Page 71 - Principles and Applications of NanoMEMS Physics

58 Chapter 2

In general, the tunneling rate will depend on the number of available (empty)
states within the QD. If Γ is the tunneling rate into level f in the QD, g is
f f
the degeneracy factor, m is the number of electrons already occupying the
f
level, and () 1F ε = (1 + exp ( kε T )) is the Fermi function, then the total
B
tunneling rate is given by,

Γ FS = ¦ Γ ( ⋅ g − m ) (εF QD − ∆ ), (40)
QD f f f f
f

where the initial and final electron energies are related by, ε FS = ε QD − ∆ ,
i f
ε FS being the initial electron energy [232], [233]. Notice that, at small bias
i
voltages, the occupancy of QD states precludes tunneling due to Coulomb
blockade.

2.2.4 Quantized Electrostatic Actuation
In contrast to conventional electrostatically-actuated MEM devices,
which exhibit continuous displacement versus bias behavior prior to pull-in,
the advent of precision nanoelectromechanical fabrication technology [72]
and carbon nanotube synthesis [17] has enabled access to beams with
dimensional features (gaps, lengths, widths, and thicknesses) of the order of
several hundred nanometers in which conditions for the manifestation of
charge discreteness become also evident. In fact, recent [73] theoretical
studies of suspended (doubly anchored/clamped) carbon nanotubes (CNTs)
in which Coulomb blockade dominates current transport have predicted that
charge quantization in the CNTs will result in quantization of their
displacement.
Specifically, Sapmaz, et al. [73] considered a single-wall nanotube
(SWNT) modeled as a rod of radius r, and length L, and separated by a gap
g over a bottom electrode, Fig. 2-9.
0

L L
z z
V V Tunnel
Tunnel
g g
0 0
x x

V V G G
Figure 2-9. Schematic of suspended CNT as doubly anchored beam.