  We aim to provide engineers with an introduction to the non-equilibrium
Green's function (NEGF) approach, which provides a powerful conceptual tool and
a practical analysis method to treat small electronic devices quantum
mechanically and atomistically. We first review the basis for the traditional,
semiclassical description of carriers that has served device engineers for more
than 50 years. We then describe why this traditional approach loses validity at
the nanoscale. Next, we describe semiclassical ballistic transport and the
Landauer-Buttiker approach to phase coherent quantum transport. Realistic
devices include interactions that break quantum mechanical phase and also cause
energy relaxation. As a result, transport in nanodevices are between diffusive
and phase coherent. We introduce the non equilbrium Green's function (NEGF)
approach, which can be used to model devices all the way from ballistic to
diffusive limits. This is followed by a summary of equations that are used to
model a large class of layered structures such as nanotransistors, carbon
nanotubes and nanowires. An application of the NEGF method in the ballistic and
scattering limits to silicon nanotransistors is discussed.
