Nanoscale device modeling: the Green's function method

The non-equilibrium Green's function (NEGF) formalism provides a sound conceptual basis for the devlopment of atomic-level quantum mechanical simulators that will be needed for nanoscale devices of the future. However, this formalism is based on concepts that are unfamiliar to most device physicists and chemists and as such remains relatively obscure. In this paper we try to achieve two objectives: (1) explain the central concepts that define the 'language' of quantum transport, and (2) illustrate the NEGF formalism with simple examples that interested readers can easily duplicate on their PCs. These examples all involve a short n^{+ +}- n⁺- n^{+ +}resistor whose physics is easily understood. However, the basic formulation is quite general and can even be applied to something as different as a nanotube or a molecular wire, once a suitable Hamiltonian has been identified. These examples also underscore the importance of performing self-consistent calculations that include the Poisson equation. The I-V characteristics of nanoscale structures is determined by an interesting interplay between twentieth century physics (quantum transport) and nineteenth century physics (electrostatics) and there is a tendency to emphasize one or the other depending on one's background. However, it is important to do justice to both aspects in order to derive real insights.