handbook of modern sensors

3.7 Pyroelectric Effect 81
Fig. 3.29. Response of a pyroelectric sensor to a thermal step function. The magnitudes of
charge Q 0 and voltage V 0 are exaggerated for clarity.
and a high Curie temperature of about 490 ◦ C. This material can be easily deposited
on silicon substrates by the so-called sol-gel spin-casting deposition method [24].
Figure 3.29 shows the timing diagrams for a pyroelectric sensor when it is exposed
to a step function of heat. It is seen that the electric charge reaches its peak value almost
instantaneously, and then decays with a thermal time constant, τ T . The physical
meaning is this: A thermally induced polarization occurs initially in the most outer
layer of the crystalline material (just few atomic layers), whose temperature nearly
instantaneously raises to its maximum level. This creates the highest thermal gradient
across the material thickness, leading to the maximum polarization. Then, heat starts
propagating through the material, is being absorbed by its mass in proportion to its
thermal capacitance C, and some of it is lost to the surroundings through thermal
resistance R. This diminishes the initial gradient the generated charge. The thermal
time constant is a product of the sensors’ thermal capacitance and thermal resistance:
τ T = CR = cAhR, (3.82)
where c is the specific heat of the sensing element. The thermal resistance R is a
function of all thermal losses to the surroundings through convection, conduction, and
thermal radiation. For the low-frequency applications, it is desirable to use sensors
with τ T as large as practical, whereas for high-speed applications (e.g., to measure
laser pulses), a thermal time constant should be dramatically reduced. For that purpose,
the pyroelectric material may be laminated with a heat sink (a piece of aluminum or
copper).