Temperature Dependent Barrier Crossover Regime in Tunneling

Nov 30, 2009 - In this case a transition point, Vtrans, characterizes the IBR at low temperatures, the MBR at high temperatures, and the BTR between t...
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J. Phys. Chem. C 2009, 113, 21413–21421

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Temperature Dependent Barrier Crossover Regime in Tunneling Single Molecular Devices Based on the Matrix of Isolated Molecules Andrei V. Pakoulev† and Vladimir Burtman*,‡,§ Department of Chemistry, UniVersity of Wisconsin, 1101 UniVersity AVe, Madison, Wisconsin 53706-1322, Geology and Geophysics Department, UniVersity of Utah, 135 S. 1460 E, Room 719, Salt Lake City, Utah 84112-0111, and Department of Physics, UniVersity of Utah, 115 S 1400 E, Room 202, Salt Lake City, Utah 84112-0830 ReceiVed: June 16, 2009; ReVised Manuscript ReceiVed: NoVember 6, 2009

This paper reports analysis of direct (low bias regime that corresponds to Simmons model) and field emission, Fowler-Nordheim (FN) tunneling, and a crossover between these regimes in molecular nanojunction. We have fabricated molecular devices based on a heterogenius mixture of molecular wires of 2-[4-(2mercaptoethyl)-phenyl]ethanethiol (Me-PET) as self-assembled monolayer (SAM) molecules incorporated into the matrix of molecular insulator spacers [penthane 1-thiol (PT)] at a concentration ratio of r ) 10-6 wires/spacers. The monolayer is sandwiched between two gold (Au) electrodes. A temperature-depended conductivity in this structure was analyzed at both low and elevated biases using models of direct tunneling (Simmons model) and field emission (FN) regime. A crossover voltage, Vtrans, between these two regimes was determined at different temperatures. Comparison of temperature-dependent Simmons and FN barriers, (ΦBSim(T) and ΦBFN(T)), and transition bias (Vtrans(T)) reveals an anomaly in position of Vtrans(T) with respect to ΦBSim(T) and ΦBFN(T) at low temperatures (15-100 K). The change in slopes of ΦBSim(T), ΦBFN(T), and Vtrans(T) at different temperatures pointed to the switching of the transport mechanism in the system as well. Activated by temperature, the observed phenomenon can be attributed to the existence of an additional transport barrier, which operates in series with the molecular barrier. As candidate for this additional barrier, the injection barrier must be considered. In this context, the transport was controlled by the injection barrier or injection barrier regime (IBR) at low temperatures (15-100 K), and by molecular barrier or molecular barrier regime (MBR) at high temperatures (150-294 K). A molecular diode, with the same structure (Me-PET/PT r ) 10-6), but with Al electrodes, was fabricated to check this assumption. While devices with Au electrodes have a low tunneling barrier (ΦBSim ≈ 1.2 eV), devices with Al electrodes have a high tunneling barrier (ΦBSim ≈ 3 eV). Only direct tunneling could be observed in measured bias range (V ) (2 V). Nevertheless the “crossover behavior” was observed in the device with Al electrodes at low temperatures (15-100 K). Therefore, observed “crossover” in the device with Al electrodes is related to the transport processes, which occurs at the electrode due to the injection barrier, rather than the transition from direct to FN tunneling in the molecule at low temperatures. In this case a transition point, Vtrans, characterizes the IBR at low temperatures, the MBR at high temperatures, and the BTR between these two regimes. 1. Introduction Currently the most accessible approaches to analyze a single molecular transport are the phenomenological WKB-derived direct tunneling model at low bias and field emission tunneling at higher biases, which are traditionally referred as Simmons model1-3 and Fowler-Nordheim (FN) tunneling, correspondingly. These approximate phenomenological models are at present a necessary step for quantifying the increasing amount of molecular transport data.2 Crossover between these two regimes (transition from a trapezoidal barrier to a triangular barrier) was recently studied4,5 in molecular junctions of differing lengths at room temperature. This transition occurs at transition point, Vtrans.4 The analysis of the tunneling crossover imposes that (i) tunneling is the main transport mechanism in organic nanomolecular diodes at various biases6 and (ii) Simmons and * To whom correspondence should be addressed. E-mail: vlad.burtman@ utah.edu. † University of Wisconsin. ‡ Geology and Geophysics Department, University of Utah. § Department of Physics, University of Utah.

FN models describe transport at the bottom and at the top of molecular barrier respectively. A comparison of these regimes and analysis of crossover area may reveal certain information on the real shape of the molecular barrier. This development proves to be useful for metrology analysis of molecular nanojunctions, because of the correlation between the energy scale of Vtrans point and the observed optical offset between EF and the nearest molecular orbital (MO).4 The optical offset can be detected independently from XPS or UPS spectra.4 For this manuscript, we conducted a temperature dependent tunneling crossover analysis to study in more details of transport mechanism of aromatic molecular wires. This analysis includes comparison of temperature dependent Simmons [ΦBSim(T)] and FN [ΦBFN(T)] barriers and the study of temperature dependent crossover [Vtrans(T)] between these two tunneling regimes. Our report utilizes the Frisbie crossover model4 for analysis of the temperature dependent transport in molecular junctions. The Vilan’s2 approach to model transport through molecular barrier was utilized to account for the barrier shape factor, R, and preexponential coefficient G0.

10.1021/jp9056576  2009 American Chemical Society Published on Web 11/30/2009

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2. Materials and Methods The nanofabrication route, which produces an organic monolayer with many molecules acting in parallel,7,8 is used to grow the self-assembled monolayer (SAM) on metallic electrodes from a diluted mixtures of molecular wires [2-[4-(2-mercaptoethyl)phenyl]ethanethiol (Me-PET)] and molecular insulating spacers [1-pentanethiol (PT)]. Our group utilized the same selfassembly and fabrication approach; a SAM of solid-state mixture, to study Me-BDT/PT (Me-BDT is abbreviation for 1,4methane benzene dithiol) system.9,10 The aliphatic tail of MePET molecule has one additional chain, compared to Me-BDT molecule, which was studied in refs 9 and 10. Synthesis and characterization of Me-PET is summarized in the Supporting Information (SI). A device having properties of a single molecule device can be achieved when the fraction of molecular “wires” is small and the device contains many independent conducting molecules acting in parallel. Prepared precursor solutions have a concentration ratio of r ) NMe-PET/NPT, where NMe-PET and NPT are their respective molar concentrations. The self-assembly mechanism and two-terminal molecular devices are shown schematically in the SI. A concentration ratio r was kept at r ) 10-6, which typically is the concentration for a single molecular devices.8,9 For consistency with our nomenclature,8,9 we will denote this as a Me-PET/PT r ) 10-6 device. We have also fabricated several devices with r ) 0; these devices were composed of insulated PT molecules with no molecular wires. In addition, PT molecules have only one thiol group, and thus were able to form a chemical bond only with the bottom electrode. Due to such a structure, the resistivity of the r ) 0 device was 102 times larger than that of the Me-PET/ PT r ) 10-6 device (see the SI). We are therefore assuming that the PT molecules do not make a significant contribution to the conduction, and the increase in conduction is due to the added conducting channel via the Me-PET molecules. Molecular diode with Al electrodes, the Al-Me-PET/PT-Al device, was fabricated similarly to the Me-PET/PT r ) 10-6 device with Au electrodes for a control experiment.9 To avoid electrode oxidation, the thermal evaporation of Al electrodes through the shadow mask was prepared in a glovebox. The temperature on thermocouple attached to the sample-holder in evaporation chamber did not exceed 130 °C during evaporation of top Au and Al electrodes. See ref 9 for more information about the fabricated of the Me-BDT/PT r ) 10-2 device (based on molecular aggregates) with Al contacts. For our research a AlMe-PET/PT-Al device (based on isolated molecular “wires”) at r ) 10-6 was fabricated.11 The successful rate of fabricated Al-Me-PET/PT-Al and PT devices was substantially smaller than for the Me-PET/PT r ) 10-6 device (SI). This rate might be increased by usage of liquid-nitrogen-cooled sample-holder stage. This method of SAM solid-state mixture preparation enables growth of spatially isolated molecular “wires” in a solid-state matrix of saturated molecules. In this case, saturated molecules, “spacers”, exhibit insulating properties. See ref 12 for more details about surface chemistry and fabrication protocols regarding SAM devices in a solid-state mixture. This approach is different from Friesbie’s group4 that mostly analyses room temperature conductivities. It also differs from researchers, who analyze the temperature dependence of saturated (not aromatic or double bond) molecules at low biases; these typically do not approach the “crossover area”, as the Reed group6 has. In our work, we use the term “single molecular devices” to denote the “single molecular devices based on matrix of isolated molecules” term. Terminal electrical measurements were per-

Pakoulev and Burtman formed with a Keithley 236 electrometer in the temperature range 15-294 K. 3. Results 3.1. Raw Data Comparison. Simmons and FN Model of Tunneling through Molecular Barrier. To justify the use of the tunneling models, three important criteria must be satisfied: (i) exponential decay of the current with molecular length, (ii) temperature independence, and (iii) the characteristic shape of the I-V curves. We will not report here any molecular length scale studies and assume that our results will be valid at different lengths of the molecular bridge. Indeed, it has been demonstrated that single molecular devices obey the law of the exponential current decay with increasing of molecular length.12 We also assume that the temperature dependent transport mechanisms operate in parallel to tunneling and could be separated from pure tunneling in molecular junctions. Room temperature measurements4 and temperature dependent tunneling has been well reported and discussed.13 The nature of tunneling temperature dependence in single molecular transport is still debated.14 Moreover, we will show that, even if temperature activated mechanisms are in serial to molecular tunneling, it still could be separated from temperature induced phenomena under certain criteria. Short (∼1 nm) organic molecules have substantial direct tunneling due to nonzero wave function at the electrodes across molecular barrier. To approximate a current-voltage response of the fabricated molecular devices, we use the Simmons model15 as a guide to electron tunneling through a thin dielectric layer. This model has also been successively applied to describe an electron tunneling through a single molecule.16-18 The list of conditions or assumptions for using the Simmons model for the tunneling in single molecular devices is summarized in ref 16. This model is based on the assumption that if the Fermi level of the metal electrode is closely aligned to a molecular energy level then the effect of the other, more distant, molecular energy levels on the charge transport is negligible. Depending on the position of the Fermi level, the tunneling barrier may be associated with either the highest occupied or lowest unoccupied molecular orbital (HOMO or LUMO, respectively). Simmons has derived a general expression, which describes the current density versus voltage over the full range of metal-dielectricmetal to field-emission tunneling.15 The Simmons model for organic or inorganic tunneling systems is restricted to low biases. If ΦBSim defines the lowest Simmons barrier in the system in electron volts and the applied bias is V < ΦBSim/e (where e is the electron charge), then the dependence of the current density J on V at zero temperature can be approximated as

{( (

) [ ) [

(

)] )]}

2(mee)1/2 2ΦSim 2ΦSim B B - V exp R -V e p e 2(mee)1/2 2ΦSim 2ΦSim B B + V exp R +V (1) e p e Here, p is a reduced Plank’s constant, me is the electron mass, and d is the barrier width. In molecular junctions, the barrier height can be approximated by the energy offset between the electrode Fermi level and the nearest molecular orbital. For a single monolayer, barrier width d should be close to the molecular length, which has been estimated to be ∼1 nm from the data obtained by ellipsometric measurements.9 Parameter R provides a way to apply the model to a nonrectangular barrier and/or to account for the effective mass of the tunneling electrons. Equation 1 is written in slightly modified presentation J(V) ) G0

(

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compared to original Simmons model by introducing a preexponential factor G0. It accounts for limited number of conducting channels in monolayer.2,19 The G0 is also known as an “equilibrium conductivity” and its meaning and contribution can also be extended to the field emission at high-bias range (FN mechanism)17 based on a different linearized presentation.4,20 Despite the absence of temperature dependence in both Simmons and FN (see below) tunneling models, the temperature dependence of tunneling parameters is a central topic in the discussion section. Equation 1 describes a trapezoidal barrier when the applied bias is less than the barrier height. In the zero-bias limit, the barrier is rectangular, and eq 1 reduces to

(

J(V) ) G0V exp -

Sim 2d√2m*Φ e B p

)

4d√2me(ΦBFN)3 1 J ) +C 3pe V V2

( )

ln

()

(4)

where C is an offset constant. Beebe et al.4 studied crossover from direct to overbarrier tunneling regime for SAM system at room temperature. We use

(2)

Now one can see that factor G0 is related to the conductivity at very low biases V , ΦB/e, when the dependence J(V) becomes linear (see also the SI). Note that in eq 2 R-factor has been incorporated into the electron effective mass so that m*e ) R2me.2,18 These two presentations are equivalent because it is impossible to distinguish the contributions of R and m*e in eq 1. At the high bias limit, when the applied bias exceeds the barrier height, ΦB, an overbarrier field emission transport model is usually applied.21 This model is also known as the Fowler-Nordheim model. FN tunneling is the process whereby electrons tunnel through a barrier in two steps: (i) tunneling into the molecular orbital and (ii) transfer to the second electrode through nontunneling mechanism. Let ΦBFN defines the biaseffected barrier in the system in electron volts and applied bias is V > ΦBFN/e. This quantum mechanical tunneling process is an important mechanism for thin barriers, which imposes the barrier transition from trapezoidal to triangular. The currentvoltage dependence can be described as follows:21

(

J(V) ∝ V2 exp -

Sim 3 4d√2m*(Φ e B ) 3peV

)

(3)

Thus, at high biases the current density J would have a parabolic dependence on applied voltage. The experimental response, J(V), of the molecular devices, and the best fits with eq 1 for low biases and with eq 3 for high biases at different temperatures are shown in Figure 1 panels A and B, respectively. Figure 2 shows an example of the traditional FN plot (ln J/V2) vs 1/V at high biases, which demonstrates a ΦBFN(negative) and has the value of 1.53 eV at T ) 250 K. In Simmons range (V , ΦB/e, eq 1), we use ΦBSim, R, and G0 as fitting parameters. The R, G0, and ΦB were determined by finding the global minima of the model over the experimental data, as in ref 16. The temperature dependence of the fitting parameters R and G0 are summarized in the SI. ΦBFN is found to be different for negative and positive voltages and we will denote these barriers as ΦBFN(positive) and ΦBFN(negative). Parameter d was fixed at 1.0 nm, to produce a Simmons fit, while for effective mass we used R values from Simmons so that m*e ) R2me, as has been discussed above. 3.2. Crossover from Direct (Simmons) Tunneling to FieldEmission Regime (Fowler-Nordheim Model) at Transition Bias, Vtrans. The FN equation for a field emission tunneling (eq 3) can be written in the following logarithmic form, which is usually arranged in linearized form to extract the FN barrier, which will be a slope of ln(I/V2) against 1/V line:

Figure 1. Analysis of electrical transport properties in SAM diodes (Au electrodes) with r ) 10-6 with the Simmons model fit (solid lines, A) over experimental data (symbols) and FN model fit (solid lines B) at low temperature (50 K) and high temperature (250 K); at low bias (A) and high bias (B) for a Simmons and FN model correspondingly. Fitting results for the tunneling barrier in the temperature range 11-294 K are summarized in Figure 3. IV’s characteristics for the SAM diodes with r ) 10-6, but with Al electrodes are shown at Figure 5. IV’s characteristics for the SAM diodes with r ) 0 (only PT molecules), with Au electrodes and parameters R and G0 are summarized in the SI.

Figure 2. FN plot ln(J/V2) vs 1/V for SAM diodes (Au electrodes, r ) 10-6 device at T ) 250 K).

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Figure 3. (A) Analysis of crossover from direct (Simmons) to FN tunneling in SAM diodes (Au electrodes) with r ) 10-6 at low temperature (50 K) and high temperature (250 K). Assumed range for direct, FN tunneling, and crossover area are marked. (B) Molecular energy diagram at zero bias (A) and simplified schematic presentation (B) of transition from direct to FN tunneling regime at elevated biases.

the same data presentation for analysis of temperature-dependent crossover between these two tunneling regimes to study temperature-dependent crossover in the Me-PET/PT 10-6 device with Au electrodes. The systematic study of the temperature dependence of the current-voltage data was recognized to be a necessary step to unambiguously assign a charge transport mechanism.4 To extract meaningful information from the lowvoltage to the high-voltage regime, Beebe et al.4 suggested that (1) a transition from direct tunneling to field emission will only be seen for the case of a small barrier height and width, such as found in metal-molecule-metal junctions and (2) experimental examination of the transition from direct tunneling to field emission requires recasting eq 2 in terms of the variables ln(I/ V2) and 1/V so it can be directly compared to eq 4. It results in the following equation for direct tunneling in the low bias regime:

2d√2meΦBSim J J ) ln + ln(G0) V 3pe V2

( ) ()

ln

(5)

From eq 5, a plot of ln(I/V2) against 1/V will exhibit a logarithmic growth in the low-bias regime. Indeed, when the applied bias is near the barrier height, the two mechanisms compete, causing a transition from logarithmic growth to linear decay following the logic of eq 4. This transition corresponds to the voltage required to change the shape of the barrier from trapezoidal to triangular, and therefore one can define the transition point between these two regimes. Figure 3A shows the I-V response for a Me-PET 10-6 device at T ) 50 and 250 K plotted in the scale specified by eq 4.

Figure 3A shows a positive branch of 1/V. Figure 3B shows the simplified schematic representations of the barrier shape at various values with low and high bias as well as the crossover area. The dashed line in Figure 3A denotes the voltage, Vtrans, required for transition from direct tunneling to field emission at each temperature. It is anticipated that the current flowing through the barrier in direct tunneling state should be comparable to one flowing in field emission state, i.e., Idir ≈ IFN at this specific bias, Vtrans, as observed with inorganic tunneling devices. In the Me-PET/PT r ) 10-6 device (with Au electrodes), a crossover area spreads between 1.4 and 1.6 V at 250 K. This value is 35% higher than the RT conducting probe-atomic force microscopy (CP-AFM) measurement of phenyl-thiol.4 This is not surprising however, since Me-PET molecule’s aliphatic tail is twice as long. The current through this molecule was reported to be less than half1 the current at the same bias through a shorter BDT-thiol molecular system without methyl side groups (Me ) methyl-thiol anchoring moiety of Me-PET molecule).21 Therefore, the molecular barrier for a Me-PET molecule is expected to be larger than for a phenyl-thiol molecule and the crossover between Simmons and FN regimes may occur at higher bias. To summarize, a room temperature measurement of Me-PET/PT r ) 10-6 devices is in well agreement with previous reports of crossover in molecular junctions.4,22 Also the shape of the curve in the two bias regions matches the shape predicted by eqs 4 and 5. Therefore, our observation is indeed consistent with conclusions that direct tunneling is indeed the charge transport mechanism in such junctions.23 The transition between Simmons and FN tunneling regimes become sharper and occurs at lower bias (Vtrans ) 0.8 V) at 50 K. Below we summarize a temperature dependence, Vtrans(T) and to compare Vtrans(T) with temperature behavior of Simmons and FN molecular barriers. 3.3. Temperature Dependences of Direct (Simmons, ΦSim B ), Field-Emission (Fowler-Nordheim Model, ΦBFN) Barriers and a Transition Bias (Vtrans). Figure 4A summarizes a temperature dependence of transition point (Vtrans, is marked as a dashed lines in Figure 3A) for a positive and negative 1/V value. Averaged curved Vtrans(T) is used to compare this value with a values of temperature depended FN and Simmons barriers in Figure 4B. Figure 4B shows the temperature dependence of values of Simmons, FN barriers, and Vtrans. Values of ΦB are given in the scale of ΦB/e to have the same dimensionality with Vtrans. As it was expected, the Simmons model (ΦBSim) is temperature independent below 150 K. ΦBSim increases by 5% from 1.19 to 1.26 eV as the temperature increases from 200 to 294 K. The increase of ΦBSim values at high temperature is consistent with a McConnell’s superexchange mechanism, which was introduced in single molecular transport by Selzer et al.24 Similar arguments were apllied to explain the vibronic contribution into conduction through asymmetric molecular junctions.25 In contrast to a Simmons process, FN barrier (ΦBFN) changes much faster with temperature. ΦFN B (negative) decreases by 28% from 2.72 eV at 15 K to 2.31 eV at 294 K. ΦBFN (positive) decreases by 26% from 1.66 eV at 15 K to 1.55 eV at 294 K. The essential temperature dependence of ΦBFN can be explained by FN model formalism itself. As a consequence of FN modeling, the tunneling in an organic diodes includes (1) tunneling into molecular orbital (MO) followed by (2) transport through MO. Transport through MOs, which is often referred to as “hopping”, is temperature activated (Figure 4C). Therefore it is not surprising that the temperature dependence ΦBFN(T) is stronger than ΦBSim(T). Decreasing of ΦBFN with a temperature

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J. Phys. Chem. C, Vol. 113, No. 51, 2009 21417 explain why mobility in MO is bias dependent.28 The weak temperature dependence of ΦBSim supports our assumption that tunneling models should describe a molecular transport mechanism, at least partially. The most intriguing feature depictured in Figure 4B is temperature dependence of the crossover point (Vtrans). First Vtrans increases very sharply with temperature from 0.7 V for 15 K to 2.43 V at 294 K. This growth can be potentially explained by McConnell’s superexchange mechanism,24 but not the position of Vtrans(T) points in respect to ΦBFN(T) and ΦBSim(T) curves. Indeed, if a transition point is located between the two tunneling Sim regimes, Vtrans(T) should settle between the ΦFN B (T)/e and ΦB (T)/ Sim e curves in the whole temperature range. The condition ΦB (T)/ e < Vtrans(T) < ΦBFN(T)/e is observed only at 200-294 K. An unexpected behavior in tunneling crossover analysis of the electrical resistance of long conjugated molecular wires was noted by Frisbie group.5 They considered alternative transport mechanisms in the metal/organic/metal junction, such as Schottky emission, Poole-Frenkel emission, and space-charge-limited transport in the presence of traps to explain observed anomalies.5 However, no reasonable explanation has been reported, and therefore, the question of abnormal behavior of molecular resistance in the crossover regime remains open. The following discussion section is focused entirely on this unique feature.

Figure 4. (A) Temperature dependence of transition point (Vtrans, dashed lines in Figure 3A) for positive and negative 1/V values. Figure 3A shows the positive branch of 1/V. Averaged curved Vtrans(T) is used to compare this term with a temperature dependent FN and Simmons barriers in panel B. (B) Analysis of temperature dependence of direct (Simmons) and FN (positive) and FN (negative) tunneling barriers for SAM diodes (Au electrodes) with the same structure (r ) 10-6 device). Temperature dependence of transition point Vtrans is shown on the same plot. Note abnormal behavior of Vtrans(T) in comparison with ΦBSim(T) and ΦBFN(T) at low temperature (15-150 K). (C) Molecular energy diagram of Simmons and FN tunneling. FN tunneling (I) includes the step of charge hopping via molecular orbital, which is temperature dependent, whereas (II) direct tunneling (Simmons model) does not involve a transport via molecular orbital. Therefore, FN tunneling is more affected by temperature than direct tunneling.

rise is likely due to fact that charge transfer through MOs is facilitated by temperature.26 The hopping model, the multiple trapping model, and the variable range hopping model27 help

4. Discussion 4.1. Shape of Molecular Barrier. For many years, theorists of molecular transport have tried to find the adequate models to account for the shape of molecular barriers. A Joachim proposal to use the analytic nonparabolic expression for description of molecular barriers29 and Galperin-Nitzan-Ratner suggestion to account for many-body interactions during electron tunneling through molecular barriers30 are examples of such attempts. A recent Vilan’s review2 summarizes the contemporary experimentalist’s approach to presentation of the molecular barrier and the role of the barrier shape factor. We will discuss the “barrier shape” factor on a phenomenological level first and then consider a relevant transport mechanism that could change effectively the shape of molecular barrier. Proposed diagrams of molecular barrier in the vicinity of zero (a), elevated (b), and high (c) biases are shown in Figure 5. Panel A of Figure 5 demonstrates a molecular barrier. The shape of this barrier is defined by placing an S shape at the top of parabolic barrier. This modification explains why the Vtrans could be smaller than the ΦBSim barrier. Indeed, panel B of Figure 5 clarifies that at elevated bias the tunneling will include both direct and FN tunneling. Panel C of Figure 5 corresponds to the case when FN eventually will define the behavior of the system regardless shape-of-the barrier factor. Note that for the operational range of molecular barrier, which is highlighted in Figure 5, panel B, the average Simmons barrier will depend on the applied bias. Averaging of the molecular barriers defines the effective sinking of Vtrans in respect to ΦBSim. The shape of molecular barrier may be alternated by temperature, time and electronic environment. Numerical modeling of molecular transport can account for the changing barrier shape factor throughout assigned position of MOs.31 However the identification of real shape of molecular barrier is still an experimental challenge.32 4.2. Introduction of Injection Barrier to Transport Mechanism. The transport processes, which are different from Simmons and FN tunneling, through molecular barrier (and a transition between these processes), could interfere with the study of direct/FN tunneling transition in molecular nanodevices.

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Figure 5. Proposed molecular energy diagram at zero (A), elevated (B), and high (C) biases, which slightly deviates from simplified presentation at Figure 3B. While Simmons and FN models provide the averaged characteristics of molecular barriers, a crossover point Vtrans is strongly depends on real shape of the molecular barrier.

This consideration is certainly similar to the FN processes in the inorganic devices,33-36 such as ultrathin Si02 films.37,38 The nature of tunneling through Si-Si02 interface is different from one in organic devices. However the similarity in crossover behavior between organic and inorganic tunneling devices point to the possible contribution from the interface, specifically the organic-electrode interface in the transport mechanism seen in molecular diodes. 4.3. Introduction of Injection Barrier. Control Experiment: Vtrans(T) Dependence in Me-PET/PT r ) 10-6 Device with Al Electrodes. To elucidate the interface factor we have fabricated a molecular device, which has the same structure described above for the Me-PET/PT r ) 10-6 device, but using Al electrodes. It is known that EFAl is shifted up to about 1 eV with respect to EFAu.39 Therefore, EF of Al (work function of ∼4.2 eV) should be much closer to LUMO than EF of Au (∼5.4 eV),40 resulting in transport of electrons through LUMO barrier for Al electrodes. It is opposite to hole transport through HOMO-EF barrier in the case of Au electrodes. Note that the EF-MO offset model was developed for LUMO-mediated electron tunneling at low biases, and HOMO at high biases, but the model also applies for HOMO-mediated hole tunneling at low biases and LUMO at high biases. What is important in this experiment is that the ΦBSim for devices with Al electrodes, ΦBSim (Al), should be much higher than ΦBSim for device with Au electrodes, ΦBSim (Au). Therefore, the conditions for FN tunneling were not achieved while measuring IV’s for Me-PET/ PT r ) 10-6 device with Al electrodes in the bias range of (2 V (a range of (6 V was used to achieve FN condition for the Me-PET/PT r ) 10-6 device with Au electrodes). Indeed the apparent ΦBSim (Al) is three times larger than ΦBSim (Au), and a ΦFN B (Al) could not be achieved in a bias range of (2 V. Figure

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Figure 6. (A) Analysis of electrical transport properties in SAM diodes (Al electrodes) with r ) 10-6 with the Simmons model fit (solid lines) over experimental data (symbols) at low temperature (50 K) and high temperature (250 K). Fitting results for the tunneling barrier ΦBSim ) 3.2 eV. R and G0 in the temperature range 15-294 K are summarized in the SI. (B) Analysis of “crossover” from direct (Simmons) to FN tunneling in SAM diodes (Al electrodes) with r ) 10-6 at low temperature (50 K) and high temperature (250 K). Note the absence of crossover at high temperature (Vtrans disappears at 150 K). Observed Vtrans does not describe the direct/FN transition for molecular barrier and is attributed to injection barrier in molecular nanodevices.

6A shows analysis of electrical transport properties in SAM diodes with Al electrodes with the Simmons model fit (solid lines) over experimental data (symbols) at low temperature (50 K) and high temperature (250 K). Values ΦBSim were 3.0 and 3.05 eV for 50 and 250 K, respectively, using eq 1. The study of the Me-PET/PT r ) 10-6 device with Al electrodes should serve as a control experiment, which should confirm the role of the injection barrier in transport mechanism in Me-PET/PT r ) 10-6 device with a Au electrodes at low biases. The crossover analysis for Me-PET/PT r ) 10-6 devices with Al electrodes is shown in Figure 6B at low temperature (50 K) and high temperature (250 K). The “crossover” point is absent indeed at high temperature, as one would expect. However the Vtrans crossover point exist for T ) 50 K. In experimental data this pseudo-Vtrans point is present in the range 15-100 K but disappears at 150 K and does not exist at any higher temperature. Therefore the Vtrans point apparently is not related to the FN/ direct tunneling crossover through the molecular barrier in the range of 15-100 K. This crossover could be related to temperature activated charge injection barrier, which will be discussed below. The junctions with Al electrodes were not robust in our experiments, so we were restraining from applying a very high voltage. Additional experiments are required to find an optimal condition of SAM on Al electrodes and device fabrication.

Tunneling Single Molecular Devices 4.4. On the Nature of the Temperature Dependent Injection Barrier. Apparent abnormal behavior of the Vtrans(T) curve FN with respect to the ΦSim B (T) and ΦB (T) curves at low temperature (Figure 4B) of Me-PET/PT r ) 10-6 device with Au electrodes, was also observed in Me-PET/PT r ) 10-6 device with Al electrodes (in this device Vtrans point disappearss at high temperature). This raises the question of the physical nature of this phenomenon. While this question remains open for a rigorous and unambiguous elucidation, a possible explanation includes the existence of an “injection barrier” in these devices. This barrier is formed between the hybridized C-S-Au (carbon-sulfur-gold) bond between the metal electrode and the molecule (low energy MO) itself. We proposed that this injection barrier is suppressed at elevated temperatures. If we will assume that temperature activated molecular vibrations result in charge delocalization on the adjacent molecules due to the proximity effect, then we can explain our observations. The nature of this phenomenon concerns the strong phononelectron coupling in organic systems that have weak charge delocalization. Briefly the temperature activates a vibration interaction in the PT spacer matrix which, in turn, activates the weak charge delocalization in PT molecule and, as a result, enables the formation of “states in the gap”.9 These states form in-plane charge delivery channels in a Me-PET molecule. The temperature activated charge delivery mechanism will bypass the injection barrier. This phenomenon was partly explored while we were studying transport in 2D molecular aggregates.9 The complete transport model, which includes thermally activated molecular vibrations and molecular proximity at high temperature, the resulting charge delocalization, and coupling between in-plane and out-of-plane conductive channels in our devices, still has to be developed in the context of interplay between charge localization and delocalization phenomena. Future experimental and theoretical efforts are required to obtain an unambiguous model. We plan to elucidate the nature of this injection barrier within vibration-induced charge delocalization processes in future publications. In this paper our discussion is restricted to a possible explanation of anomalous behavior of Vtrans(T) with respect to ΦBSim(T) and ΦBFN(T) and we do not rule out other transport mechanisms, which may explain the Vtrans(T) anomaly. 4.5. “Barrier-Transition Regime” (BTR) between Molecular and Organic/Metal Injection Barriers. We could explain the anomaly of Vtrans(T) using the suggested above model of temperature suppressed injection barrier, although more systematic study is necessary to assign unambiguously a transport FN mechanism. Figure 4B represents Vtrans(T), ΦSim B (T), and ΦB (T) changes of the line slopes at the range T ) 170-220 K. This observation can be connected to transition from a injectioncontrol-barrier regime at low temperature to a molecular-barriercontrol regime at high temperature. We call this transition a “barrier-transition regime” (BTR) for future discussion. At low temperatures, the transport in the system is injection controlled (below point A, Figure 4B). ΦFN B (T) line is the first that undergo transition to molecular controlled regime at T ≈ 170 K, both for a negative and positive branch (points A and A′, Figure 4B). It is not surprising since the applied field facilitate not only FN tunneling, but also field emission tunneling over the injection barrier. Therefore the transition to tunneling through molecular barrier regime occurs at lower temperature. ΦSim B (T) dependence switch the transport-control regime from injection to molecular barrier (point C, Figure 4B) at ∼220 K, which is 50 K higher than for a ΦBFN(T) dependence (points A and A′, Figure 4B). In the case of direct tunneling (Simmons model), the applied bias

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Figure 7. Shape of the molecular and injection barriers and averaged barrier shape correspondent to the changes in slope of the lines in Figure 4B. Injection barrier regime (IBR) is correlated to an injection barrier controlled regime; the limit of IBR area corresponds to the situation when both barriers are transferred in the FN regime; Vtrans is correlated to the middle of the BTR area in Figure 4B; the high temperature limit of this regime (Figure 4B) is correlated to the situation when the injection barrier is low enough (due to the temperature activation) to enable a direct tunneling regime in the molecular barrier; the MBR is correlated to a regime controlled by molecular barrier. The width of the injection barrier might also decrease with temperature. The gray contour line demonstrates an averaged device barrier shape for each point. This scheme illustrates that a “barrier shape” and “barrier transfer regime” phenomena are practically equivalent.

is negligible. Therefore the injection barrier could be overcome only by temperature-activated suppressing of injection barrier. In this representation, the Vtrans(TBTR) point (point B, Figure 4B) is located approximately in the middle of temperature scale between the BTR temperatures of ΦBFN(TBTR) and ΦBSim(TBTR). Therefore the point in which Vtrans(T) change the slope is in the middle of a BTR zone. Different from the original assumption4,5 that at V ) Vtrans the direct current should be comparable with field emission current (Idir ≈ IFN), which is visualized in Figure 3B, we would rather formulate that the Vtrans point characterizes any transition in the transport mechanism in molecular wires. In our study the Frisbie assumption4,5 was valid only at high temperatures in the molecular-barrier regime (MBR) [ΦB(molecular) . ΦB(injection)]. In the injection barrier regime (IBR) [ΦB(molecular) , ΦB(injection), low temperatures], the Vtrans point also characterizes the transition between field-activated and direct tunneling regimes but only for injection barrier. Position of Vtrans in the BTR, [ΦB(molecular) ≈ ΦB(injection)] characterizes a situation when the current flowing through injection barrier is equal to the current flowing through molecular barrier: IIBR ≈ IMBR. In the other words, in the BTR regime the position of Vtrans follows the changes in the shape of extended molecular barrier (chapter 4.1, Figure 5b). 4.6. Interconnection between the Shape of Molecular Barrier and BTR. The joint model, which is shown at Figure 7, clarifies the simplified relationship between the shape of the molecular barrier and BTR. Note that the shape of the device barrier (not a molecular barrier itself) changes accordingly to transformations, which occurs with injection and the molecular barrier as the temperature increases. It is the temperature dependence of the injection barrier which defines the shape of the extended molecular barrier and the BTR phenomenon. Although the IBR term is an approximation of the complex temperature-activated phenomena, it is convenient to use for analysis of molecular transport. The injection barrier could be included in the generalized (or extended) molecular barrier. This presentation clarifies the complex form of the extended molec-

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ular barrier (considering a two-parabolic approximation) and introduces temperature dependence into the extended molecular barrier. In the content of this discussion, the low temperature anomalous behavior of Vtrans(T) is explained by interface phenomena in molecular nanojunction. We will not attempt here to provide any rigorous proof of this statement, which awaits future experimental and theoretical work. 5. Conclusions This paper reports analysis of generic approaches to model transport mechanisms in molecular nanostructures. In particular, the advantage of being able to (1) study temperature dependence in fabricated SAM diodes and (2) to characterize SAM devices with different electrodes, was exploited in testing the present experimental and theoretical framework for molecular tunneling. We report here the observation of a temperature dependent transition from direct (Simmons) and field emission (FN) tunneling. We demonstrated that certain problems encountered in the investigation of crossover from direct (Simmons) and field emission (FN) tunneling models might be eliminated by studying the characteristics of SAM devices with the same structure, but with the electrodes having different workfunctionss, specifically Au and Al. In agreement with previous studies, we find that Vtrans, measured at RT in molecular junctions, follows the transition between direct and FN tunneling through molecular barrier. However this transition point, Vtrans, characterizes the transition between injection and molecular barrier at cryogenic temperatures. We found that a Me-PET/PT r ) 10-6 device operates in injection barrier controlled regime at 15-100 K and in molecular barrier controlled regime at 170-220 K with Vtrans ≈ 180 K in BTR regime. Therefore a Vtrans point in general has a more complex meaning, than was assigned during a room temperature studies.4,5 Nevertheless ours study support measurements of FN/Simmons crossover at room temperature.4,5 Our observation supports the strong contribution of an “electron environmental effect” in the single molecular transport.41 We demonstrated that molecular tunneling could be separated from temperature dependent parallel and serial transport processes. Moreover, despite the fact that tunneling should be temperature independent, the characteristics of pure molecular barriers (in devices with structures similar to those considered in our report) should be compared at high temperatures due to the fact that the injection barrier becomes more transparent at higher temperature. We would however restrain from generalizing results of our experimental observations to all type of molecular nanostructures. Acknowledgment. The authors benefited from useful discussions with V. Vardeny, M. Raikh, A. Rogachev, L. Woichek, and J. Wright. We thank Prof. A. Bezriadyn for the use of his instrumentation. Special thanks to S. Hable for the help with final redaction of the text. Finally, we thank anonymous reviewers for their constructive comments, which helped to improve this manuscript. Supporting Information Available: Details on 2-[4-(2mercaptoethyl)phenyl]ethanethiol (Me-PET) synthesis; surface chemistry and fabrication protocol; fitting strategy and definition of tunneling parameters; device failure rate; temperature dependence of tunneling; contribution of the injection barrier in crossover mechanism in SiO2/Si tunneling device and its analogy to single molecular tunneling; consideration of the difference

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