handbook of modern sensors

3.6 Piezoelectric Effect 71
Another method, called corona discharge poling, is also used to produce polymer
piezo/pyroelectrics. The film is subjected to a corona discharge from an electrode
at several million volts per centimeter of film thickness for 40–50 sec [5,6]. Corona
polarization is uncomplicated to perform and can be easily applied before electric
breakdown occurs, making this process useful at room temperature.
The final operation in preparation of the sensing element is shaping and finishing.
This includes cutting, machining, and grinding. After the piezo (pyro) element is
prepared, it is installed into a sensor’s housing, where its electrodes are bonded to
electrical terminals and other electronic components.
After poling, the crystal remains permanently polarized; however, it is electrically
charged for a relatively short time. There is a sufficient amount of free carriers which
move in the electric field setup inside the bulk material and there are plenty of charged
ions in the surrounding air. The charge carriers move toward the poled dipoles and
neutralize their charges (see Fig. 3.23C). Hence, after a while, the poled piezoelectric
material becomes electrically discharged as long as it remains under steady-state
conditions. When stress is applied, or air blows near its surface (Section 10.7 of
Chapter 10) the balanced state is degraded and the piezoelectric material develops
an electric charge. If the stress is maintained for a while, the charges again will be
neutralized by the internal leakage. Thus, a piezoelectric sensor is responsive only to
a changing stress rather than to a steady level of it. In other words, a piezoelectric
sensor is an ac device, rather than a dc device.
Piezoelectric directional sensitivities (d coefficients) are temperature dependent.
For some materials (quartz), the sensitivity drops with a slope of −0.016%/ ◦ C. For
others (the PVDF films and ceramics) at temperatures below 40 ◦ C, it may drop, and at
higher temperatures, it increases with a raise in temperature. Currently, the most popular
materials for fabrication of piezoelectric sensors are ceramics [7–9]. The earliest
of the ferroelectric ceramics was barium titanate, a polycrystalline substance having
the chemical formula BaTiO 3 . The stability of permanent polarization relies on the
coercive force of the dipoles. In some materials, polarization may decrease with time.
To improve the stability of poled material, impurities have been introduced in the
basic material with the idea that the polarization may be “locked” into position [4].
Although the piezoelectric constant changes with operating temperature, a dielectric
constant, κ, exhibits a similar dependence. Thus, according to formula (3.71), variations
in these values tend to cancel each other as they are entered into numerator and
denominator. This results in a better stability of the output voltage, V , over a broad
temperature range.
The piezoelectric elements may be used as a single crystal or in a multilayer
form where several plates of the material are laminated together. This must be done
with electrodes placed in between. Figure 3.24 shows a two-layer force sensor. When
an external force is applied, the upper part of the sensor expands while the bottom
compresses. If the layers are laminated correctly, this produces a double output signal.
Double sensors can have either a parallel connection as shown in Fig. 3.25A or a serial
connection as in Fig. 3.24C.The electrical equivalent circuit of the piezoelectric sensor
is a parallel connection of a stress-induced current source (i), leakage resistance (r),
and capacitance (C). Depending on the layer connection, equivalent circuits for the