Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2002-08-08
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
32 pages, 22 figures. Chapter to be published (2002) in the "Handbook of Nanoscience, Engineering and Technology" by CRC Press
Scientific paper
In recent years, several experimental groups have reported measurements of the current-voltage (I-V) characteristics of individual or small numbers of molecules. Our purpose in this chapter is to provide an intuitive explanation for the observed I-V characteristics using simple models to illustrate the basic physics. In contrast to the MOSFET, whose I-V is largely dominated by classical electrostatics, the I-V characteristics of molecules is determined by a more interesting interplay between nineteenth century physics (electrostatics) and twentieth century physics (quantum transport) and it is important to do justice to both aspects. We start with a qualitative discussion of the main factors affecting the I-V characteristics of molecular conductors, using a simple toy model to illustrate their role. Including the effects of: (1) Shift in the energy level due to charging effects and (2) broadening of the energy levels due to the coupling to the two contacts we obtain realistic I-V plots, even though the toy model assumes that conduction takes place independently through individual molecular levels. In general, however, the full non-equilibrium Green's function (NEGF) formalism is needed. Here, we describe the NEGF formalism as a generalized version of the one-level model. This formalism provides a convenient framework for describing quantum transport and can be used in conjunction with ab initio or semi-empirical Hamiltonians. A simple semi-empirical model for a gold wire serves to illustrate the full NEGF formalism. This example is particularly instructive because it shows the lowest possible "Resistance of a 'Molecule'" per channel.
Datta Supriyo
Paulsson Magnus
Zahid Ferdows
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