Temperature dependent charge transport across tunnel junctions of single-molecules and self-assembled monolayers: a comparative study

CP-AFM Molecular Tunnel Junctions with Alkyl Backbones Anchored Using Alkynyl and Thiol Groups: Microscopically Different Despite Phenomenological Similarity

In this paper, we report results on the electronic structure and transport properties of molecular junctions fabricated via conducting probe atomic force microscopy (CP-AFM) using self-assembled monolayers (SAMs) of n-alkyl chains anchored with acetylene groups (CnA; n = 8, 9, 10, and 12) on Ag, Au, and Pt electrodes. We found that the current-voltage (I-V) characteristics of CnA CP-AFM junctions can be very accurately reproduced by the same off-resonant single-level model (orSLM) successfully utilized previously for many other junctions. We demonstrate that important insight into the energy-level alignment can be gained from experimental data of transport (processed via the orSLM) and ultraviolet photoelectron spectroscopy combined with ab initio quantum chemical information based on the many-body outer valence Green's function method. Measured conductance GAg < GAu < GPt is found to follow the same ordering as the metal work function ΦAu < ΦAu < ΦPt, a fact that points toward a transport mediated by an occupied molecular orbital (MO). Still, careful data analysis surprisingly revealed that transport is not dominated by the ubiquitous HOMO but rather by the HOMO-1. This is an important difference from other molecular tunnel junctions with p-type HOMO-mediated conduction investigated in the past, including the alkyl thiols (CnT) to which we refer in view of some similarities. Furthermore, unlike in CnT and other junctions anchored with thiol groups investigated in the past, the AFM tip causes in CnA an additional MO shift, whose independence of size (n) rules out significant image charge effects. Along with the prevalence of the HOMO-1 over the HOMO, the impact of the "second" (tip) electrode on the energy level alignment is another important finding that makes the CnA and CnT junctions different. What ultimately makes CnA unique at the microscopic level is a salient difference never reported previously, namely, that CnA's alkyne functional group gives rise to two energetically close (HOMO and HOMO-1) orbitals. This distinguishes the present CnA from the CnT, whose HOMO stemming from its thiol group is well separated energetically from the other MOs.

Can tunneling current in molecular junctions be so strongly temperature dependent to challenge a hopping mechanism? Analytical formulas answer this question and provide important insight into large area junctions

Analytical equations like Richardson-Dushman's or Shockley's provided a general, if simplified conceptual background, which was widely accepted in conventional electronics and made a fundamental contribution to advances in the field. In the attempt to develop a (highly desirable, but so far missing) counterpart for molecular electronics, in this work, we deduce a general analytical formula for the tunneling current through molecular junctions mediated by a single level that is valid for any bias voltage and temperature. Starting from this expression, which is exact and obviates cumbersome numerical integration, in the low and high temperature limits we also provide analytical formulas expressing the current in terms of elementary functions. They are accurate for broad model parameter ranges relevant for real molecular junctions. Within this theoretical framework we show that: (i) by varying the temperature, the tunneling current can vary by several orders of magnitude, thus debunking the myth that a strong temperature dependence of the current is evidence for a hopping mechanism, (ii) real molecular junctions can undergo a gradual (Sommerfeld-Arrhenius) transition from a weakly temperature dependent to a strongly ("exponential") temperature dependent current that can be tuned by the applied bias, and (iii) important insight into large area molecular junctions with eutectic gallium indium alloy (EGaIn) top electrodes can be gained. E.g., merely based on transport data, we estimate that the current carrying molecules represent only a fraction of f ≈ 4 × 10-4 out of the total number of molecules in a large area Au-S-(CH2)13-CH3/EGaIn junction.

Can room-temperature data for tunneling molecular junctions be analyzed within a theoretical framework assuming zero temperature?

Routinely, experiments on tunneling molecular junctions report values of conductances (G_RT) and currents (I_RT) measured at room temperature. On the other hand, theoretical approaches based on simplified models provide analytic formulas for the conductance (G_0K) and current (I_0K) valid at zero temperature. Therefore, interrogating the applicability of the theoretical results deduced in the zero-temperature limit to real experimental situations at room temperature (i.e., G_RT ≈ G_0K and I_RT ≈ I_0K) is a relevant aspect. Quantifying the pertaining temperature impact on the transport properties computed within the ubiquitous single-level model with Lorentzian transmission is the specific aim of the present work. Comprehensive results are presented for broad ranges of the relevant parameters (level's energy offset ε₀ and width Γ_a, and applied bias V) that safely cover values characterizing currently fabricated junctions. They demonstrate that the strongest thermal effects occur at biases below resonance (2|ε₀| - δε₀ - 0.3 ≲ |eV| - 0.3 ≲ 2|ε₀|). At fixed V, they affect an ε₀-range whose largest width δε₀ is about nine times larger than the thermal energy (δε₀ ≈ 3πk_BT) at Γ_a → 0. The numerous figures included aim to convey a quick overview on the applicability of the zero-temperature limit to a specific real junction. In quantitative terms, the conditions of applicability are expressed as mathematical inequalities involving elementary functions. They constitute the basis of a proposed interactive data-fitting procedure, which aims to guide experimentalists interested in data processing in a specific case.

Estimating the Number of Molecules in Molecular Junctions Merely Based on the Low Bias Tunneling Conductance at Variable Temperature

Temperature (T) dependent conductance G=G(T) data measured in molecular junctions are routinely taken as evidence for a two-step hopping mechanism. The present paper emphasizes that this is not necessarily the case. A curve of lnG versus 1/T decreasing almost linearly (Arrhenius-like regime) and eventually switching to a nearly horizontal plateau (Sommerfeld regime), or possessing a slope gradually decreasing with increasing 1/T is fully compatible with a single-step tunneling mechanism. The results for the dependence of G on T presented include both analytical exact and accurate approximate formulas and numerical simulations. These theoretical results are general, also in the sense that they are not limited, e.g., to the (single molecule electromigrated (SET) or large area EGaIn) fabrication platforms, which are chosen for exemplification merely in view of the available experimental data needed for analysis. To be specific, we examine in detail transport measurements for molecular junctions based on ferrocene (Fc). As a particularly important finding, we show how the present analytic formulas for G=G(T) can be utilized to compute the ratio f=Aeff/An between the effective and nominal areas of large area Fc-based junctions with an EGaIn top electrode. Our estimate of f≈0.6×10-4 is comparable with previously reported values based on completely different methods for related large area molecular junctions.

Empirical Parameter to Compare Molecule-Electrode Interfaces in Large-Area Molecular Junctions

This paper describes a simple model for comparing the degree of electronic coupling between molecules and electrodes across different large-area molecular junctions. The resulting coupling parameter can be obtained directly from current–voltage data or extracted from published data without fitting. We demonstrate the generalizability of this model by comparing over 40 different junctions comprising different molecules and measured by different laboratories. The results agree with existing models, reflect differences in mechanisms of charge transport and rectification, and are predictive in cases where experimental limitations preclude more sophisticated modeling. We also synthesized a series of conjugated molecular wires, in which embedded dipoles are varied systematically and at both molecule–electrode interfaces. The resulting current–voltage characteristics vary in nonintuitive ways that are not captured by existing models, but which produce trends using our simple model, providing insights that are otherwise difficult or impossible to explain. The utility of our model is its demonstrative generalizability, which is why simple observables like tunneling decay coefficients remain so widely used in molecular electronics despite the existence of much more sophisticated models. Our model is complementary, giving insights into molecule–electrode coupling across series of molecules that can guide synthetic chemists in the design of new molecular motifs, particularly in the context of devices comprising large-area molecular junctions.

Quantum transport in a single molecular transistor at finite temperature

We study quantum transport in a single molecular transistor in which the central region consists of a single-level quantum dot and is connected to two metallic leads that act as a source and a drain respectively. The quantum dot is considered to be under the influence of electron-electron and electron-phonon interactions. The central region is placed on an insulating substrate that acts as a heat reservoir that interacts with the quantum dot phonon giving rise to a damping effect to the quantum dot. The electron-phonon interaction is decoupled by applying a canonical transformation and then the spectral density of the quantum dot is calculated from the resultant Hamiltonian by using Keldysh Green function technique. We also calculate the tunneling current density and differential conductance to study the effect of quantum dissipation, electron correlation and the lattice effects on quantum transport in a single molecular transistor at finite temperature.

Hexavanadate-Organogold(I) Hybrid Compounds: Synthesis by the Azide-Alkyne Cycloaddition and Density Functional Theory Study of an Intriguing Electron Density Distribution

The fully oxidized Lindqvist-type hexavanadate compounds decorated by phosphine-derivatized Au(I) moieties oriented in a transoid fashion (n-Bu₄N)₂[V₆O₁₃{(OCH₂)₃CCH₂(N₃C₂C₆H₅)AuP(C₆H₄OMe)₃}₂] (POM_N^Au) and (n-Bu₄N)₂[V₆O₁₃{(OCH₂)₃CCH₂OCH₂(C₂N₃H)AuP(C₆H₄OMe)₃}₂] (POM_C^Au) have been prepared by azide-alkyne cycloaddition reactions and characterized by various techniques, including NMR, IR, and UV/vis spectroscopy and electrospray ionization mass spectrometry. Electronic structure calculations unveil the potential of these model hybrid junctions for application in controlled charge-transport experiments on substrate surfaces.

Functional Redox-Active Molecular Tunnel Junctions

Redox-active molecular junctions have attracted considerable attention because redox-active molecules provide accessible energy levels enabling electronic function at the molecular length scales, such as, rectification, conductance switching, or molecular transistors. Unlike charge transfer in wet electrochemical environments, it is still challenging to understand how redox-processes proceed in solid-state molecular junctions which lack counterions and solvent molecules to stabilize the charge on the molecules. In this minireview, we first introduce molecular junctions based on redox-active molecules and discuss their properties from both a chemistry and nanoelectronics point of view, and then discuss briefly the mechanisms of charge transport in solid-state redox-junctions followed by examples where redox-molecules generate new electronic function. We conclude with challenges that need to be addressed and interesting future directions from a chemical engineering and molecular design perspectives.

Electric-field-driven dual-functional molecular switches in tunnel junctions

To avoid crosstalk and suppress leakage currents in resistive random access memories (RRAMs), a resistive switch and a current rectifier (diode) are usually combined in series in a one diode-one resistor (1D-1R) RRAM. However, this complicates the design of next-generation RRAM, increases the footprint of devices and increases the operating voltage as the potential drops over two consecutive junctions¹. Here, we report a molecular tunnel junction based on molecules that provide an unprecedented dual functionality of diode and variable resistor, resulting in a molecular-scale 1D-1R RRAM with a current rectification ratio of 2.5 × 10⁴ and resistive on/off ratio of 6.7 × 10³, and a low drive voltage of 0.89 V. The switching relies on dimerization of redox units, resulting in hybridization of molecular orbitals accompanied by directional ion migration. This electric-field-driven molecular switch operating in the tunnelling regime enables a class of molecular devices where multiple electronic functions are preprogrammed inside a single molecular layer with a thickness of only 2 nm.

Ferrocenes as Building Blocks in Molecular Rectifiers and Diodes

Ferrocenes have recently been reported as components of a number of molecular circuits. This short review covers reports of ferrocenes in molecular rectifiers and diodes which have appeared in the last 10 years.

Transition from direct to inverted charge transport Marcus regions in molecular junctions via molecular orbital gating

Solid-state molecular tunnel junctions are often assumed to operate in the Landauer regime, which describes essentially activationless coherent tunnelling processes. In solution, on the other hand, charge transfer is described by Marcus theory, which accounts for thermally activated processes. In practice, however, thermally activated transport phenomena are frequently observed also in solid-state molecular junctions but remain poorly understood. Here, we show experimentally the transition from the Marcus to the inverted Marcus region in a solid-state molecular tunnel junction by means of intra-molecular orbital gating that can be tuned via the chemical structure of the molecule and applied bias. In the inverted Marcus region, charge transport is incoherent, yet virtually independent of temperature. Our experimental results fit well to a theoretical model that combines Landauer and Marcus theories and may have implications for the interpretation of temperature-dependent charge transport measurements in molecular junctions.

Electroactive Self-Assembled Monolayers Detect Micelle Formation

The interfacial electrochemistry of self-assembled monolayers (SAMs) of ferrocenyldodecanethiolate on gold (FcC₁₂SAu) electrodes is applied to detect the micellization of some common anionic surfactants, sodium n-alkyl sulfates, sodium n-alkyl sulfonates, sodium diamyl sulfosuccinate, and sodium dodecanoate, in aqueous solution by cyclic voltammetry. The apparent formal redox potential (E°'_SAM) of the FcC₁₂SAu SAM is used to track changes in the concentration of the unaggregated surfactant anions and determine the critical micelle concentration (cmc). The effect of added salt (NaF) on the sodium alkyl sulfate concentration dependence of E°'_SAM is also investigated. Weakly hydrated anions, such as ClO₄^-, pair with the electrogenerated SAM-bound ferroceniums to neutralize the excess positive charge created at the SAM/electrolyte solution interface and stabilize the oxidized cations. E°'_SAM exhibits a Nernstian-type dependence on the anion activity in solution. Aggregation of the surfactant anions into micelles above the cmc causes the free surfactant anion activity to deviate from the molar concentration of added surfactant, resulting in a break in the plot of E°'_SAM versus the logarithm of the concentration of anionic surfactant. The concentration at which this deviation occurs is in good agreement with literature or experimentally determined values of the cmc. The effects of Ohmic potential drop, liquid junction potential, and surfactant adsorption behavior on E°'_SAM are addressed. Ultimately, the E°'_SAM response as a function of the anionic surfactant concentration exhibits the same features reported using potentiometry and surfactant ion-selective electrodes, which provide a direct measure of the free surfactant anion activity, thus making FcC₁₂SAu SAM electrodes useful for the detection of surfactant aggregation and micelle formation.

Protocol for disentangling the thermally activated contribution to the tunneling-assisted charge transport. Analytical results and experimental relevance

In this paper we present results demonstrating that the charge transport by tunneling in molecular junctions can exhibit a substantial temperature dependence.