Quantification of Ready-Made Molecular Bilayer Junctions Having

J. Phys. Chem. C 2008, 112, 269-281

269

Quantification of Ready-Made Molecular Bilayer Junctions Having Large Structural Uncertainty Ayelet Vilan* and Rifat A. M. Hikmet Philips Research, EindhoVen, Netherlands ReceiVed: July 16, 2007; In Final Form: October 2, 2007

A ready-made procedure for the preparation of molecular junctions at ambient conditions is reported. Junctions were constructed from bilayers of alkyl thiols at the interfaces between gold flakes and stationary gold strips. Addition of an amine or carboxylic acid end group to the alkyl thiols drastically increased the resistance (up to TΩ over a couple of nanometers only) and the breakdown voltage of the bilayer junction. These junctions pose a severe quantification challenge because of the large uncertainty regarding their microscopic morphology. A novel quantification procedure is proposed that replaces highly nonlinear tunneling or super-exchange current voltage relations by an effective analytical relation of two characteristic parameters: equilibrium conductance and shape factor. Correlating these factors over a series of systematically varying junctions allows us to evaluate the effective contact area for transfer. This approach was also extended to the fieldemission regime. Within the large spreading of the data, our analyses show that low-bias transfer occurs via most of the contact area while field emission is limited to “hot spots” of a few nanometers wide and only couple of angstroms long. The extracted length for charge transfer was only 1/4 to 1/3 of the nominal bilayer thickness, except for the polar interfaces, which were considerably thicker. The effect of polar end groups on the bilayer thickness is presumably due to weak repulsive forces at the bilayer interface, preventing the collapse of the bilayer.

1. Introduction Bottom-up fabrication of functional devices is one of the promises of nanotechnology. Assembly of small building blocks derived by chemical recognition and weak physical forces presumably holds an alternative to high-energy/high-cost common fabrication techniques. Molecular electronic devices are a natural candidate for bottom-up fabrication strategies. They pose two major challenges to traditional fabrication: feature size of one to a few nanometers and poor stability of the active molecules. This challenge can now be solved by various temporal techniques (namely, the junction disassemble at power off), such as piezo-derived “break-junction”1,2 or STM break junction;3-5 conductive probe AFM (CP-AFM);6-10 magnetically attracted cross bars;10,11 or mercury drop.12-15 Nevertheless, the technological challenge is in producing sustainable junctions that can be integrated into larger circuits. The natural choice for making a permanent top contact is by evaporation, and some groups have a long record of successful molecular devices with evaporated top contact.16-20 Unfortunately, evaporation is notorious for creating short circuits between the contacting electrodes by either chemical degradation or diffusion of the high kinetic energy metal atoms.21-23 An alternative is using a bottom-up approach, where the molecules dictate the junction, based on weak molecular forces, also known as self-assembly. Examples of such an approach include single molecule binding to gold nanoparticles to form a larger object accessible to standard lithography;24 electrochemical growth;25,26 nanotransfer printing;27 lift-off float-on (LOFO);28,29 and the use of conductive polymers as a soft top contact.30,31 * Corresponding author. Current address: Chemical Research Support, Weizmann Inst. of Science, POB 26, Rehovot, 76100, Israel. +972-89343422. E-mail: [email protected].

The two lists of contacting techniques above represent (roughly) two different approaches to molecular electronics. While the first is focused on fundamental understanding with extreme efforts toward precise contacting, the second is more technologically oriented and tolerates larger uncertainty in junction geometry. Naturally, an increase in morphological uncertainty implies substantially more complicated modeling of the junctions. Nevertheless, technology, maybe even more than science, requires reliable quantification of performance. This paper is thus concerned with the analysis of molecular junctions having large structural uncertainty. Previously, we proposed rather simplified, yet analytic I-V relations, which enable us to quantify molecular junctions without a pre-knowledge of either their accurate thickness or area.32 It relies on a simple observation that both the intercept and the slope of some linearized I-V relations depend on the length for charge transfer. The intercept is then correlated with the slope (expressing the effective transfer length) instead of relying on a nominal length. Thus, a plot of intercept versus slope could reveal the effective barrier height and contact area or at least provides a good estimate for them. The highly nonlinear transfer models33,34 can be replaced by analytical cubic relations (for low to moderate bias range),32,35,36 characterized by two empirical parameters, namely the equilibrium conductance (G0) and the shape factor (F). The extracted G0 and F could be interpreted within either tunneling33 or super-exchange;34 actually, these two transfer mechanisms are empirically indistinguishable (see Section 3.3). This method of analysis can also be extended to field emission at high-bias range (Fowler-Nordheim mechanism, Section 3.7) based on a different linearized presentation.10,17 Similarly, its intercept and slope could be correlated regardless of a nominal length.

10.1021/jp0755490 CCC: $40.75 © 2008 American Chemical Society Published on Web 12/13/2007

270 J. Phys. Chem. C, Vol. 112, No. 1, 2008

Vilan and Hikmet

The above analysis will be demonstrated on sustainable molecular bilayer junctions prepared by a novel “ready-made” approach. These junctions are made of gold flakes connecting two stationary gold electrodes with a general structure of Au/ S-R1-X1/X2-R2-S/Au, where S-R-X represents an alkyl (R) thiol (S) with an end group (X). The junctions emerge as extremely chemically sensitive, where the junction resistance varies between kΩ to TΩ by replacing an a-polar end group (Xd CH3) with a polar one (XdNH2 or CO2H). This large dynamic range, controlled by seemingly minor structural changes, provides an excellent test ground for the suggested modeling. Our analysis shows that at low to moderate bias, charge transfer occurs via a majority of the contact area, while increased bias causes a degradation of the molecular film and transition into field emission over a much smaller effective area, and, finally, an irreversible breakdown of the junctions. The effective transfer length is much shorter than the nominal bilayer thickness for a methyl end group but relatively longer for polar interfaces. This increased length accounts for the orders-of-magnitude of increase in resistance and is explained by weak repulsion at the interface, which prevents the degradation of the bilayer. The reproducibility of the ready-made junctions was rather poor and this is reflected in large uncertainty in the extracted parameters. However, the proposed quantification of imperfect molecular junctions and the dominant role of weak repulsions could find general implications in preparation and quantification of molecular junctions by any technique. 2. Experimental Section Figure 1 shows an image of the flakes’ junction (1d), its schematic cross-section (1a), top view (1b) and suggested equivalent electrical circuit (1c). The molecules used for forming the molecular layers are shown in Figure 1e. Stationary Electrodes (substrate). Sets of two interdigitated electrodes were patterned by standard lithography and evaporation of 50-nm-thick gold over 10-nm titanium (adhesion layer) over 230 nm of thermally grown oxide on top of a highly n-type doped Si wafer. The substrates were stored up to several months and cleaned immediately before use by 1 min immersion in fuming nitric acid, plunged into DI water, and dried by N2 jet and UV-ozone for 10 min. Monolayers. The clean “stationary electrodes” were immediately immersed into alkyl thiol solutions of three possible types: alkyl thiols (Figure 1eI), with 12, 18, or 22 carbon long - 2 mM ethanol solution, for about 2 h; aminohexadecanethiol (AHDT, or “N”, Figure 1eII); 1 mM in 1:4 (v/v) acetonitril/ethanol solution (due to lower solubility of AHDT in ethanol), for about 6 h; and mercapto hexadecanoic acid (MHDA, or “O”, Figure 1eIII), adsorption conditions as AHDT. After adsorption, excess molecules are removed by immersion in clean ethanol for 30 s, rinsed with jets of ethanol and heptane, and dried by an N2 jet. Flake deposition followed immediately. X-ray photoelectron spectroscopy (PHI Quantum) show that the AHDT forms a dense monolayer with a footprint of ∼25 Å2 and ∼12° tilt from normal (Table T1, Supporting Information). Gold Flakes. 50 nm thick and 5 by 50 µm wide are lithographically patterned over a release layer37 and stored up to a few weeks. Before use, the release layer is dissolved and the flakes are suspended in an organic solvent, such as dichloromethane. Dissolved residues of the release layer are removed by three centrifuge cycles, decantation, and suspension of the flakes. Finally, the suspending liquid is replaced by either a pure ethanol or adsorption solutions I-II above. The resulting flake suspension in ethanol was stable for at least 1 month, yet

Figure 1. Schematic drawing (a-c) and micrograph (d) of the flakes’ molecular junctions and the tested molecules (e). a) A schematic side view of the junction, showing the two permanent gold electrodes on top of a silicone oxide insulator and silicone substrate. A metallic flake crosses the two electrodes, and both the flake and the permanent electrodes are covered with a monolayer. The transparent circles represent the bilayer interface and junction area. b) Top view of the same junction showing the interdigitation of the permanent electrodes, with arrows indicating the junction areas. c) Suggested equivalent electrical circuit (see text) and the measurement configuration. d) An optical image of the junction (similar to scheme b) showing one flake crossing two electrodes. The large bright area on the left side is the contacting pad. e) Molecular schemes: (I) alkyl thiol, n ) 12, 18, 22; (II) amino hexadecyl thiol (AHDT); and (III) mercapto hexadecanoic acid (MHDA).

normally used within a few days, but at least 1 h after preparation to allow complete thiol adsorption. However, the electrical characterization (see Sections 3.6 and 4.3 below) indicates only partial molecular coverage of the flakes. Probably, the adsorption time was too short and the thiol concentration was too low for the huge surface area of the flakes. Placing the Flakes on the Substrate. The flakes are cleaned from excess thiols by centrifuge, decantation, and suspension in ethanol three times to ensure the removal of any residual, nonbonded molecules. The flakes are then suspended in a “wetting solvent”. A wetting solvent must fulfill two require-

Ready-Made Molecular Bilayer Junctions

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Figure 2. Various presentations of current voltage curves recorded across flake junctions of six different bilayers: a reference flake junction without deliberate adsorption (or bare interface, 0/0, black squares); three variations of Cm on flake and Cn on stationary electrodes designated as m/n; and two polar interfaces with either homogeneous end group (N/N, red circles) or heterogeneous end group (N/O, magenta down triangles). a) Full range raw data plotted on a log-log scale. b) Zoom-up on the very low scale ((5mV), showing the linear relations with slope equals equilibrium conductance (G0). The curves are magnified by a factor specified next to each curve. Inset panels show the large noise of the N/x curves. c) A conductance vs squared voltage plot. The curves are expected to be linear according to eq 1. The data is normalized by G0, such that the intercept and the slope are 1 and 96F2, respectively. I/V 2 vs 1/V plot for high bias range, testing transition into a field-emission (FowlerNordheim) transfer. All curves (except for the bare one, 0/0) show a transition point at a bias between 0.4 and 5 V. For bias above the transition point (leftward on the 1/V scale), the slope is negative with exponential relations indicative of Fowler-Nordheim relations. Curve magnitude is arbitrarily scaled, for visibility. Symbols are measured data (calculated for c and d) and lines are linear fits to the data (b and c) or guidelines to the eye (d). Assuming that we measure two junctions in series, the bias is half of the nominally applied bias, except for a.

ments in order to achieve a uniform distribution of flakes on the substrate: first it must wet the substrate (both silicon oxide and metallic features), and second, it should make a good suspension of the monolayer modified flakes so that they do not form aggregates. The first requirement means that when a drop of flake suspension is placed on the substrate it forms a uniform thin film, which dries before it breaks into droplets, concentrating the flakes on limited spots, instead of spreading over the full substrate area. For alkyl thiols with polar ends, we found that methanol gives a good wetting of the substrate, while ethanol does not. Both methanol and ethanol gave good wetting on a-polar alkyl monolayers, yet methanol was used in all cases for uniformity. Suspension of monolayer-covered flakes in a pure solvent could cause desorption of thiols back into the solution. Therefore, the duration of this stage was minimized (only a few minutes). A few drops of the final suspension is placed on the monolayer-covered substrate and let dry naturally. The concentration of flakes in the final suspension dictates the resulting density of flakes per substrate area. No attempts were made to directly characterize these nanometer-thick, micrometer-wide buried junctions. Instead, we examine how far we can use the electrical data to gain understanding of the resulting interfaces. Electrical Characterization. The substrate with flakes was placed in a probe station, and its microscope was used to detect the number of flakes crossing each interdigitated electrode set

(see Figure 1a). Only sets crossed by one to three flakes were measured by contacting their pads with micromanipulators. The current-voltage characteristics were measured by an HP 4155 parameter analyzer. The resulting device is double, that is, includes two junctions in a series, and possibly up to three such units in parallel, as drawn schematically in Figure 1c. The basic molecular junction (metal/monolayer1/monolayer2/flake) is described by a diode, to indicate its possible asymmetry. If such asymmetry really exists, then it must be reversed at the two ends of the flake; thus, the net device is expected to behave symmetrically. Nevertheless, to simplify the analysis, we ignore rectification and always assume that the applied bias is divided evenly over the two junctions, meaning that the effectiVe bias is half of the nominal one (the only exception is in Figure 2a showing the nominal applied bias). In this paper, the junctions will be coded as m/n, where for simple alkyls m is the number of carbons in the monolayer adsorbed onto the floated flakes and n is the number of carbons in the monolayer adsorbed on the stationary electrodes. The two polar bilayers are coded by their chemical nature with N/N indicating amino hexadecane thiol (AHDT) on both flakes and stationary electrodes, while N/O indicates AHDT on the flakes and mercapto hexadecanoic acid (MHDA) on the stationary electrodes. Some of the figures use the nominal thickness as the abscissa. Thickness values were derived by adding the thicknesses of the two noncontacting monolayers, based on


Vilan and Hikmet

published values for methyl-terminated alkane thiols (Figure 1e I)38 and MHDA (Figure 1e III),38 and on XPS measurements we made for AHDT on gold (Figure 1e II, see Table T1, Supporting Information). These thickness values serve as a general reference and are not considered to be accurate. 3. Results 3.1. Raw Data Comparison. We shall first show the strong qualitative effect of a polar end group on the conductance of the junctions. A more elaborate, quantitative analysis, to identify the origin of the distinctly different behavior, follows. Experimentally measured current voltage curves (I-V) are shown in Figure 2a. Typical curves for 6 bilayer combinations (out of 13 tested) are shown. As expected, the current in Figure 2a decreases with the net bilayer thickness, as long as the bilayer is composed of alkyl thiols (Figure 1eI). Introducing polar end groups into a bilayer having a similar number of atoms, like the 18/18 junction, yields about 5 orders of magnitude less current for homo polar groups (N/N) and there is a further 1.5 order of magnitude reduction in current for hetero polar groups (N/O). The slope of the double logarithmic I-V curves is close to unity (i.e., in I ∼ V n, n ∼ 1), as is typical for tunneling (in contrast to, e.g., space charge limited current, n ∼ 2). As the bias increases, the current increases faster because the transfer mechanism changes into field emission (see Section 3.7). At bias > 1 V a breakdown event is observed, where the current jumps abruptly (and irreversibly) to ∼0.1 Å (where the measurement is stopped). After such a breakdown event, the measured I-V (not shown) is very similar to that of a “bare” junction (0/0). A summary of averaged breakdown values for all measured junctions is provided in the Supporting Information. The breakdown voltage was rather characteristic for a given group of junctions, starting from 0.25 V for 0/12 , ∼1 V for 0/18, and up to 2-2.5 V for the polar bilayers. Four types of bilayers did not show any breakdown up to a limiting current of 0.1 Å. Assuming that breakdown is the creation of a defect in the bilayer,16-20 the absence of breakdown might indicate that these junctions were fairly defective to begin with. 3.2. Very Low Bias RangesReproducibility of Measured Junction Resistance. A common quantification of a molecular junction uses the equilibrium resistance (R0) extracted by linearly fitting the I-V relations at a low bias range.8,39,40 The linearity of the I-V curves at a low bias range is demonstrated in Figure 2b (all panels of Figure 2 are different presentations of a single data set). Current values are factorized (see labels in figure) for visibility. Lines are linear fits to the data over (10 mV, with the slope in conductance terms (i.e., G0 ≡ 1/R0). A critical aspect in contacting molecules is the yield of “nonshorted” devices and the reproducibility within working devices. Such statistics are demonstrated in Figure 3, where each of the six panels shows the distribution of the equilibrium resistance (R0) for a different bilayer type (the same ones as in Figure 2). Note that Figure 3 plots the data in terms of resistance (R0), rather than conductance (as used elsewhere in this report). Naturally, the elaborated preparation of the flake junctions dictates a very limited amount of sampling compared to, for example, probe techniques.3-7 Nevertheless, Figure 3 clearly demonstrates the “statistical” nature of the flake junctions. Although all of the junctions of a given bilayer type were prepared on the same wafer (on different sets of stationary electrodes) using the same batch of flake suspension, the reproducibility among them was rather poor. Figure 3 follows the qualitative trend of Figure 2a with respect to length and polarity. The resistance of polar bilayers (N/N

Figure 3. Statistical distribution of junction resistance for six configurations. Each panel plots the number of junctions vs the extracted equilibrium resistance (R0 ) 1/G0, logarithmic scale) for a given bilayer (see legend at top right corners). G0 was extracted by linearly fitting the current-voltage data at very low bias (V e ∼1 mV, see Figure 2b).

and N/O) was distributed around much higher values than the equivalent nonpolar bilayer (18/18). Among the nonpolar junctions, the resistance roughly increases with nominal thickness. In addition, the yield of non-shorted junctions was much better for polar than for nonpolar junctions. From now onward we shall consider 30 Ω (or G0 < 0.03 Ω-1)41 as the limit between shorted and non-shorted junctions and we will refer only to averages over non-shorted junctions. Table T2 (Supporting Information) provides a full account of the actual number of junctions used for each analysis. The qualitative conclusion is that polar end groups at the bilayer interface highly increase the resistance and reproducibility of the molecular junctions. Seemingly, this contradicts former observations that interfacial bonding (the N/O junction is expected to form hydrogen bonds) increases the current because bonding reduces the barrier for charge transfer.42 However, we shall argue that the lower current is due to the effective transfer length,43 which is longer in the polar than in the nonpolar bilayers. To prove this claim, we need to extract from the experimental data both the energetic parameters (e.g., changes in position of energy levels and their coupling to the electrodes) as well as the morphological ones (e.g., variation in transfer length43 or effective area for transfer20,44,45). This is in contrast to the majority of analyses, which consider the morphological parameters (length and contact area) as a priori known input parameters. Because of the high level of uncertainty, we will use an effective, simplified I-V relation (eq 1 below), which provides reliable quantization and fits well with the experimental data (Figure 2c). 3.3. Cubic I-V Relations as an Effective Transfer Mechanism. The Simmons model for describing inelastic tunneling33,35,46 (see eq A1 of the Appendix) is widely used for analysis of molecular I-V data.7,12,19,42,47 Recently, we have shown that the highly nonlinear Simmons relations can be effectively reduced to the following expression32


(

)

I F2 2 ) G0 1 + V V 96

(V < 1/3φ)


(1)

where V is the applied bias, I is the measured current, and their ratio is the conductance (in integral terms). Thus, a plot of the integral conductance (I/V)48 against the square bias is expected to be linear, with a slope equal to the equilibrium conductance, G0 (in Ω-1) and the slope over intercept is related to the shape factor, F (in V-1). Equation 1 originates from a power expansion to the Simmons relations (eq A1, Appendix) as originally suggested by Simmons.35 Later, Brinkman, Dynes, and Rowell36 reached a similar relation for differential conductance using direct derivation (also known as BDR relations, rather popular in the analysis of magneto-resistance junctions, see eqs A8 and A9 of the Appendix). In the next section, we will show that this approach is more general than the Simmons model and, thus, the characteristic parameters, G0 and F, are effective ones and can accept more than one definition. The strength of the effective approach is that it provides pure observables, regardless of any a priori assumptions. The application of eq 1 to the experimental data is shown in Figure 2c, which plots the raw data of Figure 2a as (I/V) versus V2. All of the curves are normalized by G0 (such that their intercept ≡1). The trends in Figure 2c are rather linear, supporting the applicability of the cubic I-V relation (eq 1) to the I-V of bilayer junctions. At higher bias range (not shown in Figure 2c), a deviation from linearity is observable, as expected for real data, considering that eq 1 is only an approximation. The presentation of Figure 2c is also informative, revealing the fine details of the transfer mechanism, which are generally obscured in the conventional plot (e.g., Figure 2a and b). For example, some of the curves show a clear plateau in the G-V 2 plot, with a slight (or no) change in slope after it. The continuity in slope suggests that some structural rearrangement took place at that point (e.g., a breakdown of one of the two junctions in series), but not a fundamental change in the transfer mechanism. Similar current steps were reported by Aswal, et al.17 This plateau observation serves as a top limit on the range of data useful for application of eq 1. Such an internal limit can be used as a practical solution to the reported variation in extracted parameters within the fitting range.7,19,32 Showing the validity of the effective transfer model (eq 1) to the experimental data, we now wish to understand how the equilibrium conductance and shape factor relate to barrier height, length, and so forth. Such translation depends on the assumed transfer mechanism, and eq 1 can be derived from either tunneling or from the super-exchange mechanism. 3.4. Comparison of Inelastic Tunneling and Superexchange Approaches. Searching the literature for an analytical I-V relation (in contrast to numerical simulations) reveals two basic models: (i) inelastic tunneling using the Simmons model33,35,46 (see eq A1 of the Appendix) and (ii) nonresonant super-exchange, using the Mujica-Ratner model34 (see eq B10 of the Appendix). The majority of experimental analyses used inelastic tunneling.7,12,19,42,47 In contrast, the majority of theoretical works employed super-exchange and scattering formalism, yet rarely reduced them to an analytical term necessary for the quantification of experimental data. One exception is the I-V relations based on super-exchange as formulated by Mujica and Ratner34 (eq B10 of the Appendix), suited to experimental molecular I-V.39,42 The G0 and F terms in the two models (identified by t and x superscripts for Simmons tunneling and Mujica-Ratner super-exchange, respectively) are below:

Equilibrium Conductance. Looking at eq 1, it is clear that G0 is the same equilibrium conductance (first current derivative with respect to bias) as the one extracted in Figure 2b and shown in Figure 3. Deriving this term from the Simmons relations (eq A1 of the Appendix), we get32,35,36,40

Gt0 ) 324

Am* exp(-φF) F

(2)

where A (µm-2) is the contact area of the junction, m* is the effective electron mass (dimensionless), and φ is the barrier height (V). The numerical pre-factor of 324 has the units of A‚V-2‚µm-2 (see the full term in eq A4 of the Appendix). The same first derivative can also be extracted from the Mujica-Ratner model (eq B10 of the Appendix)

Gx0 ) 15 500

( ) () ∆0 2 A φ t A0 t

-φr/2

(3)

where ∆0 is the spectral density of the electrodes at zero bias, φ is the difference from the site energy to the Fermi energy (or the barrier height), t is the transfer integral between sites, and A0 is the footprint area per molecule. Both ∆0 and t are energies, but simply expressed in V units. The factor of 15 500 comes from universal constants and has the units of A/V‚(Å/µm)2 (i.e., A and A0 in µm2 and Å2, respectively). Shape Factor. In both expressions for G0 (eqs 2 and 3), it scales with a power of φF, which we generally refer to as the “dimensionless thickness” of a barrier. The more familiar definition of the dimensionless thickness is the product of transfer length (L, in Å) by decay length (β, in Å-1; namely for tunneling βL ≡ Fφ). The concept of decay length is natural for equilibrium cases, where length is the natural variable. However, varying the applied bias turns the potential barrier height into the natural scaling, thus the physical meaning of F is the ratio of dimensionless thickness to barrier height.32 The term “shape factor” expresses both the aspect ratio of the barrier (whether the profile of the barrier is narrow and high, wide and low, etc.) and the graphical shape of the I-V curve, or how strong it deviates from linear relations (dictated by G0).32 Within the tunneling view, the shape factor equals

Ft ≡

βtL ) 1.025 φ

xm*φ L

(4)

All parameters (F,φ, β) are defined at equilibrium (V ≡ 0). The factor 1.025 expresses universal constants and has the units Å-1‚V-0.5. In the case of super-exchange, the dimensionless thickness is simply the number of transfer sites (N)

Fx)

4N 4 L ) φ φa

(5)

where a is the distance between sites along homogeneous molecules of length L (N ) L/a).34 The factor 4 was added for compatibility with eqs 4 and 1 and is dimensionless. Notice that within the super-exchange view (in contrast to the tunneling view) the decay length (β) is not simply the dimensionless thickness (∼N) divided by length (N/L ) 1/a). This is because β is conventionally defined as the exponential decay (in contrast to eq B10 of Appendix, which is a power law) leading to the following definition: βx ) (2/a) ln(φ/t). The expressions for F in eqs 4 and 5 are the accurate ones, while the slope of the G-V 2 relations expressed in eq 1 as F2/96 is an approximated term and its full, accurate expressions


Vilan and Hikmet

are given in eqs A5 and B11 of the Appendix. Note that eqs 1-3 do not include the transfer length (L), which is considered as an unknown parameter. Comparing the two expressions for the effective parameters clarifies that a different transfer mechanism will result in a different barrier height and transfer length. Using simulations, we show that starting from a fixed G0 and slope (C in eqs A5 and B11 of the Appendix), translating them to barrier parameters (e.g., φ, L, A, etc., see Table T3 of the Supporting Information) for both models and, finally, recalculating a simulated I-V curve from the original relations (eqs A1 and B10 of the Appendix for Simmons and Mujica-Ratner, respectively) results in practically identical curves (Figure S3 of the Supporting Information). This is additional proof that a reasonable fit between the model and the data does not prove the validity of the model.44 Nevertheless, choosing a relevant transfer mechanism is critical for the extracted parameters. Table T3 of the Supporting Information shows that an analysis of the same curve by the Simmons model extracts a transfer length that is more than twice that extracted by the Mujica-Ratner model and vice versa for barrier height. 3.5. Contact Area Estimation Based on Trend Lines. For quantification of the complete data set, the procedure of Figure 2c was repeated for all non-shorted junctions (i.e., G0 < 1/30Ω, except for 0/0 where all of the data was considered) and the intercept (G0) and slope (G0‚F2/96) were extracted. Equation 2 can be rewritten in two equivalent versions, as a function either of the length40 (eq 6a) or of the shape factor32 (eq 6b)

ln(Gt0L) ) ln(308Aβt) - βtL

(6a)

ln(Gt0F) ) ln(324Am*) - φF

(6b)

where eq 6a was derived from eq 2 using eq 4 and the parameter of 308 is in units of (A/V)‚(Å/µm).2 βt is defined in eq A2 in the Appendix. The analogous manipulation to eq 3 using eq 5 provides

[ () ] [ () ]

∆0 2 A - βxL t A0

(7a)

∆0 2 A φ - ln(φ/t) F t A0 2

(7b)

ln(Gx0) ) ln 15 500 ln(Gx0) ) ln 15 500

The definition for βx is given below eq 5 above. The two possible interpretations of equilibrium conductance, as a function of either nominal junction thickness (eq 6a) or extracted shape factor (eq 6b), are presented in panels a and b of Figure 4, respectively. The symbols are (geometric) averages over all of the extracted parameters, and error bars are standard deviations. The different junctions are arranged and color coded by the type of monolayer on the flake side of the bilayer, while the monolayer on the stationary electrodes varies (identical color coding is kept through Figures 5 and 6). Note that in Figure 4b the abscissa values are also experimentally extracted and their standard variation (linear averaging) is indicated as horizontal error bars. The two panels of Figure 4 also compare the two alternatives for extracting G0, namely, the linear slope of the extremely low bias range (as in Figure 2b, Figure 4a) and the intercept of the G-V 2 plot (eq 1 and Figure 2c, Figure 4b). Nevertheless, the variations in extracted G0 values were very minor. Formally, Figure 4 is plotted within the Simmons model (eq 6) because it uses the product G0L (G0F) as the independent

Figure 4. Dependence of equilibrium conductance (G0) on nominal junction thickness (L, panel a) or extracted shape factor (F, panel b). Symbols represent the geometric mean of all non-shorted junctions of a given bilayer type and error bars are the standard deviations. Averaging and deviations of F (x axis of panel b) are linear. G0 was extracted by linearly fitting 10 I-V data points closest to 0 V (or more data, up to 20 mV depending on noise, e.g., Figure 2b). L values are extracted from the literature.38 Lines are linear fits (eq 6a) to partial data groups, yielding a decay parameter of 0.93 and 0.99 Å-1 and contact area of 22 mm2 and 180 m2, for lines I and II, respectively. G0 and F in b were extracted by linearly fitting G-V 2 data (e.g., Figure 2c), over an observable linear regime. The line is a linear fit (eq 6b) to the majority of the data, yielding a barrier height (slope) equal to 0.73 V and a contact area of ∼5 µm2. Here and in all following figures, junctions are divided into five groups by the nature of the molecules adsorbed on the flake side of the bilayer: no monolayer on flakes (0/ x, black squares); dodecane thiol on flakes (12/x, green up triangles); octadecane thiols on flakes (18/x, blue down triangles); docosane thiols on flakes (cian diamonds, 22/x); and aminohexadecylthiol on flakes (N/x, red circles).

parameter and not simply G0, as expected in the Mujica-Ratner model (eq 7). This difference does not relate directly to the assumed transfer mechanism but rather to the potential profile, which is trapezoidal in Simmons33 and step-like (length independent) in Mujica-Ratner.34 The Mujica-Ratner version of Figure 4 (ln(G0) against L(F)) is given in Figure S2 of the Supporting Information. However, it did not differ much from Figure 4, except for a vertical shift downward in the data.

Ready-Made Molecular Bilayer Junctions The distribution of data in Figure 4a does not follow the expected exponential trend for length. The product G0L is fairly constant in the 0/x and 12/x sub groups, and the conductance starts decreasing only in thicker monolayers on the flake. This discrepancy can be attributed to effective length or contact area different than nominal. The data of Figure 4a is seemingly composed of two subgroups, which could be fitted exponentially, as shown by the two fitting lines marked as I and II. The slopes ()β) of the two fitting lines equal 0.93 and 0.99 Å-1 for lines I and II, respectively (or 0.83-0.82 for the Mujica-Ratner plot, see the Supporting Information), which are fairly reasonable. However, the intercepts of the fitted lines yield a contact area (A) equal to 20 mm2 and 200 m2 for lines I and II, respectively, which are orders of magnitude higher than expected (∼20 µm2 using the flake cross section (Figure 1d) of 2 × 5 µm, times 2((1) flakes in parallel). In the Mujica-Ratner analysis, the intercepts provide a contact area of 4400 µm2 and 23 cm2 for curves I and II, respectively (calculated by assuming A0 ) 20 Å2 and ∆0/t ≈ 1). These values are lower than those extracted by the Simmons model but still much higher than nominal values. Considering that the nominal bilayer thickness values overestimate the actual transfer length, by about 15 (6) and 30 (22) Å for groups I and II, respectively (Mujica-Ratner model), an according left-shift of the fitted lines would produce a reasonable intercept (contact area). Figure 4a shows that the junction thickness can only be lower than the nominal one. This means that the measured high resistance originates in an extremely thin bilayer and cannot be due to accumulated residual material. Alternatively, the exponential variation in conductance can be attributed to the varying density of pinholes or “hot spots”,44,45 which dominates the transport. A hot spot can be a direct metal-metal contact or a sharp asperity, where the tunneling distance over a limited area (pinhole) is much shorter (0 < L < Lnom) than across the majority of the contact area, where L ≈ Lnom. Therefore, the current at the hot spots is exponentially higher than that in the surrounding areas. Based solely on Figure 4a, we cannot distinguish between full area tunneling and hot-spot conduction. Such ambiguity can be somewhat resolved if we use the experimentally extracted shape factor F as the abscissa, instead of an (arbitrary) input parameter L, as shown in Figure 4b. The fairly huge error bars of F are attributed to the large uncertainty in the effective bias distribution between the two (practically) nonidentical junctions in series (see the Experimental Section and Figure 1c). An uneven bias distribution is expected for cases where the bilayer includes an intrinsic polarity (such as in the N/O junction) or if one of the two junctions in series is much more defective than the other. From eq 1, it is clear that deviation of the actual bias from the assumed one (half of the applied bias) will inversely effect the apparent F. Saying this, the data of Figure 4b is distributed surprisingly well on a single trend line. For example, compare the distribution of the 0/x and 12/x subgroups between the two panels of Figure 4. In fact, the intercept of the fitted line is practically within the expected range (extracted m*A ) 5.6 µm2 cf. nominally expected m*A ∼ 2 to 5 µm2 if m* ∼ 0.166,7,17,39). Yet, it should be noted that this intercept could change easily by an order of magnitude because of the logarithmic scale and large error bars. The slope of the exponential trend is the barrier height, which equals 0.7 V. As for Figure 4a, plotting ln(G0), rather than ln(G0F), does not change the observed trend much, just shifts it downward (see Figure S2 of the Supporting Information). The Mujica-Ratner fitting yielded A(∆0/t)2 ) 0.44 µm2 (about 10%

J. Phys. Chem. C, Vol. 112, No. 1, 2008 275 of nominal area if ∆0/t ∼ 1) and a slope of 0.8, which is equivalent to a barrier height of 2.1 eV (using eq 7b with t ) 1). The extracted barrier height values are rather low. Reported barrier heights within the Simmons model vary from 1.4 17,19 to 3 eV.42 Barrier heights extracted using the Mujica-Ratner model varied from 4 to 5 eV42 up to 10 eV39 (however, the fitting range of the last is questionable). In the conventional analysis (Figure 4a), the 22/18 junction seems perfectly normal (based on its G0 value) and only its F value reveals that some other transport mechanism is dominant. The 22/18 junction is presented twice (due to the large variance), with F values of 2200 and 0.76 V-1 for points a and b, respectively. We can explain this by the considerable accumulation of material leading to the huge F value at point a (outside the frame of Figure 4b). Occasionally, there was a pinhole in this layer leading to an extremely small F value (point b). This example demonstrates the utility of correlating G0 and F for evaluating molecular junctions. The seemingly trend line of Figure 4b is a clear improvement compared to Figure 4a. Yet, in view of the large errors, and the clear deviation of few bilayers (18/18 and N/O) we cannot confidentially exclude the contribution of defects to the net current. Nevertheless, we take the intercept of the trend line as a rough estimate for the contact area. 3.6. Detailed Parameter Extraction for Individual Junctions. The main advantage in the analysis of Figure 4b is in the complete elimination of any input parameters. However, the disadvantage is within the (hidden) assumption that all data can be related to a unifying trend line of a constant φ and A, where L (N) is the only allowed free variable (see eqs 6 and 7). To parametrize each junction individually, we must compromise and allow for one input parameter. The observed trend in Figure 4b justifies the use of the intercept (namely, m*A or (∆0/t)(A/ A0) for the two models) as a known input parameter. This allows us to calculate the detailed barrier height and length equivalent using Appendix eqs A6 and A7, respectively (or B12 and B13 for the Mujica-Ratner model). The extracted parameters are shown in Figure 5. The first observation from Figure 5 is the high similarity in trends observed by the two transfer mechanisms, although the extracted barrier height is almost double according to MujicaRatner (Figure 5c) than by the Simmons model (Figure 5a). The extracted length is only slightly higher for Simmons (Figure 5b) than for Mujica-Ratner (Figure 5d, using a C-C bond length - 1.255 Å as the distance between sites39). The extracted barrier heights were rather noisy (Figure 5a and c) for both analyses, distributed around an average value similar to the slope of the trend line in Figure 4b (0.7 V or 2 V for Simmons or Mujica-Ratner, respectively). The magnitude of the error was fairly large (0.5-1 V), smearing out most of the variation between types of bilayers. Interestingly, an increase in barrier height of about 0.5-1 V above the average is enough to account for the exceptionally low-current points of 18/18 and N/O (in contrast, a 6 orders of magnitude smaller contact area is required to account for the same net effect). The points of bilayer 22/18 were left to demonstrate the effect of possible artifacts. A defect-dominated junction (22/18b) is manifested as a ridiculously high barrier height. This is because of the inherent correlation between barrier height and contact area, see refs 32 and 44. The other junction, named 22/18a, has a very high F value, translated here into a very low barrier height (in both analyses). In contrast to the noisy barrier height values, the length equivalent (Figure 5b and d) shows a clearer trend. The majority


Vilan and Hikmet

Figure 5. Extraction of transfer parameters, based on the Simmons model (a and b) and the Mujica-Ratner model (c and d), showing the extracted barrier height (a and c) and equivalents of transfer length (b and d). In all of the panels, the extracted parameters are averaged over all good junctions of the same bilayer type and plotted against the nominal bilayer thickness. The symbols are as in Figure 4. Simmons’ barrier height was calculated using eq A6 of the Appendix and a nominal m*A ) 0.16 × 25 ) 4 µm2; Simmons’ length equivalent (Lxm*) was calculated using eq A7 of the Appendix. The slope with respect to nominal thickness (solid line) equals ∼0.3 and can be interpreted as m* ∼ 0.1 or a true bilayer thickness of only 30% of nominal thickness; Mujica-Ratner’s barrier height was calculated using eq B12 of the Appendix using the intercept of exponentially fitting Figure S2b (ln[15 500(∆0/t)2A/A0] ) 5.84); Mujica-Ratner’s length equivalent, which is the number of transfer sites per molecule, was calculated using eq B13 of the Appendix. The fitted line has a slope of ∼0.2, equivalent to one transfer site per four carbons, if the nominal length is the actual length. Alternatively, forcing a transfer site in each carbon (of 1.255 Å distance39), the actual bilayer thickness is 25% of the nominal thickness.

of the data falls on a common trend line with a slope equal to 0.3 for Simmons (Figure 5b) or 0.2 for Mujica-Ratner (Figure 5d) analyses. In the Simmons analysis, the extracted parameter is a product of two contributions (m* and L), which could not be definitely separated.32 At either extreme, the net effect can be attributed to an effective mass of charge carrier, m* ∼ 0.1, which is quite low, yet reasonable (values of m* ) 0.16 were reported6,7,17,39); or at the other extreme, the actual bilayer thickness is about one-third of its nominal value, which is low again, yet sensible, considering the rough preparation method. Using the Mujica-Ratner approach, the extracted length equivalent is the number of transfer sites. The fairly low slope suggests that either we have very few sites per alkyl chain (once each four carbons) or that the actual length is about one-quarter of the nominal one. Generally, extraction of equivalent length was more robust using Mujica-Ratner than using Simmons (e.g., compare the 0/x and the 22/18a between Figure 5b and d). The equivalent length of polar bilayers is clearly higher than the trend line. Similarly, the constant anomaly observed for the 12/x subgroup is clearly due to too short a transfer length. The two 12/x junctions actually seem to have no monolayers on their flake side (i.e., shifting these data points 15 Å to the left will bring them to the trend line). Finally, we note that the effect of the polar interface is inverted for the N/N and N/O bilayers. For the N/N interface, the barrier height was exactly like that in a-polar junctions; however, its length equivalent was much

higher. On the contrary, the N/O interface mainly increases the barrier height and has less effect on the transfer length. 3.7. Field-Emission Regime: Extraction of a Contact Area Using the Fowler-Nordheim Model. The analytical approach of correlating between intercept and slope can also be extended to field-emission transfer expected at bias above the barrier height (V . φ). Field emission is commonly described by the Fowler-Nordheim mechanism (see eq C14 of the Appendix). In this regime, data can be linearized using the following semiexponential relations10,17

ln

( ) (

)

A 1 I e2 2φβL ) m - n (|V| . φ) (8) ) ln 2 2 8πhm*φ 3V V V L

where e is the electron charge, h is Planck’s constant, β is the decay length parameter as defined in eq A2 of the Appendix, and m and n are arbitrary symbols for slope and intercept. Such a data presentation is shown in Figure 2d, where the x axis is the bias (in actual values, yet reciprocal spacing) and the y axis is I/V 2 (magnitude is arbitrarily scaled for visibility). The minimum point observed between 0.4 and 1.2 V (except the 0/0 one) is the transition point, which supposedly serves as a rough estimate for the barrier height.10 The exponential decay (linear y scale) left of the transition point (high bias) represents the field-emission regime (eq 8). The approximately linear increase rightward has the slope of G0 (cf. eqs 1 and 8). Transition into field emission was hardly observed for the 0/x



Figure 6. Intercept (m) and slope (n) of the Fowler-Nordheim model (Figure 2d) plotted against each other. The symbols are averaged values over all of the junctions that showed a Fowler-Nordheim regime and error bars are standard deviations. Junctions of the N/O type showed two distinct populations, represented by a and b. The lack of error bars for some of the thinnest junctions is because they showed a FowlerNordheim regime only once or twice. Theoretically (see eq 9), the slope should be -2, as shown by the inclined grid for a constant contact area indicated on the right y axis in length terms (for φ ) 1 V). The symbols are as in Figure 4.

subgroup. The majority of other junctions have a transition bias around 0.4 V, with the N/N junction clearly above it (∼0.8 V) and two junctions (12/22, 22/18) clearly below it (see Figure S1b of the Supporting Information). The N/O junction seems to have two transition points, first to a mild slope (at ∼0.55 V) and second into a stiffer slope (∼1.0 V). Aswal, et al. showed that the barrier height and effective mass can be extracted using the slope (n) and intercept (m) of linearly fitted I-V data, as in Figure 2d (eq 8) and the nominal junction thickness.17 Following the rationale of eqs 6b and 7b, we can avoid using a nominal length by correlating the slope and the intercept of a field-emission regime. Thus, if we express the length (L) in terms of slope (n) and plunge it into the expression for the intercept (m), we reach the following relations between intercept and slope

m ) ln(72Aφ2) - 2 ln(n)

(9)

where the factor 72 has the units AV-2µm-2 and full expressions for n and m are given in eqs C15 and C16 of the Appendix. Such an analysis is shown in Figure 6, which is the field emission analogous to Figure 4b. Exponential fittings were made for all measured I-V data of the apparent field-emission regime and averaged values for all junctions of the same bilayer are shown as symbols in Figure 6, with error bars for standard deviation. Tilted grid lines are along the theoretical -2 slope (eq 9) and represent a constant product of Aφ2 (specified on the right y axis, for φ ) 1 V). Looking at Figure 6, we see that field emission is clearly limited to hot spots and that the thicker is the bilayer, the smaller is the size of the hot spots. In principle, this decrease can also be attributed to smaller barrier height; however, such order of magnitude variations contradict the fairly similar observed transition biases. The majority of data is gathered around two locations. The monolayer junctions (0/x, except 0/0), 12/18 and 22/18, are situated at a contact dimension between 10 and 100 nm and n ) 0.3-1, or L ∼ 0.1-0.5 Å (using a rough estimate of φ ∼ 0.7 V and β ∼ 1 Å-1). The rest of the a-polar bialyers (18/x and 22/22) have a contact size of about 1 nm, with an

effective length of about 1 Å. Note that the observed, extremely low-length values refer to the defect, while the thickness of the surrounding layer is naturally thicker (at least 10-20 Å, cf. Figure 5b). Once again, the polar bilayers are exceptional. The N/N point seems to have a single defect per junction (size of ∼Å) at the length of about 3 Å. The extracted intercept and slope values for the N/O groups show two distinct subgroups, marked as a and b, representing the intermediate range (N/Oa 0.5-1 V) and the true field-emission regime (N/Ob). The defect size for N/Oa is similar to that of the 18/x bilayers (∼10 nm), but of a much higher length, of L ∼ 10 Å. The two top points of 0/0 and 12/ 22 have a contact area of almost the whole nominal size (1 µm) and basically show no field emission (namely, the data of Figure 6 refers to merely a single data set with an apparent slope inversion, see Table T2 of the Supporting Information for the net amount of junctions used in averaging). Generally, the regime of field emission has a limited bias range and was not measured very carefully. Therefore, no further attempts were made to extract detailed parameters from this regime. 4. Discussion 4.1. What is the Transfer Mechanism? The question of identifying the “correct” transfer mechanism across the bilayer junctions was somewhat ignored throughout this report. Despite our limited control over molecular length, it seems that conductance does vary exponentially with distance (Figure 5a). This is a necessary, yet not sufficient, indication for transfer by tunneling.44 A definitive identification of tunneling requires a current-temperature measurement,19,25,31 which was not done here. Nevertheless, there is accumulated evidence that transfer across junctions of alkyl chains is temperature-independent19,25,31 or that nonactivated transfer occurs (the electron (hole) does not reside on the spacer). Therefore, we consider it reasonable to assume that this is the case here. Accordingly, we looked more for an effectiVe transfer description, rather than a correct one. Our analysis reveals that inelastic tunneling and nonresonant super-exchange are empirically indistinguishable (Figure S3 of the Supporting Information) and better regarded as the same phenomenon, which is described by two different disciplines: that of solid-state oxides (tunneling) or inter/intramolecular charge transfer in solutions (super-exchange).49 The principle difference between tunneling and super-exchange is that superexchange accounts for the mixing of energy levels between the bridge and the electrodes (or donor and acceptor), while tunneling does not. However, practically, the tunneling mechanism can also account for some interaction or band-broadening by introducing an effective mass of charge carrier (m*me) different than that of a free electron (me) into the Simmons model.6,7,32 The main advantage of super-exchange over tunneling is that it directly accounts for band interactions, which is probably more accurate than the indirect, effective-mass approach. Both models are wrong at the same point, namely in the assumption of linear energy-bias relations (see more on that in ref 32). Fitting either of the models should be strictly limited to the low bias range, where the linearity assumption is justified. Thus, G0 and F emerge as general characteristic parameters, regardless of the exact transfer mechanism, as long as the linearity assumption is justified (namely at low to moderate bias). 4.2. Transition into Field Emission and Breakdown. Experimental characterization of the effective contact area (in

278 J. Phys. Chem. C, Vol. 112, No. 1, 2008 contrast to the nominal one) is critical for a meaningful evaluation of tunneling because the barrier height and the logarithm of area have a similar effect on the net current magnitude.32,44,45 Correlating the slope and the intercept of the cubic fit reveals a general trend, which intersects at the expected contact area, based on the Simmons model. If we rely on the Mujica-Ratner model, then the extracted contact area is about 10% of the nominal one, but it is also accompanied by uncertainty regarding the spectral density (∆0) and the transfer integral (t). In contrast, field emission at a higher bias range is limited to a much smaller contact area, suggesting a partial breakdown at isolated spots. This resembles the observation of Lau et al., who found high and low resistance states in junctions of Pt/H(CH2)22OOH/Ti. The current flows across all of the contact areas in a high resistance state, but, after switching into low resistance, the current is limited to a single nanometric spot per junction.20 In the bilayers reported here, such isolated breakdown was observed only in good quality bilayers and not in the monolayer junctions (reversibility was not tested). If, indeed, transition into field emission is due to deformation of the bilayer, then it implies that the transition bias into field emission does not reflect the barrier height,10 but the stability of the molecular layer or nanometric metallic migration.20 This can explain the seeming discrepancy for the N/O bilayer between the slightly higher barrier extracted for the transfer regime (Figure 5a and c) and the averaged transition bias (Figure S1b of the Supporting Information). Thus, the transition bias expresses the field for deformation, not the actual barrier. This view is in line with the narrow range from transition to field emission and to final breakdown and explains the sharp current jumps also observed at the same bias range.17 4.3. Relatively Low Values for Extracted Parameters. Generally, both the extracted length and the barrier height were rather low compared to published molecular data. The extracted length is about 25-30% of the nominal thickness. This can be partially attributed to the interpenetration of hydrocarbons between the two monolayers.43 Such penetration is expected to be worse than that in an Hg/Hg setup because of the rigidity of the Au films and the time (half an hour up to a couple of hours) elapsed between preparation and measurement, in contrast to an Hg drop, which is measured instantaneously after monolayer assembly. However, such a scenario can only account for a 50% decrease at most and the rest may be due to bad preparation. Nevertheless, most of molecular I-V analyses use the nominal length and do not extract it experimentally. An important exception is Holmlin, et al. who extracted a molecular length of ∼50% of nominal using the Mujica-Ratner model.42 We speculate that the reduced thickness might express a fundamental property of the potential profile, narrower than the geometric one.32,50 The extracted values of barrier height were also lower than those commonly reported, though the decay parameters by either Simmons plot (∼0.96 Å-1, Figure 5a) or more common ln(G0)-L plot (0.82 Å-1, Figure S2a of the Supporting Information) were fairly reasonable. Also, the breakdown bias varied from 1 to 2.5 V for the good monolayers (Figure S1a of the Supporting Information), which is in good accord with the reported 1.5 V for bilayers of alkyl thiols on gold.51 Possibly, the reported barrier height values are over estimated. Notice that overestimated length (i.e., the actual length is shorter than nominal50) directly causes an overestimate of barrier height, because their ratio (F) is the fundamental parameter.32 Alternatively, we can attribute the reduced barrier height to the

Vilan and Hikmet intrinsic uncertainty in actual bias using our electrode configuration. (Namely, do we measure two diodes in series or is one of them is short-circuited?) Looking at the original I-V relations (eqs A1 and B10 of the Appendix) reveals that the barrier height acts as a scaling factor for the bias. Therefore, if the effective bias on each junction is close to the applied bias (in contrast to half the bias, as we assumed here) then this directly implies a twice larger barrier height than the extracted values. 4.4. Effect of Polar Interfaces. Our main research question is the following: What are the factors responsible for the drastic increase in the resistance and reproducibility of bilayers with polar interfaces compared to the other bilayers? (See Figure 3.) Previously, such variations were attributed to changes in barrier height.42 Here, the extracted barrier heights (Figure 5a and c) span a considerable range (2 or 5 V for Simmons and MujicaRatner, respectively); however, error bars span half of it. In addition, the barrier height extracted for monolayers (black squares) was suspiciously noisy, hinting at an artificial contribution to the extracted barrier height. We attribute this to the intrinsic uncertainty in the effective bias drop on each of the two junctions in series (see Figure 1c). Thus, for this specific system, variations in barrier height were not conclusive enough. In contrast, the extracted length was much less ambiguous. Our analysis reveals that junctions of polar interfaces clearly have a thicker bilayer than a-polar ones of similar nominal thickness. This higher value emerges from all the above analyses: higher F (low-medium bias, Figure 4b); higher n (high bias, Figure 6); and extracted equivalent length by either Simmons (Figure 5b) or Mujica-Ratner (Figure 5d) models. The increased length was more pronounced for the homogeneous N/N interface than for the heterogeneous N/O interface, although the last has the highest resistance (Figure 3). The N/O junction seems to have a slightly higher barrier height. Seemingly, polar end groups could not affect the length of the alkyl chain underneath them. However, the softness of the molecular bilayer, combined with solution deposition, emphasizes the critical role of weak interactions. Slowinski and Majda suggested that the penetration of hydrocarbon chains between two monolayers decreases the tunneling length over time.43 We propose that the polar end group prevents such miscibility because of hydrophobic repulsion between alkyl and polar groups. Electrostatic interaction between the end groups may also contribute and, indeed, the interface of homo charges (N/ N, repulsive) revealed a longer length than the interface of opposite charges (N/O, attractive). Furthermore, a polar end group has a higher surface energy than methyl end group. The effect of surface tension was critical to the micromorphology of gold leaves deposited by the LOFO procedure.28 We speculate that a similar mechanism acts here, where higher surface energy prevents the penetration of sharp metal asperities into the monolayer, thus considerably reducing the number of shorted junctions and increasing the breakdown voltage. 5. Summary We have shown that low energy, self-assembly of electronic devices from microscopic building blocks (ready made) is feasible, provided that the interface is slightly repulsive. The equilibrium resistance and decay length of these ready-made junctions are comparable to elaborated, well-controlled alkyl thiol junctions. Analyses of I-V curves, using effective cubic relations, provides the equilibrium conductance (G0) and shape factor (F) as experimental parameters, which could be further interpreted within either tunneling or super-exchange mechanisms. Similar effective parameters can also be extracted for



field-emission transfer. In both regimes, the pre-request of known length can be avoided by correlating between these two observables. The intercept of such correlations should reveal the effective contact area (within a given model). Seemingly (considering the large errors), a reduction in contact area accompanies the transition from tunneling to field emission, suggesting that the last is due to deformation in the junction. The setup of two serial junctions considerably depreciates our analysis, which has the potential to be more informative, if the bias is well controlled. Acknowledgment. C. v. d. Marel for XPS measurements; A.V. thanks the Marie Currie Fellowship for funding and D. Cahen for valuable discussions.

Defining the cubic coefficient as C (i.e., I = G0(V + CV3 + ‚‚‚)), the exact expression for C is the following:

C)

)

(A5)

iV. Extraction of Accurate Parameters. The data for F presented in Figure 4 was extracted using the approximated cubic factor, C (i.e., approximated eq A5, see eq 1 in text), where no a priori knowledge of the contact area is required. However, after establishing a reasonable value for the product Am*, the following relations were used to extract a more accurate d value, by combining eqs A4 and A5:32

(

) (

324Am* 5 3 6 1 d - ln 1 - + 2 + 3 ) ln 2 d d d 4G0 x6C

Appendix Appendix A: More on Simmons Tunneling Relations. i. Basic Simmons Relations. I)

(

F2 F2 d+3 1≈ 96 d(d - 2) d.2 96

e2 A 2πh L2

{(

φ0 -

[

V 4π L exp 2 h

)

(

x

2m*m0eφ0 1 -

V 2φ0

(φ + V2) exp[- 4πh L x2m*m eφ (1 + 2φV )]} 0

0

)]

-

0

0

(|V| e φ0) (A1)

4π L 2m*m0eφ ) 1.024L xm*φ h x

(A2)

and the constant is calculated as:

4π 2m e ) 1.024[A˙ -1V-0.5] h x 0

L xm* )

G0 ) 310

[

(A3)

( )

I(V) )

[ ]

e A AA˙ ) 310 4π h µm Vµm2 2

Alternatively, the L in the denominator of eq A3 can be expressed in terms of F (or d), arriving at

G0 ) 324Am*

(d - 2) -d Am* -d e e ≈ 324 Fd F d.2

(A4)

and the constant is calculated as

()

8π m0

[ ]

e 1 A ) 324 2 2 h µm2 V µm 3

iii. Full Approximated Relations, with Accurate Expression for Slope, CG0.32 Equation 1 (main text) uses a factor of F2/96 as the cubic coefficient. However, this is only an approximated factor, based on the assumption of d . 2 (the same assumption as used for the approximated equality in eqs A3 and A4 above).

]

(A8)

where φ j and ∆φ are the average of and the difference between the two barriers, and F is defined for averaged barrier height (φ j , eq 4 of the main text). Integrating eq A8 from V ) 0 to V, gives

and the constant is calculated as 2

(A7)

F2 2 F ∆φ dI ) G0 1 V+ V dV 24 φ j 32

Aβ -d A e (d - 2)e-d ≈ 310 2 L L d.2

2

xdF 1.024

Vi. Approximation of Tunneling across Asymmetric (Trapezoidal) Barrier. For cases where the height of the barrier between the electrode and the insulator is different at the two sides of the barrier (i.e., the shape of the barrier at 0 V is trapezoidal rather than rectangular), Brinkman, Dynes, and Rowell suggested the following G-V relations36 (rewritten in terms of G0 and F)

ii. Full Term for Equilibrium Conductance, G0 is

e2 A (d - 2)e-d G0 ) 4π h L2

(A6)

Note that second term on the left ∼ 0 and can be neglected to get an explicit expression for d. In addition, small uncertainty in Am* has little effect on d because these parameters are logarithmically related. V. Further Fine Parameter Extraction. After the extraction of d (eq A6), the full term of eq A5 is used to extract F. Then φ ) d/F; and

Briefly, we shall define the product φF ≡ d, or dimensionless thickness

d ≡ φF ≡ βtL )

)

[

]

F ∆φ 2 F 3 dI dV ) G0 V V + V ∫0V dV 48 φ j 96 2

(A9)

For symmetric barrier (i.e., ∆φ ) 0) eq A9 reduces to eq 1. Appendix B: Power Expansion to Mujica-Ratner Superexchange I-V Relations.34 i. Original I-V Relations. Equation 8 of ref 34 with slight terminology variations

I)

[ ( )( ) ] 4e2 ∆0 h t

2

φ -2N A φ t A0 2N - 1

(1 + 2φV )

1-2N

}

{(

1-

V 1-2N 2φ

)

(|V| e 2φ - 4|t|) (B10)

where ∆0 is the spectral density of either of the two electrodes at zero bias, t is the transfer integral between sites, φ is the difference between the energy of a bridge site and the Fermi level (here it serves as the barrier height), N is the number of sites that compose a homogeneous molecular bridge, and A/A0 is the contact area to molecular footprint ratio, which equals


Vilan and Hikmet

the number of molecules per junction or number of independent conduction paths. Note that ∆0, t, and φ are energy terms, but simply expressed in V units. The relations of eq B10 are limited to bias below the transition into resonance transfer or hopping. Note that the term in square brackets equals G0 of eq 3 (main text). ii. Accurate Expression of Cubic Coefficient. Similar to Section A.iv above, the cubic coefficient of eq 1 (main text) is an approximated one also for super-exchange. The full term should be

C)

1 N 2 F2 2N 2 + N N ) fF)4 (B11) ≈ 2 6 φ 96 φ 12φ N.0.5

()

iii. Extraction of Accurate Parameters. First, the barrier height φ is expressed as a function of N and C:

φ)

x

2N 2 + N 12C

(B12)

Substituting Fφ ≡ 4N and eq B12 for φ into eq 3 (main text) we get

N ln

(

) [ () ]

∆0 2 A 2N 2 + N ) ln 15 500 - ln(G0) (B13) t A0 12t 2C

where ∆0 and t are unknowns, approximated as ∼1 eV. The resulting N is rounded into an integer and plunged into eq B12 to give φ. The extracted values for N and φ can be reused in eq B13 to extract t experimentally (for an assumed ∆0). Appendix C: Internal Correlation in the Fowler-Nordheim Model for Field Emission. At bias V > φ, the expected transfer mechanism is field emission, where the current-voltage curve is described by Fowler-Nordheim relations:

I)

8π L V2 e2 A exp φ 2m m*eφ 8πhm*φ L 3h x 0 V (|V| > φ) (C14)

() (

)

Dividing eq C14 by V 2 and taking the logarithm of both sides provides eq 8 (main text),10,17 where the slope (n) and intercept (m) are defined as

n)

2 8π φ 2m m*eφ L ) φβtL 3h x 0 3 exp(m) )

A e2 8π hm*φ L2

(C15) (C16)

Rearranging eq C15 to express L as a function of n, and substituting this into eq C16 gives

exp(m) )

φ2 72 Aφ2 16π e 3 m0A 2 ) 9 h n n2

()

(C17)

Supporting Information Available: XPS results for AHDT (T1). Amount of junctions used in each analysis (T2). Breakdown voltage and transition voltage into field emission (S1). Analogous to Figure 4 within the Mujica-Ratner approach (S2). Simulations showing the apparent identity of I-V curves predicted by tunneling and super-exchange (S3) and corresponding transfer parameters (T3). This material is available free of charge via the Internet at http://pubs.acs.org.

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Quantification of Ready-Made Molecular Bilayer Junctions Having

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