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Random telegraph signals in molecular junctions
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 474202 (8pp)
doi:10.1088/0953-8984/26/47/474202
Random telegraph signals in molecular junctions Jan Brunner1, Maria Teresa González1,2, Christian Schönenberger1 and Michel Calame1 1
Department of Physics, University of Basel, 4003 Basel, Switzerland Instituto Madrileño de Estudios Avanzados en Nanociencia, IMDEA-Nanociencia, Campus de Cantoblanco, Madrid, Spain 2
E-mail: [email protected] Received 15 March 2014, revised 6 June 2014 Accepted for publication 25 June 2014 Published 29 October 2014 Abstract
We investigate conductance fluctuations in molecular junctions using a mechanically controllable break junction setup in a liquid environment. In contrast to conventional break junction measurements, time-dependent conductance signals were recorded while reducing the gap size between the two contact electrodes. Only small amplitude fluctuations of the conductance are observed when measuring in pure solvent. Conductance traces recorded in solutions containing alkanedithiols show significantly larger fluctuations which can take the form of random telegraph signals. Such signals emerge in a limited conductance range, which corresponds well to the known molecular conductance of the compounds investigated. These large-amplitude fluctuations are attributed to the formation and thermally driven breaking of bonds between a molecule and a metal electrode and provide a still poorly explored source of information on the dynamics of molecular junctions formation. The lifetimes of the high and low conductance states are found to vary between 0.1 ms and 0.1 s. Keywords: molecular junctions, molecular electronics, random telegraph signal, break junctions. (Some figures may appear in colour only in the online journal)
1. Introduction
of a molecular junction can be strongly influenced by the time scale over which the experiment is performed. We present here measurements of conductance fluctuations in molecular junctions using a mechanically controllable break junction setup operating in liquid [9, 10]. In contrast to conventional break junction measurements where conductance traces are usually recorded during opening cycles, conductance traces were here recorded during closing cycles, starting from a widely open junction. A second major difference to previous stability measurements is that, thanks to the excellent mechanical stability of lithographically fabricated break junctions, we could stop the motion of the three-point bending mechanism and perform conductance measurements without external active driving. With this approach, we make sure that only thermally driven dynamic reconfigurations of molecular junctions are observed. By focusing on the appropriate conductance range, we can investigate conductance fluctuations in transport regimes dominated by a single molecule. We
Reliable contacts are a requirement for the possible development of molecular electronics circuits [1]. The stability of molecular junctions has often been investigated as a byproduct in experiments focusing on other aspects and carried out at particular time scales. Specific studies have been made on the mechanical and thermodynamic stability of sulphur– gold or amine–gold bonds by observing conductance traces while opening the junction in either scanning tunneling microscopy (STM) or mechanically controllable break junction (MCBJ) experiments [2–8]. Differences in the environment (solution versus vacuum) and in the experimental approaches can explain some discrepancies in the observed lifetimes of the junctions. One important aspect is that in most experiments, the stability aspects and conductance fluctuations were investigated while opening the junctions at various speeds. In some cases, it was shown that the apparent lifetime 0953-8984/14/474202+8$33.00
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(a)
(b)
(c) G
liquid cell
z
Vb
Figure 1. (a) Measurement setup: a lithographically fabricated free-standing Au bridge on a stainless steel substrate (SEM image) is positioned in a three-point bending mechanism. The bridge can be repeatedly broken and closed by moving the push rod up and down. Molecules are delivered to the metal junction using a liquid cell mounted on top of the substrate. The conductance is obtained by applying a bias voltage to the gold bridge and measuring the current with an auto-ranging I-V converter. (b) Typical G(t) trace observed in pure solvent (mesitylene) showing random, small amplitude conductance fluctuations. (c) Conductance trace measured in a hexanedithiol solution and showing two level fluctuations with conductance variations significantly larger than in pure solvent.
gain range from 104 to 109 V A−1. The junction conductance G can be determined over more than seven orders of magnitude, from mechanically closed contacts (G > 10 G0, G0 = 2e2/h) down to large tunnelling gaps (detection limit G ≈ 10−7 G0). The upper frequency limit of the amplifier is approximately 1.3 kHz at the highest gain setting (109 V A−1.) and 10 kHz at lower gains (104, 0.47 × 106 and 0.22 × 108 V A−1). All measurements were initiated with the junction completely open, i.e. for a conductance below the detection limit. For a typical tunneling slope of 0.2 nm per conductance order of magnitude in mesitylene, this corresponds to a separation between electrodes larger than at least 1.4 nm. Starting from a fully open electrodes' configuration, we demonstrate in section 3 that large and regular conductance fluctuations such as random telegraph signals (RTS) appear generically when molecular junctions are formed. In such measurements, the junction was gradually closed while recording the conductance. When large conductance fluctuations appeared, the push rod movement was stopped and the time-dependent conductance G(t) was recorded over 100 s intervals. A systematic investigation of conductance fluctuations for a single molecular compound, octanedithiol, is then presented in section 4. These measurements were performed over a more limited conductance range corresponding to the region where octanedithiols junctions are expected to form, as observed in our previous measurements [11, 12]. Starting from a fully open
obtained equivalent results for experiments performed with hexane-, octane- and nonanedithiol compounds.
2. Experimental methods The measurements were performed with a mechanically controlled break junction setup as illustrated in figures 1(a) [9]. Gold leads were fabricated on polyimide-insulated spring steel substrates by electron beam lithography and physical vapour deposition (10 nm Ti + 60 nm Au). Etching the polyimide in an O2/CHF3 plasma leads to free-standing gold bridges (see SEM image). In the measurement apparatus, the samples are bent by moving up a push rod by a distance Δz. This bending stretches the gold bridge which eventually breaks, forming two gold electrodes. When the push rod is lowered, the substrate relaxes and the junction closes again. The electrodes’ separation d depends linearly on the push rod position z with an estimated’ attenuation factor a = Δd/Δz ranging between 1.5 × 10−5 and 4 × 10−5 [11]. This low attenuation factor allows for a fine adjustment of the electrodes' separation and leads to a low sensitivity to vibrations. During measurements, the break junctions are exposed to a liquid environment consisting of either pure mesitylene or solutions of 1 mM alkanedithiols in mesitylene. A constant bias voltage Vb = 0.2 V is applied and the current is measured by an auto-ranging current-to-voltage (IV) converter with a 2
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configuration, the electrodes were first approached to reach 10−5 G0 and then further closed in small steps (Δd ≈ 0.1 Å) once every 30 s. The conductance was recorded as a function of time during these 30 s intervals. During the conductance measurement, the electrodes were not actively moved. These experiments are therefore different from conventional break junction experiments where the molecular junctions are formed during an opening cycle, i.e. upon the elongation and breaking of the metallic bridge in presence of molecules in solution. The conductance is measured during the whole opening cycle, while a mechanical force is exerted on the metallic bridge and, subsequently, the junction. Here, in contrast to this conventional approach, the metallic bridge has previously been broken and the electrodes thus created given time to relax in solution in the presence of molecules. The conductance measurement are done in the absence of an active motion of the electrodes for successively reduced inter-electrodes distances. This approach bears similarities to Scanning Tunneling Microscope (STM) experiments where it was observed that dithiolated molecules present on a Au substrate can spontaneously span the gap between the substrate surface and the nearby STM tip [13–15].
the time domain first exhibits a RTS regime (time interval (1) and is followed by a random fluctuations regime (time interval (2). To identify and analyze RTS in more detail, we turn to the frequency domain [19–22]. Figure 2(b) shows the frequency spectra for the two marked time intervals. For a two-level RTS, we expect a Lorentzian spectrum [23]. This is indeed what we observe during the first time interval which shows a clear RTS. The signal in the second time interval results in a 1/f spectrum indicating that the conductance fluctuations are random in this regime. The grey area indicates the region above the cutoff frequency of the amplifier at 1.3 kHz. figure 2(c) shows a shorter section of the same measurement in time interval 1 where a clear RTS is observed. Because the background noise is much lower than the RTS amplitude, we can extract states lifetimes τh,i from such a conductance trace, as indicated in the figure for the high conductance states. We observe here a ratio of the high level conductance to the low level conductance of Gh/Gl ≈ 3. Three reference levels (shown as horizontal dashed lines) are defined at 10, 50 and 90% of the range between the low and high conductance values. The time interval between a mid reference level crossing and the closest following one that occurs after at least one crossing of a high (low) reference level corresponds to a high-state (low-state) lifetime. The histogram of these state lifetimes τh,i is shown in figure 2(d) and shows a fast decay. Fitting an exponential decay function ∝e−t/τ (dashed red curve) to the histogram yields the average lifetime τh = 1.9 ms for the corresponding state (τl = 0.93 ms). For most observed RTS, the fit is significantly more accurate when using a sum of two exponential decays (solid green curve) or a stretched exponential. Using more than two exponential functions provides no substantial further improvements. In the following discussion, we consider various possible explanations for the emergence of the observed RTS and correlate the dynamics of the junction to microscopic aspects. The two conductance values observed in an RTS must correspond to at least two distinct geometrical configurations of the junction. Fluctuations of the number of molecules within the junction can lead to a variability of the conductances observed. The experimental situation is however particular here as we are measuring conductance during closing cycles, i.e. starting from an open junction where no molecule can bridge the electrodes. We then gradually close the electrodes until a signal showing large conductance fluctuations appears. In these conditions, the conductance signal is most probably dominated by the behavior of one molecule in the junction. In such a metal–molecule–metal junction, the fluctuations can arise from changes in the contact between the molecule and the gold electrodes, from changes in the molecular structure or from changes in the electrodes alone as well as in the direct environment of the junction. We first describe the scenario which we deem the most probable for explaining the fluctuations observed. A molecule in the junction can be either bound to both electrodes or to just one electrode with the other bond temporarily broken. Charge transport mediated by a molecular structure covalently bound to electrodes is known to be more efficient than direct tunnelling through vacuum or solvent [24–26]. For a given electrode distance, we thus expect a measurable conductance difference between a junction bearing a molecule covalently bound to one electrode only and a junction with a molecule bridging
3. Identifying random telegraph signals in different molecular solutions To illustrate the emergence of large conductance fluctuations in the presence of Au-binding molecules in solution, we show in figures 1(b) and (c) conductance traces measured in both pure solvent (mesitylene) and a solution of hexanedithiol (C6) molecules. When the electrodes are surrounded by pure mesitylene (figure 1(b)), the conductance signal consists of random fluctuations. We further examine this point below3. When the measurement is done in a hexanedithiol solution, stronger fluctuations can be observed as shown in figure 1(c). For most of the time interval, the conductance shows switching between two well-defined values. The conductance stays at one value before suddenly switching to the other value at a random point in time. The observation of large conductance fluctuations is a generic feature in such systems and is not specific to this particular molecule. It was observed here for hexane, octane and nonanedithiol molecules. The time scale of the switching events is typically smaller than 0.1 ms, i.e. shorter than what our setup can resolve. We emphasize that we focus here on conductance fluctuations linked to the presence of molecules between atomic contacts in solution and at room temperature. Conductance fluctuations and telegraph noise have also been observed in atomic contacts without the presence of molecules and in different experimental conditions [16–18]. In figure 2, we analyze in more detail a conductance trace obtained for a 1 mM nonanedithiol (C9) solution and obtained as described above. The conductance trace shown in figure 2(a) in 3 There is a small conductance drift (about 0.5 × 10−3 G0 in 100 s) which can be attributed either to a mechanical relaxation in the substrate (polyimide layer or stainless steel itself) or to a relaxation due to the adhesive tape employed to prevent shorts between the counter supports and the substrate. This slow drift, below 0.5 pm s−1, doesn't limit the observation of conductance fluctuations taking place at faster time scales.
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Figure 2. (a) Conductance trace G(t) measured in a 1mM nonanedithiol solution showing RTS during the first 30 s, then random fluctuations. (b) Power spectra of the time intervals shown in (a). (c) Section of the random telegraph signal shown in (a). High conductance state lifetimes are indicated. (d) Histogram of the high state lifetimes with exponential decay fits to obtain the average lifetime. Single exponential (dashed red) and sum of two exponentials (solid green). Inset: same data in a logarithmic scale.
further note that changes in the local geometry of a sulphur– gold bond, between for instance atop and bridge arrangement, can lead to a substantial conductance change as well [29–31]. Such microscopic rearrangements may be at the origin of the observed fluctuations. Note that, if the typical time scale for these rearrangements is below our experimental resolution (∼ 0.1 ms), we will only observe conductance values averaged over different configurations, as already discussed above for molecular backbone conformational changes. In our experimental configuration, the confined junction geometry together with intermolecular interactions between molecules at the electrodes' surface may lead to slower rearrangement time scales and measurable conductance fluctuations. A distance change between the electrodes caused by atomic rearrangements due to thermal fluctuations can also cause conductance fluctuations and even low-amplitude RTS. The signals should however be visible in solvent only as well and such RTS are quite rare in pure solvent (an example can be seen in figure 3(a), see next section). If we take a typical tunneling decay constant β ≈ 1 Å−1 [9] (which roughly corresponds to a tunneling slope of 0.2 nm per conductance order of magnitude), conductance fluctuations with a ratio of high to low conductance Gh/Gl ≈ 1.25 would correspond to a distance change of ≈ 0.22 Å which is plausible at room temperature4. The amplitude of the RTS observed for hexanedithiols (Gh/Gl ≈ 2, figure 1(c)) and nonanedithiols (Gh/Gl ≈ 3, figure 2(c)) are
the two electrodes via covalent bonds. This difference will be larger for longer molecules as the bridging can take place at larger electrodes' separation. As we measure conductance while closing the junction, we expect the amplitude of conductance fluctuations to be maximum immediately when the signal appears, i.e. when the distance between electrodes is just sufficient to allow for a bridging by the molecule. Note that the amplitudes of the conductance variations observed here are in agreement with similar STM investigations [13–15]. The amplitude of the current jumps observed in the STM experiments upon tip-substrate bridging events mediated by molecules were observed to span a range of values, from very small increases (by a few percent only) to about an order of magnitude. Different origins, other than bond breaking and forming, could explain large conductance fluctuations in molecular junctions. In particular cases, reversible conformational changes of the molecular backbone can also lead to distinct conductance states, as in molecular switches [27, 28]. Conformational changes from all-trans to one gauche defect could for instance lower the conductance by approximately a factor of ten [29, 30] or even more [31]. Such structural changes are however expected to take place at time scales between 10−11 s to 10−9 s and so only averaged values will be observed in our measurements [29, 31]. Molecular systems exhibiting stable twolevel conductance fluctuations at room temperature require a specific design to achieve stable enough states that can be identified. The observations made here are not of this nature and occur generically in molecular junctions, as previously mentioned. This is further illustrated in figure A1, appendix A where RTS signals are shown for a conjugated compound. In this case, the type of conformational changes described above can be excluded as the molecular backbone is rigid. We
4 We assume G ∝ exp(−β· d). This means that Gh/Gl = exp(−β(dh − dl)) and therefore Δd = dl − dh = − ln(Gh/Gl)/β where the indices h and l refer to the high and low conductance cases, respectively. Note that thermal fluctuations occur at a much faster time scale than the bandwidth of our setup. This means that we cannot observe the full fluctuation amplitude and the distance fluctuation is estimated as a lower limit of the true movement.
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Figure 3. Two sequences of conductance traces G(t) measured without and with octanedithiol. (a) In pure solvent, small amplitude conductance fluctuations are observed. The arrow points to the brief occurrence of a small amplitude telegraph signal. (b) In the octanedithiol containing solution, conductance fluctuations and sometimes RTS of larger amplitude were systematically observed. On the right panel, the relative fluctuation amplitudes of the conductance for each 30 s interval is plotted against the logarithmic average of its conductance. The star symbols indicate the values for the curves shown in the main panel.
however significantly larger. Note that the amplitude of RTS is larger for the longer molecule (nonanedithiol), validating the discussion in the previous paragraph. Conductance fluctuations reaching Gh/Gl ≈ 3 would correspond to a distance change between the electrodes of ≈ 1.1 Å which is improbable to repeatedly happen at room temperature. The large fluctuations observed can therefore not be attributed to thermally driven atomic rearrangements of the electrodes. Finally, the environment was shown to have little effect on the conductance of molecular junctions [32] except in special cases [33]. One may expect that changes in the environment can affect the lifetimes of RTS states but it will not be their direct cause. From the above discussion on the possible origins of conductance fluctuations in our junctions, the repeated formation and breaking of a molecule–metal bond seems the most probable one. In that case, we would expect a thermally activated formation and breaking of the bond, leading to exponentially distributed low and high conductance lifetimes, as observed experimentally. In the following we discuss the lifetime distributions in more detail. We consider an ideal two-state random telegraph signal with instantaneous transitions. When the system is in the high state, with an average state lifetime τ, there is a constant probability per unit time 1/τ for the system to switch to the low state. If A(t) is the probability that the system persists in the high state until time t, then A(t + dt) = A(t)(1 − dt/τ) and dA(t)/dt = − A(t)/τ. Integrating, we obtain A(t) = exp(−t/τ). Writing p(t)dt for the probability that the system switches from high to low within the time interval dt, we can write p(t) = A(t)/τ = τ−1 exp(−t/τ) which corresponds to the lifetimes distribution for each state (probability density). We have illustrated in figure 2(d) for the high conductance state data that the sum of two exponential decays usually provides a better fit to the observed lifetimes distribution in our experiments. This points to the fact that the average state lifetime τh in the high conductance state may vary over the measurement time of a RTS signal, suggesting that at least two microscopic arrangements with distinct lifetimes can occur. This is supported by figure B1 in appendix B where we plot the high and low state lifetimes τh, i and τl, i for a few thousand switching events in nonanedithiol junctions. While the low conductance state lifetimes average
(solid line, average over 50 points) stays essentially constant, the average lifetime for the high conductance state shows a clear increase after about 2200 events. Assuming as justified above that the RTS signal is caused by a molecule anchored within the junction where one bond is being repeatedly formed (high conductance state) and broken (low conductance state), we anticipate that the high conductance state may show slightly distinct lifetimes due the influence of the molecule electrode interaction whereas the low conductance state lifetime will only be dominated by the local diffusion of the anchor group. We however rarely observe changes in average lifetimes as clearly as that shown in figure B1. The fact that a double exponential decay better fits the observed lifetime distributions here cannot be considered as a a hallmark for the high conductance state. Note that a fit using a stretched exponential can also reproduce the lifetime distributions observed which would indicate a broad distribution of average lifetimes for the system, see e.g. [34]. The standard behavior results in a rather constant average lifetime over a single RTS signal, as illustrated in figure B2, appendix B for a hexanedithiol solution. Overall, we have investigated the lifetimes and their distribution for 16 measurement sets from 12 different samples. The lifetimes obtained vary between ≈1 ms and 100 ms where the lower limit is set by the bandwidth of the amplifier. This is comparable to the lifetimes of molecular junctions measured in a liquid environment with an STM when retracting the tip at low velocity [3] which suggests that the RTS lifetimes are also caused by a molecular junction forming and breaking. Indeed, similar conductance fluctuations were observed in the same work during slow opening cycles. Note that much longer lifetimes of molecular junctions have been observed in vacuum [4] where the mobility of the molecules can be expected to be lower due to the absence of solvent. From the signals measured within the approach described in this section, we cannot extract a clear correlation between the conductance values and lifetimes τh and τl of the two states and the relative conductance difference between the states. Clear two level signals are a relatively rare occurrence in the type of measurements presented in this section (≈1% of the time), which prevents a more advanced statistical investigation of their properties as done for instance in [35]. In the next Section, we present a different approach that 5
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Figure 4. The main panels show the standard deviations of the conductance measured during 30 s intervals and divided by the average conductance over the interval. Plot (a) is obtained from a measurement in pure mesitylene whereas for (b) a solution of octanedithiol in mesitylene was used. The dashed grey lines serve as guides to the eye and indicate the maximum fluctuation amplitude in the pure solvent. Histograms of the dG/〈G〉 data are shown to the right of the main panels. The histograms are normalized to the number of curves or data points for opening curves and closing steps, respectively. Top panels: typical histograms from opening conductance curves G(z) in mesitylene and octanedithiol solution (filled histograms) and conductance histograms of the data shown in the main panels (outlined histograms). The dashed black curve is a Gaussian fit to the octanedithiol histogram.
each 30 s interval. The plot for δGrel is shown on the right panel of figure 3(b). The star symbols correspond to the traces shown in the left panel. The square symbols show δGrel for all conductance traces measured during this closing cycle. In figure 4, we present an overview of δGrel values for several closing cycles in mesitylene (figure 4(a)) and in a solution of octanedithiols (figure 4(b)). One symbol in the main panel represents one closing cycle, starting from a fully open junction. On the right panels, the outlined histograms show the distribution of fluctuation amplitudes. The top panels show two different conductance histograms: The outlined histograms show the distribution of average conductance values measured during closing cycles. The filled histograms were generated by performing conventional conductance measurements during opening cycles of the junctions, similarly to our previous work [11, 12]. For the pure solvent, we see that the values for δGrel are spread over one order of magnitude, do not exceed a maximum amplitude δGrel = 0.2 (dashed grey line) and decrease only slightly with increasing 〈G〉. In the presence of octanedithiol molecules in solution, fluctuations of higher amplitude are present for 〈G〉 up to the known molecular conductance values reported for octanedithiol, whereas the fluctuations mostly remain below δGrel = 0.2 at higher 〈G〉. This is further emphasized by the histograms in the right panels of figures 4(a) and (b): while the distribution of δGrel is mostly symmetric for the pure solvent, a clear tail at higher fluctuation amplitudes develops in the histogram for octanedithiols. We now consider the top panel histograms for a comparison between opening (filled histograms) and closing cycles (outlined histograms). For pure mesitylene, both histograms show a rather flat profile without statistically relevant signatures. In the
provides further insight into the relative amplitude of the conductance fluctuations. 4. Systematic measurements in the presence of an octanedithiol solution In this section, we focus on a systematic approach aiming at providing a better overview of the different fluctuation amplitudes observed in the junctions. For this purpose, we focused on a single molecular compound, octanedithiols, showing conductance plateaus around 10−5 to 10−4 G0 [11, 12]. Starting from a fully open configuration, a junction was first closed to reach 10−5 G0. The electrodes were then approached in small steps (Δd ≈ 0.1 Å) once every 30 s and the conductance was recorded as a function of time during the 30 s intervals. The electrodes were not actively moved during the measurement intervals. Figures 3(a) and (b) show typical conductance traces G(t) in a logarithmic scale that were recorded in mesitylene without and with octanedithiol, respectively. The G(t) traces in pure mesitylene show conductance fluctuations and sometimes jumps of small relative amplitude. True RTS are rare and of short duration and low amplitude (arrow). The relative conductance fluctuation amplitude δGrel = δG/〈G〉 (standard deviation of G divided by the average G) does not show any dependence on conductance. With octanedithiol molecules in the solution, fluctuations of much larger amplitude are observed at low conductance, between 10−5 G0 and 10−4 G0. This conductance range corresponds very well to the values of the conductance plateaus observed for octanedithiol measurements in standard break junction measurements performed while opening the junction [11, 12]. To quantify the fluctuation amplitudes, δGrel is calculated for 6
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presence of octanedithiol molecules, both histograms show clear features demonstrating the formation of molecular junctions with a qualitatively similar overall shape. We note that the conductance histogram for the closing cycle shows a large number of counts between 10−4 and 10−3 G0 (indicated by the arrow) as compared to the typical Gaussian distribution observed in opening cycles (dashed line). This can be explained by two related mechanisms [12]: First, the slow closing of the electrodes allows for Au relaxation of the electrode apexes leading to a larger contact surface and thereby favoring the binding of more molecules in parallel. Second, layers of molecules formed on the electrodes will impede further closing of the electrodes below a separation distance on the order of one molecular length, causing a plastic deformation of the gold. This will lead to both more histogram counts in the associated conductance regime and to even blunter tips than by Au relaxation alone. The systematic measurements presented in this section show that while low-amplitude fluctuations are present in measurements with pure solvents as well as in octanedithiol solution, large-amplitude fluctuations only appear in the presence of gold-binding molecules. The amplitudes of the large conductance fluctuations are on the order of single-molecular conductance values. This explains why the fluctuations are not visible any more in conductance ranges well above the singlemolecular conductance. This also further supports that the dominant peak signature around 10−4 in the conductance histogram obtained from standard opening cycles measurements (dashed Gaussian curve in the top panel of figure 4(b)) corresponds to the signature of molecular junctions comprising already a few molecules [12].
EC FP7 ICT SYMONE project (no. 318597), the EC FP7 ITN MOLESCO project (no. 606728) and the Ministerio de Economía y Competitividad, grants CSD2007-0010 and MAT2011-25046. Appendix A. RTS observed for a rigid, conjugated oligomer
Figure A1. Telegraph signal in a 1 mM solution of dithiolated oligo (phenylene ethynylene) (OPE). The ratio of the high state to the low state conductance is about 2.
Appendix B. Time development of lifetimes
5. Conclusions In this study, we have examined random telegraph signals (RTSs) observed during break junction experiments in a solution of goldbinding molecules. We attribute the emergence of such signals to the spontaneous binding and unbinding of the molecule anchor groups to the electrode tips, thereby forming or breaking a metal– molecule–metal junction. Both the formation and the breaking of the molecule–metal bonds are thermally activated and show an exponential distribution of lifetimes for the different conductance states. The observed fluctuations are direct evidence that we are dealing with single or few molecular junctions. The varying RTS amplitudes and time scales reflect the different microscopic arrangements and conductance values possible in such experiments. A better understanding of such fluctuations in systems involving a single or only a few molecules is of particular interest for the development of novel spectroscopic characterization schemes [36]. The present study provides the first insights into such developments. To provide signatures robust enough that they will allow a fingerprinting of molecular compounds, a larger space of parameters needs to be explored, for instance by extending the characterization to different bias voltages.
Figure B1. Scatter plot of the lifetimes for high and low states obtained from the nonanedithiol measurement shown in figure 2 (region 1). The high and low state lifetimes are shown in green and red, respectively. The solid lines are logarithmically averaged values over sliding windows of 50 events. A clear change of the average high conductance state lifetime is seen around event number 2200. As discussed in section 1 and figure 2(d), the sum of two exponential decay functions is required to obtain a good fit to the lifetime distribution for such two level signals.
Acknowledgments We acknowledge support by the Swiss Nanoscience Institute (SNI), the EC FP7 ITN FUNMOLS project (no. 212942), the 7
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Figure B2. Scatter plot of the lifetimes for high and low
states observed in a hexanedithiol solution. The solid lines are logarithmically averaged values over sliding windows of 50 events. No significant changes of the average state lifetimes is observed. A single exponential decay provides a good fit to the lifetime distribution.
References [1] The special issue on molecular electronics 2013 Nature Nanotechnol. 8 377–467 and references therein [2] Huang Z, Chen F, D'agosta R, Bennett P A, Di Ventra M and Tao N 2007 Local ionic and electron heating in singlemolecule junctions Nature Nanotechnol. 2 698–703 [3] Huang Z F, Chen F, Bennett P A and Tao N J 2007 Single molecule junctions formed via au-thiol contact: stability and breakdown mechanism J. Am. Chem. Soc. 129 13225–31 [4] Tsutsui M, Shoji K, Morimoto K, Taniguchi M and Kawai T 2008 Thermodynamic stability of single molecule junctions Appl. Phys. Lett. 92 223110 [5] Tsutsui M, Shoji K, Taniguchi M and Kawai T 2008 Formation and self-breaking mechanism of stable atomsized junctions Nano Lett. 8 345–9 [6] Tsutsui M, Taniguchi M and Kawai T 2009 Quantitative evaluation of metal-molecule contact stability at the singlemolecule level J. Am. Chem. Soc. 131 10552–6 [7] Tsutsui M and Taniguchi M 2013 Fluctuated atom-sized junctions in a liquid environment J. Appl. Phys. 113 024303 [8] González M T, Díaz A, Leary E, García R, Ángeles Herranz M, Rubio-Bollinger G, Martín N and Agraït N 2013 Stability of single- and few-molecule junctions of conjugated diamines J. Am. Chem. Soc. 135 5420–6 [9] Grueter L, Gonz M T, Huber R, Calame M and Schoenenberger C 2005 Electrical conductance of atomic contacts in liquid environments Small 1 1067–70 [10] Wu S M, González M T, Huber R, Grunder S, Mayor M, Schönenberger C and Calame M 2008 Molecular junctions based on aromatic coupling Nature Nanotechnol. 3 569–74 [11] González M T, Wu S M, Huber R, van der Molen S J, Schönenberger C and Calame M 2006 Electrical conductance of molecular junctions by a robust statistical analysis Nano Lett. 6 2238–42 [12] González M T, Brunner J, Huber R, Wu S M, Schönenberger C and Calame M 2008 Conductance values of alkanedithiol molecular junctions New J. Phys. 10 065018 [13] Haiss W, Nichols R J, van Zalinge H, Higgins S J, Bethell D and Schiffrin D J 2004 Measurement of single molecule conductivity using the spontaneous formation of molecular wires Phys. Chem. Chem. Phys. 6 4330 [14] Haiss W, Wang C, Grace I, Batsanov A S, Schiffri D J, Higgins S J, Bryce M R, Lambert C J and Nichols R J 2006 8
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Random telegraph signals in molecular junctions
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 474202 (8pp)
doi:10.1088/0953-8984/26/47/474202
Random telegraph signals in molecular junctions Jan Brunner1, Maria Teresa González1,2, Christian Schönenberger1 and Michel Calame1 1
Department of Physics, University of Basel, 4003 Basel, Switzerland Instituto Madrileño de Estudios Avanzados en Nanociencia, IMDEA-Nanociencia, Campus de Cantoblanco, Madrid, Spain 2
E-mail: [email protected] Received 15 March 2014, revised 6 June 2014 Accepted for publication 25 June 2014 Published 29 October 2014 Abstract
We investigate conductance fluctuations in molecular junctions using a mechanically controllable break junction setup in a liquid environment. In contrast to conventional break junction measurements, time-dependent conductance signals were recorded while reducing the gap size between the two contact electrodes. Only small amplitude fluctuations of the conductance are observed when measuring in pure solvent. Conductance traces recorded in solutions containing alkanedithiols show significantly larger fluctuations which can take the form of random telegraph signals. Such signals emerge in a limited conductance range, which corresponds well to the known molecular conductance of the compounds investigated. These large-amplitude fluctuations are attributed to the formation and thermally driven breaking of bonds between a molecule and a metal electrode and provide a still poorly explored source of information on the dynamics of molecular junctions formation. The lifetimes of the high and low conductance states are found to vary between 0.1 ms and 0.1 s. Keywords: molecular junctions, molecular electronics, random telegraph signal, break junctions. (Some figures may appear in colour only in the online journal)
1. Introduction
of a molecular junction can be strongly influenced by the time scale over which the experiment is performed. We present here measurements of conductance fluctuations in molecular junctions using a mechanically controllable break junction setup operating in liquid [9, 10]. In contrast to conventional break junction measurements where conductance traces are usually recorded during opening cycles, conductance traces were here recorded during closing cycles, starting from a widely open junction. A second major difference to previous stability measurements is that, thanks to the excellent mechanical stability of lithographically fabricated break junctions, we could stop the motion of the three-point bending mechanism and perform conductance measurements without external active driving. With this approach, we make sure that only thermally driven dynamic reconfigurations of molecular junctions are observed. By focusing on the appropriate conductance range, we can investigate conductance fluctuations in transport regimes dominated by a single molecule. We
Reliable contacts are a requirement for the possible development of molecular electronics circuits [1]. The stability of molecular junctions has often been investigated as a byproduct in experiments focusing on other aspects and carried out at particular time scales. Specific studies have been made on the mechanical and thermodynamic stability of sulphur– gold or amine–gold bonds by observing conductance traces while opening the junction in either scanning tunneling microscopy (STM) or mechanically controllable break junction (MCBJ) experiments [2–8]. Differences in the environment (solution versus vacuum) and in the experimental approaches can explain some discrepancies in the observed lifetimes of the junctions. One important aspect is that in most experiments, the stability aspects and conductance fluctuations were investigated while opening the junctions at various speeds. In some cases, it was shown that the apparent lifetime 0953-8984/14/474202+8$33.00
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(a)
(b)
(c) G
liquid cell
z
Vb
Figure 1. (a) Measurement setup: a lithographically fabricated free-standing Au bridge on a stainless steel substrate (SEM image) is positioned in a three-point bending mechanism. The bridge can be repeatedly broken and closed by moving the push rod up and down. Molecules are delivered to the metal junction using a liquid cell mounted on top of the substrate. The conductance is obtained by applying a bias voltage to the gold bridge and measuring the current with an auto-ranging I-V converter. (b) Typical G(t) trace observed in pure solvent (mesitylene) showing random, small amplitude conductance fluctuations. (c) Conductance trace measured in a hexanedithiol solution and showing two level fluctuations with conductance variations significantly larger than in pure solvent.
gain range from 104 to 109 V A−1. The junction conductance G can be determined over more than seven orders of magnitude, from mechanically closed contacts (G > 10 G0, G0 = 2e2/h) down to large tunnelling gaps (detection limit G ≈ 10−7 G0). The upper frequency limit of the amplifier is approximately 1.3 kHz at the highest gain setting (109 V A−1.) and 10 kHz at lower gains (104, 0.47 × 106 and 0.22 × 108 V A−1). All measurements were initiated with the junction completely open, i.e. for a conductance below the detection limit. For a typical tunneling slope of 0.2 nm per conductance order of magnitude in mesitylene, this corresponds to a separation between electrodes larger than at least 1.4 nm. Starting from a fully open electrodes' configuration, we demonstrate in section 3 that large and regular conductance fluctuations such as random telegraph signals (RTS) appear generically when molecular junctions are formed. In such measurements, the junction was gradually closed while recording the conductance. When large conductance fluctuations appeared, the push rod movement was stopped and the time-dependent conductance G(t) was recorded over 100 s intervals. A systematic investigation of conductance fluctuations for a single molecular compound, octanedithiol, is then presented in section 4. These measurements were performed over a more limited conductance range corresponding to the region where octanedithiols junctions are expected to form, as observed in our previous measurements [11, 12]. Starting from a fully open
obtained equivalent results for experiments performed with hexane-, octane- and nonanedithiol compounds.
2. Experimental methods The measurements were performed with a mechanically controlled break junction setup as illustrated in figures 1(a) [9]. Gold leads were fabricated on polyimide-insulated spring steel substrates by electron beam lithography and physical vapour deposition (10 nm Ti + 60 nm Au). Etching the polyimide in an O2/CHF3 plasma leads to free-standing gold bridges (see SEM image). In the measurement apparatus, the samples are bent by moving up a push rod by a distance Δz. This bending stretches the gold bridge which eventually breaks, forming two gold electrodes. When the push rod is lowered, the substrate relaxes and the junction closes again. The electrodes’ separation d depends linearly on the push rod position z with an estimated’ attenuation factor a = Δd/Δz ranging between 1.5 × 10−5 and 4 × 10−5 [11]. This low attenuation factor allows for a fine adjustment of the electrodes' separation and leads to a low sensitivity to vibrations. During measurements, the break junctions are exposed to a liquid environment consisting of either pure mesitylene or solutions of 1 mM alkanedithiols in mesitylene. A constant bias voltage Vb = 0.2 V is applied and the current is measured by an auto-ranging current-to-voltage (IV) converter with a 2
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configuration, the electrodes were first approached to reach 10−5 G0 and then further closed in small steps (Δd ≈ 0.1 Å) once every 30 s. The conductance was recorded as a function of time during these 30 s intervals. During the conductance measurement, the electrodes were not actively moved. These experiments are therefore different from conventional break junction experiments where the molecular junctions are formed during an opening cycle, i.e. upon the elongation and breaking of the metallic bridge in presence of molecules in solution. The conductance is measured during the whole opening cycle, while a mechanical force is exerted on the metallic bridge and, subsequently, the junction. Here, in contrast to this conventional approach, the metallic bridge has previously been broken and the electrodes thus created given time to relax in solution in the presence of molecules. The conductance measurement are done in the absence of an active motion of the electrodes for successively reduced inter-electrodes distances. This approach bears similarities to Scanning Tunneling Microscope (STM) experiments where it was observed that dithiolated molecules present on a Au substrate can spontaneously span the gap between the substrate surface and the nearby STM tip [13–15].
the time domain first exhibits a RTS regime (time interval (1) and is followed by a random fluctuations regime (time interval (2). To identify and analyze RTS in more detail, we turn to the frequency domain [19–22]. Figure 2(b) shows the frequency spectra for the two marked time intervals. For a two-level RTS, we expect a Lorentzian spectrum [23]. This is indeed what we observe during the first time interval which shows a clear RTS. The signal in the second time interval results in a 1/f spectrum indicating that the conductance fluctuations are random in this regime. The grey area indicates the region above the cutoff frequency of the amplifier at 1.3 kHz. figure 2(c) shows a shorter section of the same measurement in time interval 1 where a clear RTS is observed. Because the background noise is much lower than the RTS amplitude, we can extract states lifetimes τh,i from such a conductance trace, as indicated in the figure for the high conductance states. We observe here a ratio of the high level conductance to the low level conductance of Gh/Gl ≈ 3. Three reference levels (shown as horizontal dashed lines) are defined at 10, 50 and 90% of the range between the low and high conductance values. The time interval between a mid reference level crossing and the closest following one that occurs after at least one crossing of a high (low) reference level corresponds to a high-state (low-state) lifetime. The histogram of these state lifetimes τh,i is shown in figure 2(d) and shows a fast decay. Fitting an exponential decay function ∝e−t/τ (dashed red curve) to the histogram yields the average lifetime τh = 1.9 ms for the corresponding state (τl = 0.93 ms). For most observed RTS, the fit is significantly more accurate when using a sum of two exponential decays (solid green curve) or a stretched exponential. Using more than two exponential functions provides no substantial further improvements. In the following discussion, we consider various possible explanations for the emergence of the observed RTS and correlate the dynamics of the junction to microscopic aspects. The two conductance values observed in an RTS must correspond to at least two distinct geometrical configurations of the junction. Fluctuations of the number of molecules within the junction can lead to a variability of the conductances observed. The experimental situation is however particular here as we are measuring conductance during closing cycles, i.e. starting from an open junction where no molecule can bridge the electrodes. We then gradually close the electrodes until a signal showing large conductance fluctuations appears. In these conditions, the conductance signal is most probably dominated by the behavior of one molecule in the junction. In such a metal–molecule–metal junction, the fluctuations can arise from changes in the contact between the molecule and the gold electrodes, from changes in the molecular structure or from changes in the electrodes alone as well as in the direct environment of the junction. We first describe the scenario which we deem the most probable for explaining the fluctuations observed. A molecule in the junction can be either bound to both electrodes or to just one electrode with the other bond temporarily broken. Charge transport mediated by a molecular structure covalently bound to electrodes is known to be more efficient than direct tunnelling through vacuum or solvent [24–26]. For a given electrode distance, we thus expect a measurable conductance difference between a junction bearing a molecule covalently bound to one electrode only and a junction with a molecule bridging
3. Identifying random telegraph signals in different molecular solutions To illustrate the emergence of large conductance fluctuations in the presence of Au-binding molecules in solution, we show in figures 1(b) and (c) conductance traces measured in both pure solvent (mesitylene) and a solution of hexanedithiol (C6) molecules. When the electrodes are surrounded by pure mesitylene (figure 1(b)), the conductance signal consists of random fluctuations. We further examine this point below3. When the measurement is done in a hexanedithiol solution, stronger fluctuations can be observed as shown in figure 1(c). For most of the time interval, the conductance shows switching between two well-defined values. The conductance stays at one value before suddenly switching to the other value at a random point in time. The observation of large conductance fluctuations is a generic feature in such systems and is not specific to this particular molecule. It was observed here for hexane, octane and nonanedithiol molecules. The time scale of the switching events is typically smaller than 0.1 ms, i.e. shorter than what our setup can resolve. We emphasize that we focus here on conductance fluctuations linked to the presence of molecules between atomic contacts in solution and at room temperature. Conductance fluctuations and telegraph noise have also been observed in atomic contacts without the presence of molecules and in different experimental conditions [16–18]. In figure 2, we analyze in more detail a conductance trace obtained for a 1 mM nonanedithiol (C9) solution and obtained as described above. The conductance trace shown in figure 2(a) in 3 There is a small conductance drift (about 0.5 × 10−3 G0 in 100 s) which can be attributed either to a mechanical relaxation in the substrate (polyimide layer or stainless steel itself) or to a relaxation due to the adhesive tape employed to prevent shorts between the counter supports and the substrate. This slow drift, below 0.5 pm s−1, doesn't limit the observation of conductance fluctuations taking place at faster time scales.
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Figure 2. (a) Conductance trace G(t) measured in a 1mM nonanedithiol solution showing RTS during the first 30 s, then random fluctuations. (b) Power spectra of the time intervals shown in (a). (c) Section of the random telegraph signal shown in (a). High conductance state lifetimes are indicated. (d) Histogram of the high state lifetimes with exponential decay fits to obtain the average lifetime. Single exponential (dashed red) and sum of two exponentials (solid green). Inset: same data in a logarithmic scale.
further note that changes in the local geometry of a sulphur– gold bond, between for instance atop and bridge arrangement, can lead to a substantial conductance change as well [29–31]. Such microscopic rearrangements may be at the origin of the observed fluctuations. Note that, if the typical time scale for these rearrangements is below our experimental resolution (∼ 0.1 ms), we will only observe conductance values averaged over different configurations, as already discussed above for molecular backbone conformational changes. In our experimental configuration, the confined junction geometry together with intermolecular interactions between molecules at the electrodes' surface may lead to slower rearrangement time scales and measurable conductance fluctuations. A distance change between the electrodes caused by atomic rearrangements due to thermal fluctuations can also cause conductance fluctuations and even low-amplitude RTS. The signals should however be visible in solvent only as well and such RTS are quite rare in pure solvent (an example can be seen in figure 3(a), see next section). If we take a typical tunneling decay constant β ≈ 1 Å−1 [9] (which roughly corresponds to a tunneling slope of 0.2 nm per conductance order of magnitude), conductance fluctuations with a ratio of high to low conductance Gh/Gl ≈ 1.25 would correspond to a distance change of ≈ 0.22 Å which is plausible at room temperature4. The amplitude of the RTS observed for hexanedithiols (Gh/Gl ≈ 2, figure 1(c)) and nonanedithiols (Gh/Gl ≈ 3, figure 2(c)) are
the two electrodes via covalent bonds. This difference will be larger for longer molecules as the bridging can take place at larger electrodes' separation. As we measure conductance while closing the junction, we expect the amplitude of conductance fluctuations to be maximum immediately when the signal appears, i.e. when the distance between electrodes is just sufficient to allow for a bridging by the molecule. Note that the amplitudes of the conductance variations observed here are in agreement with similar STM investigations [13–15]. The amplitude of the current jumps observed in the STM experiments upon tip-substrate bridging events mediated by molecules were observed to span a range of values, from very small increases (by a few percent only) to about an order of magnitude. Different origins, other than bond breaking and forming, could explain large conductance fluctuations in molecular junctions. In particular cases, reversible conformational changes of the molecular backbone can also lead to distinct conductance states, as in molecular switches [27, 28]. Conformational changes from all-trans to one gauche defect could for instance lower the conductance by approximately a factor of ten [29, 30] or even more [31]. Such structural changes are however expected to take place at time scales between 10−11 s to 10−9 s and so only averaged values will be observed in our measurements [29, 31]. Molecular systems exhibiting stable twolevel conductance fluctuations at room temperature require a specific design to achieve stable enough states that can be identified. The observations made here are not of this nature and occur generically in molecular junctions, as previously mentioned. This is further illustrated in figure A1, appendix A where RTS signals are shown for a conjugated compound. In this case, the type of conformational changes described above can be excluded as the molecular backbone is rigid. We
4 We assume G ∝ exp(−β· d). This means that Gh/Gl = exp(−β(dh − dl)) and therefore Δd = dl − dh = − ln(Gh/Gl)/β where the indices h and l refer to the high and low conductance cases, respectively. Note that thermal fluctuations occur at a much faster time scale than the bandwidth of our setup. This means that we cannot observe the full fluctuation amplitude and the distance fluctuation is estimated as a lower limit of the true movement.
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Figure 3. Two sequences of conductance traces G(t) measured without and with octanedithiol. (a) In pure solvent, small amplitude conductance fluctuations are observed. The arrow points to the brief occurrence of a small amplitude telegraph signal. (b) In the octanedithiol containing solution, conductance fluctuations and sometimes RTS of larger amplitude were systematically observed. On the right panel, the relative fluctuation amplitudes of the conductance for each 30 s interval is plotted against the logarithmic average of its conductance. The star symbols indicate the values for the curves shown in the main panel.
however significantly larger. Note that the amplitude of RTS is larger for the longer molecule (nonanedithiol), validating the discussion in the previous paragraph. Conductance fluctuations reaching Gh/Gl ≈ 3 would correspond to a distance change between the electrodes of ≈ 1.1 Å which is improbable to repeatedly happen at room temperature. The large fluctuations observed can therefore not be attributed to thermally driven atomic rearrangements of the electrodes. Finally, the environment was shown to have little effect on the conductance of molecular junctions [32] except in special cases [33]. One may expect that changes in the environment can affect the lifetimes of RTS states but it will not be their direct cause. From the above discussion on the possible origins of conductance fluctuations in our junctions, the repeated formation and breaking of a molecule–metal bond seems the most probable one. In that case, we would expect a thermally activated formation and breaking of the bond, leading to exponentially distributed low and high conductance lifetimes, as observed experimentally. In the following we discuss the lifetime distributions in more detail. We consider an ideal two-state random telegraph signal with instantaneous transitions. When the system is in the high state, with an average state lifetime τ, there is a constant probability per unit time 1/τ for the system to switch to the low state. If A(t) is the probability that the system persists in the high state until time t, then A(t + dt) = A(t)(1 − dt/τ) and dA(t)/dt = − A(t)/τ. Integrating, we obtain A(t) = exp(−t/τ). Writing p(t)dt for the probability that the system switches from high to low within the time interval dt, we can write p(t) = A(t)/τ = τ−1 exp(−t/τ) which corresponds to the lifetimes distribution for each state (probability density). We have illustrated in figure 2(d) for the high conductance state data that the sum of two exponential decays usually provides a better fit to the observed lifetimes distribution in our experiments. This points to the fact that the average state lifetime τh in the high conductance state may vary over the measurement time of a RTS signal, suggesting that at least two microscopic arrangements with distinct lifetimes can occur. This is supported by figure B1 in appendix B where we plot the high and low state lifetimes τh, i and τl, i for a few thousand switching events in nonanedithiol junctions. While the low conductance state lifetimes average
(solid line, average over 50 points) stays essentially constant, the average lifetime for the high conductance state shows a clear increase after about 2200 events. Assuming as justified above that the RTS signal is caused by a molecule anchored within the junction where one bond is being repeatedly formed (high conductance state) and broken (low conductance state), we anticipate that the high conductance state may show slightly distinct lifetimes due the influence of the molecule electrode interaction whereas the low conductance state lifetime will only be dominated by the local diffusion of the anchor group. We however rarely observe changes in average lifetimes as clearly as that shown in figure B1. The fact that a double exponential decay better fits the observed lifetime distributions here cannot be considered as a a hallmark for the high conductance state. Note that a fit using a stretched exponential can also reproduce the lifetime distributions observed which would indicate a broad distribution of average lifetimes for the system, see e.g. [34]. The standard behavior results in a rather constant average lifetime over a single RTS signal, as illustrated in figure B2, appendix B for a hexanedithiol solution. Overall, we have investigated the lifetimes and their distribution for 16 measurement sets from 12 different samples. The lifetimes obtained vary between ≈1 ms and 100 ms where the lower limit is set by the bandwidth of the amplifier. This is comparable to the lifetimes of molecular junctions measured in a liquid environment with an STM when retracting the tip at low velocity [3] which suggests that the RTS lifetimes are also caused by a molecular junction forming and breaking. Indeed, similar conductance fluctuations were observed in the same work during slow opening cycles. Note that much longer lifetimes of molecular junctions have been observed in vacuum [4] where the mobility of the molecules can be expected to be lower due to the absence of solvent. From the signals measured within the approach described in this section, we cannot extract a clear correlation between the conductance values and lifetimes τh and τl of the two states and the relative conductance difference between the states. Clear two level signals are a relatively rare occurrence in the type of measurements presented in this section (≈1% of the time), which prevents a more advanced statistical investigation of their properties as done for instance in [35]. In the next Section, we present a different approach that 5
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Figure 4. The main panels show the standard deviations of the conductance measured during 30 s intervals and divided by the average conductance over the interval. Plot (a) is obtained from a measurement in pure mesitylene whereas for (b) a solution of octanedithiol in mesitylene was used. The dashed grey lines serve as guides to the eye and indicate the maximum fluctuation amplitude in the pure solvent. Histograms of the dG/〈G〉 data are shown to the right of the main panels. The histograms are normalized to the number of curves or data points for opening curves and closing steps, respectively. Top panels: typical histograms from opening conductance curves G(z) in mesitylene and octanedithiol solution (filled histograms) and conductance histograms of the data shown in the main panels (outlined histograms). The dashed black curve is a Gaussian fit to the octanedithiol histogram.
each 30 s interval. The plot for δGrel is shown on the right panel of figure 3(b). The star symbols correspond to the traces shown in the left panel. The square symbols show δGrel for all conductance traces measured during this closing cycle. In figure 4, we present an overview of δGrel values for several closing cycles in mesitylene (figure 4(a)) and in a solution of octanedithiols (figure 4(b)). One symbol in the main panel represents one closing cycle, starting from a fully open junction. On the right panels, the outlined histograms show the distribution of fluctuation amplitudes. The top panels show two different conductance histograms: The outlined histograms show the distribution of average conductance values measured during closing cycles. The filled histograms were generated by performing conventional conductance measurements during opening cycles of the junctions, similarly to our previous work [11, 12]. For the pure solvent, we see that the values for δGrel are spread over one order of magnitude, do not exceed a maximum amplitude δGrel = 0.2 (dashed grey line) and decrease only slightly with increasing 〈G〉. In the presence of octanedithiol molecules in solution, fluctuations of higher amplitude are present for 〈G〉 up to the known molecular conductance values reported for octanedithiol, whereas the fluctuations mostly remain below δGrel = 0.2 at higher 〈G〉. This is further emphasized by the histograms in the right panels of figures 4(a) and (b): while the distribution of δGrel is mostly symmetric for the pure solvent, a clear tail at higher fluctuation amplitudes develops in the histogram for octanedithiols. We now consider the top panel histograms for a comparison between opening (filled histograms) and closing cycles (outlined histograms). For pure mesitylene, both histograms show a rather flat profile without statistically relevant signatures. In the
provides further insight into the relative amplitude of the conductance fluctuations. 4. Systematic measurements in the presence of an octanedithiol solution In this section, we focus on a systematic approach aiming at providing a better overview of the different fluctuation amplitudes observed in the junctions. For this purpose, we focused on a single molecular compound, octanedithiols, showing conductance plateaus around 10−5 to 10−4 G0 [11, 12]. Starting from a fully open configuration, a junction was first closed to reach 10−5 G0. The electrodes were then approached in small steps (Δd ≈ 0.1 Å) once every 30 s and the conductance was recorded as a function of time during the 30 s intervals. The electrodes were not actively moved during the measurement intervals. Figures 3(a) and (b) show typical conductance traces G(t) in a logarithmic scale that were recorded in mesitylene without and with octanedithiol, respectively. The G(t) traces in pure mesitylene show conductance fluctuations and sometimes jumps of small relative amplitude. True RTS are rare and of short duration and low amplitude (arrow). The relative conductance fluctuation amplitude δGrel = δG/〈G〉 (standard deviation of G divided by the average G) does not show any dependence on conductance. With octanedithiol molecules in the solution, fluctuations of much larger amplitude are observed at low conductance, between 10−5 G0 and 10−4 G0. This conductance range corresponds very well to the values of the conductance plateaus observed for octanedithiol measurements in standard break junction measurements performed while opening the junction [11, 12]. To quantify the fluctuation amplitudes, δGrel is calculated for 6
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presence of octanedithiol molecules, both histograms show clear features demonstrating the formation of molecular junctions with a qualitatively similar overall shape. We note that the conductance histogram for the closing cycle shows a large number of counts between 10−4 and 10−3 G0 (indicated by the arrow) as compared to the typical Gaussian distribution observed in opening cycles (dashed line). This can be explained by two related mechanisms [12]: First, the slow closing of the electrodes allows for Au relaxation of the electrode apexes leading to a larger contact surface and thereby favoring the binding of more molecules in parallel. Second, layers of molecules formed on the electrodes will impede further closing of the electrodes below a separation distance on the order of one molecular length, causing a plastic deformation of the gold. This will lead to both more histogram counts in the associated conductance regime and to even blunter tips than by Au relaxation alone. The systematic measurements presented in this section show that while low-amplitude fluctuations are present in measurements with pure solvents as well as in octanedithiol solution, large-amplitude fluctuations only appear in the presence of gold-binding molecules. The amplitudes of the large conductance fluctuations are on the order of single-molecular conductance values. This explains why the fluctuations are not visible any more in conductance ranges well above the singlemolecular conductance. This also further supports that the dominant peak signature around 10−4 in the conductance histogram obtained from standard opening cycles measurements (dashed Gaussian curve in the top panel of figure 4(b)) corresponds to the signature of molecular junctions comprising already a few molecules [12].
EC FP7 ICT SYMONE project (no. 318597), the EC FP7 ITN MOLESCO project (no. 606728) and the Ministerio de Economía y Competitividad, grants CSD2007-0010 and MAT2011-25046. Appendix A. RTS observed for a rigid, conjugated oligomer
Figure A1. Telegraph signal in a 1 mM solution of dithiolated oligo (phenylene ethynylene) (OPE). The ratio of the high state to the low state conductance is about 2.
Appendix B. Time development of lifetimes
5. Conclusions In this study, we have examined random telegraph signals (RTSs) observed during break junction experiments in a solution of goldbinding molecules. We attribute the emergence of such signals to the spontaneous binding and unbinding of the molecule anchor groups to the electrode tips, thereby forming or breaking a metal– molecule–metal junction. Both the formation and the breaking of the molecule–metal bonds are thermally activated and show an exponential distribution of lifetimes for the different conductance states. The observed fluctuations are direct evidence that we are dealing with single or few molecular junctions. The varying RTS amplitudes and time scales reflect the different microscopic arrangements and conductance values possible in such experiments. A better understanding of such fluctuations in systems involving a single or only a few molecules is of particular interest for the development of novel spectroscopic characterization schemes [36]. The present study provides the first insights into such developments. To provide signatures robust enough that they will allow a fingerprinting of molecular compounds, a larger space of parameters needs to be explored, for instance by extending the characterization to different bias voltages.
Figure B1. Scatter plot of the lifetimes for high and low states obtained from the nonanedithiol measurement shown in figure 2 (region 1). The high and low state lifetimes are shown in green and red, respectively. The solid lines are logarithmically averaged values over sliding windows of 50 events. A clear change of the average high conductance state lifetime is seen around event number 2200. As discussed in section 1 and figure 2(d), the sum of two exponential decay functions is required to obtain a good fit to the lifetime distribution for such two level signals.
Acknowledgments We acknowledge support by the Swiss Nanoscience Institute (SNI), the EC FP7 ITN FUNMOLS project (no. 212942), the 7
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Figure B2. Scatter plot of the lifetimes for high and low
states observed in a hexanedithiol solution. The solid lines are logarithmically averaged values over sliding windows of 50 events. No significant changes of the average state lifetimes is observed. A single exponential decay provides a good fit to the lifetime distribution.
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