Analysis of rates of tunneling across self-assembled monolayers (SAMs) of n-alkanethiolates SC n (with n = number of carbon atoms) incorporated in junctions having structure Ag TS -SAM//Ga 2 O 3 /EGaIn leads to a value for the injection tunnel current density J 0 (i.e., the current flowing through an ideal junction with n = 0) of 10 3.6±0.3 A·cm −2 (V = +0.5 V). This estimation of J 0 does not involve an extrapolation in length, because it was possible to measure current densities across SAMs over the range of lengths n = 1−18. This value of J 0 is estimated under the assumption that values of the geometrical contact area equal the values of the effective electrical contact area. Detailed experimental analysis, however, indicates that the roughness of the ). A comparison of the characteristics of conical Ga 2 O 3 / EGaIn tips with the characteristics of other top-electrodes suggests that the EGaIn-based electrodes provide a particularly attractive technology for physical-organic studies of charge transport across SAMs. ■ INTRODUCTIONMeasurements, using a number of techniques, of rates of charge transport by tunneling across self-assembled monolayers (SAMs) of n-alkanethiolates on silver and gold substrates show an interesting, puzzling, and unresolved mixture of consistency and inconsistency. Rates of tunneling across these SAMs follow the simplified Simmons equation,( 1) with the falloff in current density J(V) (A·cm ). Using mercury drops as top-electrodes, measurements of rates of tunneling across n-alkanes anchored to heavily doped silicon surfaces led to β = 0.9 ± 0.2 nC −1 , similar to the values observed for nalkanethiolates on Au and Ag substrates. , observed in large-area junctions using, as top-electrodes, conductive polymers, 13 Hg-drops supporting an insulating organic film (Hg-SAM), 14−16 and Ga 2 O 3 /EGaIn tips. 17−20 Why is there high consistency in values of β, but broad inconsistency in values of J 0 (V) within these systems?A priori, at least four factors might contribute to differences in J 0 (V) among methods of measurements:(i) In large-area junctions, assuming that the effective electrical contact area (A elec )the area through which current actually passescoincides with the geometrical contact area (A geo ) estimated by optical microscopy could result in errors in the conversions of values of current into current densities. Contact between surfaces occurs only through asperities distributed on the surfaces, which are always rough to some extent; in addition, only a fraction of the true, physical contact area is conductive.21−24 Estimations of the effective contact area from measurements of adhesion and friction between surfaces indicate that values of A elec /A geo vary in the range 10 −2 −10 −4 , depending on the hardness of the materials, the heights, widths, and number of asperities on both surfaces, and loads applied to the contacts. 22,23,25−27

This paper compares charge transport across self-assembled monolayers (SAMs) of nalkanethiol containing odd and even numbers of methylenes. Ultraflat template-stripped silver (Ag TS ) surfaces supported the SAMs, while top-electrodes of eutectic galliumindium (EGaIn) contacted the SAMs to form metal/SAM//oxide/EGaIn junctions. TheEGaIn spontaneously reacts with ambient oxygen to form a thin (~ 2 nm) oxide layer.This oxide layer enabled EGaIn to maintain a stable, conical shape (convenient for forming microcontacts to SAMs) while retaining the ability to deform and flow upon contacting a hard surface. Conical electrodes of EGaIn conform (at least partially) to 2 SAMs, and generate high yields of working junctions. Ga 2 O 3 /EGaIn top electrodes enable the collection of statistically significant numbers of data in convenient periods of time. The observed difference in charge transport between n-alkanethiols with odd-and even-numbers of methylenes -the "odd-even effect" -is statistically discernable using these junctions, and demonstrates that this technique is sensitive to small differences in the structure and properties of the SAM. Alkanethiols with an even number of methylenes exhibit the expected exponential decrease in current density (J) with increasing chain length, as do alkanethiols with an odd number of methylenes. This trend disappears, however, when the two datasets are analyzed together; alkanethiols with an even number of methylenes typically show higher J than homologous alkanethiols with an odd number of methylenes. The precision of the present measurements, and the statistical power of the present analysis, were only sufficient to identify, with statistical confidence, the difference between an odd and even number of methylenes with respect to J, but not with respect to the tunneling decay constant, β, or the pre-exponential factor, J 0 .3

This paper applies statistical methods to analyze the large, noisy datasets produced in measurements of tunneling current density (J) through self-assembled monolayers (SAMs) in large-area junctions. It describes and compares the accuracy and precision of procedures for summarizing data for individual SAMs, for comparing two or more SAMs, and for determining the parameters of the Simmons model (β and J 0). For data that contain significant numbers of outliers (i.e. most measurements of charge transport), commonly used statistical techniques-e.g. summarizing data with arithmetic mean and standard deviation, and fitting data using a linear, least-squares algorithm-are prone to large errors. The paper recommends statistical methods that distinguish between real data and artifacts, subject to the assumption that real data (J) are independent and log-normally distributed. Selecting a precise and accurate (conditional on these assumptions) method yields updated values of β and J 0 for charge transport across both odd and even n-alkanethiols (with 99% confidence intervals), and explains that the socalled odd-even effect (for n-alkanethiols on Ag) is largely due to a difference in J 0 between odd and even n-alkanethiols. This conclusion is provisional, in that it depends to some extent on the statistical model assumed, and these assumptions must be tested by future experiments.

Tunneling junctions having the structure Ag TS −S(CH 2 ) n−1 CH 3 // Ga 2 O 3 /EGaIn allow physical−organic studies of charge transport across selfassembled monolayers (SAMs). In ambient conditions, the surface of the liquid metal electrode (EGaIn, 75.5 wt % Ga, 24.5 wt % In, mp 15.7°C) oxidizes and adsorbs-like other high-energy surfaces-adventitious contaminants. The interface between the EGaIn and the SAM thus includes a film of metal oxide, and probably also organic material adsorbed on this film; this interface will influence the properties and operation of the junctions. A combination of structural, chemical, and electrical characterizations leads to four conclusions about Ag TS −S(CH 2 ) n−1 CH 3 // Ga 2 O 3 /EGaIn junctions. (i) The oxide is ∼0.7 nm thick on average, is composed mostly of Ga 2 O 3 , and appears to be self-limiting in its growth. (ii) The structure and composition (but not necessarily the contact area) of the junctions are conserved from junction to junction. (iii) The transport of charge through the junctions is dominated by the alkanethiolate SAM and not by the oxide or by the contaminants. (iv) The interface between the oxide and the eutectic alloy is rough at the micrometer scale. ■ INTRODUCTIONWe, and others, are developing procedures with which to study charge transport across self-assembled monolayers (SAMs). 1−32We have explored two systems, both based on electrodes made of liquid metals (Hg, and a eutectic alloy of gallium and indium, which we abbreviate as EGaIn) and focused on the latter. The latter system has two major components: (i) a SAM supported by a template-stripped silver (Ag TS ) electrode and contacted by (ii) a "top" electrode of EGaIn (75.5 wt % Ga, 24.5 wt % In, mp 15.7°C 33 ) that is a liquid at room temperature and covered with a thin metal oxide film; we refer to these junctions by a nomenclature defined earlier 1 as Ag TS −SR//Ga 2 O 3 /EGaIn, where R is an organic group (which may range in structure from simple n-alkyl groups to more complex functionalities, e.g., aromatics 28 or ferrocenes 13,34,35 ). These junctions are typically formed, characterized, and used in contact with ambient laboratory atmosphere. In these conditions, the surface of EGaIn oxidizes rapidly and spontaneously (for convenience we indicate the composite structure-oxide skin and metal electrode-as "Ga 2 O 3 / EGaIn") and it-as do all other surfaces-adsorbs adventitious contaminants (e.g., water, organic molecules, particles). The electrical resistance, thickness, and heterogeneity of the composite films of metal oxide and contaminants on the surface (and their variability from electrode to electrode, and from junction to junction) have not been characterized: the most serious ambiguity affecting the measurement of charge transport through Ag TS −SR//Ga 2 O 3 /EGaIn junctions is currently the effect of the oxide skin and adventitious contaminants.

This paper compares rates of charge transport across self-assembled monolayers (SAMs) of n-alkanethiolates having odd and even numbers of carbon atoms (n odd and n even ) using junctions with the structure M TS /SAM//Ga 2 O 3 /EGaIn (M = Au or Ag). Measurements of current density, J(V), across SAMs of n-alkanethiolates on Au TS and Ag TS demonstrated a statistically significant odd−even effect on Au TS , but not on Ag TS , that could be detected using this technique. Statistical analysis showed the values of tunneling current density across SAMs of n-alkanethiolates on Au TS with n odd and n even belonging to two separate sets, and while there is a significant difference between the values of injection current density, J 0 , for these two series (log|J 0Au,even | = 4.0 ± 0.3 and log|J 0Au,odd | = 4.5 ± 0.3), the values of tunneling decay constant, β, for n odd and n even alkyl chains are indistinguishable (β Au,even = 0.73 ± 0.02 Å ). A comparison of electrical characteristics across junctions of n-alkanethiolate SAMs on gold and silver electrodes yields indistinguishable values of β and J 0 and indicates that a change that substantially alters the tilt angle of the alkyl chain (and, therefore, the thickness of the SAM) has no influence on the injection current density across SAMs of n-alkanethiolates.