Electron Tunneling through Molecular Media:A Density Functional Study ofAu/Dithiol/Au SystemsQiang Sun,[a] Annabella Selloni,*[a] and Giacinto Scoles[a, b]

1. Introduction

The study of charge transport across nanometer-scale metal–molecule–metal junctions is not only important for the realiza-tion of molecular-based electronics, but can also be taken as abasis for understanding electron tunneling in general.[1–4] Ex-perimentally, the basic difficulty is that of forming the electricalcontacts between the molecules as well as between the mole-cules and the macroscopic world. To overcome this difficulty, anumber of novel approaches have been developed,[5–20] withvarious degrees of success. On the theoretical side, the calcula-tion of molecular electrical transport properties is a complexproblem, for which various simplified models have been intro-duced.[21–25] From all these studies, two main conduction mech-anisms have been identified.[1–4] In the first, the molecule bridg-ing the metal electrodes has states in resonance with the elec-trode states near the Fermi energy Ef, leading to electron trans-port similar to that in conventional metals (herein we alwaysrestrict ourselves to the case of small voltages). In the secondmechanism, Ef is located between the highest occupied molec-ular orbital (HOMO) and the lowest unoccupied molecular orbi-tal (LUMO), so that no resonant state is present. However, theexponential tail of the HOMO or LUMO at Ef, broadened by theinteraction between the molecule and the electrodes, opens anonresonant tunneling transport channel. Thus, to better un-derstand charge transport in molecular systems, it is helpful tofirst elucidate the detailed electronic properties of variousmetal–molecule–metal junctions under zero bias.

On the basis of their electronic properties, organic moleculescan be divided into two types: saturated and conjugated ones.Saturated molecules, such as alkanes, have large gaps (about6 eV or greater) between the HOMO and the LUMO and in thebulk and behave as insulators, whereas conjugated polymerssuch as poly(paraphenylene) possess delocalized p-electrons

with a smaller (2–4 eV) HOMO–LUMO gap and behave morelike semiconductors. While for both types of molecules theelectron transport generally belongs to the nonresonant tun-neling regime, it is significantly higher for the conjugated mol-ecules. Herein we shall restrict ourselves to the case of saturat-ed molecules, by focusing on the prototypical Au(111)/CnS2/Au-(111) system of n-alkanedithiols, CnS2 (n=4,8,12), between twoflat (111) gold electrodes (with chemical S�Au bonds at bothends). For these systems, a large number of experimental andtheoretical studies have already been done, and the generalagreement is that at low voltages the current In through a n-al-kane(di)thiol monolayer decays with an exponential depend-ence on the number n of methylene units in the alkane chain,namely In= I0<exp(�bnn), with bn�1. So far, however, theoreti-cal studies have only examined the situation of a high-densitymonolayer where the molecules between the two metal surfa-ces are in their equilibrium geometry, that is, the molecularaxis is tilted by �308 with respect to the normal direction. Insuch a situation, the distance dz between the two electrodes isuniquely defined by the chain length n. Herein, instead, weintend to consider geometries with widely different values ofthe molecular-tilt angle, so that n and dz are (at least to someextent) decoupled. Our goal is to explore the separate effectsof n and dz on the LDOS at Ef, and thus indirectly on the tun-neling current, so as to obtain insight into the tunneling mech-

[a] Dr. Q. Sun, Prof. A. Selloni, Prof. G. ScolesChemistry Department, Princeton University, Princeton, NJ 08544 (USA)Fax: (+1)609-258-6746E-mail : aselloni@princeton.edu

[b] Prof. G. ScolesInternational School for Advanced Studies and Sincrotrone TriesteTrieste (Italy)

We report a density functional theory study of the electronicproperties of n-alkanedithiols (CnS2, with n=4, 8 and 12) sand-wiched between two Au(111) infinite slab electrodes. We investi-gate the influence of the distance between the two electrodesand of the molecular chain length, tilt angle, and coverage onthe local density of states (LDOS) at the Fermi energy (Ef). Wefind that the (small) value of the LDOS at Ef near the center ofthe molecular wires—a quantity that is related to the tunnelingcurrent—is mainly determined by the length n of the alkanechains: it originates from the tails of the highest occupied molec-ular orbital (HOMO) and the lowest unoccupied molecular orbital

(LUMO) which are broadened by the interaction with the electro-des, and decays exponentially with the length of the molecularwire. This opens a nonresonance tunneling channel for chargetransport at small bias voltages. While the length of the hydro-carbon chain appears to be the determining factor, the tilt angleof the molecular wires with respect to the electrode surfaces, andtherefore the distance between these, has a small influence onthe LDOS at the center of the molecule, while the effect of cover-age can be ignored. The picture which emerges from these calcu-lations is totally consistent with a through-bond tunneling mech-anism.

1906 @ 2005 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim DOI: 10.1002/cphc.200400576 ChemPhysChem 2005, 6, 1906 – 1910

anism, in particular whether the tunneling through such mo-lecular junctions proceeds through bonds or through space.[3–4]

More specifically, we shall investigate the following questions:How does the tunneling current through an alkanedithiolmonolayer sandwiched between two electrodes at given(fixed) distance dz depend on the length n of the molecules inthe monolayer? Alternatively, how does the tunneling througha monolayer of CnS2 molecules of given (fixed) n change fordifferent tilt angles of the molecules, that is for different sepa-rations dz between the electrodes?

To answer these questions, we have carried out systematicdensity functional theory (DFT) calculations of the electronicproperties of molecular junctions of n-alkanedithiols (n=4, 8,and 12) sandwiched between two gold electrodes and theirdependence on the molecular length n, the coverage, as wellas on the distance dz between the electrodes, which is relatedto the tilt angle of the molecular backbones.

2. Results

2.1. Structural Optimization

Previous theoretical studies[27] have found that in the moststable adsorption configuration of alkanethiols on Au(111), thesulfur headgroup sits at the bridge site while the tilt angle ofthe molecular axis with respect to the surface normal is about308. In our geometry optimization of Au(111)/CnS2/Au(111), weset up the initial structure of one sulfur end based on the pre-vious results, then tilt the molecular alkane chains to fit theseparation of the two electrodes, and finally relax all atomicpositions while keeping the dimension of the unit cell alongthe surface normal fixed at different constant values.

The structural parameters and molecular adsorption energiesfor all the investigated systems are summarized in Table 1. Twodifferent surface supercells were considered, corresponding tofull and half monolayer coverages of the alkanedithiol mole-cules. For each coverage, different values of n, the molecularlength, and dz, the separation between the two Au(111) elec-trodes, are given. Correspondingly, the calculated tilt angle(with respect to the surface normal), average S�Au distance

and adsorption energy (i.e. the difference between the totalenergies of the interacting and noninteracting molecule–elec-trodes system) are reported. In the remaining part of this sec-tion we discuss in some detail only the structural results forC4S2, those for C8S2 and C12S2, which show qualitatively similarbehavior. The electronic properties of all three systems are dis-cussed in the next subsection.

Figure 1 shows the optimized geometries of C4S2 monolayersbetween two Au(111) surfaces at distance of 8 and 10 F. Forthe case dz=8 F, the two terminal sulfur atoms are both at

bridge sites of the two Au(111) surfaces, while for dz=10 F,one sulfur atom is at a bridge, and the other at a hollow site.The corresponding tilt angles are 478 and 318, while the ad-sorption energies are 2.13 eV and 3.42 eV, respectively. Thesmall value of the binding energy when dz=8 F indicates thatin this case the monolayer is strongly compressed. We calculat-ed the force to compress the C4S2 monolayer from 10 F to 8 F:the resulting value, 6.5<10�10 N per molecule, corresponds toa pressure of 2.9 GPa. From atomic force microscopy (AFM) ex-periments[29] it is known that the force between the AFM tipand the alkane monolayer necessary to tilt the axis of the mo-lecular chains beyond their 308 equilibrium values, is common-ly of the order of several nanonewtons. Thus, we find thatthere should be at least several tens of molecules interactingwith the tip. This is reasonable, considering the typical valuesof the tip radii.

For C4S2 with dz=10 F, the adsorption energy at full mono-layer coverage is 3.42 eV, that is, 0.38 eV smaller compared tothe half monolayer case. The reduction of adsorption energywith increasing coverage is a general trend for adsorbates onmetal surfaces: it has been extensively discussed for alkane-thiols on Au(111) in ref. [27].

Table 1. Optimized structural parameters and molecular binding energiesE for C4S2, C8S2 and C12S2 sandwiched between two Au(111) surfaces withvarious separation dz at one and half monolayer (ML) coverage.

Coverage/molecule dz [ F] Tilt angle [8] S�Au [F] E [eV]

1 MLC4S2 8 47 2.39 2.13

10 31 2.43 3.42C8S2 15 26 2.49 3.63C12S2 20 27 2.43 3.48

0.5 MLC4S2 10 31 2.45 3.80C8S2 10 61 2.47 3.39

15 26 2.47 3.99C12S2 15 50 2.44 3.93

20 25 2.46 4.13

Figure 1. Top and side views of C4S2 monolayers sandwiched between twoAu(111) surfaces with separations of 8 and 10 F. Au: large yellow spheres,carbon: small yellow spheres, hydrogen: small blue spheres, sulfur : grayspheres.

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Electron Tunneling through Molecular Media

2.2. Electronic Properties

We start by considering the electronic structure of C8S2 layerssandwiched between Au(111) electrodes at distances dz=10and 15 F. The coverage is half a monolayer (the dependenceof the electronic structure on the coverage is negligible, as dis-cussed later in this section) and the smaller value of dz clearlycorresponds to a much larger tilt angle of the alkane chains.We primarily focus on the LDOS at Ef, 1(r,Ef), defined by Equa-tion (1):

1ðr, EfÞ ¼X

I

jyiðrÞj2dðEi�EfÞ ð1Þ

where yi is an eigenfunction of the Au(111)/CnS2/Au(111)system and Ei is the corresponding eigenvalue. We also consid-er the closely related projected density of states (PDOS) at Ef,which is obtained by projecting 1(r,Ef) onto the atomic wave-functions of the Au, S and C atoms in the system. In Figure 2a,isosurfaces of 1(r,Ef) are shown. The logarithm of the PDOSalong the molecular wire is plotted in Figure 2b), where the re-sults for the two values of dz are compared. From this Figure, itappears that the PDOS are symmetrical with respect to a planelocated in the middle of the two electrodes, and exponentiallydecay from the end of the contact region to the center of themolecule. Similar results for C12S2 at electrode separations of15 and 20 F are reported in Figure 3 (also in this case the cov-

erage is half a monolayer). In both cases the exponential decayof the PDOS is characterized by a decay constant of about 0.8–0.9 F�1 for the larger dz (corresponding to bn�1, in units permethylene), whereas the decay is steeper for the smaller dz.We can also note that, if the plot in Figures 2b or 3b hadbeen made using the ordering number of the carbon atoms ascoordinate on the x axis, the two curves for the two differentvalues of dz would have been very similar.

Let us next focus on the PDOS at the center of the molecu-lar wire: for both C8S2 and C12S2, this PDOS is less than a factortwo larger for the smaller electrode separation (larger tiltangle) than that for the larger electrode separation (smaller tiltangle). This difference is much smaller than that obtained byextrapolating the exponential decay of the PDOS at the smallervalue of dz up to the larger dz.

The above results show how, for a given molecular chainlength, the density of states depends on the electrode separa-tion or tilt angle. While it is already rather clear that the PDOSof the molecular junction is largely determined by the length nof the molecular chains rather than by the separation dz be-tween the metal electrodes, it is also interesting to study how,for a given separation dz, the electronic density of stateschanges by changing the length of the alkanedithiol mole-

Figure 2. C8S2 layers (with half monolayer coverage) between two Au(111)surfaces with separations of 10 and 15 F: a) isosurfaces of the LDOS at Ef ;b) logarithm of the PDOS along the molecular wire. The PDOS of the two hy-drogen atoms in the methylene unit are added to that of the correspondingcarbon.

Figure 3. C12S2 layers (with half monolayer coverage) between two Au(111)surfaces with separations of 15 and 20 F. a) Isosurfaces of the LDOS at Ef ;b) logarithm of the PDOS along the molecular wire. The PDOS of the two hy-drogen atoms in the methylene unit are added to the correspondingcarbon.

1908 @ 2005 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim www.chemphyschem.org ChemPhysChem 2005, 6, 1906 – 1910

A. Selloni et al.

cules. To address this question, in Figure 4a we show thePDOS at Ef of C4S2 and C8S2 layers between gold electrodes atseparation of 10 F, while in Figure 4b) we show a similar com-parison for C8S2 and C12S2 with dz=15 F. From these figures it

appears that at the electrode separation of 10 F the PDOS atthe central carbon atoms of C4S2 is about three times largerthan that at the central carbon atoms of C8S2, while at the elec-trode separation of 15 F the PDOS at the central carbon atomsof C8S2 is about seven times larger than that of the centralcarbon atoms of C12S2. In other words, for a given value of dzthe PDOS of the central carbon atoms in the longer moleculesis always much smaller than in the shorter ones, even thoughthe distance of these central carbon atoms from the surface isthe same for the different alkanedithiols.

Finally, we need to address the coverage dependence of theelectronic properties of the alkanedithiol layers. This is impor-tant because experimentally, when pressure is applied to tiltthe hydrocarbon chains well beyond 308, different electrodeseparations may correspond to different coverages. To this endwe have considered C4S2, C8S2 and C12S2 molecules betweentwo Au(111) surfaces with separations of 10, 15 and 20 F, re-

spectively, and compared the calculated PDOS at Ef for halfand full monolayer coverages, see Figure 5. It appears that thecoverage effect on the PDOS at Ef is negligible in all cases, asthe largest PDOS difference between half and monolayer cov-erage is always smaller than a factor two.

3. Conclusions

Herein, we have presented DFT calculations of the electronicproperties of alkanedithiols sandwiched between two Au(111)surfaces, and focused on the dependence of the local densityof states at the Fermi energy on the length of the molecular

Figure 4. a) Logarithm of the PDOS along C4S2 and C8S2 between two Au-(111) electrodes at distance of 10 F. b) Logarithm of the PDOS along C8S2

and C12S2 between two Au(111) electrodes at distance of 15 F. All are at thehalf monolayer coverage.

Figure 5. PDOS at Ef for : a) C4S2 ; b) C8S2 and c) C12S2 at half and full monolay-er coverages.

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Electron Tunneling through Molecular Media

chain, on the separation between the two electrodes (or onthe molecular tilt angle) as well as on the coverage. Our objec-tive was to explore the separate effects of chain length andelectrode separation on the LDOS at Ef, and thus indirectly onthe zero-bias charge tunneling through the monolayers, inorder to obtain insight into the tunneling mechanism, for ex-ample, whether the tunneling through such molecular junc-tions proceeds through bonds or through space. Our resultsshow that, within the framework of DFT, the LDOS at Ef ismainly determined by the number of methylene units, with amuch weaker dependence on the separation between theelectrodes, and thus provide strong support to the idea thatfor these systems the tunneling is mainly through bonds. Ex-tension of these calculations to other types of molecular junc-tions should contribute to further clarify the problem of elec-tron tunneling through organic monolayers and the generalapplicability of the findings of this paper to systems of practi-cal interest.

Computational Methods

The calculations were performed within the plane-wave pseudo-potential approach using DFT in the Generalized Gradient Approxi-mation.[28] Details of the method and the parameters used herein,such as kinetic-energy cutoff for the plane-wave basis set as wellas the pseudo-potentials, can be found in ref. [26]. A repeated slabgeometry was used to model the Au(111) surfaces, and for the lat-tice constant, the theoretical value in ref. [26] was used. Experi-mentally, self-assembled monolayers of alkanedithiols on Au(111)give rise to a (

ffiffiffi3

p<

ffiffiffi3

p)R30 superlattice with respect to the (1<1)

periodicity of the unreconstructed Au(111) surface. In our calcula-tions, we used either a surface (

ffiffiffi3

p<

ffiffiffi3

p)R30 unit cell with one di-

thiol molecule every three surface Au atoms, corresponding to fullmonolayer coverage, or a (

ffiffiffi3

p<2

ffiffiffi3

p)R30 supercell (doubled along

the [1̄10] direction) with one dithiol molecule every six surface Auatoms, corresponding to a half monolayer coverage. In calculationswhere the CnS2 molecules are strongly tilted to match the distancebetween the two Au(111) electrodes, we found that full monolayercoverage indeed leads to strong intermolecular repulsions andthus to strongly deformed molecules. The Brillouin zone was sam-pled with eight special k-points for the (

ffiffiffi3

p<

ffiffiffi3

p)R30 cell, and four

special k-points for the (ffiffiffi3

p<2

ffiffiffi3

p)R30 the cell. Calculations were

performed for different values of the distance (dz=8, 10, 15 and20 F) between the two Au(111) surfaces, with the CnS2 molecules(n=4, 8 and 12) connecting the two surfaces and forming a S�Aubond at each end. In the geometry optimizations all coordinateswere relaxed until each component of the residual force on eachatom was smaller than 0.03 eV/F.

Acknowledgements

We thank S. Piccinin, S. Scandolo and R. Car for useful discus-sions. Calculations were performed on the IBM-SP3 computer ofthe Keck Computational Materials Science Laboratory in Prince-ton. This work was partially supported by NSF through GrantDMR02-13706 to the MRSEC–Princeton Center for Complex Mate-rials.

Keywords: alkanedithiol monolayers · density functionalcalculations · self-assembly · surface chemistry · through-bondinteractions

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Received: November 30, 2004Published online on August 1, 2005

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A. Selloni et al.