NANO LETTERS
Charging of Molecules during Transport Y. Gohda*,† and S. T. Pantelides†,‡
2005 Vol. 5, No. 7 1217-1220
Department of Physics and Astronomy, Vanderbilt UniVersity, NashVille, Tennessee 37235, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37861 Received April 21, 2005; Revised Manuscript Received May 29, 2005
ABSTRACT The possibility that a single molecule can acquire charge during steady-state transport is an open issue. We report first-principles calculations in a range of configurations of certain molecules and conclude the following. When a molecule is strongly coupled to the electrodes, charging is not sustainable. On the other hand, by using variable-length tunnel barriers (insulating tethers) one can enable and control charging. In particular, by using different combinations of “tethers”, we demonstrate the possibility of charging by a single electron, sustainable over a wide bias range, and also the possibility of continuous linear charging when a gate voltage is applied.
In the past few years, the transport properties of individual molecules have attracted significant attention because of potential applications as nanoelectronic devices. Currentvoltage (I-V) characteristics have been measured for a few molecules1-6 and unique properties have been found, e.g., large negative differential resistance and temperature shifting of resonant peaks.3 First-principles theoretical calculations have also been reported,7-20 complementing experimental data and providing insights into the factors that control the shape of I-V curves, the role of contacts, and the magnitude of the current. The possibility of controlled charging of individual molecules under bias has enormous potential for device functionality. In contrast to individual molecules, semiconductor quantum dots are well established to have controlled charging as a single-electron transistor, where a gate voltage controls the charging by the Coulomb blockade mechanism.21 Although this phenomenon was recently demonstrated for a molecule consisting of a single Co atom embedded in a cage of benzene rings with alkene tethers acting as tunnel barriers,22 the question whether molecules can be charged under other conditions remains wide open. When a large negative differential resistance was first observed in a molecule in 1999,3 it was suggested that charging may be the pertinent mechanism as follows: the current increases significantly upon capture of an electron and then drops precipitously upon capture of a second electron as the voltage is increased.3 Qualitative support for the notion has been provided by calculations of the electronic structure of charged molecule and examination of the localization properties of the highest occupied molecular orbital in different charge * Corresponding author. E-mail:
[email protected]. Present Address: Abt. Theoretische Chemie, Universita¨t Ulm, D-89069 Ulm, Germany. † Vanderbilt University. ‡ Oak Ridge National Laboratory. 10.1021/nl0507313 CCC: $30.25 Published on Web 06/08/2005
© 2005 American Chemical Society
states.23 No explicit calculations of a charged molecule attached to electrodes under bias have been reported to test the hypothesis. On the other hand, first-principles transport calculations have shown that a negative differential resistance is possible without charging.10 Nevertheless, the issue of charging presents a range of questions with potential impact on device functionality: Can a molecule acquire charge without a gate voltage, and what is the role of strong versus weak coupling to the electrodes? Can we determine the factors by which one can achieve and control charging? In this paper, we report first-principles transport calculations for individual molecules designed to address the above issues. We used benzene rings with and without a nitro-group substituent and with sulfur terminators in the case of strongly coupled contacts to electrodes. We find that, under steadystate conditions, if a normally N-electron molecule is forced to have N + 1 electrons (an extra electron is added in the lowest unoccupied orbital or LUMO), the modification of the molecular orbitals induced by self-consistency results in a neutral molecule and neutral electrodes at all applied biases. In other words, though an electron is added, all the other occupied orbitals collectively loose an electron to the electrode reservoirs, keeping the molecule neutral (the “N + 1 electron” neutral state is really an excited N-electron many-body state). Note that, by forcing the extra electron in the HOMO, we are effectively going beyond steady state or even mean field theory because we are examining the state of the molecule if, by whatever mechanism, an extra electron stays resident long enough for all orbitals to adjust to a new self-consistent steady state. The result seems to be general for molecules strongly coupled to electrodes, i.e., such molecules cannot be charged under steady-state conditions. We subsequently explored the possibility of charging when the molecule is weakly coupled to the electrodes by using vacuum layers as tunnel barriers (in applications, tunnel
Figure 1. (a) Valence electron density distribution of the 2-nitrobenzene-1,4-dithiolate molecule connected to two jellium electrodes. The electron density is integrated in the direction perpendicular to the plotted plane. Gray circles indicate the position of atomic cores, and the two dotted lines represent the edge of jellium electrodes. (b) Distribution of an additional one electron occupied in the LUMO.
barriers can be variable-length tethers such as those used in ref 22). Without including a gate voltage, we found conditions under which a molecule spontaneously acquires an extra electron and keeps it over a wide range of bias (a large tunnel barrier is needed on the side with the lower Fermi level and weak coupling on the other side). Finally, we investigated the effect of a gate voltage on a molecule that is strongly coupled to the electrode with the higher Fermi energy but has a large tunnel barrier on the other side. We found that, as the gate voltage is applied, the molecule is charged nearly linearly. The net conclusion is that different charging behavior can be achieved by using different tethers between the molecule and the electrodes. Our investigations were carried out by performing steadystate transport calculations using the Lippmann-Schwinger method as formulated by Lang24 and used recently to study transport through benzene rings and related molecules.7-12 We, therefore, pursued answers for well-posed questions that can be answered by such calculations. In all the calculations, the electrodes were modeled by “jellium”, i.e., the nuclei are smeared out into a positive background so that the electrons form a homogeneous gas with density equal to that of the mean electron density in gold. It should be noted that the bias voltage is applied as the difference in the Fermi energies of the two electrodes. The first set of calculations examined what happens if we force a molecule to be charged during steady-state transport when the molecule is directly attached to the electrodes (strong coupling limit). We used a 2-nitrobenzene-1,4dithiolate molecule (benzene ring with S terminators attached to the electrodes and a nitro-group substituent). This is the model molecule studied in ref 10, where negative differential resistance without charging was demonstrated. At each value of the bias voltage, during the self-consistent iterative process, we added an extra electron in the LUMO (see Figure 1), whose energy lies above the Fermi energy of the electrodes at zero bias and gradually goes lower in energy as the voltage is increased. This procedure corresponds to the constrained density functional theory25 where the LUMO is constrained to be occupied. In this calculation, the LUMO was treated as a discrete state. Self-consistency was achieved at each voltage up to 3.6 V, when the LUMO reached the 1218
Figure 2. Current-voltage characteristics of the molecule shown in Figure 1a with and without an additional one electron put into the LUMO.
Figure 3. (a) Difference in the density of states between the molecule-electrodes system and the bare-electrodes system for the molecule shown in Figure 1a with and without an additional one electron put into the LUMO for V ) 1.2 V. The peak at 2.4 eV corresponds to the additional one electron calculated as a bound state. (b) Density of states for V ) 3.6 V.
upper Fermi energy (the calculations would be meaningless for higher voltages when the LUMO enters the transport window). The resulting I-V characteristic is shown in Figure 2 and is compared with the corresponding I-V characteristic without the extra electron [N-electron and (N + 1) electron systems]. The current for the “charged” molecule is slightly lower, resulting from the slightly smaller density of states in the transport window (Figure 3). The most intriguing result is the value of the total charge on the molecule, which is examined by calculating excess charge between the jellium edges. Even though we systematically occupy N + 1 molecular orbitals and should expect a negatively charged molecule, the molecule is in fact neutral after self-consistency is achieved! The strong coupling with the reservoirs causes the molecular orbitals to readjust so that the net amplitude in the volume occupied by the molecule amounts to only N electrons. Note that our insistence on adding the extra electron in the LUMO causes all the occupied molecular levels to rise in energy (Figure 3), suggesting that we are dealing with an excited state of the neutral molecule. Unfortunately it was not practical to determine the energy of this novel and peculiar “manyelectron” excitation. The important message, however, is that the molecule “refuses” to charge up. We repeated the calculations using benzene-1,4-dithiolate (no nitro group substituent) and found essentially identical results, namely that the molecule remains neutral despite the addition of an electron in the LUMO. These results suggest that, when a Nano Lett., Vol. 5, No. 7, 2005
Figure 4. (a) Valence electron density distribution of a benzene molecule calculated as the difference in the electron density of electrodes with the molecule and bare electrodes. Shaded area indicates the positive back ground charge of the semi-infinite jellium electrodes. (b) Current-voltage characteristics of the benzene molecule configured as in (a). (c) Difference in the density of states of the electrodes with and without the molecule. The sharp peak seen at around -1.1 eV is electronic states for V ) 4.2 V corresponding to the degenerated highest occupied molecular orbital of the isolated benzene.
molecule is strongly coupled to the electrodes, charging does not occur. It should be noted that this charge neutrality occurs even if the HOMO/LUMO are far from the Fermi energy, because it is caused by the strong coupling with the electrodes. The result means that charging is an unlikely cause of negative differential resistance in molecules that are directly attached to electrodes. In the next round of calculations, we detached the molecule (benzenethiolate with and without a nitro-group substituent) from the electrode with the lower Fermi energy, creating a “tunneling barrier” of about 2-3 Å. No extra electron was added, but we monitored the net charge on the molecule as a function of bias. The current dropped, but no charging occurred. To probe the possibility of charging of a molecule with weak binding to one electrode and virtually no binding to the other electrode, we used a benzene ring without S terminators parallel to the electrode surface as shown in Figure 4a (it is known that molecules with benzene-ring cores and no S terminators chemisorb weakly in this fashion; see, e.g., ref 26. The distance between the atomic core of the molecule and the jellium edge was taken to be 2.5 Å so that the interaction between the molecule and jellium is relatively weak. Figure 4b shows the current-voltage characteristics of this system. The dependence of the current on the bias voltage is nearly exponential. This behavior is characteristic of a tunneling current, which results from the 7.33 Å tunnel barrier between the molecule and the electrode with the lower Fermi energy (Figure 4a). Figure 4c shows the density of states of the benzene molecule for bias voltages of 0.01, 1.8, and 4.2 V. The most remarkable fact in this figure is that Nano Lett., Vol. 5, No. 7, 2005
Figure 5. (a) Model for a benzenethiolate connected to one of the jellium electrodes. A pair of positively charged gate electrodes are schematically drawn. (b) Current-voltage characteristics of the benzenethiolate molecule configured as in (a). (c) Difference in the density of states of the electrodes with and without the molecule. The gate voltage is 0, 2, 4, and 6 V.
the molecule is neutral for small voltages but is charged by a single extra electron for V ) 1.8 and 4.2 V instead of gradual charging. It should be noted that the charging is caused by usual bias application, not using the addition of another electron. The LUMO is unoccupied for V ) 0.01 V. In the case of V ) 1.8 and 4.2 V, the LUMO is occupied by one electron. Due to this charging of one electron, the LUMO is essentially pinned at the higher Fermi energy, ERF . Finally, we considered a three-terminal configuration where a benzenethiolate molecule is sandwiched by two gate electrodes as schematically shown in Figure 5a. In contrast to previous works where oppositely charged gate electrodes are used to polarize molecules,8,11,27 both of the gate electrodes are positively charged in the present case so that negative charge is induced on the molecule. Supposing that the effect of the gate field is localized on the molecule, we modeled the potential corresponding to external contactless gate electrodes as follows: VGate(r) ) -Vg
exp(-R/d ) + 1 exp[(xy + (z - z0)2 - R)/d] + 1 2
where Vg is the gate bias, R ) 6 Å, d ) 1 Å, z0 is the position of the center of the benzene ring, and the molecule is in a yz plane. This potential is effectively a square well with smooth edges in the region of the molecule (the “square well” is actually a cylinder defined by the circular gate electrodes as shown in Figure 5). The depth of the well is Vg relative to the source-drain Fermi energy at zero bias. Figure 5b shows the dependence of the current on the gate voltage. The source-drain bias Vsd is fixed to be 0.01 V. As the gate voltage is increased, the molecule is charged nearly linearly. This result makes a remarkable contrast with the case in 1219
Figure 4. As seen in Figure 5c, the highest occupied molecular orbital of this molecule is located at the Fermi energy of the right electrode, and this orbital is gradually occupied as the gate bias is applied. This gradual charging is caused by the fact that the benzenethiolate molecule has strong interaction with one of the jellium electrodes through the sulfur atom, and the broadening of the orbital occurs due to this interaction. Clearly, one needs a tunnel barrier on both sides in order to get the Coulomb blockade effect with discrete electrons (the extreme case of a molecule separated by tunnel barriers from both electrodes, the classic Coulomb blockade configuration, was not treated because all molecular levels are effectively discrete, presenting numerical difficulties). In summary, we first examined the charging of a single molecule connected to two jellium electrodes by using density functional calculations including scattering states. We put one additional electron into the LUMO and found that an equivalent electron leaks out of the other occupied states collectively so that the “N + 1 electron molecule” is still neutral. This result indicates that this molecule cannot be charged because of strong interactions between the molecule and the electrodes through sulfur atoms. Furthermore, the current is not remarkably affected by the charging of the LUMO. Thus, charging is not responsible for negative differential resistance in these molecules. Second, we found that, when a benzene ring is placed close to one of the electrodes and far from the other, it acquires an extra electron and remains charged for a wide range of bias voltages. Third, we have analyzed a benzenethiolate molecule connected to one of the electrodes and applied a gate voltage. The molecule is charged nearly linearly. The above results indicate that different charging behavior can be achieved by varying the degree of coupling of molecules to electrodes, possibly by using different tethers. Acknowledgment. The authors thank Prof. S. Watanabe and Dr. X. G. Zhang for helpful discussions. One of the authors (Y.G.) acknowledges the support from the Japan Society for the Promotion of Science and the Ministry of Education, Culture, Sports, Science and Technology, Japan. The work was partially supported by the Department of
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Energy grant DEFG023ER46096 and by the William A. and Nancy F. McMinn Endowment at Vanderbilt University. References (1) Joachim, C.; Gimzewski, J. K.; Aviram, A. Nature 2000, 408, 541. (2) Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278, 252. (3) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550. (4) Oberg, K.; Edlund, U.; Eliasson, B.; Schukarev, A.; Seshadri, K.; Allara, D. J. Phys. Chem. B 2000, 104, 10627. (5) Smit, R. H. M.; Noat, Y.; Untiedt, C.; Lang, N. D.; van Hemert, M. C.; van Ruitenbeek, J. M. Nature 2002, 419, 906. (6) Ramachandran, G. K.; Tomfohr, J. K.; Li, J. K.; Sankey, O. F.; Zarate, X.; Primak, A.; Terazono, Y.; Moore, T. A.; Moore, A. L.; Gust, D.; Nagahara, L. A.; Linddsay, S. M. J. Phys. Chem. B 2003, 107, 6162. (7) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Phys. ReV. Lett. 2000, 84, 979. (8) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Appl. Phys. Lett. 2000, 76, 3448. (9) Lang, N. D.; Avouris, Ph. Phys. ReV. B 2001, 64, 125323. (10) Di Ventra, M.; Kim, S. G.; Pantelides, S. T.; Lang, N. D. Phys. ReV. Lett. 2001, 86, 288. (11) Rashkeev, S. N.; Di Ventra, M.; Pantelides, S. T. Phys. ReV. B 2002, 66, 33301. (12) Di Ventra, M.; Chen, Y. C.; Todorov, T. N. Phys. ReV. Lett. 2004, 92, 176803. (13) Taylor, J.; Guo, H.; Wang, J. Phys. ReV. B 2001, 63, 245407. (14) Brandbyge, M.; Stokbro, K.; Taylor, J.; Mozos, J. L.; Ordejo´n, P. Phys. ReV. B 2003, 67, 193104. (15) Taylor, J.; Brandbyge, M.; Stokbro, K. Phys. ReV. B 2003, 68, 121101. (16) Kaun, C. C.; Larade, B.; Guo, H. Phys. ReV. B 2003, 67, 121411. (17) Lee, Y. J.; Brandbyge, M.; Puska, M. J.; Taylor, J. Stokbro, K.; Nieminen, R. M. Phys. ReV. B 2004, 69, 125409. (18) Xue, Y.; Ratner, M. A. Phys. ReV. B 2004, 69, 85403. (19) Furuya, S.; Gohda, Y.; Sasaki, N.; Watanabe, S. Jpn. J. Appl. Phys. 2002, 41, L989. (20) Hu, C. P.; Gohda, Y.; Furuya, S.; Watanabe, S. Sci. Technol. AdV. Mater. 2003, 4, 585. (21) Kouwenhoven, L. P.; Austing, D. G.; Tarucha, S. Rep. Prog. Phys. 2001, 64, 701. (22) Park, J.; Pasupathy, A. N.; Goldsmith, J. I.; Chang, C.; Yaish, Y.; Petta, J. R.; Rinkoski, M.; Sethna, J. P.; Abrun˜a, H. D.; McEuen, P. L.; Ralph, D. C. Nature 2002, 417, 722. (23) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015. (24) Lang, N. D. Phys. ReV. B 1995, 52, 5335. (25) Dederichs, P. H.; Blu¨gel, S.; Zeller, R.; Akai, H. Phys. ReV. Lett. 1984, 53, 2512. (26) Hauschild, A.; Karki, K.; Cowie, B. C. C.; Rohlfing, M.; Tautz, F. S.; Sokolowski, M. Phys. ReV. Lett. 2005, 94, 36106. (27) Lang, N. D. Phys. ReV. B 2001, 64, 235121.
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Nano Lett., Vol. 5, No. 7, 2005
