Page 196 - MEMS Mechanical Sensors

8.2 Micromachined Accelerometer 185

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Assuming typical values for such a sensor of a proof mass m = 0.1 10 kg, a
resonant frequency of f = 10 kHz, and a nominal capacitance of 100 fF, the result-
R
ing static displacement for 1 mG is only 0.025Å and the resulting differential capaci-
tance is about 10 attofarads. Measuring such tiny deflections and capacitances can
only be achieved with reasonable performance by on-chip electronics.
These sensors have typical performance figures of a resolution below 0.1 mG in
a bandwidth of about 100 Hz. Their performance is primarily limited by the
Brownian noise from the proof mass as it is usually an order of magnitude smaller
than that of bulk-micromachined devices. If the sensing element is packaged at a
lower pressure, it is possible to reduce the Brownian noise floor considerably, at the
expense of a more complex fabrication and packaging processes. The choice of con-
trol system is exactly the same as for bulk-micromachined sensors, open loop opera-
tion, or closed loop force-feedback. Examples of open loop devices are described in
[27, 28], and examples of sensors using an analog force-feedback system are given
in [29, 30]. Digital closed loop sensors are reported mainly by researchers from the
University of California at Berkeley [31] with an excellent overview given in [32]. A
more detailed example of such an accelerometer is given in Section 2.2.6.
One of the highest performance capacitive accelerometers created was developed
by Yazdi and Najafi [33]. It uses a combination of bulk and surface micromachining
that allows the fabrication of the sensing element on a single wafer, thereby avoiding
the need to bond several wafers together, but nevertheless having the advantage of a
wafer-thick proof mass. The latter is compliant to acceleration in the z-direction and
moves between electrodes fabricated from polysilicon, which was deposited on a
thin sacrificial silicon dioxide layer on the top and bottom wafer surface. These poly-
silicon electrodes are very thin (2 to 3 µm) but have an area of several square
millimeters, and hence needed to be stiffened. This was achieved by etching 25- to
35-µm-wide vertical trenches into the wafers, which were refilled with polysilicon.
The holes in the polysilicon electrodes lower the squeeze film damping effect, so that
a design with critical damping is possible. Low cross-axis sensitivity of the sensor
was achieved by a fully symmetrical suspension system consisting of eight beams,
two on each side of the proof mass. The sensing element is shown in Figure 8.11.
This results in a high-precision accelerometer with a measured sensitivity of 2–
19.4 pF/G for a proof mass area of 2 × 1 mm and 4 × 1 mm, respectively. The
reported noise floor was around 0.2 µG/√Hz. The sensor was again incorporated in
a sigma-delta modulator control system to electrostatically force-balance the proof
mass.

8.2.2.3 Piezoelectric Accelerometers

Macroscopic accelerometers quite commonly use piezoelectric materials for the
detection of the proof mass. There has been a range of micromachined accelerome-
ters reported that are based on this principle. The advantage is the higher bandwidth
of these sensors, which can easily reach several tens of kilohertz. The major draw-
back, however, is that they do not respond to static and low-frequency acceleration
signals because of unavoidable charge leakage. An early device was reported by
Chen et al. [34], which consisted of a cantilever beam onto which the piezoelectric
material, ZnO, was sputtered. Interestingly, this sensor has integrated, simple