Page 170 - Organic Electronics in Sensors and Biotechnology

Integrated Pyr oelectric Sensors 147

the substrate. Of course, all substrate-related considerations are only
important in the low-frequency range, when the penetration depth of
the thermal wave is sufficiently high to reach down to the substrate.
The penetration depth is defined as the distance in which the tempera-
ture has fallen to 1/e of its maximum value. In the high-frequency
range (above 1 kHz), the penetration depth is shorter than the thick-
ness of the pyroelectric layer. Since it is the average of the tempera-
ture lift T in the pyroelectric layer that is important, T decreases
with a faster excitation, due to a shorter penetration depth λ at higher
frequencies according to λ = 2K/ ω with K being the thermal
diffusivity.
The blue line in all diagrams of Fig. 4.17 corresponds to a calcula-
tion without any substrate, hence it does not change from one substrate
to another. The frequency where the influence of the substrates is start-
ing to become visible is around 10 kHz, and this frequency is the same
for all substrates. But the extent to which the temperature lift is low-
ered by the substrate depends on its heat conductivity. The highest
response is hence obtained for the PET foil (Melinex), having a heat
conductivity in the range of the P(VDFTrFE) layer. Silicon is the worst
substrate in the interesting frequency range between 0.1 and 100 Hz
with respect to the magnitude of the voltage and current response
because of its high thermal conductivity. With increasing thickness of
the substrate the lowering of the temperature lift is extended to smaller
frequencies. In Fig. 4.18a to c the different current and voltage responses
are plotted. It is shown that they strongly depend on the substrate
thickness in the low-frequency range. Again the detailed characteris-
tics of these curves are determined and explained by the temperature
lifts calculated and displayed in Fig. 4.17.

Comparison of Different Pyroelectric Layer Thicknesses The thickness of
the pyroelectric layer has an influence on the response functions of
the sensor as well (see Fig. 4.19a to c). At low frequencies, when due
to the large penetration depth the whole sample is excited, the pyro-
electric current is equal for all thicknesses of the pyroelectric layer. At
higher frequencies the pyroelectric layer is activated only partly,
resulting in a lower average temperature in the pyroelectric layer. It is
interesting that for the high thermally conductive silicon substrate, the
thin pyroelectric layer does not give the highest response, because the
heat is conducted away by the substrate. However, for each layer
thickness on the silicon substrate, there is a frequency range where
the current response is maximized.

Influence of Impedance and Capacitance of the Measurement Circuit As
expected from Eq. (4.31) the voltage response is strongly influenced
by the input resistance of the measurement instrument or, strictly
speaking, by the cutoff frequency ω (see Sec. 4.2.4), whereas the
c
current response is independent of ω and only determined by the
c