Electron movement within and between molecules--that is, electron transfer--is important in many chemical, electrochemical, and biological processes. Recent advances, particularly in scanning electrochemical microscopy (SECM), scanning-tunneling microscopy (STM), and atomic force microscopy (AFM), permit the study of electron movement within single molecules. In this Account, we describe electron transport at the single-molecule level. We begin by examining the distinction between electron transport (from semiconductor physics) and electron transfer (a more general term referring to electron movement between donor and acceptor). The relation between these phenomena allows us to apply our understanding of single-molecule electron transport between electrodes to a broad range of other electron transfer processes. Electron transport is most efficient when the electron transmission probability via a molecule reaches 100%; the corresponding conductance is then 2e(2)/h (e is the charge of the electron and h is the Planck constant). This ideal conduction has been observed in a single metal atom and a string of metal atoms connected between two electrodes. However, the conductance of a molecule connected to two electrodes is often orders of magnitude less than the ideal and strongly depends on both the intrinsic properties of the molecule and its local environment. Molecular length, means of coupling to the electrodes, the presence of conjugated double bonds, and the inclusion of possible redox centers (for example, ferrocene) within the molecular wire have a pronounced effect on the conductance. This complex behavior is responsible for diverse chemical and biological phenomena and is potentially useful for device applications. Polycyclic aromatic hydrocarbons (PAHs) afford unique insight into electron transport in single molecules. The simplest one, benzene, has a conductance much less than 2e(2)/h due to its large LUMO-HOMO gap. At the other end of the spectrum, graphene sheets and carbon nanotubes--consisting of infinite numbers of aromatic rings--have small or even zero energy gaps between the conduction and valence bands. Between these two limits are intermediate molecules with rich properties, such as perylene derivatives made of seven aromatic rings; the properties of these types of molecules have yet to be fully explored. Studying PAHs is important not only in answering fundamental questions about electron transport but also in the ongoing quest for molecular-scale electronic devices. This line of research also helps bridge the gap between electron transfer phenomena in small redox molecules and electron transport properties in nanostructures.

We have carried out Hall measurement on back-gated graphene field effect transistors (FET) with and without a top dielectric medium. The gate efficiency increases by up to 2 orders of magnitude in the presence of a high κ top dielectric medium, but the mobility does not change significantly. Our measurement further shows that the back-gate capacitance is enhanced dramatically by the top dielectric medium, and the enhancement increases with the size of the top dielectric medium. Our work strongly suggests that the previously reported top dielectric medium-induced charge transport properties of graphene FETs are possibly due to the increase of gate capacitance, rather than enhancement of carrier mobility.

Graphene is a novel new material with an unusual zero-gap band structure, where electrons and holes are closely connected through a relativistic Dirac equation. It is of interest to study the various scattering mechanisms and the transport through device structures fabricated on this new material. Here, we use Rode's method to study the transport through gated graphene devices. The results are compared with recent results obtained for both back-gates and electrochemical gates. The transport is dominated by the trapped charge at the graphene-SiO 2 , but phonon scattering is shown to be important.