Interface geometry and molecular junction conductance: geometric fluctuation and stochastic switching

Amine-gold linked single-molecule circuits: experiment and theory

A combination of theory and experiment is used to quantitatively understand the conductance of single-molecule benzenediamine-gold junctions. A newly developed analysis is applied to a measured junction conductance distribution, based on 59 000 individual conductance traces, which has a clear peak at 0.0064 G0 and a width of +/-47%. This analysis establishes that the distribution width originates predominantly from variations in conductance across different junctions rather than variations in conductance during junction elongation. Conductance calculations based on density functional theory (DFT) for 15 distinct junction geometries show a similar spread. We show explicitly that differences in local structure have a limited influence on conductance because the amine-Au bonding motif is well-defined and flexible, explaining the narrow distributions seen in the experiments. The minimal impact of junction structure on conductance permits an unambiguous comparison of calculated and measured conductance values and a direct assessment of the widely used DFT theoretical framework. The average calculated conductance (0.046 G0) is found to be seven times larger than experiment. This discrepancy is explained quantitatively in terms of electron correlation effects to the molecular level alignments in the junction.

Contact transparency of nanotube-molecule-nanotube junctions

The transparency of contacts between conjugated molecules and metallic single-walled carbon nanotubes is investigated using a single-particle Green's function method which combines a Landauer approach with ab initio density functional theory. We find that the overall conjugation required for good contact transparency is broken by connecting through a six-member ring on the tube. Full conjugation achieved by an all-carbon contact through a five-member ring leads to near perfect contact transparency for different conjugated molecular bridges.

Negative differential resistance and switching behavior of redox-mediated tunnel contact

Theoretical description of various properties of redox-mediated tunnel contacts is presented. The dependences of the current on the overpotential and bias voltage under the sweeping voltammetry conditions are addressed. The effect of switching between two redox states on the shape of current/voltage characteristics is discussed. The shot noise and telegraph noise of the bridged contacts involving redox group are considered. Functional properties of the contact as a means for the information processing are discussed.

Efficient atomic self-interaction correction scheme for nonequilibrium quantum transport

Density-functional theory calculations of electronic transport based on local exchange and correlation functionals contain self-interaction errors. As a consequence, insulating molecules in weak contact with metallic electrodes erroneously form highly conducting junctions. Here we present a fully self-consistent and still computationally undemanding self-interaction correction scheme that overcomes these limitations. The method is implemented in the transport code SMEAGOL and applied to the prototypical case of benzene molecules and gold electrodes. The Kohn-Sham highest occupied molecular orbital now reproduces closely the negative of the molecular ionization potential and is moved away from the gold Fermi energy. This leads to a drastic reduction of the low-bias current in much better agreement with experiments.

Generalized survival in step fluctuations

The properties of the generalized survival probability, that is, the probability of not crossing an arbitrary location R during relaxation, have been investigated experimentally (via scanning tunneling microscope observations) and numerically. The results confirm that the generalized survival probability decays exponentially with a time constant tau(s) (R). The distance dependence of the time constant is shown to be tau(s) (R) = tau(s0) exp[-R/w (T)], where w2 (T) is the material-dependent mean-squared width of the step fluctuations. The result reveals the dependence on the physical parameters of the system inherent in the prior prediction of the time constant scaling with R/L(alpha), with L the system size and alpha the roughness exponent. The survival behavior is also analyzed using a contrasting concept, the generalized inside survival S(in) (t,R), which involves fluctuations to an arbitrary location R further from the average. Numerical simulations of the inside survival probability also show an exponential time dependence, and the extracted time constant empirically shows (R/w)(lambda) behavior, with lambda varying over 0.6 to 0.8 as the sampling conditions are changed. The experimental data show similar behavior, and can be well fit with lambda = 1.0 for T = 300 K, and 0.5 < lambda < 1 for T = 460 K. Over this temperature range, the ratio of the fixed sampling time to the underlying physical time constant, and thus the true correlation time, increases by a factor of approximately 10(3). Preliminary analysis indicates that the scaling effect due to the true correlation time is relevant in the parameter space of the experimental observations.

Electron tunneling through alkanedithiol self-assembled monolayers in large-area molecular junctions

The electrical transport through self-assembled monolayers of alkanedithiols was studied in large-area molecular junctions and described by the Simmons model [Simmons JG (1963) J Appl Phys 34:1793-1803 and 2581-2590] for tunneling through a practical barrier, i.e., a rectangular barrier with the image potential included. The strength of the image potential depends on the value of the dielectric constant. A value of 2.1 was determined from impedance measurements. The large and well defined areas of these molecular junctions allow for a simultaneous study of the capacitance and the tunneling current under operational conditions. Electrical transport for octanedithiol through tetradecanedithiol self-assembled monolayers up to 1 V can simultaneously be described by a single effective mass and a barrier height. There is no need for additional fit constants. The barrier heights are in the order of 4-5 eV and vary systematically with the length of the molecules. Irrespective of the length of the molecules, an effective mass of 0.28 was determined, which is in excellent agreement with theoretical predictions.

Metal-molecule interface fluctuations

We have created self-assembled circular chains of C60 laterally bound to a layer of Ag atoms as a model system for characterizing fluctuations at a metal-molecule interface. STM measurements show that the Ag and C60 sides of the interface fluctuate independently, with frequency-dependent amplitudes of magnitude 0.1 nm at approximately 1 Hz for the Ag edge and approximately 0.01 Hz for the C60 ring. The measured frequency spectra of the metal and molecule fluctuation amplitudes will contribute characteristic signatures to transport measurements involving such interfaces.

Electric field effects on the performance of a candidate multipole molecular switch: a quantum computational study

Structural and electronic responses of the organic molecule di(4-nitro-2-methylenamine phenyl) diazene a candidate molecular switch, as an active device in a nanoelectronic circuit, to the external electric fields with strengths 5 x 10(-4) - 1.8 x 10(-2) a.u. included explicitly in the Hamiltonian are studied using B3LYP/6-31G* method. This study shows that thermodynamic formation functions are not affected significantly by the applied field. Electronic spatial extent show a negligibly small change (<2%) over the studied range of the electric field strength. Calculated electric dipole moments show significant sensitivity to the external electric field, which result consequently in much stronger interactions with the electrodes (poles) of the mother nanoelectronic circuit at higher electric field strengths. Natural bond orbital atomic charges analysis shows different field effects on different atoms depending on their positions with respect to the direction of the field. The applied field increases HOMO, LUMO, and the Fermi level energies; however, decreases the HOMO-LUMO gap (HLG) values. Results of this study show that it is possible to control field-induced charge redistribution over the molecule by using push-pull effects of different substitution via their connection points to the extended pi-system.

Measurement of Single-Molecule Conductance

What is the conductance of a single molecule? This basic and seemingly simple question has been a difficult one to answer for both experimentalists and theorists. To determine the conductance of a molecule, one must wire the molecule reliably to at least two electrodes. The conductance of the molecule thus depends not only on the intrinsic properties of the molecule, but also on the electrode materials. Furthermore, the conductance is sensitive to the atomic-level details of the molecule-electrode contact and the local environment of the molecule. Creating identical contact geometries has been a challenging experimental problem, and the lack of atomic-level structural information of the contacts makes it hard to compare calculations with measurements. Despite the difficulties, researchers have made substantial advances in recent years. This review provides an overview of the experimental advances, discusses the advantages and drawbacks of different techniques, and explores remaining issues.

The effect of molecular conformation on single molecule conductance: measurements of π-conjugated oligoaryls by STM break junction

Measurements of molecular break junction reveal quantitatively the correlation between the single-molecule conductance and the conformation of pi-conjugated molecules with 6-18 conjugated double bonds.

Conformational analysis of diphenylacetylene under the influence of an external electric field

Theoretical investigation of the torsional potentials of a molecular wire, diphenylacetylene, was carried out at the B3LYP/6-311+G** level by considering the influence of the external electric field (EF). It demonstrates that many molecular features are sensitive to the EF applied. In particular, the torsional barrier increases and the LUMO-HOMO gap decreases with the increase of EF. Quantitative correlations between these features and the external EF were revealed. The current-voltage behavior corresponding to different conformers was studied as well by non-equilibrium Green's function method combined with the density functional theory. Further, the evolution of the LUMO-HOMO gap and the spatial distribution of molecular orbital were used to analyze these structure-property relationships.

Electron transport in molecular junctions

Building an electronic device using individual molecules is one of the ultimate goals in nanotechnology. To achieve this it will be necessary to measure, control and understand electron transport through molecules attached to electrodes. Substantial progress has been made over the past decade and we present here an overview of some of the recent advances. Topics covered include molecular wires, two-terminal switches and diodes, three-terminal transistor-like devices and hybrid devices that use various different signals (light, magnetic fields, and chemical and mechanical signals) to control electron transport in molecules. We also discuss further issues, including molecule-electrode contacts, local heating- and current-induced instabilities, stochastic fluctuations and the development of characterization tools.

Effect of Anchoring Groups on Single-Molecule Conductance: Comparative Study of Thiol-, Amine-, and Carboxylic-Acid-Terminated Molecules

We studied the effect of anchoring groups on the conductance of single molecules using alkanes terminated with dithiol, diamine, and dicarboxylic-acid groups as a model system. We created a large number of molecular junctions mechanically and analyzed the statistical distributions of the conductance values of the molecular junctions. Multiple sets of conductance values were found in each case. The I-V characteristics, temperature independence, and exponential decay of the conductance with the molecular length all indicate tunneling as the conduction mechanism for these molecules. The prefactor of the exponential decay function, which reflects the contact resistance, is highly sensitive to the anchoring group, and the decay constant is weakly dependent on the anchoring group. These observations are attributed to different electronic couplings between the molecules and the electrodes and alignments of the molecular energy levels relative to the Fermi energy level of the electrodes introduced by different anchoring groups. For diamine and dicarboxylic-acid groups, the conductance values are sensitive to pH due to protonation and deprotonation of the anchoring groups. Further insight into the binding strengths of these anchoring groups to gold electrodes is obtained by statistically analyzing the stretching length of molecular junctions.

The symmetry of single-molecule conduction

We introduce the conductance point group which defines the symmetry of single-molecule conduction within the nonequilibrium Green's function formalism. It is shown, either rigorously or to within a very good approximation, to correspond to a molecular-conductance point group defined purely in terms of the properties of the conducting molecule. This enables single-molecule conductivity to be described in terms of key qualitative chemical descriptors that are independent of the nature of the molecule-conductor interfaces. We apply this to demonstrate how symmetry controls the conduction through 1,4-benzenedithiol chemisorbed to gold electrodes as an example system, listing also the molecular-conductance point groups for a range of molecules commonly used in molecular electronics research.

Single molecule electron transport junctions: Charging and geometric effects on conductance

A p-benzenedithiolate (BDT) molecule covalently bonded between two gold electrodes has become one of the model systems utilized for investigating molecular transport junctions. The plethora of papers published on the BDT system has led to varying conclusions with respect to both the mechanism and the magnitude of transport. Conductance variations have been attributed to difficulty in calculating charge transfer to the molecule, inability to locate the Fermi energy accurately, geometric dispersion, and stochastic switching. Here we compare results obtained using two transport codes, TRANSIESTA-C and HUCKEL-IV, to show that upon Au-S bond lengthening, the calculated low bias conductance initially increases by up to a factor of 30. This increase in highest occupied molecular orbital (HOMO) mediated conductance is attributed to charging of the terminal sulfur atom and a corresponding decrease in the energy gap between the Fermi level and the HOMO. Addition of a single Au atom to each terminal of the extended BDT molecule is shown to add four molecular states near the Fermi energy, which may explain the varying results reported in the literature.

Molecular origins of conduction channels observed in shot-noise measurements

Measurements of shot noise from single molecules have indicated the presence of various conduction channels. We present three descriptions of these channels in molecular terms showing that the number of conduction channels is limited by bottlenecks in the molecule and that the channels can be linked to transmission through different junction states. We introduce molecular-conductance orbitals, which allow the transmission to be separated into contributions from individual orbitals and contributions from interference between pairs of orbitals.

Effects of hydration on molecular junction transport

The study of charge transport through increasingly complex small molecules will benefit from a detailed understanding of how contaminants from the environment affect molecular conduction. This should provide a clearer picture of the electronic characteristics of molecules by eliminating interference from adsorbed species. Here we use magnetically assembled microsphere junctions incorporating thiol monolayers to provide insight into changing electron transport characteristics resulting from exposure to air. Using this technique, current-voltage analysis and inelastic electron tunnelling spectroscopy (IETS) demonstrate that the primary interaction affecting molecular conduction is rapid hydration at the gold-sulphur contacts. We use IETS to present evidence for changing mechanisms of charge transport as a result of this interaction. The detrimental effects on molecular conduction discussed here are important for understanding electron transport through gold-thiol molecular junctions once exposed to atmospheric conditions.

Interpretation of stochastic events in single molecule conductance measurements

The electrical conductance of a series of thiol-terminated alkanes, (1,6-hexanedithiol (HDT), 1,8-octanedithiol (ODT), and 1,10-decanedithol (DDT)) was measured using a modified scanning tunneling microscope break junction technique. The interpretation of data obtained in this technique is complicated due to multiple effects such as microscopic details of the metal-molecule junctions, superposition of tunneling currents, and conformational changes in the molecules. A new method called the last-step analysis (LSA) is introduced here to clarify the contribution of these effects. In direct contrast to previous work, LSA does not require any data preselection, making the results less subjective and more reproducible. Finally, LSA was used to obtain the conductance of single molecules (HDT, (3.6 x 10(-4))G(o); ODT, (4.4 x 10(-5))G(o); DDT, (5.7 x 10(-6))G(o)). The tunneling decay parameter (beta) was calculated, and it was found to be approximately 1.0 per carbon atom.

Orbital Interaction Mechanisms of Conductance Enhancement and Rectification by Dithiocarboxylate Anchoring Group

We study computationally the electron transport properties of dithiocarboxylate terminated molecular junctions. Transport properties are computed self-consistently within density functional theory and nonequilibrium Green's functions formalism. A microscopic origin of the experimentally observed current amplification by dithiocarboxylate anchoring groups is established. For the 4,4'-biphenyl bis(dithiocarboxylate) junction, we find that the interaction of the lowest unoccupied molecular orbital (LUMO) of the dithiocarboxylate anchoring group with LUMO and highest occupied molecular orbital (HOMO) of the biphenyl part results in bonding and antibonding resonances in the transmission spectrum in the vicinity of the electrode Fermi energy. A new microscopic mechanism of rectification is predicted based on the electronic structure of asymmetrical anchoring groups. We show that the peaks in the transmission spectra of 4'-thiolato-biphenyl-4-dithiocarboxylate junction respond differently to the applied voltage. Depending upon the origin of a transmission resonance in the orbital interaction picture, its energy can be shifted along with the chemical potential of the electrode to which the molecule is more strongly or more weakly coupled.

Electronic transportation through asymmetrically substituted oligo(phenylene ethynylene)s: Studied by first principles nonequilibrium Green’s function formalism

Theoretical investigations of a series of asymmetrically substituted conducting molecular wires [oligo(phenylene ethynylene)s] have been carried out using density functional theory and nonequilibrium Green's function formalism. To get the molecular rectification, the electron-donating group (-NH2) and the electron-withdrawing group (-NO2) are placed on the different positions of the molecular wire. The dependences of spatial distribution and lowest unoccupied molecular orbital (LUMO) energy level on the applied voltage have been found playing dominating but opposite roles in controlling the rectification behavior. In the tested bias range, since the shift LUMO energy level is more important, the electrons transfer more easily from donor to acceptor through the molecular junction in general.

Adsorption of Benzene-1,4-dithiol on the Au(111) Surface and Its Possible Role in Molecular Conductance

It is a consensus in the field of molecular electronics that the transport of charge across a single molecule depends sensitively on the details of the interaction between the molecule and the metallic leads, such as the molecular orientation. To advance the design of complex molecular devices, it is crucial to have a detailed understanding of these many aspects that influence the electron transport. A simple system that has been used as a paradigm of the class of conjugated aryl molecules is the benzene-1,4-dithiol (BDT). However, we still do not have a full understanding of the BDT transport experiments. Usually the geometries considered in transport calculations assumed that the BDT was connected to the two Au leads via the S atoms, and that the molecule was either perpendicular or close to a perpendicular configuration relative to the Au surfaces. Using ab initio calculations, we show that, for an isolated molecule, the configuration with largest adsorption energy has the BDT phenyl ring closer to being parallel to the surface, and we then argue, based on nonequilibrium Green's function-density functional theory calculations, that, depending on the experimental procedure, this may be the relevant configuration to be used in the transport calculations.

Dithiocarbamate Anchoring in Molecular Wire Junctions: A First Principles Study

Recent experimental realization [J. Am. Chem. Soc., 127 (2005) 7328] of various dithiocarbamate self-assembly on gold surface opens the possibility for use of dithiocarbamate linkers to anchor molecular wires to gold electrodes. In this paper, we explore this hypothesis computationally. We computed the electron transport properties of 4,4'-bipyridine (BP), 4,4'-bipyridinium-1,1'-bis(carbodithioate) (BPBC), 4-(4'-pyridyl)-peridium-1-carbodithioate (BPC) molecule junctions based on the density functional theory and nonequilibrium Green's functions. We demonstrated that the stronger molecule-electrode coupling associated with the conjugated dithiocarbamate linker broadens transmission resonances near the Fermi energy. The broadening effect along with the extension of the pi conjugation from the molecule to the gold electrodes lead to enhanced electrical conductance for BPBC molecule. The conductance enhancement factor is as large as 25 at applied voltage bias 1.0 V. Rectification behavior is predicted for BPC molecular wire junction, which has the asymmetric anchoring groups.

Modulation of Molecular Conductance Induced by Electrode Atomic Species and Interface Geometry

We present a systematic theoretical investigation of the interaction of an organic molecule with gold and palladium electrodes. We show that the chemical nature of the electrode elicits significant geometrical changes in the molecule. These changes, which are characteristic of the electrode atomic species and the interface geometry, are shown to occur at distances as great as 10 Angstrom from the interface, leading to a significant modification of the inherent electronic properties of the molecule. In certain interface geometries, the highest occupied molecular orbital (HOMO) of the palladium-contacted molecule exhibits enhanced charge delocalization at the center of the molecule, compared to gold. Also, the energy gap between the conductance peak of the lowest unoccupied molecular orbital (LUMO) and the Fermi level is smaller for the case of the palladium electrode, thereby giving rise to a higher current level at a given bias than the gold-contacted molecule. These results indicate that an optimal choice of the atomic species and contact geometry could lead to significantly enhanced conductance of molecular devices and could serve as a viable alternative to molecular derivatization.

Single-molecule circuits with well-defined molecular conductance

We measure the conductance of amine-terminated molecules by breaking Au point contacts in a molecular solution at room temperature. We find that the variability of the observed conductance for the diamine molecule-Au junctions is much less than the variability for diisonitrile- and dithiol-Au junctions. This narrow distribution enables unambiguous conductance measurements of single molecules. For an alkane diamine series with 2-8 carbon atoms in the hydrocarbon chain, our results show a systematic trend in the conductance from which we extract a tunneling decay constant of 0.91 +/- 0.03 per methylene group. We hypothesize that the diamine link binds preferentially to undercoordinated Au atoms in the junction. This is supported by density functional theory-based calculations that show the amine binding to a gold adatom with sufficient angular flexibility for easy junction formation but well-defined electronic coupling of the N lone pair to the Au. Therefore, the amine linkage leads to well-defined conductance measurements of a single molecule junction in a statistical study.

Variability of Conductance in Molecular Junctions

The conductance of molecular junctions, formed by breaking gold point contacts dressed with various thiol functionalized organic molecules, is measured at 293 K and at 30 K. In the presence of molecules, individual conductance traces measured as a function of increasing gold electrode displacement show clear steps below the quantum conductance steps of the gold contact. These steps are distributed over a wide range of molecule-dependent conductance values. Histograms constructed from all conductance traces therefore do not show clear peaks either at room or low temperatures. Filtering of the data sets by an objective automated procedure only marginally improves the visibility of such features. We conclude that the geometrical junction to junction variations dominate the conductance measurements.

Covalently Bridging Gaps in Single-Walled Carbon Nanotubes with Conducting Molecules

Molecular electronics is often limited by the poorly defined nature of the contact between the molecules and the metal surface. We describe a method to wire molecules into gaps in single-walled carbon nanotubes (SWNTs). Precise oxidative cutting of a SWNT produces carboxylic acid–terminated electrodes separated by gaps of ≤10 nanometers. These point contacts react with molecules derivatized with amines to form molecular bridges held in place by amide linkages. These chemical contacts are robust and allow a wide variety of molecules to be tested electrically. In addition to testing molecular wires, we show how to install functionality in the molecular backbone that allows the conductance of the single-molecule bridges to switch with pH.