Page 134 - An Introduction to Microelectromechanical Systems Engineering

Sensors and Analysis Systems 113

coupled system has two resonant frequencies: in phase, and out of phase. In the in-
phase oscillation mode, the instantaneous displacements of the two masses are in
the same direction. In the out-of-phase mode, the masses are moving, at any
instant, in opposite directions. A careful selection of the coupling spring provides
sufficient separation between the in-phase and out-of-phase resonant frequencies.
Lorentz forces generated by an electric current loop within a permanent mag-
netic field excite only the out-of-phase mode. The oscillation electromagnetically
induces a voltage in a second current loop that provides a feedback signal propor-
tional to the velocity of the masses. The resulting Coriolis forces on the two masses
are in opposite directions but orthogonal to the direction of oscillation. Two poly-
silicon surface-micromachined accelerometers with capacitive comb structures
(similar in their basic operation to the ADXL family of sensors) measure the Corio-
lis accelerations for each of the masses. The difference between the two accelera-
tions is a direct measure of the angular yaw rate, whereas their sum is proportional
to the linear acceleration along the accelerometer’s sensitive axis. Electronic cir-
cuits perform the addition and subtraction functions to filter out the linear accel-
eration signal.
For the Bosch sensor, the out-of-phase resonant frequency is 2 kHz, and the
maximum oscillation amplitude at this frequency is 50 µm. The measured quality
factor of the oscillator at atmospheric pressure is 1,200, sufficiently large to excite
resonance with small Lorentz forces. The stimulated oscillation subjects the masses
to large accelerations reaching approximately 800G. Though they are theoretically
perpendicular to the sensitive axis of the accelerometers, in practice, some coupling
remains, which threatens the signal integrity. However, because the two temporal
signals are in phase quadrature, adopting synchronous demodulation methods
allows the circuits to filter the spurious coupled signal with a rejection ratio exceed-
ing 78 dB. This is indeed a large rejection ratio but insufficient to meet the require-
ments of inertial navigation.
The peak Coriolis acceleration for a yaw rate of 100º/s is only 200 mG. This
requires extremely sensitive accelerometers with compliant springs. The small
Coriolis acceleration further emphasizes the need for perfect orthogonality between
the sense and excitation axes. Closed-loop position feedback of the acceleration
sense element compensates for the mechanical poles and increases the bandwidth of
the accelerometers to over 10 kHz.
The fabrication process simultaneously encompasses bulk and surface
micromachining: the former to define the masses and the latter to form the
comb-like accelerometers (see Figure 4.28). The process sequence begins by depos-
iting a 2.5-µm layer of silicon dioxide on a silicon substrate. Epitaxy over the oxide
layer grows a 12-µm-thick layer of heavily doped n-type polysilicon. This layer
forms the basis for the surface-micromachined sensors and is polycrystalline
because of the lack of a seed crystal during epitaxial growth. In the next step, alu-
minum is deposited by sputtering and patterned to form electrical interconnects
and bond pads. Timed etching from the back side using potassium hydroxide thins
the central portion of the wafer to 50 µm. Two sequential DRIE steps define the
structural elements of the accelerometers and the oscillating masses. The following
step involves etching the sacrificial silicon dioxide layer using a gas phase process
(e.g., hydrofluoric acid vapor) to release the polysilicon comb structures. Finally, a