Large tunable image-charge effects in single-molecule junctions
M.L. Perrin, C.J.O. Verzijl, C.A. Martin, A.J. Shaikh, R. Eelkema, J.H. van Esch, J.M. van Ruitenbeek, J.M. Thijssen, H.S.J. van der Zant, D.Dulić
LLarge tunable image-charge effects in single-molecule junctions
Mickael L. Perrin, Christopher J.O. Verzijl, Christian A. Martin, AhsonJ. Shaikh, Rienk Eelkema, Jan H. van Esch, Jan M. van Ruitenbeek, Joseph M. Thijssen, Herre S.J. van der Zant, and Diana Duli´c Kavli Institute of Nanoscience, Delft University of Technology,Lorentzweg 1, 2628 CJ Delft, The Netherlands Department of Chemical Engineering, Delft University of Technology,Julianalaan 136, 2628 BL Delft, The Netherlands Kamerlingh Onnes Laboratory, Leiden University,Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
Abstract
The characteristics of molecular electronic devices are critically determined by metal-organicinterfaces, which influence the arrangement of the orbital levels that participate in charge transport.Studies on self-assembled monolayers (SAMs) show (molecule-dependent) level shifts as well astransport-gap renormalization, suggesting that polarization effects in the metal substrate play akey role in the level alignment with respect to the metal’s Fermi energy. Here, we provide directevidence for an electrode-induced gap renormalization in single-molecule junctions. We studycharge transport in single porphyrin-type molecules using electrically gateable break junctions.In this set-up, the position of the occupied and unoccupied levels can be followed in situ andwith simultaneous mechanical control. When increasing the electrode separation, we observe asubstantial increase in the transport gap with level shifts as high as several hundreds of meVfor displacements of a few ˚Angstroms. Analysis of this large and tunable gap renormalizationwith image-charge calculations based on atomic charges obtained from density functional theoryconfirms and clarifies the dominant role of image-charge effects in single-molecule junctions. a r X i v : . [ c ond - m a t . m e s - h a ll ] M a r his is a postprint version of “Perrin et al. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26In self-assembled monolayers (SAMs), the influence of the molecule-metal interface on thealignment of the molecular orbital level with respect to the Fermi energy of the substrate hasbeen extensively studied with UV and X-ray photo-emission spectroscopy (UPS and XPS) ,Kelvin probe measurements , and scanning tunneling spectroscopy . Such measurementshave indicated the formation of an interfacial dipole that is associated with substantial work-function shifts , which affect all molecular orbitals in a similar way. Several mechanismscausing this interfacial dipole have been identified. In physisorbed systems the compressionof the tail of the electron density outside the metal (“pillow” or “push-back” effect) playsan important role, while for chemisorbed systems charge transfer causes, in addition, asurface dipole to be formed near the metal-molecule interface . Additionally, strainingthe molecular junction may shift the orbital levels ; upon stretching or compression of themolecular junction, the shifts of the occupied and unoccupied level were found to be nearlyuniform for the frontier orbitals . Finally, the interaction of the (almost) neutral moleculewith its own image-charge distribution at zero bias may also lead to a uniform level shift.This effect is present in both physisorbed and chemisorbed systems.In contrast to the previously mentioned effects, UPS experiments probing the ionizationand electron addition energies for decreasing layer thicknesses have shown that the occupiedlevels move up and the unoccupied ones down in energy, – this is called ‘gap renormalization’.Transport gap renormalization has also been observed in single-molecule devices andis commonly explained by the formation of image charges in the metal upon addition orremoval of electrons from the molecule . This effect occurs repeatedly when a current ispassing through it and is particularly apparent in molecules that are weakly coupled to theelectrodes.When varying the electrode separation, the molecular orbital levels are therefore subjectto a uniform shift, combined with gap renormalization. Hence, distinguishing the dominanttrend in single-molecule junctions requires the combination of an adjustable electrode sepa-ration with an electrostatic gate. Although mechanical control over molecular conductancehas been reported in various studies , in only very few reports it has been combinedwith an electrostatic gate . In particular, systematic studies based on explicit monitoringof the dependence of occupied and unoccupied orbital levels on molecule-electrode distanceare lacking. 2his is a postprint version of “Perrin et al. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26 FIG. 1.
Illustration of the experiments. (a) Structural formula of ZnTPPdT (b) Lay-out ofthe mechanically controllable break (MCBJ) junction set-up (c) Colorized SEM image of a three-terminal MCBJ device. The gate is made of aluminum and covered with an plasma-enhancednative aluminum oxide layer. The gold electrodes are deposited on top of the gate dielectric (d)Colorized SEM image of a two-terminal MCBJ.
Curent-voltage characteristics
We have investigated the influence of the metal electrodes on the energy levels in single-molecule junctions using two- and three-terminal mechanically controllable break junctions(MCBJs) in vacuum at 6 K. This architecture (shown in Fig. 1b) allows the distance betweenthe electrodes to be tuned with picometer precision by bending the flexible substrate sup-porting partially suspended electrodes . In three-terminal MCBJ devices an additionalgate electrode allows electrostatic tuning of the energy levels of the molecular junction .The molecules in this study were thiolated porphyrins, which offer great architectural flex-ibility and rich optical properties. The thiol-terminated Zn-porphyrin molecules [Zn(5,15-di(p-thiolphenyl)-10,20-di(p-tolyl)porphyrin)], abbreviated as ZnTPPdT and shown in Fig.3his is a postprint version of “Perrin et al. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.261a, were dissolved in dichloromethane (DCM, 0.1 mM) and deposited on the unbroken elec-trodes using self-assembly from solution. The electrodes were then broken in vacuum atroom temperature, cooled down and current-voltage I-V characteristics were recorded as afunction of electrode spacing. All measurements were performed at 6K. Details concerningthese “systematic I-V series” and other experimental procedures (synthesis of the molecules,measurement setup, etc.) are provided in the Supplementary Information.In Fig. 2a we present typical
I-V characteristics of a two-terminal MCBJ (sample A) thathas been exposed to a solution of ZnTPPdT. We start monitoring the junction-breakingor fusing process at some electrode separation which we call d . All characteristics showvery low current around zero bias, indicating that transport occurs in the weak-coupling(Coulomb-blockade) regime. Steps at higher bias mark the transition to sequential tunnelingtransport . In the differential conductance, dI/dV , these steps are visible as peaks (seeFig. 2b). The peak location identifies the position of the molecular orbital level with respectto the Fermi energy of the electrodes. We will refer to these peaks as resonances from nowon. Fig. 2a,b show that with decreasing inter-electrode distance, the spacing between theresonances is strongly reduced.We have studied eight different junctions, which all displayed similar mechanically tun-able resonances in dI/dV . Devices exposed to pure solvent, in contrast, showed featurelesscharacteristics, typical of vacuum tunneling through a single barrier (see Fig. 2c, 2d). As theinter-electrode distance is reduced, the maximum current in these clean junctions increasessmoothly, as a result of the decreasing tunneling barrier width.To visualize the systematic evolution of the resonance position for hundreds of dI/dV curves, we have plotted a two-dimensional map of consecutive I-V measurements in Fig. 2e,where the gradual shift of the resonances becomes even more apparent. Due to the stabilityof the electrodes and the fine control over their spacing , the energy levels can be shiftedover several hundreds of meV by purely mechanical means.In the following, we will refer to these shifts as mechanical gating and quantify them interms of an efficiency factor, the mechanical gate coupling (MGC). The MGC is expressedin V/nm and defined as the ratio between the shift of each resonance and the electrodedisplacement required to achieve this shift. From Fig. 2e, for example, we find a MGC ofabout 1 V/nm, with a slight asymmetry for positive and negative bias which may be causedby differences in capacitive coupling to the two electrodes. The reverse process (opening the4his is a postprint version of “Perrin et al. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26 FIG. 2.
Mechanical gating of charge transport in ZnTPPdT junctions. (a) Current-voltagecharacteristics and (b) differential conductance for MCBJ devices which have been exposed to asolution of ZnTPPdT. In (c) and (d) the same quantities are plotted for junctions exposed to thepure solvent (DCM). (e,f) Two-dimensional visualization of dI/dV for ZnTPPdT as a function ofbias voltage and electrode displacement (e) while fusing sample A and (f) for three making/breakingcycles of a different device (sample B). A clear dependence of the Coulomb gap on the electrodespacing is visible. The differential conductance has been normalized and the estimated electrodedisplacement is relative to d , the initial electrode separation. junction) leads to a widening of the Coulomb gap, as illustrated in Fig. 2f, where severalconsecutive opening and closing cycles are shown for a different sample. The figure clearlyshows that the resonances shift consistently and with similar magnitudes, demonstratingthe robustness of the effect and the stability of the setup.While recording systematic I-V series, we occasionally observe a very weak dependenceof the resonance positions on the electrode separation, and conversely, occasionally ob-serve MGC’s as large as 1.5 V/nm (see Supplementary Information for the statistics of theMGC’s). This is probably due to a rearrangement of the molecule inside the junction .Alongside gradual changes in the position of the resonances, the plots in Fig. 2e,f display5his is a postprint version of “Perrin et al. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26sudden irreversible jumps in the dI/dV ’s. These differences and variations could be causedby atomic-scale changes in the geometry of the molecular junction. Evidence of similar rear-rangements has also been obtained during room-temperature conductance measurements onporphyrin molecules . Throughout all the samples, however, the trends remain the same;reducing the electrode distance brings the resonances closer together, whereas increasingthe distance moves them further apart. Gate diagrams
To obtain additional information about the origin of the shifts of the molecular or-bital levels involved in charge transport, we employed electrically gated mechanical breakjunctions . The electrostatic gate in these devices controls the potential on the moleculeand lowers/raises all molecular orbital levels for positive/negative gate voltage , as shownin Fig. 3c. Keeping the electrode spacing fixed, we measure the current as a function of boththe bias- and gate voltage and plot dI/dV as a two-dimensional map; in this paper we willrefer to such a plot as a gate diagram.In such a gate diagram the resonances associated with an occupied level move away fromthe Fermi level with increasing gate voltage. An unoccupied level, on the other hand, movescloser to the Fermi level and thus displays the opposite trend. This allows us to identify theresonance in Fig. 3a as the HOMO, whereas Fig. 3b shows an unoccupied level (this is notthe LUMO of the gas phase molecule, see below). The HOMO level position depends on thegate voltage with an electrostatic gate coupling (EGC) of about 15 mV V − ; for the unoccu-pied level, we find an EGC of about 25 mV V − . Fig. 4a–b shows the mechanical gate plotsrecorded immediately after the measurements shown in Fig. 3b and Fig. 3a, respectively.Both the occupied and unoccupied levels move away from the Fermi level while we increasethe distance between the electrodes (MGC = 0 .
40 V/nm for the occupied and 0 .
18 V/nmfor the unoccupied level). This implies a widening of the gap and means that the mechanismbehind the shifts cannot be a rigid change in the work function only, but must also include atransport-gap renormalization. It is the combination of electrostatic and mechanical gatingwhich leads us to this conclusion, and in the following we will demonstrate using densityfunctional theory (DFT) based calculations that this gap renormalization is caused by theformation of image charges upon charge addition to/removal from the molecule.6his is a postprint version of “Perrin et al.
Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26 FIG. 3.
Level shifts by electrostatic gating. (a,b) Gate diagrams recorded on sample C fordifferent junction configurations and during different breaking events. Color-coded dI/dV plottedversus gate- and bias voltage. The slope of the lines allows us to attribute resonances in (a) to anoccupied level (HOMO-like, located approx at 0.3eV for zero gate voltage) and those in (b) to anunoccupied level (LUMO-like, located approx at 0.75eV for zero gate voltage). (c) The effect ofa rigid shift of the levels under electrostatic gating by a potential V g applied to a gate electrodebelow the junction for an occupied and unoccupied level. Here, β is the electrostatic gate coupling, φ m the metal work function, ∆ the shift of the potential V S outside the surface due to the presenceof the molecule, and (cid:15) F the Fermi energy of the metal. (cid:15) occ , (cid:15) unocc and (cid:15) (cid:48) occ , (cid:15) (cid:48) unocc are the occupiedand unoccupied levels for V g = 0 and V g (cid:54) = 0, respectively. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26 FIG. 4.
Level shifts by mechanical gating. (a,b) Systematic I-V series of sample C, recordedright after Fig. 3 a and b, respectively. (a) HOMO-like (located approx at 0.3eV for zero dis-placement) and (b) LUMO-like level (located approx at 0.75eV for zero displacement) both moveaway from the Fermi energy for increasing electrode spacing. (c) The shift of the occupied andunoccupied molecular orbital levels with the distance to the metal. The effects contained in ∆shift all levels in the same direction, while image-charge effects are responsible for occupied andunoccupied levels moving closer to the Fermi energy of the metal (gap renormalization). Again, φ m represents the metal work function, ∆ the interfacial dipole, V ∞ the potential at infinity, V S thepotential at the surface and (cid:15) F the Fermi energy. (cid:15) occ , (cid:15) unocc and (cid:15) (cid:48) occ , (cid:15) (cid:48) unocc are now the occupiedand unoccupied levels of the molecule in gas phase and at the interface, respectively. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26 DFT calculations
We now turn to the theoretical analysis of the experimentally observed phenomena. Us-ing a quantum chemistry approach we study the electronic structure of the molecules ingas phase and sandwiched between gold atoms in the junctions, as well as their transportproperties (see supplementary information for details). In agreement with the literature, ourcalculations predict a chemisorbed system with ZnTPPdT acting as acceptor, and thehollow site as the most stable configuration. Fig. 5 shows the computed zero-bias transmis-sion of the single-molecule junction. We find that the low-bias transport is dominated bythe HOMO and HOMO-2 states of the molecule coupled to gold atoms (illustrated in Fig5a), visible as peaks in the transmission near the Fermi level.We also observe that the resonances which correspond to the gas-phase LUMO andLUMO+1 levels are located far above the Fermi level of the leads (although the precise loca-tion of these resonances cannot accurately be predicted within DFT). Being more stronglylocalized at the center of the molecule than the better-hybridizing HOMO-like orbitals, theyare expected to have poor conductance properties, and as a consequence are characterized byvery narrow peaks in the calculations. A few additional peaks occur slightly above the Fermienergy, and inspection of these states reveals that they have no direct gas-phase counterpart.They are new states, which essentially consist of those parts of the gas-phase HOMO andLUMO that are located on the arms of the molecule and stabilized by the presence of theinterface. Forcing an extra electron onto the molecule by applying a positive gate voltageindeed shows that charge is added to these levels, rather than to a LUMO state.As discussed above, there is a correction ∆ to the background potential which representsa work function shift, as illustrated in Fig. 4c. This shift is usually treated empirically, andis typically negative on Au surfaces. Experiments have reported shifts in the range -0.5to -1 eV for H TPP and ZnTPP films , without the presence of the thiols in ZnTPPdT.This corrections is, in principle, distance dependent, and leads to a uniform shift of theoccupied and unoccupied levels. This is in contrast with the experimentally observed gaprenormalization, indicating that, although this effect may, to some extent, be present, it isnot the dominant mechanism responsible for the large level shifts.Image-charge effects, including their contribution to gap renormalization, can, in prin-ciple, be assessed by performing GW calculations , which allow for the determinationof the ionization potentials and electron addition energies. However, such calculations are9his is a postprint version of “Perrin et al.
Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26infeasible for the large molecules of this study. Instead, we calculate image-charge effectsusing classical electrostatics based on the atomic charges on the molecule obtained fromDFT. In the region where the transport is blocked (corresponding to zero bias and gate)the molecule is approximately, but not exactly, neutral. We call this the ‘reference state’.The combination of the negatively charged thiols with the positive core of the molecule inthe reference state can lead to a contribution of the image charges effect to the uniformshift. This contribution either moves the levels up or down, depending on the exact chargedistribution in the junction. To include gap renormalization, one also has to consider thedifferent charged states of the molecule. To access the different charge states in the junction,we added or removed one electron from the molecule by applying a local gate field, in thespirit of a ∆ − SCF method (see supplementary information for details). The image-chargeeffect corrections are calculated for the different charge states by summing the electrostaticinteractions of the atomic charges between two parallel plates with all image charges. Theposition of the image plane is taken to be 1 . ± .
25 ˚A outside the metal surface, as isusually done in the literature . For comparison with experiment, the distance betweenthe electrodes has been varied.The calculated shifts, illustrated in Fig. 5c, predict an image-charge contribution tothe MGC’s in the range of 1.1–2.8 V/nm for an occupied level, and 0.4–2.1 V/nm foran unoccupied level depending on electrode separation. The different molecular orbitallevels (shown in Fig. 5a) thus experience different image charge effects, as observed in theexperiments, although the calculated MGC’s are larger than the experimental ones. Thiscan be due to the sharp contacts in the MCBJ experiment, which imply a smaller image-charge effect than the large parallel-plate contacts used in the calculation. We modeled thereduction of the image-charge effect with finite contacts, finding it to be roughly a factorof 1 . − ◦ .To assess the contribution to the molecular orbital level shifts originating from struc-tural deformation of the molecule, we performed DFT calculations for increasing gold-golddistance while letting the molecule relax between the contacts. We found that the energyshifts of the occupied and unoccupied level are at most of the order of 50-60 meV, and more10his is a postprint version of “Perrin et al. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26importantly, do not lead to transport-gap renormalization, but rather cause an uniform, up-ward shift. In addition, the HOMO is predicted to move up for increasing electrode-spacing,while the experiments show the opposite trend.We conclude that image-charge effects can largely explain the experimentally observeddistance dependence of the position of the molecular orbital levels with respect to the Fermilevel of the contacts. Our calculations further reveal that the contributions to the im-age charge effect of the charge distribution in the reference state contributes substantially(roughly half as much as the gap renormalization) to the MGC of the molecular orbitallevels.The time needed for forming image charges is associated with the plasma frequency ofthe metallic contacts, corresponding to an energy of a few e V. This is short enough to berelevant even in co-tunneling processes. In recent years, several attempts have been made tocapture the image charge-induced gap renormalization using either single point charges or atomic charge distributions , based on DFT results for gas-phase molecules. In thepresent system, however, it seems that the states used for electron transport are definedby the presence of the contacts. Therefore, taking the atomic charge distributions for thedifferent charge states inside the junctions is the appropriate starting point for calculatingimage-charge effects.
Conclusion
In summary, we have studied the influence of the electrode separation on the molecularorbital levels in porphyrin single-molecule junctions using electrostatically-gated MCBJ de-vices. Using this method we demonstrate experimentally a combined effect of mechanicaland electrostatic gating of the molecular levels. We find that both occupied and unoccupiedlevels move significantly towards the Fermi level upon reduction of the electrode spacing.We attribute this dominantly to gap renormalization as a result of electron interaction withimage charges in the metal leads. Our findings are corroborated by DFT-based calculations.The experiments show surprisingly large level shifts, suggesting that image-charge effectsmay be responsible for the large spread in conductance values that is often observed insingle molecule junctions. These effects should therefore be considered in quantitative com-parisons between computations and experiment in single-molecule junctions. At present,calculations for molecular devices result at best in the prediction of trends, or they shed11his is a postprint version of “Perrin et al.
Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26 Image-Plane Distance
HOMOHOMO-2 LUMO+1LUMOGap Type I Gap Type II a)b) c)
FIG. 5.
Transport calculation and image-charge model. (a) Zero-bias transmission and molecularorbital levels of ZnTPPdT coupled to Au, from DFT and DFT+NEGF calculations, respectively. The Fermienergies are with respect to the Fermi energy of the metal electrodes, marked by the vertical black line.ZnTPPdT is located at 2.59 ˚A from each lead, with hollow-site binding. (b) Image-charge model geometry,with the image plane located 1 ˚A outside the first atomic layer (uncertainty bands derived from a 0.25 ˚Adeviation). (c) Shifts predicted by the image-charge model (with uncertainties) showing the occupied- andunoccupied-levels both shifting towards (cid:15) f for decreasing electrode separation with MGC’s in the range of0.4–2.8 V/nm, assuming a symmetrically applied bias. These values may be significantly reduced for realisticelectrode geometries. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26light on the possible transport mechanisms. Improvements in geometric and electrostaticcontrol may bring quantitative agreement between the two closer. We have demonstratedthat capturing the image-charge effects is a crucial step in this development. From a differ-ent perspective, the observed effects may be exploited to mechanically gate single moleculesand thereby tune the alignment of the orbital levels with respect to the Fermi level.13his is a postprint version of “Perrin et al. Nature Nanotechnology , 282287 (2013)”doi:10.1038/nnano.2013.26 Ishii, H., Sugiyama, K., Ito, E. & Seki, K. Energy level alignment and interfacial electronicstructures at organic/metal and organic/organic interfaces.
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J. Chem. Phys. , 111103 (2008). • Acknowledgments
This research was carried out with financial support from theDutch Foundation for Fundamental Research on Matter (FOM), the VICI (680-47-305) grant from The Netherlands Organisation for Scientific Research (NWO) andthe European Union Seventh Framework Programme (FP7/2007-2013) under grantagreement no 270369. The authors would like to thank Ruud van Egmond for experttechnical support and Dr. Johannes S. Seldenthuis for fruitful discussions. • Author Contributions
D.D. and H.v.d.Z. designed the project. C.M., H.v.d.Z. andJ.v.R. designed the setup and the devices. M.P. and C.M. fabricated the devices. A.S.,R.E. and J.v.E provided the molecules. M.P and D.D. performed the experiments.C.V., M.P. and J.T. performed the calculations. M.P., C.V., D.D., J.T. and H.v.d.Z.wrote the manuscript. All authors contributed to the discussion of the results and themanuscript. • Competing Interests