Rectification in Tunneling Junctions: 2,2#-Bipyridyl-Terminated n -Alkanethiolates

Molecular rectification is a particularly attractive phenomenon to examine in studying structure-property relationships in charge transport across molecular junctions, since the tunneling currents across the same molecular junction are measured, with only a change in the sign of the bias, with the same electrodes, molecule(s), and contacts. This type of experiment minimizes the complexities arising from measurements of current densities at one polarity using replicate junctions. This paper describes a new organic molecular rectifier: a junction having the structure Ag TS /S(CH 2 ) 11 -4-methyl-2,2'-bipyridyl//Ga 2 O 3 /EGaIn (Ag TS : template-stripped silver substrate; EGaIn: eutectic gallium-indium alloy) which shows reproducible rectification with mean r + = | J (+1.0V)|/| J (-1.0V)| = 85 ± 2. This system is important because rectification occurs at a polarity opposite to that of the analogous but much more extensively studied systems based on ferrocene. It establishes (again) that rectification is due to the SAM, and not to redox reactions involving the Ga 2 O 3 film, and confirms that rectification is not related to the polarity in the junction. Comparisons among SAM-based junctions incorporating the Ga 2 O 3 /EGaIn top-electrode and a variety of heterocyclic terminal groups indicate that the metal-free bipyridyl group, not other features of the junction, is responsible for the rectification. The paper also describes a structural and mechanistic hypothesis that suggests a partial rationalization of values of rectification available in the literature.


INTRODUCTION
One goal of the field of molecular electronics is to relate the electrical behavior of molecular junctions to the chemical structure of the molecules they incorporate. Molecular rectificationthe asymmetric response of currents to applied potentials of equal magnitude but opposite sign in electrode-molecule(s)-electrode junctions-was an early justification for the study of molecular electronics. 1 The potential to control rectification by designing molecule(s), and/or their contacts with the electrodes in these junctions, has been the subject of a number of theoretical and experimental studies. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Interpreting ostensible examples of rectification, and understanding the mechanism of rectification in these examples, has been difficult because some of the reported data have not been independently validated. One system that has been thoroughly studied, and reproduced in several laboratories [18][19][20][21] uses the well-described "EGaIn-junction" 18,[20][21][22][23][24][25][26][27][28] with the form Ag TS /S(CH 2 ) 11 Fc n //Ga 2 O 3 /EGaIn (where Fc n is either ferrocene or biferrocene). These junctions give rectification ratios of |J(-1.0V)|/|J(+1.0V)| = ~150 for Fc, 20 and ~500 for Fc 2 . 21 The higher current is at negative polarity (e.g., the electrode close to the Fc group is oxidizing). The mechanism of this rectification is well defined (the detailed energy diagrams for rectification are discussed elsewhere 20,21 ): it involves a change in mechanism-from tunneling across the entire molecule at one bias, to hopping (from the Fc to the electrode due to energetic proximity of HOMO of Fc (-5.0 eV) to the Fermi level of the Ga 2 O 3 /EGaIn electrode (−4.3 eV) at zero bias) 29 followed by tunneling at the opposite polarity. The generality of rectification in SAM-based junctions remains unclear, as does the range of mechanisms that can produces rectification.
This work had three objectives. i) It was intended to use the Ga 2 O 3 /EGaIn top-electrode to search for compositionally well-defined junctions-other than the Fc-containing systems-to study rectification. ii) It was particularly concerned with finding examples of molecules that rectify at polarity opposite to that required for rectification in Fc and Fc 2 , in order to demonstrate that redox reactions involving the Ga 2 O 3 film on the surface of the EGaIn electrode do not play a role in rectification. iii) It was designed to examine examples of rectification reported in the literature, and to search for common conceptual threads to correct them. This paper describes a molecular rectifier (Figure 1a) that shows a large, reproducible, unambiguous rectification ratio (|J(+1.0V)|/|J(-1.0V)| = ~ 85) having polarity opposite to that of the Fc n -based junctions; this junction has the structure Ag TS /S(CH 2 ) 11 BIPY//Ga 2 O 3 /EGaIn ( Figure 1a), where TS denotes a template-stripped substrate; 30 BIPY is a 4-methyl-2,2'-bipyrid-4'-yl group; and Ga 2 O 3 /EGaIn is the eutectic gallium-indium alloy (EGaIn) top-electrode (specifically, what we call an "unflattened" conical tip) 22,24,26 covered with a self-limiting thin film of gallium oxide (Ga 2 O 3 , ostensibly ~0.7 nm, but undoubtedly thicker in portions of the junctions where it is buckled) 24,31 . We determined experimentally that rectification (Figure 1b, c) in this system stems from the BIPY terminal groups in the SAM, and not from other features of the EGaIn-based junction.
The rectification ratio (r) is the quotient of current density (J, A/cm 2 ) measured at applied biases of opposite polarities (+V and -V). We define r with two different equations (Eq. 1 and 2),

EXPERIMENTAL DESIGN
We chose 2,2'-bipyridyl as a relatively easily reduced heterocycle, and one with potential for other uses (e.g., as a chelating agent). 33 We attached it to an 11-undecanethiol (R(CH 2 ) 11 SH). We used this polymethylene chain as the basis for the SAM because Nijhuis and coworkers have demonstrated that HS(CH 2 ) 11 Fc gave the largest value of r among a series of Fc-terminated nalkanethiolates HS(CH 2 ) n Fc (n = 6 -15). 20 We performed three separate types of experiments, focusing on trends in r with the structure of the SAM. To probe the role of structure of BIPY terminal group in the rectification, we characterized tunneling junctions having SAMs terminated in four aromatic groups that are related to BIPY in conformation or composition, and that test the influence of conformation and composition ( Figure 2).

RESULTS AND DISCUSSION
The SI summarizes the syntheses, purification, characterization of the molecules used, the preparation of SAMs, and the collection of J-V data. We used selected, unflattened conical tips (i.e., those not having observable filaments after formation of tips; see the SI for detailed information). These procedures repeat those used previously. 22,24   We measured tunneling current densities (at ±1.0V) in a SAM whose length is similar in the number of non-hydrogen atoms to SC 11 BIPY (18 non-hydrogen atoms in linear connection from the sulfur to the distal atom closest to the EGaIn electrode): n-octadecanethiol, HSC 18 . We compared the tunneling current densities measured for both molecules, and found the differences in J(V) were significant at +1.0V but not at -1.0V ( Figure 3): the |J(+1.0V)| mean of SC 11 BIPY was approximately a factor of 30 higher than SC 18 , but J(-1.0V)| mean is only a factor of two lower than that the charge transport process through SC 11 BIPY at positive bias does not purely rely on a tunneling mechanism (but, presumably, on hopping plus tunneling). The rates of charge transport at negative bias for SC 11 BIPY and SC 18 , are indistinguishable, and this observation suggests that the charge transport at negative bias is based on a pure-tunneling regime.
A plot of r + versus the magnitude of applied bias ( Figure S1 in the SI) showed an approximately exponential increase; log|r + | was directly proportional to applied voltage V. The log|r + |-V relation indicates that the difference in log|J(V)| at opposite biases (△log|J(V)| = log|J(+V)| -log|J(-V)|) is in direct proportion to applied voltage. Significant rectification ratios (r + >5) appeared from V = +0.5V to V = +1.0V. We did not examine higher voltages, because the junctions often failed. Figure 1c shows histograms of values of log|r + | and r + at ±1.0 V for the SC 11 BIPY SAM.
The histogram of values of log|r + | approximately fit a Gaussian curve. The rectification ratio (r + = 85) in the BIPY-terminated SAM was statistically significant, and reproducible. Current density was higher when the EGaIn electrode was reducing than when it was oxidizing. The polarity of rectification was opposite to the polarity observed in Fc-based junctions. 18,21 At positive bias, the Ga 2 O 3 /EGaIn electrode is reducing relative to the silver bottom-electrode, and the current density is higher (×85) than at negative bias, where the Ga 2 O 3 /EGaIn electrode is oxidizing relative to the silver electrode.
We measured the XPS spectrum of a SAM of SC 11 BIPY before and after we assembled a junction ( Figure S2 in the SI). The XPS spectra of a pristine SC 11 BIPY SAM and a SC 11 BIPY SAM contacted with the Ga 2 O 3 /EGaIn top-electrode are indistinguishable, and indicate that there is no evidence-at the precision of the XPS instrument we used-of the formation of complexes of BIPY with gallium or indium.

Comparisons of Junctions with Different Bottom-electrodes (Ag vs. Au).
We replaced the silver bottom-electrode with gold, and fabricated Au TS /SC 11 BIPY//Ga 2 O 3 /EGaIn junctions using the same procedure used with Ag TS . Electrical measurements of these junctions ( Figure 4) showed a rectification ratio with similar polarity and magnitude (log|r + | mean ~1.6; r + mean ~40) similar to that of the Ag TS /SC 11 BIPY//Ga 2 O 3 /EGaIn junctions (log|r + | mean ~1.9; r + mean ~85). These results establish that the rectification is caused neither by redox behavior of an Ag/AgO x layer on the Ag TS electrode, nor by the chelation of silver ions by the BIPY group. SAMs of SC 11 PYR, SC 7 CONHC 2 BIPH, and SC 11 PHEPY do not rectify currents at ±1.0V on Ag TS substrates ( Figure S3): Table 1 summarizes the values for rectification for those compounds. In contrast, a SAM composed of SC 11 PHE on Ag TS showed a rectification ratio (log|r + | mean = ~1.8; r + = ~64) similar to that of (and with the same polarity as) the SAM of SC 11 BIPY (Figure 1). This comparative study indicates, inter alia, that any conformational changes (e.g., syn-coplanar versus anti-coplanar isomers in two pyridine groups) induced by the applied electric field (up to ~1 GV/m) are not responsible for the rectification in the SC 11 BIPY SAM. 9

Correlations of Structure and Rectification Ratio.
This work-combined with data from the literature-suggests a correlation between the magnitude of rectification and the structure of the terminal group. We assume that J(-V) for SC 11 BIPY and J(+V) for SC 11 Fc are based on a pure-tunneling regime; J(+V) for SC 11 BIPY and J(-V) for SC 11 Fc are based on the combination of hopping (due to BIPY and Fc) and tunneling, but the tunneling current is dominated by the tunneling barrier provided by the SC 11 group. Using the simplified Simmons To test the hypothesis that there might be a relationship between rectification and "size" (as measured by some molecular dimension or metric) of the rectifying moiety, we estimated values of d RM based on two limiting, simplifying approximations. i) In one, we assume an extended trans structure (as presented in Figure S5 in the SI), and calculate d RM We also assume (lacking any other information) that the tunneling decay constant (β RM ) for the rectifying moieties are the same, and equal to those for either oligophenylenes (β = ~0.6 Å -1 ) or polymethylenes (β = ~0.7 Å -1 ). 23,24 These values of β were determined at ±0.5V for both oligophenylenes and polymethylenes and are almost certainly not accurate at ±1.0V; to determine if difference in the size of the T group were, at least, compatible with the observed values of rectification, these values of β are, however, sufficient. The values of |r| calcd approximated with β ~0.6 Å -1 based on the two structural approximations are in rough accord with the empirical results ( Table 2).
The ability to estimate rectification ratios for several systems described in Table S1 allowed us to compare calculated values (|r| calcd ; see Figure S5 and  rmean = 500 a Calculations were based on the assumptions that i) terminal groups Fc n , BIPY and PHE are spherical in shape, and the width of tunneling barrier of terminal group (d RM ) is d RM = 2×(3V/4π) -3 ; or ii) the terminal groups are in extended trans structure. b The width was estimated by including the methyl substituents in the BIPY and PHE group. We do not know the role of the methyl substituent in hopping; if the methyl groups are excluded, the values of d RM are 6.6Å for BIPY and 6.8Å for PHE, and the values of |r| calcd for β = ~0.6Å -1 and ~0.7Å -1 are 51 and 98 for BIPY, and 59 and 116 for PHE. c Calculations were based on the literature values of volumes for Fc and Fc 2 . 37-40 d See Figure S5 in the SI for detailed molecular structures. e Values of |r| calcd were calculated with Eq. 3, assuming that the tunneling decay constants characteristic of attenuation through PHE and BIPY are equal to that either of oligophenylenes (β ~0.6 Å -1 ) or of polymethylenes (β ~0.7 Å -1 ). f Note that our calculations for determining d RM do not include information about the supramolecular structure of groups in a SAM. Figure 5. A plot of reported, experimentally observed rectification ratios (|r obsd |) (on a logarithmic scale) for systems taken from the literature and described in Table S1 (in the SI), against rectification ratios (|r calcd |) calculated using Eq. 3, and values of the width of the barrier for rectifying moiety (d RM ). Values of d RM were estimated using the molecular volume of terminal groups-those assigned as a rectifying moiety-(□: based on the approximation that the terminal groups are spherical in shape; •: based on the approximation that the terminal groups are in extended trans conformations). For ref. 14 (see Figure S5 for assumed, detailed molecular structures in the SI) we calculated d RM by using one quarter of the volume or width of Cu(II)phthalocyanine group (as reported in the reference).
approximations described above) in Figure 5 suggests that our hypothesis-that the terminal group T for SC n T system is conducting at one polarity and insulating at the other polarityroughly accounts for the rectifications in the previously described systems. We used a log/log plot here for convenience to summarize the broad range of data. We recognize that such a plot tends to convert a range of data into linear relationships, but point out that the greatest deviation  there is little usefully detailed information about the influence of these characteristics on rectification for most of the rectifiers reported previously. There is also no information on junctions that might have been expected to rectify based solely on Figure 5, but did not (and were thus not reported).

The rectification of BIPY-terminated SAM is dominated by a change in current in
one direction. When the electrode proximal to the BIPY is reducing, the current is higher than that for a length-matched n-alkanethiolate. When that electrode is oxidizing, the currents are the same and indistinguishable statistically. This observation is compatible with a basic mechanistic hypothesis that Fc and BIPY follow similar mechanisms, but with opposite redox behaviors. The SAM of S(CH 2 ) 11 Fc has been established to rectify by a process in which the current density in one direction (at +1.0V) is rate-limiting tunneling across the (CH 2 ) 11 moiety, and in the other direction (at -1.0V) involves an initial step of hopping (that is, electron transfer to convert Fc to Fc + ) followed by rate-limiting tunneling across the insulating (CH 2 ) 11 moiety. [18][19][20][21] The difference in the tunneling distances-the thickness of the tunneling barrier, which we take to be the distance between the bottom sulfur and the distal atom closest to the top electrode-determines the differences in current densities, and thus the rectification. In the case of BIPY, we postulate that the same mechanism-tunneling at negative bias, versus hopping plus tunneling at positive bias-occurs at the opposite polarity, and thus implies that the hopping step is the reduction of BIPY to BIPY∸ by one-electron reduction. 44 The redox potentials of the terminal (T) groups structurally related to the BIPY are in qualitative accord with the expectation that the more easily reduced compounds would rectify more than those that are less easily reduced. For example, the reduction potentials determined experimentally for both 2,2'-bipyridine and o-phenanthroline are -2.1V vs. SCE in 0.1 M acetonitrile solution of tetrabutylammonium tetrafluoroborate, while that for biphenyl it is -2.7V vs. SCE in the same conditions. 44 The reported value of reduction potential for pyrazine is -1.25V vs. SCE, but the reduction involves proton-assisted two-electron reduction, 45 which is mechanistically distinct from the one-electron process with BIPY, and of unknown relevance in an environment with limited availability of protons. Note that the values of the reduction potential were determined in solution; the high electric field (~1 GV/m) in SAM-based junctions, and the difference in solvation, may cause shifts in redox potential. 46 Fc and Fc 2 show oxidation potentials, +0.38 V vs. SCE 47  Simmons model, is compatible with the hypothesis that most of rectifiers previously reported use a mechanism similar-at least in part-to that proposed for the SC 11 Fc system. 21 In this approximation, for SAMs terminated in redox-active groups, the magnitude of rectification is related to the size or shape (by some metric, or combination of metrics) of the terminal group, and to the accessibility of a one-electron redox process allowing hopping to or from the