Page 199 - MEMS Mechanical Sensors

188 Inertial Sensors

string. The main advantage of this approach is that a frequency output can be con-
verted easily into a digital format by using a frequency counter and is, in general,
more immune to noise.
A high resonant frequency is desirable to achieve a good sensitivity, which is in
terms of change of frequency per acceleration (∆f/G). Consequently the resonator
should have a high nominal frequency and hence be made of beams with small geo-
metries, which lends itself to fabricating them in surface-micromachining technol-
ogy. Furthermore, to achieve a high quality factor, the resonator should ideally be
sealed in vacuum.
A resonant silicon accelerometer combining bulk and surface micromachining
was presented by Burns et al. [38]. It consists of three wafers bonded together.
The middle wafer contains the proof mass, which has the thickness of the full
wafer. It is formed, together with the flexures, by a wet etching process. Prior to
these bulk-micromachining process steps, the resonators are fabricated by surface
micromachining. They consist of two beams of 200-µm length, 40-µm length, and
2-µm thickness. The beams are electrostatically excited to vibrate out of the wafer
plane and have a base frequency of 500 kHz. They are located on the flexures at
points where the highest stress occurs when the proof mass moves. As they are inside
a vacuum enclosure, the air-damping is minimized, thereby resulting in a quality fac-
tor in excess of 20,000. Thus, ac voltages, in the range of only a few millivolts, are
required to sustain the resonance. An additional dc bias voltage of 5V is required.
Implanted piezoresistors are used to sense the resonance frequency. Two resonators
are placed in such a way that the resonance frequency increases for one of them
under applied acceleration, whereas the frequency of the other decreases, resulting
in a differential output signal, which rejects common mode errors. A third resonator
is used for temperature sensing, which can be used for compensating temperature
drift effects. Accelerometers for ranges of ±10G, ±20G, and ±50G have been fabri-
cated and tested. The scale factor of the ±20G device was as high as 743 Hz/G with
a temperature frequency shift of about 45 ppm/°C.
A fully integrated, surface-micromachined resonant accelerometer was reported
by Roessig et al. [39]. The nominal frequency of the double-ended tuning fork reso-
nator was 68 kHz, and the scale factor of the sensor was measured to be 45 Hz/G.
The resonator beams had comb drives attached to sense their motion via a capaci-
tance change and to excite them into resonance using electrostatic forces. This is
achieved by incorporating them into an oscillation loop. The coupling of the
mechanical force caused by motion of the proof mass into the resonators was
achieved by a novel mechanical leverage system that amplifies the force.
A range of other resonant devices has been reported in the literature. For further
information, the reader is referred to [40, 41].

8.2.2.6 Multiaxis Accelerometers

A relatively recent innovation for micromachined accelerometers is sensors that are
capable of measuring acceleration along two or three axes simultaneously. This is of
interest for many applications, for example, inertial sensing, virtual reality, and
medical applications. Although it is possible to mount three single-axis devices per-
pendicular to each other, an integrated version has advantages in cost, size, and