To gain more information about the structural evolution of these junctions, we per-formed AFM-BJ measurements on DAF and DAT molecules. We measure conductance and force simultaneously during the elongation and rupture of the junctions, using a custom-built AFM-BJ setup [26]. We use the measured conductance to identify the dif-ferent junction structures such as metallic point-contact, monomer or dimer junctions, then we analyze the measured force signal to determine and compare the mechanical properties of these junctions.
Typical conductance and force traces are shown on Figure 4.11 measured with DAT and DAF molecules. During the elongation of a stable gold contact, the measured force increases linearly as the junction is elastically deformed until the atoms of the electrode rearrange causing a sudden force drop. These repeated load and rupture events result in a saw-tooth shaped pattern in the measured force signal. In the case of a molecular junction, there are usually multiple load and rupture events present, which are generally attributed to the linkers changing the attachment position on the electrodes [21]. The last loading event before the rupture of the molecular junction corresponds to a junction, where the molecule bridges the smallest gap between the electrodes and is being stretched as the electrodes are further separated. We observe that even in the case of the dimer junctions, the measured force does not go continuously to noise, instead, a clear force loading is visible before the rupture of the dimer junction.
We explore the rupture force of the stacked dimers by examining the force necessary to rupture the monomer and dimer junctions. We define the rupture force as the difference between the force acting on the junction when it ruptures and the force measured after the final rupture event when there are no mechanical connections between the sample and tip. A commonly used technique for extracting the average rupture force of a given junction structure is to construct two-dimensional force histograms. First, the measured conductance is used to determine the displacement position of the rupture event. Then the force traces are aligned at this point both along the displacement and the force axis:
each trace is offset to have zero displacement and zero force at the position of the rupture event. One can extract the average force curve from such a force histogram by fitting each vertical line with a Gaussian and overlaying the peak position on top of the two-dimensional force histogram [26].
Figure 4.11: Sample conductance and force vs. displacement traces for DAT (A,B) and DAF (C,D) molecules. Regions of the monomer and dimer junctions are highlighted with red and yellow background. Multiple load and rupture events are observed during a single conductance plateau.
Figure 4.12 shows two-dimensional conductance and force histograms aligned at the point of rupture for metallic, monomer and dimer junctions. In case the traces are aligned at the final rupture event (Figure 4.12/F), the average rupture force can be determined by measuring the drop of the average force curve after the point of the rupture. This method can be used to extract the rupture force of the dimer junctions but not the monomers.
In the case of the monomers (Figure 4.12/D), when the junction breaks, a force loaded dimer junction is formed. Therefore the drop of the average force curve, when aligned at the monomer rupture point, will be smaller than the actual force necessary to rupture these junctions.
Figure 4.12: Two-dimensional conductance and force histograms for DAF, aligned at the rupture of the metallic (A,B), the monomer (C,D) and the dimer (E,F) junction.
Due to the monotonic nature of conductance traces, all three features (single atom
contact, monomer, dimer) can be identified on all of the conductance histograms (Fig-ure 4.12/A,C,E) and thus the evolution of the meas(Fig-ured conductance can be inferred independently of the alignment point. On the contrary, the measured force signal is not monotonic, it shows several load and rupture events and the length of these events is different on every measured trace. As a result, the overlaid traces quickly become blurred when moving away from the alignment point. Thus the average force curve, extracted from the two-dimensional force histograms, is only valid in the close vicinity of the alignment point, the only valid information it provides is the amount, the force signal drops when transitioning from one junction structure to the other. Therefore these force histograms and the average force curve does not allow us to compare the force that is required to rupture the different junction structures.
To overcome this problem, we construct a new type of scaled two-dimensional conduc-tance and force histograms where we align the measured traces at multiple points along the horizontal axis (Figure 4.13/A,B and D,E for DAF and DAT molecules). The align-ment points are the rupture of the metallic, monomer and dimer junctions. To achieve this, we need to scale the length of the conductance plateaus, such that the length of the monomer/dimer junctions is the same on all of the overlaid traces. We scale each molecular plateau so that the length would equal the average step length measured in the corresponding conductance range, as determined from an analysis of plateau lengths (see the inset on Figure 4.13/A and D). Thus we label the X axis as averaged displacement.
Force traces are also aligned along the vertical axis by offsetting each trace to have zero force at the position after the final rupture event. Since the horizontal axis is scaled, the relative displacement information is lost but force information is retained throughout the rupture process: the resulting average force curve shows how the measured force changes during the extension of the junction. Using such a two-dimensional scaled force histogram, the rupture force for both the monomer and the dimer junctions can be determined by simply evaluating the average force curve at the point where the corresponding molecular junction breaks. In the case of the DAF molecule (Figure 4.13/B), monomer junctions break at 0.72 nN, while dimer junctions rupture at a significantly lower force of 0.12 nN.
Similarly, DAT molecule (Figure 4.13/E) also shows a significant difference between the rupture force of the monomer (0.43 nN) and dimer junctions (0.05 nN). In principle, a dimer junction can either rupture at a molecule-gold bond on one electrode or at the molecule–molecule interface. This significant difference in their rupture forces indicates that the dimer junctions rupture at the inter-molecular interface.
A closer examination of the scaled conductance and the force histogram reveals that during the elongation of the dimer junctions, both the average conductance and force are decreasing. This is even more visible on a conductance versus force histogram obtained by simply plotting the measured conductance against the force for each trace and overlaying the resulting curves (Figure 4.13/C and F for DAF and DAT molecules) [27, 108]. In the region of the dimer junction, there is a tilted elliptic feature indicating a positive correlation between conductance and force. To determine the value for the correlation, we fit the conductance region of the dimer junctions with a 2D Gaussian, contours of the fit are indicated with dashed black line. From the parameters of the fit, we determine, that the correlation is 0.31 and 0.34 for DAF and DAT dimer junctions, respectively.
Figure 4.13: Scaled conductance and force histograms and conductance versus force his-tograms for DAF (A-C), DAT (D-F) and 4,4’ bipyridine (G-I) molecules. The inset on the scaled conductance histograms shows the distribution of the plateau length, as measured in the conductance region of the lower (red line), higher (blue line) histogram peak and in the entire molecular conductance range (black). When constructing the scaled two-dimensional histograms, the average values of the plateau length in the different conductance regions are used for scaling the overlaid conductance and force traces.
We used the monomer junctions to verify the significance of these levels of correlation.
Thus we performed the same fit for the region of the monomer junctions (see the contours on Figure 4.13/C and F, in the conductance region of the monomers). The resulting cor-relations are 0.04 and 0.09, significantly smaller compared to the corcor-relations determined for dimer junctions. We identify the correlation between the measured conductance and force signals as a characteristic property of dimer junctions. We expect that both con-ductance and force depend largely on the extent of the overlap at the molecule–molecule interface, which results in correlated conductance and force signals.
To support the above statement, that the observed correlation is indeed characteristic to dimer junctions, we compared the conductance and force histograms of DAT and DAF molecules with measurements on a control molecule. Previous investigations on 4,4’-Bipyridine (BP) have shown that this molecule exhibits a high and a low conductance junction configuration. In contrast to DAT and DAF molecules in the case of BP, both junction configurations correspond to a single molecule bridging the gap between the two electrodes [21, 82]. Figure 4.13/H shows the scaled force histogram for BP junctions.
The rupture force of the final, low conducting configuration (0.26 nN) is significantly larger compared to the rupture force of DAT and DAF dimer junctions. The scaled force histogram also shows, that during the elongation of the low conducting configuration the average rupture force is constant, in contrast to DAT and DAF dimer junctions which show a decrease in the measured force signal during the elongation of the junction. Furthermore, conductance versus force histogram (Figure 4.13/I) shows that both the high and low conducting junctions exhibit uncorrelated conductance and force signals. The correlation coefficient obtained from 2D Gaussian fits is less than 0.02 in both cases. This is negligible compared to the correlation measured with DAT and DAF dimer junctions (around 0.3).