Page 202 - MEMS Mechanical Sensors

8.2 Micromachined Accelerometer 191

suspending beams. In-plane accelerations cause the proof mass to tilt, and out-of-
plane acceleration moves the proof mass perpendicular to the wafer plane; this is
illustrated in Figure 8.16(b).
The effective spring constants for all three axes were designed to be the same,
and also the rate of change for the differential shift in capacitance of acceleration
along all three axes was equal; hence, uniform sensitivity was achieved for all axes.
The sensor suffered from relatively high cross-axes sensitivity from z-axis to x-axis
(10%) due to asymmetries in the beams of the suspension system. However, this
could be removed by an arithmetic operation, yielding a cross-axis sensitivity below
0.8%. The signal pick-off electronics are off-chip, and hence, the commercial device
based on this design would be a two-chip solution.
An example of a three-axis accelerometer with a modified piezoresistive pick-
off is described by Takao et al. [45, 46]. A bulk-micromachined proof mass is sus-
pended by four beams onto which sensing p-MOSFETs are integrated. They can be
used directly as piezoresistive stress-sensing elements because the carrier mobility in
the inversion layer of the transistor changes linearly with the induced stress. The
same devices are used as input transistors to a CMOS differential amplifier. The
modal response of the proof to acceleration along three axes is similar to the capaci-
tive device described above. Optimizing the placement of the sensing MOSFETs
results only in a differential output voltage for acceleration along one particular
axis; cross-axis accelerations are common mode signals and are cancelled out.
Three axial accelerometers with a single proof mass are still in the prototype
stage and have not been commercialized; however, this is expected to happen in the
near future. Analog Devices offers a commercial dual-axis accelerometer, which is
described later.

8.2.2.7 Other Position Measuring Methods
A range of other position measuring methods have been reported, but none of them
has gained major importance so far. Optical means of detecting the proof mass posi-
tion have the advantage of being insensitive to electromagnetic interference and not
requiring electrical power directly at the proof mass. A drawback is that an optical
fiber has to be brought into close proximity of the proof mass, which requires hand
assembly, thereby negating the advantage of batch-fabrication. Schröpfer et al. [47]
reports on an accelerometer with optical read-out; the optical fiber and the vertical
sidewall of the sensing element, from which the light is reflected, form a simple
Fabry-Perot interferometer with an optical cavity size between 45 and 135 µm. Any
in-plane movement of the proof mass results in a wavelength shift that modulates
the spectrum; the highest reported sensitivity, in terms of wavelength change per
acceleration, was 462 nm/G.
Other researchers use a simple red LED and a PIN photodetector to measure the
motion of the proof mass [48]. The proof mass consists of a grid structure with a
pitch of 40 µm, 22-µm-wide beams, and 18-µm-wide slots. It acts as an optical shut-
ter that modulates the flux of incident light from the LED to the detector, resulting
in a proportional change of photodiode current.
The only class of accelerometer that does not rely on the displacement measure-
ment of a mechanical proof mass is that of thermal devices. They work by heating up