Page 102 - MEMS Mechanical Sensors

5.2 Piezoelectricity 91

and

open circuit electric field strain developed
⋅
g = (Vm N ) = (mC ) (5.15)
applied mechanical stress applied charge density
Table 5.2 shows some properties of various types of piezoelectric material. A
search through the literature will reveal a wide variation in some of these values. In
general, manufacturers of bulk piezoelectric materials quote a relatively wide toler-
ance (20%) on the values of the piezoelectric properties. Measurement of the prop-
erties of films deposited onto substrates is notoriously difficult, as the boundary
conditions can grossly affect the measured value. Additionally, some materials, such
as PZT, are available in a variety of compositions (4D, 5H, 5A, 7A) each exhibiting
vastly different figures for their piezoelectric coefficients. The figures quoted in the
table are only intended as a rough comparison.
Quartz is a widely used piezoelectric material that has found common use in
watches and as a resonant element in crystal oscillators. There are no available
methods to deposit it as a thin-film over a silicon substrate. PVDF is a carbon-based
polymer material that is readily available in a light, flexible sheet form of typical
thickness 9 to 800 µm. It is possible to spin-on films of PVDF onto substrates, but
this must be polarized (poled) after processing in order to obtain piezoelectric
behavior. Barium titanate and PZT are two examples of piezo ceramic materials
and each of these can be deposited onto silicon using a variety of methods including
sputtering, screen-printing, and sol-gel deposition. PZT is generally characterized
by its relatively high value of d and is thus a desirable choice of piezoelectric mate-
33
rial. Both zinc oxide and lithium niobate can be deposited as polycrystalline thin-
films, but consistent data about their properties is not readily available.
In general, because of the relatively high voltages required for piezoelectric
actuators to generate displacements in the micron range, they are not often used.
For subnanometer movement, however, they provide an excellent method of actua-
tion. Their high sensitivity to small displacements means that they offer many
advantages as micromachined sensors. Devices such as surface acoustic wave sen-
sors (SAWS) and resonant sensors utilize both modes of operation, meaning that
only a single material is required for both the sensing and actuating mechanism.
An approximate electrical equivalent circuit of a piezoelectric material is
depicted in Figure 5.4. Electrical engineers will recognize the circuit as a series-
parallel resonant system. A plot of impedance against frequency is also shown.
The impedance exhibits both resonant and antiresonant peaks at distinct
frequencies.

Table 5.2 Properties of Relevant Piezoelectric Materials
Material Form d (pC/N) Relative Permittivity (ε )
33 r
Quartz Single crystal 2 4
PVDF Polymer 20 12
Barium titanate Ceramic 190 2,000
PZT Ceramic 300–600 400–3,000
Zinc oxide Single crystal 12 12
Lithium niobate Single crystal 6–16 30