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Pulsed Performance of
Pyroelectric Detectors
S. Efthymiou and K.B.
1School
1
Ozanyan
of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL, United Kingdom,
<[email protected]>
Introduction
Pyroelectric Detectors (PEDs) are in mass production, most notably in the area of security and intruder detection systems1. PEDs are mainly presented in literature in terms of their AC response to low-frequency sinusoidal modulation or to
square wave pulses with 1:1 duty cycle. This approach is unsuitable for developing a signal detection scheme for pulsed detection e.g. in our case of nanosecond (ns) THz pulses of duty cycle of 1:1000 (kHz pulse repetition frequency) resulting
from difference-frequency THz generation with two near-IR fibre laser/amplifier sources. Thus, in contrast to assume infinite or insulated boundary constraints, as described in 1D heat transfer models, the full-time resolved thermal and
electrical response to a chosen pulsing strategy e.g. burst of low duty-cycle under a low-frequency envelope is obtained by simulating a 3D model of the PED using Numerical Methods such as FEM. This allows future accurate estimates of the
appropriate signal processing methods such as phase-sensitive detection, depending on the front-end electronic circuit.
PED Thermal Model
A heat conduction problem, such as heat transferred to a pyroelectric element by laser radiation is nonlinear, either due to the non-linearity of the differential equation or the boundary conditions or both.
Finite Element Methods (FEM) are numerical methods widely used to solve both transient and steady
state heat conduction problems and are available in standard software packages. The temperature of
bodies such as a pyroelectric element can be assumed to be as a function of time only T( t ). A
simplified “lumped” thermal model of the PED can be approximately represented using an equivalent
electrical RC network2,3 considering a uniform internal distribution at all times T( t ) as shown in Figure
1. The standard “lumped” approach yields to a temperature distribution as a function of time, taking
into account only the thickness of each layer of the element. However, the geometry of the detector is
more complex and crude assumptions may result to a less accurate result. A system where high
irradiation power is available, this approach may be well suited but a system governed by very low
irradiation power (nanowatts) a more rigorous analysis could yield to a more accurate result.
Figure 2: Illustration of the layer structure a commercial PED
(SPH-43) from Spectrum Detectors
Figure 1: Simplified lumped thermal model with the equivalent
“heat circuit” using equivalent electrical components
Voltage Mode
Finite Element Methods
Using numerical methods, such FEM or FDM (Finite Difference
Methods), the success of the model depends on the relevance of the
defined boundary conditions. A particular PED, SPH-43 from
Spectrum Detectors has been modelled by using FEM within the
COMSOL Multiphysics software. A realistic model of the PED with
actual dimension has been created where each boundary of the
model is assigned within the software as illustrated in the Figure 3.
Simulated temperature
Pyroelectric Current
distribution
to
Current Mode
a
Following from the pyroelectric properties4 of the crystal the
pyroelectric current is proportional to the rate of the polarization
change with the temperature, known as the pyroelectric coefficient.
The total pyroelectric current is the sum of the contributions from
each volume element (voxel) calculated from the temperature
distribution on a regular 3D grid, exported from COMSOL (Figure
4). By considering the PED as a very high-impedance low-current
source a voltage signal can be obtained as an output of current to
voltage (I-V) converter. Two modes are applicable, the “current
mode” and the “voltage mode”. Each mode has different frequency
response due to different electronic circuits.
Figure 5: Circuit diagrams of current to voltage converters
Figure 3: Three dimensional representation of the SPH-43
from Spectrum Detectors
x
Crystal
Figure 4: Calculation of the 3D temperature field in the pyroelectric crystal obtained from a full thermal model of a
commercially available PED, illuminated with a 2ns pulse
Results
A 3D heat transfer model of the PED is constructed in COMSOL Multiphysics to determine its thermal response to a wide range of irradiation scenarios (Figure 4). The converter circuits (Current Mode) is simulated in NI Multisim, taking
into account an ideal amplifier. The complete model is verified experimentally by simple experiments based on an LED illumination. Figure 6 shows the three graphs depicting the PED’s voltage response for three cases. The yellow graph in
Figure 6 shows the voltage response to a step at t=0, where the rate of temperature dΔTd/dt is obtained using FEM in COMSOL and the I-V in Multisim. The purple graph was solely simulated in Multisim combining everything as one
equivalent electronic since the “lamped” approach was used. The results are all normalised to their maximum value and compared with the experimental results (blue graph). Further, towards the ultimate goal of modeling, Figure 7 shows the
response of the PED in the case of a 15ms burst of 2ns pulses with 1:1000 duty cycle. With an increasing value of the electrical time constant a notable gain difference of the low-frequency (on/off) envelope responses is observed for each
electrical time constant “τth”..
Conclusions
Figure 6: Chart indicating the voltage step response of the
PED
[1]
[2]
[3]
[4]
Figure 7: Comparison of the overall pulsed response for
varying electrical time-constant
A 3D thermal model of a commercial PED (SPH-43) was
successfully performed using FEM in COMSOL Multiphysics to
derive the rate of temperature change due to incident pulsed
radiation. While the thermal behaviour of the PED could have been
simulated using the tradition lumped approach, not only COMSOL
has yield to a more accurate result but the opportunity of exploring
3D modelling of heat transfer problems was given. According to Fig.
8, PEDs have high performance when operated at low frequencies
where the 1/f noise is dominating due to large electrical time
constant. Therefore the thermal and electrical time constants are the
key parameters in obtaining the optimum frequency of the
modulating signal for high responsitivity and best signal to noise ratio
(SNR).
REFERENCES
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Vladimir B. Samoilov and Yung Sup Yoon, Member IEEE, in Frequency Response of Multilayer Pyroelectric Sensors ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 45, no. 5, september 1998
W.P. Wheless, Jr. L.T. Wurtz J.A. Wells ,in An Equivalent-Circuit Radiation Sensor Model, 0-7803-1797-11941$3.00 0 1994 IEEE
Porter, S. G. (1981), in A brief guide to pyroelectric detectors, Ferroelectrics, 33:1, 193 – 206