Online proceedings - EDA Publishing Association

measured may be reduced to several nano-ampere even
pico-ampere. In general, it is difficult to measure and acquire
such small amplitude of displacement current. Therefore, a
100 kHz sine waveform signal has been designed to carry the
lower frequency signal through the coupling capacitor.
Although, the displacement current obtained from the
capacitor has low frequency and high frequency components,
the lock-in amplifier added here can extract the low frequency
signal that are needed for our measurement from the mixed
signal with a 100kHz reference signal. Capacitance of the
coupling capacitor can be easily determined through the
comparison of the other reference capacitor that has a known
capacitance. The other capacitor also has a 100kHz bias signal,
but has 180 degree phase off with another 100kHz sine wave.
The schematic of the measurement tool is shown in Fig.5. Fig.
5 (a) shows 3-D diagram and (b) shows the cross-section view
of entire system with details in each part. This capacitance
measurement was controlled using Labview software and a PC.
The electrical circuit design of entire capacitance
measurement is shown in Fig.6.
11-13 May 2011, Aix-en-Provence, France
Fig. 6. Schematic of measurement signal circuit design
During the experiment, a step voltage was provided on the
bottom electrode. The sensing device started vibration after
sudden turned off the deflection voltage. The dynamic response
of the sensing device will be recorded continuously until the
sensing beam gets back to its balance position. The amplitude
of vibration will be reduced with time because of the air
damping due to the gaseous atoms.
IV. RESULTS AND DISCUSSION
Fig. 7 shows the results of one particular experiment tested
at the low vacuum (1.6 x 10 -2 torr). The figure shows the proof
mass position was slight decreased from its maximum value at
the beginning. The maximum value of each cycle can be fitted
using an exponential decay function defined as (1). Decay rate
of the entire damping behavior can be calculated using (2).
)( ⋅= (1) , δ ( ) (2)
0
⋅− t
eAta
δ = ln / aa
nn
+ 1
In Fig. 7, the free decay response of the beam vibrated at the
low vacuum has a decay time constant in 3.05 second. Not
only the vacuum pressure would affect the decay time constant
in the dynamic behavior of the sensing beam but also the
intrinsic property in its material. Silicon is one of the low loss
materials which can be used to avoid the decay time constant
influenced by the variation of intrinsic material properties.
Fig. 5. Schematic view of measurement apparatus (a) 3D view
(b) cross-section view
Fig. 7. Sample free damping decay versus time at 10 -2 torr
Here we carried out a series of experiments at the different
vacuum pressures. Vacuum pressure can be adjusted form the
lowest pressure to the nearly atmosphere. The decay time
constant obtained here shows a significant difference between
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