeropoint vibrational energy was considered, we found that there was a correction of less than 0.05 nN for the forces in general. Moreover, a correction of less than 0.02 nN was obtained for the breakdown forces. That is, the zero-point vibrational energy played a small role in describing the elongation process of the molecular junction. Based on eqs 13 and application of the QCME code, we obtained the sourcedrain currents of the molecular junctions. The sourcedrain currentvoltage curves for the four configurations are shown in Figure 3. From Figure 3a, one can see that the currents for Conf1 and Conf3 are very weak in the bias voltage windows. However, for Conf 2, the current rapidly increased with the bias voltage from 0.6 V, and the current value was 0.084 μA at 1.0 V. In contrast, for Conf4, the current rapidly increased from zero voltage and reached 0.11 μA at 1.0 V. The results indicate that the currents of the molecular junctions are closely related to their configurations. According to eqs 1 and 2, the coupling energies between the molecules and electrodes and the electronic distributions of the molecular orbitals are two key factors determining the transmission spectra. Here, we discuss only the coupling energy between the terminal sulfur atom and the gold cluster (i.e., U1S or UND) because of its main contribution to the coupling energy between the molecule and the electrode. The coupling energy was calculated based on eq 3 and found to be about 1.15, 0.95, 1.89, and 1.91 eV for configurations Conf1Conf4, respectively. It is clearly seen that the molecular configuration Conf4 had the largest coupling energy. For Conf1, Conf2, and Conf4, the conductive channels opened at about 0.80, 0.52, and 0.75 eV, respectively (see inset 15588
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Figure 3. (a) Sourcedrain IV properties of 3T1DT and 4T1DT molecular junctions with the configurations shown in Figure 1. Transmission spectra are shown as an inset. (b) Numerical IV curves of 3T1DT and 4T1DT molecular junctions with respective Conf1 and Conf4 configurations compared to experimental results.
in Figure 3a), whereas for Conf3, no conductive channel opened below 1.0 eV; therefore, the current for this configuration was very weak in the bias voltage window (0, 1.0 V). Under a bias of 1.0 V, Conf1 and Conf2 exhibited two transmission peaks, whereas Conf4 exhibited one transmission peak. One can see that the peak for Conf4 is very broad and its magnitude is similar to those of the other configurations. Thus, the 4T1DT junction with the Conf4 configuration was found to be more conductive than the 3T1DT junction with the Conf1 configuration. Considering the preceding discussion of the formation of the molecular junctions, we estimate that Conf2 is difficult to form experimentally. Thus, we predict that Conf1 for 3T1DT and Conf4 for 4T1DT are the probable conformations in the experiments8 (see Figure 3b). The gate effect on the electron-transport properties of 3T1DT and 4T1DT molecular junctions with the Conf1 and Conf4 configurations, respectively, was further investigated. When no gate field is added to a molecular device, the potential distribution in real space is dominated by the structure of the molecular junction and the external bias voltage. However, when a gate field is applied by an electrochemical gate, the potential distribution is changed by the gate field, and the molecular orbitals are thus shifted up/down.5,18 In our simulations, we allowed the potential shift to fit the gate voltage at 0.12 nm away from the molecular surface5 and carried out our first-principles calculations. The electron-transport properties of the molecular devices were then simulated at different gate voltages. Plots of the sourcedrain current versus gate voltage for 3T1DT and 4T1DT molecular junctions are shown in Figure 4a with a sourcedrain bias of 0.1 V. One can see that, for the 3T1DT molecular system, the sourcedrain current was nearly zero at negative gate voltages, whereas for positive gate voltages, the current increased with increasing gate voltage. For 4T1DT, the sourcedrain current was very weak at negative gate voltages and rapidly increased with the increase of the gate voltage in the positive range. As mentioned above, the coupling energies between the terminal atoms and the electrodes are important factors for determining the electron-transport properties of molecular junctions. From the
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Figure 4. (a) Sourcedrain currents of the 3T1DT and 4T1DT molecular junctions with respective Conf1 and Conf4 configurations for different gate voltages. The sourcedrain voltage is taken as 0.1 V. The inset shows the coupling energy between the electrodes and the oligothiophene molecules. (b,c) Corresponding transmission spectra for different gate voltages.
inset of Figure 4a, one can see that the coupling energies between the terminal atoms and the electrodes exhibited variation trends similar to those of the ISDVg curves. It also can be seen that the coupling energies were obviously influenced by the gate field. The transmission spectra are given in Figure 4b,c. It should be noted that, VSD = 0.1 V is a lower bias voltage. Usually, at a lower bias voltage, no electronic pathway opens, and the sourcedrain current is contributed by the tail of the conducting bands, which consist of a group of delocalized conjugated orbitals. That is, at lower bias voltages, the sourcedrain current is determined by nonresonant transport. From Figure 4b, one can see that the transmission intensity in the range of 00.1 eV at the gate voltage Vg = 0.50 V was larger than those in other cases. For the gate voltages of Vg = 0.32 and 0.40 V, although there exist two high transmission peaks from 0.25 to 0.50 eV, the transmission intensity in the range of 00.1 eV is much weaker than those for the gate voltages of Vg = 0.20 and 0.50 V. One can see from Figure 4c that the mean transmission intensities in the range of 00.1 eV under different gate voltages for 4T1DT give similar understandings to that for 3T1DT. The positions of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) relative to the Fermi energy and the HOMOLUMO gap are also two important factors determining the transport properties of molecular junctions.8 The numerical results show that the HOMOLUMO gap changed slightly under negative gate voltages. However, it became narrower as the positive gate voltage increased. As a result, the current values at positive gate voltages were larger than those at negative gate voltages.
IV. CONCLUSIONS In conclusion, based on first-principles calculations, we determined the breakdown positions of oligothiophene molecular 15589
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’ ASSOCIATED CONTENT
bS
Supporting Information. Explanation of the statement about the experimentally difficult formation of Conf2 and optimized structures of the molecular systems. This information is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China under Grants 10804064 and 10974121. ’ REFERENCES (1) Ma, C. L.; Nghiem, D.; Chen, Y. C. Appl. Phys. Lett. 2008, 93, 222111. (2) Saha, K. K.; Lu, W.; Bernholc, J.; Meunier, V. Phys. Rev. B 2010, 81, 125420. (3) Shen, X.; Yi, Z. L.; Shen, Z. Y.; Zhao, X. Y.; Wu, J. L.; Hou, S. M.; Sanvito, S. Nanotechnology 2009, 20, 385401. (4) Yamada, R.; Kumazawa, H.; Noutoshi, T.; Tanaka, S.; Tada, H. Nano Lett. 2008, 8, 1237. (5) Su, W. Y.; Jiang, J.; Lu, W.; Luo, Y. Nano Lett. 2006, 6, 2091. (6) Xu, B. Q.; Xiao, X, Y.; Yang, X. M.; Zang, L.; Tao, N. J. J. Am. Chem. Soc. 2005, 127, 2386. (7) Albrecht, T.; Guckian, A.; Ulstrup, J.; Vos, J. G. Nano Lett. 2005, 5, 1451. (8) Xu, B. Q.; Li, X. L.; Xiao, X. Y.; Sakaguchi, H.; Tao, N. J. Nano Lett. 2005, 5, 1491. (9) Xia, J. L.; Diez-Perez, I.; Tao, N. J. Nano Lett. 2008, 8, 1960. (10) Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278, 252. (11) Teramae, Y.; Horiguchi, K.; Hashimoto, S.; Tsutsui, M.; Kurokawa, S.; Sakai, A. Appl. Phys. Lett. 2008, 93, 083121. (12) Chen, F.; Huang, Z. F.; Tao, N. J. Appl. Phys. Lett. 2007, 91, 162106. (13) Xiao, X. Y.; Xu, B. Q.; Tao, N. J. Nano Lett. 2004, 4, 267. (14) Dadosh, T.; Gordin, Y.; Krahne, R.; Khivrich, I.; Mahalu, D.; Frydman, V.; Sperling, J.; Yacoby, A.; Israel, B. J. Nature 2005, 436, 677. (15) Frank, S.; Poncharal, P.; Wang, Z. L.; de Heer, W. A. Science 1998, 280, 1744. (16) Liu, Z. M.; Yasseri, A. A.; Lindsey, J. S.; Bocian, D. F. Science 2003, 302, 1543. (17) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550. (18) Song, H.; Kim, Y.; Jang, Y. H.; Jeong, H.; Reed, M. A.; Lee, T. Nature 2009, 462, 1039. (19) Miao, F.; Ohlberg, D.; Stewart, D. R.; Williams, R. S.; Lau, C. N. Phys. Rev. Lett. 2008, 101, 016802.
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