Page 164 - Organic Electronics in Sensors and Biotechnology

Integrated Pyr oelectric Sensors 141

layer thickness, results in an R = R /d = 50 MV/(W ⋅ m) that is sig-
V’ V
nificantly larger than the associated value R = 20 MV/m obtained
V’
for the commercial PVDF film. That illustrates the sufficiently large
crystallinity of the ferroelectric copolymer thin films and the effec-
tiveness of the poling procedure for a parallel orientation of the
dipoles.

Modelling of the Pyroelectric Response—Heat Distribution Models Next
to the pyroelectric coefficient of the layer, the design of the sensor
device is important to improve the pyroelectric current and voltage
responses. The performance of the sensor is especially influenced by
the substrate (material and thickness), the thickness of the pyroelec-
tric layer, and the absorber structures. To determine the different
influences qualitatively and quantitatively, two models for the ther-
mal conduction in a sensor element were developed. The knowledge
of the actual temperature change in the pyroelectric layer is necessary
not only for the improvement of the design of the sensor element, but
also for the determination of the pyroelectric coefficient of a given
material.
The first model is a one-dimensional model that enables calcula-
tion of the temperature variations at any position in vertical direction
from the surface of the sensor through the different material layers of
the sample. This model is then used to calculate the average tempera-
ture change in the pyroelectric layer to compare various sensor
designs, and the influences from different parameters of the sensor
design on the pyroelectric response are investigated. Parameters
under investigation are the substrate material and thickness, thick-
ness of the pyroelectric layer, and surface area of the sensor. By solv-
ing the basic heat distribution equation, Eq. (4.26), for a set of adjacent
layers, the average temperature variation in the pyroelectric layer can
be calculated. The as-calculated temperature variations are then used
to model the expected pyroelectric responses in the frequency range
−4
from 10 to 10 Hz by using an appropriate equivalent circuit for the
6
measurement setup. The as-obtained current and voltage responses
for different sensor designs (different area, substrate material, sub-
strate thickness, thickness of pyroelectric layer) are compared with
the results obtained from pyroelectric measurements performed in
the way described in Sec. 3.3. The model helps thus to design a sensor
with a maximum pyroelectric response in the targeted frequency
range as well as to tailor the frequency dependence of current and
voltage response.
The second model is based on a finite element method (FEM)
using the MATLAB Partial Differential Equation (PDE) toolbox. Solv-
ing the heat transfer equation in two dimensions helps to calculate
lateral resolution limits, which are important for designing an array
of close-packed sensor elements. Consideration is also given to the
time resolution limits of the sensor device which occur because the