Page 165 - Organic Electronics in Sensors and Biotechnology

142 Cha pte r F o u r

heat from a previous event has to be conducted away before a subse-
quent excitation occurs.

One-Dimensional Model
In accordance with the publication of Setiadi and Regtien, a one-
31
dimensional heat distribution equation has been used, enabling one
to calculate the amplitude and time dependence of the temperature
variations in the sensor. The first model takes into account the dif-
ferent specific heat capacities, thermal conductivities, and densities
of the different materials in the thin-film system. A sketch of a mod-
eled layer system is given in Fig. 4.14. The excitation of heat waves
is done with a laser, intensity-modulated with a sine function. To
extract the pyroelectric current and voltage responses, a suitable
equivalent circuit for the sensor element had to be taken into
account. To compare the results with the experimental data, the
frequency-dependent measured values for C and R (obtained with
p p
an LCR meter) from the respective sensor elements were used as an
input for the model.
The principal equation for heat conduction within the nth layer is

(,
2
(,
∂Tx t) δ ∂ Tx t)
= n n (4.26)
∂t c ⋅ d ∂x 2
n n
where δ = heat conductivity
n
c = specific heat
n
d = mass density of the nth layer
n
As the intensity of the incident light is assumed to vary according
to a sine wave (P = P e ⋅ i tω ), producing heat variations in the sensor
i o
element, T can be written as
n
ω
Tx t) = Tx) ⋅ e it (4.27)
(,
(
n n
FIGURE 4.14 Layer Incident radiation
setup for the Absorber
one-dimensional
model. w1
w2 P(VDF-TrFE) Electrodes
w3

w4 Substrate