Voltage-Controlled Binary Conductance Switching in Gold–4,4′-Bipyridine–Gold Single-Molecule Nanowires

We investigate gold–4,4′-bipyridine–gold single-molecule junctions with the mechanically controllable break junction technique at cryogenic temperature (T = 4.2 K). We observe bistable probabilistic conductance switching between the two molecular binding configurations, influenced both by the mechanical actuation and by the applied voltage. We demonstrate that the relative dominance of the two conductance states is tunable by the electrode displacement, whereas the voltage manipulation induces an exponential speedup of both switching times. The detailed investigation of the voltage-tunable switching rates provides an insight into the possible switching mechanisms.

T he field of single-molecule electronics 1 envisions the exploitation of single molecule interconnects between conducting electrodes as functional devices. A key component toward this goal is the well-controlled manipulation of the conductance states by external parameters. 2−5 Single-molecule conductance switching was already induced by mechanical actuation, 6,7 by light irradiation, 8−12 or by the voltage applied on the junction. 13 −19 In the latter case, usually complex molecules are applied, where either a charged or polarizable segment of the molecule is actuated by the electric field or the charge state of the molecule is manipulated. Here, we demonstrate voltage-tunable probabilistic conductance switching with a simple benchmark molecule, 4,4′-bipyridine (BP).
Previous measurements on Au−BP−Au single-molecule structures have shown, that the BP molecule can attach to gold electrodes in two different binding geometries resulting in double-step molecular plateaus on the conductance versus electrode separation traces 6,20−25 after the rupture of a singlemolecule gold junction with G ≈ 2e 2 /h = 1 G 0 conductance. It is suggested that at a smaller electrode separation, the molecule binds on the side of the metallic junction, such that both the nitrogen linker and the aromatic ring are electrically coupled to the metal electrode (G ≈ 10 −3 G 0 ). Upon increasing the gap, the molecule slides to the apex and only the linkers couple to the electrodes, yielding a decreased junction conductance (G ≈ 3 × 10 −4 G 0 ). 6,20,21 In the following, we refer to these two binding geometries as HighG and LowG configurations, which are also reflected by two clear peaks on the conductance histograms. A mechanically controlled binary conductance switching between these two configurations was also reported; 6 however, the voltage-controlled manipulation of the con-ductance states was hindered by the limited junction stability in the room temperature break junction environment.
Here we utilize a cryogenic temperature (T = 4.2 K) mechanically controllable break junction (MCBJ) setup to investigate the voltage-controlled binary conductance switching in Au−BP−Au single-molecule junctions. The superior low-temperature stability enables us to map the response of the junction to the manipulation of the external parameters in detail. We observe bistable switching between the two molecular configurations, influenced both by the mechanical actuation and by the applied voltage. We find that, at low bias voltage, the electrode separation determines the preferred junction configuration, similarly to prior room temperature measurements. 6 However, as the voltage is increased, a probabilistic switching is induced. We demonstrate that the relative dominance of the two configurations can be tuned through adjusting the electrode separation, while the switching rates are controlled by the applied voltage. This behavior resembles the characteristics of probabilistic bit devices. 26,27 Finally, we confront the measured switching phenomena with possible switching models, like (i) simple two-level system models, (ii) temperature activated switching models, (iii) a vibrational pumping model, (iv) a double-well potential inversion model, and (v) a heuristic model relying on the molecule's energy dependent transition probability.
We performed measurements using a cryogenic MCBJ setup with high purity gold wires. After cooling the setup, a histogram is recorded to ascertain the cleanliness of the junction; then molecules are dosed using an in situ evaporation technique. 23,25 We show an example pair of conductance traces in Figure 1a, black corresponds to the opening while gray to the closing trace, both exhibiting molecular plateaus. While the room temperature conductance histograms acquired by the same setup 23 reproduce the common double-peak structure, 6,20,22 the histogram for our low-temperature measurement shows a significant difference (black curve on Figure 1b), exhibiting an enhanced peak at the LowG interval and only a slight shoulder in the HighG region. In our previous work, 25 we have shown that this phenomenon is related to the lowtemperature single-atomic-chain-pulling mechanism typical for gold. 28−30 The probable atomic chain formation process in the stable low-temperature environment yields such wide gaps after the chain rupture that are unable to accommodate the HighG molecular configuration.
Compared to the low-temperature opening histogram, the peaks in the closing histogram (gray curve in Figure 1b) are shifted toward higher values. Furthermore, the HighG peak becomes more pronounced, although the LowG peak remains dominant. We explain this by the adhesive instability of the junction. 31 In the opening process a stretched molecular junction is formed inside a wider gap between the gold electrodes, whereas in the closing process, the electrodes and the molecule are relaxed, which leads to a somewhat higher conductance.
Next, we investigate how changing the electrode separation affects the molecular binding configuration. In their prior study Quek et al. reported mechanically controlled binary conductance switching between the two binding configurations. 6 This was realized by stopping the opening process and applying a short (∼60 ms) periodic signal to the piezo actuator to mechanically perturb the junction by repeatedly compressing and stretching it with 2 Ångstroms amplitude. When a molecule was caught in the junction during the period of the mechanical perturbation, the conductance indicated periodic switching between the two binding configurations. In Figure  1c,d,e, we reproduce this mechanical switching at 2 orders of magnitude longer time scales, utilizing the enhanced mechanical stability of the junction in the low-temperature environment. Thanks to the superior stability, we can also resolve the sub-Ångstrom displacement interval, where a conductance hysteresis is observed along the displacement cycles ( Figure 1c).
We continue by investigating the current−voltage characteristics of BP single-molecule junctions. Typical I(V) curves (Figure 2a,b) show that at low bias voltage, the present state of the junction is stable. However, when the applied voltage is increased, the junction exhibits binary probabilistic switching between two distinct conductance states. Upon further increasing the voltage, the switching rates also increase. Figure  2c shows the distribution of the high and low conductance states (i.e., the on and off conductances) deduced from a statistical amount of switching I(V) curves. As a reference, the closing conductance histogram is reproduced from Figure 1b   Utilizing the atomic chain pulling mechanism of gold, 28 we have used the interpeak distance in the length distribution of the 1 G 0 plateaus to calibrate the displacement axis. 30 The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter conductance states suggest that the molecular junction is switching between the HighG and LowG binding configurations, as observed during the closing of the junction. This result is consistent with our previous argument that the difference between the opening and closing histograms is caused by the strain acting on the junction in the opening process. During these I(V) measurements, the junction has time to relax, so that the strain acting on the molecule is reduced, leading to similar HighG and LowG conductance values as seen in the closing conductance histogram. These findings demonstrate that besides mechanical, we can also achieve electric switching between the two configurations of the BP molecule. Next, we correlate the bistable electric switching with the displacement of the electrodes. During this measurement, we identify the displacement interval of the hysteretic conductance switching at low bias (V = 30 mV; see black line in Figure 3a), and afterward we stop at distinct displacement values (green signs in Figure 3a Figure 3 demonstrate the distribution of the times spent in the HighG (τ on , red) and LowG (τ off , blue) conductance states between two subsequent switching events for the entire length of the time traces (22 s) at the displacement points c and d, where a telegraph-like conductance fluctuation was observed. By recording the low bias conductance hysteresis at the end of the measurement again (gray line in Figure 3a), we estimate the stability of the junction to be on the scale of <40 pm on the time scale of the entire measurement (≈400 s). This displacement inaccuracy is ≈15% of the Au−Au interatomic distance in a gold chain. On the basis of these measurements and further similar measurements, we find the following clear tendencies: (i) The bistable electrical switching is focused around the displacement range of the low-bias conductance hysteresis (see Figures 3c,d). (ii) Within this range the average times spent in the two states cross, i.e., at a smaller displacement the HighG state, whereas at larger displacement the LowG state is dominant (Figures 3e,f). (iii) Further away from the hysteresis, the electrical switching vanishes (Figure  3b), and the corresponding state is stable even under an elevated voltage. Note that the sub-Ångstrom displacement interval of the conductance hysteresis is almost an order of magnitude narrower than the ≈2 Å average displacement between the centers of the HighG and LowG conductance plateaus on the two-dimensional conductance−displacement histograms. 6,25 To resolve the temporal dynamics of the switching, we have performed a statistical amount of time-resolved measurements at various driving voltages. This was achieved by an automated measurement setup, where a real-time FPGA controller monitored the conductance and stopped the junction elongation once the predefined trigger conductance of G = 0.005 G 0 was reached. At this point, the displacement (i.e., the voltage on the piezo actuator) was fixed, and a voltage staircase was applied on the junction (see the scheme of the measurement in Figure 4a). Around 8% of the 8000 automated measurements yielded molecular contacts that were stable throughout the voltage sweep. Note that this number is partly related to the low molecular pick-up rate in the lowtemperature measurements. 25 Out of these stable molecular contacts ≈5% matched the displacement range, where the voltage dependent bistable switching was observable. These 35 independent traces are used to investigate the voltage dependence of the bistable switching in Figures 4b−j. One of these measurements is exemplified in Figure 4c , respectively, where we use the reference time τ 0 = 1 s to make the argument of the logarithm dimensionless. This means that the switching exponentially speeds up upon linearly increasing the voltage. Furthermore, the red and blue lines demonstrate that the switching simultaneously speeds up in the two states. To confirm these tendencies for a statistical amount of data, we investigate the correlations between the a on/off intercept and b on/off slope values for all measurements (Figure 4g−j). Despite The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter the scattering of the data, clear tendencies are observable: (i) for a certain (on/off) state a larger intercept is accompanied by a larger slope (see Figure 4g,h); (ii) a larger slope/intercept value for a certain state is accompanied by a larger slope/ intercept for the other state as well (see Figure 4i,j). The clear correlation between the b on and b off slope values in Figure 4i underpins the simultaneous speedup of the switching times for the two states. This is further illustrated by the red and blue shaded areas in Figure 4b. These are constructed by taking the particular intercept values related to the on and off states of the example data Figure 4b, but considering the scattering of the slope values in the region of these intercept values for all data. The latter is illustrated by the horizontal error bars in Figure  4g,h, where the bright red/blue dots correspond to the measurement data in Figure 4b. Summarizing this analysis, Figure 4 demonstrates the following major conclusions: (i) the switching times are well-fitted with an exponential probability density function (Figure 4c Finally, we discuss our results on the bistable resistance switching in terms of simple model considerations. According to the model fitting of force measurements in ref 32, the binding energies of the HighG and LowG molecular configurations are respectively 1.6 and 0.9 eV with a large, 700 meV energy difference. A hypothetical switching between states with such energy offset would rely on an even higher barrier value in the lower energy configuration. These values, however, correspond to relaxed configurations. In our case the switching happens in the sub-Ångstrom hysteretic conductance region, where both states are stable. In this region, we anticipate a stretched HighG and a compressed LowG configuration with significantly smaller energy difference and energy barrier between the two states. This is consistent with the observation, that a voltage range of ≈100 mV can induce the switching. We model the bistable molecular states as a double-well potential in the molecule's configuration space considering an E energy release by the electrons to the molecule during a single switching event (see Figure 5). From the electrons' point of view a Fermi-function integral describes this process giving the probability of scattering from an occupied state in the higher chemical potential electrode to a lower energy unoccupied state in the lower chemical potential electrode (see the Supporting Information). Once the molecule receives this energy, it switches to its other metastable state with Γ(E) probability (see the illustration in Figure 5). In the following, we consider different switching models as various limiting cases of this model.
(i) Simple two-level system models. We can consider either a coherent two-level system model with a finite tunneling probability between the two states and a fixed E excitation energy 33,34 or an incoherent two-level system model where the tunneling transition is not possible, and the switching requires an excitation above the E b barrier height in the actual state. In  Figure 4b illustrate the best fits with the former voltage scaling, which is clearly inconsistent with the measured data. Even if the divergence at eV = E is blurred due to a broader energy distribution, the high bias 1/V scaling of this simple model is much shallower than the measured voltage dependence of the data, which also holds for the 1/V 2 scaling in the incoherent model. Note that a 1/V and 1/V 2 dependencies would yield a factor of 3 or 9 speedup between 50 and 150 mV driving in contrast to the observed ≈2 orders of magnitude speedup (see Figure 4b). In Figure 4g,h this 3fold and 9-fold speedup would relate to slope values of b ≈ − 5 V −1 and b ≈ − 10 V −1 , which are also much shallower slopes than the typically observed b ≈ − 30 to − 20 V −1 values. Accordingly, these models are excluded.
(ii) Temperature activated switching model. In the former twolevel system models the direct voltage excitation is not possible at eV < E or eV < E b voltage. In this limit the temperature a c t i v a t i o n c a n s t i l l i n d u c e a t r a n s i t switching times (see Supporting Information). Such a temperatureactivated process is unrealistic at T = 4.2 K temperature, as the energy scale in the numerator of the exponent is almost 3 orders of magnitude larger than the thermal energy in the denominator. Furthermore, this scaling would provide a slope of b = −e·log(e)/kT ≈ − 10 3 V −1 , whereas the largest measured slopes are restricted to b ≈ − 30 V −1 (see Figure  4g,h).
(iii) Vibrational pumping model. So far we have considered models where the energy release from the electrons kicks the molecule to its other state within a single event. Alternatively, the electrons may release smaller E = ℏω vibrational quanta to the molecule, and the transition happens once this vibrational degree of freedom is pumped 35,36 to an energy exceeding the barrier height. According to the consideration in the Supporting Information, the average occupation number of a v i b r a t i o n a l m o d e c a n b e e s t i m a t e d a s ω ̅ = · ℏ − n e V ( /2) ( / 1) . Considering the ≈ − 10 3 transmission probability of the molecule, the eV < 150 mV voltage range and ≈10−100 meV typical vibrational energies 37 ̅ ≪ n 1 follows, i.e., the vibrational pumping, and related local overheating of the junction is unrealistic. As a simple explanation this result is related to the fact that the vibrational mode is much more efficiently cooled than excited in the ≪ 1 limit.
(iv) Double-well potential inversion model. Recent studies reported single-molecule switching, where the voltage excitation reversed the dominance of the two molecular states; i.e., it induced an inversion of the minima in the double-well potential 12 (see the illustration in the Supporting Information). This was reflected by the clear crossing in the voltage dependence of the switching times. In our system the dominance of the states is manipulated by the displacement, but at a fixed electrode separation the switching of the two configurations speeds up simultaneously, and the initially dominant state remains dominant throughout the studied voltage train; i.e., the double-well potential inversion model is also excluded.
(v) Heuristic model relying on the molecule's energy dependent transition probability. To be able to describe the simultaneous exponential decay of the switching times with linearly increasing voltage, we consider a strong (exponential) energy dependence of the molecule's transition probability Γ(E) (see left illustration in Figure 5). This may relate to an energy dependent tunnelling probability between two conformational states, as implied on the figure, but several other processes, like the reduction of the barrier with the applied voltage, or the influence of electron-wind forces may play a role. A more detailed understanding of the precise microscopic processes would require first principle model calculations.
In conclusion, we have demonstrated well-controlled voltage-induced probabilistic conductance switching in cryogenic temperature Au−BP−Au single-molecule junctions. This behavior resembles probabilistic bit devices with two tunable parameters: the relative dominance of the two conductance states is manipulated by the electrode displacement, whereas the voltage manipulation induces an exponential speedup of both switching times.
We have compared our experimental results with possible model considerations and argued against simple two-level system models, temperature activated switching models, a vibrational pumping model, and a double-well potential inversion model. Finally, we proposed a heuristic model relying on the exponential energy dependence of the molecule's transition probability.

* sı Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.0c02185. Discussion of the model considerations and details on the fitting of the switching time distributions (PDF) Figure 5. Illustration of the model considerations. The probability of the switching event includes two components: (i) the probability that an electron from an occupied state releases E energy ending up in an unoccupied state (right cartoon) and (ii) the Γ(E) probability that the molecule can switch to its other state after gaining E energy (left cartoon). Note that a reflected electron does not find unoccupied final states at E ≫ kT energy release; i.e., this process requires the transmission through the molecule with ≈ − 10 3 probability. In a vibrational pumping model one also has to consider the process where the electrons absorb E energy from the molecular vibrations (see the semitransparent arrows in the right cartoon). In this case, a reflected electron also finds unoccupied final states, and therefore the ≈ / 10 3 ratio makes the cooling of the vibrational mode much more efficient than the pumping.