Electron transport through molecular junctions
Introduction
At present, we observe a long lasting process of miniaturization of electronic devices. The ultimate limit for the miniaturization of electronic components is set by the atomic scale. However, in the case of conventional “top-down” fabrication methods and usual semiconductor materials, the smallest attainable size of the electronic components is well above this ultimate limit. Many ways for further miniaturization have been and still are suggested, including those using graphene and carbon nanotubes. Molecular electronics is known to be one of the most promising developments of nanoelectronics, and the last two decades have seen an extraordinary progress in this field [1], [2], [3], [4], [5]. Present activities in the field of molecular electronics reflect the convergence of two trends in the fabrication of nanodevices, namely, the “top-down” device miniaturization through lithographic methods and “bottom-up” device manufacturing through atom-engineering and self-assembly approach. The principal goal of molecular electronics is to construct electronic circuits in a “bottom-up” fashion, so that specifically designed molecules could take parts of active components as well as interconnects.
Currently, molecular conductors represent the ultimate in device miniaturization with the important advantages of spontaneous self-assembly, remarkable flexibility and chemical tunability. The key element and basing block of molecular electronic devices is a junction including two metal electrodes (leads) linked by a molecule, as schematically shown in the Fig. 1. Usually, the electrodes are microscopically large but macroscopically small contacts which may be connected to a battery to provide the bias voltage across the junction. Accordingly, the most of theoretical and experimental studies so far have been concentrated on various aspects of electron transport through metal–molecule–metal junctions (MMMs).
A molecule included into the junction may be treated as a quantum dot coupled to the charge reservoirs. The discrete character of energy spectrum on the dot (molecule) is combined with nearly continuous energy spectra on the reservoirs (leads) occurring due to their comparatively large size, and this combination determines transport properties of the junction. To a considerable extent, transport characteristics of a certain MMM depend on the composition and structure of the molecular linker. It opens opportunities to take advantage of the variability of chemical compounds to design MMMs with the desired properties for use as elements in molecular electronic devices, so the molecular electronic research often requires participation of chemists as well as physicists. Therefore, molecular electronics is a multidisciplinary research field.
Successful transport experiments with MMMs [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17] confirm their significance as active elements of nanodevices. These include applications as rectifiers (molecular diodes), field effect transistors (molecular triodes) switches, memory elements and sensors. Also, these and other experiments emphasize the importance of thorough analysis of the physics underlying electron transport through molecular junctions. Detailed understanding of the electron transport at the molecular scale is a key step to device designing and controlling. Theory of electron transport through MMMs is being developed in the last two decades, and main transport mechanisms are currently elucidated in general terms. However, progress of experimental capabilities in the field of molecular electronics brings new theoretical challenges causing further development of the theory.
In practical molecular junctions the electron transport is always accompanied by nuclear motions in the environment. Accordingly, the MMM conduction is affected by the coupling between electronic and vibrational degrees of freedom. Nuclear motions underlie the interplay between the coherent electron tunneling through the junction and inelastic thermally assisted hopping transport [1]. Also, electron–phonon interactions may result in polaronic conduction [18], [19], [20], and they are directly related to the junction heating [21] and to some specific effects such as alterations in both shape of the molecule and its position with respect to the leads [22], [23]. At present, the research community becomes interested in studies of energy transfer through diverse nanodevices including MMMs [15], [17], [21]. These studies are very important for further development of nanoelectronics because functionalities and reliabilities of molecular devices crucially depend on their thermal properties. A combination of small heat capacity, which is typical for some molecules, with insufficient heat transfer to the ambience may cause significant heating of the device destroying its operation abilities. Also, thermal properties of molecules and metal–molecular junctions are of importance and interest for they significantly differ from thermal properties of bulk materials. Some specific effects such as thermopower and thermal conductance oscillations may appear in junctions including molecules and/or quantum dots.
When the coupling between the electrodes and the molecular linker is sufficiently strong, the effects of electron–phonon interactions may be manifested in the inelastic tunneling spectra (IETS), which present the second derivative of the current in the MMM versus the applied bias voltage [24], [25], [26]. The inelastic tunneling spectroscopy may be a valuable method for identification of molecular species within the conduction region, especially when employed in combination with scanning microscopy. However, one may remark that the theory suggested so far needs further development to ease its application to practical MMMs.
As well, transport characteristics of molecular junctions could show effects originating from electron–electron interactions, which give rise to such interesting quantum transport phenomena as Coulomb blockade and Kondo effect. Both suppression of the electron transport through molecular junctions at low values of the bias voltage occurring due to the charging energy in the molecule (Coulomb blockade) and the increase in the electrical conduction of the junction near zero bias voltage (Kondo effect) were observed in experiments on molecular and carbon junctions [2], [8], [27], [28], [29], [30], [31], [32], [33]. Theory of electron transport through MMMs and quantum dots taking into account electron–electron interactions on the dot is being developed during the last two decades (see e.g. Refs. [34], [35] and references therein). However, this theory is not completed so far, and it still meets with unresponded challenges.
Presently, significant attention of the research community is being given to studies of transport properties of magnetic molecules. Break-junction experiments and modeling of the electron tunneling through Mn12 complexes were reported [36]. The effect of spin blockade, when a molecule traps an electron and blocks the current because transitions out of the trapping state are forbidden due to the spin conservation rules is also being studied [36], [37]. Another interesting subject is the electron transport through molecular networks made out of metal nanoparticles linked by molecules [38], [39], [40], [41], [42]. These systems reveal significant potentialities for nanoelectronic applications. To properly study electron transport in the networks one may treat them as sets of MMM junctions, each including two metal clusters connected by a molecular linker. An important issue in these studies is the effect of the electron structure of the clusters (nanoelectrodes) which in this case cannot be ignored. Another important aspect is to develop an approach enabling to compute the network conductance taking into account its geometry, which is a nontrivial and currently unresolved task.
Being a very interesting research subject by itself, the studies of electron transport through molecules are equally important due to essential similarities between the latter and long range electron transfer chemical reactions, which are already studied for several decades. These reactions could be developed in donor–bridge–acceptor molecular systems. The donor is some molecule (reductant) or a part of a macromolecule, which donates an electron to the acceptor (oxidant) via the molecular bridge. The long range electron transfer plays an essential part in biological processes such as signal transduction across membranes, photosynthesis, enzyme catalysis and some other [43]. Historically, studies of the long range electron transfer strongly contributed to the “birth” of molecular electronics, which is often placed in 1974, when Aviram and Ratner first suggested to use a metal–donor–bridge–acceptor–metal system for current rectification [44]. Similarities between the electron transport through MMMs and long range electron transfer reactions were repeatedly emphasized in theoretical works (see e.g. [45], [46], [47], [48], [49], [50], [51], [52]). Thus the studies of electron transport through molecular junctions may bring new insight in the nature and characteristics of the long-range electron transfer reactions.
Molecular electronics is a diverse and rapidly growing field. Currently there exists a multitude of works reporting the results of both theoretical and experimental studies of transport properties of molecules and MMMs. The purpose of the present work is to give an overview of the main physical mechanisms controlling the transport and the main characteristics of the latter. As far as possible we avoid the detailed descriptions of computational formalisms commonly used to theoretically analyze electron transport through molecules as well as experimental techniques. These methods and formalisms are described elsewhere. In the first Chapter of this review we introduce basic concepts, which enter into a description of the electron transport through molecular junctions and briefly describe relevant experimental methods. In the next Chapter we describe theoretical methods commonly used to analyze the electron transport through molecules. The next three Chapters of the review contain a description of various effects manifested in the electron transport through MMMs as well as the basics of density-functional theory and its applications to electronic structure calculations in molecules. Some nanoelectronic applications of molecular junctions and similar systems are discussed in the last Chapter.
Section snippets
Conduction through a single molecule
We start our analysis of MMMs transport properties adopting an extremely simplified model for the junction. We consider the molecule (presented as a set of energy levels) placed in between two leads (left and right ). The leads are treated as free electron reservoirs with nearly continuous energy spectra. Currently, we omit from consideration electron–electron correlations (Coulomb interactions) and electron–phonon interactions. The effects of these interactions on the electron transport are
Electron transmission and Landauer expression for the current through a MMM junction
The standard approach to the elastic and phase coherent transport through metal–molecular junctions is suggested by the Landauer–Buttiker formalism [1]. This formalism was developed in the context of mesoscopic physics. Within this approach, the expression for the current through a phase coherent conductor connected to the electron reservoirs (source and drain) may be obtained if one calculates the total probability for an electron to travel between two electrodes at a certain tunnel energy
Charge transfer and electrostatic potential distribution in unbiased junctions
As it was briefly mentioned above, the contact of a molecule with the leads significantly changes some important properties of the molecule. The perturbation induced by the metal–molecule coupling initiates the response from the molecule. The response is determined by two most important electronic processes occurring in the MMM junction, namely: the charge transfer between the leads and the molecular linker and the changes in the spatial distribution of the electrostatic potential. These
Vibration-induced features in the electron conductance and current through MMM junction
Interaction of electrons with molecular vibrations is known to be an important source of inelastic contribution to the electron transport through molecules. Theoretical studies of vibrationally inelastic electron transport through molecules and other similar nanosystems (e.g. carbon nanotubes) were carried out over the past decade by a large number of authors [24], [25], [26], [98], [99], [100], [101], [102], [103], [104], [105], [106], [305], [306]. Also, manifestations of the electron–vibron
Basic equations of the density functional theory
First-principles electronic structure calculations are commonly recognized as the indispensable basis for studies of important observable properties in the variety of materials. These calculations are widely used in condensed matter physics and quantum chemistry, providing useful predictions for solids and solid surfaces nanostructures, molecules and atoms. Correspondingly, a great number of computational methods and approaches were developed to carry out the electron structure calculations.
Field effect transistors
It is a common knowledge that the first functioning transistor was invented in the late forties by Bardeen, Brattain and Shockley, and this invention had marked the starting point for the microelectronic revolution. The metal–oxide–silicon field effect transistors (MOSFETs) appeared in sixties, and they dominated the development of microelectronics in the following forty years. Computer industry and digital communication systems give two examples of MOSFET applications. One of the most
Concluding remarks
At present, the electron transport through molecule-scale systems is being intensively studied both theoretically and experimentally. Largely, unceasing efforts of the research community to further advance these studies are motivated by important application potentialities of single molecules as active elements of various nanodevices intended to compliment and/or to replace the silicon based electronics. Elucidation of physics underlying electron transport through molecules is necessary for
Acknowledgments
The authors are sincerely grateful to all colleagues with whom they collaborated during the years given to these studies. We thank G. M. Zimbovskiy for his help in preparation of the manuscript. This work was partly supported by NSF-DMR-PREM0353730.
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