RESEARCH ARTICLE www.advancedscience.com Bias-Polarity-Dependent Direct and Inverted Marcus Charge Transport Affecting Rectification in a Redox-Active Molecular Junction Yingmei Han, Cameron Nickle, Maria Serena Maglione, Senthil Kumar Karuppannan, Javier Casado-Montenegro, Dong-Chen Qi, Xiaoping Chen, Anton Tadich, Bruce Cowie, Marta Mas-Torrent, Concepció Rovira, Jérôme Cornil, Jaume Veciana,* Enrique del Barco,* and Christian A. Nijhuis* 1. Introduction This paper describes the transition from the normal to inverted Marcus region in solid-state tunnel junctions consisting of self-assembled monolayers of Understanding the mechanisms of charge transport across molecules and molecule– benzotetrathiafulvalene (BTTF), and how this transition determines the electrode interfaces is important in count- performance of a molecular diode. Temperature-dependent normalized less areas of research,[1] and in particular in differential conductance analyses indicate the participation of the HOMO molecular electronics to guide the design of (highest occupied molecular orbital) at large negative bias, which follows efficient functional devices, such as, molec- typical thermally activated hopping behavior associated with the normal ular diodes,[2] molecular memory,[3] and Marcus regime. In contrast, hopping involving the HOMO dominates the optoelectronic devices.[4] Naturally, it is im- portant to control the mechanism of charge mechanism of charge transport at positive bias, yet it is nearly activationless transport between thermally activated and indicating the junction operates in the inverted Marcus region. Thus, within activationless charge transport regimes to the same junction it is possible to switch between Marcus and inverted ensure maximal performance of molecular Marcus regimes by changing the bias polarity. Consequently, the current only junctions, but such control over charge decreases with decreasing temperature at negative bias when hopping is transport regimes to improve device perfor- mance has not yet been demonstrated. The “frozen out,” but not at positive bias resulting in a 30-fold increase in the mechanisms of charge transport/transfer molecular rectification efficiency. These results indicate that the charge across molecules are often described us- transport in the inverted Marcus region is readily accessible in junctions with ing either one of the two extreme cases: redox molecules in the weak coupling regime and control over different Landauer theory which describes (essen- hopping regimes can be used to improve junction performance. tially) temperature-independent coherent tunneling in solid-state junctions, or Dr. Y. Han, Dr. S. K. Karuppannan, Dr. X. Chen, Prof. C. A. Nijhuis Dr. M. S. Maglione, Dr. J. Casado-Montenegro, Dr. M. Mas-Torrent, Department of Chemistry Prof. C. Rovira, Prof. J. Veciana National University of Singapore Institut de Ciència de Materials de Barcelona (ICMAB-CSIC)/CIBER-BBN 3 Science Drive 3, Singapore 117543, Singapore Campus de la UAB E-mail: c.a.nijhuis@utwente.nl Bellaterra 08193 Spain Dr. C. Nickle, Prof. E. del Barco E-mail: vecianaj@icmab.es Department of Physics Dr. D.-C. Qi University of Central Florida Centre for Materials Science Orlando FL 32816, USA School of Chemistry and Physics E-mail: delbarco@physics.ucf.edu Queensland University of Technology Brisbane Queensland 4001, Australia Dr. A. Tadich, Dr. B. Cowie The ORCID identification number(s) for the author(s) of this article Australian Synchrotron Clayton can be found under https://doi.org/10.1002/advs.202100055 Victoria 3168 Australia © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH. Prof. J. Cornil This is an open access article under the terms of the Creative Commons Laboratory for Chemistry of Novel Materials Attribution License, which permits use, distribution and reproduction in University of Mons any medium, provided the original work is properly cited. Place du Parc 20 Mons B-7000, Belgium DOI: 10.1002/advs.202100055 Adv. Sci. 2021, 8, 2100055 2100055 (1 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Marcus theory which describes thermally activated incoherent tunneling (which is also called hopping) under wet electrochem- ical conditions.[5] There are quite a few examples of molecular junctions, however, whose charge transport characteristics can- not be straightforwardly explained with either theory, involving anomalous temperature dependencies, unusually small tunnel- ing decay coefficients, or long-range tunneling phenomena.[1e,6] Here, we report a 30-fold improvement in the performance of a molecular diode by switching from charge transport in the nor- mal Marcus to the inverted Marcus region by changing the bias polarity. As a result, the activation barrier in inverted Marcus re- gion at forward bias is eliminated, while at reverse bias thermally activated hopping can be frozen out by lowering the ambient temperature. These findings are important as they demonstrate how molecular–electronic devices can be improved by eliminat- ing leakage currents and energy barriers (i.e., activation energy) for hopping. The molecular diode is based on a self-assembled monolayer (SAM) of benzotetrathiafulvalene derivative (BTTF; Figure 1) which can be pushed into the activationless inverted Marcus re- gion for hopping in one bias polarity, but not in the other, directly affecting its diode performance in terms of the rectification ra- tio R = J(+V)/J(−V) where J = current density and V = applied voltage. This results in a complex temperature-dependent recti- fication behavior with the best diode performance at low tem- perature (T = 170 K) with R = 124 (30 times improvement over R at T = 320 K) when the leakage current at negative bias, i.e., J(−V), via hopping in the normal Marcus region is “frozen out.” In contrast, the diode remains “on” due to the activationless na- ture of hopping in the inverted Marcus region at positive bias, i.e., J(+V). Our results highlight the unique opportunity molec- ular junctions offer to study charge transport in the, otherwise difficult to access, inverted Marcus region. In coherent tunneling, J decays exponentially defined by the tunneling decay coefficient 𝛽 as a function of the tunneling dis- tance d. In this regime, charge transport is essentially indepen- dent of T, and the general tunneling equation (Equation (1)) ap- plies where J0 is a pre-exponential factor J = J0 e−𝛽d (1) In the case of hopping, J depends on T, and the current through the molecule is described by the Arrhenius equation (Equation (2)) Figure 1. a) Schematic illustration of the Au-S(CH2 )11 S-BTTF//GaOx / J = J0 e−Ea ∕kB T (2) EGaIn junction where EGaIn = eutectic alloy of Ga and In, GaOx is highly conductive and 0.7 nm thick, and “//” indicates the van der Waals contact.[7] Here, the bottom gold electrode is grounded and the bias is applied to top EGaIn electrode. b) Nonadiabatic Marcus parabolas for dif- Prof. C. A. Nijhuis ferent redox reaction energies as explained in the text. Centre for Advanced 2D Materials and Graphene Research Center National University of Singapore 6 Science Drive 2 Singapore 117546, Singapore Prof. C. A. Nijhuis where Ea is the activation energy and kB is the Boltzmann con- Hybrid Materials for Opto-Electronics Group stant. In this regime, the current also depends on d but with Department of Molecules and Materials significantly smaller 𝛽 than that of coherent tunneling.[5b,8] Fig- MESA+ Institute for Nanotechnology and Center for Brain-Inspired Nano ure 1b graphically illustrates the Marcus parabolas for charge Systems Faculty of Science and Technology transfer (or hopping) for an exothermic redox process where University of Twente the black/green parabola depicts the potential energy curves of P.O. Box 217 Enschede AE 7500, The Netherlands the donor–acceptor pair consisting of neutral molecule (here Adv. Sci. 2021, 8, 2100055 2100055 (2 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com BTTF)/charged molecule (here BTTF·+ ).[6g,9] The Ea is defined by tion peak (146 mV) indicates that the SAMs are well-ordered the crossing between the two parabolas, representing the energy and densely packed.[15] With photoelectron and X-ray absorption that must be overcome to enable charge hopping, ΔE0 is the en- spectroscopy, we determined the energy of the lowest unoccupied ergy difference between neutral and charged states, and 𝜆 is the molecular orbital (ELUMO ), highest occupied molecular orbital molecular reorganization energy. The blue parabola shows a sce- (EHOMO ), and HOMO-1 (EHOMO-1 ) as described in Section S2 in nario in which the crossing point between both parabolas lies at the Supporting Information. The offset in energy between ELUMO the minimum potential eliminating Ea leading to temperature- and the Fermi level (EF ) of the electrode (𝛿ELUMO ) is 2.17 eV, and independent charge transport; this is the transition point into the the energy offsets between EHOMO and EHOMO-1 and EF (𝛿EHOMO inverted Marcus region beyond which an activation barrier is gen- and 𝛿EHOMO-1 ) are 0.44 and 2.09 eV, from which we conclude that erally re-established again, as given by red parabola and double the HOMO is energetically accessible in the applied bias window. arrow, respectively. As discussed in more detail below, in molec- ular junctions, however, due to the availability of electronic states in the electrodes, the charge transport in the inverted Marcus re- 2.2. Temperature-Dependent Rectification gion remains activationless.[6g] Although Marcus predicted the inverted Marcus region in We performed J(V,T) measurements using a top electrode of 1956,[10] it was not until 1984 the inverted Marcus region was EGaIn stabilized in a microchannel in polydimethylsiloxane experimentally proven[11] because the electron transfer rate was aligned over micropores (with an area of 3.1 × 102 µm2 ) in 10 nm much larger than the diffusion rate of the reactants in solu- thick AlOx on template-stripped Au as reported in ref. [16] (Sec- tion and, consequently, the charge transfer rate was diffusion tion S3, Supporting Information). We only selected junctions that limited.[12] By using donor–bridge–acceptor (D-b-A) compounds had their J(V) characteristics within one Gaussian log-standard in solution, the charge transfer reaction between D and A could deviation of the G versus V curve, which is reported in be pushed into the inverted Marcus region because of the dis- ref. [17], to perform the J(V,T) measurement (Section S4, Sup- tance between D and A was fixed by a rigid spacer eliminat- porting Information). Figure 2a shows a J(V) characteristic of ing the diffusion limit.[11] In contrast, in molecular tunnel junc- the Au-S(CH2 )11 S-BTTF//GaOx /EGaIn junction measured at T = tions, the charge transfer across the molecules is studied in the 170 K and that this junction rectifies at positive bias with a recti- solid state, and the molecules are connected to the electrodes: fication ratio R = 124 with R defined by Equation (3) molecular tunnel junctions are therefore not diffusion limited and should in principle be good test beds to study charge trans- R ≡ J (+1.5 V) ∕ ||J (−1.5V )|| (3) port in the inverted Marcus region. However, only recently we reported a solid-state molecular junction with a D-b-A molecule where J(−1.5 V) is defined as the leakage current[18] that that can be pushed from the normal to the inverted Marcus re- flows across the diode in the off-state. The junctions show gion via intramolecular orbital gating (which requires chemical a small, but significant, hysteresis. A similar hysteresis has modifications to the molecule to control intramolecular orbital also been observed for molecular diodes of the form of Ag- gating)[7] (since then a second example has been reported in a S(CH2 )11 Fc//GaOx /EGaIn (Fc is ferrocene).[19] This hysteresis thin organic film device based on hot-electron injection[13] and a was associated with charging of the Fc unit to Fc+ at forward third example based on a bipyridyl molecular junction where the bias and discharging of the Fc+ units back to Fc at reverse bias, authors propose that a gating effect induced by Fermi level pining probably stabilized by the GaOx layer. Therefore, we believe that could push the junction in the Marcus inverted region[14] ). Here, the small hysteresis is caused by (dis)charging of the BTTF or we demonstrate junctions with only electron donor units (which BTTF·+ units. Here, we note that despite the similar redox prop- have a much simpler structure than D-b-A units) can be pushed erties of BTTF and Fc, the direction of rectification is reversed into the inverted Marcus region via gating by the applied electric for these two types of molecular diodes. We attribute this rever- field because the BTTF in the neutral state only responds weakly, sal of the rectification to the different coupling strength between while the cationic BTTF•+ unit responds strongly, to changes in the redox units and EGaIn top electrode where the BTTF units the applied electric field. interact much weakly with the EGaIn top electrode (see figure 7 of ref. [17]) than the Fc units (see figure 8 of ref. [19]). Besides, a 2. Results and Discussion small current near 0 V was observed, which can be caused by the capacitive behavior of the junctions, or involve the GaOx layer as 2.1. Monolayer Characterization we have explained in previous work.[20] Figure 2b shows the J(V,T) curves in the temperature range of The SAMs of S(CH2 )11 S-BTTF on Au were prepared with a pre- 170–320 K. Close to room temperature (RT), at large negative ap- viously reported procedure (Section S1, Supporting Informa- plied bias a clear upturn of the current is visible which indicates tion). The cyclic voltammogram (CV) of S(CH2 )11 S-BTTF SAM that the HOMO enters the conduction window, but with decreas- on Au (Section S2, Supporting Information) shows two pairs ing T conduction through this orbital at −1.5 V decreases by a fac- of well-resolved redox peaks at Epa /Epc = +0.51 V/+0.53 V and tor of 31 (indicated by the black arrow) which is characteristic for +0.87 V/+0.89 V which corresponds to the oxidation of BTTF hopping (see below). In contrast, conduction through the HOMO unit to radical cation (BTTF•+ ) and dication (BTTF2+ ). The fact at +1.5 V positive bias depends only weakly on T. This decrease in that the full-width-at-half maximum (FWHM) of the second ox- the current is the reason why R is large at low T, but small at RT, idation peak is (76 mV) smaller than that of the first oxida- as reduction of T only lowers the leakage current—the current Adv. Sci. 2021, 8, 2100055 2100055 (3 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Figure 2. a) Representative J(V) curve of Au-S(CH2 )11 S-BTTF//GaOx /EGaIn junction recorded at T = 170 K (black line). The black arrows indicate the voltage scan direction. The red line is the fit to the single level model. b) Temperature-dependent J(V) curves from 170 to 320 K at intervals of 10 K. The black arrow indicates the increase of J with T. c) 3D surface with color map of R plotted against V and T and d) of the corresponding NDC plots using the J(V) curves shown in panel (b). The red and black arrows in panel (c) indicate how R changes with V and T, respectively. The blue and black arrows in panel (d) indicate how the HOMO peaks evolve with T at positive and negative bias, respectively. The red arrow indicates how NDC curves evolve with V at low temperature (see Figure S5 in the Supporting Information for the corresponding 2D plots). that flows at −1.5 V when the diode is in the off-state—and not the where n is the number of molecules contributing to conduc- current that flows across the diode in the on-state at +1.5 V (Equa- tion, 𝛾 L and 𝛾 R are the tunneling rates between the molecule tion (3)). Figure 2c shows the 3D color map of R(V,T) and that at and the left (the EGaIn top electrode) and right (the Au bottom RT the R(V) goes through a maximum value because first R in- electrode) electrodes (respectively), DE′ (E) is the electronic den- creases when the HOMO enters the conduction window at rela- sity of states of the molecular level (represented by a normal- tively small positive bias, but R decreases again when the HOMO ized Lorentzian function centered at energy E ′ + (𝜂 − 12 )V and enters the conduction window at relatively large negative bias (as width 𝛾 = 𝛾 L + 𝛾 R ) with its connection to the electrodes rep- indicated by the red arrow). resented by the voltage division parameter 𝜂 = VR /(VL + VR ), G𝜖 (E′) is a Gaussian function (with center 𝜖 and width 𝜎) that rep- resents the inherent dispersion of the molecular level energy in 2.3. Modeling of the Diode Behavior an ensemble of molecules (rather than a single-molecule junc- tion), and fL (E) and fR (E) are the Fermi functions representing We have modeled the current through the junction with the stan- the electronic occupation of the left and right electrodes, respec- dard Landauer theory for a single level tunnel junction using the tively (see for details ref. [5c] ). A good fitting to the data (Figure 2a) following expressions[5c] is achieved for T = 170 K and the following set of parameters: 𝜀 ≡ 𝛿EHOMO th ∕e = 0.83 V (zero-bias energy of the molecular or- q ∞ ( ) 𝛾L 𝛾R [ ] bital with respect to the Fermi energy of the electrodes, due to the I=n dEdE ′ DE′ (E ) G𝜀 E ′ fL (E ) − fR (E ) charge transfer between BTTF molecule and top EGaIn electrode, h ∫ ∫ −∞ 𝛾L + 𝛾R the HOMO level downshift by 0.4 eV compared to that measured 𝛾∕2𝜋 for SAMs[17] (Table S2, Supporting Information)), n = 150, 𝛾 L = DE′ (E ) = ( ( ) ))2 ( (4) 9.92 × 10−3 eV, 𝛾 R = 9.88 × 10−7 eV, 𝜂 = 0.37, and 𝜎 = 0.11 eV. E − E ′ + 𝜂 − 12 V + (𝛾∕2)2 As demonstrated in Figure 1a, the BTTF units are separated from ( ′ ) ( ) (E − 𝜀)2 the Au electrode by the long alkyl chains but are in van der Waals G𝜀 E ′ = exp 2𝜎 2 contact with top EGaIn electrode, resulting in 𝛾 L ≫ 𝛾 R . As can be Adv. Sci. 2021, 8, 2100055 2100055 (4 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com extracted from Equation (4), the overall tunneling rate in the junc- since the redox units are separated from the bottom electrode by 𝛾 𝛾 tion is given by Γ = 𝛾 L+𝛾R = 9.88 × 10−7 eV, denoting a molecule the alkyl chain and form a weak van der Waals contact with the L R weakly coupled to the electrodes. This analysis confirms that the top electrode where the thin GaOx layer weakens the molecule– HOMO dominates charge transport both bias polarities, but that top electrode interaction even further,[16] and BTTF units are it enters the bias window at different voltages which explains the well-known to be redox active. Remarkably, after reaching a mechanism of rectification.[21] maximum value, Ea decreases with increasing V. This behavior The complex interplay between R and tunneling involving cannot be directly explained by coherent tunneling described the HOMO level at opposite bias polarities is confirmed by nor- by Landauer–Buttiker theory or hopping described by Marcus malized differential conductance (NDC) analysis, where NDC = theory for the following reasons.[6g,7] The small Ea in coherent (dI/dV) * (V/I),[16,22] of the J(V) curves as a function of T shown tunneling originates from the Fermi-level broadening which is in Figure 2d. NDC is similar to dI/dV analysis which is widely very small (and often not observed in molecular tunnel junc- used in community to identify molecular resonances.[22,23] There- tions apart from a few exceptions[24b,24c,27] ) and decreases with fore, here the resonance peak at +0.90 V with NDC = 9 indicates increasing bias.[5c,24c] However, in this work, the observed Ea is charge transport through the HOMO (red arrow), and the large larger than 200 meV and first increases and then decreases with NDC value is characteristic for diode behavior.[22] Strikingly, this the applied voltage. Second, the activation energy for hopping NDC peak is quite insensitive to changes in T (blue arrow). At remains constant as a function of applied voltage (after an initial negative bias, no peaks are visible to about −1.15 V as expected sharp increase when the molecular orbital enters the conduction for off-resonant tunneling, but at large negative bias the NDC window). On the other hand, although Poole–Frenkel transport value increases and a peak is visible at V = −1.36 V for T > 250 K and thermionic emission also result in a voltage-dependent confirming the HOMO enters the conduction window. The NDC activation energy, they predict a linear relationship between Ea value of this HOMO peak is highly temperature sensitive and and V1/2 , which is not the case in this system.[6c] In the following decreases from 15 (at 320 K) to 4.5 (at 170 K) as indicated by the section, we will explain this behavior in more detail by using the black arrow, which implies that hopping dominates the mecha- combined model proposed by Migliore et al.[6g] which reproduces nism of charge transport at large negative bias. This “freezing the bell-shaped Ea versus V curve well. In contrast, EGaIn junc- out” of the hopping mechanism lowers the leakage currents re- tions lacking redox-active units,[16,28] the bell-shaped Ea versus sulting in an increase of R (the black arrow in Figure 2c). Such V curve is not observed, which demonstrates that this transition behavior where the temperature dependency of incoherent hop- is unique to the redox-active molecular junctions. At negative ping changes within the same junction at different bias polarities bias, Ea increases with increasing bias when the HOMO enters has not been reported before. the conduction window. Here, the downturn of Ea is not visible because the junctions are not stable at an applied bias larger than −1.5 V. Interestingly, in the temperature range of 220–130 K, a 2.4. Determination of Activation Energies small but reproducible negative Ea (−30 meV for V = 1.5 V) is observed (Figure 3a). It is well known that TTF•+ dimerizes.[29] To investigate the reason why conduction through the HOMO Schröder et al.[29c] have demonstrated that TTF•+ is the dom- at +1.5 V depends only weakly on T, we determined the values inant species at ambient temperatures, but the fraction of the of Ea as a function of positive applied bias. From the J(V) curves dimer increases with decreasing temperature. This dimerization recorded at different temperatures (as shown in Figure 2b), we could account for the observed negative Ea in our junctions as constructed the Arrhenius plots from which the Ea was extracted follows. At high temperatures, there is large fraction of BTTF•+ at temperatures above 260 K with Equation (2) for each applied monomers and charge transport predominantly proceeds via voltage (Figure 3). Figure 3c shows that the Ea plotted against V these monomers. With increasingly low temperatures, more and goes through a maximum at +0.87 V, which is very similar to the more dimers form through which then charge transport occurs. resonance peak observed in the NDC plots at +0.90 V. Therefore, We have shown before that for viologen dimers (whose radical we explain this bell-shaped Ea versus V curve as follows. As soon form also forms dimers) the charge transport rates are about 100 as the HOMO enters the bias window, the mechanism of charge times larger than for the monomers.[3a] Therefore, the current transport changes from (activationless) coherent off-resonant across the junctions may increase with decreasing temperature tunneling to (temperature dependent) incoherent tunneling (as because of dimer formation across which tunneling is more evident from the NDC analysis) resulting in an increase of Ea .[24] efficient than across the monomers, resulting in an apparent Due to the broadening of HOMO level, this transition of the negative Ea . Alternatively, a temperature-dependent change in system from the point when the HOMO starts to enter the con- the molecule–electrode coupling could possibly account for the duction window to the point when the HOMO has fully entered negative Ea .[30] the conduction window needs to go through a certain voltage range, resulting in the increase of Ea with applied bias until a maximum value of Ea = 224 meV at 0.87 V is reached. In princi- 2.5. Charge Transport in the Inverted Marcus Region ple, when the HOMO is close to the Fermi level of the electrode, coherent on-resonant tunneling can occur provided that the To explain the data in Figure 3c, we have used the model devel- molecule interacts strongly with the electrodes, i.e., strong cou- oped by Migliore et al.[6g] to fit our data (Section S5, Supporting pling regime,[25] or have unfavorable 𝜆 (and are, consequently, Information) and Figure 4 summarizes the mechanism of charge not redox active),[26] which is not the case in our EGaIn junction transport explaining the observed Ea (V) curve. In this model, the Adv. Sci. 2021, 8, 2100055 2100055 (5 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Figure 3. Arrhenius plots a) from 0.21 to 1.5 V with 60 mV intervals and b) from −0.21 to −1.5 V with −60 mV interval for the data set in Figure 2b (note due to capacitive background currents and noise at low bias, the data points from 0 to 0.21 V and 0 to −0.21 V were omitted from the modeling). The solid and dashed lines are fits to Equation (2) (see Figure S5 in the Supporting Information for the full dataset). Here, we note that some data points at high temperatures and at large applied bias suffer from noise likely because these conditions approach the breakdown voltage of our devices.[31] c) Ea versus V at positive bias. The solid red line is a fit using the Marcus rates given in Equations (5a) and (5b). As explained in the main text, the increase in Ea originates from the HOMO entering the bias window, which indicates that the junction is not in the Marcus hopping regime until the maximum Ea was reached. Therefore, only half of the bell-shaped curve was used (solid red line) to fit our data. d) Ea versus V at negative bias. e) Activation energy as a function of gate voltage according to Migliore’s model using Marcus charge transfer rates in the hopping regime. We used the red solid line to fit the experimental data in panel (c). f) Charge distribution used for the fitting in panel (c). rates of the charge transfer from the neutral BTTF and charged here Γ(E) is the golden rule rate for electron transfer between the BTTF·+ states are given by Equations (5a) and (5b) single electron level on the molecule and single electron states of energy 𝜖 on the metal, f(E) is the Fermi distribution of the 1 − (ΔE+E−𝜆)2 electron occupation in the electrodes which accounts for a weak KBTTF→BTTF⋅+ = √ dEΓ (E )e 4𝜆kB T f (E ) (5a) 4𝜋𝜆kB T ∫ temperature dependence via Fermi level broadening, ΔE = ΔE0 + 𝜇, where ΔE0 = 𝛿EBTTFth ⋅+ − 𝛿EBTTF is the energy difference be- th 1 − (ΔE+E−𝜆)2 [ ] tween the two molecular charge states (BTTF and BTTF·+ in our KBTTF⋅+ →BTTF = √ dEΓ (E )e 4𝜆kB T 1 − f (E ) (5b) 4𝜋𝜆kB T ∫ case) at zero bias and 𝜇 is the electrochemical potential of the Adv. Sci. 2021, 8, 2100055 2100055 (6 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Figure 4. a–d) Marcus parabolas of the BTTF→BTTF·+ redox reaction inside the junction for different applied bias to the left electrode. The black arrows indicate charge transport between the electrodes and the BTTF unit. The red arrows indicate the transition between BTTF and BTTF·+ . e–h) The corresponding redox reaction depicted on a reaction coordinate (rc) with respect to 𝜇. i–l) The Ea versus Vg where the red dots correspond to the Ea in different charge transport regimes as sketched in panels (a)–(d). electrodes. According to the model by Migliori et al.,[6g] a gating ing effect of BTTF·+ ). To be more specific, the change in Ea is electric potential changing the relative energy difference (ΔE(Vg )) induced by shifting the Marcus parabolas with respect to each between the two charge states (i.e., affecting one orbital differ- other because the different charge states of BTTF molecule inter- ently than the other and shifting the energy of the correspond- act differently with the applied electric field: BTTF·+ interacts very ing Marcus parabolas with respect to each other), would lead strongly with the applied field (because of its charge) in contrast to a gate-dependent activation energy that can be calculated as to neutral BTTF which can only interact weakly with the applied Ea /kB T = T∂ln(RMarcus )/∂T (where RMarcus is the sum of the two field. Likely, intermolecular interactions (e.g., 𝜋–𝜋 interactions, Marcus rates in Equations (5a) and (5b)). This Ea versus Vg de- dimer formation, or polarization effect via induced dipoles) be- pendence is shown in Figure 3e. As discussed above, we used tween neighboring BTTF•+ units likely also help to stabilize the half of the bell shape (red solid line) to calculate the parameters charge on the molecules.[3a,32] used below to fit the experimental data in Figure 3a, where the The activation energy expected from this model only applies gate voltage is taken proportional to the charge in the molecule: when the transport through the molecule is through hopping, Vg = Q(V)∕CC∗ , with Q increasing with bias and where CC∗ is a which only occurs for sufficiently large bias. At low applied bias fitting parameter that represents the capacitive coupling strength (Figure 4a), the HOMO is not energetically accessible because 𝜇 between the molecule and the electrode (responsible for the gat- lies above the energy of BTTF and BTTF·+ states in equilibrium Adv. Sci. 2021, 8, 2100055 2100055 (7 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com with the environment. Figure 4e shows the transition from BTTF 3. Conclusions and BTTF·+ on the reaction coordinate (rc) which is represented by the dashed green line (not to be confused with distance). In summary, our results show that complex temperature- The bottom row shows the evolution of Ea as a function of the dependent behavior—involving bias polarity-dependent Marcus “gate voltage,” Vg , which increases with bias and changes E0 and inverted Marcus regions—can be readily observed in molec- (as defined in Figure 1). In this situation, the mechanism of ular tunneling junctions because molecular junctions are not charge transport across the junction is temperature independent diffusion limited. Thus, the Inverted Marcus region is not only off-resonant coherent tunneling. As discussed above, Ea in- limited to D-b-A molecules where the energy of the HOMO can creases with increasing bias when the HOMO starts to enter the be shifted with respect to the LUMO via intramolecular orbital conduction window. Ea reaches a maximum value when HOMO gating[7] and can be accessed in other types of redox molecules fully enters the conduction window (Figure 4j). Now the redox only consisting of donor units as we show here. To obtain large reaction BTTF→BTTF·+ becomes important and the mechanism enough “gating” voltages resulting in the changes in ΔE0 needed of charge transport changes to thermally activated incoherent to push the system into the inverted Marcus region, charges have hopping (Figure 4b). Thus, from this point onward, the junction to relax on the molecule and, consequently, junctions in the weak enters the normal Marcus region when 𝜇 lies between BTTF and coupling regime with redox-active molecules are good candidates BTTF·+ on the reaction coordinate (Figure 4f) and Ea decreases to observe this kind of complex temperature-dependent behav- with increasing bias. With increasing applied V, the BTTF·+ ior. As mentioned above, the low value of Γ = 9.88 × 10−7 eV state is stabilized by the increasing electric field and therefore indicates that our junctions operate in the weak coupling limit. lowered in energy with respect to the parabola of the neutral The coupling between the BTTF and EGaIn top electrode is state (which is essentially nonresponsive to the changes in the weak (compared to junctions in the strong coupling regime with electric field because it is charge neutral). This “gating” effect of chemisorbed species) because of the physisorbed nature of this BTTF·+ increases E0 until one of the parabolas intersect the min- contact and the presence of the 0.7–1.0 nm thick GaOx layer imum of the other (Figure 4c,g,k) at which point Ea decreases and the –(CH2 )11 – alkyl chain decouples the BTTF units from to 0 eV. Beyond this point, increasing V would further force the bottom electrode. This explains why Marcus inverted region the junction into the inverted Marcus region (Figure 4d) and has so far been only rarely observed in solid-state junctions be- Ea should increase again (as indicated by the red arrows in Fig- cause usually molecular junctions operate in the strong coupling ure 1b). However, this does not happen in metal-molecule-metal regime (especially for single-molecule junctions) and intramolec- junctions because the continuous availability of electronic states ular orbital gating voltage was not high enough. Our results sug- below the Fermi energy of the electrodes would pin the system gest that the inverted Marcus region may be readily accessible to the minimum of the BTTF Marcus parabola (Figure 4h,i), in other junction platforms and provide guidelines for future resulting in activationless charge transport for any larger bias. experiments to explore and investigate complex temperature- Figure 3f shows the Q(V) functional that was used as a result dependent charge transport phenomena in general. We also note of the electronic current through the junction, where its inflec- that although the inverted Marcus region is reached in both BTTF tion point (𝜀Q ≡ 𝛿EHOMO th ∕e) and width (𝜎 Q ) of the charging curve and bipyridyl[14] based molecular junctions, the dependence of are also fitting parameters constrained by the experimental J(V) the rectification behavior on the temperature is different: for curves (𝜀Q ∼ 𝜀 ≡ 𝛿EHOMOth ∕e and 𝜎Q ∼ 𝜎). The model fits well to BTTF-based molecular junctions, the rectification ratio increases the data resulting in 𝜆 = 1.20 eV, ΔE0 = 0.75 eV, 𝜖 Q = 0.83 V( = (by a factor of 30) with decreasing temperature, while in the 𝜖), 𝜎Q = 0.25 eV(∼ 𝜎), and CC∗ = 1.31 × 10−19 F, accounting for bipyridyl-based molecular junctions, the rectification ratio does the decrease in activation energy and proving that the junction not depend on the temperature. It also would be very interesting at large positive bias moves toward the inverted Marcus regime. to extend our studies to single-molecule transistors where it is in This model implies that the energy of the charged BTTF·+ state principle possible to study the mechanisms of charge transport is highly stabilized by the applied bias resulting in large shifts as function of the oxidation state of the BTTF unit. (i.e., the maximum gate potential obtained when the orbital is fully charged, Q (V = 1.5 V) = e is Vgmax = e∕CC∗ = 1.18 V) with respect to the energy of the neutral state (i.e., ΔE0 ), which is Supporting Information conceivable given the large electric fields on the order of GV/m Supporting Information is available from the Wiley Online Library or from typically encountered in molecular junctions. Although a clear the author. maximum in the Ea versus V plot followed by a decrease in Ea are observed in all junctions (Figure 3c and Figure S8, Supporting Information), we note that a small Ea is observable at very small Acknowledgements applied bias and also at large positive bias. This “background” Ea cannot be caused by hopping involving molecular orbitals since Y.H., C.N., M.S.M., and S.K.K. contributed equally to this work. The au- none fall in the bias window at low bias, but it may involve con- thors acknowledge the Ministry of Education (MOE) for supporting this re- search under award no. MOE2019-T2-1-137. Prime Minister’s Office, Sin- formational changes[29a,29b] or thermal broadening of the Fermi gapore under its Medium sized centre program is also acknowledged for level of the electrode.[5c] At large positive bias, dimer formation supporting this research. The authors also gratefully acknowledge the Aus- (it is well-known that TTF radical cations can dimerize[33] with tralian Synchrotron (ANSTO) soft X-ray spectroscopy beamline where the an activation energy of several hundred meV[34] ) could explain SAM characterization was conducted. C.N. and E.d.B. acknowledge sup- the observed Ea . port from the US National Science Foundation (grant no. ECCS#1916874). Adv. Sci. 2021, 8, 2100055 2100055 (8 of 10) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com D.Q. acknowledges the support of the Australian Research Council (Grant [5] a) J. C. Cuevas, E. Scheer, Molecular Electronics: An Introduction to The- No. FT160100207). Authors also acknowledge the Marie-Sklodowska- ory and Experiment, World Scientific Publishing, Singapore 2010; b) C. Curie project ITN iSwitch (GA-642196), Spanish Ministry of Economy and Joachim, M. A. Ratner, Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 8801; Competitiveness (project FANCY CTQ2016-80030-R, GENESIS PID2019- c) A. R. Garrigues, L. Yuan, L. Wang, E. R. Mucciolo, D. Thompon, E. 111682RB-I00 and Severo Ochoa programme for Centers of excellence in del Barco, C. A. Nijhuis, Sci. Rep. 2016, 6, 26517. R&D (SEV-2015-0496)). J.C. is a research director of the Belgian National [6] a) D. N. Beratan, Annu. Rev. Phys. Chem. 2019, 70, 71; b) C. D. Bostick, Fund for Scientific Research (FNRS). S. Mukhopadhyay, I. Pecht, M. 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