Chapter 10
COHERENT TRANSPORT AND
MESOSCOPIC DEVICES
10.1INTRODUCTION .................................
In quantum mechanics electrons are waves (or wavepackets) which have a discrete charge
(1.6× 10 −^19 C), amplitude and phase and have a spin ( 1 / 2 ). Yet none of the electronic devices
we have considered explicitly use these features. Conventional electronic devices do not use
the wave nature of electrons (e.g interference effects are not used), nor is the discrete nature of
electron charge reflected in the current or conductance. The spin of electrons is also not directly
used in diodes or transistors. There are several reasons for this. The devices are large so that
scattering effects dominate and electron phase information is lost. Also the number of electrons
is very large (say in billions or more) so that the discrete nature of electron charge is unimportant.
Finally in traditional semiconductors there is no simple way to distinguish electron spin.
Charge transport in devices discussed so far is described within Born approximation or the
Fermi golden rule. This involves free flight and scattering processes. While such an approach
is quite relevant to modern microelectronic devices there are a number of important issues that
are not described by this approach. These issues relate to the wave nature of the electrons, the
discrete nature of charge in current flow and the spin of electrons. As semiconductor devices
evolve and shrink, these issues are becoming increasingly important. In this chapter we will
discuss some transport issues and devices that come into prominence as devices become smaller
and smaller. In particular we will discuss devices that exploit electron phase, discrete electron
charge and electron spin.
Let us recall how scattering is influenced by crystal quality and device dimensions. In fig-
ure 10.1 we show several types of structural properties of materials. In figure 10.1a we show a
perfect crystal where there are no sources of scattering. Of course, in a real material we have
phonon related fluctuations even in a perfect material. However, for short times or at very low
temperatures it is possible to consider a material with no scattering. There are several types of
transport that are of interest when there is no scattering: i) ballistic transport, where electrons