500 CHAPTER 10. COHERENT TRANSPORT AND MESOSCOPIC DEVICES
10.5 MESOSCOPICSTRUCTURES..........................
In mesoscopic structures single electron effects arising from phase coherence or from charge
quantization become important. The structures are so small that density of states is not a con-
tinuous function but has discreteness to it. As a result mesoscopic structures show a number of
interesting transport effects.
10.5.1 Conductance Fluctuations and Coherent Transport ............
In very small structures electron waves can flow from one contact to another maintaining phase
coherence. Additionally the structures are so small that the change in electron number by unity
creates observable effects. In structures that are∼100–500A this occurs at low temperatures, ̊
since at high temperatures the random scattering due to phonons removes the coherence in the
transport process. A dramatic manifestation of the phase coherence is the fluctuation seen in
conductivity of mesoscopic structures as a function of magnetic field, electron concentration,
etc.
The origin of the fluctuations can be understood on the basis of Landauer formalism which
allows one to study transport in terms of the scattering processes directly. For simplicity consider
a one-dimensional system with scattering centers. Each of these scatterers is characterized in
terms of a transfer matrix which describes what fraction of the incident electron is “reflected”
after scattering and what fraction is transmitted. The scatterer is described by the reflection and
transmission coefficients shown in figure 10.9. The reflection and transmission coefficients are
RandTfor an incident wave from the left or right. We will provide a simple formulation to
understand the origin of conductance fluctuations in mesoscopic structures. We assume a one
dimensional flow of charge from one contact to another. This allows us to use 1-dimensional
density of states to describe carrier density changes.
X
S
a
b
d
c
Mesoscopic system transport
Figure 10.9: Transport in a mesoscopic structure. A schematic showing the effect of the scatter-
ing center S on electron wavesaandcincident from the left and right respectively. The wavesb
anddemerge as a result of reflection and transmission.