Conductance of Stretching Oligothiophene Single-Molecule Junctions

Nov 11, 2011 - We analyze conductance switching properties during the stretching of ... This breaking point, occurring at a longer stretching distance...
4 downloads 0 Views 2MB Size
Download PDF
ARTICLE pubs.acs.org/JPCC

Conductance of Stretching Oligothiophene Single-Molecule Junctions: A First-Principles Study Y.-H. Tang,†,‡ V. M. K. Bagci,† Jing-Han Chen,† and Chao-Cheng Kaun*,†,§ †

Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan Department of Physics, National Central University, Jung-Li 32001, Taiwan § Department of Physics, National Tsing-Hua University, Hsinchu 30013, Taiwan ‡

ABSTRACT: We analyze conductance switching properties during the stretching of Au oligothiophene dimethylene dithiol Au single-molecule junctions, by using first-principles calculations based on the density functional theory and the nonequilibrium Green’s function approach. Our results of these σ π hybrid molecular systems agree well with the experimental data and confirm that the longer molecular junction (four thiophene rings) has higher conductance than the shorter one (three thiophene rings). We attribute this behavior to their differently located molecular levels, with respect to the Fermi energy, at the point of the junction break. This breaking point, occurring at a longer stretching distance for the shorter molecule, affects the junction conductance significantly and can be determined by several characteristics of the junction.

’ INTRODUCTION A quantitative understanding of electrical transport through single-molecule junctions,1,2 consisting of a central molecule sandwiched by two leads, is key to the evolution of molecular electronics.3 To date, efforts have been made to bridge firstprinciples calculation and experiment for a molecular junction formed by a σ-saturated molecule, such as alkanedithiol,4 8 or built by a π-conjugated molecule, such as oligophenyldiamine9 and bipyridine.10 However, a σ π hybrid molecular junction may allow versatile choices of molecular structures and electronic properties to fit the desired conduction properties of nanoscale electronic devices. Although the decay constant β of the oligophenylene methylene (CH2) thiol molecule has been compared between theory11 and experiments12,13 for a σ π hybrid system, a comparison of conductance on a single molecule basis has not yet been well addressed. By repeating thousands of scanning probe microscope break junction measurements, conductance of a σ π hybrid singlemolecule junction, constructed by a oligothiophene dimethylene dithiol molecule (nT1DT, where n is the number of thiophene rings) with two Au contacts, has been statistically determined.14 It shows that the longer 4T1DT is more conductive than the shorter 3T1DT, a finding that does not obey the expected nonresonant tunneling process where conductance of a molecular wire decays exponentially with the increasing length.15,16 This interesting conduction behavior has been attributed to the shift of the highest occupied molecular orbital (HOMO) level with the change of the oligothiophene ring number.14 These results offer an excellent opportunity to shed insight into the transport properties of σ π molecular junctions. Although conductance of oligothiophene molecular junctions has been studied theoretically,17,18 only one work,19 so far, has included r 2011 American Chemical Society

the methylene groups (the σ part) and stretching processes when modeling Xu’s experiment,14 by using extended molecule approximation where electrodes are reduced to gold atom clusters. However, as observed in measurements, gold nanowires form at the single molecule ends during the stretching.20 The nanowire feature, and thus the band structure, of the electrodes should be taken into account in an atomistic computational modeling.8,21,22 Moreover, we often need to know what happens during a molecular-junction-breakdown and how it can be controlled in realizing a stable electronic circuit, especially at the nanoscale. In this work, we investigate theoretically the conductance of Au oligothiophene dimethylene dithiol Au molecular junctions during the stretching processes. We compare our results with the experimental data quantitatively and attempt to give a detailed understanding of the observed intriguing phenomena.14 We study how to determine the position of a breaking point and what happens when a junction breaks. How contacts and molecular orbitals affect the junction conductance is also discussed.

’ METHODS The junction geometries were optimized using density functional theory (DFT)23 within the generalized gradient approximations (GGA) in the PBE form.24 During the optimization, the molecule was fully relaxed, and two gold adatoms were allowed to move along the junction axis, while the other gold atoms (five layers of the [111] orientated electrodes on each side of it) were kept fixed at the experimental lattice constant of 4.08 Å. The atop atop configuration corresponded to the local minimum of the Received: October 8, 2011 Revised: November 10, 2011 Published: November 11, 2011 25105

dx.doi.org/10.1021/jp209671v | J. Phys. Chem. C 2011, 115, 25105–25108

The Journal of Physical Chemistry C

ARTICLE

Figure 1. (a) The total energy and the bond lengths, dL and dR (distances between Au adatom and the electrode), during the stretching of the 3T1DT junction. (b) Relaxed 3T1DT junction geometries, before (1.89 Å) and at the breaking point (2.36 Å).

free energy. First-principles transport calculations were done by using Atomistix ToolKit,25,26 based on the nonequilibrium Green’s functions formalism and the DFT approach, within GGA in the forms of PBE24 for 4T1DT and revPBE27 for 3T1DT. The scattering region4 included a sufficiently large part (five layers) of the [111] orientated electrodes bonded through the adatoms to a single oligothiophene dimethylene dithiol in between. The Hamiltonian was expanded in real space having s, p, d double-ζ with a polarization atomic orbital basis set. The atomic cores were defined by the Troullier Martins pseudopotentials.28 The conductance value G = T(EF)*G0, where T(E) is the transmission spectrum, EF is the Fermi energy, and G0 = 2e2/h is the quantum of conductance.29 For comparison, the conductance of 3T1DT (4T1DT) is 0.052 (0.035) mG0, with the PBE24 (revPBE27) form.

’ RESULTS AND DISCUSSION To simulate the stretching process, we first optimized the junction geometries, then stretched the junction by increasing the distance between the two electrodes, optimized it again, and continued to do so, until the junction broke down. Dynamics of the stretching is neglected, because the stretching rate is much slower than the system relaxation speed (40 nm/s14 versus 194 m/s,6 respectively). Figure 1a presents the calculated total energy (the right axis) as a function of the stretching distance for a 23.6 Å long (electrode to electrode) 3T1DT junction. With elongation, the total energy first increases, drops near a distance of 2.36 Å, then increases again, which is similar to the behavior of a spring breakdown, giving a maximum force (from the slope of this curve) to be about 1.5 nN. There is a local minimum of the energy at 2.36 Å, implying that the molecular junction breaks at that point. To verify the junction breakdown, we define dL (dR) as the distance between the left (right) Au adatom and the Au electrode, as shown in Figure 1b. Figure 1a shows that before an extension of 1.89 Å, dL and dR are almost the same (assuming dL is shorter), and the molecule itself extends, and then both dL and dR increase as the junction stretches further. When the extension approaches 2.36 Å, dR increases considerably and dL drops. This

Figure 2. Conductance curves during the stretching of 3T1DT and 4T1DT junctions (natural logarithm of conductance, the bottom panel). Vertical dashed lines represent the breaking points of the two junctions. Two horizontal solid lines with error bars mark the measured conductance.14 The sloping solid lines are the best fits of the data points after the break.

indicates that the junction breaks between the right Au adatom and the right electrode (see Figure 1b), so that the molecule shrinks back toward the left Au electrode, agreeing with the experimental findings that the junction breakdown force is similar to that of Au Au bond breakdown.14,30 Thus, the breakdown of a 3T1DT junction occurs at about 2.36 Å, denoted as the breaking point. Following a similar process, we can also determine that the breaking point of a 27.8 Å long 4T1DT junction is at about 2.09 Å. The top panel of Figure 2 plots the calculated zero-bias conductance (see Methods) during the stretching of both 3T1DT and 4T1DT junctions. The conductance decreases dramatically as the junction is elongated, and it approaches zero after the breaking point. At the breaking point, the conductance of 3T1DT (4T1DT) is 0.029 (0.081) mG0. The shorter 3T1DT has smaller conductance than does the longer 4T1DT, because 3T1DT breaks at a longer stretching distance (2.36 Å) than does 4T1DT (2.09 Å). If 3T1DT also broke at 2.09 Å, its conductance would be higher than 4T1DT. The experimental conductance value of a single-molecule junction is identified from a broad peak of the conductance histogram, constructed by about 500 repeated individual measurements,14 which is marked by the horizontal solid line for its peak value and the error bar for its distribution in Figure 2. The measured conductance of 3T1DT (4T1DT) is 0.029 (0.075) mG0. Therefore, our calculated conductance at the breaking point agrees well with the experimental observation. However, in our calculated results, the conductance plateau does not appear, suggesting that such plateaus stem from the atomic rearrangements of the Au electrode.30 The abrupt decrease of conductance after the breaking point is also absent from our calculated results, which can be attributed to the 25106

dx.doi.org/10.1021/jp209671v |J. Phys. Chem. C 2011, 115, 25105–25108

The Journal of Physical Chemistry C

ARTICLE

Figure 4. The local density of states of 3T1DT (lefts) and 4T1DT (rights) junctions at the Fermi energy, before (top) and at the breaking point (bottom).

Figure 3. Transmission spectra of (a) 3T1DT and (d) 4T1DT junctions. The projected density of states (PDOS) of 3T1DT junction (b) before (2.24 Å) and (c) at the breaking point (2.36 Å). The PDOS of 4T1DT case (e) before (1.95 Å) and (f) at the breaking point (2.09 Å).

sudden change of the junction configuration out of the junction axis direction in the measurements.14 The bottom panel of Figure 2 shows the conductance in the natural logarithm scale. Because a gap exists after the breaks, both junctions have the same decay rate, which is larger than those of before the breaks, confirming the positions of the breaking points. Because the position of the junction break controls the junction conductance, we next address the transport properties of the junction, before and at the breaking point. Figure 3a displays transmission spectra, T(E), of the 3T1DT junction before (2.24 Å) and at the breaking point (2.36 Å), where E = 0 eV is the Fermi level EF. Once the breakdown occurs between the right Au adatom (Au_R) and the lead, the two transmission peaks, A1* and A2*, shift toward lower energies, and their magnitudes decrease significantly, becoming A1, A2, and A3. To understand this behavior, the projected density of states (PDOS) on the molecule (3T1DT), the left adatom (Au_L), and the right adatom (Au_R), before and at the breaking point, are calculated and shown in Figure 3b and c, respectively. Regarding the overlap of the PDOS in energy shown in Figure 3b, the A1* (A2*) peak results from the couplings between 3T1DT and both adatoms (solely Au_R). The PDOS of Au_R is distributed at lower energies than that of Au_L, possibly due to the weaker bonding between Au_R and the electrode than the other side (for dR is longer than dL). Stretching the junction until it breaks between the Au_R and the lead, the peak A2* shifts to the peak A3, and the peak A1* is split into the peaks A1 and A2. The peak A3 stems from the 3T1DT Au_R coupling, while the peak A1 (A2) comes from the 3T1DT Au_L(Au_R) coupling. Thus, at the breaking point, conductance can be traced as the tail of transmission peak A1, related to the renormalized HOMO of 3T1DT, where influences of the electrodes (via Au_L) are included.31 Therefore, the breakdown of a junction can also be verified by comparing its transmission spectra, before and at the breaking point.

For the 4T1DT case, the dramatic change of T(E) prior to (1.95 Å) and at the breaking point (2.09 Å) is shown in Figure 3d. Similarly, two main transmission peaks, B1* and B2*, shift to lower energies and split into three peaks, B1, B2, and B3, at the breaking point. B1 (located at 0.16 eV) is closer to EF than is A1 (located at 0.23 eV), leading to the higher conductance of 4T1DT than 3T1DT, at their breaking points. The corresponding PDOS values of the transmission peaks, before and at the breaking point, are plotted in Figure 3e and f, respectively. While the PDOS of Au_L remains the same as the junction breaks, the PDOS of Au_R and the PDOS of 4T1DT shift and split, being responsible for the change of transmission spectra. However, for the 3T1DT (4T1DT) junction, the renormalized HOMO of the central molecule constitutes the transmission peak A1 (B1) and determines the conductance at the breaking point. Because the PDOS of Au_L near EF is almost the same for both 3T1DT and 4T1DT cases, the conductance difference between 3T1DT and 4T1DT, at their breaking points, correlates to the location change of the HOMO for different central molecules. Therefore, although the interfacial contact between Au_L and the central molecule dominates the conductance, the larger conductance of 4T1DT is due to its higher HOMO location than that of 3T1DT. To better understand the tunneling processes spatially, we plot the local density of states (LDOS) of 3T1DT junction at the Fermi energy, before and at the breaking point, at the top left and the bottom left of Figure 4, respectively. The LDOS extends from the electrodes to the molecule. Before the junction breaks, the LDOS distributes mainly on both Au adatoms and on the 3T1DT molecule, particularly, at dithiol, dimethylene, and carbon atoms of the thiophene rings. However, the LDOS is larger at the left side than at the right side, because the coupling of the left contact is stronger than the right one. When the junction breaks at the right contact, the LDOS is only present from Au_L, the left thiol, the left methylene, to carbon atoms of the left thiophene ring in the 3T1DT molecule. The right part of Figure 4 shows the similar LDOS for a 4T1DT junction. Before the junction breaks, the LDOS distributes uniformly over both Au adatoms and the 4T1DT molecule. When the junction breaks at the right contact, the LDOS on Au_R, the right methylene and a few carbon atoms of the most right thiophene ring are absent. It is clearly shown that while the HOMO of 4T1DT is higher than that of 3T1DT, the LDOS of 4T1DT is more extended than that of 3T1DT.

’ CONCLUSIONS Conductance switching properties during the stretching of Au oligothiophene dimethylene dithiol Au single-molecule junctions are addressed from first-principles. Our results of these σ π hybrid molecular systems agree well with the experimental 25107

dx.doi.org/10.1021/jp209671v |J. Phys. Chem. C 2011, 115, 25105–25108

The Journal of Physical Chemistry C data and provide a quantitative understanding of observed intriguing phenomena.14 We suggest that the 4T1DT junction has a larger conductance than the 3T1DT junction does, because the former breaks at a shorter stretching distance (2.09 Å) than the latter (2.36 Å), and at these breaking points, the former has a higher HOMO than the latter. However, the existing contact (the left one) still dominates the conductance of both junctions. These breaking points, controlling the junction conductance, can be determined by several characteristics of the junction, such as the shape of the total energy curve, the variation in bond lengths, the change in conductance decay rates, and the differences of transmission spectra.

ARTICLE

(24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (25) Taylor, J.; Guo, H.; Wang, J. Phys. Rev. B 2001, 63, 245407. (26) Brandbyge, M.; Mozos, J.-L.; Ordejon, P.; Taylor, J.; Stokbro, K. Phys. Rev. B 2002, 65, 165401. (27) Zhang, Y.; Yang, W. Phys. Rev. Lett. 1998, 80, 890. (28) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993–2006. (29) Datta, S. Electrical Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, UK, 1997. (30) Rubio, G.; Agrait, N.; Vieira, S. Phys. Rev. Lett. 1996, 76, 2302. (31) Larade, B.; Taylor, J.; Zheng, Q. R.; Mehrez, H.; Pomorski, P.; Guo, H. Phys. Rev. B 2001, 64, 195402.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was partially supported by the National Science Council (Contract No. NSC 96-2112-M-001-013-MY2), the National Center for Theoretical Sciences, and the National Center for High-Performance Computing, Republic of China. ’ REFERENCES (1) Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384–1389. (2) Tao, N. J. Nat. Nanotechnol. 2006, 1, 173–181. (3) Joachim, C.; Gimzewski, J. K.; Aviram, A. Nature 2000, 408, 541–548. (4) Kaun, C.-C.; Seideman, T. Phys. Rev. B 2008, 77, 033414. (5) Li, C.; Pobelov, I.; Wandlowski, T.; Bagrets, A.; Arnold, A.; Evers, F. J. Am. Chem. Soc. 2008, 130, 318–326. (6) Paulsson, M.; Krag, C.; Frederiksen, T.; Brandbyge, M. Nano Lett. 2009, 9, 117–121. (7) Sheng, W.; Li, Z. Y.; Ning, Z. Y.; Zhang, Z. H.; Yang, Z. Q.; Guo, H. J. Chem. Phys. 2009, 131, 244712. (8) Sen, A.; Kaun, C.-C. ACS Nano 2010, 4, 6404–6408. (9) Quek, S. Y.; Choi, H. J.; Louie, S. G.; Neaton, J. B. Nano Lett. 2009, 9, 3949–3953. (10) Quek, S. Y.; Kamenetska, M.; Steigerwald, M. L.; Choi, H. J.; Louie, S. G.; Hybertsen, M. S.; Neaton, J. B.; Venkataraman, L. Nat. Nanotechnol. 2009, 4, 230–234. (11) Kaun, C.-C.; Larade, B.; Guo, H. Phys. Rev. B 2003, 67, 121411. (12) Wold, D. J.; Haag, R.; Rampi, M. A.; Frisbie, C. D. J. Phys. Chem. B 2002, 106, 2813–2816. (13) Ishida, T.; Mizutani, W.; Aya, Y.; Ogiso, H.; Sasaki, S.; Tokumoto, H. J. Phys. Chem. B 2002, 106, 5886–5892. (14) Xu, B. Q.; Li, X. L.; Xiao, X. Y.; Sakaguchi, H.; Tao, N. J. Nano Lett. 2005, 5, 1491–1495. (15) Joachim, C.; Vinuesa, J. F. Europhys. Lett. 1996, 33, 635–640. (16) Magoga, M.; Joachim, C. Phys. Rev. B 1997, 56, 4722–4729. (17) Zhou, Y. X.; Jiang, F.; Chen, H.; Note, R.; Mizuseki, H.; Kawazoe, Y. Phys. Rev. B 2007, 75, 245407. (18) Peng, G.; Strange, M.; Thygesen, K. S.; Mavrikakis, M. J. Phys. Chem. C 2009, 113, 20967–20973. (19) Li, Z.-L.; Zhang, G.-P.; Wang, C.-K. J. Phys. Chem. C 2011, 115, 15586–15591. (20) He, J.; Sankey, O.; Lee, M.; Tao, N. J.; Li, X.; Lindsay, S. Faraday Discuss. 2006, 131, 145–154. (21) Kaun, C.-C.; Guo, H.; Gr€utter, P.; Lennox, R. B. Phys. Rev. B 2004, 70, 195309. (22) Luzhbin, D. A.; Kaun, C.-C. Phys. Rev. B 2010, 81, 035424. (23) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. J. Phys.: Condens. Matter 2009, 21, 395502. 25108

dx.doi.org/10.1021/jp209671v |J. Phys. Chem. C 2011, 115, 25105–25108