Page 101 - MEMS Mechanical Sensors

90 Mechanical Transduction Techniques

If a ferroelectric material is exposed to a temperature exceeding the Curie point,
it will lose its piezoelectric properties. Hence, there is a limit beyond which they can-
not be used as sensors (or actuators). The Curie point of PZT type 5H is around
195°C, and its maximum operating temperature is generally lower than this value.
In addition to this, the piezoelectric coefficients of the material also vary with tem-
perature, and this is referred to as the pyroelectric effect. This can be exploited in its
own right, and pyroelectric sensors based on modified PZT are often used as the
basis of infrared sensor arrays.
Owing to the anisotropic nature of piezoelectric materials, a system of identify-
ing each axis is required in order to specify its parameters. By convention, the
direction of polarization is taken as the 3-axis, with the 1- and 2-axes being
perpendicular. For example, the material shown in Figure 5.3 has the electrodes
across the thickness of the material, and hence, this is the 3-axis. An important
piezoelectric parameter is the charge coefficient d (C/N). This relates the amount of
ij
charge generated on the surfaces of the material on the i-axis to the force applied on
the j-axis. In the example given, the force applied and the charge generated are both
across the thickness of the material, and hence, this charge coefficient is denoted
as d . If a force, F , is applied to the piezoelectric sample, then the charge generated
33 3
is given by

Q = d F 3 (5.11)
3
33
and so the voltage produced from a rectangular block of area A, thickness t, and
relative permittivity ε is
r
Q dF t
V = 3 = 33 3 (5.12)
3
C εε A
0 r
where ε is the permittivity of free space. For a 10 × 10-mm slab of PZT 5H (d =
0 33
600 pC/N, ε = 3,000) of thickness 1 mm, an applied force of 100N will produce an
r
open circuit voltage of 22.6V. Strictly, the value of the relative permittivity is also
dependent upon the direction in which it is used and the boundary conditions
imposed upon the material. The nomenclature becomes a little cumbersome, how-
ever, and for the purpose of this text it should be assumed that the value quoted is for
the direction in which the piezoelectric is being used.
Another important piezoelectric constant is the voltage coefficient denoted as g .
ij
It is related to the d coefficient as shown here:
d
g = ij (5.13)
ij
εε
0 r
Owing to the inverse piezoelectric effect, an applied electric field will result in a
deformation of the material. This gives rise to two definitions of the d and g
coefficients:

strain developed charge density
d = (mV ) = (CN ) (5.14)
applied electric field applied mechanical stress