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5.5 Resonant Techniques 99

The excitation and detection of resonance in silicon microresonators are not so
straightforward because silicon is not intrinsically piezoelectric. Other mechanisms
must therefore be fabricated on or adjacent to the resonator structure. There are
many suitable mechanisms and these are all based on the sensing and actuating prin-
ciples described in this chapter. For example, the resonators vibrations can be
electrostatically excited and detected using implanted piezoresistors. Since the
implanted piezoresistors could be used directly to measure the strain in the sensing
structure, the added complexity of a resonant approach is only justifiable in high-
performance sensing applications.
The various excitation and detection mechanisms used with silicon resonators
are summarized in Table 5.4. Many of the mechanisms listed can be used to both
excite and detect a resonator’s vibrations, either simultaneously or in conjunction
with another mechanism. Devices where a single element combines the excitation
and detection of the vibrations in the structure are termed one-port resonators.
Those that use separate elements are termed two-port resonators.
The suitability of these mechanisms for driving or detecting a resonator’s
vibrations depends upon a number of factors: the magnitude of the drive forces gen-
erated, the coupling factor (or drive efficiency), sensitivity of the detection mecha-
nism, the effects of the chosen mechanism upon the performance and behavior of
the resonator, and practical considerations pertaining to the fabrication of the reso-
nator and the sensors final environment.

5.5.2 Resonator Design Characteristics
5.5.2.1 Q-Factor
As a structure approaches resonance, the amplitude of its vibration will increase, its
resonant frequency being defined as the point of maximum amplitude. The magni-
tude of this amplitude will ultimately be limited by the damping effects acting on the
system. The level of damping present in a system can be defined by its quality factor
(Q-factor). The Q-factor is a ratio of the total energy stored in the system (E )tothe
M
energy lost per cycle (E ) due to the damping effects present:
C
 E 
Q =2π  M  (5.20)
 E 
C
A high Q-factor indicates a pronounced resonance easily distinguishable from
nonresonant vibrations, as illustrated in Figure 5.10. Increasing the sharpness of the
resonance enables the resonant frequency to be more clearly defined and will
improve the performance and resolution of the resonator. It will also simplify the
operating electronics since the magnitude of the signal from the vibration detection

Table 5.4 Summary of Excitation and Detection Mechanisms
Piezoelectric Piezoelectric
Magnetic Magnetic
Electrothermal Piezoresistive
Optothermal Optical
Source: [8].