Page 92 - Principles and Applications of NanoMEMS Physics

80 Chapter 3

Then, depending on the particular device structure, behavior such as
interference, diffraction, etc., characteristic of waves, or Coulomb
interaction, characteristic of particles, may be prominent. The various types
of behavior are presented next.

3.1.1 Quantization of Electrical Conductance

The concept of electrical conductance quantization emerges from
considering electron transport in short, narrow (quantum) wires, Figure 3-2.

E E E E
F2
F1
F1 F2
d d
e e

V V
+ -
+ -

Figure 3-2. Electron transport down short, narrow wire between electron reservoirs with
Fermi levels E and E , under the influence of applied voltage V.
F 1 F 2
Here we have a short, narrow wire connected between two electron
reservoirs characterized by Fermi seas (contacts) filled up to energy levels
E and E , Under the influence of an applied voltage V, which misaligns
F 1 F 2
the Fermi levels, electrons travel from reservoir E towards reservoir E F 2 ,
1
F
in an effort to equalize the Fermi levels and, as a result, establish a current.
Since the wire is very short, transport evolves without scattering, i.e.,
ballistically. However, since the wire is very narrow, the uncertainty
principle forces its transverse momentum (and consequently, its energy) to
be quantized, i.e., p ~ n= d , where n is an integer representing the band
⊥
in which transport is occurring.

3.1.1.1 Landauer Formula

The question before us is: What is the conductance of this system? The
answer was determined by Landauer [113], and may be arrived at as follows
[76]. The current is the balance between the number of electrons being
launched from the left-hand reservoir into the wire, and the number of
electrons being launched from the right-hand reservoir into the wire. In