handbook of modern sensors

3.7 Pyroelectric Effect 79
through the resistor and voltage across the resistor represent the heat-flow-induced
charge. It can be characterized by two pyroelectric coefficients [21]:
P Q = dP s
dT
P V = dE
dT
Pyroelectric charge coefficient,
Pyroelectric voltage coefficient,
(3.76)
where P s is the spontaneous polarization (which is another way to say electric charge),
E is the electric field strength, and T is the temperature (in K). Both coefficients are
related by way of the electric permitivity, ε r , and dielectric constant, ε 0
P Q
P V
= dP s
dE = ε rε 0 . (3.77)
The polarization is temperature dependent and, as a result, both pyroelectric coefficients
(3.76) are also functions of temperature.
If a pyroelectric material is exposed to a heat source, its temperature rises by T
and the corresponding charge and voltage changes can be described by the following
equations:
Q = P Q AT , (3.78)
V = P V hT . (3.79)
Remembering that the sensor’s capacitance can be defined as
from (3.78–3.80) it follows that
C e = Q
V = ε rε 0
A
h , (3.80)
A ε r · ε 0
V = P Q T = P Q T . (3.81)
C e h
It is seen that the peak output voltage is proportional to the sensor’s temperature rise
and pyroelectric charge coefficient and inversely proportional to its thickness.
When the pyroelectric sensor is subjected to a thermal gradient, its polarization
(electric charge developed across the crystal) varies with the temperature of the crystal.
A typical polarization–temperature curve is shown in Fig. 3.28. The voltage pyroelectric
coefficient, P v , is a slope of the polarization curve. It increases dramatically
near the Curie temperature where the polarization disappears and the material permanently
loses its pyroelectric properties. The curves imply that the sensor’s sensitivity
increases with temperature at the expense of nonlinearity.
To select the most appropriate pyroelectric material, the energy conversion efficiency
should be considered. It is, indeed, the function of the pyroelectric sensor to
convert thermal energy into electrical. "How effective is the sensor" is a key question
in the design practice. A measure of efficiency is kp 2 , which is called the pyroelectric