Page 165 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 153

Casimir effect-based oscillator, a magnetomechanically actuated beam, and
array-based functions. We conclude with an example of exploiting quantum
squeezing to reduce noise in mechanical structures.

4.2.2.2.1 Charge Detector

This device was experimentally demonstrated by Krömmer et al. 176]. In
this device a low-power RF signal propagates through a suspended
resonator, Figure 4-3, and sets it into vibration.

TOP VIEW
TOP VIEW
END VIEW
END VIEW
Resonator
Resonator
w w
RF Signal
RF Signal
Gate
Gate
SIDE VIEW
SIDE VIEW
G G
B B g g 0 0

L L
Substrate
Substrate
Transmission Lines
Transmission Lines
Figure 4-3. Schematic of charge detection resonator system [22].

With an in-plane magnetic field applied perpendicular to beam, a Lorentz
force perpendicular to the substrate surface is developed. Application of a
voltage, V, between the gate and the beam, induces a charge, Q, on the beam
via the relation, Q = CV , and essentially, modifies its stiffness (spring
constant). This results in a mechanical resonance frequency shift of

¨ −
f δ = Q 2 § 1 C ′ ′z 2 ·
¸ , where C is the gate-beam coupling capacitance, and
2 C ¨ 2 C ¸
¹
©
C ′′ represents the second derivative of the capacitance with respect to beam
elongation amplitude, z(t), evaluated at z=0. Optimum charge detection
(maximum frequency shift) is obtained when RF power drives the beam to
the verge of nonlinear amplitude vibration. For a gate bias of V = ± 4 V , a
magnetic field of 12T, and an RF power of -52.8dBm at 37.29MHz, a charge