Interface Geometry and Molecular Junction Conductance: Geometric

NANO LETTERS

Interface Geometry and Molecular Junction Conductance: Geometric Fluctuation and Stochastic Switching

2005 Vol. 5, No. 9 1668-1675

H. Basch,† R. Cohen,‡ and Mark A. Ratner*,‡ Department of Chemistry, Bar-Ilan UniVersity, Ramat Gan, Israel, and Department of Chemistry and Nanotechnology Center, Northwestern UniVersity, EVanston, Illinois 60208 Received April 15, 2005; Revised Manuscript Received June 10, 2005

ABSTRACT Metal/molecule/metal transport junctions can transport charge in the elastic scattering (Landauer) regime if the injection gap is large and the molecule is relatively short. Stochastic switching and broad conduction peak distributions have been observed in such junctions. We examine the effect of altering interface geometry on transport, using density functional calculations. For most structures, variations in conductance of order 0−300% are found, but when an atomic wire of Au binds to the molecule, symmetry changes can modify currents by a factor of 103.

I. Introduction. The topic of molecular electronics features molecular structures that have interesting internal dynamics, such as switching, optical response, bistability, and mechanistic change.1-7 Because of important early measurements, the molecules p-benzenedithiol (BDT), R,ω-xylenedithiol (XDT),8-10 and thiolated alkanes11-15 have become prototypical cases for examining the nature of transport in meta/ molecule/metal (mmm) junctions. The actual measurement of transport in junctions is difficult. Many schemes and test beds have been developed, usually based either on adlayers16-21 (effectively, selfassembled monolayers utilizing the gold/thiol interaction to bind) or on a single molecule break-junction measurement.2,5,7,8,22-28 In any of these measurements, one both expects to see and can see fluctuations, depending on the stability of the structure. The most significant fluctuations in the tunneling regime will be those from changing geometry at the interface. Although there has been a recent focus on different sorts of switching arising from vibronic, stereochemical, photochemical, bond-adjustment, and other intrinsic molecular mechanisms,1-7 these hold in particular design circumstances. More generally, the dominant sort of switching observed in molecular transport junctions is stochastic switching corresponding to random changes in the measured transport, evolving in time.29-35 This stochastic switching is seen both in multiple measurements on the same system and on measurements in replica systems that are, putatively, identical.22,24,25,35,36 * Corresponding author: [email protected]. † Bar-Ilan University. ‡ Northwestern University. 10.1021/nl050702s CCC: $30.25 Published on Web 08/11/2005

© 2005 American Chemical Society

The stochastic switching almost certainly arises from structural evolutionsthat is, the transport measured at one instant will be in a slightly different molecular geometry (or interfacial or solvent geometry) than the one measured slightly later.31,32,34,37 Recent measurements suggest the generality of such stochastic switching in traditional molecular junctions based on thiol/gold electrode interaction,30,31,33,35,37 except in certain cases (such as well-packed monolayers) in which such evolution is specifically limited.32,34 Stochastic switching is expected for the same reasons that blinking and spectral diffusion are seen in single molecule spectroscopy experiments:38-40 the geometric change of the environment causes modification in the molecular signatures. Because of the propensity of gold to electromigrate,41 to form necks under applied fields,25 and to reconstruct, stochastic switching is particularly prevalent in molecular measurements made with gold electrodes,32,34 it is less probable in harder metals such as platinum,42 and seems to be entirely absent in well-constructed, covalently bonded structures involving transport on a silicon surface, with covalent binding between the silicon and the molecule.43 However, stochastic switching is an intrinsic molecular phenomenon, and its observation and characterization constitute a well-defined field.29-35,37 It is simply necessary to characterize the behavior (as it is in single-molecule spectroscopy) in a different way. In this paper, we attempt to characterize both average behaviors and geometrically determined stochastic switching phenomena by demonstrating the extreme sensitivity of transport to molecular structural evolution in transport junctions. We use the simple nonequilibrium Green’s function/ density functional (NEGF-DFT) approach that has been

published and utilized extensively6,44-53 to examine the geometric dependence of transport. We utilize the TranSIESTA code, which incorporates the NEGF formalism and a simple DFT treatment of the electronic structure.47,49,50,52 We report calculations of the conduction for the three prototype molecules (BDT, XDT, alkanethiols) and the changes in that conduction upon modification of the relative geometry at the interface. We consider sulfur binding to gold in three different positionssthe 3-fold, 2-fold, and atop structuressand find substantive changes in transport depending on the geometry. Very large changes in conductance are found for symmetry breaking distortions. Some of these changes follow from simple bonding considerations and others from the orthogonality of the π-type and σ-type orbitals. We compare these computations with the experimental results, to help comprehend both reported fluctuations and some of the magnitude and voltage dependences. II. Computational Approach. We use the NEGF-DFT approach.6,45-53 While other approaches, including those based on the Lippman-Schwinger scattering method for the molecule itself coupled with the jellium representation of the electrodes,54,55 on Hartree-Fock type methods,56-58 or on analytic forms for the self-energies,59,60 are also used, the NEGF formulation deals specifically with the nonequilibrium situation, which makes it an attractive way to approach these issues. One then calculates the current as an appropriately weighted average over the transmission coefficient T(E,V). The current is given by I(V) )

2e h

∫T(E,V)[fi(E) - ff(E)] dE

(1)

Here E, V, e, and h are, respectively, the energy variable, the applied voltage, the electronic charge, and Planck’s constant. The terms in brackets are the Fermi functions for the initial and final states, respectively. The transmission coefficient itself is given by T(E,V) ) Tr{ Γi(E,V)GR(E,V)Γf(E,V)GA(E,V)}

(2)

Here GR is the retarded Green’s function, whose conjugate is the advanced Green’s function, GA. The spectral densities Γi for the initial state and Γf for the final state also depend on the energy and on the voltagesthey are effectively twice the imaginary part of the self-energies Γλ ≡ i[Σλ - Σλ+]

λ ) i,f

(3)

Here the self-energy, Σ, describes the coupling of the Hamiltonian system of the molecule (or extended molecule, see below) with the electrode environment. In a simple Hamiltonian coupling picture, these self-energies are given by ΣL ) Nano Lett., Vol. 5, No. 9, 2005

∑i HLiGiiLHiL

(4)

Here GL is Green’s function of the lead that couples to the L state of the transport junction. HLi couples the device region for the extended molecule with the L lead (the same is true for the ΣR, with GRii replacing Green’s function in eq 4). The surface Green’s functions GL can be computed, using standard methodologies. Within the extended molecular structure itself, the retarded Green’s function is given by GcR(E,V) ≡ [E - H - ΣTOT]-1

(5)

assuming an orthogonal basis and with H representing the Hamiltonian of the extended molecule. In this expression, the broadening of Green’s function is given by the imaginary part of the total self-energy, which is the sum of the selfenergies due to the left and right electrode interactions with the molecular levels ΣTOT ) ΣR + ΣL

(6)

This effectively is the formalism involved in the calculation. We used the LDA exchange/correlation functional, with the DZP basis set on the molecules, and with SZP (5d,6s,6p) basis set on the Au cluster of the so-called extended molecules (that is, the finite number of metallic lead atoms included in the calculation). All atoms have internally stored (numerical) pseudopotentials. These were essentially the defaults in the TranSIESTA-0.9 package. The metallic leads used for our production calculation employed the standard default cluster used in the program TranSIESTA,50,52,61 that is, 36 gold atoms on one electrode and 45 gold atoms on the other electrode. Utilizing this computational scheme for the transmission coefficient and the current (the Landauer limit of elastic scattering), it is necessary only to describe the assumed molecular structure and junction geometry. Following the usual assumptions, we assume that the thiol species loses a neutral H atom. The initial dithiol loses both hydrogens, thus effectively becoming a singlet or a triplet biradical. We have examined elsewhere the differences between these,62,63 and in the current calculations assume that the biradical is always found in the singlet state. The geometries of the isolated molecules were optimized in Gaussian98 using the B3LYP hybrid exchange/correlation functional,64,65 with the CEP basis set,66 and were then used for the transport calculations without change. For the geometry of the sulfur atoms vis-a`-vis the metal atoms in the extended molecule, we use different assumptions depending on the calculation, as described in the next section. III. Computational Results. A. Alkanethiols. Alkanes are the simplest organic molecules, and uninteresting from several electronic viewpoints. They are saturated, with a very large gap between occupied and empty states, and therefore transport is expected to be very inefficientsthe barrier between the electrons in the metal (at the Fermi surface) and the frontier molecular orbitals is simply too large for efficient transport. Using a simple Huckel-type argument 1669

Figure 1. (A) The assumed transport geometry of a representative dithiolated alkane for which the I-V was calculated. The 3-fold site is a face centered cubic (fcc) hollow site. (B) The calculated length dependence of the transport in mono- and dithiolated alkane junctions as a function of the number of methylene units and of Au-Au distance. β ) 0.71 and 0.76 Å-1 for monothiolated alkanes and dithiolated alkanes, respectively. Calculations used V ) 1 V.

within a superexchange picture, one expects the conduction in oligoalkanes to decay exponentially with length, effectively because the Green’s functions in eq 2 do. Several previous theoretical arguments and direct calculations have shown that the conductance or the rate constants in donor/ acceptor structures through an oligoalkane bridge indeed scale according to eq 73,6,20,25,34,67-78 g ∝ exp{-βR}

(7)

Here R is the length of the oligoalkane chain and β is the characteristic falloff parameter describing the exponential tunneling decay through the oligoalkane. β depends a bit on the metals involved and also a bit on the nature of the interfaces, and since the exponential length here arises largely from Green’s functions (rather than the spectral densities) in eq 2, this decay parameter is less sensitive to the interface than is the prefactor that is absent from the right-hand side of eq 7. The decay factor β is expected to be voltage dependent, effectively because the gap between the injection energy and the frontier orbital energies decreases as voltage is applied.69 Transport through oligoalkanes in surface adlayer structures has been measured by a number of groups, all of which indeed find exponential decay.20,25,34,69-77,78 Reed’s group reports complete analyses of transport in oligoalkanes as a function of chain length, voltage, and temperature.69 Comparable results are reported from other laboratories using other test beds.15,77,79,80 Figure 1 sketches the assumed transport geometry for dithiolated hexane. The length of the dithiolated oligoalkane 1670

is optimized, and it is placed between large clusters representing the leads. The structure shown in Figure 1A is the so-called “extended molecule”. This is coupled to the surface Green’s function of the bulk gold electrode, and the resulting self-energy is calculated according to eq 4. For the metals, we used the tight-binding representation with the appropriate band structures. Figure 1B shows the calculated length dependence of the transport in di- and monothiolated alkane junctions. While such figures were obtained at all biases, a convenient direct comparison is an applied bias of 1 V, where the computed slope for monothiolated alkanes (β parameter of eq 7) is deduced as 0.71/Å. This differs by about 10% from the reported data by Reed et al. (∼0.77/ Å).69 Additionally, we expect no temperature dependence for this purely tunneling event, once again in agreement both with Reed’s measurement69 and with an analysis based on use of the Simmons equation for tunneling through adlayers.69,81 While the length dependence of the conductance for these Au/monothiol and dithiols systems agrees with the measurements on both species, the prefactors (0.001 and 0.005 S) differ substantially from those reported elsewhere.15 This is, we suspect, because of a very poor model for the interface geometries, especially in the monothiolated alkanes, where the methyl group on the opposite end of the chain has somehow to be matched with the metal geometry. We tried several different distances and local geometries on the methyl/gold terminussthese resulted in substantial changes in the prefactors but very minor changes in the decay length, β. This agrees with the expected mechanism involving pure tunneling transport either through the occupied or the empty Nano Lett., Vol. 5, No. 9, 2005

molecular manifolds. On the basis of previous results,62,67 on intuition, on the computed transmittance, and on the relative insensitivity of the results to the presence of the second thiol, we suspect that in gap tunneling transport is dominated by the peaks in G (eq 8 below) from the occupied manifoldsthis is then hole-type superexchange (in the language of electron transfer),6 which we expect to be dominant in most pure hydrocarbon structures. Repeated measurements on hundreds of samples find only small variation in the transport properties of the oligoalkanes.69 These measurements were made in adlayers. Because the spatial demands of the methylene subunits of the alkane are effectively commensurate with those of the thiol/gold interface, alkanethiol films tend to be well organized, with few defects and substantial long-range order. Measurements on different alkanethiol films give similar data,69 effectively because the local structure does not vary. B. Spectral Densities and Geometry Variation. In alkanethiols, band gap is very large and the simple tunneling is expected. Molecules with more interesting electronic properties have smaller band gaps and are almost always unsaturated, at least partially. Because the chains are either stiffer or less regular than simple alkanes, the films tend to be more disordered. Accordingly, measurements of transport using adlayer films (effectively self-assembled monolayers) report substantial variations both from sample to sample, and even on the very same sample as time evolves.29-31 These two properties (fluctuations from sample to sample, and timedependent fluctuations on measurements throughout the same sample) are strongly reminiscent of the spectral diffusion phenomena observed in single molecule spectroscopy.38-40 We believe that the cause is effectively the same: the structures change in time (especially at ambient temperature) because of the relatively low barriers involved in motion at the thiol/gold interface, and because of the availability of grain boundaries caused both by the metal itself and by the incommensurate space demands of the thiol headgroup on gold and the extended molecular tail. To account theoretically for the observed fluctuations, eq 2 suggests that different geometries would have to change the spectral densities, Γ. Because of chemical bonding considerations, one suspects that local changes in geometry from 3-fold sites to bridging sites to atop sites should change the overlap and therefore (in accord with eq 4) the spectral densities. Depending on how large the finite metal clusters shown at the ends of the molecule in Figure 1A are, the importance of the spectral density effects will change. For large extended molecules such as that shown in Figure 1A, the self-energy of eq 4 is computed between gold clusters (treated in a finite basis as part of the DFT calculation) and the bulk of the electrode. This then is largely a gold/gold overlap, and one expects much smaller contributions from the real part of the self-energy. On the basis of standard physical organic chemistry concepts, one expects that transport in unsaturated species will be supported largely by the delocalized, π-type levels Nano Lett., Vol. 5, No. 9, 2005

Figure 2. The assumed geometries in the model calculations of BDT/Au junctions and their different conductance. In (A) the BDT is in the same plane of the gold electrode but elevated from the surface by 1 Å. In (B) the BDT is in the same plane of the gold electrode. In (C) the Ph ring is in the same plane of the gold electrode; however the S atoms are slightly outside the plane (not visible). In (D) the BDT molecule is parallel to the electrode plane but elevated from it by 1.8 Å.

(especially in aromatics and conjugated structures: localized double bonds can have other effects, being investigated at Delft82). We therefore carried out a series of slightly artificial calculations utilizing the p-benzenedithiol species as the bridging molecule. Because of early measurements8 and an extensive set of calculations,51,62,63,71,83-100 this has become one of the prototype molecules for molecular transport junctions. (For example, our own group has previously reported many aspects of the transport in such structures, including a maximum of the conductance at about 1.3 eV, finite conductance at zero gap, transmittance almost entirely dominated by the occupied orbitals, and a substantial variation between the reported and calculated transport magnitudes.62,63) In the model calculations shown in Figure 2, we assumed that the molecule/metal interface comprised a link between a single atom of metal and the sulfur atom. Tao and his collaborators have suggested that this assumption may not be so artificial after all, at least as applied to their experiment: they make measurements of the transport by progressively separating a gold tip from a gold surface and argue that because of the very soft and weakly nondirectional bonding in the gold system there may be a “pull out” phenomenon, in which gold atoms form short monomolecular chains before first breaking (as has been studied beautifully and extensively by Takayanagi101) and then adsorbing the thiol on both ends.24,25 1671

Figure 3. The three different extended molecule geometries that were used in the calculations. In (A) the sulfur atoms are above the hollow fcc site. In (B) they are singly coordinated to gold atoms in the ATOP site, and in (C) they are above the hollow hexagonal close packed site.

The structures in Figure 2 demonstrate the striking effects of interface symmetry on transport. The variation in conductance by roughly 3 orders of magnitude with subtle changes in geometry reflects this symmetry: gold is largely an S-type metal, whereas we expect the transport through the benzene ring to be dominated by π orbitals (this is fully consistent with previous calculations, based both on the transmittance as a function of energy and on the actual currents, calculated as a function of geometry).102 The structure in the top line of Figure 2 results in near orthogonality between the S-type channel of the metal and π-type channel on the benzene ring, resulting in substantially reduced conductance. As this symmetry is broken by elevating or twisting the benzene ring compared to the gold layer, we observe much larger conductances. This extremely strong sensitivity is to some extent an artifact of the linear structure assumed for the gold layer but reminds us that this particular Lewis type interaction between the sulfur and the gold does have substantial sensitivity to geometry. 1672

It is also sensitive to coordination environment and to distance. Figure 3 shows a cluster similar to that of Figure 1, on which more extensive calculations of the transport were based. We find that moving the sulfur on one end from the atop site (effectively single coordinated) to the symmetric site, while maintaining the gold/sulfur distance at 2.4 Å, changes conductance by roughly a factor of 1.5. Since the barriers for such motion should be relatively small, this would account for some of the substantial variation from sample to sample seen in many measurements.23-25,35,69,76 In particular, the electrochemical work demonstrates that the histograms for repeated measurements on these BDT/gold structures are very broad.24 Although there is a maximum within these structures, the breadth of the histogram distribution argues eloquently (as do other results)22,23,36,103 that the local geometry at the interface substantially changes the transport in gold/thiol based molecular junctions. C. Aromatic Junctions. For both BDT and XDT, histograms show clear conductance peaks.24 When these are Nano Lett., Vol. 5, No. 9, 2005

Figure 4. Current-voltage characteristics of benzenedithiol (BDT) on gold. (A) is the experimental I-V curve for single BDT as reproduced from ref 24. (B) Calculated TranSIESTA I-V curves for the ATOP (blue) and the fcc (pink) geometries shown in Figure 3.

Figure 5. Current-voltage characteristics of benzenedimethanethiol (XDT) on gold. (A) Experimental I-V curve for single XDT as reproduced from ref 24. (B) Calculated TranSIESTA I-V curves for the ATOP (blue) and the fcc (pink) geometries shown in Figure 3. Table 1. Conductance (in units of g0 ) 2e2/h) at 0.3 eV Bias

BDT XDT

experimenta

ATOP1b

ATOP2b

ATOP3b

Threefold1b

Threefold2b

Threefold3b

0.011 0.0006

0.619 0.00614

0.441 0.0144

0.213 0.0554

0.472 0.0161

0.559 0.0171

0.787 0.0225

a Reference 24, quoted as the most probable g. b The ATOP site represents dipole coordination of S by Au, Threefold is the hollow site. 1, 2, and 3 correspond to Au-S distances of 2.46, 2.66, and 2.96 Å, respectively, for ATOP and 2.42, 2.57, and 2.80 Å for Threefold.

normalized, a current/voltage structure (that is stable up to roughly 0.6 eV) can be deduced. Experimental data24 are shown in Figures 4 and 5, for BDT and XDT, respectively. In the approximately linear regime, the conductance is simply the slope of current/voltage plot. At low voltage, the deduced single molecule conductances are roughly 0.011g0 for BDT and 0.0006g0 for XDT. The former value is substantially higher than that originally reported;8 the latter value is similar to data arising from the measurement of Coulomb blockade structures.104 Figures 4 and 5 also show our calculated values for the current/voltage structure, both using an atop geometry (single coordination of the thiol to gold) and the 3-fold hollow site often assumed for this bonding. These curves are roughly parallel to one another, and in fair agreement with ref 24, as summarized in Table 1. The substantial drop in going from BDT to XDT is explained in chemical terms by the presence of the (nonconjugated) methylene group and has been discussed extensively.89,92 Table 1 shows the sensitivity of the computation to the assumed distances between sulfur and gold. We see that a small change in the Au-S bond length (0.2 Å) influences Nano Lett., Vol. 5, No. 9, 2005

the conductance in the ATOP configuration (50%-100%); however, the 3-fold site is less affected by the distance change.105 With the BDT molecule, other groups have reported conductance calculations whose values are quite similar to ours: 0.5g0,85 ∼0.15g0,89 ∼0.1g0,62 0.2g0,99 and 0.04g055 (at a small external bias). Since the methodologies used in all the papers except for refs 55 and 99 were also based on a combination of DFT and NEGF methods, the overall similarity in the computed conductance is not surprising. The higher conductance of the aromatic species BDT and XDT, compared to the alkanes, is easily understood in terms of the gap: in a simple orbital picture, Green’s function element between orbital I (perhaps on the left sulfur) and orbital F (perhaps on the right sulfur) is approximated by

GIF(E) )

〈I|µ〉〈µ|F〉

∑µ E - 

µ

-Σ

(8)

Here, µ is the orbital energy for molecular orbital µ. In the gap (where the measured and calculated conductances 1673

occur), this sum may be dominated by the contribution from the frontier molecular orbitals. For these systems, both chemical intuition and previous calculations62,63 suggest that the conductance is dominated by the highest occupied molecular orbital, the only orbital for which DFT energy levels can indeed be interpreted as ionization energies. If the small shift arising from the real part of the self-energy is ignored, eq 8 suggests that the reduction of the conductance is due to the existence of a finite gap (denominator of eq 8) and of a frontier molecular orbital, µ, that is not entirely delocalized between the initial and final states on the bridging sulfur (numerator). For a dihydrogen bridge, the numerator will be fully delocalized, so that if injection occurred near resonance, the right side of eq 8 would simply be the inverse of the self-energy, which would then cancel the self-energy term in eq 2, resulting in unit conductance. This has been reported for the H2/Pt junction.42,106 IV. Discussion. Linear tunneling transport in molecular junctions will change with changes in molecular geometry, interface geometry, and molecular electronic structure. Recent experiments have investigated the first two quite extensively,2,3,5-7,22-25,29-32,34,35 and therefore these calculations have examined three different classes of molecules, investigating the low-voltage transport regime, its geometry dependence, and its dependence on the interfacial coordination of the thiol. The histograms of ref 24 show substantial fluctuations in the conductance from one structure to another. This is almost certainly due to the relatively fluid geometry of the thiol/ gold interaction, which has been established independently largely through investigations of adlayers.2,5,7,69 Our calculations indeed show that changing either the coordination nature of the interface (from 3-fold to 1-fold coordination) or the bond length changes the conduction by factors between 2 and 10. This is consonant with extensive experimental measurements showing both lack of reproducibility from sample to sample and spectral diffusion as a function of time in junctions containing aromatic species with thiol/gold interfaces.2,22-25,29-32,34,35 In the special case of Au single-atom wires (Figure 2), small symmetry breaking geometric changes can change the conductance tremendously. In conclusion, computational analysis of some prototype molecules shows that small changes in the geometry of the molecule with respect to the gold electrode can significantly modify the conductance. Conductance can change either by factors of 2-10 or by orders of magnitude, depending on spectral density overlap between the molecular π system and the gold electrode. Since fluctuations resulting from changing geometry at the interface are anticipated in most gold-thiol junctions, both single molecule and adlayers, our calculations rationalize the occurrence of the common stochastic switching phenomena, observed in most gold/thiol transport junctions. The systematic large discrepancies between computed and measured conductances (the former too large by factors of 10-100) almost certainly are due to the (inconsistent) use of static mean-field methods (DFT) to characterize nonequilibrium transport. 1674

Acknowledgment. We are grateful to M. Reed, A. Xue, G. Wendin, S. Lindsay L. Venkataraman, J. Ulrich, and J. Kushmerick for helpful discussions. The research was sponsored by the DARPA MOLEAPPS effort, by the NASA URETI program, and by the NSF through the Purdue NCN Institute. We are grateful to Dr. K. Stokbro for use of the ATOMISTIX program suite. References (1) (2) (3) (4) (5) (6) (7) (8) (9)

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