Defect Scaling with Contact Area in EGaIn-Based Junctions: Impact on

Dec 12, 2014 - and Christian A. Nijhuis*. ,†,§. †. Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543...
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Defect Scaling with Contact Area in EGaIn-Based Junctions: Impact on Quality, Joule Heating, and Apparent Injection Current Li Jiang,† C. S. Suchand Sangeeth,† Albert Wan,† Ayelet Vilan,‡ and Christian A. Nijhuis*,†,§ †

Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543, Singapore Department of Materials and Interfaces, Weizmann Institute of Science, P.O.B. 26, Rehovot 76100, Israel § Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore ‡

S Supporting Information *

ABSTRACT: Although the tunneling rates decrease exponentially with a decay coefficient β close to 1.0 nC−1 across nalkanethiolate (SCn) monolayer based tunneling junctions determined over a multitude of test beds, the origins of the large spread of injection current densitiesthe hypothetical current density, J0 (in A/cm2), that flows across the junction when n = 0of up to 12 orders of magnitude are unclear. Every type of junction contains a certain distribution of defects induced by, for example, defects in the electrode materials or impurities. This paper describes that the presence of defects in the junctions is one of the key factors that cause an increase in the observed values of J0. We controlled the number of defects in AgTS-SCn//GaOx/EGaIn junctions by varying the geometrical contact area (Ageo) of the junction. The value of J0 (∼102 A/cm2) is independent of the junction size when Ageo is small ( 9.6 × 102 μm2) probe more defects than small junctions; these defects cause large leakage currentscurrent that flows through thin-area defectsand increase the value of J0. Small junctions (Ageo < 9.6 × 102 μm2) were not dominated by defects, and the values of J0 were independent of Ageo. Although these results do not account for the full range of the reported J0 values across test beds, our results show the importance of demonstrating that J0 is independent of Ageo to prove that the junctions are not dominated by leakage currents. There are several types of defects present in junctions including step edges and grain boundaries in the electrodes, the

presence of impurities, phase boundaries of the SAMs, or damage to the SAMs during the fabrication process.11,37,47−49 Defects can be classified as “thin-area” or “thick-area” defects, according to whether they decrease or increase the value of d.11 Thin-area defects reduce the effective electrode spacing, deff (in nm), and lead to high local values of J, whereas the thick-area defects increase deff and decrease J (eq 1). Thick-area defects only scale with area and do not significantly contribute to the measured value of J, while a small number of thin-area defects can dominate the measured value of J. Figure 1 shows a thin-area defect induced by a grain boundary schematically and that the current that flows through

Figure 1. Schematic illustration of a thin-area defect in a SAM-based junction. The current is large at the defect site because of the small d and exponential dependence on d (eqs 1−3). The arrows indicate the direction of current flow (here shown for the case that the current flows from the top to the bottom electrode). The red ellipses indicate the area where Joule heating in the electrodes could be important.

a defect may be much higher than a defect-free part of the junction. Although every type of SAM-based junction contains a certain distribution of defects, the role of defects in the electrical characteristics of junctions has been rarely investigated. Akkerman et al. investigated the influence of defects in alkanedithiolate SAM-based junctions with PEDOT:PSS top electrodes.50 Weiss et al. showed that the topography of the Ag bottom electrode in Hg-drop junctions affects the yields and reproducibility of the junctions: junctions with templatestripped (TS) Ag bottom electrodes with large grains (and small areas of exposed grain boundaries) can be generated with higher reproducibility and yields in working junctions rather than junctions with bottom electrodes with small grains (and large number of grain boundaries) prepared by direct metal evaporation (AgDE).11 Recently we related the surface topography of the bottom electrode to the value of β and J0 (see below) and showed that rough AgDE electrodes with a large fraction of exposed grain boundaries resulted in low values of β = 0.41 nC−1 while smooth AgTS electrodes with large grains (and consequently a low fraction of exposed grain boundaries) resulted in values of β close to 1.0 nC−1 in junctions with GaOx/ EGaIn top electrodes.37 We also showed that the performance of molecular diodes depends on the topography of the bottom electrode and that mainly grain boundaries induced defects that lower the performance of the diodes.51 From these studies we conclude that grain boundaries are the primary sources of defects in GaOx/EGaIn junctions with n-alkanethiolate SAMs (junctions with different types of SAMs and/or electrode materials may be affected by other types of defects). 961

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Figure 2. (A) Schematic illustration of the junctions (not drawn to scale). (B) Photograph of a complete device. Optical micrographs of the top electrodes with Ageo = 4.9 × 102 (C), 2.8 × 103 (D), or 1.1 × 104 μm2 (E) in contact with ITO (see Figure S3 (SI) for the optical micrographs for the other values of Ageo).

Values of β in the range of 1.2−1.4 nC−1 have been attributed to defects in the SAMs and to chain-to-chain tunneling.52 Slowinski et al. showed that the gauche defects of SAMs cause disorder of molecules, and therefore the efficiency of electron tunneling decreases due to the chain-to-chain tunneling.52,53 We showed that the liquid-like character of thin SAMs compensates for defects in the bottom electrode better than the rigid crystalline-like character of thick SAMs in GaOx/ EGaIn junctions (similar observations were made by Vilan et al.54 for phosphonate SAMs on the AlOx electrode in contact with Hg-drop top electrodes). Consequently, the values of J for junctions with SAMs of SC10 supported by eight different types of electrodes with a large range of surface roughness (the bearing volume ranged nearly 3 orders of magnitude) were indistinguishable, while those for junctions with SAMs of SC18 changed 2 orders of magnitude (in this experiment Ageo was kept constant at ∼250 μm2, and thus the density of defects in the bottom electrode was changed). Junctions with rough bottom electrodes had values of β as low as 0.4−0.5 nC−1 which, consequently, resulted in low values of J0 of 2−5 A/cm2, in contrast to junctions with smooth AgTS electrodes that had β of 0.99 ± 0.016 nC−1 with a J0 of 3.3 × 102 A/cm2. The temperature of the molecules inside the junction increases when the charges that flow across them excite molecular bonds or because of Joule heating of the leads.55−57 Rabson et al. reported that the curvature of the dJ/dV curves can reveal (at least qualitatively) whether local heating effects are important (see below). A positive curvature indicates that charge transport via tunneling dominates, while a negative curvature indicates that Joule heating is important and charge transport via defects dominates.58 Rabson et al. performed their calculations while assuming pinholesdirect contact by a metal filament between the two metal electrodesacross which the

local current density is high and Joule heating occurs. In our junctions we do not know the nature of defects, but we believe that high local current densities in the electrode material cause Joule heating; these high currents occur at defect sites that locally lower the value d which do not require metal filaments as schematically indicated in Figure 1. We hypothesize that the defects are randomly distributed in SAM-based junctions. As stated above, the primary cause of thin-area defects in AgTS−SCn//GaOx/EGaIn junctions are grain boundaries. We used AgTS bottom electrodes that have large grains with an average size (Agr) of 0.8−1.0 μm2.37 The value of Aelec of junctions with AgTS bottom electrodes and GaOx/EGaIn top electrodes is a factor 104 times smaller than Ageo.8 Consequently, junctions with a value of Aelec ≪ Agr have a low probability of probing grain boundary induced defects, and their charge transport characteristics are dominated by the properties of the SAMs. The opposite is true for junctions with Aelec ≫ Agr. We assume that the defect density is constant because in all of our experiments we kept the fabrication methods of the bottom and top electrode the same. As indicated schematically in Figure 1, we expect the current that flows across defect sites to be larger than the current that flows across “ideal” parts of the junctions. On the basis of this hypothesis, defects may dominate the charge transport characteristics when Aelec is comparable to or larger than Agr. Here, we fabricated AgTS−SCn//GaOx/EGaIn (n = 10, 12, 14, 16, or 18) junctions with the GaOx/EGaIn stabilized in microfluidic channels to determine the values of J0 as a function of Ageo in the range of 1.8 × 102 to 1.8 × 104 μm2.38 The value of J0 increased by a factor of 103, and yields of nonshorting junctions decreased from 78 to 44% (and even 0% for n = 10 or 12) when the Ageo increased from 9.6 × 102 to 1.8 × 104 μm2 (or Aelec increased from roughly 0.096 to 1.8 μm2 which is 962

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Figure 3. Plots of the Gaussian mean of the values of ⟨log10|J|⟩G vs applied bias and histograms of log10|J| at −0.50 V with Gaussian fits to these histograms, respectively, for junctions with n = 10, 12, 14, 16, or 18 and Ageo of 4.9 × 102 μm2 (A and B), 2.8 × 103 μm2 (C and D), or 1.1 × 104 μm2 (E and F).

similar to Agr). In addition, the curvature of the dJ/dV curves flattens with increasing Ageo. Fits to the full Simmons equation (eq 3) indicate that the deff decreases with increasing Ageo and is smaller than the molecular length (or thickness of the SAM). Thus, the charge transport characteristics are dominated by thin-area defects. In contrast, the value of J0 and the yield of nonshorting junctions were constant for junctions with Ageo < 9.6 × 102 μm2; the curvature of the dJ/dV curves is positive; and the data fit well to the full Simmons equation for values of d that equal the molecular length. Thus, the charge transport characteristics are dominated by the properties of the SAMs. Therefore, to judge the quality of SAM-based tunneling junctions by the values of β and yields of working junctions is not sufficient, and the value of J0 has to be considered: the value of J0 should be independent of Ageo.

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connect to a through-hole (see Supporting Information (SI) for more details). Channel 2 is filled with the liquid-metal after which vacuum is applied to channel 1 to fill the through-hole with the liquid-metal. The diameter of channel 1 is chosen such that it does not fill with the liquid-metal because of the high surface tension of the bulk EGaIn (624 N/m).38 In a final step we placed the top electrode in contact with the SAMs. This method is compatible with template-stripped (TS) surfaces which are readily accessible in ordinary laboratory conditions, do not need to be cleaned prior to use, and are smoother than metal surfaces obtained by direct metal deposition methods.59 The bottom electrode does not need to be patterned and therefore has never been exposed to photoresist (which is often difficult to remove)60 and does not contain edges at which SAMs cannot form well.9,61 For these reasons this method generates J(V) data that are reproducible and result in distributions of log10|J| with small log-standard deviations (σlog = 0.12−0.25; see below and ref 38). Optical micrographs of several top electrodes in contact with ITO with different values of Ageo are shown in Figure 2C−E (see Figure S3 (SI) for optical micrographs of the other top electrodes). These images show that because of the high surface tension of the liquid metal the through-hole was not completely filled, and a gap between the GaOx/EGaIn and the wall of PDMS was always present (as indicated by an arrow in panels C, D, and E). Before we started the experiments, we imaged the

RESULTS AND DISCUSSION

Fabrication of the Junctions. We used a previously reported technique to fabricate the SAM-based tunneling junctions of the form of AgTS−SCn//GaOx/EGaIn (n = 10, 12, 14, 16, or 18) with a large range of Ageo of 1.8 × 102 to 1.8 × 104 μm2.38 The liquid-metal is stabilized in a microfluidic device made of a transparent rubber of polydimethylsiloxane (PDMS). Figure 2 shows a schematic of the junction along with an optical photograph. The microchannels 1 and 2 (as indicated in Figure2A) are fabricated in two separate steps, and both 963

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The Journal of Physical Chemistry C Table 1. Values of ⟨log10|J|⟩G, β, and the Yield in Working Junctions vs the Geometrical Junction Area Ageo (μm2)

no. of junctions

yield (%)a

Nb

× × × × × × ×

96 99 96e 110 134 160 102

78 76 78e 68 56 47 44

3000 3000 3000e 3000 3000 3000 1800

1.8 4.9 9.6 2.8 6.4 1.1 1.8

2

10 102 102e 103 103 104 104

log10|J0|c 2.5 2.5 2.4 3.5 4.0 4.2 5.6

± ± ± ± ± ± ±

0.3 0.2 0.2e 0.2 0.3 0.3 0.8

log10|J0| (LAD)d 2.5 2.6 2.4 3.5 4.1 4.0 5.8

± ± ± ± ± ± ±

0.2 0.2 0.2e 0.1 0.2 0.1 0.2

βc 1.01 1.01 1.00 1.12 1.15 1.14 1.22

± ± ± ± ± ± ±

0.046 0.033 0.026e 0.029 0.046 0.041 0.113

β (LAD)d 0.99 1.01 1.00 1.13 1.14 1.14 1.27

± ± ± ± ± ± ±

0.016 0.031 0.023e 0.024 0.035 0.026 0.031

σlogc 0.25 0.20 0.18e 0.25 0.20 0.31 0.30

a Defined as the number of nonshorting junctions divided by the total number of junctions. bThe total number of J(V) curves. cObtained by leastsquares fitting of Gaussian means of log10|J| to eq 2. dObtained by least absolute deviation fitting (see SI for details) to eq 2. eData taken from ref 38.

assuming that the data follow normal distributions and (ii) all values of log10|J| by minimizing the error of the least absolute values of the error (least absolute deviation LAD, Figure S7, SI) without making any assumptions regarding the type of the distribution the data follows. The results for both fitting methods are summarized in Table 1. This table shows that both methods give similar values of β and J0 and indicates that the error introduced by assuming that the data follow log-normal distributions is below the uncertainty of the fitted parameters.38 Figure 5 shows the values of log10|J0|, β, the yield of nonshorting junctions, and σlog, as a function of Ageo (the dashed red lines only serve as guides to the eye and do not represent fits to any models). This figure shows that for small junctions with Ageo < 9.6 × 102 μm2 the values of log10|J0| (Figure 5A), β (Figure 5B), and the yield in nonshorting junctions (Figure 5C) are independent of Ageo. In contrast, for large junctions with Ageo > 9.6 × 102 μm2 the values of log10|J0| and β increase, while the yield in nonshorting junctions decreases, with increasing values of Ageo. The values of σlog seem to increase with increasing values of Ageo although this correlation is weak. These results indicate that small area junctions are of higher quality than large area junctions for three reasons. (i) The constant value of log10|J0| as a function of Ageo indicates that these junctions are not dominated by leakage currents. (ii) The value of β of 1.0 nC−1 is very close to the consensus value of β. (iii) High yields and small σlog values indicate high reproducibility and that the scatter in the data due to defects is minimal. As mentioned in the Introduction, values of β > 1.0 nC−1 have been associated with junctions dominated by defective SAMs,54 and therefore we believe that the increase of β from 1.0 to 1.2 nC−1 is caused by defects. These results show that observing an exponential decay of the currents as a function of SAM thickness (despite moderate to good yields in working junctions) is not sufficient to justify conclusions regarding the quality of our junctions. Rabson et al. argued that pinholes may mimic the exponential decay of J with d in tunnel junctions based on inorganic oxides.63 Thus, in general, conclusions regarding the mechanism of charge transport solely based on J(V) data as a function of d should be made with care. Joule Heating. In all of our experiments, we kept the topography of the bottom electrode constant which means that the number of defects increases with increasing Ageo (but the density of defects remains constant as explained in the Introduction). Rabson et al.64 argued that currents that flow through defects can result in a local increase of the temperature of the electrodes because of Joule heating. As the current increases with increasing bias, Joule heating becomes more important and impedes the current flow. Thus, the rate at which the current increases decreases with increasing bias at

top electrode to determine its geometrical area, and we found the gap size was roughly constant (10 ± 2 μm). Electrical Characteristics as a Function of the Junction Area. We measured the J(V) curves as a function of Ageo over the bias range of ±0.50 V. For each type of junction, we determined the log-average J(V) curves following previously reported procedures.37 Briefly, we recorded statistically large numbers of J(V) data (40 scans in steps of 25 mV per stable nonshorting junction; trace and retrace). The values of log10|J| measured at each bias were plotted in histograms to which Gaussians were fitted to derive the Gaussian mean of log10|J| (⟨log10|J|⟩G) and the log-standard deviation (σlog); these values were used to construct the average J(V) curves. Figure 3 shows these J(V) curves (the error bars indicate σlog) and the histograms of log10|J| determined at V = −0.50 V for junctions with Ageo = 4.9 × 102, 2.8 × 103, and 1.1 × 104 μm2 (see Figure S4 (SI) for the data obtained for the other junctions with Ageo = 1.8 × 102, 9.6 × 102, 6.4 × 103, or 1.8 × 104 μm2; see Figures S5 and S6 (SI) for the J(V) curves on linear scales). Table 1 summarizes the electrical characteristics. For each value of Ageo, we determined the electrical characteristics of the junctions with SCn SAMs with n = 10, 12, 14, 16, or 18 except for junctions with Ageo = 1.1 × 104 μm2 because these junctions with n = 10 or 12 were too defective and short. Figure 4 shows the values of ⟨log10|J|⟩G determined at −0.50 V as a function of n for each value of Ageo. Figures S5 and S6

Figure 4. Values of ⟨log10|J|⟩G as a function of nC for junctions with different values of Ageo.

(SI) show the mean J as a function of voltage of junctions with Ageo of 4.9 × 102 μm2 and 1.1 × 104 μm2 so the nonlinear characteristics are more easily visualized. Reus et al.62 discussed in detail that the accuracy and precision of the values of β and J0 depend on the method that is used to fit eq 2 to the data. Therefore, we used two different methods to fit the data: (i) least-squares fitting of the values of ⟨log10|J|⟩G (Figure 4) while 964

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Figure 5. Values of log10|J0| (A), β (B), the yield in working devices (C), and the log-standard deviation σlog (D), as a function of Ageo. The red dashed lines are guides to the eye.

thin-area defects. The opposite is true when tunneling dominates the mechanism of charge transport because the effective tunneling barrier height decreases with increasing bias. Thus, the rate at which the current increases with increasing bias increases when tunneling dominates. Rabson et al. showed theoretically that dJ/dV curves with negative curvature are characteristic for junctions dominated by thin-area defects, while positive curvature is characteristic for junctions that are dominated by tunneling. They also calculated that the curvature gradually changes from positive to negative with increasing number of (or size of the) defects. We, therefore, hypothesize that local heating effects are important in our large junctions but not in the small junctions (we rule out other mechanisms that could result in negative curvatures, such as on and off resonance tunneling,65 because SCn SAMs have large HOMO− LUMO gaps of 8−9 eV across which tunneling is the mechanism of charge transport7). To test this hypothesis, we recorded the dJ/dV curves of AgTS−SC18//GaOx/EGaIn junctions in the bias range of ±1.0 V. Figure S8A (SI) shows the J(V) plots at negative bias for AgTS−SC18//GaOx/EGaIn junctions as a function of Ageo with fits to eq 3 (Figure S8B (SI) shows all average J(V) curves determined by averaging the data obtained from six junctions (120 J(V) curves) that had their J(V) characteristics within one σlog from the ⟨log10|J|⟩G). These data are in excellent agreement with the data shown in Figure 3. Figure 6A shows the corresponding dJ/dV curves with the differential conductance normalized to the differential conductance at 0.05 V as a function of Ageo. The solid lines only indicate the curvature and do not represent fits to any models. The differential conductance for junctions with Ageo < 9.6 × 102 μm2 shows positive curvature; this positive curvature indicates that the junctions are relatively free of defects and that the mechanism

Figure 6. Normalized differential conductance curves as a function of Ageo for junctions with AgTS (A) and AgDE electrodes (B). The solid lines are guides to the eye.

of charge transport is dominated by tunneling. The differential conductance for junctions with Ageo > 9.6 × 102 μm2 gradually changes and flattens the curvature with increasing Ageo; this 965

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The Journal of Physical Chemistry C flattening of the curvature indicates that the junctions are defective and the mechanism of charge transport is dominated by defects. For junctions with AgTS electrodes, we did not observe negative curvature, but we observed negative curvature for junctions with SAMs of SC18 immobilized on rough Ag surfaces (obtained by direct evaporation of Ag on Si/SiO2, AgDE) in the bias range of ±1.0 V. Figure 6B shows the corresponding dJ/dV curves with the differential conductance normalized to the differential conductance at 0.05 V with AgDE electrodes (see Figure S8 (SI) for the J(V) curves); junctions with Ageo > 6.4 × 103 μm2 only yielded shorts. This negative curvature confirms that Joule heating induced by defects is important for defective junctions, and examination of the dJ/dV curves provides qualitative information regarding the quality of the junctions: flattening or negative curvatures indicated defective junctions, while positive curvature indicates good quality junctions. Estimation of the Effective Thickness. As mentioned above, we believe that large junctions are defective and contain defects that result in an effective tunneling distance deff which is lower than the value d (or the thickness of the SAM). In principle, fitting the J(V) curves to the full form of the Simmons equation given by eq 3 where m is the electron mass, d the barrier width, ΦB the barrier height, V the applied bias, and α a dimensionless fitting parameter would yield deff.3,66 In practice this method is not straightforward for a number of reasons including poor understanding of α, uncertainties in the effective electrical area or contact resistance, difficulties in obtaining good fits in both the high and low bias range, and too many fitting parameters.20,21,43 Here we only use this procedure to crudely estimate the relative values of deff as a function of Ageo, and we stress that the fitting results listed in Table 2 are

J(V) data for junctions with Ageo = 9.6 × 102 μm2 by optimizing ΦB and α and used these values as the initial values to fit the other J(V) curves by optimizing all three parameters. Figure S9A (SI) shows the J(V) plots for AgTS−SC18//GaOx/EGaIn junctions as a function of Ageo with fits to eq 3. Table 2 shows that deff decreases with increasing Ageo (Figure S9B, SI). The value of α decreases from roughly 0.86 for small junctions to 0.74 for large junctions and falls in the range of previously reported values.19,68 The value of ΦB increases with increasing thin-area defects. This increase in the apparent barrier height reflects the change in curvature, while the reduction in deff accounts for the higher current density due to defects.

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CONCLUSIONS Value of J0 Is Independent of the Junction Area When the Number of Defects Is Low. We formed SAMs on ultraflat and clean Ag electrodes. We used GaOx/EGaIn top electrodes confined in a through-hole in a transparent rubber (PDMS) which allowed us to control the junction size by simply changing the diameter of this through-hole. This procedure made it possible to investigate the charge transport characteristics of SAM-based junctions as a function of the geometrical contact area in the range of 1.8 × 102 to 1.8 × 104 μm2. The J(V) characteristics depend on the junction area when the area exceeds a certain threshold value (here 9.6 × 102 μm2), but below this threshold value the J(V) characteristics were independent of Ageo. Here, in the same system, we obtained values of J0 ranging from 102 to 105 A/cm2, while the value of β only varied from 1.0 to 1.22 nC−1 with increasing junction size. Shape of the J(V) Curve Is Sensitive to the Thin-Area Defects. By increasing the junction size we increased the number of defects in the junctions while keeping the density of defects constant. By fitting the J(V) curves to the full form of the Simmons equation (we did not correct the value of J for effective electrical contact area or contact resistance), we found that thin-area defects decrease the effective barrier width and attenuate the bias sensitivity of the transport which is expressed as higher effective barrier height as well as flattening of the dJ/ dV curves with increasing Ageo. The mild bias response is attributed to Joule heating which becomes important for junctions with Ageo > 9.6 × 102 μm2 but not for junctions with Ageo < 9.6 × 102 μm2. We believe that this Joule heating is caused by the high local currents that flow through thin-area defects. Examination of the curvature of dJ/dV as a function of Ageo can be done for each molecular length, in contrast to β and J0 which require comparing a set of molecules varying in length. Defects Can Cause a Factor of 105 Change in the value of J0. As mentioned in the Introduction, the apparent value of J0 depends on various factors that complicate comparison across the test bed. The major source of defects in AgTS−SCn//GaOx/EGaIn junctions is the exposed grain boundaries in the bottom electrode. We showed that rough surfaces, i.e., surface with a large fraction of exposed grain boundaries, cause defects in the SAMs and, consequently, the assumption that d = nC does not hold resulting in low β values of 0.4−0.5 nC−1 and consequently in a factor of 102 decrease of the value J0.37 Here we show that when Aelec is large relative to the grain size the value of J0 increases by a factor of 103 with a relatively modest increase in β from 1.0 to 1.27 nC−1. In other words, defects can account for differences of a factor of 105 (at least in AgTS−SCn//GaOx/EGaIn junctions; the types of

Table 2. Fitting Results for Junctions with a SAM of SC17CH3 Ageo (μm2)

ΦB (eV)

α

deff (Å)

× × × × × × ×

2.15 2.18 2.16 2.22 2.41 2.71 3.12

0.86 0.86 0.87 0.86 0.83 0.81 0.74

25.7 25.7 25.7 25.2 24.5 23.3 22.3

1.8 4.9 9.6 2.8 6.5 1.1 1.8

2

10 102 102 103 103 104 104

effective values (see SI for more details) and should not be regarded as genuine properties. J=

⎧⎛ ⎛ e ⎞⎪ eV ⎟⎞ ⎜ ⎟ ⎨⎜ Φ − 2 2 ⎪⎝ ⎝ 4π ℏd ⎠⎩ B 2⎠ 1/2 ⎤ ⎡ 2(2m)1/2 α ⎛ ⎛ eV ⎞⎟ eV ⎞⎟ ⎜Φ − d ⎥ − ⎜ΦB + × exp⎢ − B ⎝ ⎠ ⎝ 2 2⎠ ℏ ⎣ ⎦ 1/2 ⎤⎫ ⎡ 2(2m)1/2 α ⎛ ⎪ eV ⎟⎞ ⎜Φ + d ⎥⎬ × exp⎢ − B ⎪ ⎝ ⎠ 2 ℏ ⎣ ⎦⎭

(3)

Because of the positive curvature of the differential conductance data and the fact that J was independent of Ageo (as described above) for Ageo ≤ 9.6 × 102 μm2, we believe that these junctions are dominated by tunneling through the SAMs, and therefore the deff is assumed to be the molecular length (2.57 nm).67 Therefore, we used deff = d = 2.57 nm to fit the 966

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defects and how they affect the electrical characteristics of other types of junctions have been rarely investigated and are often not known) in the observed value of J0 from what one would expect from defect-free junctions. Thus, we believe that it is important to establish the independence of J0 of Ageo to rule out leakage currentscurrents that flow through defectswhile the value of β remains constant at 1.0 nC−1. We Propose a Value of J0 of 106±0.2 A/cm2 at 0.5 V Bias and 104±0.2 A/cm2 around 0 V Bias, for Junctions with nAlkanethiolate SAMs. We showed by impedance spectroscopy that the contact resistance of the GaOx/EGaIn electrode with the SAM is 2.9−3.6 × 10−2 Ω·cm2. The resistance of the GaOx layer itself is 3.3−5.8 × 10−4 Ω·cm2.8,46 These resistances are orders of magnitude smaller than, and in series with, the SAM resistance and therefore do not contribute significantly to the apparent J0 value in our junctions. The value of J0 is bias dependent (J0 increases by a factor of 103 from 0 to 0.50 V for AgTS−SCn//GaOx/EGaIn junctions;6 see Figure S10 (SI) for a plot of J0 vs bias) when determined from fits of the simple form of the Simmons equation to plots of log10|J| vs d, and therefore only J0 values determined at identical bias can be compared across test beds except when the dependency of J0 on the bias is known and when they were determined by the same methods. We also show here that the value of J0 is independent of Ageo for junctions with Ageo < 9.6 × 102 μm2 which rules out the role of leakage currents. We found that J0 is 2.5 × 102 A/cm2 (the average of the three values for small junctions; Table 1), and correcting the J0 values for the effective electrical contact area of 104 as proposed by Felice et al. yields a value of J0 of 2.5 × 106 A/cm2 at 0.5 V. This value is essentially the same (within 1 order of magnitude) as the value reported by Felice et al., and both are similar to values determined by single molecule experiments.23,69 Figure S10 (SI) shows the bias dependency of the value of J0 and that J0 around zero applied bias is 1.8 A/cm2 or 2 × 104 A/m2 after correcting for effective area. What is a “Working” Junction? The values of β, J0, σlog, and the yields in working devices must all be considered to estimate the quality of SAM-based junctions. The values of β and J0 should be constant as a function of junction size. High yields and small σlog are still important, but these parameters are not a priori very sensitive to the quality of junctions (at least for junctions with GaOx/EGaIn top electrodes). Our results show that junctions with reasonable yields and log-standard deviations may be dominated by thin-area defects and suffer from local heating effects; these heating effects can be qualitatively identified by examining the shape of the J(V) curves. The results described here show that widely used indicatorsobserving an exponential decay of J as a function SAM thickness and good yields in nonshorting junctionsare not sufficient to draw meaningful conclusions regarding the quality of the junctions: a junction that is dominated by currents that flow through defects may show similar characteristics as what would be expected for an “ideal” junction. We propose that the following tests give at least qualitative information regarding the junction quality: (i) the value of J0 should be independent of the Ageo, (ii) the curvature of the dJ/ dV should be positive, and (iii) the value of β should be close to 1.0 nC−1 (for junctions with aliphatic SAMs). Currently, we are investigating how AC methods (i.e., impedance spectroscopy46) and temperature-dependent J(V) measurements can help to understand the role of defects in the charge transport properties of our junctions in more detail.

Article

ASSOCIATED CONTENT

S Supporting Information *

Experimental details, atomic force microscopy images of the bottom electrodes, electrical characterization of the junctions, optical microscopy images of the top electrodes, and the least absolute deviation fitting procedure. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Singapore National Research Foundation (NRF Award No.NRF-RF 2010-03 to C.A.N.) is kindly acknowledged for supporting this research.

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REFERENCES

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