Exceptionally Small Statistical Variations in the Transport Properties of

Communication pubs.acs.org/JACS

Exceptionally Small Statistical Variations in the Transport Properties of Metal−Molecule−Metal Junctions Composed of 80 Oligophenylene Dithiol Molecules Zuoti Xie,⊥,† Ioan Bâldea,*,⊥,§,∥ Abel T. Demissie,† Christopher E. Smith,† Yanfei Wu,† Greg Haugstad,‡ and C. Daniel Frisbie*,† †

Department of Chemical Engineering and Materials Science and Department of Chemistry, ‡Characterization Facility, University of Minnesota, Minneapolis, Minnesota 55455, United States § Theoretical Chemistry, Heidelberg University, INF 229, D-69120 Heidelberg, Germany ∥ Institute of Space Sciences, NILPRP, RO 077125 Bucharest-Măgurele, Romania S Supporting Information *

both the energetic alignment of the dominant molecular orbital (HOMO in the case considered here) relative to the electrodes’ Fermi energy (ε = EF − EHOMO) and the average level width (Γ) determined by the molecular coupling to the electrodes.4−6 Correspondingly, relative resistance deviations δR/R are often 50−100% extracted from thousands of measurements on repeatedly formed single molecule break junctions.7−12 Achieving better microscopic control of the low bias resistance (R) and the overall current−voltage (I−V) behavior is an essential step toward predictable electronic properties in molecular junctions.6,13,14 One possible strategy to improve precision is to increase the number of molecules in the junction (N), for example by making metal contacts having areas of 10 nm2 or more to selfassembled monolayers (SAMs) of electronically functional molecules.15−17 Typical molecular coverages for SAMs are ∼3 molecules/nm2 such that a 10 nm2 junction would contain ∼30 molecules. One could anticipate that if all 30 molecules in a junction were “active” (i.e., well connected to the two electrodes) and served as parallel conductors that the resulting random resistance (conductance) fluctuations in a single measurement would be √30 = 5.5 times smaller than for a single molecule junction (see section 6 in the Supporting Information (SI)). It is a basic question in molecular electronics whether such statistical arguments hold, and indeed whether junctions with precisely controlled areas on the order of 10 nm2 can be fabricated reproducibly. Conducting probe atomic force microscopy (CP-AFM), in which a metal-coated AFM tip is brought into controlled contact with a SAM, provides a simple and so far unique approach to making such junctions with contact areas on the order of 10 nm2.5 However, the nature of statistical fluctuations in these junctions has not been characterized quantitatively and it appears that there are several possible sources for imprecision. For example, it seems unlikely that all the individual metal−molecule contacts in a given CP-AFM junction will be identical. Also, there will be fluctuations in the tip−SAM contact area and molecular surface coverage, especially when surface roughness is considered.18 The resulting stochastic fluctuations in N, previously claimed to extend over

ABSTRACT: Strong stochastic fluctuations witnessed as very broad resistance (R) histograms with widths comparable to or even larger than the most probable values characterize many measurements in the field of molecular electronics, particularly those measurements based on single molecule junctions at room temperature. Here we show that molecular junctions containing 80 oligophenylene dithiol molecules (OPDn, 1 ≤ n ≤ 4) connected in parallel display small relative statistical deviationsδR/R ≈ 25% after only ∼200 independent measurementsand we analyze the sources of these deviations quantitatively. The junctions are made by conducting probe atomic force microscopy (CP-AFM) in which an Au-coated tip contacts a self-assembled monolayer (SAM) of OPDs on Au. Using contact mechanics and direct measurements of the molecular surface coverage, the tip radius, tip-SAM adhesion force (F), and sample elastic modulus (E), we find that the tipSAM contact area is approximately 25 nm2, corresponding to about 80 molecules in the junction. Supplementing this information with I−V data and an analytic transport model, we are able to quantitatively describe the sources of deviations δR in R: namely, δN (deviations in the number of molecules in the junction), δε (deviations in energetic position of the dominant molecular orbital), and δΓ (deviations in molecule-electrode coupling). Our main results are (1) direct determination of N; (2) demonstration that δN/N for CP-AFM junctions is remarkably small (≤2%) and that the largest contributions to δR are δε and δΓ; (3) demonstration that δR/R after only ∼200 measurements is substantially smaller than most reports based on >1000 measurements for single molecule break junctions. Overall, these results highlight the excellent reproducibility of junctions composed of tens of parallel molecules, which may be important for continued efforts to build robust molecular devices.

D

espite significant advances, molecular electronics remains confronted with the challenge of creating reproducible devices.1−4 Variances in electrode−molecule contacts impact © 2017 American Chemical Society

Received: February 23, 2017 Published: April 10, 2017 5696

DOI: 10.1021/jacs.7b01918 J. Am. Chem. Soc. 2017, 139, 5696−5699

Communication

Journal of the American Chemical Society

Figure 1. (A) Schematic representation of the CP-AFM setup for Au−OPDn−Au junctions (n = 1, 2, 3, 4). Representative histograms for (B) low bias resistance R; (C) transition voltage Vt.

Equation 2 implies that the fluctuations in the CP-AFM junctions arise from contributions of three variables: (1) the number of molecules (N) in the contact area; (2) the HOMO energy offset ε for charge (hole5) tunneling; (3) the interface coupling of the junctions Γ. The relative standard deviations δR/R, δN/N, and δε/ε can be determined from experimental data, while δΓ2/Γ2 can be obtained by subtraction via eq 2. Figure 1B displays the R-histograms of our OPDn CP-AFM junctions. About ∼200 resistance measurements were collected for each junction as described elsewhere.5 The relative standard deviations δR/R for OPD1−OPD3 junctions are 25%; these values are listed in Table 1. The slightly larger deviations δR/R ≈

several orders of magnitude,19 may be expected to play an important role in the statistics of CP-AFM junctions, yet a detailed investigation of the deviations δN is missing to date. The goals of the current work were to determine N and δN and also to gain a quantitative understanding of the principal sources of variance in R for CP-AFM junctions. We chose as a model system SAMs of oligophenylene dithiols (OPDs) on Au, Figure 1A, because OPDs are commonly employed in molecular electronics experiments8−10,20 and we have measured their transport properties previously.5 Our analysis was aided by a recently developed analytical model for junction conductance that provides quantitative estimates of ε and Γ from I−V characteristics.5,21−23 Thus, by combining chemical, mechanical, and electrical measurements we were able to (1) determine the values of N, δN, ε, δε, Γ, and δΓ for CP-AFM junctions based on OPD1−4; (2) unambiguously demonstrate that fluctuations in N do not represent the major source of R-variance; and (3) show that after ∼200 measurements values of δR/R = 25%, substantially smaller than those obtained after thousands of measurements on single molecule break junctions. Importantly, we find that N is about 80 for CP-AFM junctions based on OPDs andthis is the crucial point for molecular electronicsincreasing the number of molecules in the junction by a factor of 80 does not increase statistical deviations compared to single molecule measurements, but rather decreases it with a scaling that approximately matches expectations for a parallel array of molecules. Our approach is to consider the individual sources of variance theoretically and then measure the contributions in benchmark CP-AFM junctions consisting of OPDs linked to gold electrodes, i.e. Au−OPDn−Au junctions (n = 1, 2, 3, 4), Figure 1A. The assembly of these junctions is described elsewhere.5 A key feature of our work is that we have analyzed the fluctuations using a single level off-resonant tunneling model. For charge transport dominated by Lorentzian transmission through a single (HOMO) level located at ε = EF − EHOMO sufficiently far away from the electrode Fermi energy (ε ≫ Γ), the low bias resistance R of a bundle of N molecules forming a junction can be expressed as R 0/R = N (R 0/R1) = N Γ 2/ε 2

Table 1. Summary of the Main Results for the OPD-Based CPAFM Junctions Studied in the Present Work OPD1

OPD2

OPD3

OPD4

R (kΩ) δR/R Σ (molec/nm2) A (nm2) F (nN) δF/F N δN/N ΔΦ (eV) δ(ΔΦ)/ΔΦ Vt (V) δVt/Vt ε (eV) 2δε/ε Γ (meV) δ Γ2/Γ2

6.06 0.23 3.3 24 −13.4 0.02 80 0.02 −0.90 0.01 1.01 0.07 0.87 0.14 141.88 0.18

26.83 0.24 3.3 25 −13.8 0.02 82 0.01 −0.85 0.01 0.84 0.08 0.73 0.15 56.23 0.19

150.41 0.26 3.3 25 −13.5 0.02 81 0.01 −0.90 0.01 0.65 0.12 0.56 0.23 18.17 0.12

638.68 0.51 3.3 24 −13.4 0.02 80 0.02 −0.84 0.01 0.55 0.11 0.47 0.22 7.54 0.46

50% for OPD4 junctions, also shown in Table 1, may be related to the more special case of this molecular species.5 By and large, these fluctuations are altogether small, a fact that we mainly attribute to the flat substrate, the high quality of the OPD SAMs, and the significant “signal averaging” that occurs due to the N parallel molecules in the contact, as discussed further below.18 To understand the sources of resistance fluctuations, eq 2, we first focus on N and its standard deviation δN. N is a key quantity of a CP-AFM junction, as it makes the difference between total resistance R and R1, the resistance of a single molecule junction. To obtain the value of N, we employed nuclear analysis techniques to determine the SAM coverage Σ (= N/A) and adhesion (pull-off) force F measurements to determine the tip− SAM contact area A via contact mechanics.

(1)

where R0 = 12.9 kΩ is the resistance quantum.5 By assuming normal statistical distributions of the quantities entering the righthand side of eq 1, the following relationship between the corresponding relative statistical variances can be obtained (see derivation in the SI). 2 ⎛ δR ⎞2 ⎛ δN ⎞2 ⎛ δε ⎞2 ⎛ δ Γ 2 ⎞ ⎜ ⎟ ≈ ⎜ ⎟ + ⎜2 ⎟ + ⎜ ⎟ ⎝R ⎠ ⎝N ⎠ ⎝ ε⎠ ⎝ Γ2 ⎠

Quantity

(2) 5697


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Figure 2. Results for OPDn (n = 1, 2, 3, 4) self-assembled on Au: (A) NRA C spectra; (B) surface coverage Σ determined by NRA and RBS.

Figure 3. Representative histograms of (A) adhesion force F, (B) contact areas computed as indicated in the SI, and (C) SAM-driven change in work function ΔΦ for OPDn (n = 1, 2, 3, 4) adsorbed on gold.

(δN /N )2 = (δA /A)2 + (δ Σ /Σ)2 ;

Recently, we have shown that nuclear reaction analysis (NRA) and Rutherford backscattering spectrometry (RBS) are excellent tools to determine the coverage of SAMs on metals.24 In NRA, incident high energy 42He2+ particles penetrate 12 6 C forming an intermediate excited 16 O* nuclear states that immediately decay 8 4 2+ back to the ground state 12 6 C by emission of a 2He particle at a well-defined energy.24 This process has approximately 100-fold greater cross section than conventional RBS. The emitted 42He2+ particles are counted to yield the surface coverage of C atoms. The NRA carbon spectrum for OPD SAMs is shown in Figure 2A; the C signal increased with the number of phenyl rings, as expected (see also Figure S2C). The molecular surface coverage Σ shown in Figure 2B was obtained by dividing the atomic coverages Σ C by the corresponding stoichiometry (atoms/molecule). The average coverages for OPDn (n = 1, 2, 3, 4) on Au are ΣC/6n = 3.5 ± 0.1 molecules/nm2. We also employed RBS to measure the surface coverage of S atoms, ΣS (see Supporting Information and Figure 2B). Again, normalizing by the stoichiometry, we found ΣS/2 = 3.2 ± 0.1 OPDn molecules/nm2, in good agreement with the NRA results. The coverages Σ in Table 1 are the average values of NRA and RBS results for OPDn. Next, to determine the tip−SAM contact area A = πa2, we employed continuum contact mechanics (i.e., the Maugis− Dugdale (MD) model)25 in combination with measured values of the tip−SAM adhesion force F (Figure 3A), tip radius R, and equivalent sample modulus E, which are listed in Table 1 and discussed in more detail in the Supporting Information. Note that the deviations in F, Figure 3A and Table 1, are again small, on the order of 1−2%. From the MD model we thus find that the contact areas are approximately 25 nm2 for all OPD SAMs, Figure 3B. Using the surface coverage Σ, Table 1, the number of OPD molecules N = AΣ in each junction is about 80, independent of molecular length, Table 1. As discussed in the Supporting Information, the relative variance in N is given by

δ Σ /Σ≈δ(ΔΦ)/|ΔΦ|

(3)

and can be determined from measurements of the adhesive force F (since A = πa2, and a = a(F) depends on F, cf. eqs S7 and S8 in the SI) and of the SAM-driven changes in the Au electrode work function ΔΦ = ΦSAM − Φ. The latter can be deduced from scanning Kelvin probe microscopy (SKPM). The changes in the work function ΔΦ show an odd−even effect, Figure 3C, which is related to the different symmetries revealed by our ab initio calculations: OPD1 and OPD3 have Ci symmetry, while OPD2 and OPD4 have C2 symmetry. To the point, however, the very small and comparable relative fluctuations δA/A and δ(ΔΦ)/ |ΔΦ| imply via eq 3 equally small relative fluctuations both in the number N of molecules in the junctions and the SAM coverage Σ. This further demonstrates that the OPD SAMs are homogeneous both over small regions (∼A) and large areas (≫A). The result is that the relative deviations in N for all junctions

δN /N ≤ 2%

(4)

are much less than the deviations in the low bias resistance, Figure 1B and Table 1. Thus, fluctuations in N are not the principal cause of deviations in R. Returning to eq 2, the relative deviation δε/ε can be directly extracted from the I−V data by using transition voltage spectroscopy (TVS5,26) as follows, ε=

3e Vt /2; δε /ε = δVt /Vt

(5)

where e and Vt are the elementary charge and the transition voltage, respectively. Figure 1C displays the Vt histograms for OPDn junctions, and from Table 1 it is evident that δε/ε ranges from 7% to 12% which is far greater than δN/N. Moreover, with δN/N and δε/ε in hand, we are in a position to determine δΓ2/Γ2 from eq 2. Values of δΓ2/Γ2 are shown in Table 1 and are 12−19% for OPD1−3. The relative deviations presented in Table 1 demonstrate that fluctuations in the coupling Γ have a larger 5698



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contribution to the fluctuations of R than the HOMO energy offset ε, while the fluctuation in the number N of molecules in the junction is negligible. The relatively large role of Γ indicates that there is room for improvement in the metal−molecule contacts in CP-AFM junctions. Still, even with this source of imprecision, the deviations in R are smaller for multimolecule CP-AFM junctions (δR/R = 25% after ∼200 measurements) than for many single molecule break junctions at room temperature (δR/R ≈ 50− 100% after 1000 measurements). This is likely due to the greater number of molecules N in the CP-AFM junction, which gives simultaneous averaging over various molecular configurations in a single measurement. In the simplest approximation that assumes the causes of random error are identical in the two junctions, one expects that fluctuations in R will decrease as √Nt, where t is the number of separate junctions formed and tested. Therefore, R measurements on 100 junctions containing 100 molecules should have √10 ≈ 3 times smaller deviation than R measurements on 1000 single molecule junctions. In so far as we are able to make the comparison based on results in the literature,9−11 it appears that our results here are approximately consistent with this picture. Clearly more experiments are required to determine the precise scaling of δR/R on N and t. To conclude, we have presented a detailed analysis of the causes of stochastic fluctuations in CP-AFM molecular junctions featuring 25 nm2 contacts to close-packed SAMs of conjugated molecules. We have shown that variations in the number of molecules N in the junctions are not the source of resistance variations; rather, variations in ε and Γ dominate. Furthermore, resistance variations for these multimolecule junctions appear to be smaller than for single molecule junctions, suggesting that increasing junction contact areas to increase N may provide a route to molecular junctions with more precisely defined electrical properties. Overall, the experimental and theoretical methods reported provide a useful framework to design experiments to suppress the effects of fluctuations, which is an important step toward improving the reproducibility of molecular devices and the precision of molecular electronics measurements.

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ACKNOWLEDGMENTS Financial support for this work from US National Science Foundation (CHE-1213876) and the Deutsche Forschungsgemeinschaft (Grant BA 1799/3-1) is gratefully acknowledged. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from the NSF through the MRSEC program, and computational resources were provided by the State of Baden-Württemberg through bwHPC and the German Research Foundation (DFG) through Grant No. INST 40/467-1 FUGG.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b01918.

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Experimental and theoretical details, supplementary tables and figures (PDF)

AUTHOR INFORMATION

Corresponding Authors

*[email protected] *[email protected] ORCID

Zuoti Xie: 0000-0002-1828-0122 Ioan Bâldea: 0000-0003-4860-5757 Christopher E. Smith: 0000-0002-2991-6050 Author Contributions ⊥

Z.X. and I.B. contributed equally.

Notes

The authors declare no competing financial interest. 5699


Exceptionally Small Statistical Variations in the Transport Properties of

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