StructureâProperty Relationships in Atomic-Scale Junctions

Article pubs.acs.org/accounts

Structure−Property Relationships in Atomic-Scale Junctions: Histograms and Beyond Mark S. Hybertsen*,† and Latha Venkataraman*,‡ †

Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, United States Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States

‡

S Supporting Information *

CONSPECTUS: Over the past 10 years, there has been tremendous progress in the measurement, modeling and understanding of structure−function relationships in single molecule junctions. Numerous research groups have addressed significant scientific questions, directed both to conductance phenomena at the single molecule level and to the fundamental chemistry that controls junction functionality. Many different functionalities have been demonstrated, including single-molecule diodes, optically and mechanically activated switches, and, significantly, physical phenomena with no classical analogues, such as those based on quantum interference effects. Experimental techniques for reliable and reproducible single molecule junction formation and characterization have led to this progress. In particular, the scanning tunneling microscope based break-junction (STM-BJ) technique has enabled rapid, sequential measurement of large numbers of nanoscale junctions allowing a statistical analysis to readily distinguish reproducible characteristics. Harnessing fundamental link chemistry has provided the necessary chemical control over junction formation, enabling measurements that revealed clear relationships between molecular structure and conductance characteristics. Such link groups (amines, methylsuflides, pyridines, etc.) maintain a stable lone pair configuration that selectively bonds to specific, undercoordinated transition metal atoms available following rupture of a metal point contact in the STM-BJ experiments. This basic chemical principle rationalizes the observation of highly reproducible conductance signatures. Subsequently, the method has been extended to probe a variety of physical phenomena ranging from basic I−V characteristics to more complex properties such as thermopower and electrochemical response. By adapting the technique to a conducting cantilever atomic force microscope (AFM-BJ), simultaneous measurement of the mechanical characteristics of nanoscale junctions as they are pulled apart has given complementary information such as the stiffness and rupture force of the molecule-metal link bond. Overall, while the BJ technique does not produce a single molecule circuit for practical applications, it has proved remarkably versatile for fundamental studies. Measured data and analysis have been combined with atomic-scale theory and calculations, typically performed for representative junction structures, to provide fundamental physical understanding of structure−function relationships. This Account integrates across an extensive series of our specific nanoscale junction studies which were carried out with the STM- and AFM-BJ techniques and supported by theoretical analysis and density functional theory based calculations, with emphasis on the physical characteristics of the measurement process and the rich data sets that emerge. Several examples illustrate the impact of measured trends based on the most probable values for key characteristics (obtained from ensembles of order 1000−10 000 individual junctions) to build a solid picture of conductance phenomena as well as attributes of the link bond chemistry. The key forward-looking question posed here is the extent to which the full data sets represented by the individual trajectories can be analyzed to address structure−function questions at the level of individual junctions. Initial progress toward physical modeling of conductance of individual junctions indicates trends consistent with physical junction structures. Analysis of junction mechanics reveals a scaling procedure that collapses existing data onto a universal force−extension curve. This research directed to understanding the distribution of structures and physical characteristics addresses fundamental questions concerning the interplay between chemical control and stochastically driven diversity.

1. INTRODUCTION

development of the scanning tunneling microscope based break-junction technique (STM-BJ)7 and the discovery of selective link chemistry for reproducible bonding of the target molecule to the gold electrodes8 played a significant role. With

The early vision of encoding electronic device functionality in a single organic molecule1 came into the realm of practical experimental realization in the 1990s,2 albeit with significant challenges.3 The last ten years have seen rapid progress in the reliable formation of single molecule electronic junctions and reproducible measurement of conductance phenomena.4−6 The © XXXX American Chemical Society

Received: January 5, 2016

A

DOI: 10.1021/acs.accounts.6b00004 Acc. Chem. Res. XXXX, XXX, XXX−XXX

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Accounts of Chemical Research

conductance traces show a sequence of conductance plateaus with values near integer multiples of the conductance quantum (G0 = 2e2/h), characteristic of a gold point contact. The simultaneously measured force trace shows a sequence of linear ramps and rapid drops corresponding to elastic (reversible stretching) and plastic (irreversible drops in force due to junction rearrangement) deformations of the junction. The final rupture of the gold point contact (at ∼0.2 nm) is associated with a sharp drop in conductance and the opening of a physical gap of ∼0.5−1.0 nm. Molecules terminated with appropriate end groups, such as 1,4-bis(methylsulfide)butane (Figure 1a), bridge this physical gap with a relatively high probability, restoring electrical continuity (conductance around 10−3G0). As the junction is pulled apart further, the structure continues to evolve. The conductance changes abruptly a few times while the force undergoes several elastic-plastic deformation cycles. At the final junction rupture (near 0.4 nm), force drops to zero and conductance falls to the noise floor. This single experimental trace evinces a rich set of structures and kinetic events that govern the evolution of the electronic conduction and sustained force as a function of applied strain. The STM-BJ or AFM-BJ measurements can easily be repeated to build a data set with thousands of individual traces. The details of the sequence of conductance plateaus and the cycles of elastic−plastic deformation vary from junction to junction. However, specific signatures remain in a statistical analysis of the full data set. In particular, when all conductance data are collected into a single conductance histogram (Figure 1c), clear peaks emerge that denote most probable junction conductances for both the gold point contact and the single molecule junction. Similarly, with modest data analysis, the junction stiffness prior to the final rupture and the associated drop in force can be identified for each trace. A histogram of this rupture force and stiffness provides a chemically distinguishable measure of the link bond characteristics (Figure 1d). We have used the STM- and AFM-BJ technique to measure and understand structure−function relationships, complemented by atomic scale theory and calculations for representative junction structures.8,9,11,17−31 The histograms establish reproducible characteristics quantified by the most probable (peak) values. However, they clearly summarize much richer data. Each new trajectory represents a new physical realization of the target nanoscale junction that undergoes a driven, dynamical evolution. By integrating across our studies to date, this Account summarizes our current understanding of the key physical processes probed in the technique and illustrates the primary structure−function analyses that can be performed, emphasizing current challenges in probing structure−function relationships at the individual junction level. Section 2 provides a brief summary of the experimental and theoretical methods used. Section 3 is focused on studies of electronic characteristics. Section 4 is devoted to mechanical properties. A brief outlook appears in Section 5.

large conductance data sets for each specific molecular junction, reproducible measurements of basic conductance characteristics of single molecule circuits led to specific transport characteristics being clearly related to molecular structure and design.9 Further development of the STM-BJ technique has extended these studies to characteristics such as electrochemical10 and electromechanical11 switching, and thermopower.12 Complementary techniques, such as the mechanically controlled breakjunction, have provided advantages, such as stability over long periods allowing inelastic tunneling spectroscopy measurements at cryogenic temperature.13−15 The adaptation to conducting atomic force microscopy (AFM-BJ) enabled the simultaneous measurement of mechanical force during junction elongation,16 providing new and complementary bond rupture force characteristics of specific molecular backbones and link chemistry.17 This Account focuses specifically on the STM- and AFM-BJ technique, highlighting the rich data sets and new understanding of electronic and mechanical characteristics for nanoscale junctions. Broader comparisons of diverse approaches to molecular junctions appear in recent reviews.4−6 The basic principles of the AFM-BJ measurement are illustrated in Figure 1a. A gold-coated cantilever tip makes

Figure 1. (a) Schematic diagram of the AFM-BJ setup illustrating simultaneous conductance and force measurements for 1,4-bis(methylsulfide)butane junctions with Au electrodes. Reproduced with permission from ref 21. Copyright 2014 American Chemical Society. (b) Measured conductance (red) and force (blue) plotted against junction displacement. The molecular conductance plateau and the junction rupture location are highlighted; dashed line indicates final junction stiffness. (c) One-dimensional logarithm-binned conductance histograms created from 10 000 consecutive conductance-displacement measurements. (d) Histogram of rupture forces (inset junction stiffness) determined from over 5000 traces.

2. SUMMARY OF MEASUREMENT, ANALYSIS, AND THEORETICAL METHODS The STM-BJ and AFM-BJ measurements were performed with a tip and substrate immersed in a solution of the target molecules in nonpolar solvents or by depositing a layer of molecules on the substrate through thermal evaporation. The AFM-BJ method used a relatively stiff cantilever (50−100 nN/ nm) and standard optical detection techniques.18 The time

and breaks contact with a gold substrate while the current and the cantilever deflection are monitored, probing electronic conductance and applied force over the junction elongation trajectory. The junction is typically pulled apart several nanometers until electrical continuity is lost and the mechanical connection is irreversibly ruptured (Figure 1b). Individual B


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local atomic-scale structure was determined by energy minimization using density functional theory (DFT) based calculations, constrained by electrode separation. Electronic transport was calculated in the Landauer approach, conceptually based on determining electron reflection and transmission coefficients, but often calculated in a Green’s function approach.32 The linear response conductance was determined by G = G0T(EF), based on the electron transmission at the Fermi energy (Figures 2a−c). Further insight was gained from transmission as a function of energy over a range that included the frontier orbital of the molecule (Figure 2b). Often, transport calculations were carried out using electronic states derived from a DFT-based treatment, despite the fact that these methods exhibit inherent errors in determining the gap between frontier orbital energies and their alignment to the electrode Fermi energy.33 These lead to systematic errors in the computed conductance in comparison to experiment, for example, as benchmarked for 1,4-diaminobenzene.19 Theorists have extensively discussed these errors. Significant progress includes use of the GW approach to include electronic correlations.19,34,35 Estimates of the corrections needed to DFT-based calculations appear in our original papers. As illustrated by the electron transmission in Figure 2b, transport through most junctions studied has been via throughbond tunneling. Furthermore, it is often dominated by a single molecular orbital (dashed line in Figure 2b). Figure 2c illustrates the single-level model for through-bond tunneling yielding a single Lorentzian transmission function (Figure 2d) whose amplitude may be reduced due to asymmetry in electronic coupling to the electrodes, e.g., due to physical link bond structure. Simplified models are particularly useful for direct analysis of experimental data. The symmetric single-level model has just two parameters. In a more detailed model, the frontier orbital energy of an oligomer derives from an energy assigned to each monomer and the electronic coupling between them. The exponential dependence of the off-resonance through-bond tunneling on the molecular length follows naturally. Other physical effects include the impact of link bond derived gateway states, e.g., in the five-parameter model introduced in section 3. Figure 3a illustrates a basic mechanical model of the AFM-BJ setup for molecules with stiff backbones linked to electrodes with bonds having similar binding characteristics. For the stiff cantilevers used here, their contribution to the measured force−extension curve is minimal. The experimental time scales being much slower than the atomic scale response of the

resolution of the current and force data was limited by the electronics to a bandwidth of ∼40−100 kHz. Abrupt events in the traces thus corresponded to changes in junction structure over a 10−100 μs time scale. The basic STM-BJ method was extended in several ways through programming the extension, the bias conditions, applying a controlled temperature difference between the tip and substrate11 as well as through automated algorithms to detect and analyze conductance and force features at the individual trace level.19 For example, the piezo trajectory was programmed to hold for a period of time while the voltage underwent defined changes, enabling the measurement of AC response for an individual junction.20 Seebeck coefficients were measured from the thermoelectric current across the junction biased with a known temperature difference.12,27,31 Force traces were analyzed to isolate the final stretch and rupture event, allowing extraction of the junction stiffness and rupture force.18 Theoretical calculations were typically done for exemplary junction structures, such as the one visualized in Figure 2a. The

Figure 2. (a) Gold-1,4-diaminobenzene junction structure used for DFT-based transmission calculations. (b) DFT-based transmission calculations (data from ref 24) showing a Lorentzian fit to the highest occupied molecular orbital-derived peak that dominates transport. (c) Model system: single level at energy E0 coupled to the left and right electrode with self-energies iΓL/2 and iΓR/2 (in eV). (d) Transmission calculated from the model (equation inset) using E0 = −2 eV, ΓL = 0.15, ΓR = 0.5 eV. Shaded area is proportional to the current under applied bias.

Figure 3. (a) Schematic mechanical model of the junction together with the AFM cantilever. Reproduced with permission from ref 21. Copyright 2014 American Chemical Society. (b) Relaxed junction geometries at two points along an adiabatic elongation trajectory modeling gold-1,4diaminobutane junctions. (c) Junction characteristics versus elongation. Upper: Binding energy. Middle: Applied force (energy derivative with respect to elongation). Lower: Low-bias conductance. (b, c) Adapted with permission from ref 23. Copyright 2009 American Physical Society. C


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Accounts of Chemical Research perturbed bonds, simple mechanics for static equilibrium apply. With mechanical constraints, the atomic-scale, adiabatic potential surface that describes the microscopic junction elongation has been studied based on DFT for the total energy and various atomic-scale models for the electrodes,11,22,23 for example, in Figure 3b, with exemplary results shown in Figure 3c.23 Further details of the physical description appear in section 4.

Figure 4a and b shows two-dimensional conductanceelongation histograms,23 created by binning all data while retaining the relative displacement information. This data showed that single molecule junction conductance could extend for a distance that was proportional to molecule length and well beyond that expected for the rupture of a single N−Au bond (less than 0.1 nm).23 As illustrated by the traces in Figure 1b, these single molecule junctions often undergo several cycles of elastic-plastic deformation while maintaining a similar electronic conductance. This implies that despite changes in link bond attachment point, a similar electronic coupling is maintained. DFT-based calculations showed that the link bond formed by amines, and by other link groups with filled lone-pair states, specifically engaged an undercoordinated gold atom.8,19 When placed in other locations, like the threefold hollow or bridge site on a gold cluster or surface asperity, the structure was not stable. Minimization of the energy shifted the link bond to a specific gold atom. The strength of the donor−acceptor bond varied with the link group. For amines, it was typically in the range of 0.5−1 eV, depending on the details of the gold atomic structure, the molecular orientation and to a smaller extent, the details of the DFT methodology.8,19,22,23 This bond is strong enough to sustain the junction on the experimental time scales (10 μs to 10 ms) or longer. DFT-based calculations for elongation of model structures with thiol linkages showed significant rearrangement of nearby gold atomic structure under stress,36−38 in contrast to those with amine linkages.23,37 An exemplary computed adiabatic trajectory for 1,4-diaminobutane (Figure 3c) started with one of the amines initially bonded to an edge atom of Au model electrode motif (structure 1). Near 2 Å of elongation, the system underwent a jump. The upper nitrogen went from coordinating a gold atom on the pyramid edge to one on the pyramid top. Subsequently, a new elastic regime was entered. The maximum sustainable force for this structure was reached in the region near structure 2. The bottom N−Au bond rapidly stretched after this point, leading to bond-rupture under stress. Throughout, the conductance showed almost no change through those structural rearrangements until the final rupture where a through space tunneling regime was seen. Other junctions showed more variations in conductance with structure, but in a range that was consistent with the width of the measured conductance histograms.23 This concretely supports the hypothesis that the selective bonding motif effectively controls the electronic coupling. One of the striking discoveries in this research was that of in situ formation of junctions with covalent C−Au link bonds.25−27 Alkanes with trimethylstannane terminations were found to readily form single molecule junctions with gold electrodes and to exhibit conductance roughly 100 times larger than junctions formed with amine link groups. A unifying hypothesis, involving in situ Au-catalyzed Sn−C bond scission and direct Au−C bond formation, explained all the data, with support from DFT-based calculations of energetics and conductance.25 This reaction was subsequently observed for the model compound benzyltrimethylstannane on Au surfaces using X-ray spectroscopies to elucidate the impact of undercoordinated Au atoms on Au−C bond formation.28 Highly conducting junctions were also demonstrated with oligophenyls with one to four phenyls (P1−P4). The trimethylstannane was attached to the ring via an intervening methylene group to enable strong electronic overlap from the

3. ELECTRONIC CONDUCTION CHARACTERISTICS OF JUNCTIONS We first consider basic molecular wires formed from alkanes and oligophenyls. The insets of Figure 4a and b show one-

Figure 4. Two-dimensional conductance-displacement histograms junctions formed with (a) 1,6-diaminohexane and (b) 1,10diaminodecane. Insets: Logarithm-binned one-dimensional conductance histograms. (c) Logarithm-binned conductance histograms for junctions with amine-terminated oligophenyls. Data from ref 24. (d) Conductance as a function of N−N length in amine-terminated alkanes and oligophenyls with exponential fits. Data from ref 22.

dimensional histograms that provide a distribution of all measured conductance values from all traces for 1,6diaminohexane and 1,10-diaminodecane, respectively. The most probable conductance for 1,10-diaminodecane was found to be 50× smaller than that of 1,6-diaminohexane. The full range of 1,N-diaminoalkanes (N = 2−12) showed an exponential dependence of the most probable conductance as a function of molecule length (Figure 4d),22 expected for through bond electronic tunneling: G ∝ exp(−βL). The inferred decay constant was 0.76 ± 0.01 Å−1, well within the expected range for alkanes.3,4 Data for oligophenyls (Figure 4c) revealed a decay constant that was smaller (Figure 4d),9,22,24 as expected for tunneling through π-conjugated backbones.3,4 An overview of conductance results for junctions formed using 40 distinct molecules terminated with amine link groups illustrated clear correlations between the most probable conductance for the ensemble of junctions formed by each molecule and the molecular structure,22 such as a decrease in conductance with increasing internal dihedral angle as cos2 ϕ for biphenyls.9 D


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Accounts of Chemical Research Au−C bond to the ring π-electron states. In particular, the P1 junction, formed with 1,4-dimethylenebenzene (xylylene), exhibited a conductance approaching the quantum of conductance (most probable conductance near 0.9G0).26 A model structure for the P4 junction is shown in Figure 5a with an isosurface plot representing the transmitted wave at the

energy peak is pinned near the Fermi energy resulting in very high transmission in this case.27 Thermopower measurements for junctions formed with P2− P4 showed very high values (23.9 mV/K for P4). Furthermore, the length dependence (Figure 5d) suggested saturation. The DFT-based transmission calculations overestimated both conductance and thermopower due to DFT energy level alignment errors (section 2). With both thermopower and conductance data versus backbone length, this data set was ideal to test transport models. The single-level Lorentzian model (Figures 2c with Γ = ΓL = ΓR) requires just two parameters. However, the DFT-based, calculated transmission functions in Figure 5b suggested that a more complex model was appropriate. The features in the transmission between −1 eV and the Fermi energy robustly require near resonant gateway states coupled to off-resonance frontier orbitals on the backbone (Figure 5a). This physically motivated, five-parameter model (Figure 5a) gave the best overall fit to the available data by assigning an orbital to each phenyl group. It naturally explained the exponential decrease in conductance with length and the saturation in the thermopower.27 We now turn to discuss the widths observed in conductance histograms. Histogram widths for oligophenyls clearly vary with molecular backbone length (Figure 4c). Focusing on a large data set for the shortest, 1,4-diaminobenzene, automated algorithms detected the average value and slope of each molecular conductance plateau in each trace from the data for a large ensemble of individual junctions. Analysis showed that the width of the conductance histogram was due to junction-tojunction variation in conductance and not variations in individual plateaus as a function of elongation.19 This put the focus on understanding variations in conductance due to different junction structures. In the accompanying theoretical study, 15 junction structures were analyzed including six different metal tip atomic conformations. This limited sampling of structure motifs showed a ± 35% spread in the calculated conductance, remarkably similar to the width of the experimental histogram (±50%).19 With reference to Figure 2, variations in the nearest resonance position and electronic coupling, as well as link structure driven deviations from a simple Lorentzian form, contributed. The systematic increase in the width of conductance histograms for longer members of the oligophenyl series suggested a further role for soft molecule conformations that are easily accessed.9 Experiments where the Au−linker−backbone torsion angle can be either locked or free to rotate further confirmed this basic idea.29 For longer molecules, the individual traces and the two-dimensional histograms often showed a systematic downward tilt, contributing to the width. This drop in conductance may be due to changes in nonspecific direct, through-space backbone electronic coupling to the electrodes,30 or π−π coupling through aromatic stacks,39 as the electrode spacing opens up. Finally, variations in the image potential with electrode separation affects conductance through the level position (Figure 2c).40 Further progress in understanding electrical characteristics of individual junctions requires sufficient data beyond low bias conductance to fit an appropriate physical model, such as the two-parameter, single-level model in Figure 6a Linear response conductance probes T(EF), highlighted in Figure 6a. The Seebeck coefficient (−ΔV/ΔT) is proportional to the energy derivative of T(E) at EF (not shown). Simultaneous measurement supports fitting both Γ and E0.31,41 Another approach,

Figure 5. (a) Upper: Optimized geometry of a P4 junction with an isosurface plot of the scattering state at EF. Lower: Schematic diagram of the tight-binding model for P4 showing the five model parameters. Transmission curves for P1−P4: (b) calculated using DFT and (c) as determined by the tight binding model using the best-fit parameters. (d) Conductance values and (e) thermopower determined form experiment, tight-binding model, and DFT versus the number of phenyl units in the chain. Reproduced with permission from ref 27. Copyright 2013 American Chemical Society.

Fermi energy. The root of this state is a gateway orbital centered on the Au−C bond with σ-bonding character. On the oligophenyl backbone, the decay of this state due to the through-bond tunneling character is evident. Figure 5b shows a set of electron transmission curves as a function of energy for P1−P4. The gateway states from the Au−C bond on each side of the junction, couple by tunneling through the backbone. For P2−P4, these states form a peak centered near −0.6 eV. The width and intensity of these peaks are larger for the shorter backbones due to stronger tunnel coupling. Finally, for P1, the splitting is so large that two peaks are evident. The higher E


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applied bias. Since some junctions formed at low biases can not sustain high bias, the distribution of junction structures sampled was generally different in the two measurements. Another significant factor is the simplifications of the single level model. A second, near-by level was seen in atomic-scale calculations and other interface-related electronic states within the fundamental gap of the molecule also made small contributions to the transmission.20 These lead to deviations from the simple Lorenztian form assumed in fitting the data. More information in each individual trace would be needed to reliably apply plausible, but more complex models, for example, those in Figure 2c or 5a.

4. MECHANICAL CHARACTERISTICS OF JUNCTIONS The AFM-BJ measurements provide data for what is in general a sequence of incomplete potential surfaces (Figure 1b). The final rupture and the potential surface immediately prior to it are easily distinguished statistically and represent reproducible, physical properties of the metal-molecule link bonds; histograms of the rupture force and stiffness (Figure 1d) exhibit clear, most probable values that depend on the molecular backbone and the linking bonds.17,21 Measured results for six nanoscale junctions are collected in Table 1. The measureFigure 6. (a) Single-Lorentzian transmission curves for two junction structures based on the single-level model (Figure 2c assuming Γ = ΓL = ΓR). (b) Two-dimensional conductance-displacement histogram for Au-Bipyridine-Au junctions showing two distinct conductance peaks (high-G and low-G) that occur sequentially upon junction elongation. Right panel shows a 1D conductance histogram from the same data. Data from ref 31. (c, d) Histograms of model parameters defined in (a), derived from measurements on all traces from an ensemble of individual junctions for low-G and high-G conductance configurations of 4,4′-bipyridine junctions. Main panels: electrode coupling, 2Γ. Insets: energy level, E0. (c) Parameters from over 2000 zero-bias conductance and thermopower measurements. Data from ref 31. (d) Parameters from over 1000 AC based measurements at 750 mV DC bias. Data from ref 20.

Table 1. Series of Nanoscale Junction Mechanical Characteristicsa expt junction Au−C4NH2 Au−BDA Au−BP (low-G) Au−C4SMe Au−Au Ag−Ag

expt fit

theory

Frupt (nN)

Fmax (nN)

Lbind (Å)

Fmax (nN)

Lbind (Å)

Ebind (eV)

0.6 0.4 0.8

0.8 1.0 1.0

1.4 1.4 1.2

0.85 0.46 1.04

1.23 1.09 1.15

0.65 0.37 0.63

0.7 1.5 0.9

0.9 1.8 1.1

1.4 1.9 1.2

0.85 1.49 0.87

1.27 1.01 1.06

0.69 0.92 0.67

a

Comparison of the most probable values from experiment to those derived from DFT-based calculations (refs 16 and 20; Figure S2). The specific molecular junctions formed with Au electrodes: Au−C4NH2, 1,4-diaminobutane; Au-BDA, 1,4-diaminobenzene; Au-BP, 4,4′-bipyridine; and Au−C4SMe, 1,4-bis(methylsulfide)butane. Metal point contacts: gold (Au−Au) and silver (Ag−Ag).

based on AC techniques, yields both parameters based on measurement of differential conductance and second derivative information at finite bias.20 Both methods have been applied to 4,4′-bipyridine junctions formed with Au electrodes. Prior studies showed that 4,4′-bipyridine junctions distinguishably formed with high and low conductance peaks observed in a bimodal histogram (Figure 6b).11 Accumulated evidence showed that the high-G junction conformation formed first, when the junction was relatively compressed with the molecule tilted relative to the electrode and with additional dispersion interactions between the pyridine ring and local asperities in the gold electrodes.18 In this geometry, an enhanced coupling to the electrodes gave a higher conductance.11 The low-G junction emerged in near-vertical geometries, bound to the electrodes only through Au−N donor−acceptor bonds, in the last stage of junction elongation. In both cases, conductance was dominated by the lowest empty π-orbital. Figure 6c shows the distributions of model parameters, derived trace by trace from simultaneously measured low-bias conductance and thermopower.31 Overall, Γ was smaller in the low-G junctions, consistent with the physical picture of junction formation, while the values for E0 spanned a wide range. Figure 6d shows results for the same parameters determined from AC measurements.20 The trend for Γ was similar, but the two methods gave distributions that differ. This may be in part because the AC measurement was carried out at 750 mV of

ments for single molecule junctions distinguish chemical trends in bonding, in agreement with DFT-based calculations discussed below. For example, 1,4-diaminobutane, with its sp3-derived lone-pair makes a stronger donor−acceptor bond to gold than 1,4-diaminobenzene, where the lone-pair mixes with the π-states on the ring, reducing the Au−N bond strength. The rupture force from the high-G configuration for 4,4′bipyridine is considerably larger than that from the low-G configuration, as is the junction stiffness, due to a significant dispersion interactions between the pyridine rings and the Au electrodes.18 The simulations in Figure 3 provide the potential surface for an exemplary junction structure with amine link bonds, including an internal jump in structure and the final rupture of a link bond. The junction force−extension curve can be followed through a maximum sustainable force (Fmax) and well into the regime when the weakest bond has only a small attraction. The overall potential surface or force−extension curve is a property of the full mechanical system. However, F


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To make further progress in probing link bond characteristics from the AFM-BJ data, we need a physical description of the force−extension curve with a minimal number of parameters that can be applied to the measured, individual segments, which generally do not start at the energy minimum or end at the force maximum. The system drops into the potential for the last structure probed prior to final rupture under a condition of finite stress and ruptures stochastically, typically near the maximum force region. Using DFT-based calculations as a guide, we investigated simple interaction forms with two parameters, including Leonard−Jones and Morse potentials, but found that the shape did not fit well.21 However, we were able to develop a new, two-parameter functional form for the potential surface that combined an elastic model around the potential minimum with a simple, symmetric logistical function in the region of the force maximum.21 The two parameters that characterize this potential, or equivalently, the force−extension curve, are the force maximum (Fmax) and the distance Lbind from the potential minimum to Fmax (Figure 7b) as detailed in the original paper. This form has been found to make an excellent fit to a large body of measured force extension curves (Figure 8a) with individual fit values that form physically plausible distributions (Figure 8b). The most probable fit values are shown in Table 1. The value for Fmax is systematically larger than the rupture force, as it should be on physical grounds, and correlates very well with the DFT calculations. The most probable values of Lbind are larger than those found in the simulations, perhaps reflecting the limited model structures for the electrodes. This analysis revealed that a simple rescaling by Fmax and Lbind resulted in dramatic data collapse. When applied to the computed force−extension curves, the scaled curves aligned nearly perfectly over the region from zero to the force maximum (Figure 7c). In the region beyond the force maximum, there was more spread and asymmetry. Turning to the measured data, on a trace-by-trace basis, each experimental force−extension curve was scaled by individually fitted Fmax and Lbind values. Then results of measurements from an entire ensemble of individual junctions were plotted together in a scaled, two-dimensional histogram.21 In fact, the entire data set spanning the six different junction types has been collapsed into the histogram shown in Figure 8c. It follows a universal force− extension curve to a remarkable degree. The asymmetry around Fmax seen in Figure 7c has a simple physical explanation. Referring to the mechanical model in Figure 3a, energy is stored in both link bonds during initial elongation, reducing the effective stiffness prior to bond rupture, compared to the potential surface of a single bond. As dictated by static equilibrium, the weakest of the link bonds determines the maximum sustainable force. Beyond that point, the sustained force drops. The weaker bond extends toward complete rupture. At the same time, the stronger bond relaxes back toward its potential minimum, releasing stored energy. The relaxation of the stronger bond acts to reduce the junction separation, at the same time the weaker bond is continuing to open up. As a consequence the drop in force per unit extension beyond the maximum is more abrupt than would be expected from the potential surface of a single bond. If the stronger bond is much stiffer than the weaker one, the net effect leads to minimal asymmetry around the maximum force. On the other hand, the force−extension curve is most asymmetric for nearly equivalent bonds in which the strong bond stores nearly as much energy as the weaker bond that undergoes final rupture.

based on static equilibrium, the forces exerted by the stretched link bonds on the molecular backbone must be equal and opposite. Therefore, the maximum sustainable force will be a property of the weakest bond in the junction, which is typically one of the link bonds. In the experiments, since the AFM cantilever is much stiffer than the link-bond that ruptures, it does not introduce any mechanical instabilities.21 The linkbond ruptures due to stochastic events involving other microscopic degrees of freedom. As a consequence, the measured rupture force need not be the same as the maximum sustainable force, with rupture observed both before the maximum and, albeit more rarely, after it. Calculated binding energy curves for metal/molecule pairs in Table 1 have been obtained using Au clusters to represent the electrodes,17 maintaining the same overall junction structure to enable direct comparison of trends with experiment (Figure 3b, structure 2, and Figure S1). The results are plotted in Figure 7a and b, showing a range of link bond energy and maximum sustainable force among these nanoscale junctions. The Fmax for each exemplary junction structure is given in Table 1, showing a good correlation to the most probable measured rupture forces.

Figure 7. Calculated junction binding energy (a) and force (b) versus elongation for representative structures. (c) Normalized, calculated force−extension curves together with the model form (solid line). See Table 1 and Figure S1 for the specific junctions. G


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5. CONCLUDING REMARKS We have illustrated the remarkably versatility of the STM- and AFM-BJ techniques, combined with the donor−acceptor class of metal-molecule link groups, in the study of single molecule junction structure−function relationships. We have highlighted the rich data sets that emerge for ensembles of individual junction structures in the measurements and initial research directed to map and interpret the physical characteristics across those ensembles. Key issues for future research include the relative simplicity of the two-parameter models used and the need for more distinguishable information to be collected for each individual trace, for example, more extensive I−V curves or force−extension data beyond the force maximum. Equally important will be to better understand the distribution of physical junction structures that result due to variations in control and environmental variables such as competing chemical species, temperature, measurement dynamics, and applied voltage. Such research will probe grand-challenge questions directed to the degree of chemical control over functional characteristics that can be exerted in nanoscale systems.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.accounts.6b00004. Model junction structures and histograms of derived Fmax values supporting Table 1 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].

Figure 8. (a) Sample of measured force traces for Au−1,4bis(methylsulfide)butane junctions and Au single-atom contacts showing fits of the last force feature to the model curve. (b) Histogram of Fmax derived from fits to more than 2000 individual Au− 1,4-bis(methylsulfide)butane junction force traces. Inset: Histogram of Lbind. (c) Composite two-dimensional histogram of normalized force and displacement determined from over 13 500 force traces measured for six different junction types in Table 1. Solid line: model curve. Data from ref 21 and Figure S2.

Notes

The authors declare no competing financial interest. Biographies Mark S. Hybertsen received his Ph.D. in Physics from University of California at Berkeley (1986). Following appointments at Bell Laboratories (1986−2002) and Columbia University (2003−2006), he is now leading the Theory and Computation Group in the Center for Functional Nanomaterials at Brookhaven National Laboratory. Latha Venkataraman earned her Ph.D. in Physics at Harvard University (1999). She is currently an Associate Professor at Columbia University in the Departments of Applied Physics and Applied Mathematics and of Chemistry.

In a large sample of junctions, the two link bonds will rarely be closely matched, but some asymmetry is to be expected. Experimentally, very few junctions rupture beyond Fmax (Figure 8c) due to the bond energy scale and the experimental time scales relative to the impact of thermal fluctuations. The asymmetry seen in the simulations and that we can expect on physical grounds to vary from junction to junction, requires further research directed both to extended models and obtaining further data. A challenging goal is to derive the binding energy for each individual junction. The energy depends on the specific form of the force−displacement curve in the region beyond Fmax. This is unfortunately precisely the region where the present measured data is sparse, and where simulations indicate a variation in shape of the force−displacement curve that depends on the link bond asymmetry in the junction. While the present model gives plausible results, this requires further investigation as well.

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ACKNOWLEDGMENTS We thank our collaborators who contributed to the work described here. This work was supported by the NSF DMR1507440 and the Packard Foundation. A portion of this work was performed using facilities in the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science User Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704.

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