J. Phys. Chem. C 2007, 111, 1535-1540
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Electron Transport through Heterogeneous Intermolecular Tunnel Junctions Mousumi Das and Barry D. Dunietz* Department of Chemistry, UniVersity of Michigan, Ann Arbor, Michigan 48109 ReceiVed: August 30, 2006; In Final Form: NoVember 2, 2006
Quantum charge transport through intermolecular tunnel junctions is studied. Intermolecular tunnel junctions can be defined by the end groups of pairs of self-assembled monolayers of functionalized conjugated alkenes on gold surfaces. Conductivity dependence on the tunnel distance has been compared for various junctions. It is found that for junctions dominated by attractive interactions, for example, systems involving hydrogen bonding, conductivity exhibits less dependence on the tunneling distance than with junctions dominated by dispersive interactions. Junctions with stronger distance dependence conductivty are desired for applications related to chemical sensors. Our study provides insight for designing an efficient chemical sensor that is based on heterogeneous tunnel junction, which may involve conductivity through a combination of the attractive hydrogen-bonding channel and repulsive dispersive interactions.
Introduction Recent progress in the field of self-assembly and microfabrication techniques encourages the design of single molecule devices1 with strong potential and properties for device application.2-6 In the field of molecular electronics, focus is provided to electronic charge transport properties of different kinds of single molecular junctions or molecular monolayer junctions. The strong chemical affinity of thiol to gold has led to wide use of self-assembled monolayers (SAMs) of thiolated molecules on gold surfaces.7 These include gold SAMs of dithiolbenzene (DTB),1,8 thiolated alkanes,9-13 molecular wires of atoms, polymers, carbon nanotubes, and fullerenes.14-19 Monolayer coated gold nanoparticles have been synthesized and used as relevant materials for catalysis, molecular electronics, and chemical sensing.20-24 In electrical circuits the coated nanoparticles introduce tunnel junctions through which conductivity is realized.20,21,24 Devices employing nanoparticles have been employed as chemical sensors.25-29 These microsensors offer fundamental advantages for achieving improved functionality. The fundamental sensing capacity is defined through the involved molecular scale sensing unit, which is utilized to reduce the required sample size as well as to shorten the response times. The microsensor operation is based on changes of tunneling conductivity induced by subjecting the sensing unit to analyte pressure. These changes may be due to physical swelling of the electrode gap or induced changes in the dielectric of the conducting thiolate ligands.25 Computational studies can assist in enhancing the molecular level understanding of processes involved with the molecular conductivity changes. Recent observations suggest that in densely packed conjugated SAMs, the charge transport mechanism depends also on intermolecular interactions.30-32 However, in another example, tunneling contribution to the overall conductivity was demonstrated to be negligible for highly ordered and densely packed SAMs of long-chain alkanes deposited on silicon wafers in contrast to higher conductivity values due to tunneling in disordered monolayers.33 Bre´das et al. have evaluated the hopping transport as described in Marcus theory employing * Address correspondence to this author. E-mail:
[email protected].
semiempirical techniques between π stacked molecular planes.34,35 More recently, the relationships of different overlapping orientations of π conjugated systems on the intermolecular energetics and hopping transport have been systematically analyzed.36 This has nicely demonstrated the importance of intermolecular forces on charge transport. Similar treatments have compared effects of different intermolecular interactions on charge transport rates, where it was demonstrated that the rate of decay with the distance parameter of weakly interacting orientations is comparable to that of systems involving stronger hydrogen-bonding (H-bonding) interactions.37 Cukier and Cave have shown that the pre-exponential factor related to the decay of transport through a tunnel gap defined by a specific intermolecular pair is comparable and sometimes bigger than the factor associated with chemically bonded interactions.38 Additional studies on tunnel junction (TJ) electron conductance mediated by intermolecular interactions have been investigated theoretically by employing Green’s function (GF) based approaches.14,39-42 Decrease of conductance is reported in a junction with a perpendicular relative arrangement of a pair of phenyl rings.40 Effects of lateral interactions on the conductance of two benzene molecules aligned in parallel to semi-infinite leads have been studied by Liu et al.41 Their calculations found an increase in conductance due to indirect intermolecular interaction mediated through the Au electrodes. Effects of lateral interactions on conductance have also been theoretically investigated for a cofacially arranged self-assembled monolayer (SAM) of organic molecules.42 These computational studies highlight the important role of the metal surface in mediating the intermolecular effect which affects tunnel conductance. In this paper we study electron transport through heterogeneous intermolecular TJs formed by different functionalized conjugated alkenes. We calculate the junction conductivity and study its dependence on the tunneling distance. Conductance dependence on the tunnel separation is fundamental for the operation of chemical sensors. The ability to enhance the dependence of conductance on the distance may result in the design of optimal sensors with increased sensitivity. We find that while TJs not involving attractive interactions depend more strongly on the distance, TJs dominated by attractive interactions
10.1021/jp065640o CCC: $37.00 © 2007 American Chemical Society Published on Web 12/30/2006
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Figure 1. Nonattractive symmetric (a1, a1′), single (a3), and double asymmetric (a4) junctions. Attractive hydrogen-bonded junctions (b1, b2).
as with hydrogen bonding lead to a longer range of distances where conductivity is still apparent. Therefore, our study indicates that a special setup leading to a combination of these two types of interactions may result with an optimal sensor. These TJs can be engineered only by introducing heterogeneous TJs. Computational Scheme and Models Computational Scheme. Molecular conductivity is obtained by integrating the quantum mechanical transmission function according to the Landauer scattering view:
∫
I(V) ) 2e/h T(E,V)[fl(E,µl) - fr(E,µr)] dE
(1)
where fl and fr are the Fermi distributions of left and right leads and T(E) is the quantum transmittance function. In this approach, transmission function is evaluated by using
T(E,V) ) Tr[GRc ΓlGAc Γr]
(2)
after subdividing the system into device (c) and electrode (l and r) regions.43-50 In the last equation, Gc represents the device Green function (GF) and Γ is the broadening function of the molecular states due to coupling to the left and right (l and r) electrodes. The bulk broadening functions are expressed as
Γ ) i[Σ - Σ†]
(3)
where Σ’s are the self-energies (SE) and are evaluated by projecting the bulk GFs (Gl and Gr) on the central device region through electronic coupling terms
Σl(E) ) (Hcl - EScl)Gl(E)(Hlc - ESlc)
(4)
The left (right) bulk GF, Gl (Gr), represents the electronic structure of the semi-infinite electrode. This is evaluated by implementing a tight-binding (TB) calculation
Gl ) (R - βGlβT)-1
(5)
The bulk GF (l and r) calculation is accelerated by solving for the surface and bulk GFs simultaneously.51-52 This is repeated at every energy step in the integration grid. The SEs represent the effect of the bulk on the device and are used to obtain the GF of the device:
Gc ) (EScc - Hcc - (Σl - Σr))-1
(6)
The electronic structure information used in this GF based scheme is obtained at the level of density functional theory (DFT) with the B3LYP functional53,54 and LANL2DZ basis set55 by employing the Qchem program package.56 Modeling Chemosensors Based on Heterogeneous Tunnel Junctions. Conductivity through tunnel junctions involving few
nanoparticles is expected to further increase the sensing ability and to reduce the sample size requirements. This depends on the proximity of the two electrodes. Furthermore, the ability to immerse only a single array of nanoparticles between electrodes with a spacing of the nanoparticles size has been realized by electrostatic trapping technique.57 This allows the introduction of heterogeneous TJs, where the electrodes are coated with an organic self-assembled layer having complementary tail groups to those of the layer coating the nanoparticle.58-60 The ability to fabricate the heterogeneous tunnel junction may result in optimal response to the presence of the analyte molecules. The distance dependence conductivity through heterogeneous TJ is compared below to homogeneous TJs. The conductivity dependence on the distance parameter has been evaluated for several junctions. The considered SAMs are mainly derivatives of alkene chains, where the terminal carbon is functionalized by 0, 1, or 2 hydroxy ions. These different TJs are depicted in Figure 1. In a1, the unsubstituted alkene thiols are used to define the TJ. This clearly does not involve strong attractive interactions between the end groups. We note that in the real system the effect of the well-packed SAMs leads to stabilized configurations involving these repulsive interactions. However, the determination of the exact acquired geometry due to the presence of the full SAM is beyond the scope of this study nor it is crucial for the effects studied. Here we consider, instead, a range of relative orientations as depicted in the figure. This ensures the avoidance of arbitrariness in the definition of the considered potential energy surface (PES) along which the transport study is performed. For example, in a1′ we depict the same TJ where one side has been shifted in the direction perpendicular to the PES coordinate. We also consider TJs involving energetic stabilization due to interactions between the end groups, for example, through a H-bonding network involving carboxylic groups. This is illustrated by the structures illustrated in parts b1 and b2 of Figure 1. We note, however, that while the structure in b1 corresponds to homogeneous TJs, the junctions in b2 correspond to a special experimental setup where different SAMs are used on either side of the junction. This is also the case in structures a3 and a4, where only one side of the TJ alkene chain is terminated with either 1 (a3) or 2 (a4) hydroxy groups. Each symmetric intermolecular TJ geometry is obtained by performing first separate geometry optimizations on the monomers attached to an atomic wire of Au. In these optimizations, the Au atoms are constrained. We note that due to the roughness of the energy surface defined by the gold-thiol coupling several geometrical minima can be obtained. Therefore, we have chosen each monomer to adopt the minimum with an orientation where the angle formed between the gold-thiol bond and the gold wire axis is near 90°. This choice is crucial to ensure a consistent comparison between the different TJs. In a recent study, the transmission dependence on this angle was studied and has shown that large variation of transport can be induced by small
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Figure 2. Potential energy curves of the tunnel junctions with the gold wires as electrode model as a function of junction separation. In all figures, d is the distance coordinate defined by the dotted lines in the inserts which graphically illustrate the edge atoms defining the TJ.
angle variations.61 Below, we also confirm that this choice is not biasing our observations on the conductance trends. Next, TJs are defined, when possible, by a full dimer optimization originated with the optimized monomers. In the cases where no attractive interactions are present to guide the dimer optimization a range of orientations as described above is being employed. Transport calculations are performed along the PES defined by the distance parameter (d) with 0.1 Å increaments. The distance parameter is defined as the shortest distance between edge atoms across the TJ and is illustrated in all figures by the dotted lines in the graphical inserts (see below).
Figure 3. Transmission functions at various junction separations for the nonattractive symmetric junctions formed by alkene dimers.
Results and Discussion The PESs of the different TJs discussed above (see Figure 1) are provided in Figure 2. The PESs are defined with respect to the separation variable (d) between the edge atoms. The distance coordinate (d) for each PES is illustrated by graphical inserts through the dotted lines connecting the relevent atoms across the TJ. We begin the transmission analysis by considering first the TJs between thiolated alkene chains, where one chain is functionalized at the terminal carbon by 0, 1, or 2 hydroxy groups. These are associated with the three repulsive PESs in the figure. We comment on the strength of their repulsive interaction at short distances, where it is apparent that the symmetric junction involving no hydroxy group on either monomer features a less steep PES than the polarized TJs. The consequence of the varying steepness of the PES on the distance dependence of the conductance for these TJs is described below. We consider first their corresponding transmission plots. The corresponding transmission function of the symmetric TJ (a1) is plotted in Figure 3a at several separation values (d). It is shown that the transmission function is dominated by two peaks at -7.3 and -7.6 eV. These peaks are shown to decay gradually with the distance beyond d values of 1.4 Å. The transmission in this region of the PES is dominated by pure tunneling behavior. At the shorter distances, where the repulsive energetic short-range wall is apparent, a more complex transmission function is observed. The transmission peak is split at the distance region of (0.7-1.1 Å) and becomes smoother from 1.2 Å onward. As discussed above the repulsive PES does not allow us to guide unambiguously our choice of the structures to be included in the transmission evaluation. Therefore, to test the consistency of our observations, we have calculated the conductance of several junctions featuring different relative orientations of the
Figure 4. Conductance as a function of the inverse junction separation for TJs with unsubstituted alkene thiols having (a) 120° and (b) 90° angular orientation of the Au-S bond with the gold wire. Similarly, part c represents the conductance behavior for the shifted orientation.
two repulsive monomers. Figure 3b shows transmission functions of a shifted orientation of one monomer with respect to the other, whereas in the upper panel (a) the two gold wires form a single line if connected. Both panels, however, feature very similar results especially for the transmissions evaluated for d values beyond 1.9 Å. This is more importantly and clearly demonstrated by considering the conductance. In Figure 4 we provide the conductance calculated from these transmission functions. (The procedure of obtaining distance dependent conductance from transmission functions is discussed later.) We also include the resulting conductance plot obtained by another alternative orientation of thiol molecules. In this geometry the monomers each adopt a different minima, where an angle of 120° of the Au-S bond to the wire axis is formed as opposed to the 90° adopted for most TJs in this study. The angle dependence transmission has been analyzed in detail elsewhere.13,61 It is found that for TJs a noted angle effect on the tunneling transmission is only apparent for small d values. From
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Figure 6. Transmission functions at different separations of (a) double hydrogen-bonded junction formed by two terminal carboxylic acid groups and (b) singly hydrogen-bonded junction between aldehyde and terminal hydroxy alkenes.
Figure 5. Transmission functions at different separations for the asymmetric nonattractive junctions (structures a3 and a4, respectively).
the results shown in Figure 4 it is suggested that different orientations do not affect our observations on the distance dependent conductance corresponding to these different TJs. Next, we consider the transmission peaks shown in Figure 5 of two other asymmetric junctions, which are illustrated in Figure 1 (a3 and a4). In Figure 5a, the transmission due to TJ with a single hydroxy group is provided, while the transmission plotted in the lower part (b) of the figure involves two hydroxy groups on one side of the junction. Both systems feature a single peak around -7.2 eV at large enough d separations, which decays as expected at these d values. At shorter distances, the transmission function is more complex and delocalized. It involves different features in the energy region ranging from -7.5 to -7.0 eV. The separation at which the transmission behavior switches is about 1.7 Å for the system with a single hydroxy group, where the addition of the second group seems to push this value to 2.3 Å due to stronger repulsive interactions. For all the TJs discussed above the transmission dependence on the junction separation is calculated. The expected tunneling decay behavior is demonstrated for distance values above a specific d value. In this separation the energy penalty is less than 15 kcal/mol. These d values are highlighted by vertical short black lines in the corresponding PES curves in Figure 2 for a1, a3, and a4 TJs defined in Figure 1. The distances are related to the turning point on the repulsive PESs. Next, to complete our survey of the transmission functions through TJs, we consider the systems which involve PESs with attractive intermolecular interactions. We now turn to consider the transmission through the TJs denoted b1 and b2 above, which involve intermolecular attractive interactions. These TJs involve hydrogen bonding where b1 features double hydrogen bonding interactions due to the two terminal carboxylic acid groups and b2 involves a relatively reduced strength of the hydrogen bonded interaction. The PESs along the O-H distance variable of these TJs are also provided in Figure 2. The PES of b1 shows strong repulsive behavior at small d values (0.74-1.24 Å). The potential minimum is at 1.5
Å with about 22 kcal/mol stabilization energy due to the two hydrogen bonds in b1 and 12 kcal/mol for b2. The energy penalty remains below 5 kcal/mol at a range of 1.35-1.84 and 1.35-2.13 Å distances for b1 and b2, respectively. The transmission functions are plotted in Figure 6 at various O-H distances. The trends noticed with the transmission plots of the attractive PESs do not involve a tunneling-switching point as seen with the plots above. Namely, the plots at the distances considered are more consistent. The transmission peaks in Figure 6a,b are wider and remain within the range of about -6.0 to -6.5 eV. Similar observations are realized with the second TJ featuring attractive PES (part b). In both of these TJs, the transmission functions feature the onset of the tunneling decay starting at small d values. We note, however, that the TJ in b2 involves both attractive hydrogen bonding and a repulsive H-H interaction (see b2 in Figure 1 for illustration). The consequence of such a setup on chemical sensor applicability will be evident by considering the conductance distance dependence below. The current has been calculated by following the Landauer prescription for integrating the transmission function around the Fermi energy weighted by the Fermi distribution function (see eq 1). At each value of junction separation d, the conductance (dI/dV) at optimal bias voltage in the range of 0-2 V for different junctions has been established. This scheme has been used above for comparing the conductance dependence on the distance for comparing TJs with alkene chains with the different thiol-gold bond orientations and shifted monomers (see Figure 4). In Figure 7 the (log) conductance dependence on the distance (d) is resolved for all the considered TJs. First we note in Figure 7 the conductance comparison of the series of the repulsive PESs, where either 0, 1 or 2 hydroxy groups are placed on one terminal carbon (see a1, a3, and a4 in Figure 1). The symmetric TJ (a1) features conductance with the least dependence on the distance parameter, where increasing the polarity across the tunnel gap by adding more hydroxy groups leads to a steeper curve of the conductance dependence on the distance parameter. We have also included in the figure conductances at distances shorter than the turning point for the repulsive PESs. The turning point distances are noted by vertical black lines as in the PES figure. The conductance at these short distances is shown to deviate greatly from the expected linear relation. In contrast to the purely repulsive PESs, the conductance of the attractive PES decreases along a wider range of distances obeying the expected tunneling regime. The conductances of the two attractive TJs each at the minimum energy separation differ by a factor of 2. At this distance the conductance is dominated by the optimal hydrogen bonding and the TJ, which features double bonding (b1),
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Figure 7. The conductance as a function of the junction separation (d) in a logaritmic scale (2e2/h). The linear region is denoted by fitted linear plots. Additional conductance values outside the linear regime are denoted as well.
conducts therefore twice more than the singly bonded TJ (b2). We note, however, that the decay of the conductance with the distance in the asymmetric junction (b2) is steeper. In this TJ, conductivity is generated from contributions of the two types of transport channels, the repulsive and attractive. The relative conductance of this TJ at shorter distances becomes larger. The two curves are, therefore, shown to intersect at sufficiently small distances. Furthermore, we also note that the strong contribution of repulsive channels is evident by the larger conductances of the nonattractive TJ than the H-bonded ones, again at sufficiently small d values. The singly H-bonded TJ (b2) features, therefore, both a wider range of distances along which predicted conductance can be realized and larger sensitivity of the conductance to changes in the distance parameter than with the alternative considered TJs. These are both important qualities for molecular sensors. The range of the observed conductance trends with respect to the distance parameter can be associated with different patterns involving the relevant molecular orbitals and projected DOS. It is instructive to compare the trends of the DOS which underly the varying transmission response to the tunnel gap. The DOS dependence on the distance is illustrated for the different TJs in Figure 8. The DOSs of two nonattractive PESs and the two H-bonded TJs are provided respectively in parts a, b and c, d of the figure. The DOSs in parts a and b become narrower with the increase of the tunnel distance, since the number of MOs contributing to the transmission at the relevant energy interval decreases as the distance increases. This enhances the decay of the transmission peak for these TJs. The DOS trends related to the hydrogen-bonded TJs are different, however. The DOSs related to the TJs involving the attractive interactions lead to more delocalized curves with wider peaks, where the peak values are much smaller than in parts a and b. Furthermore, the TJs with the attractive interactions feature less dependence of the DOS on the separation distance. It is interesting to note that the DOS in part c shows a feature that is distance dependent, whereas the DOS in part d is almost entirely distance independent. This is related to the combination of the hydrogen bonded and the repulsive hydrogen-hydrogen interactions present in the TJ structure in part c, whereas part d involves 2 H-bonding interactions and both parts a and b have only repulsive H-H and O-H interactions. The consequence of these different DOS trends on the conductance through the TJs is essentially summarized in Figure 7.
Figure 8. DOS as a function of junction separation for two nonattractive and two attractive hydrogen-bonded junctions as illustrated.
The conductance slopes with respect to the distance parameter (d) are compared in Figure 7. It is apparent that the slopes for TJs which feature less distance dependence DOS are less steep. The TJ with 2 hydrogen-bonding interactions exhibits the least steep slope. This is associated with a more stable DOS at the corresponding energy range. The transmission through the series of the TJs with 0, 1, and 2 hydroxy groups on one side of the TJ also suggests a hierarchy with respect to the slope steepness, where the TJ with larger polarity involves the steeper distance relationship. We note, however, that the variance between these three slopes is quite small. Finally, the TJ that involves both types of interactions features both a rather steep slope and a wide range of distances where the conductance does not collapse. Concluding Remarks We have studied charge transport through TJs involving intermolecular interactions between functionalized SAMs of alkene chains. Junction conductance dependence on the gap size is shown to depend on the composition of the end groups. Therefore, the ability to fabricate this composition allows us to manipulate the rate of the conductance decay. It is apparent that SAMs which do not introduce intermolecular attractive interactions will feature a steeper drop of the conductance. This is associated with the decrease of the electronic DOS at the relevant energy region due to stabilization of MOs with the increase of the distance. The TJs with attractive intermolecular interactions, on the other hand, feature DOSs, which remain almost unaltered upon distance changes. For these junctions the transmission is associated with a fixed number of MOs whose contribution to transmission decays with the gap increase. This is expected in a tunneling dominated region. This study, therefore, points to the interesting possibility of introducing TJs which involve a combination of channels, where one type of channel is identified by repulsive interaction whereas attractive
1540 J. Phys. Chem. C, Vol. 111, No. 3, 2007 force dominates the second type of channels. We remark that in the context of fabrication of SAMs on gold electrodes and nanoparticles the possibility to stabilize the system in spite of the repulsive interaction is available by using well-packed SAMs in nanogap junctions. This study, therefore, highlights the possible benefit from engineering heterogeneous TJs, where the tunnel conductance can be tuned more readily. This can be utilized in the field of chemical sensors to devise junctions with enhanced conductance sensitivity to changes in the gap length. Acknowledgment. B.D.D. acknowledges support from the University of Michigan and useful discussions with Profs. Matzger, Kurdak, Goldman, and Zellers from the University of Michigan campus. References and Notes (1) Andres, R. P.; Bein, T.; Dorogi, M.; Feng, S.; Henderson, J. I.; Kubuak, C. P.; Mahoney, W.; Osifchin, R. G.; Reifenberger, R. Science 1996, 272, 1323. (2) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550. (3) Collier, C. P.; Wong, E. W.; Belohradsky, M.; Raymo, F. M.; Stoddart, J. F.; Kuekes, P. J.; Williams, R. S.; Heath, J. R. Science 2000, 200, 1172. (4) Gittins, D. I.; Bethell, D.; Schiffrin, D. J.; Nichols, R. J. Nature 2000, 408, 67. (5) Donhauser, Z. J.; Mantooth, B. A.; Kelly, K. F.; Bumm, L. A.; Monnell, J. D.; Stapleton, J. J.; Price, D. W.; Rawlett, A. M.; Allara, D. L.; Tour, J. M.; Weiss, P. S. Science 2001, 292, 2303. (6) Stokbro, K.; Taylor, J.; Brandbyge, M. J. Am. Chem. Soc. 2003, 125, 3674. (7) Ulman, A. Chem. ReV. 1996, 96, 1533. (8) Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278, 252. (9) Slowinski, K.; Fong, H. K. Y.; Majda, M. J. Am. Chem. Soc. 1999, 121, 7257. (10) Wold, D. J.; Frisbie, C. D. J. Am. Chem. Soc. 2001, 123, 5549. (11) York, R. L.; Nguyen, P. T.; Slowinski, K. J. Am. Chem. Soc. 2003, 125, 5948. (12) Engelkes, V. B.; Beebe, J. M.; Frisbie, C. D. J. Am. Chem. Soc. 2004, 126, 14287. (13) Basch, H.; Cohen, R.; Ratner, M. A. Nano Lett. 2005, 5, 16681675. (14) Lang, N. D.; Avouris, P. Phys. ReV. B 2000, 62, 7325. (15) Reichert, J.; Ochs, R.; Beckmann, D.; Weber, H. B.; Mayor, M.; v. Lo¨hneysen, H. Phys. ReV. Lett. 2002, 88, 176804. (16) Xu, B.; Tao, N. Science 2003, 301, 1221. (17) Hu, W.; Nakashima, H.; Furukawa, K.; Kashimura, Y.; Ajito, K. T. Appl. Phys. Lett. 2004, 85, 115. (18) Trans, S. J.; Verschueren, A. R. M.; Dekker, C. Nature 1999, 393, 49. (19) Park, H.; Park, J.; Lim, A. K. L.; Anderson, E. H.; Alivisatos, A. P.; Mceuen, P. L. Nature 2000, 407, 57. (20) Sato, T.; Ahmed, H.; Brown, D.; Johnson, B. F. G. J. Appl. Phys. 1997, 82, 696. (21) Snow, A. W.; Wohltjen, H. Chem. Mater. 1998, 10, 947. (22) Whetten, R. L.; Shafigulin, M. N.; Khoury, J. T.; Schaaff, T. G.; Vezmar, I.; Alvarez, M. M.; Wilkinson, A. Acc. Chem. Res. 1999, 32, 397. (23) Tempelton, A. C.; Wuelfing, E. P.; Murray, R. Y. Acc. Chem. Res. 2000, 33, 27. (24) Wuelfing, E. P.; Green, S. J.; Pietron, J. J.; Cliffel, D. E.; Murray, R. Y. J. Am. Chem. Soc. 2000, 122, 11465.
Das and Dunietz (25) Wohltjen, H.; Snow, A. W. Anal. Chem 1998, 70, 2856. (26) Evans, S.; Johnson, S. R.; Cheng, Y. L.; Shen, T. J. Mater. Chem. 2000, 10, 183. (27) Cioffi, N.; Farella, I.; Torsi, L.; Valentini, A.; Tafuri, A. Sensor Actuators B 2002, 84, 49. (28) Zhang, H. L.; Evans, S. D.; Henderson, J. R.; Miles, R. E.; Shen, T. H. Nanotechnology 2002, 13, 439. (29) Cai, Q. Y.; Zellers, E. T. Anal. Chem. 2002, 7, 3533. (30) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Science 2001, 294, 571. (31) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Nagahara, L. A.; Lindsay, S. M. J. Phys. Chem. B 2002, 106, 8609. (32) Kushmerick, J. G.; Naciri, J.; Yang, J. C.; Shashidhar, R. Nano Lett. 2003, 3, 897. (33) Boulas, C.; Davidovits, J. V.; Rondelez, F.; Vuillaume, D. Phys. ReV. Lett. 1996, 76, 4797. (34) Cornil, J.; Beljonne, D.; Calbert, J. P.; Bre´das, J. L. AdV. Mater. 2001, 13, 1053. (35) Bre´das, J. L.; Calbert, J. P.; da Silva, D. A.; Cornil, J. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 5804. (36) Hutchinson, G. R.; Ratner, M.; Marks, T. J. J. Am. Chem. Soc. 2005, 127, 16866-16881. (37) Cukier, E.; Daniels, S.; Vinson, E.; Cave, R. J. J. Phys. Chem. A 2002, 106, 11240-11247. (38) Cukier, E.; Cave, R. J. Chem. Phys. Lett. 2005, 402, 186-191. (39) Magoga, M.; Joachim, C. Phys. ReV. B 1999, 59, 16011. (40) Emberly, E. G.; Kirczenow, G. Phys. ReV. B 2001, 64, 235412. (41) Liu, R.; Ke, S. H.; Baranger, H. U.; Yang, W. J. Chem. Phys. 2005, 122, 44703. (42) Geng, H.; Yin, S.; Chen, K.-Q.; Shuai, Z. J. Phys. Chem. B 2005, 109, 12304. (43) Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: New York, 1995. (44) Samanta, M. P.; Tian, W.; Datta, S.; Henderson, J. I.; Kubiak, C. P. Phys. ReV. B 1996, 53, R7626-R7629. (45) Tian, W.; Datta, S.; Hong, S.; Reifenberger, R.; Henderson, J. I.; Kubiak, C. P. J. Chem. Phys. 1998, 109, 2874-2882. (46) Yaliraki, S. N.; Roitberg, A. E.; Gonzalez, C.; Mujica, V.; Ratner, M. A. J. Chem. Phys. 1999, 111, 6997-7002. (47) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Phys. ReV. Lett. 2000, 84, 979-982. (48) Nitzan, A. Annu. ReV. Phys. Chem. 2001, 52, 681. (49) Damle, P.; Ghosh, A. W.; Zahid, F.; Datta, S. Chem. Phys 2002, 171-187, 225. (50) Stokbro, K.; Taylor, J.; Brandbyge, M.; Mozos, J. L.; Ordejon, P. Comput. Mater. Sci 2002, 27, 151-160. (51) Lopez Sancho, M. P.; Lopez Sancho, J. M. L.; Rubio, J. J. Phys. F: Met. Phys. 1985, 15, 851-858. (52) Nardelli, M. B. Phys. ReV. B 1999, 60, 7828-7833. (53) Becke, A. D. J. Chem. Phys. 1993, 98, 1372. (54) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (55) Wadt, W. R.; Hay, J. P. J. Chem. Phys. 1985, 82, 299. (56) Shao, Y.; et al. Phys. Chem. Chem. Phys. 2006 8, 3172. (57) Bezyradin, A.; Dekker, C.; Schmid, G. Appl. Phys. Lett. 1997, 71, 1273. (58) Kurdak, C.; Rimberg, A. J.; Ho, T. R.; Clarke, J. Phys. ReV. B 1998, 57, R6842-R6845. (59) Rowe, M. P.; Plass, K. E.; Kim, K.; Kurdak, C.; Zellers, E. T.; Matzger, A. J. Chem. Mater. 2004, 16, 3513. (60) Kurdak, C.; Kim, J.; Kuo, A.; Lucido, J. J.; Farina, L. A.; Bai, X.; Rowe, M. P.; Matzger, A. J. Appl. Phys. Lett. 2005, 86, 073508. (61) Das, M.; Dunietz, B. D. J. Phys. Chem. B. To be published.
