Understanding nanoscale conductors

Summary form only given. It is common to differentiate between two ways of building a nanodevice: a top-down approach where we start from something big and chisel out what we want and a bottom-up approach where we start from something small like atoms or molecules and assemble what we want. When it comes to describing electrical resistance, the standard approach could be called a "top-down" one where we start from large complex resistors and work our way down to molecules primarily because our understanding has evolved in this top-down fashion. However, it is instructive to take a bottom-up view of the subject starting from the conductance of something really small, like a molecule, and then discussing the issues that arise as we move to bigger conductors. This is the subject of this tutorial lecture (S. Datta, Nanotechnology, vol. 15, p. S433, 2004). Remarkably enough, no serious quantum mechanics is needed to understand electrical conduction through something really small, except for unusual things like the Kondo effect that are seen only for a special range of parameters. The presentation begins with (1) energy level diagrams, (2) shows that the broadening that accompanies coupling limits the conductance to a maximum of (q 2/h) per level, (3) describes how a change in the shape of the self-consistent potential profile can turn a symmetric current-voltage characteristic into a rectifying one, (4) shows that many interesting effects in "nanoelectronics" can be understood in terms of a simple model, and (5) introduces the nonequilibrium Green\´s function (NEGF) formalism as a sophisticated version of this simple model with ordinary numbers replaced by appropriate matrices. Finally the distinction between the self-consistent field regime and the Coulomb blockade regime and the issues involved in modeling each of these regimes are described.