Resolving metal-molecule interfaces at single-molecule junctions

Electronic and structural detail at the electrode-molecule interface have a significant influence on charge transport across molecular junctions. Despite the decisive role of the metal-molecule interface, a complete electronic and structural characterization of the interface remains a challenge. This is in no small part due to current experimental limitations. Here, we present a comprehensive approach to obtain a detailed description of the metal-molecule interface in single-molecule junctions, based on current-voltage (I-V) measurements. Contrary to conventional conductance studies, this I-V approach provides a correlated statistical description of both, the degree of electronic coupling across the metal-molecule interface, and the energy alignment between the conduction orbital and the Fermi level of the electrode. This exhaustive statistical approach was employed to study single-molecule junctions of 1,4-benzenediamine (BDA), 1,4-butanediamine (C4DA), and 1,4-benzenedithiol (BDT). A single interfacial configuration was observed for both BDA and C4DA junctions, while three different interfacial arrangements were resolved for BDT. This multiplicity is due to different molecular adsorption sites on the Au surface namely on-top, hollow, and bridge. Furthermore, C4DA junctions present a fluctuating I-V curve arising from the greater conformational freedom of the saturated alkyl chain, in sharp contrast with the rigid aromatic backbone of both BDA and BDT.


Scan rate dependence of the I-V curves
shows examples of I-V curves for the BDA molecular junctions measured for both forward and backward bias voltage scans. We checked bias-voltage-scan-rate dependence of the current fluctuation within the range of 4 to 400 Hz and found that, for BDA molecular junctions, the current fluctuation was considerably scan-rate dependent ( Figure S1). Because the BDA molecule has rigid benzene backbone, the current fluctuation is most probably due to the effects of structural variation in the metal-molecule contact configuration. At slower scan rates, current fluctuation is apparent, which can be ascribed to current-induced heating and resulting structural changes in the metal-molecule contact configuration (see the upper panel in Figure S1). We found that a scan rate of between 40 and 400 Hz was fast enough to obtain I-V curves without the large current fluctuations most probably arising from structural changes in the metal-molecule contact configuration. Figure S1. Examples of I-V curve and normalized (dI/dV)/I-V plot for the BDA molecular junction measured for both forward and backward bias voltage scans. The scan rate is (a,d) 4 Hz, (b,e) 40 Hz, and (c,f) 400 Hz. In (d)-(f), data in the lower bias range is not plotted due to inaccuracy in the bias voltage.
To statistically analyze the current fluctuation, we calculated the following quantity for each I-V curve.
where n is number of the current-data points in each I-V curve, Imeasure is measured current at each data point, Iexpect is expected current, which was calculated from linear fitting using 10 data points before the data point of Imeasure. Figures S2a,b show histograms of the current fluctuation of σ (see eq. 1) for I-V curves with the scan rates of 40 Hz and 400 Hz for the BDA junction. At the lower scan rate of 40 Hz, the current fluctuation exhibits a peak value at 10 -3 , while, at the faster scan rate at 400 Hz, the current fluctuation-peak shifted to lower value at 10 -3.5 . It should be noted that I-V curves were taken at the lower scan rate of 4 Hz but we could not constantly curves with the larger current fluctuation from 10 -2 to 10 -1 revealed that the current fluctuation was partially originated from discrete transition of current values in I-V curves, which can be due to sudden change in the BDT junction (i.e., change in the metal-molecule contact configurations).
Based on the structural models ( Fig. 5), the structural changes correspond to the change in the metal-molecule contact configurations between the hollow and bridge binding geometries. In contrast to the on-top binding geometry at a larger electrodes-separation, the hollow and bridge binding geometries can formed at a similar and smaller electrodes-separations, which can enable the structural transition between the he hollow and bridge binding geometries. clarified the existence of several preferential conductance states, the identification of the conductance states is still a challenging task, most probably due to difficulties in routinely performing repeated spectroscopic measurement of the single molecular junctions and analyzing the spectroscopic data in a qualitative manner.
In this study, we developed a statistical approach to measure the I-V characteristics of single molecular junctions in a qualitative manner using the single channel transport model and to identify the junction-structures on the basis of the I-V data. Curve fitting on the bias of Eq. 3 for the two preferential conductance states of the BDT junction (i.e., the two averaged I-V curves in Figure 2b) yielded values of Γ = 85 meV and ε0 = 0.68 eV and Γ = 105 meV and ε0 = 0.70 eV for low and high conductance states, respectively, in which the number of bridging molecules, n, was fixed to be 1. On the other hand, the high conductance state can be fitted by varying n, and we found a fitting result of Γ = 75 meV and ε0 = 0.71 eV for n = 2 for the high conductance state (see also Table 1). The number n is likely to be arbitrary, but it has been reported in a large number of the previous single molecular conductance-studies that (i) the most probable number is 1, (ii) the maximum number of n is typically less than n = ~3 or 4, and (iii) formation probability of the multiple molecular junctions are low (e.g., triple junction-formation probabilities of < 28% S8 , 18-55% S9 , and N.A. S10 can be estimated by a comparison of molecular conductance-peak-intensities in conductance histograms. Therefore, the initial curve-fitting was performed with n = 1 and then the multiple-junction formation with n> 1 were considered in our I-V fitting procedure). The obtained set of Γ and ε0 values were closely similar to those found for the low conductance state. The obtained set of Γ and ε0 is closely similar to that found for the low conductance state. For the BDA molecular junctions, the "single" conductance state and the corresponding set of Γ and ε0 values were obtained by fitting statistically averaged I-V characteristics within a reasonable choice of n, which indicates that the single BDA junction displays a single conductance state with a preferential metal-molecule contact configuration.
It should be noted that, in a separate STM-BJ experiment at a fixed bias voltage, formation of the double BDA molecular junction with n = 2 can be seen, as shown in Figure S3.

Normalization of the averaged I-V curves of the BDT molecular junction
To take into account the number of bridging molecules (n), the statistically averaged I-V curves of M1, M2, and L were normalized to overlap them each other on the basis of the current at 0.3 V ( Figure S6). The multiplication factors are 3, 1, and 0.5 for the curves of L, M1, and M2, respectively. The normalized curves of M1 and M2 are almost identical in the full bias-voltage arrangement, while there is a striking mismatch between L and M (M1 and M2). These results indicate that M1 and M2 belong to the same conductance state (i.e., M) with different values of n = 1,2 (see Figure S6); furthermore, this reconfirms that M and L are distinct conductance states.
It should be note here that the conductance of H is more than one order of magnitude larger than that of M, and therefore, the difference in the conductance between H and M is unlikely to be explained by the difference in the number of the bridging molecules (n).  Figure S7 shows the conductance histogram for the single BDT molecular junction measured at the fixed bias voltage of 20 mV using the STM-BJ method. The histogram shows three peaks at 0.7, 2, and 20 mG0, which correspond to the three states observed by the I-V measurement (see Table 1). The difference of the conductance value between the STM-BJ experiment and the I-V experiment can be explained by the experimental conditions. The conductance of the single molecular junction is measured during the stretching the contact at the fixed low bias voltage (20 mV) in STM-BJ experiment, while it is measured at the fixed electrode separation by sweeping the wide voltage-range (±1 V) for the I-V measurement.  Table S2. List of the BDT-single molecular conductance obtained by STM-BJ experiment.

Symmetry analysis in the shape of the I-V characteristics
Statistical analysis in the I-V characteristics of the single molecule junctions revealed that BDA and BDT studies here display symmetric shapes in the I-V characteristics with α = 0.5 (α = ΓL / ΓR. See Eqs 1-3 and Tables 1 and S1). Figure S8 shows histograms of the current ratio in the molecular I-V curves at the bias voltages of ±1.0 V for the BDA and BDT molecular junctions.
The current ratio was calculated by dividing the current at 1 V with that at -1 V in the I-V curves.
The I-V curves were found to be symmetric at the positive and negative bias voltages with log(current ratio) = 0 ( Figure S8).

Theoretical models
Figures S9 and S10 show theoretical models of BDT molecular junctions. In the present theoretical models of the BDT junctions, the Au electrodes (clusters) with different shapes consist of different numbers of Au atoms. Therefore, we could not directly compare the energetic stability of the calculated system. In previous theoretical studies, related energetic stability has been investigated for models with thiolate sitting on hollow, bridge and on-top sites on Au surface S11-S13 . Although there are (small) discrepancy on the relative energetic stability among the theoretical calculations, the theoretical studies have suggested the existence of the hollow, bridge and on-top adsorption geometries for thiolate on Au surface. Based on the previous findings, the BDT-junction-models with the hollow, bridge and on-top adsorption-geometries were relaxed and used for the transport calculations in the present study. In addition to the above-mentioned Au/thiolate/Au junctions, we considered formation of Au/thiol/Au junctions, in which the S atom in the Au-S binding group is hydrogenated S14,S15 . It should be noted that, although it has been commonly accepted that a thiol group becomes dehydrogenated during the adsorption and molecular film-formation process on Au surface S16 , theoretical studies have demonstrated existence of Au/thiol/Au junctions (e.g., see refs [S11,S12]). In relaxed hydrogenated geometry (on-top geometry), molecular orbital that is responsible for charge transport displayed spatially localized nature, which leads to significant reduction of low bias molecular conductance.