Abstract
We present a theoretical analysis aimed at understanding electrical conduction in molecular tunnel junctions. We focus on discussing the validity of coherent versus incoherent theoretical formulations for single-level tunneling to explain experimental results obtained under a wide range of experimental conditions, including measurements in individual molecules connecting the leads of electromigrated single-electron transistors and junctions of self-assembled monolayers (SAM) of molecules sandwiched between two macroscopic contacts. We show that the restriction of transport through a single level in solid state junctions (no solvent) makes coherent and incoherent tunneling formalisms indistinguishable when only one level participates in transport. Similar to Marcus relaxation processes in wet electrochemistry, the thermal broadening of the Fermi distribution describing the electronic occupation energies in the electrodes accounts for the exponential dependence of the tunneling current on temperature. We demonstrate that a single-level tunnel model satisfactorily explains experimental results obtained in three different molecular junctions (both single-molecule and SAM-based) formed by ferrocene-based molecules. Among other things, we use the model to map the electrostatic potential profile in EGaIn-based SAM junctions in which the ferrocene unit is placed at different positions within the molecule, and we find that electrical screening gives rise to a strongly non-linear profile across the junction.
Highlights
Contact with the top-electrodes[21] and models are often used to extract the relevant transport parameters
A molecular junction can be represented by the schematic diagrams shown in Fig. 1, where the molecule sandwiched between two electrodes is represented by a discrete set of levels separated from the electrostatic potential in the electrodes by tunnel barriers
In the junctions discussed in this work, where the molecules are present in solid-state devices and charge transport is studied in the absence of solvent, outer-sphere reorganization processes do not likely play an important role in the electrical conduction through the junction
Summary
The single-level transport model: Coherent versus incoherent tunneling. In the simplest approximation, a molecular junction can be represented by the schematic diagrams shown in Fig. 1, where the molecule sandwiched between two electrodes (three in the case of a SET) is represented by a discrete set of levels (with N representing the number of electrons in each level) separated from the electrostatic potential in the electrodes by tunnel barriers. Note the different causes of level broadening, which we can separate into two main contributions: (i) broadening due to the coupling of the molecule to the electrodes, with tunneling rate γ = γL +γR, and, (ii) broadening arising from the coupling of the electron to other degrees of freedom of the molecule, γ0 This is just a simplification (virtual transitions to high-energy molecular states take place during the conduction process, leading to renormalized parameters) and should be taken as such. Even a single-level coherent transport model can explain the exponential thermal enhancement of the conductance through a molecular junction without the need to invoke Marcus relaxation processes This is because the temperature dependence of the conductance naturally arises from the thermal broadening of the energy of the electrons in the leads (see, e.g., the work by van der Zant et al.[37]). It is possible to relax the condition of very small broadening γ kBT, ε , μL − μR and incorporate the effect of a finite level broadening into the rate equation calculation by introducing a broadened density of states (DOS) in the shape of a Lorentzian centered at the energy level ε, Dε (E )
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