Zoltán
Balogh
a,
Dávid
Visontai
b,
Péter
Makk
a,
Katalin
Gillemot
b,
László
Oroszlány
c,
László
Pósa
a,
Colin
Lambert
b and
András
Halbritter
*a
aDepartment of Physics, Budapest University of Technology and Economics and MTA-BME Condensed Matter Research Group, 1111 Budapest, Budafoki ut 8, Hungary. E-mail: halbritt@mono.eik.bme.hu
bPhysics Department, Lancaster University, LA1 4YB, Lancaster, UK
cDepartment of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, 1111 Budapest, Budafoki ut. 8., Hungary
First published on 29th September 2014
Experimental correlation analysis and first-principles theory are used to probe the structure and evolution of Ag–CO–Ag single-molecule junctions both before the formation and after the rupture of the junctions. Two dimensional correlation histograms and conditional histograms demonstrate that prior to the single-molecule bridge configuration the CO molecule is already bound parallel to the Ag single-atom contact. This molecular precursor configuration is accompanied by the opening of additional conductance channels compared to the single-channel transport in pure Ag monoatomic junctions. To investigate the post-rupture evolution of the junction we introduce a cross-correlation analysis between the opening and the subsequent closing conductance traces. This analysis implies that the molecule is bound rigidly to the apex of one electrode, and so the same single-molecule configuration is re-established as the junction is closed. The experimental results are confirmed by ab initio simulations of the evolution of contact geometries, transmission eigenvalues and scattering wavefunctions.
In this paper we address the additional question of how one can investigate the evolution of the binding molecule prior to the formation of a single-molecule junction, and after junction rupture. To this end we investigate the interaction of carbon-monoxide molecules with silver atomic-sized junctions using two dimensional correlation histograms and conditional histograms, and we introduce a new type of correlation histogram based on the cross-correlation analysis of opening and subsequent closing traces.
Based on the correlation analysis of opening traces we find that the formation of the single-molecule junction can be foreseen from the appearance of a molecular precursor configuration,29–31 which has additional open conductance channels compared to clean Ag single-atom contacts. This precursor configuration is associated with a CO molecule bound parallel to a dimer Ag single-atom contact. After this precursor configuration, single-molecule bridges are formed, which are identified by the conductance histogram itself. A final configuration conductance histogram is capable of resolving the splitting of the single-molecule peak into two subpeaks, which are interpreted as the perpendicular/parallel orientation of the CO molecule with respect to the contact axis. Finally, the cross-correlation analysis of opening and subsequent closing traces implies that after junction rupture, the CO molecule stays rigidly bound to the apex of one electrode instead of leaving the junction or flipping to the side of the apex. The experiments are supported by ab initio simulations, which confirm both the interpretation of the molecular precursor configuration and the post-rupture evolution, i.e. the rigid binding of the molecule to the apex of one electrode.
The histogram peak of single-molecule junctions seems to exhibit a shoulder at ≈0.2G0. To further analyze this, we have constructed a final configuration histogram (see the inset in Fig. 1), i.e. a conductance histogram for the last 10 datapoints of each conductance trace before the conductance jumps below a threshold of ≈0.01G0. According to our estimation this histogram is related to the final ≈1 Å displacement before the contact rupture. The final configuration histogram shows a clear splitting of the single-molecule peak: two subpeaks are observed at ≈0.18G0 and ≈0.33G0, which we interpret as a perpendicular and a parallel CO molecule, like in Pt–CO–Pt single-molecule junctions.9 In the traditional conductance histogram the finite slope of the single-molecule plateaus leads to the fusion of these two subpeaks.
The final configuration histogram is also an appropriate tool to estimate the probability of molecular contact formation. According to the weight of the molecular and the single-atom region in the inset of Fig. 1, one can state that approximately 20% of all traces break from a single-molecule junction, whereas the rest of the junctions break from an Ag single-atom contact.
We note that the clear subpeaks in the histogram support the assumption that a single molecule is contacted: multiple molecules would lead to a broader variety of contact geometries and a smearing of the histogram peak. Additionally, the small probability of molecule binding (≈20%) makes the formation of multiple molecule junctions unlikely.
As a next step we analyze the statistical relationship of the various contact configurations. To this end we apply the two dimensional correlation histogram (2DCH) technique introduced by some of the authors in ref. 24,25. The 2DCH is defined as a two-dimensional correlation function:
(1) |
Fig. 2b shows the 2DCH for Ag–CO junctions. The two axes correspond to the two conductances, and the color shows Ci,j. Negative correlations are shown by cold colors (blue and black), positive by warm (yellow-red), and the green areas mark the regions where the correlation is zero within the accuracy of the method. For further investigation we have defined three conductance regions, which are shown by different colors in panels (a) and (c), and are separated by black dashed lines on panel (b). Region I (RI, orange) is related to the molecular configuration (0.1G0–0.8G0), the second interval (RII, yellow) corresponds to conductance of the single-atom Ag contacts (0.8G0–1.15G0) and the third (RIII, red) to the conductance region slightly above the single-atom peak (1.15G0–1.4G0). Fig. 2b shows a clear anti-correlation between RI and RII and between RII and RIII. However, a positive correlation is observed between RI and RIII, which suggests that region III corresponds to a so-called precursor configuration from which the single-molecule junction is likely to be formed. Optionally a pure Ag single-atom contact is formed, but then neither the precursor configuration, nor the single-molecule configuration is observed. These two optional trajectories are demonstrated by the two sample traces on panel (c). Note that the 2DCH does not resolve any clear distinction between the two molecular subpeaks demonstrated in the inset of Fig. 1.
To obtain further justification we also study the correlations with the conditional histogram technique, i.e. with histograms constructed only from those traces that have larger than average number of datapoints in a certain conductance interval.25 In Fig. 2a the blue curve represents the conditional histogram for RI, the green curve is the conditional histogram for RII, whereas the black histogram is the traditional histogram for the entire dataset. By definition all the histograms are normalized to the number of included traces. Again, a clear anti-correlation is seen for the two selections: for the green histogram (selection for RII) the molecular peak disappears, whereas for the blue one (selected for RI) the peak at 1G0 disappears, and instead a new, wider peak appears around 1.3G0. This positive correlation was already seen in the 2DCH and corresponds to the precursor configuration of the molecular junction, indicating that the CO molecule first binds to the side of the Ag–Ag junction and by opening an additional transport channel increases the conductance from 1G0 to 1.3G0.
It is well known from conductance fluctuation measurements that pure Ag monoatomic junctions have a single, highly-transmitting conductance channel, and the further channels give negligible contribution to the conductance.33 This single-channel transport is related to conduction solely by s electrons.35 As a consequence, the histogram of pure Ag shows a sharp upper edge of the single-atom peak at 1G0. With this knowledge it is clear that the precursor configuration – which has a conductance significantly above 1G0 – is definitely not a pure monoatomic Ag junction. Conceivably it is rather a monoatomic Ag junction with a CO molecule bound to the side. In the latter case the CO molecule may open up parallel channels for transport, and so conductance is no longer limited to 1G0.
It is to be emphasized that the molecular precursor configuration is hidden in the traditional conductance histogram, as it is suppressed by the sharp peak due to pure Ag monoatomic configurations. Similarly, the traditional conductance histogram does not reveal the fate of the molecule after the rupture of the junction, which is analyzed in the next section.
After rupture of the junction the molecule may either stay rigidly bound to the apex of one electrode tip, or alternatively, it may flip to the side of the electrode, or even diffuse further away. These two situations can be distinguished based on the closing trace, i.e. by recording the conductance trace when the junction is closed after the complete rupture. If the molecule stays rigidly bound to the junction, it is likely that the closing trace will show the same molecular configuration as the opening trace. On the other hand, if the molecule leaves the junction, the closing trace will not show any molecular configuration (see illustration in Fig. 3).
To investigate this, we introduce a new type of correlation histogram based on the cross-correlation of the opening and the subsequent closing traces:
(2) |
Here, r denotes an entire opening–closing trace pair, Ni(r) is the number of datapoints in bin i within the opening part of the trace, whereas N′j(r) is the number of datapoints in bin j within the closing part. In contrast to eqn (1) the diagonal of the opening–closing cross-correlation function is not unity, C′i ≠ 1, as Ni(r) and N′i(r) are not related to the same part of a conductance trace. Therefore, a high positive value of C′ around the diagonal indicates that the closing part of the traces follows similar junction configurations as the opening part. Specifically for the Ag–CO–Ag single-molecule junctions a positive correlation is expected between the RI of the opening part and the same conductance interval of the closing part (denoted by RI′) if the molecule stays rigidly bound to the tip apex, whereas a close to zero correlation is expected between RI and RI′ if the molecule flips to the side after the contact rupture.
Fig. 4b shows the correlation matrix obtained with the definition above. The vertical axis belongs to the opening, whereas the horizontal to the subsequent closing process. Going along a horizontal line gives the relationship between a given configuration of the opening process and the various configurations along the subsequent closing process. The dashed lines mark the same conductance regions as those in Fig. 2. It is clear that the molecular configuration in the closing part (RI′) positively correlates with the molecular configuration in the opening part (RI), whereas the single-atom configuration in the closing part (RII′) is negatively correlated with the molecular configuration in the opening part (RI). The correlation diagram indicates that if the molecular junction was formed during the opening process, then it is likely that it will be formed during the closing process as well, whereas if no sign of the presence of the molecules was seen during the opening, then this will likely be the case for the closing process too.
This is even better demonstrated by Fig. 4a, where the conditional histograms are plotted for the closing traces. Here the conditional histograms were selected according to the opening process: the blue line shows the histogram for the closing part of those traces, in which the molecular configuration (RI) has higher than average weight during the opening part, whereas the green curve shows the closing histogram for the traces with higher than average weight of the single-atom configuration (RII) along the opening part. As a reference the closing histogram for all Ag–CO traces (black histogram) and the closing histogram for a pure Ag dataset (grey) are also shown. The clear peak at 0.3G0 in the blue histogram again demonstrates that whenever a single molecule Ag–CO–Ag junction is formed along the junction opening, it usually stays rigidly bound to one apex after the rupture, and so the molecular junction is re-established during the closing process. Note that this feature is hidden in the closing histogram for the entire dataset (black).
To verify the above interpretation of the experimental results, we performed ab initio simulations both of junction evolution and electronic transport properties (see Methods for details). To obtain starting configurations for initiating simulations of junction evolution, first we inserted the CO molecule close to an Ag dimer junction in various positions and orientations, and allowed the systems to relax. Afterwards we simulated the opening and closing traces of clean dimer-like Ag single atom contacts (Fig. 5d1, d2) and Ag–CO molecular junctions (Fig. 5b1–c4) by increasing or decreasing the electrode separation in steps of 0.01 nm and after each step relaxing the junction. The junction geometries illustrated in Fig. 5b1–c4 are examples of the stable configurations obtained from this procedure.
The theoretical opening and closing traces for the Ag–CO junction are shown in Fig. 5a as red and blue curves, respectively, together with the geometries for selected points on the traces (see green points and the corresponding geometries under the figure). An extended plateau appears around 0.5–0.7G0, which corresponds to a configuration in which the CO molecule sits between the electrodes in a perpendicular configuration (b3), with the carbon atom in the binding axis. After further elongation the conductance shows a step-like decrease when the molecule rotates into a parallel configuration as shown in Fig. 5b4. The parallel configuration has an initial conductance of ≈0.12G0, which decreases to zero during further elongation.
The calculated conductance of the perpendicular/parallel configuration overestimates/underestimates the corresponding experimental peak positions in the inset of Fig. 1. As the simulation is constrained to an idealized contact geometry, it is reasonable that the results of the simulations somewhat deviate from the experimental findings.36 It is possible that experimentally the CO molecule is not bound to an ideal Ag dimer, but to a less regular Ag structure.
After breaking of the junction, the molecule stays attached to the electrode and does not flip to the side. The closing trace, which is shown with blue on the right in Fig. 5a shows similar behaviour to the opening traces; first the parallel configuration is formed and the CO molecule rotates from the parallel to the perpendicular configuration during further closing (see in Fig. 5c1–c3). Both the parallel and the perpendicular configurations have similar, but a bit higher conductance than in the opening process, as also seen in the experiment. This results from the smaller (unstretched) atom–atom distance which is formed during the closing process. To check the relevance of the rigid binding of the molecule to one apex, we rotated the molecule to various angles with respect to the contact axis, and afterwards we relaxed the system. For all the cases demonstrated in Fig. 5e, the molecule has relaxed towards the contact axis, which justifies that the molecule preferably stays in the contact axis.
We also investigated the precursor effect with the help of the simulations: the black curve in Fig. 5a shows the opening trace of the clean Ag dimer, which is now compared to the molecular trace. At small tip–tip distances, the conductance of the Ag–CO junction is higher than in the clean case. The difference between an Ag single-atom contact and the molecular precursor configuration is even better demonstrated by the transmission eigenvalues of the simulated junctions (Fig. 6). In accordance with the experiment33 the clean Ag dimer has a single dominant conductance channel, and the remaining channels give a negligible contribution. However, the CO molecule bound to the side of the Ag–Ag dimer indeed opens up new channels: the molecular precursor configuration (see Fig. 6b1) has three non-vanishing transmission eigenvalues. All these demonstrate that our previous interpretation of the precursor configuration as a CO molecule bound to the side of an Ag dimer is reasonable.
Fig. 6 Evolution of the transmission eigenvalues for the simulated opening traces of Fig. 5. (a) For clean Ag junction the transport is dominated by a single channel. (b) In the Ag–CO single-molecule junction two additional conductance channels open due to the binding of the CO molecule parallel to the Ag–Ag junction. |
For further illustration we demonstrate the scattering wavefunctions of the first two conductance channels in Fig. 7. Usually the nature of these two channels is not well distinguishable; however, for the b2 configuration it is clear that the first channel is related to the transport through the CO molecule bound to the side, whereas the second channel is rather related to the direct transport between the Ag tip atoms.
Fig. 7 Illustration of the scattering wavefunctions for the first and second conductance channels related to the contact geometries b1–b4 in Fig. 5. |
As the junction is further opened, the direct transport between the Ag tip atoms vanishes, and the current is dominated by the transport through the perpendicular/parallel CO molecule (Fig. 7b3/b4). In this case only a single conductance channel dominates the transport (Fig. 6b).
Our findings demonstrate that the correlation analysis supplemented with the cross-correlation histograms between opening and closing traces supplies valuable information about precursor molecular configurations and the post-rupture evolution of single-molecule junctions. As these methods do not require special experimental conditions, they can be applied in any break junction measurement where conductance histograms are recorded.
The precise dosing of CO molecules was performed with a home-made vacuum-system from a high purity container through a heated tube. The dosing method was performed as follows: first we measured the clean Ag sample in a cryogenic vacuum;after around 20000–30000 opening–closing cycles we heated the dosing tube to 90 K (above the CO boiling point) and a few “fake” dosing processes were done without opening the CO molecule container. With this procedure we could check the cleanness of our vacuum-system. After making sure that the junction was not contaminated, and the dosing system was clean, we conducted the real dosing procedure. The temperature of the tube was 90–100 K and we observed signs of the molecule on the histogram after the dosage of 5 × 10−6 mol of the CO molecule. As the molecular peaks appear in the histogram the tube heating is turned off. At moderate bias voltage (≈30–50 mV) the molecular peak is present for a long time without further dosing. Presumably the bias voltage slightly heats the junction, which aids the diffusion of the molecules on the junction surface. At elevated bias voltage (≥200 mV) the molecules are desorbed, and the clean Ag histogram is re-established.
4 × 4 <001> Ag electrodes were constructed with pyramid shaped tips, and then the system was relaxed for a large number of independent geometrical configurations, meaning different electrode separations and different starting positions for the CO molecule (e.g. different angle between the transport axis and the axis of the CO molecule, different distances between the junction and the CO) (see Fig. 5e for some examples). Except for the case when the CO was too far from the junction, from all other initial positions the molecule always relaxed into the same local minimum corresponding to the specific electrode separation.
For the simulation in Fig. 5 we have chosen one of the over-squeezed initial geometries with a lower tip–tip distance than the ideal Ag–Ag distance and simulated a full MCBJ opening and closing cycle in which we consecutively relaxed the system and increased the electrode separation with 0.01 nm steps. To verify the first pulling curve, we then performed another pulling sequence, and found no deviation from the first cycle. The whole simulation was carried out for both when the CO molecule was present in the junction, and for the clean Ag–Ag junction as well.
Attaching 6 more layers of <001> silver to each electrode, the Hamiltonian was calculated at each step of the above opening–closing cycle. The corresponding conductance traces, the channel decompositions and scattering wavefunctions were then obtained by the Gollum code.40
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