Charge Transport and Rectification in Arrays of SAM-Based Tunneling Junctions

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Introduction
Molecular electronics 1 originally promised that molecule(s) bridging two or more electrodes would generate electronic function, and overcome the scaling limits of conventional semiconductor technology. 2 So far, there have been no commercially successful electronic devices employing small molecules as the active element.
Fabricating even simple molecular circuits that incorporate more than a handful of molecules is a challenge: most fabrication techniques have low yields, 3 produce junctions that are dominated by artifacts 4 (especially conducting filaments 5,6,7,8 ), and generate too few reliable data for statistical analysis (the work of Lee et al. provides an exception 9 ).
Largely absent are physical-organic studies connecting molecular structure and electrical properties, and studies that include measurements as a function of temperaturemeasurements necessary to determine the mechanism(s) of charge transport across SAMbased junctions (the work of Allara et al. 10 and Tao et al. 11 provide examples of successful studies). Here we describe a technique that generates small arrays (seven junctions) of SAM-based junctions with satisfactory yields (70 -90%) of working devices; this technique makes it possible to conduct physical-organic studies with statistically large numbers of data (N = 400 -800), and to do so over a range of temperatures (T) from 90 to 293 K.
Studying the rectification ratios, rather than current densities, has the advantage that the current measured in one direction of bias serves as a reference for the current measured at the opposite bias and, thus, eliminates many of the uncertainties related to contact resistances or contact areas. The junction at one bias is the reference for the junction at the opposite bias.
Most research, both theoretically and experimentally, that has had the objective of developing the molecular analogue of a diode has been based on the so-called "electron donor-bridge-acceptor" compounds described in a seminal paper by Aviram and Ratner. 12 Tunneling junctions incorporating these molecules, 13,14,15 and others, 16,17 (including one example reported by us 18 ) have rectified currents, but neither the mechanism of charge transport nor the origin of the observed rectification have been unambiguously established in any junction. Four factors underlie this ambiguity: i) structural information on SAMs only exists for a relatively small number of molecular precursors; 19 virtually no structural information is available for SAMs incorporating molecules with the donorbridge-acceptor architecture, due to their structural complexity. ii) Asymmetries other than an electric dipole, present in either the SAMs themselves or in the junctions, can 4 contribute to rectification; 20 many of the previous studies do not rule out these other possible sources of rectification using appropriate controls and statistics. iii) The reported rectification ratios have typically been low (1 < R < 5. 16,17,18 ). Without adequate statistical support, most of these values are not distinguishable from R ~1. iv) J(V) measurements as a function of temperature have not been conducted. 10,11,21 These studies, as a group, have not considered molecular rectifiers in which a change occurs in the mechanism of charge transport (e.g., from tunneling to hopping) as applied bias switches from one direction to the other; we believe that such junctions have the potential to yield large rectification ratios (R > 10 2 ).

Fabrication of the Devices
We have reported that a eutectic alloy of gallium and indium (EGaIn) with its superficial layer of Ga 2 O 3 , can be molded into cone-shaped tips that are useful to form electrical contacts with SAMs 22,23 : the properties of Ga 2 O 3 /EGaIn resemble that of a non-Newtonian fluid. 24 This method affords SAM-based junctions, with high yields of working devices, and enables statistical analysis through the collection of large numbers of data. These junctions -with the top-electrode suspended from a syringe -are convenient to use, but they lack the encapsulation and addressability needed to operate in a pressure-and temperature-controlled chamber. Figure 1 Figure 2 shows optical micrographs of a complete device.
Figs. 1F and 1G show idealized views of the junctions. In reality, the SAMs have defects due to i) step edges, ii) phase boundaries, iii) pin holes, iv) impurities, and v) grain boundaries. 19 To reduce the number of defects in the SAM relative to the number present in the rough top-surface of evaporated silver, we used ultra-flat, template-striped silver (Ag TS ) electrodes embedded in cured optical adhesive (OA). 25 It is important to embed the electrodes in OA to prevent free-standing structures of Ag on the wafer, with edges at which the SAMs can not pack densely, 26 that may cause shorts once the channels are filled with Ga 2 O 3 /EGaIn.
The atomic force micrograph shows two important characteristics of these electrodes  9 This procedure, thus, generates embedded electrodes that are flat, but the topography at the interface between the metal and OA is not completely smooth. Figure 1H sketches this AO/Ag TS interface schematically.

Statistical Analysis.
To account for defects in the tunneling junctions, to discriminate artifacts from real data, and to determine the yields of working devices, we believe it is essential to collect, and to analyze statistically, large numbers of data. 9 Although statistical analyses are common in (and an essential part of) studies involving break junctions, 30 and junctions involving scanning probes, 11 Lee et al. 9 was the first to address, with statistical analysis of many data, the shortcomings of SAM-based junctions having evaporated metal topelectrodes prepared using the very low-yielding procedures reported in most prior work.
We used a procedure for the statistical analysis of the data that we have described previously (see Additional Information and Methods). 23 We constructed histograms of all values of J for each measured potential. We fitted all our data to single Gaussian functions using a non-linear least squares fitting procedure to obtain the log-mean value of J for each measured potential, and its log-standard deviation. We emphasize that no data are omitted: we have not selected data.

Junctions with SAMs of SC n-1 CH 3
Figures 3A and B show, as expected from a large body of previous work, that the current density through SAMs of alkanethiols 4,9,31,32,33 i) depends exponentially on the thickness (d (Å)) of the SAM, ii) depends linearly on the bias in the low-bias regime, and 11 iii) is independent of the temperature T. All these observations indicate that the mechanism of charge transport is tunneling. The tunneling decay coefficient β (Å -1 ) can be determined using eq. 2 (J 0 (A/cm 2 ) is a constant that depends on the system and includes contact resistance). (2) We found that β = 0.80 ± 0. including those obtained with cone-shaped tips of Ga 3 O 2 /EGaIn. 22 (Our initial description 22 of these cone-shaped electrodes gave values of J that we interpreted to indicate a significantly lower value: β = 0.6 per CH 2 . We now believe this interpretation was incorrect, and that a value of β = 1.0 per CH 2 is correct. We will discuss the origin of this error in a separate paper. 34 ). Figure 3A shows a temperature-dependent measurement of J(V) of a Ag TS -SC 13 CH 3 //Ga 2 O 3 /EGaIn junction (see Methods; " TS " = template stripped). The devices we used in this study could be cooled from 293 K to 110 K, and warmed again to 293 K, without changing their J(V) characteristics (in vacuum at 1 × 10 -6 bar). From this experiment we conclude that neither i) solidification of EGaIn at ~ 250 K, nor ii) the differences between the thermal expansion coefficients for PDMS (3 × 10 - Inset, the histogram of the rectification ratios with a Gaussian fit to this histogram. We did not select data prior to analysis, and the Gaussian function is a fit to all data (see additional information for details). D) Three J(V) curves measured at three different temperatures (T = 110, 250, and 293 K). 13 14

The Layer of Ga 2 O 3
The junctions have three uncertainties all related to the layer of Ga 2 O 3 . i) The resistance of the layer of Ga 2 O 3 : we estimated the resistance of the layer of Ga 2 O 3 and concluded that the resistance is approximately four orders of magnitude less than that of a SAM of SC 10 CH 3 (see Additional Information). 23 ii) The thickness of the layer of Ga 2 O 3 : we measured the thickness of the layer of Ga 2 O 3 on a drop of Ga 2 O 3 /EGaIn to be less than 2.0 nm (see Additional Information). 24 iii) The topography of contact of We believe that a layer of Ga 2 O 3 at the PDMS interface forms during filling of the channels, since PDMS is permeable to oxygen. 24 This layer interacts strongly with the walls of the microchannel and is important for stabilizing the EGaIn in the microchannel (EGaIn has a higher surface tension than Hg, but Hg -because its surface tension is not lowered by formation of an oxide layer --does not form stable features in microchannels in PDMS). 24 We have no direct evidence describing the interface between the Ga 2 O 3 /EGaIn and the SAM, but we infer that a discontinuous layer of Ga 2 O 3 forms at this interface (see Additional Information). In our discussions we assume that the layer of Ga 2 O 3 is present. In any case, a layer of Ga 2 O 3 may influence the values of J, but it will not influence the value of R, because the value of R is the ratio of the current densities measured at opposite bias across the same junction (eq. 1).

Temperature-Dependent Measurements of Ag TS -SC 11 Fc//Ga 2 O 3 /EGaIn Junctions
To clarify the mechanisms of charge transport across the Ag TS -SC 11 Fc//Ga 2 O 3 /EGaIn junctions, we measured the dependence of J(V) on temperature. Figure 3D shows three  Hence, at T < 190 K, tunneling is the dominant mechanism of charge transport over the entire range of applied bias (-1.0 V to 1.0 V). (3)

The Mechanism of Rectification
All these observations can be rationalized by the model of charge transport proposed in Figure   20 Activation of the hopping mechanism at negative bias led to values of J that were two orders of magnitude higher (at room temperature) than those observed with tunneling alone at positive bias; thus, in our junctions, hopping is more efficient in the transport of charge than tunneling (Fig. 4). We infer that tunneling is the rate-limiting step in the transport of charge, and that the life-time of the Fc + species is probably short. We do not know how many Fc groups are oxidized at any given time, or how the Fc + -ions interact with Ga 2 O 3 -layer. The Fc + -ions will probably have a stronger interaction (perhaps ionic) with the Ga 2 O 3 -layer than neutral Fc moieties. We believe that the layer of Ga 2 O 3 does not significantly affect the mechanism of charge transport across the SAMs (see above and Additional Information).

The Large Value of R
The large observed rectification ratio (R ≈ 130) for the Ag TS -SC 11 Fc//Ga 2 O 3 /EGaIn junctions cannot be explained solely either by the presence of an asymmetrical tunneling barrier within the junction, or by citing the difference in potential drops across the Fc moiety and the alkyl chain. Theoretical studies incorporating either of these effects have suggested that for molecular tunneling junctions, the rectification ratios can not exceed ~ 20. 47 Those studies did not, however, consider a change in the mechanism of charge transport between forward and reverse bias as a mechanism that might result in high rectification ratios. The values of R can be rationalized by the fact that hopping (when k B T ≥ E a ) is more efficient in the transport of charge (i.e. allows for a higher current) than tunneling ( Figure   4). When the HOMO of the Fc does not participate in charge transport, the charge must tunnel (elastically or inelastically) through the entire width of the junction, i.e., roughly the whole length of SC 11 Fc molecule defined by the lengths of the SC 11 chain (d SC11 , 1.3 nm) and the Fc moiety (d Fc , 0.66 nm). When the HOMO of the Fc falls between the Fermi levels of the electrodes, charge can tunnel from the HOMO of the Fc across the C 11 chain, followed by hopping across the Fc moiety. This change in the mechanism of charge transport from tunneling to hopping effectively reduces the width of the tunneling barrier from d SC11 + d Fc to d SC11 . Thus, the rectification ratio is approximately the ratio of the tunneling current densities across the whole SAM (J SC11Fc ) to the tunneling current density across the SC 11 moiety (J SC11 ) and can be estimated using eq. 6 (with β SC11 = the decay constant across SC 11 (Å -1 , or per CH 2 ) and β Fc = the decay constant across the Fc moiety (Å -1 , or per CH 2 )): We do not know the value of β Fc , but have assumed β alkyl = β Fc = 0.80 Å -1 (or 1.0 per CH 2 ) to obtain a lower-limit value of = 2.0 × 10 2 . This semi-quantitative theoretical estimation of R is compatible with the observed rectification ratio of R ≈ 1.3 × 10 2 . This proposed model also agrees with the observation that the rectification ratios are close to unity at temperatures less than 190 K (Fig. 4A), because hopping becomes less efficient than tunneling when k B T << E a . At low temperatures, therefore, the hopping mechanism is eliminated and the Fc moiety becomes part of the tunneling barrier in both directions of bias. 24

Conclusions
To realize potential applications of SAM-based devices, the mechanisms of charge transport across these SAM-based junctions must be understood. This

Methods
Preparation of the SAMs. The synthesis of HSC 11 Fc followed a procedure described in the literature. 49  Flipping the glass/OA/Ag composite exposed the ultra-flat silver electrodes that were originally in contact with the Si/SiO 2 wafer (Fig. 1G). 50 We immersed the electrodes in the ethanolic solutions of the thiols which we kept under an atmosphere of N 2 within 5 s after template-stripping to minimize contamination of the metal surfaces.
Oxidation of the PDMS with an air-plasma (500 mTorr, 60 s) prior to alignment improved the interaction of the Ga 2 O 3 with the PDMS inside the microchannels. We positioned the microchannels (30 µm wide, 30 µm deep, and 8000 µm long) in PDMS perpendicularly to the electrodes. The PDMS formed a contact with the OA/Ag TS surface that was strong enough to withstand further handling, and provided enough mechanical stability to withstand everyday handling in the lab; it also was sufficiently stable to perform J(V) measurements as a functions of temperature. We filled the microchannel with EGaIn by applying reduced pressure (500 Torr) to the outlet of the channel with a drop of Ga 2 O 3 /EGaIn at the inlet of the channel. To facilitate contact with the outlet of the channel in PDMS, we fitted a metal tube to one end of a rubber hose, the other end of which was connected to house vacuum. The vacuum was just enough to force the EGaIn through the channel. We believe that metallic EGaIn fills the channels and that, afterwards, a layer of Ga 2 O 3 forms at the surface of EGaIn (see Additional Information).
We applied and removed the vacuum gently, for we found that applying large forces on the PDMS (with the channel filled with Ga 2 O 3 /EGaIn) resulted in shorts. During filling, the Ga 2 O 3 /EGaIn behaves as a liquid and readily fills the channel, but returns to its elastic state once the channel is filled and atmospheric pressure is restored. 24 We hypothesize that the strong interaction of the Ga 2 O 3 with the oxidized PDMS inside the microchannels resulted in mechanically stable structures (see Additional information).

Temperature-Dependent
To these histograms, we fitted Gaussians to obtain the log-mean for J and log-standard deviation (see Additional Information).