Page 169 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 157

z ϕ ϕ + + V V
b b z - -

Piezo Stage
Piezo Stage
(a)
Angular Amplitude Angular Amplitude D ec r ea sin g o scilla to r -sp h er e s e p a r a tio
D ec r ea sin g o scilla to r -sp h er e s e p a r a tio n n

F req ue ncy R es pons
F req ue ncy R es ponse e
(b)
Figure 4-7. Schematic of torsional MEMS oscillator and sketch of Casimir effect on
resonance response [22].
However, as the sphere-oscillator distance was decreased, in particular, at
141nm, 116.5nm, and 98nm, the resonance frequency shifted, according to,
ω = ω [ 1 b− 2 F () 2 ωIz ′ 2 ], where F ′ () z is the first derivative of the
1 0 0
external force evaluated at z, and the angular amplitude frequency response
asymmetric and hysteretic. This behavior was shown to be consistent with
the dynamics of a mass-spring-Casimir force system. The ramifications of
this beautiful experiment are enormous, in particular, it may be concluded
that the Casimir force will be one of the factors limiting the integration level
or density of NEMX.

4.2.2.2.5 Magnetomechanically Actuated Beams

This idea was proposed and theoretically analyzed by Blom [182]. In
addition to their function as mechanical elements (actuators), narrow metal-
coated nanoscale beams also embody mesoscopic wires. If such a beam is
elongated due to, say, electrostatic actuation, this results in a reduction in its
cross-sectional area, and in particular, that of the current-carrying
metallization/wire, and as a consequence, the conductance of the latter
changes as transverse quantized modes are pushed above the Fermi level.
The change in thermodynamic potential as the wire elongates, in turn
produces a force along the length of the wire, which is given by,