Page 170 - Principles and Applications of NanoMEMS Physics

158 Chapter 4

F = ¦ 2 2 m 2 ­ 4 (E F − E n c ) 3 / 2 − 2 (E F − E n c ) 1 / 2 E n c ½ , (3)
®
¾
n π = ¯ 3 ¿
c
where E is the Fermi energy, m the electron mass, and E is the energy of
F n
the transverse modes. This force manifests as force and beam deflection
fluctuations. On the other hand, if the beam is not electrostatically actuated,
but a magnetic field is applied along its length, it will also cause
conductance changes as the Landau levels [60] push the energy above the
Fermi level. Thus, the beam is magnetomechanically actuated. This devices
has the potential to exploit charge discreteness effect.

4.2.2.2.6 Systems—Functional Arrays

The dynamic properties of the collective modes in a MEMS resonator
array were studied experimentally by Buks and Roukes [183], and
theoretically by Lifshitz and Cross [184]. In this concept, the lateral
electrostatic coupling of an array of doubly-anchored beams leads to
collective modes that resemble phonons. Adjustment of the coupling serves
to tune the diffraction properties of the mechanical lattice the array
embodies. In a related concept, De Los Santos [185] unveiled the idea of
populating a rigid photonic band-gap crystal lattice with a sub-array of
MEMS switches. Then, by exploiting the noninvasive properties of these,
i.e., their ideal ON/OFF states, localized states modes could be formed that
enabled the ON/OFF switching of pass bands within the photonic band-gap,
thus making the system programmable.

4.2.2.2.7 Noise—Quantum Squeezing

Ultimately, the purity of resonator vibration is determined by its zero-
point fluctuations. In this context, quantum squeezing techniques [186] may
be applied to reduce the fluctuations in flexural motion. Application of
quantum squeezing to mechanical resonators has been studied theoretically
by Blencowe and Wybourne [187]. Accordingly, by exciting the resonator
with a pumping voltage of the form, V () =Vt cos (ω t + ) φ , its spring
p 0 p
constant becomes, k = mω 2 + ∆ k , where ∆ k = C V 2 2g , and
2
0 0 0 0 0
k p () ∆= kt cos ( ω t + ) φ 2 . When the effective resonator spring constant,
2
p
k = k + k () t , increases, the curvature of the effective potential narrows
0 p
[187] and this squeezes the wavefunction. In particular, for a phase
φ = − π 4 , the quantum uncertainty in the flexural displacement becomes,