Current and Charge Control in Molecular Transistors

In a simple, conceptual model for a molecular transistor\footnote{ P.M. Solomon and C.R. Kagan, ``Understanding the Molecular Transistors,'' in \textit{Future Trends In Microelectronics-The Nano Millenium}, Luryi, Zaslavsky, Xu (Eds.), Wiley Interscience, New York, 2004.} current and charge control mechanisms analogous to that of a conventional ballistic field effect transistor were assumed, where the molecular levels are translated with respect to source and drain Fermi levels by the self-consistent potential in the center of the molecule resulting from the gate, source and drain voltages and the internal `space' charge. It was also shown that a single resonant level is inadequate for achieving a large on-off ratio concomitant with high performance, leading to the concept of using molecules to design an electronic filter. The assumptions of this model were tested by the present authors using a model `biphenyl' molecular transistor, and self-consistently solving Schr\"{o}dinger's and Poisson's equations within the density-functional formalism\footnote{ N. D. Lang, Phys. Rev. B \textbf{2001}, 64, 235121.}. While some gross features of the simple model were preserved, other types of behavior were completely unexpected, such as the observation of non-monotonic potential progression with a monotonically increasing gate voltage. In contrast to the simple model, polarization of levels well below the Fermi level dominated the charge control. This new, complex and interesting behavior will be discussed along with its bearing on the molecular transistor as a logic element.