NANO LETTERS
Effects of Coadsorption on the Conductance of Molecular Wires
2002 Vol. 2, No. 10 1047-1050
Norton D. Lang and Phaedon Avouris* IBM Research DiVision, T. J. Watson Research Center, Yorktown Heights, New York 10598 Received June 3, 2002; Revised Manuscript Received July 24, 2002
ABSTRACT We use density-functional theory to calculate the effects of coadsorption near the molecule/electrode junction on the conductance of a molecular wire. We find significant changes in both the density of states of the molecular wire and its conductance; electrostatic effects as well as short-ranged interactions are found to be responsible. It is clear that successful implementation of molecular electronics will require the control of such interactions.
Molecular electronics is considered by many as the most promising candidate to replace silicon electronics when the latter technology reaches its limits sometime in the next 10 to 15 years.1 Despite the strong interest in molecular electronics, however, there are still large gaps in our understanding of the electrical properties of individual molecules, and even less is known about the impact of external factors on these properties. In previous work2 we examined how the electronic structure of a molecule affects its electrical conductance G. We found that at small applied bias, the G of molecules is determined in many cases by the density of states in the vicinity of the Fermi energy [DOS(EF)].3 Recently, in studies of the conductance of semiconducting carbon nanotubes, it was observed that exposure of the metal/semiconductingnanotube/metal system to gases such as oxygen leads to large changes in the electrical characteristics of the nanotube.4-6 On the basis of a number of different measurements5-7 and theoretical modeling,8 it was argued that the electrical changes are caused by the coadsorption of the gas at the metal/nanotube junction. While in macroscopic junctions such as the silicon/metal junction the band bending is determined by factors intrinsic to the bulk material, junctions involving only a few interface bonds, as in the case of nanotubes, or even a single bond, as in single-molecule devices, may be sensitive to the local fields and electronic structure changes produced by coadsorbed species. Here we use first-principles calculations based on densityfunctional theory to explore the effect of coadsorption on the electrical properties of molecular wires. Specifically, we employ as a model molecular wire a biphenyl diradical (BPH: -C6H4-C6H4-) bonded to two metal electrodes (see Figure 1). * Corresponding author. 10.1021/nl020202o CCC: $22.00 Published on Web 08/27/2002
© 2002 American Chemical Society
Figure 1. Schematic top and side views of the structure of the 4,4′-biphenyl diradical (biphenyl molecule with hydrogens removed from the 4 and 4′ carbons), which we refer to in the text as BPH. Gray circles are carbons, blue circles are hydrogens. We treat the carbon rings as being coplanar in our discussion.
We use two different coadsorbates: (a) lithium atoms, which are electropositive, and (b) oxygen atoms, which are electronegative. Our calculations show that coadsorption can lead to large (order of magnitude) changes in the conductance of the molecule. The mechanism by which the coadsorbates affect the molecular conductance is analyzed. The theoretical technique used to calculate the conductance G of the metal/molecule/metal system has been described in detail before.9 Briefly, the calculation was performed within the density-functional formalism.10 First, the singleelectron wave functions Ψ0(r b) and the electron density n0(r b) of the two bare metal electrodes, described by the rs ) 2 uniform-positive-background (jellium) model,11 are computed and used in the Lippman-Schwinger equation to obtain the full single-electron scattering wave functions in the presence of the bridging molecule, Ψ(r b), from which the current is calculated.9 The distance from the positive background edge to C4 (and C4′) is 0.9 Å to O is 0.1 Å and to Li is 1.3 Å.
Table 1: Electrical Conductance (G) and Density of States at the Fermi Level [DOS(EF), states/eV] of the BPH Molecule and the Coadsorption Systems
Figure 2. Density of states (see ref 3) for BPH linking two metal electrodes at zero bias (arbitrary units) in the vicinity of the Fermi level, which is depicted as a dashed line at E ) 0. Three of the cases discussed in the text are shown: no impurities (green), four coadsorbed Li impurities (red), and four coadsorbed O impurities at the larger distance (blue).
The lateral distances from C4 to the closer O impurity and to Li were taken to be the same (2.0 Å); the lateral distance from C4 to the further O impurity was taken to be 2.9 Å. Thus the total distance from C4 to the closer O is 2.2 Å, to the further O is 3.0 Å, and to the Li is again 2.0 Å to this accuracy. (For brevity, we speak of the Li and the closer O as being at a distance of 2 Å from C4 and the further O as being at a distance of 3 Å.) The biphenyl diradical -C6H4C6H4- is adsorbed between the two electrodes with the two benzene rings coplanar, so as to maximize their π-overlap interaction.12 The coadsorbates are placed as noted above at a distance of 2 Å from the carbon atoms (C4 and C4′) bonding the BPH molecule to the metals. The plane of the BPH rings is perpendicular to the plane defined by the four coadsorbates. The G and DOS of four different configurations were computed: (a) metal/BPH/metal, (b) metal+2O/BPH/ metal (both O atoms on the same electrode), (c) metal+2O/ BPH/metal+2O, (d) metal+2Li/BPH/metal+2Li. An additional calculation was performed [configuration (e)] for system (c) but with the O atoms at 3 Å from C4 and C4′. In Figure 2 we show the calculated valence density of states (DOS) spectrum of system (a), i.e., the BPH bonded to the two metal electrodes (green curve), as well as the spectra of systems (d), and (e), given by the red and blue curves, respectively. Significant shifts in the energies of the levels of the BPH molecule are observed. Along with the energy-level changes, significant changes in the DOS(EF) are found. Table 1 gives the computed conductance G (in units of 2e2/h) and the DOS(EF) (in units of states/eV) of BPH and the combined systems. Large changes in G of more than an order of magnitude are found. The relative changes in DOS(EF) are smaller but roughly follow the same trend. We now consider the origin of the computed changes in the electronic structure and electrical conductance of BPH induced by the coadsorbates. Considering the DOS spectra, we see that the energy levels of BPH, especially the deeper levels, move nearly rigidly to lower binding energy upon addition of lithium. The shifts induced by oxygen are to higher binding energy and are more complex in character. 1048
system
G(2e2/h)
DOS(EF)
RG
RDOS
RG/RDOS
BPH BPH+2O (2 Å) BPH+4O (2 Å) BPH+4O (3 Å) BPH+4Li (2 Å)
0.09 0.4 1.2 0.6 1.1
0.45 1.5 2.0 2.2 3.5
1.0 4.4 13.3 6.7 12.2
1.0 3.3 4.4 4.9 7.8
1.3 3.0 1.4 1.6
To understand the origin of these shifts we show in Figure 3 (top) the difference of the electrostatic potential Ves(r b) 13 for a system consisting of just the four adsorbed Li impurities together with the electrodes, minus the sum of Ves(r b) for the bare electrodes and Ves(r b) for four free Li atoms (at the same positions). We observe a net decrease (blue area) of Ves(r b) in the region that is to be occupied by the BPH molecule, while near the Li atoms, Ves(r b) is increased (red areas). These changes are consistent with the ionic character of the chemisorption bond of Li on a metal surface.14,15 The decrease in Ves(r b) 13 in the region of the BPH molecule is responsible for the increase in the binding energy of its levels. Along with the energy-level shifts, there is charge transfer from the metal to the molecule as shown in Figure 3 (center), which gives the electron number density difference that is defined in the figure caption for the system: metal+2Li/ BPH/metal+2Li. The transferred electronic charge occupies the π symmetry levels of BPH (red areas) and reduces the electrostatic shift to higher binding energy. A charge transfer in the opposite direction (blue areas) involving the σ states is also clearly seen in Figure 3 (center). The case of oxygen adsorption is more complex and cannot be explained simply in terms of electrostatic shifts. This is to be expected from the more covalent nature of the metaloxygen bond. In this case, direct chemical and “throughthe-metal” interactions of the oxygen atoms with BPH are likely to dominate.15 Such interactions should be strongly dependent on the distance between the oxygen atom and BPH. Figure 4 indeed shows this type of behavior. Figure 4 (top) gives the density difference defined in the caption of Figure 3 for the system metal+2O/BPH/metal+2O at an O-C4 and O-C4′ distance of 3 Å, while Figure 4 (bottom) gives the same electron density difference evaluated for a distance of 2 Å. The short-range nature of the interaction is clearly visible in Figure 4 (bottom). Next we consider the effects of coadsorption on DOS(EF) and the low bias G.16 From Figure 2, it is clear that the origin of the changes of DOS(EF) lies in the shifts of the energy levels of BPH upon coadsorption. In extended (bulk) systems, G(EF) ∝ DOS(EF). We can test to what extent this relation applies to the molecule/coadsorbate systems studied here. In Table 1 we give the ratios, R, of G(EF) and DOS(EF) of the planar BPH system to those of the BPH plus coadsorbate systems. We find that increasing DOS(EF) does lead to an increased G(EF), but the correlation is only qualitative. In previous work2 we showed that deviations from the G(EF) ∝ DOS(EF) behavior can arise from the fact that Nano Lett., Vol. 2, No. 10, 2002
Figure 3. (top) Translucent isosurfaces of Ves(r b) (see ref 13) for a system consisting of just the four adsorbed Li impurities together with the electrodes, minus the sum of Ves(r b) for the bare electrodes and Ves(r b) for four free Li atoms (at the same positions). Isosurface values: blue, -2.4 eV; red, +0.7 eV. (There are no positive values for this Ves(r b) difference as large as +2.4 eV.) Unmarked gray circles show C atom positions of the BPH that is to be inserted into this impurity configuration. (center) Translucent isosurfaces of δn(r b) for the system consisting of the BPH molecule bonded to the electrodes together with the coadsorbed Li impurities minus the sum of δn(r b) for just the BPH bonded to the electrodes and δn(r b) for just the impurities bonded to the electrodes. Here δn(r b) is the electron number density for the given system minus the density for the bare electrodes. The density difference given in this plot shows the changes in the electron density due to the interaction between the BPH molecule and the coadsorbed Li impurities. Isosurface values: red, +0.002 au; blue, -0.002 au. View is along the plane of the BPH molecule (rings taken coplanar). Gray dots show Li and C atom positions. (bottom) Same as plot in center except view is perpendicular to the plane of the molecule.
molecular wires, unlike atomic wires or carbon nanotubes, have an inhomogeneous electronic structure along their axis. A particular molecular orbital can have a large amplitude at certain parts of the molecule, e.g., at the ends or center of the molecule, and vanishing amplitude in others. Thus, an orbital can make a significant contribution to the integrated DOS(EF), but be localized in only a small region of the molecule, thus contributing less to G(EF) than another orbital Nano Lett., Vol. 2, No. 10, 2002
Figure 4. Same density difference plot as in Figure 3 (center) but for the case with four O impurities. (top) 3Å impurity-C4 spacing. (bottom) 2Å impurity-C4 spacing. Same isosurface values as in Figure 3 (center).
with smaller overall DOS(EF) that has amplitude along the entire length of the molecule. From Table 1 we see that the largest deviation from the G(EF) ∝ DOS(EF) relation occurs in the BPH+4O system with the O atoms at 2 Å lateral distance from the atoms C4 and C4′ of BPH. The charge density difference plots in Figure 4 indeed show that this is the system that involves the most extensive charge rearrangement, i.e., it shows the maximum distortion of the wave function near EF upon coadsorption. In conclusion, we have shown that the electrical properties of individual molecules connected to metal electrodes can be very sensitive to the presence of other molecules and impurities coadsorbed nearby on the same electrodes. According to our calculations, the effect is not necessarily due to local changes in the work function but may involve direct chemical interaction and through-the-substrate coupling of the molecular wire and the coadsorbate. The resulting energy shifts and modification of the molecular levels is responsible for the observed changes in conductance. Our findings suggest that the electrical properties of a molecular wire can be modified not only by intramolecular modification but also by modification (doping) of the electrodes. Stable and reliable operation of molecular devices would require the protection (e.g., by encapsulation) of the electrode surfaces. 1049
Acknowledgment. We are grateful to R. Martel for his extensive help with the graphics. References (1) Molecular Electronics II; Aviram, A.; Ratner, M. A.; Mujica, V., Eds.; New York Academy of Sciences: New York, 2002. Joachim, C.; Gimzewski, J. K.; Aviram, A. Nature 2000, 408, 541. Reed, M. A. Proc. IEEE 1999, 87, 652. Carbon Nanotubes: Synthesis, Structure, Properties and Applications, Dresselhaus, M.; Dresselhaus, G.; Avouris, Ph., Eds.; Springer-Verlag: Berlin, 2001. (2) Lang, N. D.; Avouris, Ph. Phys. ReV. B 2001, 64, 125323. (3) By density of states (DOS) we mean the difference in density of energy eigenstates between two systems: the pair of electrodes together with the molecule connecting them and coadsorbed impurities if any, and the same pair of electrodes (with the same spacing) without the molecule and impurities. The eigenstates referred to are those of the single-particle equations of the density-functional formalism. (4) Collins, P. G.; Bradley, K.; Ishigami, M.; Zettl, A. Science 2000, 287, 1801. (5) Derycke, V.; Martel, R.; Appenzeller, J.; Avouris, Ph., Appl. Phys. Lett. 2002, 80, 2773. (6) Derycke, V.; Martel, R.; Appenzeller, J.; Avouris, Ph. Nano Lett. 2001, 1, 453. (7) Martel, R.; Derycke, V.; Lavoie, C.; Appenzeller, J.; Chan, K.;
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Tersoff, J.; Avouris, Ph. Phys. ReV. Lett. 2001, 87, 256805. (8) Heinze, S.; Tersoff, J.; Martel, R.; Derycke, V.; Appenzeller, J.; Avouris, Ph. Phys. ReV. Lett. 2002, 89, 106801. (9) Lang, N. D. Phys. ReV. B 1995, 52, 5335. Di Ventra, M.; Lang, N. D. Phys. ReV. B 2002, 65, 045402. (10) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, A1133. (11) Lang, N. D. In Theory of the Inhomogeneous Electron Gas; Lundqvist, S., March, N. H., Eds.; Plenum Press: New York, 1983; p 309. We take rs ) 2 au, typical of a high-electron density metal, where (4/3)πrs3 ≡ n-1, with n the mean interior electron number density in the metal. (12) It has been shown by Baudour, J. L. [Acta Cryst. B 1991, 47, 935] that in solid biphenyl, the equilibrium configuration has a twist angle of 13.3° between the two carbon rings, but that at room temperature, the average configuration is planar. For the gas phase, electron diffraction measurements [Almenningen, A.; Bastiansen, O.; Fernholt, L.; Cyvin, B. N.; Cyvin, S. J.; Samdal, S., J. Mol. Struct. 1985, 128, 59] show a twist angle of 44.4°. (13) By “electrostatic potential” we mean here the electrostatic potential energy of an electron; this is the potential that appears in the Schro¨dinger equation for the electrons. (14) Lang, N. D.; Williams, A. R. Phys. ReV. B 1978, 18, 616. (15) Zangwill, A. Physics at Surfaces, Cambridge University Press: Cambridge, 1988. (16) The bias used in the calculation of G was 0.01 V.
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