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National University of Tainan
Graduate Institute of Mechatronic
System Engineering
2009 spring Industry Research Master
Program in Precision Industry
Master Dissertation
The Study of the Thermal Effect on the ZnO Pyroelectric Film
Temperature Sensor
Student name: Doan Van Tan
Advisor
: David. T.W. Lin
Jan 2011
The Study of the Thermal Effect on the ZnO Pyroelectric Film
Temperature Sensor
by
Doan Van Tan
National University of Tainan
Graduate Institute of Mechatronic System Engineering
Master Dissertation
A Thesis
submitted in partial fulfillment of the requirements
for the Master of Engineering degree
in Graduate Institute of Mechatronic System Engineering
2009 spring Industry Research Master Program
in Precision Industry
in the College of Science and Engineering of
National University of Tainan
Advisor: David. T.W. Lin
Jan 2011
The Study of the Thermal Effect on the ZnO
Pyroelectric Film Temperature Sensor
Student: Doan Van Tan
Advisor: David. T.W. Lin
Graduate Institute of Mechatronic System Engineering
2009 spring Industry Research Master Program in Precision Industry
National University of Tainan
Tainan, Taiwan, R.O. C
ABSTRACT
The purpose of this study is to quantify the response of the proposed pyroelectric ZnO
film sensor and approach the optimal design by the integration of experiment and numerical
method. The experiment has been done to find the relationship between voltage response and
temperature input. This study develops an effective method to design the performance of this
proposed film sensor. The optimal method is adopted by the simplified conjugated gradient
method (SCGM) combined with the finite element method. For designing a novel film sensor,
four kinds of top electrode of the film pyroelectric ZnO temperature sensors are discussed. In
addition, the temperature variation rate is enhanced significantly through the optimal process.
Through the quantification and optimization of this study, the proposed sensor can be
applied on the proximity sensing and thermal sensing more exactly. In addition, this proposed
optimal method will build an effective way to simplify the engineering design procedure.
Key word: ZnO pyroelectric film sensor, voltage response, temperature variation rate,
optimization, SGCM.
i
ACKNOWLEDGEMENT
I would like to express my sincere gratitude to the people who provided invaluable
encourage and help to me during my first two years life in Taiwan.
Foremost, I would like to thank my advisor Dr. David.T.W.Lin for his advice, guidance,
encouragement and continuous support during my graduate study and research. Without his
help, this work would not be possible. I could not have imagined having a better advisor and
mentor for my graduate study.
A special thanks to Dr. Yuh-Chung Hu for the help he provided the experiment sample,
the idea, and the verification in this research. Beside that, thanks to Dr. Jui-Ching Hsieh who
supports me to write the program and gives me the suggestion in my experiment. I also would
like to thank my fellow lab mates in Optimization Lab.
Last but not the least, I would like to thank my family especially my dear parents, for
giving birth to me at the first place and supporting me spiritually throughout my life. It is the
everlasting love from them to my whole life that creates my tomorrow.
ii
CONTENTS
ABSTRACT ................................................................................................................................ i
ACKNOWLEDGEMENT .......................................................................................................... ii
CONTENTS .............................................................................................................................. iii
TABLE CAPTIONS .................................................................................................................. iv
FIGURE CAPTIONS ............................................................................................................... vii
NOMENCLATURE ................................................................................................................ viii
1. INTRODUCTION ................................................................................................................. 1
1-1 Background.................................................................................................................. 1
1-2 Literature review ......................................................................................................... 3
2. NUMERICAL AND OPTIMAL APPROACH ..................................................................... 9
2-1 Theory.......................................................................................................................... 9
2-2 Numerical modeling .................................................................................................. 12
2-3 Optimal method ......................................................................................................... 14
3. EXPERIMENT .................................................................................................................... 27
3-1 Instrument list ............................................................................................................ 27
3-2 Experimental procedure............................................................................................. 30
4. RESULTS AND DISCUSSIONS ....................................................................................... 33
4-1 Experiment ................................................................................................................ 33
4-2 Model simulation ....................................................................................................... 35
4-3 Optimization result .................................................................................................... 37
5. CONCLUSIONS ................................................................................................................. 92
REFERENCE ........................................................................................................................... 94
iii
TABLE CAPTIONS
Table 1 Parameters of the model for simulation ..................................................................... 18
Table 2 The variable variation in the initial guess and optimal process of Rectangle type .... 59
Table 3 The variable variation in the initial guess and optimal process of Criss-cross type .....
.................................................................................................................................... 60
Table 4 The variable variation in the initial guess and optimal process of Target type .......... 61
Table 5 The variable variation in the initial guess and optimal process of Web type ............. 62
iv
FIGURE CAPTIONS
Fig. 1 The photos of the flexible ZnO pyroelectric sensor [20] .............................................. 6
Fig. 2 The structure of flexible ZnO pyroelectric sensor [20] ................................................. 7
Fig. 3 The schematic diagram of the ink-jet printing system [20]........................................... 8
Fig. 4 Schematic two-dimensional electrically polar lattice [34] .......................................... 19
Fig. 5 Sawyer - Tower circuit for observing hysteresis loops of pyroelectric materials [34] ...
..................................................................................................................................... 20
Fig. 6 The schematic diagram of pyroelectric sensor [35] .................................................... 21
Fig. 7 Shape of the top electrode in the pyroelectric film sensor .......................................... 22
Fig. 8 Layer of the pyroelectric film sensor .......................................................................... 23
Fig. 9 The meshing model of the pyroelectric film sensor .................................................... 24
Fig. 10 The flow chart of the optimization process ................................................................. 25
Fig. 11 Connection among optimizer and direct solver problem ............................................ 26
Fig. 12 The Rectangular ZnO pyroelectric film sensor ........................................................... 31
Fig. 13 The schematic diagram of experimental system ......................................................... 32
Fig. 14 The voltage response profile and temperature profile with the fitting curve from the
multinomial function ................................................................................................... 62
Fig. 15 The temperature distribution of top electrode in the pyroelectric film sensor at 0.1s .....
..................................................................................................................................... 63
Fig. 16 The temperature profiles of pyroelectric film sensor with different shape type of top
electrode ...................................................................................................................... 64
Fig. 17 The temperature variation rate of pyroelectric film sensor with different shape type
of top electrode ............................................................................................................ 65
v
Fig. 18 The second order derivative of temperature in the pyroelectric film sensor with
different shape type of top electrode .......................................................................... 66
Fig. 19 The design variable in different kinds of ZnO pyroelectric sensor ............................. 67
Fig. 20 The temperature distribution in the initial guess and optimal of Rectangle type at
0.05s ............................................................................................................................ 68
Fig. 21 The temperature profile in the initial guess and optimal of Rectangle type................ 69
Fig. 22 The temperature variation rate profile in the initial guess and optimal of Rectangle
type .............................................................................................................................. 70
Fig. 23 The second order derivative of temperature profile in the initial guess and optimal of
Rectangle type ............................................................................................................. 71
Fig. 24 Convergence process of the objective function in different initial value for
Rectangle type ............................................................................................................. 72
Fig. 25 The variation of the design variable through the optimal process for Rectangle type ....
..................................................................................................................................... 73
Fig. 26 The temperature distribution in the initial guess and optimal of Criss-cross type at
0.05s ............................................................................................................................ 74
Fig. 27 The temperature profile in the initial guess and optimal of Criss-cross type .............. 75
Fig. 28 The temperature variation rate profile in the initial guess and optimal of Criss-cross
type .............................................................................................................................. 76
Fig. 29 The second order derivative of temperature profile in the initial guess and optimal of
Criss-cross type ........................................................................................................... 77
Fig. 30 Convergence process of the objective function in different initial value for Criscross type ..................................................................................................................... 78
Fig. 31 The variation of the design variable through the optimal process for Criss-cross type ..
vi
..................................................................................................................................... 79
Fig. 32 The temperature distribution in the initial guess and optimal of Target type at 0.05s ....
..................................................................................................................................... 80
Fig. 33 The temperature profile in the initial guess and optimal of Target type ..................... 81
Fig. 34 The temperature variation rate profile in the initial guess and optimal of Target type ...
..................................................................................................................................... 82
Fig. 35 The second order derivative of temperature profile in the initial guess and optimal of
Target type ................................................................................................................... 83
Fig. 36 Convergence process of the objective function in different initial value for Target
type .............................................................................................................................. 84
Fig. 37 The variation of the design variable through the optimal process for Target type ..... 85
Fig. 38 The temperature distribution in the initial guess and optimal of Web type at 0.05s ... 86
Fig. 39 The temperature profile in the initial guess and optimal of Web type ........................ 87
Fig. 40 The temperature variation rate profile in the initial guess and optimal of Web type ......
.................................................................................................................................... .88
Fig. 41 The second order derivative of temperature profile in the initial guess and optimal of
Web type ..................................................................................................................... 89
Fig. 42 Convergence process of the objective function in different initial value for Web type ..
..................................................................................................................................... 90
Fig. 43 The variation of the design variable through the optimal process for Web type ........ 91
vii
NOMENCLATURE
A
:
detector area ( m 2 )
P
:
pyroelectric coefficient (C.m .k )
dT / dt
:
temperature variation rate
C
:
heat capacity per unit volume ( J
k
:
thermal conductivity
T
:
temperature ( K )

:
relaxation time respectively

:
density (kg / m )
Cp
:
the heat capacity at constant pressure
Q
:
heat source or a heat sink (W
t
:
time
L
:
length
(m)
W
:
width
(m)
H
:
height
(m)
q
:
heat flux

:
temperature gradient
2
1
( K / s)
m3 .K
)
(W / m.K )
(1/ K )
3
(s)
(W / m / k )
viii
m3
)
( J / kg.K )
.
1. INTRODUCTION
1-1 Back ground
The measurement of temperature is one of the fundamental requirements for
environmental control system, as well as certain chemical, electrical and mechanical system.
Many kinds of temperature sensors are commercially available and used such as DDR3
memory module, metal processing industry and biomedical implanted chip etc. Beside that, in
the textile industry, flexible electronics are embedded into the fiber or clothes to perform the
human health detection.
In recent years, the ferroelectric materials have been developed gradually in MEMS. One
of them is pyroelectric material, they have been successfully used in many applications, and
possess the advantages of integrality on a chip, uncooled detecting, operation at room
temperature, fast and wide spectral response, high sensitivity and low cost, beside that flexible
films sensor can capture the image from biomedicine, artificial skin, and wearable electronics.
ZnO is a pyroelectric material; the pyroelectric voltage is induced as temperature variation
is subjected to ZnO material. In this study, the flexible ZnO pyroelectric sensor is shown in
Fig. 1. This film sensor includes a top electrode layer made of nano silver, a flexible aluminum
sheet which serves as the bottom electrode, and a ZnO layer as the pyroelectric layer. Different
designs of top-electrode in the flexible ZnO pyroelectric sensor discussed in this study are
Rectangle, Criss-cross, Target and Web shape, respectively. The diagrams of these sensors are
shown in Fig. 2. In the fabrication of micro sensor, they use fully inkjet printing process are
shown in Fig. 3. After deposit process, they continue annealing under different temperature.
This thesis focuses on the behavior of sensor by the experimental verification and optimal
design of the top electrode through the numerical study. An experimental model is built up to
1
find out the transfer function between temperature and voltage response in ZnO pyroelectric
film sensor. This system consists of the hot plate, thermocouple and data acquisition system
for data collection. Besides that, the simulation of transient heat conduction of the pyroelectric
film sensor is built and combined with the optimal method to design the best shape of the top
electrode. We can demonstrate that the maximum response can be reached as the optimal
design of the top electrode is obtained.
The structure of this thesis includes four sections. The first section introduces the
characteristics of ZnO pyroelectric film sensor and more investigations for applications and
simulations of pyroelectric material. In the second section, it illustrates the numerical and
optimal approach. Besides that, the third section describes the experimental procedure. The
results and discussions of experimental process, simulation in different design of top electrode
shape, and the new design of top electrode in optimization process are presented in the fourth
section. All contribution possible applications of this study are concluded in the final section.
2
1-2 Literature review
The pyroelectric effect plays an important role in the pyroelectric sensor. It’s
characterized as non-centrosymmetrical crystal and has a specific polar axis along the
direction of spontaneous polarization [1]. When the heat is applied to the pyroelectric
material, the positive and negative charges move to opposite ends of the material and generate
an electrical charge. Many kinds of pyroelectric material depended on the different crystal
structure exist, such as Perovskite ferroelectric materials (PZT, PbTiO3, PLT) [2-5], polymer
film (Polyvinylidene fluoride (PVDF), vinylidene fluoride trifluoroethylene (VDF/TrFE))
[6-8], and nonferroelectric material (ZnO, CdS, CdSe) [3,9,10]. The pyroelectric effects
distinguish as primary and secondary effect. Primary pyroelectric effect is dependent on the
temperature variation and refers as strain-free or constant strain case. The secondary
pyroelectric effect is resulted from the pyroelectric charge of piezoelectricity [9-11]. The
primary pyroelectric effect dominates the pyroelectric response in (Zr0.54Tie0.46)O3 and PbTiO3
thin films while ZnO thin film is dominated by secondary pyroelectric effect [12]. Different
kinds of deposition methods are studied to fabricate the pyroelectric sensor such as DC or RF
sputtering [13], metal organic chemical vapor deposition (MOCVD) [14], metal organic
decomposition (MOD) [15], sol-gel method [16], spray pyrolysis [17], aesol deposition
method (AMD) [18,19] and full inkjet printing [20].
C.S. Wei et al. [12] fabricate and investigate three groups of the ZnO pyroelectric sensor
with various layer thickness, effective area, partially and fully covered electrode. Their results
show that the responsibility of the partial-electrode sensors is four times higher than the one
of the full-electrode sensors in the frequency range of 10-1000Hz. The effects of other design
parameters such as thickness of ZnO, SiO2 and Si3N4 on the responsibility are also discussed.
Liao et al. [20] propose a new flexible ZnO pyroelectric sensor and four kinds of top electrode
3
(Rectangle type, Criss-cross type, Target and Web type) are fabricated and investigated. The
results show that the sensor with the Web type has the highest responsibility resulted from the
higher annealing temperature. They present the design of top electrode is a critical factor to
affect the temperature variation rate in the pyroelectric film in advance [21]. In addition, the
voltage responsibility will toward identically as the modulating frequency increase to a certain
value. Chen et al. [22] discover that PT/P(VDF-TrFE) detector has higher voltage and current
responsibilities than the P(VDF-TrFE) copolymer for sensing elements with the same
thickness. Tang et al. [23] present the results of better pyroelectric response, those can be
expected by controlling temperature below 700C during the fabrication of the pyroelectric
detectors, selecting absorption layer with high absorption coefficient, and decreasing the
thickness of the ments. Li et al. [24] use ANSYS to simulate the temperature field of
multilayer pyroelectric thin film sensor and show that the porous silica film as a thermalinsulation layer reduces obviously the loss of heat from the pyroelectric film sensor to the Si
substrate. Xie et al. [25] consider the energy harvesting using the pyroelectric materials such
as PZT-5A and thin-films. A simple model is used to predict the power generation based on
the temperature as a function of time. Vanderpool et al. [26] convert the waste heat into
electricity using the pyroelectric materials directly. In addition, they propose a simulation of
prototype pyroelectric converter by FEM Liu et al. [27] illustrate a solid precursor used to
prepare PZT thin films by the sol-gel deposition method for uncooled pyroelectric IR sensors.
Akedo et al. [28] make PZT thick films formed on several kinds of substrates by impact
consolidation of PZT, ultrafine particles through an aerosol deposition method. The PZT
layers are shown to have a high breakdown voltage about 700kV/cm after annealing from
room temperature to 10000C. Ko et al. [29] verify the theoretical analysis of the micro
machined Pb(Zr0.3Ti0.7)O3(PZT30/70) thin film pyroelectric detectors with different silicon
4
substrate thickness. Limbong et al. [30] investigate that the effect of a varying bias field on
the pyroelectric properties of sub-micron ferroelectric polymer films and the magnitude and
phase of the pyroelectric signal reflects the hysteresis in the polarization resulted from the
bias field. Ozgur et al. [31] detect the stimulated emission measured from ZnO thin films
grown on c-plane sapphire by RF sputtering. Free exciton transitions are clearly observed at
10K in the photoluminescence, transmission, and reflection spectra of the sample annealed at
10000C. Kohli et al. [32] propose a pyroelectric thin film point detector array manufactured
by sol-gel deposited PZT thin film elements on micromachined SiN4/SiO2 membranes. The
measured current and voltage response is compared with FEM simulations. Häusler et al. [33]
propose a method to examine the conjugated thermal-electrical-mechanical problems by FEM
package. The complex interactions are realized by implementing a two-step approach.
From the above citing references, the issue of explore the pyroelectric effect and improve
the quality of pyroelectric film sensor is very important. This study proposes an experimental
process to explore the relationship between temperature and voltage, besides that we combine
optimization method with finite element method to gain the greatest benefits in the shape
design of top electrode on the pyroelectric film sensor.
5
Fig. 1 The photos of the flexible ZnO pyroelectric sensor [20]
6
Rectangle type
Criss-cross type
Target type
Web type
Fig. 2 The structure of flexible ZnO pyroelectric sensor [20]
7
Fig. 3 The schematic diagram of the ink-jet printing system [20]
8
2. NUMERICAL AND OPTIMAL APPROACH
2-1 Theory
Pyroelectric materials are the crystalline substances capable of generating an electrical
charge in response to the heat flow. This material can be applied in the film sensor field, as a
pyroelectric sensor. The pyroelectric sensor is essentially a capacitor that can be charged by
an influx of heat not require any external electrical bias. Contrary to the thermocouple, which
produces a steady voltage when two dissimilar metal junctions are held at steady but different
temperatures, the pyroelectric sensor generates charge in response to the temperature
variation. Since a change in temperature essentially requires thermal propagation, a
pyroelectric device is a heat flux detector rather than a thermal detector.
Pyroelectricity is based on a pronounced temperature dependence of the electric
displacement field in a piezoelectric material. The effect occurs in any piezoelectric
material (single crystal, ceramic or polymer) which possesses polar point symmetry.
Microscopically, the pyroelectric effect occurs because of the asymmetric environment
experienced by electrical charged species within the crystal structure of the material. This can
be viewed schematically as shown in Fig. 4, which shows a two-dimensional lattice of cations
and anions. The cations are displaced relative to the unit cells ‘centre of gravity’ to give rise to
an electrical dipole moment (or spontaneous polarization Ps) along the line x1-x2.
Quantitatively, the pyroelectric effect is described in terms of a vector, the pyroelectric
coefficient P, given by the rate of change of Ps with temperature (T).
p
dPs
dT
(1)
9
Polarization P is the electric dipole moment per unit volume. The polarization P may be
expressed as the bound surface charge per unit area of a free surface normal to the direction
of P. Polarization is related to electric displacement D through the linear expression.
Di  Pi   0 Ei
(2)
Where the derived constant ε0 is equal to 8.854x10-12C/Vm (permittivity of free space), E
represents the applied field, D is the electric displacement, and P is the polarization as well. In
pyroelectric materials both D and P are nonlinear functions of E may depend on the previous
history of the material. When the term ε0E in the above equation is negligible compared to
P, D is nearly equal to P. Therefore, the D versus E and P versus E plots of the hysteresis loop
become, in practice, equivalent. In addition, permittivity is defined as the incremental change
in electric displacement per unit electric field when the magnitude of the measuring field is
very small compared to the coercive electric field. The small signal relative permittivity K
is equal to the ratio of the absolute permittivity ε to the permittivity of free space ε0.
K   0
(3)
The value of the polarization Ps that remains after an applied electric field is removed is
defined as the remanent polarization. The remanent polarization can be measured by
Sawyer -Tower Circuit which is shown in Fig. 5. The hysteresis loop of polarization versus
electric field is recorded on an x-y plotter or an oscilloscope using Sawyer-Tower circuit. The
interaction of hysteresis loop and y-axis is remnant polarization. The value of Ps measured by
this method usually depends on both the frequency and amplitude of the sine-wave voltage
applied on the pyroelectric material. After applying high voltages, charge will be generated
and measured through a capacitor and an electrometer. The charge and voltage are recorded
10
using an oscilloscope and data acquisition system. Since Ps varies with the temperature, the
pyroelectric discharge current on heating is given by equation 4.
 dQ   dT
i   s 
 dT   dt
 AdPs  dT 



dT  dt 

(4)
Or
i  pA
dT
dt
(5)
Where A is the area of the pyroelectric material, and Qs is the total charge stored by the
capacitor when the sample is heated from room temperature to a temperature above Tc.
11
2-2 Numerical and modeling
Nowadays, the pyroelectric materials are gradually applied in the film temperature sensor
field. Fig.6 presents the structure of pyroelectric film sensor. Here, pyroelectric materials are
used in the form of thin slices or films with electrode deposited on opposite sides to collect
the thermally induced charges. The pyroelectric sensor has two electrodes on opposite sides
and the heat source is applied along axis 3 from the bottom and escapes upward.
From Eq (5), we can see that the response current of the multilayer pyroelectric thin film
sensor is proportion to temperature variation rate of the pyroelectric film sensor. A large scale
of temperature variation rate leads to higher response current. In addition, the top electrode
design also affects the response current. In this study, there are four kinds of the top electrode
namely the Rectangle type; the Crisscross type, the Target type, and the Web type are
simulated. The design of top electrode is a critical factor to affect the temperature variation in
the pyroelectric film sensor which proposed by Hu et al. [18].
The mathematical model of heat equation is expressed:
 C
T
T   T    T    T 
. C
 k
 k
 k
Q
t
t x  x  y  y  z  z 
 xi , yi , zi  V
(6)
For the energy transport through the heat conduction, a heat flux vector can be
approximated by
q  kT
(7)
The present finite element model of the ZnO pyroelectric film sensors is generated with
FEM including the different four cases. Fig. 7 shows all types of pyroelectric film sensor. The
thermal properties of the films are given in Table 1. Fig. 8 presents the structure of ZnO
pyroelectric sensor; it includes four main components such as substrate, membrane layer,
12
pyroelectric layer and electrode. Substrate is a medium layer for heat transfer and diminishing
the volume of substrate. The material of the substrate used in this study is Al. The membrane
layer is used as supporting layer and it has the significant effect on the heat transfer and
responsibility. Two kinds of materials is SiO2 and Si3N4 are usually used in membrane, the
advantage of theseq materials are high stiffness and serve as thermal barrier layer for the high
heat capacity and low temperature conductivity [3,10]. The material of membrane is SiO2 in
this study. The material of electrode is Ag in this study. It’s also use for energy absorption
layer. A dark coating on the upper electrode is usually used as a near transparent absorber for
the incident energy [9]. In order to compare the result of the four models, some parameters of
the films are assumed the same properties in the modeling, and changed the designs of the top
electrode to get the different thermal response. The mesh number of the geometry in the
modeling for four models is normal mesh and shows in Fig.9. In the boundary conditions, the
ambient temperature is 300K and the temperature on top electrode of the surface is 301K. The
interface between layer and layer is assumed continuity and other outside boundary conditions
in the model are assumed insulation.
Continuity
nu .(KuTu )  nd . kd d   0
(8)
Insulation
n.(kT )  0
(9)
13
2-3 Optimal method
According to the above simulation part, the geometry of top electrode is one of factors to
affect the temperature variation rate. Thus, when we design a new type film sensor, this factor
has to be considered. In this study, we have a discussion of the dimensions of the top
electrode in four types ZnO pyroelectric film sensor. The purpose of this discussion is to
create a new shape which can improve the thermal response. In the Rectangle and Criss-cross
type, the length and the width of the top electrode shape will be considered as the variables.
Beside that, for the Target and Web type, we consider the length, the width and the radius are
the optimal variable. We propose the objective function being the temperature variation rate J,
and the maximum J being the value we desire.
J
dT
dt
(10)
In this manner, as the objective function J is approaching its maximum value in the
optimal process with the definition of J, the temperature variation gradually reaches a
maximum value. This implies that the phenomena of temperature variation rate will be
increased.
Assume that, ai , i  1,2,..., l be the set of undetermined coefficients to be optimized in
the iterative process. Different combinations of these coefficients represent different
dimension of electrode shape, from which the optimal location arrangement may be found. In
other words, the coefficients ai , i  1,2,..., l are updated iteratively toward the maximization
of the object function through this optimal process.
The maximum of the objective function is accomplished by using the SCGM method.
The method evaluates the gradient functions of the objective function and sets up a new
14
conjugate direction for the updated undetermined coefficients with the help of a direct
numerical sensitivity analysis.
We perform the direct numerical sensitivity analysis to determine the gradient functions
J / Ja  , i  1, 2,..., l in
n
i
the nth step. First, give perturbation
 ai  to
each of the
undetermined coefficients in the first step, and then find the change of the objective function
 ai  caused
by ai . The gradient function with respect to each of the undetermined
coefficients can be calculated by the direct numerical differentiation as
J
J

ai ai
(11)
Then, we can calculate the conjugate gradient coefficients,  i and the search directions,
n
 in 1 , for each of the undetermined coefficients with
2
  J  n 

 
  ai  
n
i  
, i  1, 2,..., l
n 1 



J


  ai  
(12)
n

n 1
i
 J 
n n

   i  i , i  1, 2,..., l

a
 i
(13)
The step sizes  i , i  1,2,..., l will be assigned for all the undetermined coefficients and
leave it unchanged during the iteration. In this study, the fixed value is determined by a trial
and error process, and the value is set to be 1.0×10-6 typically. The difficulty lies with the fact
that how to decide the suitable value of the step size. The undetermined coefficients will be
updated.
ain 1  ain   i in 1 , i  1, 2,..., l
(14)
15
The procedure for applying the SCGM method is described briefly in the following:
(1) Make an initial guess for the shape profile by giving initial values to the set of
undetermined coefficients. With initialization accomplished, the run itself can begin.
(2) Use the direct problem solver to predict the temperature distribution and calculate the
objective function
J
.
(3) When the objective function reaches a maximum, the solution process is terminated.
Otherwise, proceed to step (4).
(4) Through the Eq. (11), to determine the gradient functions  J / ai  ,  i  1, 2,..., l  .
n
n
(5) Through the Eq. (12) and (13), to calculate the conjugate gradient coefficients,  i ,
n 1
and the search directions,  i , for each of the undetermined coefficients.
(6) Assign a fixed value to the step sizes  i , i  1,2,..., l for all the undetermined
coefficients ai , i  1,2,..., l and leave it unchanged during the iteration.
(7) According the Eq. (14), to update the undetermined coefficients and re-new the
geometry of the film sensor top, and go back to step (2).
The flow chart of the optimization process is plotted in Fig. 10. The self-developed
optimizer and the commercial COMSOL code are connected through an interface program
COMSOL Script. The interface program is written by MATLAB language. Using the
interface it is possible to pass messages among the direct problem solver and the optimizer.
The message of necessary changes in the designed parameters suggested by the optimizer is
sent to the direct problem solver for building the updated geometrical model and generating
grid system for computation. Next, the direct problem solver is executed based on the updated
information to yield the numerical predictions of the flow fields and the objective function as
16
well, which are further transferred back to the optimizer for calculating the consecutive
searching directions. Connection among the optimizer and the direct problem solver is shown
in Fig. 11.
17
Table 1 Parameters of the model for simulation
Material
Thermal
Density
Heat capacity
Length
Width
Conductivity
(Kg/m)
At constant pressure
(m)
(m)
(W/m-K)
(J/kg-k)
Al
237
2700
940
9x10-3
4x10-3
ZnO
6
5767
385
6.775x10-3
3x10-3
Ag
429
10500
235
-
-
18
Fig. 4 Schematic two-dimensional electrically polar lattice [34]
19
Fig. 5 Sawyer - Tower circuit for observing hysteresis loops of pyroelectric materials [34]
20
Fig. 6 The schematic diagram of pyroelectric sensor [35]
21
(a) Rectangle type
(b) Criss-cross type
(c) Target type
(d) Web type
Fig. 7 Shape of the top electrode in the pyroelectric film sensor
22
Ag layer
ZnO layer
Ag layer
Fig. 8 Layer of the pyroelectric film sensor
23
(a) Rectangle type
(b) Criss-cross type
(c) Target type
(d) Web type
Fig. 9 The meshing model of the pyroelectric film sensor
24
Fig.10 The flow chart of the optimization process
25
Fig. 11 Connection among optimizer and direct solver problem
26
3. EXPERIMENT
The purpose of this chapter is to build up an experiment for the transfer function between
temperature and voltage response in ZnO pyroelectric film sensor.
3-1 Experimental Instrument
In the present study, an experimental study of transient heat conduction in a differentially
heated ZnO film sensor is performed. In a heat transfer experiment, except for a transient test,
it may take a long time for the apparatus to reach its steady state. Thus, it may consume lots of
time and much power to conduct an experiment in a thermal system. Experimental
automation, including sequential control of the experiment, auto-data-acquisition and
processing, is of significance in reducing the human errors during the measurements. The
experimental system, as schematically shown in Fig. 13, is made of three major parts: (1)
Rectangle ZnO pyroelectric film sensor, (2) thermocouple, (3) silver inks, (4) spot welding
equipment, (5) Data acquisition and (6) Hot plate.
(1) ZnO pyroelectric film sensor structure.
The Fig. 12 shows the real Rectangle ZnO pyroelectric film sensor used in this
experiment. The structure of this film sensor type includes three layers, and the geometry of
the top electrode is rectangular. The Al layer serves as the bottom electrode, the top electrode
is Ag layer and the ZnO layer plays a role as the sandwich layer. The size of each layer is
9 mm  4 mm  15  m ; 4.8mm  3mm  1 m ; 6.775mm  4 mm  5  m , separately.
(2) Hot plate.
The hot plate YS-300s is used be a heat source for this experiment. The temperature
range of this hot plate is from room temperature to 3000C with the dimensions being
30*30*17H and the heated power being 1500W. We can adjust the PV (measure value and
27
indicator parameter name) and SV (setting value and indicator parameter value) function
provided from the hot plate to create temperature variation.
(3) Silver inks.
In the experimental process, we need to connect the Rectangle ZnO pyroelectric sensor
with thermocouple to get the electric signal. The positive pole of thermocouple is connected
with the top layer and the negative pole is connected with the bottom layer. We use silver inks
to create the connecting. This material has good conductivity, dries fast and very sticky. After
welding, we harden the soldering by keep in 1000C about five minute.
(4) Thermocouple.
Thermocouples utilize the so-called Seebeck effect in order to transform a temperature
difference to a voltage difference. A thermocouple consists of two electrical conductors that
are made of dissimilar metallic materials and have at least one electrical connection. This
electrical connection is referred to as a junction. A thermocouple junction may be created by
welding, soldering, or by any method that provides good electrical contact between the two
conductors, such as twisting the wires around one another. A typical thermocouple circuit has
two junctions. The output of a thermocouple circuit is a voltage, related to the temperatures of
the junctions that make up the circuit.
Thermocouples are characterized according to the alloys that are used for their
construction. The following four classes are the most popular ones: J–type (iron constantan),
K–type (chromel–alumel), E–type (chromel–constantan), and T–type (copper–constantan). Ttype thermocouple at low temperature has the best linearity and stability so this study we used
the smallest of T-type thermocouple (Model AWG-40), the reaction time is only 0.003
seconds.
(5) Spot welding equipment
28
We use T-type thermocouple to measure the temperature. Therefore, to get the Seebeck
effect, we create a thermocouple junction by welding the positive pole with negative pole
using spot welding equipment. The temperature range of welding process is 200~2600C.
(6) Data acquisition system
During the test, the voltage signals from the thermocouples are transferred to
YOKOGAWA MX100 recorder, and then to a personal computer for further data processing.
In the present study, data collection is normally started when the temperature reaches the
steady or statistical state. In this experiment, the input signal from T-type thermocouple will
be transmitted through 20 channels of YOKOGAWA MX100 data acquisition system. This
system is designed to enable desired measurement environments by combining three
elements: the main module, input/output modules, and a base plate. These features of this data
acquisition system are shortest measurement interval of YOKOGAWA 10ms, possible to
acquire data from up to 1200 channels and reinforced insulation between the input terminal
and the case handles 3700Vrms for one minute, or 600Vrms/VDC continuous. To treat the
output signal from data acquisition system, we use a kind of software to connect a single MX
unit to perform data acquisition. This software performs real-time monitoring and logging of
measured data.
29
3-2 Experimental procedure
In the present study, temporal voltage response in the ZnO film sensor is measured by
directly thermocouples of T-type. The T-type thermocouples with diameter 0.0254mm are
fixed at the electrode. Prior to installation, the thermocouples are calibrated by the LAUDA
thermostats and high precision liquid-in-glass thermometers. All the data are then sent to the
personal computer for further data processing. The time history of the data is recorded on the
strip chart and also stored in a magnetic disk. Additionally, to check the background noise, a
temperature measurement about initialization is first performed.
In the experimental system, the Rectangle ZnO pyroelectric sensor is used to measure
voltage response and temperature, respectively. The ZnO film sensor is fixed on the surface of
hot plate and connected with the data acquisition system through the thermocouple. In the
System Setting of MX logger software, we choose the record interval being five seconds and
adjust channel 1 being voltage and channel 2 being temperature. The voltage range keeps in
200mV equivalent with the Span is (min -200, max 200).
When apply the heat to the surface of ZnO film sensor, the variation of temperature
convert to the corresponding electric signal because of the pyroelectric effect. The first
thermocouple will transform this signal to data acquisition system. Beside that, at the junction
of the second thermocouple, it appears the Seebeck effect. Therefore, this thermocouple has
the output voltage signal. Data acquisition system receives and converts two kinds of signals
become different output signals. Channel 1 and channel 2 of data acquisition system have
function accepting these output signals and sending them to computer. And this computer
uses MX logger software to analyze these signals. The interface of Monitor Window indicates
the value and the diagram of output signals (voltage response in channel 1, temperature
response in channel 2). And, we get the detail data by export to excel.
30
Fig. 12 The Rectangular ZnO pyroelectric film sensor
31
Fig. 13 The schematic diagram of experimental system
32
4. RESULTS AND DISCUSSIONS
4-1 Experiment
Through the experimental process, we adjust the PV and SV setting to get the
temperature fluctuation. The experiment time used in this process is 1325s. As can be seen
that the temperature curve has the sine shape with the range from 52.80C to 82.50C. Similarly,
the variation of voltage response has trend as the variation of temperature, and it varies from
1.16mV to 2.66mV.The peak value of voltage response curve is not at the peak value of
temperature curve.
From the collection data in the experiment, we use Matlab software to find out the output
function of temperature follow the time:
T (t )  7.14  1019 t 7  1.03  1015 t 6  2.96 1012 t 5  7.57 109 t 4  5.77 106 t 3
1.56  103 t 2  0.055t  55.29
(17)
And, the function of voltage response follow the time is:
V (t )  1.15 1019 t 7  4.46 1016 t 6  6.05 1013 t 5  3.15 1010 t 4  2.46 108 t 3
1.63 105 t 2  0.0151t  1.2
(18)
In the Fig. 14 describes the fitting curve of the temperature and the fitting curve of the voltage
response from the multinomial function (17), (18). Beside that, this figure also shows the
voltage response profile and temperature profile from the real data in the experiment. This
figure point out the fitting curve of temperature and voltage response can reach to the same
position with the voltage response and temperature profile. And, it also proves that we can use
these multinomial functions to substitute the real data in the experiment.
In addition, the transfer function between voltage response and temperature output can be
expressed as:
33
From (17) and (18), the transfer function between voltage response and temperature output
can be expressed as:
6 3
4 2
3.25 10 T  9 10 T  0.0279T  0.597 ( a ); T2  T1
V (T )  
4 3
2
(b); T2  T1
1.22 10 T  0.0231T  1.4T  28.92
(19)
And the approximate function is:
0.0379T  0.7035
V (T )  
0.0405T  0.5444
( a ); T2  T1
(b); T2  T1
(20)
In (20), we can see that the transfer function has two forms; it depends on the variation of
temperature. If the temperature variation increases, the transfer function has form (a), and if
the temperature variation decreases, the transfer function has form (b). The result function
proves that the voltage response is in proportion to temperature, and the proportion to
temperature reflects right phenomenon of pyroelectric effect in pyroelectric film sensor.
However, this experiment data are just collected from one sample (Rectangle ZnO
pyroelectric film sensor), so it is very poor. Thus, this transfer function has not reflected
exactly the relationship between voltage response and temperature yet. In addition, this data
cannot show the factor in pyroelectric sensor, which influences the voltage response, and the
data can also not use to compare with the simulation result in this study. In the next time, we
can combine the experimental data collection from the four models of ZnO pyroelectric film
sensor to show out the accuracy of phenomena of pyroelectric effect in ZnO pyroelectric film
temperature sensor.
34
4-2 Model simulation
The simulated results are assumed to expose 0s to 1s under the room-temperature. This
study uses the transient process with time dependent option to solve the temperature profile of
the pyroelectric film sensor. In this model, the dimension of the length and width are not in
proportion to the height, so it is hard to mesh. Therefore, we have to increase Z-direction scale
factor in the finite element method package.
Fig. 15 (a) - 15 (d) show the temperature distribution on the top electrode with different
shape types in pyroelectric film sensor. From these figures, we could compare the distribution
of temperature in four types. The temperature range of the rectangle electrode type is higher
than of the rest of three electrode types.
Fig. 16, it shows the response time of temperature field from 0s to 1s and we can discover
the temperature to increase during 0s to 0.4s rapidly. As can be seen in Fig. 16, the
temperature response of the pyroelectric film sensor is affected by the electrode shape exactly.
When the simulated time arrives at 0.1s, the temperature of the film sensor with rectangle type
electrode approaches to 300.84K, and the web type electrode approaches to 300.76K.
Through the comparison between two shapes of the different top electrode on ZnO film
sensor, Fig. 16 shows that the heat transfer rate of the film sensor with the rectangle type
electrode is higher 10% than the one with the web type electrode at 0.1s. The other kinds of
the top electrode have the similar trends as the temperature variation of the film sensor with
the web type electrode.
Fig. 17 presents the temperature variation rate (dT/dt) with different types of the top
electrode in the pyroelectric film sensor. The value of the temperature variation rate on ZnO
film sensor decreases from 0s to 0.4s. After the time is equal 0.4s, the temperature variation
rate converges to 0. From these results, it is concluded that the effect of electric area is
35
important. This figure also shows that the initial temperature variation rate of the rectangle
type is higher than others. It is obviously that the temperature response of the film sensor with
the rectangle type electrode is faster than the ones with other type electrode. But, the
temperature variation rate of the other type of the film sensor will be larger than the rectangle
type of the film sensor gradually as the time after 0.1s. This means that the response of the
film is affected by the different type of the film sensor is important within 0~0.1s. This is the
reason that the hyperbolic heat transfer phenomena happen in this model. More clear
phenomena can be seen from Fig. 18.
From the Fig. 18, the second order derivative temperature (d2T/dt2) is proposed in the
different type electrode of the pyroelectric film sensor. As can be seen from Fig. 17 and Fig.
18, the temperature variation rate (dT/dt) of the film sensor with the rectangle type electrode
not only increases highest than the others, but also the second order temperature derivative
decreases highest. As deduced from here, we know that each of the different shape type of the
top electrode trends the same response after 0.1s. In the other words, the temperature variation
rate before 0.1s is an important issue on the speed of the temperature response.
From these results of this simulation, it proves that the shape of electrode top is direct
affect to thermal response of pyroelectric film sensor is an important problem. The results can
combine the finite element method with optimal method to design the top electrode of optimal
shape and it would gain greatest benefits for improving the temperature variation rate and find
out the substance of pyroelectric phenomena in ZnO pyroelectric film sensor.
36
4-3 Optimization result
In this study, the aim is to achieve the maximum temperature variation rate through
SCGM combined with Comsol for four models of ZnO pyroelectric sensor. And, through the
optimal result, the phenomena of pyroelectric in film sensor are showed and verified. In this
section, according the above simulation results, it proves that the geometry of top electrode
directly affect the temperature variation rate. Therefore, the variation of top electrode area is
the key point which we focus when executes the optimization process. Fig.19 presents the
design variable in every model for ZnO pyroelectric film sensor. The boundary for
optimization program is the variation for the dimension of top electrode with the limit being
the size of the surface on second layer of ZnO pyroelectric sensor. Depending on the
geometry property of top electrode, we have different ways to choose different variables like
the width, the length and radius. To verify and confirm the optimal result, we choose three
different kinds of initial guess with the same boundary in the optimization process for every
model. These initial guesses are summarized as follow:
1. Rectangle model
The variable is the width (X) and length (Y) of top electrode shape. And, the ranges of X
variable and Y variable in the SCGM program are:
Case 1: X = 0.0051m, Y = 0.0032m; 0.0048m ≤ X ≤ 0.0058, 0.003m ≤ Y ≤ 0.004m
Case 2: X = 0.0048m, Y = 0.003m; 0.0048m ≤ X ≤ 0.0058, 0.003m ≤ Y ≤ 0.004m
Case 3: X = 0.0048m, Y = 0.0035m; 0.0048m ≤ X ≤ 0.0058, 0.003m ≤ Y ≤ 0.004m
2. Criss-cross model
The variable is the width (X) and length (Y) of top electrode shape. And, the ranges of X
variable and Y variable in the SCGM program are:
Case 1: X = 0.00505m, Y = 0.00325m; 0.0048m ≤ X ≤ 0.0058, 0.003m ≤ Y ≤ 0.004m
37
Case 2: X = 0.0048m, Y = 0.0035m; 0.0048m ≤ X ≤ 0.0058, 0.003m ≤ Y ≤ 0.004m
Case 3: X = 0.0048m, Y = 0.003m; 0.0048m ≤ X ≤ 0.0058, 0.003m ≤ Y ≤ 0.004m
3. Target model
The variable is the width (X) and length (Y) of top electrode shape. And, the ranges of X
variable and Y variable in the SCGM program are:
Case 1: X = 0.00484m, Y = 0.003m; 0.00484m ≤ X ≤ 0.00634, 0.003m ≤ Y ≤ 0.004m
Case 2: X = 0.00519m, Y = 0.0033m; 0.00484m ≤ X ≤ 0.00634, 0.003m ≤ Y ≤ 0.004m
Case 3: X = 0.005325m, Y = 0.00331m; 0.00484m ≤ X ≤ 0.00634, 0.003m ≤ Y ≤ 0.004m
4. Web model
The variable is the width (X) and length (Y) of top electrode shape. And, the ranges of X
variable and Y variable in the SCGM program are:
Case 1: X = 0.00479m, Y = 0.003m; 0.00479m ≤ X ≤ 0.00629, 0.003m ≤ Y ≤ 0.004m
Case 2: X = 0.005115m, Y = 0.00319m; 0.00479m ≤ X ≤ 0.00629, 0.003m ≤ Y ≤ 0.004m
Case 3: X = 0.005245m, Y = 0.00333m; 0.00479m ≤ X ≤ 0.00629, 0.003m ≤ Y ≤ 0.004m
4-3-1 Rectangle model
Fig.20 (a) - 20 (b) show the temperature distribution of initial guess and optimal result on
top electrode of case 1. Through these figures, we can see that the distribution of temperature
color has a lot of variations. In (b) the red color, yellow color spread wider and the blue color
reduces smaller than in (a), that means there has the increasing of temperature in (b) compare
with (a).
Go to the detail of this phenomenon, Fig.21 (a) - 21 (c) show out the temperature profile
in initial guess and optimal result of Rectangle ZnO pyroelectric sensor. After 0.1s, the
temperature value of optimal result is bigger than of initial guess in case 1, case 2 and case 3
38
are 6.4%, 9.7% and 9.1%. We can evidently see that the temperature curves of the optimal
result are also higher and more uniform than of the initial guess in three cases.
In the next Fig.22 (a) - 22 (c), it presents the temperature variation rate (dT/dt) profiles of
initial guess and optimal result. Here, the value of optimal result curve decreases from 0s to
0.3s, and after 0.3, it starts converging to 0. In case 1, we show the comparison between the
result of the initial guess and the final result through the optimization process with the initial
guess condition, it is clear to see that the temperature variation rate is 8.27K/s at t=0.1s , and
after the optimization, there has improved the temperature variation rate to 9.325K/s. In case
2, it is apparently to see that the highest temperature variation rate is 8.43K/s at t = 0.1sin the
initial guess condition and the temperature variation rate has been raised to 9.34K/s when the
program finishes the convergence process. In case 3, the optimal result shows that at t = 0.1s
the temperature variation rate increase from 8.49K/s to 9.346K/s. Those results obviously see
that the temperature response of optimal results is faster than of initial guesses.
On the other hand, the second order derivative of temperature (d2T/dt2) is presented in
Fig.23 (a) - 23 (c). From case (a), (b) and (c), as can be seen, the second order derivative of
optimal results has the lower value than of initial guesses at 0s, but increase and get the
biggest value at 0.25s. Where the slope of the optimal curves have the highest value from 0s
to 0.1s. At 0.1s, the second order derivative of temperature of optimal result is bigger than of
initial guess in case 1, case 2 and case 3 are 12.55%, 19.35% and 17.6%. In the application
scope, the response speed is an important factor to verify the effect of film temperature sensor.
So, with the increase the second order derivative of temperature value as above in the interval
from 0s to 0.1s, it proves that the dimension value of top electrode after optimization can
improve the quality of the ZnO pyroelectric sensor in our study.
39
The Fig. 24 (a) shows the variation of the objective function during the optimization with
the first initial guess. In general, through global of the boundary, the value of the objective
function is continuously increasing and it fluctuate very trouble. However, there have some
differences in every stage of the process. From the 1st iteration to about the 230th iteration, the
objective function fluctuates with the amplitude smaller than with after from the 230th
iteration. To go to the target optimal result, this optimization needs 341 iterations to increase
the objective function value from 15.71K/s to 17.8K/s. The raising of this objective function
is 11.7%. From the results, we can easily realize the influence of top electrode area to the
temperature variation rate. When SCGM program updates the variable value in the
optimization process, the dimension of top electrode is broaden and make the top electrode
area which contacts with heat source become bigger. So, it increases the ability for absorption
the heat of pyroelectric film sensor. Thus, it has the raise of temperature variation rate in the
optimization process.
The Fig. 24 (b) presents the optimal result with the second initial guess. From the
convergence map, we can see that the variation of the objective function has trend like case 1,
but through the optimization process, the fluctuation of the objective function can be divided
into three stages. From the 1st iteration to about the 200th iteration, the objective function
value fluctuates with the amplitude bigger than the fluctuation amplitude of the stage has the
iterations from the 200th iteration to about the 350th iteration, and after 350th iteration, the
objective function value fluctuates with the biggest amplitude to find the optimal value.
Whole process needs 509 iterations and the objective function increases from 15.1K/s to
17.82K/s. The percentage of the optimal value is higher than of initial guess value about
15.2%. The result shows that this optimization program can effectively increase the objective
function value.
40
Beside that, Fig. 24 (c) illustrates another optimization process with the third initial
guess. In this process, the variation of objective function is very similar trend to the case 1.
From the 1st iteration to about the 230th iteration, the objective function fluctuates with the
amplitude smaller than the amplitude of the objective function after from the 230th iteration.
In this case, the objective function converges after 466th iterations. At this time, the SCGM
program gets the maximum value of objective function at 17.86K/s with the initial guess
being 15.27K/s. The increasing percentage of this maximum value is 14.5%. After the
optimization of three cases, we see that although the variation of the objective function
through the boundary has the difference about the fluctuation amplitude and iteration in every
case, altogether, the objective function value always fluctuates with the biggest amplitude in
the final stage of every process to find the maximum value of objective function.
From Fig 24 (a) - Fig 24 (c), we can see the impact of different initial value to the number
of iteration and the increase of objective function in the optimization process. The numbers of
iterations required to reach the optimal designs are roughly 341,509 and 466 for case 1, case 2
and case 3, respectively. And, the maximums of objective functions in every case in turn are
17.8K/s, 17.82K/s, 17.86K/s. The results prove that even the initial value and the iteration are
not the same; the objective function will be raised to the same value at the same surrounding
enactment.
Next, we discuss about the relationship between variation of the variable and the
iteration. In the first initial guess, the variation of the optimization process is showed in Fig.
25 (a). Here, the initial values are x = 0.0051m and y = 0.0032m, these variables are the width
and the length of top electrode shape. They increase after 341 iterations and converge with the
value x = 0.005748m, y = 0.003048m. As can be seen in this figure, X variable linearly
increases upward; however, at the end of this line, there are some X values decrease. Beside
41
that, Y variable just varies in a small range, and always fluctuates no steady to find the
optimal value.
Fig. 25 (b) presents the variation of second initial guess. In this case, X variable starts at
0.0048m and Y variable starts at 0.003m, these dimensions also are the original dimensions of
the model. In this process, to get the maximum objective function, it needs 509 iterations and
the variable converges at x = 0.005792m and y = 0.003138m. From this figure, we see that the
variation of X variable is similar trend to the case 1, but at the end of this line, X variable is
not only decrease but also increase. And, although Y variable also fluctuates, the oscillation
trend is raise, not reduce like the case 1.
The variation of third initial value is verified in Fig. 25 (c), two curves of X, Y variables
begin at x = 0.0048m and y = 0.0035m. At x = 0.00572m and y = 0.003448m, the objective
function gets the maximum value. This optimization process needs the number of iteration
being 446 times; it is smaller than of the case 2 and bigger than of the case 1. The variation of
the X variable varies linearly through the boundary; the variation of the Y variable also has
the fluctuation trend like the case 1.
The variation of variable in the initial and optimal process is shown in table 2. The X
variable for case 1, case 2 and case 3 are raised from 0.0051m, 0.0048m and 0.0048m to
0.005748m, 0.005792m and 0.00572m, respectively. These results make the length of top
electrode wider. Beside that, the variable Y varies from 0.0032m, 0.003m, and 0.0035m to
0.003048m, 0.003138m and 0.003448m, respectively. From these results, it can be seen that
the variation of two variables is different, X variable increase with the large range, by contrast,
Y fluctuates follow a small cycle or periodicity, it easily realizes that the effect of X variable
to the temperature variation rate is higher than of Y variable in this model. Besides that,
compare the area of top electrode after the optimization process in every case in turn are
42
1.75×10-5m2, 1.81×10-5m2 and 1.97×10-5m2 correlative with 17.8K/s, 17.82K/s, and 17.86K/s,
respectively. It proves that the temperature variation rate depends on the area of top electrode
and expresses the right phenomena of pyroelectric in film temperature sensor.
4-3-2 Criss-cross model
The Fig. 26 (a) - 26 (b) show the temperature distribution of initial guess and optimal
result on the top electrode of case 1. Through these figures, we can see that the distribution of
temperature color has a lot of changes. In (b) the red color, yellow color spread wider and the
blue color reduces smaller than in (a), that mean there has the increase of temperature in (b)
compare with (a).
Go to the detail of this phenomenon, Fig. 27 (a) - 27 (c) show out the temperature profile
in initial guess and optimal result of Criss-cross ZnO pyroelectric sensor. After 0.1s, the
temperature value of optimal result bigger than of initial guess in case 1, case 2 and case 3 are
6.73%, 9.55% and 11.57%. We can evidently see that the temperature curves of the optimal
result are also higher and more uniform than of initial guess in three cases.
In the next Fig. 28 (a) - 28 (c), it presents the temperature variation rate (dT/dt) profiles
of initial guess and optimal result. Here, the value of optimal result curve decreases from 0s
to 0.3s and after 0.3s, it starts converging to 0. In case 1 , we show the comparison between
the result of the initial guess and the final result through the optimization process with the
initial guess condition, it is clear to see that the temperature variation rate 8.71K/s is at t =
0.1s, and after the optimization, there has improved the temperature variation rate to
9.339K/s. In case 2, it is apparently to see that the highest temperature variation rate is
8.44K/s at t = 0.1s in the initial guess condition and the temperature variation rate has been
raised to 9.332K/s when the SCGM program finishes the convergence process. In case 3, the
optimal result shows that at t = 0.1s the temperature variation rate increase from 8.23K/s to
43
9.307K/s. Those results obviously see that the temperature response of optimal results is faster
than initial guesses.
On the other hand, the second order derivative of temperature (d2T/dt2) is presented in
Fig. 29 (a) - 29 (c). From case (a), (b) and (c), as can be seen, the second order derivatives of
optimal results has the lower value than of initial guesses at 0s, but increase and get the
biggest value at 0.25s, where the slope of the optimal curves has highest value from 0s to 0.1s.
At 0.1s, the second order derivative of temperature of optimal result bigger than of initial
guess in case 1, case 2 and case 3 are 13.4%, 18.41% and 22.4%. In the application scope, the
response speed is an important factor to verify the effect of film temperature sensor. So, with
the increase the second order derivative of temperature value as above in the interval of
response time from 0s to 0.1s, it proves that the dimension value of top electrode after
optimization can improve the quality of the ZnO pyroelectric sensor in our study.
Fig. 30 (a) shows out the relationship between the objective function and the iteration
with the first initial guess. In general, the value of the objective function is continuously
increasing and it fluctuate very trouble through global of the boundary. In this case, the
objective function value increases from 15.91K/s to 17.78K/s with 346 iterations. The raising
of this objective function is 10.5%. From the results, we can easily realize the influence of top
electrode area to the temperature variation rate. When SCGM program updates the variable
value in the optimization process, the dimension of top electrode is broaden and make the top
electrode area which contacts with heat source become bigger. So, it increases the ability for
absorption the heat of pyroelectric film sensor. Thus, it has the raise of temperature variation
rate in the optimization process.
Fig. 30 (b) presents the optimal result with the second initial guess. From the
convergence map, we can see that the variation of the objective function has similar trend to
44
case 1. Whole the optimization process needs 492 iterations and the objective function
increases from 15.3K/s to 17.8K/s. The percentage of the optimal value is higher than of
initial guess value about 15%. The result shows that this optimization program can effectively
increase the objective function value.
Beside that, Fig. 30 (c) illustrates another optimal result with the third initial guess. In
this optimization process, the objective function curve also has similar trend to case 1 and 2.
After 478 iterations, the objective function is converged. The SCGM program starts from
14.66K/s and gets the optimal value at 17.83K/s. The increasing percentage of this maximum
value is 17.7%.
From Fig. 30 (a) - Fig 30. (c), we can see the impact of different initial value to the
number of iteration and the increase of objective function in the optimization process. The
numbers of iterations required to reach the optimal designs are roughly 364, 492 and 487 for
case 1, case 2 and case 3, respectively. And, the maximums of objective functions in every
case in turn are 17.78K/s, 17.8K/s, 17.83K/s. The results prove that even the initial value and
the iteration are not the same; the objective function will be raised to the same value at the
same surrounding enactment.
Next, we discuss about the relationship between variation of the variable and the
iteration. In the first initial guess, the optimization process is showed in Fig. 31 (a). Here, the
initial values are x = 0.00505m and y = 0.00325m, these variables are the length and the width
of top electrode. When the SCGM program operates, the objective function increases and
converges after 364 iterations with the optimal values of variable are x = 0.005744m and y =
0.003256m, as can be seen in this figure, X variable linearly increases upward, but at the end
of this line has some X values decrease. Beside that, Y variable just varies in a small range,
and always fluctuates no steady to find the optimal dimension.
45
Fig. 31 (b) presents the variation of the variable with the second initial guess. In this case,
X variable starts at 0.0048m and Y variable starts at 0.0035m, in this process, to get the
maximum objective function, it needs 492 iterations and the variables are converged at x =
0.005742m and y = 0.003618m. From this figure, we also see that the variation of X and Y
variable has similar trend to case 1.
The variation of third initial value is verified in Fig. 31 (c), two curves of X and Y
variables begin at x = 0.0048m and y = 0.003m, these dimensions also are the original
dimensions of top electrode in this model. At x = 0.005768m and y = 0.00321m, the objective
function gets the maximum value. This optimization process needs the number of iteration is
478 times, it smaller than case 2 and bigger than case 1. The variation of X variable varies
linearly through the boundary and Y variable also has the fluctuation trend like the case 1.
The variation of variable in the initial guess and optimal process is shown in table 3. The
variable X for case 1, case 2 and case 3 are raised from 0.00505m, 0.0048m and 0.0048m to
0.005744m, 0.005742m and 0.005768m, respectively. This result makes the length of top
electrode will be wider. Beside that, the variable Y varies from 0.00325m, 0.0035m and
0.003m to 0.003256m, 0.003618m and 0.00321m, respectively. From these results can be
seen that the variation of two variables is different, X variable increase through the boundary
with the large range, by contrast, Y fluctuates follow a small cycle or periodicity, it easily
realize that the effect of X variable to the temperature variation rate is higher than Y variable
in this model.
From the optimal result of model 1 and model 2, it can be seen that those results have
nearly equal value. Although two models have same original dimensions and geometrical
properties, but the top electrode of model 2 has these windows. Follow the theory, the
window in the top electrode shape make the second layer (ZnO pyroelectric layer) direct
46
contact with heat source. Consequently, increase the heat absorption of pyroelectric film
sensor. That means improve the temperature variation rate in the pyroelectric film sensor. So,
the temperature variation rate in model 2 must bigger than model 1. Here, we have the
opposition in the conclusion, going to the phenomena of this problem. In the simulation
process of model 1 and 2, when the heat transfers from the surface of top electrode to the
surface of second layer, the Comsol software cannot simulate accurate the temperature value
because the thickness of top electrode is too small 1µm. Therefore, with the same simulation
time, the temperature value in the surface of second layer in the model 1 is equal the
temperature value in the surface of second layer in the model 2. That‘s why, the variations of
temperature in model 1 and model 2 are the same. These results prove that because of the
geometrical property of the model and the restriction of Comsol software, we cannot see the
effect of the window in the top electrode to the temperature variation rate of the ZnO
pyroelectric film sensor in this research.
4-3-3 Target model
Fig. 32 (a) - 32 (b) show the temperature distribution of initial guess and optimal result
on the top electrode of case 1. Through these figures, we can see that the distribution of
temperature color has a lot of variations. In (b) the red color, yellow color spread wider and
the blue color reduces smaller than in (a), it points out there has the increasing of temperature
in (b) compare with (a). And, the detail of temperature value is presented in next figures.
Fig. 33 (a) - 33 (c) show the temperature profile in initial guess and optimal result of
Target ZnO pyroelectric sensor. At t = 0.1s, the temperature values of initial guess in case 1,
case 2, and case 3 are 300.783K, 300.841K, and 300.861K, respectively. After optimization,
at t=0.1s, the temperature values of optimal results are 300.964K, 300.964K, and 300.962K
correlative with case 1, case 2, and case 3, respectively. We can evidently see that the
47
temperature curves of the optimal result are also higher and more uniform than of the initial
guess in three cases.
In the next Fig. 34 (a) - 34 (c), it presents the temperature variation rate (dT/dt) profiles
of initial guess and optimal result. Here, the value of optimal result curve decreases from 0s to
0.3s, and after 0.3s, it starts converging to 0. In case 1, we show the comparison between the
result of the initial guess and the final result through the optimization process with the initial
guess condition, it is clear to see that the temperature variation rate is 7.83K at t = 0.1s, and
after the optimization, there has improved the temperature variation rate to 9.64K/s. In case 2,
it is apparently to see that the highest temperature variation rate is 8.41K/s at t = 0.1s in the
initial guess condition and the temperature variation rate has been raised to 9.64K / s when the
SCGM program finishes the convergence process. In case 3, the optimal result shows that at t
= 0.1s the temperature variation rate increase from 8.61K/s to 9.62K/s. Those results
obviously see that the temperature response of optimal results is faster than of initial guesses.
On the other hand, the second order derivative of temperature d2T/dt2 is presented in Fig.
35 (a) - 35 (c). From case (a), (b) and (c), as can be seen, the second order derivative of
optimal results has the lower value than of initial guesses at 0s, but increase and get the
biggest value at 0.25s, where the slope of the optimal curves has the highest value from 0s to
0.1s. At 0.1s, the second order derivative of temperature of optimal result is bigger than of
initial guess in case 1, case 2 and case 3 are 34.71%, 24.21% and 20.48%. In the application
scope, the response speed is an important factor to verify the effect of film temperature sensor.
So, with the increase the second order derivative of temperature value as above in the interval
of response time from 0s to 0.1s, it proves that the dimension value of top electrode after
optimization process can improve the quality of the ZnO pyroelectric sensor in our study.
48
Fig. 36 (a) shows out the convergence of objective function in the optimization process.
From this map, we can see that the objective function has the continuously upward
phenomenon and fluctuates troublous through the boundary. From 1st iteration to about the
250th iteration, the increasing property of objective function likes a linear line and after 250th
iteration it still increases but the trend like a curve. Finally, this optimization program
converges with the total iteration being 469 iterations. At this time, the objective function
varies from 13.81K/s to 18.97K/s. The increasing percentage of this maximum value is
27.22%.
Fig. 36 (b) presents the optimal result of case 2 with the second initial guess. In general,
the graph varies similar trend to case 1, but at about the 120th iteration the objective function
begin transform from the linear line to the curve. Eventually the program needs 344 iterations
to finish this optimization. The objective function increases from 15.34K / s and gains the
optimal result at 18.95K/s. The percentage of the optimal value is higher than of initial guess
value about 19%.
Fig. 36 (c) illustrates another optimal result with the third initial guess. The convergence
map has a little bit different with case 1 and case 2. From 1st iteration to about the 140th
iteration, the objective function increases linear, after 140th iteration, it still increases follow a
curve and after about the 270th iteration, this curve converts to a line. In this final stage, the
SCGM program finds maximum value of objective function for whole process. The objective
function converges after 334th iterations. And, at this time, it has the optimal value being
18.9K/s with the initial value being 16K/s. The increasing percentage of this maximum value
is 15.34%. The results of case 1, case 2 and case 3 show that this optimization program can
effectively increase the objective function value.
49
From Fig 36 (a) - Fig 36 (c), we can see the impact of different initial value to the number
of iteration and the increase of objective function in the optimization process. The numbers of
iterations required to reach the optimal designs are roughly 469, 344 and 334 for case 1, case
2 and case 3 , respectively. And, the maximums of objective functions in every case in turn
are 18.97K/s, 18.95K/s and 18.9K/s. The results prove that even the initial value and the
iteration are not the same; the objective function will be raised to the same value at the same
surrounding enactment.
Next, we discuss about the variation of variable and the iteration. In the first initial guess,
the convergence process of variable is showed in Fig. 37(a). Here, the initial value is x =
0.00484m and y = 0.003m, these dimensions also are the original dimensions of top electrode
in this model. When the SCGM program operates, the variables are automatically updated to
find the maximum value of the objective function. In this process, X variable and Y variable
increase linearly. But at the end segment of two optimal curves, there have some X values and
Y values raise no steady to find the optimal value. The optimization program converges after
469 iterations, and the values of optimal variables are x = 0.006248m and y = 0.00394m. The
increasing percentage of X variable and Y variable are 22.53% and 23.87%. And the result
proves that the influence of X, Y variable is the same in the improving temperature variation
rate of this model.
Fig. 37 (b) describes the relationship between the variation of the variable and the
iteration of case 2 with the second initial value. In this case, X variable starts at 0.00519m and
Y variable begins at 0.0033m, these variables are the width and the length of top electrode.
From this figure, we also see that the variation of X variable linearly develops through the
boundary, beside that Y variable linearly develops and just has a little no stable at the end of
the process, . In this process, the SCGM program needs 344 iterations to get the maximum
50
value of the objective function, and two variables are converged at x = 0.006213m and y =
0.003974m. The percentage of the optimal value is higher than of initial guess value about
16.4% with X variable and 19.6% with Y variable. The result shows that, the increasing
percentage of Y variable is higher than of X variable. However, when we compare the optimal
values of X variable and Y variable between case 1 and case 2, there have the inconsiderable
differences in values. Thus, the big difference of percentage between X variable and Y
variable has the reason from the initial guess. Because the X initial value is nearer with the
optimal location than Y initial value, therefore, there has the increase of X variable is lower
than of Y variable. And, this result demonstrates that the impact of X, Y variable to the
temperature variation rate in the optimization of this case is the same.
The variation of third initial value is verified in Fig. 37 (c). This optimization process
needs the number of iteration being 334 times. In general, the variation of X, Y variable also
has the similar trend to case 1 and case 2. But, from about the 280th iteration, X and Y
variable fluctuate with small magnitude to find the optimal dimension. Two curves of X, Y
variables begin at x = 0.005325m, y = 0.00331m and finish at x = 0.006219m, y = 0.003914m.
The percentage of the optimal value is higher than of initial guess value about 14.3% and
15.4% correlative with X variable and Y variable. In this case, following the result from the
optimization process, we also see that the effect of two variables in this model to the
increasing temperature variation rate is the same.
The variation of variable in the initial guess and optimal process is shown in table 4. The
X variable for case 1, case 2 and case 3 are raised from 0.00484m, 0.00519m and 0.005325m
to 0.006248m, 0.006213m and 0.006219m, respectively. Beside that, the Y variable varies
from 0.003m, 0.0033m and 0.00331m to 0.00394m, 0.003974m and 0.003914m, respectively.
The optimization makes the width and the length of top electrode become larger. And, those
51
dimensions reach to the restriction of the boundary to obtain the maximum value of
temperature variation rate. The expansion of top electrode makes the top electrode area which
contacts with heat source become bigger. So, it increases the ability for absorption the heat of
pyroelectric film sensor. Thus, it has the raise of temperature variation rate in the optimization
process.
4-3-4 Web model
Fig. 38 (a) - 38 (b) show the temperature distribution of initial guess and optimal result
on the top electrode of case 1. Through these figures, we can see that the distribution of
temperature color has a lot of variations. In (b) the red color, yellow color spread wider and
the blue color reduces smaller than in (a), it points out there has the increasing of temperature
in (b) compare with (a). And, the detail of temperature value is presented in next figures.
Fig.39 (a) - 39 (c) show out the temperature profile in initial guess and optimal result of
Web ZnO pyroelectric sensor. At t = 0.1s, the temperature value of initial guess in case 1,
case 2 and case 3 are 300.767K, 300.826K and 300.846K, respectively. After optimization, at
t = 0.1s, the temperature value of optimal results are 300.948K, 300.949K and 300.951K
correlative with case 1, case 2, and case 3, respectively. We can evidently see that the
temperature curves of the optimal result are also higher and more uniform than of the initial
guess in three cases.
From Fig. 40 (a) - 40 (c), it present the temperature variation rate (dT/dt) profiles of
initial guess and optimal result. Here, the value of optimal result curve decreases from 0s to
0.3s, and after 0.3s, it starts converging to 0. In case 1, we show the comparison between the
result of the initial guess and the final result through the optimization process with the initial
guess condition, it is clear to see that the temperature variation rate is 7.67K/s at t = 0.1s, and
after the optimization, there has improved the temperature variation rate to 9.48K/s. In case 2,
52
it is apparently to see that the highest temperature variation rate is 8.26K/s at t = 0.1s in the
initial guess condition and the temperature variation rate has been raised to 9.49K/s after the
optimization. In case 3, the optimal result shows that at t = 0.1s the temperature variation rate
increase from 8.46K/s to 9.51K/s. Those results obviously see that the temperature response
of optimal results is faster than of initial guesses.
On the other hand, the second order derivative of temperature (d2T/dt2) is presented in
Fig. 41 (a) - 41 (c). From case (a), (b) and (c), as can be seen, the second order derivative of
optimal results has the lower value than of initial guesses at 0s, but increase and get the
biggest value at 0.25s. Where the slope of the optimal curves has the highest value from 0s to
0.1s. At 0.1s, the second order derivative of temperature of optimal result is bigger than of
initial guess in case 1, case 2 and case 3 are 35.5%, 24.75% and 21.25%. In the application
scope, the response speed is an important factor to verify the effect of film temperature sensor.
So, with the increase the second order derivative of temperature value as above in the interval
of response time from 0s to 0.1s, it proves that the dimension value of top electrode after
optimization process can improve the quality of the ZnO pyroelectric sensor in our study.
Fig. 42 (a) shows the convergence of the objective function in the optimization process
for the first initial guess. From this map, we can see that the objective function has the
continuously upward phenomenon and fluctuates troublous through the boundary. Where,
from 1 iteration to about the 270th iteration, the increasing property of objective function likes
st
a linear line, and after 270th iteration, it still increases but the trend like a curve. Finally, this
program stops at the 437th iteration. At this time, the objective function varies from 13.3K/s to
18.46 K/s. The increasing percentage of this maximum value is 27.95%.
Fig. 42 (b) presents the optimal result of case 2 with the second initial guess. In general,
the objective function curve has the trend linear increase and always fluctuates through the
53
boundary. This process needs 317 iterations to gain the optimal result .The objective function
increases from 14.98K/s to 18.49K/s. The percentage of the optimal value is higher than of
initial guess value about 18.98%.
Fig. 42 (c) illustrates another optimal result with the third initial guess. We can see that
the convergence map has similar trend to case 2. When the optimization program is at the
267th iteration, the maximum value of objective function is 18.62K/s with the initial value
being 15.49K/s. The increasing percentage of this maximum value is 16.8%. The results of
case 1, case 2 and case 3 show that this optimization program can effectively increase the
objective function value.
In this research, following the conclusion of the results from the Rectangle model and the
Criss-cross model, we know that the window in the top electrode of ZnO pyroelectric sensor
does not effect to the improving the temperature variation rate. Therefore, the optimal values
of Target model and Web model will reach to the same optimal value after the optimization
because they have same optimal conditions; those are geometry property of the model, the
definition of design variable and the restriction of the boundary. However, the optimal result
of Web model is smaller than of Target model. From the optimization, we can see that, when
the variables near the boundary, the updated model cannot simulate. So, the SCGM stops at
those dimensions. This problem comes from the geometrical property of the Web model. This
model has some windows in the top electrode whose the dimensions are very small, and the
thickness of top electrode is 1µm. Thus, this model gets the difficulty to create the mesh in the
simulation process. When the variables are updated by SCGM program and reach to the
restriction of the boundary, at this time, in this location, there exist these dimensions make the
degenerated tetrahedrons appear inside the model. So, Comsol software cannot mesh in the
simulation process. And, we get the optimal values at this place. From Fig 42 (a) - Fig 42 (c),
54
we can see that with different initial values, the numbers of iterations required to reach the
optimal designs are roughly 437, 317 and 267 for case 1, case 2 and case 3, respectively. And,
the maximum values of objective functions in every case in turn are 18.46K/s, 18.49K/s and
18.62K/s, respectively.
Next, we discuss about the variation of variable and the iteration. In the first initial guess,
the convergence process of variable is showed in Fig. 43 (a). Here, the initial values are x =
0.00479m and y = 0.003m, these dimensions also are the original dimensions of the top
electrode in this model. When the SCGM program operates, the variables are automatically
updated to find the optimal value. In this process, X variable and Y variable increase linearly,
but in the optimal lines, we see that, there have some X values and Y values raise no steady.
And after 469 iterations, this program finishes the optimization process at x = 0.006075m and
y = 0.003846m. The increasing percentages of X, Y variables are 20.32% and 21.99% and the
result proves that the influence of X, Y variable is the same in the improving the temperature
variation rate of this model.
Fig. 43 (b) describes the relationship between the variation of variable and iteration of the
case 2 with the second initial value. In this case, X variable starts at 0.005115m and Y
variable starts at 0.00319m, these variables are the width and the length of top electrode
shape. From this figure, we also see that the variations of X, Y variables develop linearly
through the optimization process. The program needs 317 iterations to reach the maximum
value of objective function. At this time, the variable values are x = 0.006067m and y =
0.00383m. The percentage of the optimal value is higher than of initial guess value about
15.69% with X variable and 16.71% with Y variable. The result demonstrates that the impact
of X, Y variable to the temperature variation rate in the optimization is the same.
55
The variation of third initial value is verified in Fig. 43 (c). This optimization process
needs the number of iteration being 267 times. In general, the variation of X, Y variable also
has the similar trend to case 2. Two curves of X, Y variables begin at x = 0.005245m, y =
0.00333m and the optimization program obtain the optimal value when two variables are x =
0.006091m, y = 0.003894m. The percentage of the optimal value is higher than of initial
guess value about 13.88% and 14.48% correlative with X variable and Y variable. In this
case, following the result from the optimization process, we also see that the effect of two
variables in this model to the increase temperature variation rate is the same.
The variation of variable in the initial guess and optimal process is shown in table 5. The
variables X for case 1, case 2 and case 3 are raised from 0.00479m, 0.005115m and
0.005245m to 0.006075m, 0.006067m and 0.006091m, respectively. Beside that, the variable
Y varies from 0.003m, 0.00319m and 0.00333m to 0.003846m, 0.00383m and 0.003894m,
respectively. The optimization makes the width and the length of top electrode become larger.
And, those dimensions reach to the restriction of the boundary to obtain the maximum value
of temperature variation rate. The expansion of top electrode makes the top electrode area
which contacts with heat source become bigger. So, it increases the ability for absorption the
heat of pyroelectric film sensor. Thus, it has the raise of temperature variation rate in the
optimization process.
In this optimization part, we can divide four models become two groups by the geometry
property of top electrode for convenient in the comparison the optimal result and the
phenomena occur in the ZnO pyroelectric film sensor. The first group includes Rectangle and
Criss-cross model with the top electrode is rectangular shape. The second group includes
Target and Web type; they have the top electrode being rectangular shape combine with
cylinder shape. After the optimization, we can see the variations of X variable and Y variable
56
in the first group are different, X linearly increase through the boundary, but Y just varies
with a small cycle or periodicity. Beside that, in the second group X variable and Y variable,
together, varies linearly through the boundary. Thus, we can realize that the influence of Y
variable in group 1 to the temperature variation rate is smaller than in group 2. That the
reason, the objective function values in the group 1 always fluctuate with the magnitude
bigger than in the group 2 to find the optimal value. In addition, the optimal results of group 1
are smaller than of group 2. When we build up the variable for the SCGM program, although
we consider that the variable form for four models is similar, in two groups, they have
different about the geometry property in the top electrode. So, the combination between X
variable and Y variable to create the new updated model in the optimization process make the
length of top electrode shape in the group 2 has the update value bigger than of group 1.
Therefore, SCGM program can broaden the area of top electrode in group 2 bigger than in
group 1 and that is why the optimal values of group 2 are bigger than of group 1.
57
Table 2 The variable variation in the initial guess and optimal process of Rectangle
type
Variable (m)
X
Y
Initial
0.0051
0.0032
Optimal
0.005748
0.003048
Initial
0.0048
0.003
Optimal
0.005792
0.00313
Initial
0.0048
0.0035
Optimal
0.00572
0.003448
Case 1
Case 2
Case 3
58
Table 3 The variable variation in the initial value and optimal process of Criss-cross
type
Variable (m)
X
Y
Initial
0.00505
0.00325
Optimal
0.005744
0.003256
Initial
0.0048
0.0035
Optimal
0.005742
0.003618
Initial
0.0048
0.003
Optimal
0.005768
0.00321
Case 1
Case 2
Case 3
59
Table 4 The variable variation in the initial guess and optimal process of Target type
Variable (m)
X
Y
Initial
0.00484
0.003
Optimal
0.006248
0.00394
Initial
0.00519
0.0033
Optimal
0.006213
0.003974
Initial
0.005325
0.00331
Optimal
0.006219
0.003914
Case 1
Case 2
Case 3
60
Table 5 The variable variation in the initial guess and optimal process of Web type
Variable (m)
X
Y
Initial
0.00479
0.003
Optimal
0.006075
0.003846
Initial
0.005115
0.00319
Optimal
0.006067
0.00383
Initial
0.005245
0.00333
Optimal
0.006091
0.003894
Case 1
Case 2
Case 3
61
Fig. 14 The voltage response profile and temperature profile with the fitting curve from the
multinomial function
62
(a) Rectangle type
(b) Criss cross type
(c) Target type
(d) Web type
Fig. 15 The temperature distribution of top electrode in the pyroelectric film sensor at 0.1s
63
Fig. 16 The temperature profiles of pyroelectric film sensor with different shape type of top
electrode
64
Fig. 17 The temperature variation rate of pyroelectric film sensor with different shape type of
top electrode
65
Fig. 18 The second order derivative of temperature in the pyroelectric film sensor
with different shape type of top electrode
66
(a) Rectangle type
(b) Criss-cross type
(c) Target type
(d) Web type
Fig. 19 The design variable in different kinds of ZnO pyroelectric sensor
67
(a) Initial guess
(b) Optimal
Fig. 20 The temperature distribution in the initial guess and optimal of Rectangle type at 0.05s
68
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 21 The temperature profile in the initial guess and optimal of Rectangle type
69
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 22 The temperature variation rate profile in the initial guess and optimal of Rectangle
type
70
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 23 The second order derivative of temperature profile in the initial guess and optimal
of Rectangle type
71
(a) Case 1
(b) Case 2
(c) Case 3
Fig.24 Convergence process of the objective function in different initial value for Rectangle
type
72
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 25 The variation of the design variable through the optimal process for Rectangle type
73
`
(a) Initial guess
(b) Optimal
Fig. 26 The temperature distribution in the initial guess and optimal of Criss-cross type at
0.05s
74
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 27 The temperature profile in the initial guess and optimal of Criss-cross type
75
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 28 The temperature variation rate profile in the initial guess and optimal of Criss-cross
type
76
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 29 The second order derivative of temperature profile in the initial guess and optimal of
Criss-cross type
77
(a) Case 1
(b) Case 2
(c) Case 3
Fig.30 Convergence process of the objective function in different initial value for Criss-cross
type.
78
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 31 The variation of the design variable through the optimal process for Criss-cross type
79
(a) Initial guess
(b) Optimal
Fig. 32 The temperature distribution in the initial guess and optimal of Target type at 0.05s
80
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 33 The temperature profile in the initial guess and optimal of Target type
81
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 34 The temperature variation rate profile in the initial guess and optimal of Target type
82
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 35 The second order derivative of temperature profile in the initial guess and optimal of
Target type
83
(a) Case 1
(b) Case 2
(c) Case 3
Fig.36 Convergence process of the objective function in different initial value for Target type.
84
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 37 The variation of the design variable through the optimal process for Target type
85
(a) Initial guess
(b) Optimal
Fig. 38 The temperature distribution in the initial guess and optimal of Web type at 0.05s
.
86
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 39 The temperature profile in the initial guess and optimal of Web type
87
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 40 The temperature variation rate profile in the initial guess and optimal of Web type
88
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 41 The second order derivative of temperature profile in the initial guess and optimal of
Web type
89
(a) Case 1
(b) Case 2
(c) Case 3
Fig.42 Convergence process of the objective function in different initial value for Web type.
90
(a) Case 1
(b) Case 2
(c) Case 3
Fig. 43 The variation of the design variable through the optimal process for Web type
91
5. CONCLUSION
In this study, a transfer function between voltage response and temperature is presented.
The result demonstrates that voltage response is an important factor to detect the temperature
in the film temperature sensor. Although the experiment data are just collected from one
sample (Rectangle ZnO pyroelectric film sensor), they can reflect the right phenomena of
pyroelectric effect in pyroelectric film sensor. However, this experiment result is still not
enough to gain the success in exact verification the relationship between voltage response and
temperature. This problem can be continuingly studied in the next researches to find out the
real substance of ZnO pyroelectric film temperature sensor.
Beside that, the temperature variation rate of pyroelectric film sensor is simulated by the
finite element method in this study. The simulated results prove that the shape of top electrode
of pyroelectric film sensor affects the temperature variation rate. And, it also shows that the
response variation value of dT/dt and d2T/dt2 obviously varies from 0s to 0.1s. In general, the
temperature variation rate is an important problem on the ZnO pyroelectric film sensor. In
order to obtain the different response, it presents the simulation for the different kinds of
shapes design of the top electrode in this study. It shows that the thermal response of the ZnO
pyroelectric film sensor can be affected and improved by the different kinds of the electrode.
In addition, we combine SCGM method and Comsol software to gain the greatest
benefits in the shape design of top electrode on the ZnO pyroelectric film sensor for four
models. Where the Rectangle type, the Criss-cross type, the Target type, and the Web type
have the raising of the temperature variation rate about 15.26%, 17.79%, 27.22% and 27.95%,
respectively. On the other hand, the optimal results also show out the second order derivative
of temperature has the increasing percentage in Rectangle type, Criss-cross type, Target type
92
and Web type in turn about 19.35%, 22.4%, 34.71% and 35.5%. Beside that with the interval
of response time from 0s to 0.1s; the slope of the second order derivative temperature curve
has the highest value. These results prove that this optimization can obtain the desire top
electrode shape to develop the quality of ZnO pyroelectric film sensor in the application field.
And, through the optimal results, we explore the different effects of top electrode shape to the
temperature variation rate. Where the cycle shape in creation the highest temperature variation
rate of this film sensor type has the trend more broaden than the rectangle shape has in the
optimization process. But the influence of the window in top electrode has not found out yet
in this study. In the future, with the improvement of the Comsol software, we can consider the
ratio between the size of the ZnO layer contacting windows and dispersion of the top
electrode. This is the key factor to develop the ZnO pyroelectric film sensor for the
applications in technology.
93
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