Analyzing Molecular Current-Voltage Characteristics with the Simmons Tunneling Model: Scaling and Linearization

Use of the Simmons model for analyzing tunneling transport across molecular junctions is reviewed, and its inherent limitations are examined, specifically for cases where there are no molecular length-dependent data (to extract a decay parameter), be it for experimental reasons or because of changes of the molecular energetics or packing with molecular length. The potential barrier across a molecular junction is shown to be strongly bias-dependent, much more so than is assumed in the commonly used version of the Simmons model. The means to distinguish true tunneling from conduction via pinholes (or hot spots) are also considered. Power expansion to the Simmons model shows that I/V vs V2 plots should be linear over that range, thus providing a simple and standardized parameter extraction. From such plots, we can extract values for the equilibrium conductance and for the “shape factor”, a complementary parameter that describes the shape of the I−V relations. The applicability of these two parameters for describing actual transport is illustrated by analyzing data for three different types of molecular junctions. The linearity of the I/V vs V2 plots can be used to evaluate if, and if so, at which bias (and if at all) direct tunneling occurs and under which conditions this is not the case. The extracted equilibrium conductance and the “shape factor” provide an empirical method for quantifying electronic transport across practical molecular junctions where the exact packing of the molecules is rather uncertain. As such, the analysis can be used to weigh and classify the effect of chemical modifications to molecular junctions or compare contacting methods, so as to allow a deeper understanding of transport via molecular junctions

Quantification of Ready-Made Molecular Bilayer Junctions Having Large Structural Uncertainty

A ready-made procedure for the preparation of molecular junctions at ambient conditions is reported. Junctions were constructed from bilayers of alkyl thiols at the interfaces between gold flakes and stationary gold strips. Addition of an amine or carboxylic acid end group to the alkyl thiols drastically increased the resistance (up to TΩ over a couple of nanometers only) and the breakdown voltage of the bilayer junction. These junctions pose a severe quantification challenge because of the large uncertainty regarding their microscopic morphology. A novel quantification procedure is proposed that replaces highly nonlinear tunneling or super-exchange current voltage relations by an effective analytical relation of two characteristic parameters:  equilibrium conductance and shape factor. Correlating these factors over a series of systematically varying junctions allows us to evaluate the effective contact area for transfer. This approach was also extended to the field-emission regime. Within the large spreading of the data, our analyses show that low-bias transfer occurs via most of the contact area while field emission is limited to “hot spots” of a few nanometers wide and only couple of angstroms long. The extracted length for charge transfer was only 1/4 to 1/3 of the nominal bilayer thickness, except for the polar interfaces, which were considerably thicker. The effect of polar end groups on the bilayer thickness is presumably due to weak repulsive forces at the bilayer interface, preventing the collapse of the bilayer

Molecule−Metal Polarization at Rectifying GaAs Interfaces

Metal/organic monolayer/GaAs junctions, prepared by adsorbing a set of dicarboxylic ligands, with systematic change of ligand substituents, on GaAs, are measured and characterized electrically. The molecules are chemically bound to the semiconductor surface under ambient conditions and form roughly a monolayer (MoL), with average order in the direction perpendicular to the semiconductor surface. This suffices to yield systematic changes in electron affinity and work function of the modified GaAs. Junctions are made by a soft metal deposition method, used here for Au and Al. Experimentally, we find strong molecular effects, reaching differences in current at a given voltage of up to 6 orders of magnitude, depending on the substituent on the molecules making up the monolayer. These and the changes in the effective barrier height of the metal/MoL/GaAs junctions, extracted by analyses of their current−voltage characteristics, can be explained by electrostatic effects of the molecular layer, rather than by electrodynamic ones (current flow through the molecular film). This can be understood by realizing that the samples are relatively large area devices with extremely narrow (∼1 nm) films of organic molecules, showing only average order, which makes dominance of tunneling effects very unlikely. We show that not only the molecule's electronic and electrical properties but also the way the metals contact the molecules, as well as the doping type of the semiconductor, can determine the direction of the molecular effect. Also the type of metal governs the effect that we identify as being due to interfacial dipoles formed as a result of triple metal/organic molecule/semiconductor interaction

Molecule−Metal Polarization at Rectifying GaAs Interfaces

Metal/organic monolayer/GaAs junctions, prepared by adsorbing a set of dicarboxylic ligands, with systematic change of ligand substituents, on GaAs, are measured and characterized electrically. The molecules are chemically bound to the semiconductor surface under ambient conditions and form roughly a monolayer (MoL), with average order in the direction perpendicular to the semiconductor surface. This suffices to yield systematic changes in electron affinity and work function of the modified GaAs. Junctions are made by a soft metal deposition method, used here for Au and Al. Experimentally, we find strong molecular effects, reaching differences in current at a given voltage of up to 6 orders of magnitude, depending on the substituent on the molecules making up the monolayer. These and the changes in the effective barrier height of the metal/MoL/GaAs junctions, extracted by analyses of their current−voltage characteristics, can be explained by electrostatic effects of the molecular layer, rather than by electrodynamic ones (current flow through the molecular film). This can be understood by realizing that the samples are relatively large area devices with extremely narrow (∼1 nm) films of organic molecules, showing only average order, which makes dominance of tunneling effects very unlikely. We show that not only the molecule's electronic and electrical properties but also the way the metals contact the molecules, as well as the doping type of the semiconductor, can determine the direction of the molecular effect. Also the type of metal governs the effect that we identify as being due to interfacial dipoles formed as a result of triple metal/organic molecule/semiconductor interaction

Rethinking Transition Voltage Spectroscopy within a Generic Taylor Expansion View

Transition voltage spectroscopy (TVS) has become an accepted quantification tool for molecular transport characteristics, due to its simplicity and reproducibility. Alternatively, the Taylor expansion view, TyEx, of transport by tunneling suggests that conductance–voltage curves have approximately a generic parabolic shape, regardless of whether the tunneling model is derived from an average medium view (e.g., WKB) or from a scattering view (e.g., Landauer). Comparing TVS and TyEx approaches reveals that TVS is closely related to a bias-scaling factor, V0, which is directly derived from the third coefficient of TyEx, namely, the second derivative of the conductance with respect to bias at 0 V. This interpretation of TVS leads to simple expressions that can be compared easily across primarily different tunneling models. Because the basic curve shape is mostly generic, the quality of model fitting is not informative on the actual tunneling model. However internal correlation between the conductance near 0 V and V0 (TVS) provides genuine indication on fundamental tunneling features. Furthermore, we show that the prevailing concept that V0 is proportional to the barrier height holds only in the case of resonant tunneling, while for off-resonant or deep tunneling, V0 is proportional to the ratio of barrier height to barrier width. Finally, considering TVS as a measure of conductance nonlinearity, rather than as an indicator for energy level spectroscopy, explains the very low TVS values observed with a semiconducting (instead of metal) electrode, where transport is highly nonlinear due to the relatively small, bias-dependent density of states of the semiconducting electrode

Long-Range Substrate Effects on the Stability and Reactivity of Thiolated Self-Assembled Monolayers

The reactivity of the tail group of molecules absorbed in a self-assembled monolayer is affected significantly by the substrate through long-range charge redistribution occurring during the adsorption. Alkyl dithiol monolayers on GaAs are highly stable as compared to monolayers of monothiols on GaAs or dithiols on gold. X-ray photoelectron spectroscopy (XPS) measurements reveal fairly weak binding of monothiol layers on GaAs, prone to rapid oxidation at the molecule−substrate interface. This is in contrast with the high stability of monothiols on gold. However, in the case of dithiols, the situation is reversed. When adsorbed on gold, the top thiol group tends to oxidize, whereas on GaAs, it does not. Furthermore, the monolayer was found to be stable in ambient for months. Contact potential difference (CPD) measurements showed a significant difference in charge distribution on the monolayers adsorbed on the two substrates, gold and GaAs. The change in reactivity and stability is attributed to the difference in the substrate-induced charge distribution across the adsorbed molecules

Hydrolysis Improves Packing Density of Bromine-Terminated Alkyl-Chain, Silicon−Carbon Monolayers Linked to Silicon

Bromine-terminated alkyl-chain monolayers, bound to oxide-free Si substrates, were prepared by self-assembly. Infrared spectroscopy and atomic force microscopy imply that monolayer packing density improves after hydrolysis, despite an increase in the presence of oxide. The probable reason is that OH-mediated intermolecular H-bonding along the monolayer emerges after hydrolysis and rearranges the molecular components of the insulating layer. Current−voltage and differential capacitance measurements show that also the interfacial electronic properties of these junctions are changed by hydrolysis of the Br groups. This is expressed in an increased effective Schottky barrier height and a decreased junction ideality factor. We correlate the proposed structural changes of the monolayer with the change in the interfacial electronic properties, with the help of the inhomogeneous Schottky barrier height model. The role of oxide in the charge transport through the monolayer is discussed, as well

Electrically Controlled Bimetallic Junctions for Atomic-Scale Electronics

Forming atomic-scale contacts with attractive geometries and material compositions is a long-term goal of nanotechnology. Here, we show that a rich family of bimetallic atomic-contacts can be fabricated in break-junction setups. The structure and material composition of these contacts can be controlled by atomically precise electromigration, where the metal types of the electron-injecting and sink electrodes determine the type of atoms added to, or subtracted from, the contact structure. The formed bimetallic structures include, for example, platinum and aluminum electrodes bridged by an atomic chain composed of platinum and aluminum atoms as well as iron–nickel single-atom contacts that act as a spin-valve break junction without the need for sophisticated spin-valve geometries. The versatile nature of atomic contacts in bimetallic junctions and the ability to control their structure by electromigration can be used to expand the structural variety of atomic and molecular junctions and their span of properties

Defect Scaling with Contact Area in EGaIn-Based Junctions: Impact on Quality, Joule Heating, and Apparent Injection Current

Although the tunneling rates decrease exponentially with a decay coefficient β close to 1.0 n_C^–1 across <i>n</i>-alkanethiolate (SC_<i>n</i>) monolayer based tunneling junctions determined over a multitude of test beds, the origins of the large spread of injection current densitiesthe hypothetical current density, <i>J</i>₀ (in A/cm²), that flows across the junction when <i>n</i> = 0of up to 12 orders of magnitude are unclear. Every type of junction contains a certain distribution of defects induced by, for example, defects in the electrode materials or impurities. This paper describes that the presence of defects in the junctions is one of the key factors that cause an increase in the observed values of <i>J</i>₀. We controlled the number of defects in Ag^TS-SC_<i>n</i>//GaO_<i>x</i>/EGaIn junctions by varying the geometrical contact area (<i>A</i>_geo) of the junction. The value of <i>J</i>₀ (∼10² A/cm²) is independent of the junction size when <i>A</i>_geo is small (<9.6 × 10² μm²) but increased by 3 orders of magnitude (from 10² to 10⁵ A/cm²) when <i>A</i>_geo increased from 9.6 × 10² to 1.8 × 10⁴ μm². With increasing <i>J</i>₀ values the yields in nonshorting junctions decreased (from 78 to 44%) and β increased (from 1.0 to 1.2 n_C^–1). We show that the quality of the junctions can be qualitatively determined by examining the curvature of the d<i>J</i>/d<i>V</i> curves (defects change the sign of the curvature from positiveassociated with tunnelingto negativeassociated with Joule heating) and fitting the <i>J</i>(V) curves to the full Simmons equation to (crudely) estimate the effective separation of the top- and bottom-electrode <i>d</i>_eff. This analysis confirmed that the electrical characteristics of large junctions are dominated by thin-area defects, while small junctions are dominated by the molecular structure