Online proceedings - EDA Publishing Association

piezoelectric displacement transducers. Each of the two
opposite ends of the seismic mass is supported by two
parallel suspension beams. The thickness of suspension
beams is defined by the silicon-on-insulator (SOI). Two
transducers are patterned on each suspension. From a proper
interconnection among the transducers, triaxial accelerations
can be measured without cross-axis interference [9].
The design of the accelerometer depends on the processes
of bulk micromachining for the seismic mass. The seismic
mass can be fabricated from either Deep Reactive Ion
Etching (DRIE) as shown Figure 1, or chemical wet etching
as shown in Figure 2, following by dry etching to release the
suspension beams. Flexibility for the crystalline orientation
of suspension beams and high aspect ratio of seismic mass
are possible for DRIE. The suspension beams are often [100]
oriented in the previous studies [3][4][5][6]. Chemical wet
etching of (100) silicon wafer using such as KOH and
TMAH has the cost advantage over dry etching. However,
the sloping walls of the seismic mass cause additional
constraints in the dimensional design on account of the
required convex corner compensation in the masking layer of
wet etching. Also, the crystalline orientation of the
suspension beams will be restricted to [110].
Figure 1 Design of the accelerometer using DRIE dry etching for the seismic
mass
Figure 2 Design of the accelerometer using wet etching for the seismic mass
The out-of-plane (z axial) acceleration will result in a
symmetric vibration, and in-plane (x and y axial)
accelerations will produce asymmetric and torsional
vibrations. The inertia force will introduce bending and
torsional stress on the beams that will produce electrical
charge by the piezoelectric transducers. The seismic mass
from dry etching often provides higher sensitivity because
the distance between the surfaces of suspension beams to the
11-13
May 2011, Aix-en-Provence, France
center of mass is larger in contrast with that of the seismic
mass from wet etching.
III. ANALYTICAL MODEL
The system model of the accelerometer is consisted of a
mechanical subsystem and an electric subsystem. The
mechanical subsystem is assumed a spring-mass-damper
system. The equivalent stiffness of the suspension and the
equivalent seismic mass are two deterministic factors for the
structure modeling. Laminated beam theory is applied to
obtain the equivalent bending rigidity of the supported beams.
The application of area moment method provides the
formulation of suspension stiffness for three vibration modes.
The piezoelectric transducers convert beam stresses into
output charge.
A. Equivalent bending rigidity of the laminated beam
The derivation of the structure model is based on the
following assumptions:
(1) the influence of electrodes on the beam stiffness is
negligible;
(2) the seismic mass and rim of the structure are rigid;
(3) the deflections of substrate material and piezoelectric
films of supporting beams observe linear elasticity and
Hooke’s Law;
(4) the piezoelectric material is anisotropic;
(5) the supported beams are wide and flat, and thin beam
theory (Euler-Bernoulli beam model) is applied; the
stresses in the z-direction and the strains in the
y-direction are negligible compared with others [7].
Therefore,
0543
(1)
0542
The constitutive equation can be simplified as follows
for an orthotropic piezoelectric thin film such as PZT:
1
p p
CCC
p
1 3, 2, 1,
0 1
2 p,21
p,22
CCC
p,23
0
2
(2)
3 p p
CCC
p
3 3, 2, 1,
0 3
6
000
C
p 6 6,
6
From the stress/strain assumptions in (1) and the expression
for σ 3 in (2), we obtain
C
3
(3)
C
p 3 1,
1
p 3 3,
Similarly, with the aid of (3), stress σ 1 can be represented as
follows:
CC
(4)
,13CC
pp
,31
CE (5)
,13 pp
,31
1
C
p 1 1,
1
EP
1
C
p 3 3,
pP 1 1,
C
p 3 3,
where E p is the effective modulus of elasticity for the
piezoelectric film.
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