NANO LETTERS
Interpretation of Stochastic Events in Single Molecule Conductance Measurements
2006 Vol. 6, No. 10 2362-2367
Sung-Yeon Jang,†,‡,§ Pramod Reddy,§,| Arun Majumdar,*,‡,|,⊥ and Rachel A. Segalman*,†,‡ Department of Chemical Engineering, UniVersity of California Berkeley, Berkeley, California 94720, Materials Science DiVision, Lawrence Berkeley Laboratory, Berkeley, California 94720, Applied Science and Technology Program, UniVersity of California Berkeley, Berkeley, California 94720, and Departments of Mechanical Engineering & Materials Science and Engineering, UniVersity of California Berkeley, Berkeley, California 94720 Received April 27, 2006; Revised Manuscript Received August 3, 2006
ABSTRACT The electrical conductance of a series of thiol-terminated alkanes, (1,6-hexanedithiol (HDT), 1,8-octanedithiol (ODT), and 1,10-decanedithol (DDT)) was measured using a modified scanning tunneling microscope break junction technique. The interpretation of data obtained in this technique is complicated due to multiple effects such as microscopic details of the metal−molecule junctions, superposition of tunneling currents, and conformational changes in the molecules. A new method called the last-step analysis (LSA) is introduced here to clarify the contribution of these effects. In direct contrast to previous work, LSA does not require any data preselection, making the results less subjective and more reproducible. Finally, LSA was used to obtain the conductance of single molecules (HDT, (3.6 × 10-4)Go; ODT, (4.4 × 10-5)Go; DDT, (5.7 × 10-6)Go). The tunneling decay parameter (β) was calculated, and it was found to be ∼1.0 per carbon atom.
Impressive progress has been made by several groups in developing experimental techniques to study electron transport in metal-molecule junctions using mechanically controllable break junctions,1 nanopores,2 mercury-drop junctions,3,4 cross-wire junctions,5 electromigrated break junctions,6 scanning tunneling microscopy (STM),7,8 and conducting probe atomic force microscopy (CP-AFM)9,10 to study charge transport in metal-molecule-metal junctions. Although each of these techniques has significant merits and is suitable for probing different aspects of charge transport in molecules, they are limited by either having low measurement yields or measuring an ensemble of molecules as opposed to a single molecule.11 Tao and co-workers12 introduced the scanning tunneling microscopy based break junction (STMBJ) technique, where the measurement of conductance is performed by repeatedly making and breaking Au-molecule* Corresponding authors,
[email protected] and Segalman@ berkeley.edu. † Department of Chemical Engineering, University of California Berkeley. ‡ Materials Science Division, Lawrence Berkeley Laboratory. § These authors contributed equally to this paper. | Applied Science and Technology Program, University of California Berkeley. ⊥ Departments of Mechanical Engineering & Materials Science and Engineering, University of California Berkeley. 10.1021/nl0609495 CCC: $33.50 Published on Web 08/31/2006
© 2006 American Chemical Society
Au junctions in a dilute molecular solution at room temperature. In this technique, a large number of measurements are made in a short time. Furthermore, the conductance of a single molecule, rather than an ensemble of molecules, can be measured. Since the formation of electrical contacts with a single molecule at room temperature is a stochastic event and is subject to fluctuations,13 statistical analysis and interpretation of data are critical to obtain the electrical conductance of single molecules. Statistical analysis is further complicated by the additional contribution of tunneling current to the molecular conductance. While some statistical analysis has been presented in the past,14 it should be noted that many of the conclusions from previous work are based on preselection of data prior to statistical analysis, a process which may not only make the results subjective and irreproducible but can also bias scientific interpretation due to potential artifacts. In this Letter, factors affecting the interpretation of data are discussed and a new analysis method for studying single molecule conductance is introduced. We use a modified STM-BJ in which Au-molecule-Au junctions are created using a Au STM tip and a molecule-covered Au substrate15 in ambient conditions. The new analysis method is used to
Figure 1. Conductance traces of Au-Au point contacts (A) and corresponding conductance histogram (B) constructed from ∼1000 traces using the conventional method.
obtain the electrical conductance of thiol-terminated alkanes as a function of molecular length. In this experiment a customized control circuit drives a Au STM tip smoothly at a constant speed toward a Au substrate covered with thiol-terminated molecules (Supporting Information). When the current reaches a preset value, which indicates the formation of a large number of Aumolecule-Au bridges due to the chemical interaction between the thiol groups and the gold surface,16 the tip is then withdrawn until all the molecular bridges in the junctions are completely broken, which is indicated by a current below detection limit. The current between the tip and substrate is continuously monitored using a current amplifier, and the current trace during withdrawal is recorded using an analog/digital converter. The approaching and withdrawing speeds used in the experiments ranged from 4 to 40 nm/s and the applied bias was between 20 and 200 mV. Statistical analysis of the conductance traces obtained in the STM-BJ experiments has traditionally been done by building histograms. One of the well-studied examples is conductance quantization behavior in metal-metal point contact measurements.17-19 Figure 1A shows the conductance trace of Au-Au point contact between a Au STM tip and a bare Au surface. In accordance with other reports, the conductance decreases in a stepwise fashion as the Au-Au contact is pulled apart.20,21 The steps occur preferentially around integer multiples of Go ) 2e2/h (1/13 kΩ ) 77 µS). Statistical analysis is performed using ∼1000 conductance curves by building a histogram using the conventional method reported elsewhere.22,23 In this method, the histogram Nano Lett., Vol. 6, No. 10, 2006
Figure 2. (A) Conductance traces of 1,6-hexanedithiol (HDT) obtained by breaking Au-molecule-Au bridges formed between a Au STM tip and HDT-covered Au substrate. The inset shows the semilog plot of the same conductance traces. (B) Conductance traces obtained by breaking Au-Au point contacts formed between a Au STM tip and a bare Au substrate in the same conductance regime used for HDT. The inset shows the semilog plot of the conductance traces. The applied bias was 100 mV, and the withdrawal speed of these experiments was 30 nm/s.
is constructed by dividing the conductance scale (y-axis of Figure 1A) into intervals or bins of a certain fixed width and counting the number of data points in the conductance trace which fall in each bin. Therefore, the count is decided by the length at each conductance value during the withdrawal. The histogram of the conductance of Au-Au point contacts obtained from our experiment using the conventional analysis method is shown in Figure 1B, which is similar to observations of others.12,18,23 The histogram shows distinct peaks at integer multiples of conductance quantum Go, suggesting conductance quantization of Au-Au point contacts. It should be noted that ∼1000 consecutively obtained conductance curves were used to construct the histogram without any data selection. Conductance measurements of thiol-terminated alkanes were performed using a Au STM tip and a molecule-covered Au substrate. Figure 2A shows the conductance curves obtained using 1,6-hexanedithiol (HDT) covered Au substrate. The conductance traces show stepwise features signifying sudden changes in conductance during tip withdrawal. To verify that these features originate from the molecules, we performed control experiments in the absence of molecules (on a bare Au substrate) in the same conductance regime where the stepwise features in Figure 2A are observed. No stepwise features are observed in the absence 2363
Figure 3. Representative conductance traces of (A) 1,6-hexanedithiol (HDT), (C) 1,8-octanedithiol (ODT), and (E) 1,10-decanedithol (DDT) obtained by breaking Au-molecule-Au bridges formed between a Au STM tip and molecule-covered Au substrate. The arrows point to the conductance traces which show only tunneling current indicating no molecular bridges are present during withdrawal. The applied bias was 100 mV and the withdrawal speed of these experiments was 30 nm/s. The histograms of (B) HDT, (D) ODT, and (F) DDT were constructed using a new analysis method based on the magnitude of the rapid conductance drop in the last step. Approximately 1000 consecutive conductance traces were used to construct histograms.
of molecules as shown in Figure 2B. All the conductance curves in Figure 2B exponentially decay as the distance between the tip and the surface is increased linearly. This is further verified in the inset of Figure 2B, where the semilog plot of conductance as a function of distance between electrodes shows linear behavior, indicating that tunneling current between tip and substrate is the only source of conductance. In contrast, the semilog plot of HDT conductance curve (Figure 2A inset) shows pronounced steps. The occurrence of stepwise features only in the presence of HDT molecules confirms that the molecules are the cause of these features. The rapid conductance drops associated with stepwise features in Figure 2A can result from various reasons. During 2364
withdrawal, the molecular bridges between Au electrodes will break away as the electrodes are pulled apart, resulting in the sudden drop of the conductance. Another cause can be the change in the microscopic details of metal-molecule configurations during the withdrawal.24-26 This change in the spatial arrangement of the Au atoms at the contact can stem from the mobility27 of Au atoms at room temperature and may be further facilitated by the stretching force on the molecular bridges bound to Au surfaces. Furthermore, the conductance can also fluctuate due the conformational change of the molecule during measurement.28 The left side of Figure 3 shows representative conductance traces of 1,6-hexanedithiol (HDT), 1,8-octanedithiol (ODT), and 1,10-decanedithol (DDT) covered Au substrate, respecNano Lett., Vol. 6, No. 10, 2006
Table 1. Conductance of 1,6-Hexanedithiol, 1,8-Octanedithiol, and 1,10-Decandithiol, Obtained Using the Peak Value of the Histograms in Figure 3 and Full Width at Half-Maximum (fwhm) of the Corresponding Histograms conductance (Go) 1,6-hexanedithiol 1,8-octanedithiol 1,10-decandithiol
10-4
3.6 × 4.4 × 10-5 5.7 × 10-6
fwhm (Go) 3.7 × 10-4 4.3 × 10-5 6.1 ×10-6
tively. A significant fraction of the conductance traces of the alkanedithiols contain stepwise features with rapid drop. However, this fraction depends on the length of the molecule and is as follows: 46% for HDT; 64% for ODT; 78% for DDT. Almost all the remaining curves do not contain steps, but they do show exponential decay indicating that molecular bridges are not formed. It should be noted that a small percentage (∼5%) of conductance traces show erratic behavior, which exhibit neither steps nor exponential decays. In the past,14 analysis of conductance data from metalmolecule-metal junctions was performed by first preselecting those conductance-distance curves that show some steps and rejecting those that do not seem to demonstrate this expected behavior. We feel that this process is rather subjective and user dependent, which not only could make the results irreproducible but also could potentially produce artifacts that lead to errors in scientific interpretation. We now propose that to obtain the statistics of single molecule conductance, one should focus on the rapid conductance drop in the last step. This last-step analysis (LSA) (Supporting Information) is motivated by the fact that the last conductance drop can only occur by the breakaway of the last molecular bridge(s) connecting the Au electrodes, whereas other drops can occur due to variation of microscopic details of metalmolecule configurations, change in molecular conformation, or molecule breakaway. Furthermore, the last-step conductance is least susceptible to interference from tunneling conductance, which drops exponentially with distance and, therefore, its contribution to the last step is much less than that for the earlier steps. The histograms thus constructed using LSA of the conductance curves of HDT, ODT, and DDT are shown on the right side of Figure 3, respectively. We used consecutively obtained ∼1000 conductance curves to construct histograms without any preselection of the raw data. The conductances of HDT, ODT, and DDT, obtained using the peak values of the last step histograms shown in Figure 3 are given in Table 1. For comparison, histograms following the conventional method12,14 described earlier were also constructed, but without any preselection of the data. Figure 4A shows the conductance histogram of HDT constructed using the same set of conductance curves used in Figure 3A. As compared to the results in Figure 3A, the histogram does not contain any distinctive peaks. We suspected that the lack of the distinctive peak is because of the strong contribution of conductance curves that show pure tunneling behavior (exponential decay), which could possibly wash out the peaks. To test this possibility, histograms were constructed after selectively removing those conductance traces that show Nano Lett., Vol. 6, No. 10, 2006
Figure 4. (A) Conductance histogram of HDT constructed using the conventional method (ref 23) from ∼1000 conductance traces that were used in Figure 3B. (B) Conductance histogram of HDT constructed using the conventional method after eliminating conductance traces which show only tunneling current indicated by exponential decay (see the marked trace in Figure 3A).
exponential decay. The histograms thus obtained (Figure 4B) still did not show a distinctive peak although it shows a faint shoulder around the peak value observed in the last-step histograms (Figure 4A). Moreover, there are no second or third peaks similar to the peaks in the conductance histograms of alkanedithiol molecules reported in earlier works12 suggesting that the second and third peaks shown in earlier works result from significant data preselection practices that could potentially produce artifacts.14 It should be noted that even the conductance traces that do not show pure tunneling behavior do contain the contributions of the tunneling current. This results in broadening of the peaks in histogram, and if this broadening effect is strong enough, it could lead to the loss of the peaks, especially the second and third peaks. This is one of the reasons why the conductance histograms constructed using this conventional method do not show peaks. Furthermore, the conductance of molecules may fluctuate continuously during tip withdrawal due to change in microscopic details of metalmolecule configurations or conformational changes in the molecules which may further broaden the conventional histograms in Figure 4B. In contrast, the LSA proposed in this Letter is not affected by contributions from the tunneling 2365
which can be used to obtain the tunneling decay parameter β. The value β obtained from the slope in Figure 5 is β ) 1.0 per carbon atom, which is in good agreement with previous reports.29-31 In summary, we measured conductance of thiol-terminated alkanes using modified STM-BJ. A new statistical analysis methodslast-step analysis (LSA)senables us to obtain single molecule conductance by minimizing the contribution of the tunneling current and the stochastic behavior of molecular conductance. The conductances of thiol-terminated alkanes and tunneling decay parameters are obtained.
Figure 5. Natural logarithm of resistance obtained from the histograms in Figure 3 vs the number of carbon atoms in the alkanedithiol chains.
current and the continuous conductance fluctuations because only the last rapid drops, associated with breaking of all the molecular bridge(s), are used to construct the histogram. Note, however, that all the conductance traces are included in LSA without any data preselection. The peak conductance values shown in Table 1 correspond to the most probable conductance of the HDT, ODT, DDT junctions just before complete breakaway of all molecular bridges. These most probable conductances can correspond to a few different scenarios. First, molecules can breakaway sequentially while the electrodes move apart. In this case, the last conductance drop must be ascribed to the breakaway of a single molecular bridge. Another scenario is that the last drop may correspond to a case where several molecular bridges suddenly breakaway in a small time interval faster than the time resolution of the measurement (4 kHz). Unless there is a preferential breakaway of a fixed number of molecular bridges in all the experiments, the fact that the full width at half-maximum (fwhm) is of almost the same size as the conductance value indicates that the last drop cannot correspond to junctions with a varying number of molecules. To the best of our knowledge, there is no a priori reason to believe that a certain number of molecular bridges breakaway preferentially. Furthermore, no change in the results is seen when the withdrawal speed is decreased by an order of magnitude (from 40 to 4 nm/s) indicating that the time resolution of the measurement is sufficient to measure these molecular breakaway events. Thus, the peak in the last step histograms corresponds to an event where a single molecule bridging the electrodes is broken. It should be noted that all the results that we obtained here (the nature of histograms, values of conductance, and the fwhm) are almost identical to the results obtained when we measure the conductance of these molecules using dilute solutions (1 mM) in toluene. The resistance of alkanedithiol molecules connected to gold electrodes near zero bias is expected to show an exponential increase with length.26 In particular, the resistance R is expected to be proportional to exp(βN), where N is the number of carbon atoms in the alkanedithiol and β is the tunneling decay parameter. Figure 5 shows the dependence of single molecule conductance on the length of molecules, 2366
Acknowledgment. We gratefully acknowledge support from the National Science Foundation under Grant No. EEC0425914 and the NSF-NSEC COINS, Berkeley-ITRI Research Center, and DOE-BES Thermoelectrics Program and DOE-BES Plastic Electronics Program at Lawrence Berkeley National Laboratory. We thank Nongjian Tao and Bingqian Xu for their help in understanding the STM break junction experimental technique. Supporting Information Available: Experimental details and additional details of analysis method. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278, 252-254. (2) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550-1552. (3) Holmlin, R.; Haag, R.; Chabinyc, M. L.; Ismagilov, R. F.; Cohen, A. E.; Terfort, A. Rampi, M. A.; Whitesides, G. M. J. Am. Chem. Soc. 2001, 123, 5075-5085. (4) Slowinski, K.; Fong, H. K. Y.; Majda, M. J. Am. Chem. Soc. 1999, 121, 7257-7261. (5) Kushmerick, J. G.; Holt, D. B.; Pollack, S. K.; Ratner, M. A.; Yang, J. C.; Schull, T. L.; Naciri, J.; Moore, M. H.; Shashidhar, R. J. Am. Chem. Soc. 2002, 124, 10654-10655. (6) Park, H.; Park, J.; Lim, A. K. L.; Anderson, E. H.; Alivisatos, A. P.; McEuen, P. L. Nature 2000, 407, 57-60. (7) Guisinger, N. P.; Yoder, N. L.; Hersam, M. C. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 8838-8843. (8) Moth-Poulsen, K.; Patrone, L.; Stuhr-Hansen, N.; Christensen, J. B.; Bourgoin, J.-P.; Bjornholm, T. Nano Lett. 2005, 5, 783-785. (9) Wold, D. J.; Frisbie, C. D. J. Am. Chem. Soc. 2001, 123, 55495556. (10) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Science 2001, 294, 571-574. (11) Lee, T.; Wang, W.; Klemic, J. F.; Zhang, J. J.; Su, J.; Reed, M. A. J. Phys. Chem. B 2004, 108, 8742-8750. (12) Xu, B.; Tao, N. J. Science 2003, 301, 1221-1223. (13) Ramachandran, G. K.; Hopson, T. J.; Rawlett, A. M.; Nagahara, L. A.; Primak, A.; Lindsay, S. M. Science 2003, 300, 1413-1416. (14) He, J.; Sankey, O.; Lee, M.; Tao, N. J.; Li, X.; Lindsay, S. M. Faraday Discuss. 2006, 131, 145-154. (15) Molecule-covered Au substrates layers were prepared using Au-coated mica substrates by exposing the surfaces to a 1 mM solution of alkanedithiols in toluene for a few hours and were subsequently rinsed with pure toluene and dried in nitrogen. (16) Love, J. C.; Estroff, L. A.; Kriebel, J. K.; Nuzzo, R. G.; Whitesides, G. M. Chem. ReV. 2005, 105, 1103-1169. (17) Yanson, A. I.; van Ruitenbeek, J. M. Phys. ReV. Lett. 1997, 79, 2157. (18) Gai, Z.; He, Y.; Yu, H.; Wang, W. S. Phys. ReV. B 1996, 53, 10421045. (19) Smit, R. H. M.; Noat, Y.; Untiedt, C.; Lang, N. D.; van Hemert, M. C.; van Ruitenbeek, J. M. Nature 2002, 419, 906-909. (20) Yanson, A. I.; Bollinger, G. R.; van den Brom, H. E.; Agrait, N.; van Ruitenbeek, J. M. Nature 1998, 395, 783-785.
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