ANALYSES AND APPLICATIONS OF THERMOELECTRIC MODULES:
ELECTRICALLY PARALLEL AND SERIAL STRUCTURES
by
GUANGXI WU
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
Dissertation Adviser: Dr. Xiong (Bill) Yu
Department of Electrical Engineering and Computer Science
CASE WESTERN RESERVE UNIVERSITY
May, 2016
CASE WESTERN RESERVE UNIVERISTY
SCHOOL OF GRADUATE STUDIES
We hereby approve the dissertation of
Guangxi Wu
candidate for the
(signed)
Doctor of Philosophy
degree *.
Xiong (Bill) Yu
(chair of the committee)
Christian A. Zorman
Philip Feng
Hongping Zhao
Chung-Chiun Liu
Alp Sehirlioglu
(date)
March 25th, 2016
*We also certify that written approval has been obtained for any proprietary
material contained therein.
Dedicated to
My parents and
My fiancée Jessie Liyi Peng
TABLE OF CONTENTS
LIST OF TABLES ............................................................................................... V
LIST OF FIGURES ............................................................................................ VI
ACKNOWLEDGEMENTS ............................................................................ XVI
ABSTRACT.. ................................................................................................. XVIII
Chapter 1. INTRODUCTION AND MOTIVATION ..................................... 1
1.1.
Literature review of TE research ...................................................... 2
1.1.1.
Analytical and numerical analysis of TEM performance.............. 2
1.1.2.
TE materials .................................................................................. 4
1.1.3.
TEM structures .............................................................................. 7
1.1.4.
TEG applications ......................................................................... 12
1.2.
Overview of this study ................................................................... 14
Chapter 2. EXPERIMENTAL OBSERVATIONS OF ELECTRICALY
PARALLEL TEM ........................................................................ 17
2.1.
Overview ........................................................................................ 17
2.2.
Material preparation ....................................................................... 18
2.3.
Cold pressing process ..................................................................... 20
2.4.
Material property characterization ................................................. 22
2.4.1.
Seebeck coefficient ..................................................................... 22
2.4.2.
Electrical conductivity/resistivity................................................ 23
2.4.3.
Thermal conductivity .................................................................. 28
2.5.
TEM fabrication ............................................................................. 36
2.6.
TEG electrical output performances............................................... 39
2.7.
TEG performance comparison among different TEM structures ... 48
I
2.8.
Thermoelectric cooler (TEC) performance comparison ................ 54
2.9.
Summary ........................................................................................ 55
Chapter 3. ANALYTICAL ANALYSIS OF THE ELECTRICALLY
PARALLEL TEM ........................................................................ 57
3.1.
Overview ........................................................................................ 57
3.2.
Traditional electrically serial TEM efficiency ............................... 58
3.3.
Electrically parallel TEM efficiency .............................................. 62
3.3.1.
When the wire effects are neglected ........................................... 63
3.3.2.
When the wire effects are considered ......................................... 67
3.4.
Carrier driving mechanisms for electrically parallel TEM ............ 73
3.5.
Summary ........................................................................................ 76
Chapter 4. FINITE ELMENT ANALYSIS OF ELECTRICALLY
PARALLEL TEM ........................................................................ 78
4.1.
Overview ........................................................................................ 78
4.2.
Governing equations....................................................................... 79
4.3.
Material properties ......................................................................... 79
4.4.
Simulation model verification ........................................................ 82
4.4.1.
Coefficient Form PDE module .................................................... 82
4.4.2.
Weak Form PDE module ............................................................ 85
4.4.3.
Built-in Thermoelectric module .................................................. 86
4.5.
Modeling of electrically serial TEM .............................................. 88
4.5.1.
Geometry setup of electrically serial unit TEM .......................... 88
4.5.2.
Optimization of the cross-sectional area ratio ............................. 90
4.5.3.
Simulation results of electrically serial unit TEMs ..................... 92
4.6.
Modeling of electrically parallel TEM ........................................... 95
II
4.6.1.
Geometry setup of electrically parallel unit TEM ....................... 95
4.6.2.
Simulation results of electrically parallel unit TEMs.................. 96
4.7.
Comparison among the electrically parallel and serial unit TEMs
...................................................................................................... 101
4.8.
Summary ...................................................................................... 102
Chapter 5. BACK-END STEP-UP DC-DC CONVERTER DESIGN FOR
ELECTRICALLY PARALLEL TEM ..................................... 103
5.1.
Overview ...................................................................................... 103
5.2.
Capacitive and inductive step-up DC-DC converters .................. 104
5.3.
Back-end step-up DC-DC converter performance for the TEM .. 105
5.4.
Starter circuit design to toggle the switches ................................. 109
5.5.
Summary ...................................................................................... 111
Chapter 6. TE ENERGY HARVESTING FROM PAVEMENT
STRUCTURE ............................................................................. 112
6.1.
Overview ...................................................................................... 112
6.2.
Computer-aided optimization of aluminum heat changer ............ 114
6.3.
In-lab experiment ......................................................................... 117
6.3.1.
Experiment setup ....................................................................... 118
6.3.2.
Power management circuit ........................................................ 120
6.3.3.
Temperature distribution ........................................................... 121
6.3.4.
Electric output of the TE energy harvesting system ................. 122
6.4.
Outdoor experiment ...................................................................... 125
6.4.1.
TEM is placed on top of the asphalt concrete sample ............... 126
6.4.2.
TEM is placed beneath the asphalt concrete sample ................. 129
6.5.
Nationwide evaluation of TEM output energy harvested from
pavements ..................................................................................... 136
III
6.5.1.
Temperature gradient across asphalt concrete layer of pavements
…………………………………………………………………136
6.5.2.
Output power of TEM harvesting from pavements .................. 141
6.6.
Summary ...................................................................................... 142
Chapter 7. CONCLUSIONS AND SUGGESTIONS FOR FUTURE
RESEARCH ................................................................................ 145
7.1.
Conclusions of this study ............................................................. 145
7.2.
Suggestions for future research .................................................... 146
7.3.
Stencil printing process to fabricate flexible TEMs ..................... 151
7.3.1.
TE ink preparation ..................................................................... 151
7.3.2.
Screen and stencil design .......................................................... 152
7.3.3.
Printing process ......................................................................... 152
7.3.4.
TEM electric output characterization ........................................ 155
7.3.5.
Material property characterization ............................................ 156
Appendix A. THERMAL FLASH METHOD TO MEASURE THERAML
DIFFUSIVITY ............................................................................ 158
Appendix B. MATLAB SCRIPTS TO PROCESS LTPP DATA ................. 167
REFERENCES .................................................................................................. 183
IV
LIST OF TABLES
Table 1-1. A summary of the state-of-art TE materials (n-type materials are
shaded, while p-type materials are unshaded). .................................... 6
Table 2-1. Material property summary of the TE materials used in this study .... 36
Table 2-2. A summary of the dimension information of TE legs that make up
TEMs. ................................................................................................ 37
Table 2-3. Calculated results of several parameters with respect to different TEM
structures. .......................................................................................... 46
Table 3-1. Material properties of a pair of thermoelectric materials (Bi2Te3). ... 61
Table 6-1. Parameters and size definition of materials used in FEM simulations.
......................................................................................................... 116
Table A-1. Experiment and calculation result summary of aluminum rod......... 164
Table B-1. Detailed location information of the data used in this study. ........... 179
Table B-2. Calculation results with respect to a year ......................................... 180
Table B-3. Calculation results with respect to January. ...................................... 181
Table B-4. Calculation results with respect to July. ........................................... 182
V
LIST OF FIGURES
Fig. 1-1. A summary of the state-of-art TE materials. Red bars represent p-type
materials. Green bars represent n-type materials. .................................... 5
Fig. 1-2. TEM with Π structure. Temperature gradient is in cross-plane direction.
Substrates are rigid. (a) The whole TEM. (b) Unit TEM......................... 9
Fig. 1-3.Multilayered stack structure, in-plane thermal flux, flexible substrate. .. 10
Fig. 1-4. Roll-up sheet structure, cross-plane thermal flux, flexible substrate. .... 10
Fig. 1-5. Uni-leg structure, cross-plane thermal flux, rigid substrate. .................. 11
Fig. 1-6. Traditional TEM is electrically in series and considered as voltage
source. .................................................................................................... 14
Fig. 1-7. Electrically parallel TEM where TE legs are considered as current source.
(a) p-type (b) n-type. .............................................................................. 16
Fig. 2-1. Tube driver used as ball mill in the material preparation process. ......... 19
Fig. 2-2. The involved sieve holding a piece of 200 mesh copper. ...................... 19
Fig. 2-3. Machined mold for cold pressing process .............................................. 20
Fig. 2-4. Curing temperature profile of the oven .................................................. 21
Fig. 2-5. Seebeck effect and Seebeck coefficient ................................................. 23
Fig. 2-6. Working principle of four-point probe method on electrical conductivity
measurement. ......................................................................................... 24
Fig. 2-7. Four-point probe testing system used in this measurement, composed of
LUCAS LABS 302 manual four point resistivity probing equipment and
KEITHLEY 2400 source meter. ............................................................ 25
Fig. 2-8. Geometry setup of the finite element simulation ................................. 26
VI
Fig. 2-9. Correction factor with respect to different thickness. ............................ 27
Fig. 2-10. Experiment setup of the thermal diffusivity measurement. ................. 30
Fig. 2-11. Heater used in this experiment with no electrical insulator layer on top.
................................................................................................................ 30
Fig. 2-12. The voltage profile corresponding to the n-type TE leg, together with
its smoothed data (Loess algorithm) and the time derivative of the
smoothed data. ....................................................................................... 33
Fig. 2-13. The voltage profile corresponding to the p-type TE leg, together with
its smoothed data (Loess algorithm) and the time derivative of the
smoothed data. ....................................................................................... 34
Fig. 2-14. Specific heat capacity measurements of n-type TE material. .............. 35
Fig. 2-15. Specific heat capacity measurements of p-type TE material. .............. 35
Fig. 2-16. Printed heater as top cap of unit TEM.................................................. 38
Fig. 2-17. The fabricated unit TEM (traditional serial structure). ........................ 38
Fig. 2-18. Experiment setup to characterize the unit TEM. .................................. 39
Fig. 2-19. Trans-impedance amplifier design to monitor the output current and
voltage of the unit TEM. ........................................................................ 42
Fig. 2-20. Output characteristics of n-type electrically parallel structure unit TEM.
(a) Output current VS output voltage. (b) Output power VS output
voltage. ................................................................................................... 43
Fig. 2-21. Output characteristics of p-type electrically parallel structure unit TEM.
(a) Output current VS output voltage. (b) Output power VS output
voltage. ................................................................................................... 44
VII
Fig. 2-22. Output characteristics of electrically serial structure unit TEM. (a)
Output current VS output voltage. (b) Output power VS output voltage.
................................................................................................................ 45
Fig. 2-23. The comparison on output characteristics among different TEM
structures under 30 °C temperature difference. (a) I-V curves. (b) Output
power...................................................................................................... 49
Fig. 2-24. The comparison on output characteristics among different TEM
structures under 50 °C temperature difference. (a) I-V curves. (b) Output
power...................................................................................................... 50
Fig. 2-25. The comparison on output characteristics among different TEM
structures under 70 °C temperature difference. (a) I-V curves. (b) Output
power...................................................................................................... 51
Fig. 2-26. The comparison on output characteristics among different TEM
structures under 100 °C temperature difference. (a) I-V curves. (b)
Output power. ........................................................................................ 52
Fig. 2-27. The comparison on the generated temperature difference among
different TEM structures when used as TE coolers. .............................. 54
Fig. 3-1. The mismatch of material properties between n-type TE materials and
their p-type counterparts. ....................................................................... 60
Fig. 3-2. Electrically parallel TE generator unit module where (a) both legs are
p-type semiconductor materials (b) both legs are n-type semiconductor
materials. The arrows represent the current directions. ......................... 62
VIII
Fig. 3-3. Module’s figure-of-merit increase by using the electrically parallel
structure, compared to the corresponding electrically serial structure,
under the assumption that the involved materials can be made
electrically parallel or serial. .................................................................. 66
Fig. 3-4. When temperature difference mainly falls on load electronics, where
T1>T2. (a) p-type (b) n-type.................................................................... 68
Fig. 3-5. When all the temperature difference falls on the wire, where T1>T2. (a)
p-type (b) n-type. ................................................................................... 71
Fig. 3-6. Comparisons on the module's figure-of-merit among different module
structures and different assumptions...................................................... 72
Fig. 3-7. Sandwich structure of electrically parallel unit TEM, where T1>T2. (a) ptype (b) n-type. ....................................................................................... 73
Fig. 3-8. Band structure of n-type TE materials under temperature gradient. ...... 74
Fig. 3-9. Band structure of p-type TE materials under temperature gradient. ...... 75
Fig. 3-10. Band structure of electrically serial TEM under temperature gradient. 76
Fig. 4-1. Seebeck coefficient of the materials used to carry out the calculation. . 80
Fig. 4-2. Thermal conductivity of the materials used to carry out the calculation.
................................................................................................................ 80
Fig. 4-3. Electrical conductivity of the material used to carry out the calculation.
................................................................................................................ 81
Fig. 4-4. Figure-of-merit of the material used to carry out the calculation. ........ 81
IX
Fig. 4-5. The electrochemical potential distribution along the p-type TE leg under
a 10K temperature difference modeled by the Coefficient Form PDE
module. (a) bottom 340 K, top 330 K. (b) bottom 330 K, top 340 K. ... 85
Fig. 4-6.The electrochemical potential distribution along the p-type TE leg under
a 10K temperature difference and modeled using Weak Form PDE
module. (a) bottom 340 K, top 330 K. (b) bottom 330 K, top 340 K. ... 87
Fig. 4-7. The electrochemical potential distribution along the p-type TE leg under
a 10 K temperature difference and modeled using Weak Form PDE
module. (a) bottom 340 K, top 330 K. (b) bottom 330 K, top 340 K. ... 87
Fig. 4-8.Geometry of the electrically serial unit TEM when used as TEG with a
load resistor. ........................................................................................... 89
Fig. 4-9. Another option of coupling the SPICE module to consider the load
resistor. ................................................................................................... 90
Fig. 4-10. The output power as a function of the electrical conductivity of load
resistor and the cross-sectional area ratio Wn/Wp. ................................. 91
Fig. 4-11. Temperature distribution of the electrically serial unit TEM, when
bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 105.7 S/m. .......................................................................... 93
Fig. 4-12. The electrochemical potential distribution of the electrically serial unit
TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 105.7 S/m. ....................................................... 93
X
Fig. 4-13. The current density magnitude distribution of the electrically serial unit
TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 105.7 S/m. ....................................................... 94
Fig. 4-14. The current flowing direction of the electrically serial unit TEM, when
bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 105.7 S/m. ........................................................................... 94
Fig. 4-15. Geometry of the electrically parallel unit TEM when used as TEG with
a load resistor. ........................................................................................ 95
Fig. 4-16. Temperature distribution of the n-type electrically parallel unit TEM,
when bottom temperature is 610 K, the top temperature is 600 K and the
load resistance is 106.8 S/m. ................................................................... 97
Fig. 4-17. The electrochemical potential distribution of the n-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top
temperature is 600 K and the load resistance is 106.8 S/m. .................... 97
Fig. 4-18. The current density magnitude distribution of the n-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top
temperature is 600 K and the load resistance is 106.8 S/m. .................... 98
Fig. 4-19. The current flowing direction of the n-type electrically parallel unit
TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 106.8 S/m. ....................................................... 98
Fig. 4-20.Temperature distribution of the p-type electrically parallel unit TEM,
when bottom temperature is 610 K, the top temperature is 600 K and the
load resistance is 106.1 S/m. ................................................................... 99
XI
Fig. 4-21. The electrochemical potential distribution of the p-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top
temperature is 600 K and the load resistance is 106.1 S/m. .................... 99
Fig. 4-22. The current density magnitude distribution of the p-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top
temperature is 600 K and the load resistance is 106.1 S/m. .................. 100
Fig. 4-23. The current flowing direction of the p-type electrically parallel unit
TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 106.1 S/m. ..................................................... 100
Fig. 4-24. Output characteristics comparisons among different structured unit
TEMs when the bottom boundary temperature is 610 K and the top
boundary temperature is 600 K. ........................................................... 101
Fig. 5-1. Circuit of the switched-mode step-up inductive boost DC-DC converter.
.............................................................................................................. 106
Fig. 5-2. A comparison between (a) the traditional electrically serial unit TEM,
and (b) the newly proposed electrically parallel n-type unit TEM. ..... 107
Fig. 5-3. The comparison between the two unit modules with different structures
on the output voltage and current flowing through the inductor of the
back-end step-up DC-DC converter..................................................... 108
Fig. 5-4. Starter circuit design that can realize the function of SW1 in Fig. 5-1. 111
Fig. 6-1. Example measured daily temperature variations under pavement [112]
.............................................................................................................. 113
Fig. 6-2. Schematic of the TE energy harvesting system. .................................. 114
XII
Fig. 6-3. TE module’s output power VS thermal insulator length [113]. ........... 116
Fig. 6-4. Temperature distribution across the pavement structure. ..................... 117
Fig. 6-5. Experiment set up in the lab. ................................................................ 118
Fig. 6-6. The picture of the entire experiment setup. .......................................... 119
Fig. 6-7. Diagram of the back-end energy management circuit. ........................ 120
Fig. 6-8. Monitored temperature process at different locations in the TE energy
harvesting system. ................................................................................ 122
Fig. 6-9. (a) Voltage profiles at the TE element output electrode, capacitor and
LED, (b) Zoom in between 120 to 125 min. ........................................ 123
Fig. 6-10. The installation process of the TE energy harvesting system outdoors.
.............................................................................................................. 125
Fig. 6-11. Locations where temperatures were monitored. ................................ 126
Fig. 6-12. Temperature data of two consecutive summer days. ......................... 128
Fig. 6-13. Output voltage of the TEM with 10 Ω load resistor. The corresponding
temperature difference between two boundaries of the TEM is also
plotted. ................................................................................................. 128
Fig. 6-14. Calculated output power data with time. ........................................... 129
Fig. 6-15. The bottom heat treatment of the asphalt concrete samples............... 130
Fig. 6-16. Heat sink as a heat exchanger used in control group. ........................ 131
Fig. 6-17. Temperature monitoring locations. .................................................... 131
Fig. 6-18. Temperature data of the full time range. ............................................ 132
Fig. 6-19. Temperature data zoomed in to the second and third day. ................. 133
XIII
Fig. 6-20. Output voltage comparison between using Al heat exchanger and heat
sink. ...................................................................................................... 133
Fig. 6-21. Output power comparison between using Al heat exchanger and heat
sink. ...................................................................................................... 134
Fig. 6-22. Temperature sensor locations inside the asphalt concrete layer of the
pavement structure. .............................................................................. 137
Fig. 6-23. Testing locations of the data involved in the calculations in this study.
.............................................................................................................. 138
Fig. 6-24. The average temperature gradient across the pavement structure in a
year. The unit of the numbers in the figure is K/m. ............................. 140
Fig. 6-25. The average temperature gradient across the pavement structure in
January. The unit of the numbers in the figure is K/m. ....................... 140
Fig. 6-26. The average temperature gradient across the pavement structure in July.
The unit of the numbers in the figure is K/m. ...................................... 141
Fig. 7-1. Electrode screen designs for (a) electrically serial and (b) parallel TEM
structure................................................................................................ 152
Fig. 7-2. Stencil designs for (a) left TE legs and (b) right TE legs. .................... 153
Fig. 7-3. Printing process for both electrically serial and parallel structure TEM.
.............................................................................................................. 153
Fig. 7-4. Printed electrically serial TEM on flexible polyimide substrate. ........ 154
Fig. 7-5. The rolled-up printed TEM on flexible polyimide substrate................ 154
Fig. 7-6. Output characteristics of printed TE devices with electrically parallel
structure (n-type). ................................................................................. 155
XIV
Fig. 7-7. Output characteristics of printed TE devices with electrically parallel
structure (p-type). ................................................................................. 155
Fig. 7-8. Aluminum reverse mold to make silicone mold. ................................. 157
Fig. 7-9. Silicone mold used to cast TE inks and cured in oven to form test
samples. ................................................................................................ 157
Fig. A-1. Thermal flash method’s boundary conditions. ................................... 158
Fig. A-2. Temperature profile for 20 mm sample when the heat flux starts from
time zero and the thermal contact is perfect, where the thermal
diffusivity is 7×10-4 m2/s...................................................................... 159
Fig. A-3. Temperature profile for 20 mm sample when the heat flux starts from
time zero and there is thermal contact. The thermal diffusivity is
assumed to be 7×10-4 m2/s. The incoming heat flux is 1 W/m2. The
thermal conductivity is 1 W/(m∙K). ..................................................... 161
Fig. A-4. Relation between the time constant and thermal diffusivity for 20 mm
sample. The incoming heat flux is 1 W/m2. The thermal conductivity is 1
W/(m∙K). .............................................................................................. 162
Fig. A-5. The voltage profile and its time derivative profile of 1 cm aluminum rod.
.............................................................................................................. 163
Fig. A-6. The voltage profile and its time derivative profile of the 2 cm aluminum
rod. ....................................................................................................... 164
Fig. A-7. The voltage profile and its time derivative profile of the 3 cm aluminum
rod. ....................................................................................................... 164
XV
ACKNOWLEDGEMENTS
I would like to take this opportunity to extend my most sincere gratitude to
my advisor, Dr. Xiong (Bill) Yu, who has role modeled to me over the years not
only how to become good researcher, but also a good man. It is his excellent
guidance, patience and trust that have immersed me into the happiness of doing
research in areas that we are interested in. His understanding, care and assistance
have helped me live a balanced, happy life during and even beyond my graduate
studies at Case Western Reserve University. His mentorship will always benefit
me along the road, as I pursue my career and life goals.
I would like to express my special thanks to my co-advisor, Dr. Christian
A. Zorman, who is always ready to share his constructive suggestions and
experiences for my research and life. I do hope to continue our intimate research
collaborations to further push forward the development of thermoelectric
technology and its applications.
I would also like to appreciate Dr. Chung-Chiun Liu for his generous
support on experiments involved in this study, Dr. Alp Sehirlioglu for his
professional instructions from his technical background in the thermoelectric
research areas, Dr. Philip Feng and Dr. Hongping Zhao for their considerate
suggestions and assistance in improving the quality of this research.
I would like to recognize the professional assistance from Laurie Dudik,
the managing engineer at Electronics Design Center (EDC), Jim Berilla,
XVI
department technician, and Ina Martin, director of MORE center. Without their
help, the experiments in this study would not have been realized.
I would like also like to take a moment to thank Nancy Longo, the
department secretary, who has always been willing to help during my daily
research life. I am extremely grateful for the help from all the Ph.D. alumni from
our research group and the Ph.D. students still in the group: Dr. Yan Liu, Dr. Bin
Zhang, Dr. Zhen Liu, Dr. Junliang Tao, Dr. Ye Sun, Quan Gao, Jianying Hu,
Yang Yang, Chanjuan Han, Jiale Li, Yuan Guo, and Shaoyang Dong. I would also
like to thank two undergraduate students who once worked with me on my
research, Moria Corsi and Ferin Neff.
The research in this dissertation is funded by National Science Foundation
and Ohio Department of Transportation. I highly appreciate these agencies for
providing financial support that makes this study possible.
Finally, but most importantly, I would like to thank my fiancée Jessie Liyi
Peng and my parents. It is their everlasting love and support that fill my life with
happiness. It is their silent support and unlimited dedication that make me always
feel energetic and optimistic. Without their understanding and encouragement, I
could not have finished my graduate studies.
XVII
Analyses and Applications of Thermoelectric Modules: Electrically Parallel
and Serial Structures
ABSTRACT
by
GUANGXI WU
Conventional thermoelectric modules (TEMs) are composed of n-type and
p-type thermoelectric (TE) legs connected electrically in series and thermally in
parallel. The development of TE technology based on the traditional TEM
structure has been limited by its low efficiency and high cost. Most of ongoing
research nowadays focuses on developing new TE materials that have higher
intrinsic efficiency.
This research analyzes the TE problem from an electrical engineering
angle. The conventional electrically serial structure considers TE legs as voltage
power sources. In contrast, this research takes advantage of TE legs as current
power sources, leading to an alternative TEM structure, where all TE legs are
made from single type of TE material and connected in parallel both electrically
and thermally.
Experimental, analytical and numerical analysis have been carried out to
evaluate the performance of unit modules with the newly proposed electrically
parallel structure. It indicates that the modules’ figure-of-merit and energy
conversion efficiency can be increased within a certain device area limit, the
XVIII
fabrication cost can be decreased, the power density and mechanical durability
can be increased, while the temperature gradient is kept in the cross-plane
direction. It can also increase the device lifetime, because on the one hand, there
is no mismatch between the thermal expansion rate among TE legs. On the other
hand, for serial structure, even a single break of the connection can lead to the
failure of the device. However, for the electrically parallel structure, a small break
of the junction will not affect the performance significantly.
Meanwhile, the proposed electrically parallel structure can also benefit the
back-end step-up DC-DC converter design. It can produce a higher output voltage
(so a higher output power and efficiency) to the load, and possibly work under a
slower switching frequency to decrease the switching energy loss.
In addition, the electrically parallel structure can also stimulate innovative
applications of TEM, because of its simplified multilayered device structure. An
innovative TEG energy harvesting system from pavement structures has been
implemented and has proved promising to periodically power low energy
consumption sensors to monitor civil infrastructure’s health in the long-term.
XIX
Chapter 1.
INTRODUCTION AND MOTIVATION
Energy shortages and environmental degradation have become two of the
most critical current issues [1]. The world’s escalating demand for energy
accelerates the combustion of fossil fuels, because of the lack of alternative
energy resources, which further deteriorates the environment by means of global
warming, greenhouse gas emission, climate change, ozone layer depletion, acid
rain, etc. Renewable energy harvesting techniques, such as thermoelectric (TE)
technology, have received extensive attention, driven by their potential to mitigate
both the energy and environmental crises. The energy consumption by the U.S. in
2014 is about 10 Trillion kWh and predicted to continue increasing annually [2].
More than half of the primary energy utilized is wasted in form of heat [3] and
given off by power stations, heating systems, plants, vehicles, etc. Thermoelectric
module (TEM) used as power generator (TEG) can directly convert waste heat,
as well as heat from solar, biomass, and earth sources [4] into electricity, which
makes TE technology even more attractive than other types of renewable energy
harvesting techniques.
TE technology possesses advantages such as gas-free emissions, vast
scalability, maintenance-free operation without any moving parts and chemical
reactions, no damage to the environment during operation, and solid-state
operation which leads to a long life span [5]. However, its disadvantages of low
energy-conversion efficiency and corresponding high material and fabrication
cost have become the bottleneck that limits its development and implementation.
1
As a result, massive research has been carried out from various aspects, including
analytical and numerical analysis of TEM performances, TE material
development, TEM device structure design, TEG application, etc.
1.1. Literature review of TE research
1.1.1. Analytical and numerical analysis of TEM performance
Design and optimization of TEM relies on precise modeling of its
fundamental working principles and energy-conversion mechanisms. Researchers
have made much effort in modeling the behaviors and performances of TE
devices by solving governing equations analytically. Temperature dependency of
material properties and the induced Thomson effect and are usually neglected in
order for people to get qualitative analog solutions [6-10]. More precise modeling
processes have also been proposed by including temperature dependency of
material properties [11-13] and the Thomson effect [14]. However, the
shortcomings of the analytical method limit its potential in modeling TE devices.
The computational complexity makes this method time consuming and easy to
induce errors. Most calculations are limited to one dimensional for simplicity. The
visualization of the calculation results is not straightforward.
Electrical analogy method appeals to many researchers because the mature
knowledge in the area of electric circuits can be utilized in the thermal field
analysis [15, 16]. It also makes it possible to couple the thermal field and electric
field in the same simulation environment, such as the finite difference software
SPICE (Simulation Program with Integrated Circuit Emphasis), which is widely
2
used in the area of circuit analysis [17-21]. Even though this method is powerful
for simulating complicated load electric circuits of TEGs, the disadvantages
impact its popularity. The electrical abstraction of the thermoelectric device
overly emphasizes lumped properties of the TEM, such as the output power,
temperature difference between the two ends, etc. Parameter distributions
(especially three dimensional distributions) inside the TEM are not convenient to
be visualized. This method lacks the sensitivity of the module size influence on
the TEM performance, which causes difficulties for researchers to optimize the
shape of the TEM. In order to increase the visualization ability of the electrical
analogy method, a three dimensional TCAD (Synopsys Technology Computer
Aided Design) implementation has been carried out [22-25]. However, the
governing equations and the working performances of the TEM are not fully
verified.
As commercial finite element multi-physics simulation software quickly
improves, researchers are attracted to model TEM performances numerically
using finite element method (FEM) [26-31]. Thomson effects and temperature
dependency of the TEM properties can be coupled in the governing equations
conveniently [32-34]. The finite element method not only has advantages of
adjustable visualization and friendly user interface, but also predicts more
precisely [35]. The multi-physics software makes the thermal field and electrical
field compatible, as well as other physics field. It makes it possible for researchers
to learn other properties of the TEM, such as the mechanical properties [36, 37],
thermal, and electrical properties.
3
1.1.2. TE materials
TE materials that form TEMs have fundamental influence on the module
behaviors. Researchers have been working on either finding [38] or developing
new TE materials that can lead to higher intrinsic efficiency and lower material
cost [39-48]. TE materials that have been investigated can be categorized into
three groups: semiconductors [43], semiconducting oxide ceramics [44] and
polymers [45]. Among them, semiconductor TE materials possess relatively
higher intrinsic efficiency, but they are typically made from high atomic weight
elements [49] with small band-gaps and high-mobility carriers [40]. The material
resources on earth are rare and frequently environmentally unsafe, which
consequently lead to high material cost [43]. In contrast, metal oxide ceramics and
polymers are significantly more abundant and cost-effective. But they have
tremendously lower intrinsic efficiency [44, 45] and higher inner resistance.
In addition to selecting from the existing known materials, researchers are
also dedicated to create new materials where the carrier (electron, hole, phonon,
etc.) transport performances can be engineered to increase the intrinsic efficiency.
There have been two primary approaches to achieve this goal: synthesizing new
complex solid-state materials that have complex crystal structures [5], such as
Skutterudite [42], Clathrate [50], Half-Heusler [46-48] materials; as well as
creating nanostructured materials, such as nanocomposites (3D) [51], superlattices
(2D) [52], nanowires (1D) [53, 54], and quantum dots (0D) [55].
The state-of-the-art thermoelectric materials with the high figure-of-merit
(ZT) value are summarized in Fig. 1-1 and Table. 1-1. The ZT value determines
4
the overall TEM energy efficiency. The higher the ZT, the higher the energy
efficiency. The ZT value of a certain TE material can be calculated based on the
material’s Seebeck coefficient  , electrical conductivity  (or resistivity  ), the
thermal conductivity  and the working temperature T , shown as equation (1.1).
ZT 
 2
2
T=
T


(1.1)
Although high intrinsic material efficiency has been reported for many TE
materials, it comes at the expense of fabrication cost. Researchers have struggled
to balance between the efficiency and cost. A new solution to simultaneously
improve the efficiency and decrease the cost of the TE technology is desperately
needed.
#15 Ba8.0Ga15.9Zn0.007Sn30.1
#19 SrTiO3
#17 Cu2Se
#16 Ba8Ga16Sn30
#18 Bi2Te3/Sb2Te3
#20 Bi2Te3/Bi2Te2.83Se0.17
#14 PbSeTe/PbTe
#13 DD0.59Fe2.7Co1.3Sb11.8Sn0.2
#12 Sr0.09Ba0.11Yb0.05Co4Sb12
#7 Hf0.6Zr0.4NiSn0.995Sb0.005
#10 SnSe
#9 (Si95Ge5)0.65(Si70Ge30P3)0.35
#6 PbTe, 4mol%SrTe, 2mol % Na:SPS
#8 BiCuSeO
#11 Si80Ge20
#5 b-Cu2Se
#4 Si80Ge20
#2 Bi2Te3
#1 Bi2Te3
#3 FeNb1-xHfxSb (x=0.12)
Fig. 1-1. A summary of the state-of-art TE materials. Red bars represent p-type
materials. Green bars represent n-type materials.
5
Table 1-1. A summary of the state-of-art TE materials (n-type materials are shaded, while p-type materials are unshaded).
#
1
2
3
4
TE materials
Bi2Te3
Bi2Te3
FeNb1-xHfxSb (x=0.12)
Si80Ge20
Comments
6
Crystal, doped
Crystal, doped
Half-Heusler, heavy-band
Nanostructured, P doped
Phonon-liquid and electron crystal
5 b-Cu2Se
(PLEC), phase change
PbTe, 4mol%SrTe, 2mol % High temperature, all scale hierarchical
6
Na:SPS
structure
Half-Heusler without nanostructure,
7 Hf0.6Zr0.4NiSn0.995Sb0.005
annealed at 1350 °C for 30 min
Ba heavily doped, carrier concentrations as
8 BiCuSeO
high as 1.1×1021 cm-3
9 (Si95Ge5)0.65(Si70Ge30P3)0.35 nanocomposites
crystal b axis, high temperature, layered
10 SnSe
and anisotopic crystal structure
11 Si80Ge20
Nanostructured, B doped
Skutterudites, high temp, after severe
12 Sr0.09Ba0.11Yb0.05Co4Sb12
plastic deformation (SPD) via highpressure torsion (HPT), T up
Skutterudites, high temp, after high13 DD0.59Fe2.7Co1.3Sb11.8Sn0.2
pressure torsion (HPT), T increase
Quantum-dot superlattices (QDSL), Bi
14 PbSeTe/PbTe
doped
15 Ba8.0Ga15.9Zn0.007Sn30.1
Clathrate, single crystal
16 Ba8Ga16Sn30
Clathrate, doped with Cu
Phonon-liquid and electron crystal
17 Cu2Se
(PLEC), phase change
Superlattice, 10Å/50Å, 2.67μm thick,
18 Bi2Te3/Sb2Te3
carrier concentration of 9×1018cm-3
19 SrTiO3
Metal oxide, 2DEG supperlattice
20 Bi2Te3/Bi2Te2.83Se0.17
Superlattice, 10Å/50Å,
p/
n
p
n
p
n


(μV/K)
190.94
-201.75
246.41
-284
(mΩ∙cm)
1
1
1.23
5.01
W/(m∙K)
1.95
1.91
4.15
0.93
T (K)
ZTmaterial
Year
Ref.
300
300
1200
1073
0.56
0.64
1.42
1.84
1958
1958
2015
2014
[56]
[56]
[57]
[58]
p
295.12
7.70
0.74
1000
1.53
2012
[59]
p
283
3.45
0.95
915
2.2
2012
[60]
n
-223.15
1.04
3.64
900
1.2
2015
[61]
p
181.81
5.57
0.49
923
1.1
2012
[62]
n
-245.32
1.28
4.42
900
1.0
2012
[63]
p
342
11.93
0.35
923
2.6
2014
[38]
n
-250
1.78
2.50
900
1.3
2008
[64]
n
-203
0.92
2.04
835
1.8
2014
[65]
p
181
1.51
1.25
825
1.44
2015
[66]
n
-401.31
5.31
0.49
580
3.6
2005
[67]
p
n
398.89
-261.32
8.20
3.64
0.91
0.67
500
520
1.07
1.45
2015
2012
[68]
[69]
n
-166.5
2.4
0.2
400
2.3
2013
[70]
p
142.33
0.53
0.49
300
2.34
2001
n
n
-850
-238
0.75
1.23
12
0.945
300
300
2.4
1.46
2007
2001

[52,
71]
[72]
[52]
1.1.3. TEM structures
The most widely used TEM at present is composed of p-type and n-type
materials that are connected thermally in parallel and electrically in series. For
bulk TE materials, including nanocomposites fabricated using bulk process, the
most popular device structure is the so-called Π structure, shown in Fig.1-2,
where the temperature gradient is along the cross-plane direction, which is
suitable for most TEG applications. However, the spatial zigzag structure of plegs and n-legs inevitably leaves spaces among TE legs (i.e. fill factor<1), which
deteriorate the device’s volume power density and mechanical durability.
Meanwhile, the fabrication process of this zigzag structure is relatively
complicated, resulting in a high fabrication cost. In addition, the module is usually
supported using hard substrate materials, such as ceramics, in order to provide
mechanical support and electrical insulation from the ambient environment.
Consequently, TEM using Π structure is not flexible, which severely limits the
application of TEM in areas of soft surface energy conversion, such as the human
body skin-based energy generation to power consumer electronics.
For film TE materials, such as superlattices, quantum dots [1], and TE
inks [73], the TE device structure can be either the layered stack structure as in
Fig.1-3 [74] , or the roll-up sheet structure as in Fig.1-4 [75]. The TEM using
multilayered-stack structure can be flexible. However, the temperature gradient
has to be applied along the in-plane direction, which still dramatically limits the
application. It has to be pointed out that even though the substrate in the roll-up
7
sheet structure can be flexible, the final device is usually rigid after rolled-up. The
device area is usually limited by the length of the substrate. Temperature gradient
is along the in-plane direction for the substrate, but along the cross-plane direction
for the roll-up module.
All the Π structure, multilayered stack structure and the roll-up sheet
structure are made up by two different types of TE materials, resulting in a
different thermal expansion rate. It severely impacts the lifetime of TEM,
especially when working under high temperature region and periodical
temperature boundary conditions. In order to increase the reliability, a uni-leg
device structure is proposed, as shown in Fig.1-5, where only one type of TE
material (either n-type or p-type) makes up the TEM [76-80]. However, the
module’s energy efficiency is dramatically decreased. It is equivalent to that one
type of high efficiency TE material is replaced by metal, compared to other
aforementioned structures.
All the four types of structure introduced above follow the principle where
all TE legs are connected electrically in series, which makes the TEM vulnerable
to environmental or artificial deterioration. Even a single break in any contact
between the TE materials and the metal inner connectors can lead to the function
failure of the TEM. This problem is even severe for the first three types of TEM
structures, because of the potential mismatch of thermal expansion between ntype and p-type TE materials. Meanwhile, the device surface area is also limited
because of the complicated device structure.
8
Hence, an innovative TE device structure that can overcome all the
aforementioned contradictions will significantly benefit the applications of the TE
technology. An ideal TEM should have cross-plane temperature gradient,
possibility to be flexible, high energy efficiency, low fabrication cost, immunity
to ambient damage and have a large surface area.
Substrate
(Ceramics)
-
+
(a)
n-leg
p-leg
Metal Inner
connector
(b)
Fig. 1-2. TEM with Π structure. Temperature gradient is in cross-plane direction.
Substrates are rigid. (a) The whole TEM. (b) Unit TEM.
9
Electrode
Electrical Insulator
n-type

e e  e e  
e e

p-type

h  h h h h 
h
Electrode
Fig. 1-3.Multilayered stack structure, in-plane thermal flux, flexible substrate.
Metal interconnector
n-leg
p-leg
Flexible substrate
Fig. 1-4. Roll-up sheet structure, cross-plane thermal flux, flexible substrate.
10
Substrate
(a)
TE leg
Inner Connector
(b)
Fig. 1-5. Uni-leg structure, cross-plane thermal flux, rigid substrate.
11
1.1.4. TEG applications
TEG can directly convert heat energy to electric energy. Once provided a
temperature gradient across the device, TEG can produce power to its electric
load. TEG has been widely used for decades. The power production ranges over
15 orders of output power magnitude from milli-microwatt all the way up to
multi-hundred megawatt [81]. TEG applications can be conveniently categorized
by its source of heat: fossil fuel, nuclear decay, waste heat, solar thermal energy,
etc.
The temperature gradient for the TEG can be directly generated by
burning fossil fuel, under situations where either the fossil fuel in the specific
application location is abundant and cost-effective or other types of energy
resources are not accessible. For example, fossil-fueled TEGs are utilized to
provide cathodic protection for pipelines that deliver natural gas in remote areas.
However, this type of application is limited because of the possibility of
environment pollution and the constraints of fossil fuel sources.
The TEG powered by nuclear decay is an ideal option for applications in
remote, inaccessible and hostile environments, such as in outer space and
undersea. The heat source from nuclear materials has a long lifetime and high
energy density. However, this type of applications is limited due to the high cost
and radiation of the nuclear reactor.
TEG for civil uses are typically driven by waste heat [82, 83] from plants,
vehicles [84-87], heat pipes [88], microprocessors [89], human bodies [90], etc.
These types of applications are significant because vast quantities of produced
12
energy are discarded into the earth’s environment as waste heat that are too low
grade to be recovered using other conventional electrical power generators.
Thermoelectric power generators can also be driven by solar thermal
energy, which is a green energy source that helps to reduce the fossil fuel uses.
The solar thermal energy has low energy density resulting in low temperature
gradient.
Methods such as the use of lenses [91] or locating the TEGs in
greenhouses [92] have been studied to concentrate the solar heat.
The applications of TEG are still limited mostly by the low-energy
efficiency and high cost. However, there are various types of naturally existing
temperature gradient that have not been taken advantage of. For example, the
temperature gradient across the pavement structure, the windows of buildings or
automobiles, human body skins, etc. Harvesting energy from those free-of-cost
energy resources using TE technology can still be economical.
The applications of TEG are also limited partially by the complexity of
heat exchanger design at the TEM cold side, which also plays a significant role in
improving the energy TE harvesting system’s efficiency. The cooling agent of the
heat exchanger that takes away the discarded heat from the cold side of the TEM
is usually air [93-96], water [97, 98], liquid nitrogen [99], etc. Heat exchanging
efficiency can be optimized through adjusting the contact area between the cold
side of the TEM and the cooling agent (such as by using metal fin structure) or
adjusting the cooling agent’s speed or volume when flowing by (such as utilizing
fans, valves, etc.). All these heat exchanger designs complicate the system at the
cold side of the TEG, which further limits its application.
13
In order to make use of the naturally existing temperature gradient based
on TE technology, innovative energy harvesting system needs to be designed.
Firstly, high intrinsic energy efficiency, low cost and large surface area TEM
should be developed while keeping the temperature gradient in the cross-plane
direction. Secondly, a heat exchanger at the cold side of the TEM that has low
complexity and high feasibility when applied to large area energy harvesting
scenarios needs to be realized.
1.2. Overview of this study
The traditional TEM structures are all electrically in series. Each TE leg
has been considered as a voltage source with a finite inner resistance, as shown in
Fig.1-6. The TEM’s overall open-circuit output voltage is a superposition of each
TE leg’s open-circuit output voltage. However, the short-circuit current still
remains small.
p
n
p
n
p
n
Fig. 1-6. Traditional TEM is electrically in series and considered as voltage source.
14
The ultimate goal of TE research is to increase the output power of TEG,
which equals to the product of output voltage and output current corresponding to
a certain load resistance. Traditional TEMs using electrically serial structure
enhance the output power through increasing the output voltage. However, there
should be another path that is to increase the output current by connecting the TE
legs electrically in parallel, where only one type of TE materials (either n-type or
p-type) is used, shown in Fig.1-7. Each TE leg is treated as a current power
source. The current source is still equivalent to the voltage source based on
Thévenin's theorem with respect to the output characteristics.
This dissertation analyzes the behaviors of the electrically parallel TEMs,
trying to explore possible systematical solutions to those aforementioned
contradictions. Firstly, both electrically serial and parallel TEM were fabricated
using the cold pressing process. The electrical output characteristics were
recorded and compared to differentiate which structure generates a higher output
power. The details are introduced in Chapter 2. Chapter 3 and 4 attempt to
explain the experimental observations from analytical and numerical perspectives,
respectively. The electrically parallel TEM’s output voltage is too small to be
directly utilized. Chapter 5 discusses back-end step-up DC-DC converter design
to make the output power applicable. Chapter 6 introduces an innovative
application of TEG to harvest energy from pavement structures, which is inspired
by the electrically parallel structure TEMs.
Finally, the conclusions and
suggestions for future research are highlighted in chapter 7.
15
p
p
p
p
p
p
n
n
(a)
n
n
n
n
(b)
Fig. 1-7. Electrically parallel TEM where TE legs are considered as current source.
(a) p-type (b) n-type.
16
Chapter 2.
EXPERIMENTAL OBSERVATIONS OF
ELECTRICALY PARALLEL TEM
2.1. Overview
The investigations on electrically parallel TEM begin with experimental
observations, which are introduced in this chapter. N-type and p-type TE material
preparation details are first described in Section 2.2. Because the raw materials
were already doped with impurities, the cold pressing process was utilized to
generate TE legs, which is introduced in Section 2.3. In order to compare the
maximum output power between the electrically parallel structure and the
conventional electrically serial structure, the energy conversion efficiency of latter
needs to be optimized. This requires optimization of the cross-sectional area ratio
between n-type and p-type TE legs that form a unit electrically serial TEM. The
optimization process is based on material properties (Seebeck coefficient,
electrical conductivity or resistivity and thermal conductivity) of the TE materials
involved in this study. The material property characterization process is discussed
in Section 2.4. For convenience sake, only unit TEMs with optimized crosssectional area ratios were generated. The assembling process is described in
Section 2.5. The electrical output characteristics of the unit TEMs were recorded
using a self-designed trans-impedance amplifier, which is introduced in Section
2.6. The device performances of the proposed electrically parallel TEM and the
conventional electrically serial TEM are compared in Section 2.7. Section 2.8
describes the author’s observations when the unit TEMs were used as
thermoelectric coolers (TECs).
17
2.2. Material preparation
The raw materials of n-type and p-type Bi2Te3 used in the fabrication
process were bought from Merit Technology Group (MTG) Co., Ltd in coarse
powder format. In order to increase the ZT of the materials, the nanocomposite
[51, 63] bulk processing process was emulated, where ZT is increased because of
the limitation of phonon transport inside the material by grain boundary scattering.
Raw materials were first ball milled using a tube driver, shown in Fig.2-1 with
mass ratio of 10:1 between stainless steel balls and the TE powder. Isopropanol
(IPA) that can right immerse the powder and stainless steel balls was used as
grinding agent. The rotation speed was set at mode 3 (~2200 rpm) for 1 minute,
next at mode 5 (~3500 rpm) for 1 minute, then at mode 7 (~4700 rpm) for 1
minute and finally at mode 9 (~6000 rpm) for 5 minutes.
The resulting mixture in the tube was transferred into a container, while
the stainless steel balls were filtered out for the next run. After several runs, the
ground powder immersed in the grinding agent IPA in the container was dried in
an air hood to evaporate the IPA thoroughly. The dry powder then was filtered
using a sieve holding a piece of 200 mesh copper (TWP Inc.), as shown in Fig.2-2.
The maximum grain size of the filtered TE powder is limited to 76 microns,
because the copper wire diameter is 0.0508 mm (0.002 inch) and there are 200
meshes per 2.54 cm (1 inch).
18
Fig. 2-1. Tube driver used as ball mill in the material preparation process.
Fig. 2-2. The involved sieve holding a piece of 200 mesh copper.
19
2.3. Cold pressing process
A mold was designed and fabricated using pre-heat-treated steel for the
cold pressing process, as shown in Fig.2-3 with sample bottom surface dimension
of 20 mm × 3 mm. The height of the final sample depends on how much powder
is loaded into the mold and how much pressure is applied on the inserting part.
Fig. 2-3. Machined mold for cold pressing process
Initially, TE leg samples were first generated. 1 gram of the pre-prepared
semiconductor powder was casted into the mold. Load applied to the inserted part
was 20,000 lb (~1.48 GPa). The generated n-type TE leg samples have a height of
about 2.1 mm. Meanwhile the p-type leg samples have a height of about 2.4 mm.
After all the material properties were characterized, the optimized cross-sectional
area ratio between two legs of a unit TEM can be calculated, which requires
adjustment of the dimensions of TE legs. In that case, only the mass of powder
20
casted into the mold was adjusted, while the pressure applied to the mold
remained the same.
The prepared cold-pressed TE legs were annealed in a vacuum oven under
around -90 kPa. The temperature profile of the oven was designed to have slow
temperature changing rate in order to prevent from potential cracking issues
caused by instant thermal expansion, shown as Fig.2-4. Detailed setup is
described as follows. The oven’s temperature control knob was set at mode 3, 5, 7,
9, and 10 in sequence. Each step was kept for 1 hour. The peak curing
temperature was about 280 °C.
Then, the oven was turned off to let the
temperature return gradually to the room temperature. The TE legs were then
ready to be characterized.
300
Temperature (C)
250
200
150
100
50
0
0
2
4
6
Time (hour)
Fig. 2-4. Curing temperature profile of the oven
21
8
10
12
2.4. Material property characterization
Material properties of both n-type and p-type TE legs need to be
characterized to calculate the optimized cross-sectional area ratio between two
legs of a unit TEM and verify the electrical output performances. Seebeck
coefficient  , electrical conductivity  /resistivity  , and thermal conductivity
 are the main material properties under discussion here. These three parameters
determine the figure-of-merit ZT of a certain TE material, shown as equation (1.1).
2.4.1. Seebeck coefficient
When TEMs are used as TEGs, the core physical effect is the so-called
Seebeck effect, which is illustrated as Fig.2-5 (a). In a open circuit with two
dissimilar materials A and B, if the two junctions are maintained at different
temperatures T and relatively higher T+  T, an electromotive force (emf) appears
that depends only on the two materials and the junction temperatures, which is
described by the following equation:
EAB   AB  T
(2.1)
where  AB is Seebeck coefficient difference between the two materials A and B,
which is positive if the emf causes a current to flow in a counterclockwise
direction, shown as Fig. 2-5 (b).
For a single TE leg, its Seebeck coefficient can be calculated by the open
circuit voltage difference between its two ends divided by the temperature
difference applied to the two ends. Usually, the Seebeck coefficient is positive for
22
p-type semiconductor TE materials, and negative for n-type semiconductor TE
materials.
Open circuit
Closed circuit
A
A
T+ T
T+ T T
T
_
B
V
+
B
B
(a)
B
(b)
Fig. 2-5. Seebeck effect and Seebeck coefficient
The experiment setup of the Seebeck coefficient measurement can be the
same as the setup of the electrical output performance measurements for
electrically parallel TEMs. The Seebeck coefficient of n-type and p-type materials
can be calculated from the open circuit points of the output I-V curves of n-type
and p-type electrically parallel unit TEM, which is introduced in Section 2.6.
Only the calculation results are listed out here. The Seebeck coefficient of n-type
and p-type material are -199 μV/K and 61 μV/K under room temperature region.
2.4.2. Electrical conductivity/resistivity
The electrical resistivity/conductivity of n-type and p-type materials was
characterized using the four-point probe method, whose working principle is
depicted in Fig.2-6. Four electrical probes are placed with equal space S and in
contact with the sample under test. An independent current source powers the
outer two electrodes. The voltage difference between the inner two electrodes is
23
measured. Then the electrical resistivity  of the sample can be calculated using
equation (2.2).

1

=A 
V
=A  R
I
(2.2)
where A is a correction factor in unit meter. I is the constant current value
powered by the independent current source. V is the measured voltage between
the inner two probes. Some measurement systems directly show the ratio R
between V and I in unit of Ω.
V
H
S
S
S
L
Fig. 2-6. Working principle of four-point probe method on electrical conductivity
measurement.
For an ideal thin film sample, the height (or thickness) H of the sample is
far less than the probe span S, i.e. H<<S. Under this assumption, the electrical
resistivity of the sample can be calculated analytically from equation (2.3) where
the correction factor A= H / ln 2 .
24
V
I
  A =
H V

ln 2 I
(2.3)
For an ideal bulk sample, the height of the sample is far more than the
probe span, i.e. H>>S. The sample’s electrical resistivity can be calculated using
equation (2.4), where the correction factor A=2 S .
  A
V
V
=2 S 
I
I
(2.4)
Considering the n-type TE leg sample’s dimension of 20 mm×3 mm×2.1
mm, the p-type TE leg sample’s dimension of 20 mm×3 mm×2.4 mm, and the 1
mm probe span of the four-point system used in this measurement, shown in Fig.
2-7, the correction factor should be a number between those two ideal cases.
Fig. 2-7. Four-point probe testing system used in this measurement, composed of
LUCAS LABS 302 manual four point resistivity probing equipment and
KEITHLEY 2400 source meter.
25
A finite element simulation was carried out to precisely calculate the
correction factor individually for the n-type and p-type TE leg samples. The
software involved was COMSOL, where the Electric Currents module was
utilized. The governing equations are the charge carrier conservation equation
(2.5) and the Ohm’s law (2.6).
  J =0
(2.5)
J = E=-V
(2.6)
W
1A
1A
P1
H
P4
P2
P3
L
Fig. 2-8. Geometry setup of the finite element simulation
The geometry setup is as shown in Fig. 2-8. The length L is set to be 20
mm. The width is set as 3 mm. The height is swept from 2.0 mm to 2.5 mm. Mesh
size is set as extremely fine. All boundaries of this geometry are electrically
insulated, except the four points P1, P2, P3 and P4 on the top surface of the
geometry. An inject point current source with a magnitude of I is assigned to P1.
An extract point current source with the same magnitude I is assigned to P4. P3 is
26
set as electrical ground. The electric potential V at point P2 is monitored. The
material’s electrical resistivity of the geometry is arbitrarily assigned as  . It has
no influence on the final calculation results of the correction factor. Therefore, the
correction factor can be calculated according to equation (2.2). The results are
shown in Fig. 2-9, which indicates that the calculated correction factor for the ntype (H = 2.1 mm) and p-type (H = 2.4 mm) TE leg samples is 4.069×10-3 m and
4.275×10-3 m, respectively. The measurement readings from the measurement
system for the n-type and p-type samples are 0.020 ±0.001Ω and 0.021 ±0.001 Ω,
respectively. Therefore, the electrical resistivity for n-type and p-type TE legs is
about (8.14±0.4)×10-5 Ω∙m and (8.98±0.4)×10-5 Ω∙m, respectively. The electrical
conductivity for n-type and p-type TE legs is (1.23 ± 0.25)×104 S/m and (1.11 ±
0.25)×104 S/m, respectively.
4.35
Correction factor (mm)
4.30
4.25
4.20
4.15
4.10
4.05
4.00
3.95
2.0
2.1
2.2
2.3
2.4
Thickness (mm)
Fig. 2-9. Correction factor with respect to different thickness.
27
2.5
2.4.3. Thermal conductivity
The thermal conductivity can be measured using steady-state techniques
or transient techniques. The steady-state techniques include heat flow meter
method, hot wire method, 3-Ω method, thermo-reflectance method, etc. Even
though through the value of thermal conductivity can be directly measured using
those steady-state techniques, they all suffer from the difficulty of eliminating the
measurement errors induced by thermal contact resistance. Among the
aforementioned methods, only the 3-Ω method can be independent from the
thermal contact resistance. However, it is time-consuming and complicated to
deal with its three harmonic frequencies. In addition, all these steady state
methods require complicated experiment setups and long experiment timespans.
Transient techniques can be independent from the thermal contact
resistance. In addition, the experiment only needs simple setup and short period of
time. However, it is the thermal diffusivity that can be measured, instead of
thermal conductivity. The thermal conductivity has to be calculated given the
specific heat capacity and density, following equation (2.7), where k is the
thermal conductivity,  m is the density, c p is the specific heat capacity and  is
the thermal diffusivity. This study takes advantage of a so-called thermal flash
method [100-103], one type of the transient techniques. The specific heat capacity
was measured through Modulated Differential Scanning Calorimetry (MDSC).
Then the thermal conductivity can be calculated.
k  mc p
28
(2.7)
The experiment setup of the thermal flash method is shown as Fig. 2-10,
where the bottom end of the cold-pressed Bi2Te3 TE leg under test was thermally
connected to an aluminum heat sink immersed in room-temperature water.
Therefore, the temperature at the bottom end can be considered as a constant. The
top end of the TE leg was exposed to a heater, which was thermally connected to
the TE leg at time zero. Therefore, the top end of the TE leg can be considered to
have a constant incoming heat flux. The heat conduction in the TE leg can be
considered as a one-dimensional heat conduction problem. The temperature
profile at the top end of the TE leg has analytical solution with the
aforementioned boundary conditions. Detailed derivation process is summarized
in Appendix A.
In order to prevent the TE leg from falling down, thermally insulated foam
was placed surrounding the TE leg to provide mechanical support. The bottom
end and the top end of the TE leg were coated with silicone heat transfer
compound (MG Chemicals, 860-150G) to form relatively good thermal contact, in
order to increase the signal-noise ratio. The entire system was in a roomtemperature air environment.
The heater is a device made up of platinum resistors printed on Al2O3
ceramics with inner resistance of about 67 Ω provided by Electronic Design
Center (EDC) at Case Western Reserve University, as shown in Fig. 2-11. Before
the heater was placed on top of the TE leg, it was powered by a 0.1 A current
source for a long enough time, in order to ensure a steady-state initial condition.
29
Heater
Cold-pressed TE leg
Foam to provide
mechanical support
Aluminum heat sink
Room-temperature
Water
Fig. 2-10. Experiment setup of the thermal diffusivity measurement.
Fig. 2-11. Heater used in this experiment with no electrical insulator layer on top.
30
When the temperature at the top end of the TE leg increases, the
corresponding local temperature of the heater decreases. If a time constant τ is
defined as the time it takes for the temperature at the top end of the TE leg to
become a constant, then the time it takes for the temperature of the heater to
become a constant should be the same as τ. Furthermore, the inner resistance of
the platinum depends on temperature. Therefore, the time that the voltage at the
two ends of the heater needs to become a constant is exactly the time constant τ.
The voltage profile of the heater was monitored using PicoScope 3424
during the experiment in order to determine the time constant τ, which can be
further used together with the length of the TE leg L to calculate the thermal
diffusivity of the TE material. The relation is described in equation (2.8). Detailed
derivation process can be referred to Appendix A.

  1
n 0
n

  n  1 L  
 nL 
  
 ierfc 
ierfc 

 

  
   
  


  n  1 L   
L
 nL 

  n  1  erfc 
 n  erfc 
   0

 
  
    

(2.8)
The voltage data corresponding to the n-type TE leg is plotted in Fig. 2-12,
together with its smoothed data (based on Loess algorithm embedded in
OriginLab) and the time derivative of the smoothed data. The heater connected to
the top end of the n-type TE leg at t0 = 21.7 s. The time derivative of the heater’s
voltage become zero at tτ = 143.39101 s. Therefore, the time constant for the ntype TE leg is τ = 121.69101 s. Considering the leg length of 20 mm, the thermal
31
diffusivity of the n-type TE material is calculated as 5.373×10-5 m2/s. The
calculation process is carried out by solving equation (2.8) using MATLAB. The
scripts of the MATLAB code is attached in Appendix A.
The voltage data corresponding to the p-type TE leg is plotted in Fig. 2-13,
still together with its smoothed data and the time derivative of the smoothed data.
The heater was connected to the top end of the p-type leg at t0 = 20.297 s. The
time derivative of the heater’s voltage became zero at tτ = 122.31501 s. Therefore,
the time constant for the p-type TE leg is τ = 102.01801 s. The calculated thermal
diffusivity of the p-type TE material is 6.492×10-5 m2/s.
The specific heat measured using MDSC (TA Instruments Q100) is
plotted in Fig. 2-14 and 2-15 for n-type and p-type material, respectively. Each
type of material was tested twice using two individual cold-pressed disc samples,
with a diameter of 6.3 mm and thickness of 0.4 mm. The final value of the
specific capacity of each type of TE material is the average of the two
measurements. For the n-type TE material involved in this research, the specific
heat capacity is 173.7 ± 3.1 mJ/(g∙K). For the p-type TE material, the measured
specific heat capacity is 172.5 ±9.8 mJ/(g∙K).
Considering the n-type TE leg dimension of 20 mm×3 mm×2.1 mm and
the p-type TE leg dimension of 20 mm×3 mm×2.4 mm, as well as the weight of
each TE leg of 1 gram, the density of n-type TE leg and p-type TE leg is
7.937×106 g/m3 and 6.944×106 g/m3, respectively.
32
Fig. 2-12. The voltage profile corresponding to the n-type TE leg, together with its
smoothed data (Loess algorithm) and the time derivative of the smoothed data.
33
Fig. 2-13. The voltage profile corresponding to the p-type TE leg, together with its
smoothed data (Loess algorithm) and the time derivative of the smoothed data.
34
Specific heat capacity (mJ/g/K)
250
200
150
100
50
n-type, disc sample 1
n-type, disc sample 2
0
-50
-2
0
2
4
6
8
10
12
14
16
18
20
Time (min)
Fig. 2-14. Specific heat capacity measurements of n-type TE material.
Specific heat capacity (mJ/g/K)
200
150
100
50
p type, disc sample 1
p type, disc sample 2
0
-2
0
2
4
6
8
10
12
14
16
18
Time (min)
Fig. 2-15. Specific heat capacity measurements of p-type TE material.
35
20
According to equation (2.7), the overall thermal conductivity of n-type and
p-type TE materials is 74.07±1.32 W/(m∙K) and 77.77±4.42 W/(m∙K),
respectively. The characterized room temperature region (300 K) material
properties of the TE materials used in this study are summarized in Table 2-1.
Table 2-1. Material property summary of the TE materials used in this study
Seebeck
coefficient
(μV/K)
ntype
ptype
Electrical
Electrical
Thermal
resistivity conductivity conductivity
(10-5 Ω∙m)
(104 S/m)
(W/m/K)
Figure-of-merit
ZT
198.67±1.33
8.14±0.4
1.23±0.25
74.07±1.32
(1.97±0.11)×10-3
61.33±0.67
8.98±0.4
1.11±0.25
77.77±4.42
(1.59±0.12)×10-4
Therefore, the cross-sectional area ratio between the n-type and p-type TE
legs that can maximize the output power for conventional electrically serial
device structure is [104]
 p p
Sn

 0.97  1
Sp
 n n
(2.9)
The two legs that form the unit TEM with the electrically parallel structure
are the same type of material (either n-type or p-type). In this study, the same
material is used for both legs. In this case, no matter how the cross-sectional area
ratio changes, the output energy is always under the optimal condition. The claim
here is theoretically proved in Chapter 3.
2.5. TEM fabrication
As discussed in Section 2.4.3, the cross-sectional area ratio between two
legs that make up the unit TEM with electrically serial structure is optimized to be
36
around 1. In order to realize that, the dimensions of the n-type leg remained
unchanged (2.1 mm × 3 mm × 20 mm), while the dimensions of the p-type TE
legs were adjusted as follows: 0.9 g p-type TE powder was casted into the mold
pressed under the same pressure 20,000 lb (~1.48 GPa). The dimensions of the ptype legs then became approximately the same as the n-type legs.
For the unit TEMs with the electrically parallel structure, the TE legs have
the same dimensions as the TE leg samples involved in the material property
characterization in the previous section (i.e. For n-type TE legs, the weight is 1 g
and the thickness is 2.1 mm. For p-type TE legs, the weight is 1 g and the
thickness is 2.4 mm). All the aforementioned dimension information of TE legs
that make up the TEMs is summarized in Table 2-2.
Table 2-2. A summary of the dimension information of TE legs that make up TEMs.
TEM
structure
Electrically
serial
Electrically
parallel
TE material
type
n
Weight
(g)
Length Width Thickness
(mm) (mm)
(mm)
1
20
3
2.1
p
0.9
20
3
2.1
n
1
20
3
2.1
p
1
20
3
2.4
The TE legs were sandwiched between two substrates to provide
mechanical support and electrical insulation. The bottom substrate was ceramic
(Al2O3). The top substrate was a printed platinum resistor on ceramic (Al2O3)
substrate as shown in Fig. 2-16, provided by Electronics Design Center (EDC) at
Case Western Reserve University. There is an electrical insulation layer (blue
37
color) on top of the platinum. It is convenient to adjust the temperature at the top
end of the TEM by adjusting the current flowing through the heater.
Fig. 2-16. Printed heater as top cap of unit TEM.
Fig. 2-17. The fabricated unit TEM (traditional serial structure).
38
The TE legs were electrically connected using silver epoxy H31 (EPOXY
Technology) and hardened under temperature of 150 °C for about 2 hours. The
overall unit TEM is shown in Fig. 2-17, taking the conventional electrically serial
structure as an example. Both electrically serial and parallel structures were
fabricated. All the bounding wires were mechanically protected by using silicone
rubber (DOW CORNING 3140 MIL-A-46146 RTV Coating) as force relief agent.
2.6. TEG electrical output performances
When the fabricated unit TEMs are used as TEGs, the electric output
characteristics of both electrically serial and parallel structures were recorded
using the experiment setup shown in Fig. 2-18.
Heater as
substrate
Device
under test
CR1000 data
acquisition
device
Ice water as
heat sink
Laptop to visualize
collected data
Trans-impedance
amplifier
Fig. 2-18. Experiment setup to characterize the unit TEM.
The bottom boundary of the unit TEM was thermally connected to an
aluminum heat sink immersed in ice water, using silicone heat transfer compound
(MG Chemicals) to keep a constant temperature at around 0 °C. Temperature at
39
the top boundary of the unit TEM was adjusted by controlling the current flowing
through the platinum heater, whose inner resistance is around 100 Ω.
A trans-impedance amplifier was designed to simultaneously collect the
output voltage and current of the unit TEM with high accuracy, as shown in Fig.
2-19, where an operational amplifier (OPA350PA) is utilized and powered by
±1.5 V power source provided by AAA batteries. The non-inverting input pin is
grounded. The inverting input pin is connected to the positive output electrode of
the unit TEM. A resistor R bridges between the inverting input and the output of
the op-amp. A diode (LM4041DIZ-1.2/NOPB) is reversely biased, resulting a
fixed potential difference of about 1.2 V between the ground and one end of R1,
whose another end connects to the -1.5 V power source. Two electrically serial
resistors, R2 and R3 (a potentiometer), used as a voltage divider of the 1.2 V
potential difference, are in parallel with the reversely biased diode. The middle
pin of the potentiometer R3 connects to the negative output electrode of the unit
TEM. When the knob of the potentiometer R3 rotates, the output voltage of the
unit TEM changes. Meanwhile, the load resistance of the TEM changes
accordingly. The advantage of this circuit design is that the output I-V curve of
the TEM can be captured along with step changes of its output voltage. Voltages
at the negative output electrode of the unit TEM (V1) and the output pin of the
op-amp (V2) are collected, which correspond to the output voltage (-V1) and the
output current (-V2/R), respectively. The higher the value of the trans-resistor R,
the higher the accuracy of the output current of the unit TEM. For example, if
R=1 GΩ, nano-ampere scale of output current can be captured. Capacitors are
40
placed between the power source and the ground, as well as between two ends of
the trans-resistor R, in order to integrate thermal noise. The whole circuit was
embedded inside a metal box to get rid of impact from the electromagnetic noise.
The voltages V1 and V2 were recorded using data acquisition device
CR1000 (CAMPBELL Scientific Inc.). Temperatures at the top and bottom
boundaries of the unit TEM were measured using k-type thermocouples. The two
thermocouples’ output voltages were also recorded by the CR1000. Data
sampling frequency was 1 Hz. There are at least 30 data samples with respect to
each step of the output voltage. Four temperature scenarios were tested, in which
temperature differences of 30 °C, 50 °C, 70 °C and 100 °C were created between
the top and bottom boundaries.
The collected data was then processed to generate the output I-V curves
and output power curves of the unit TEMs under a certain temperature boundary
condition. The output voltage and output current data were averaged with respect
to each output voltage step. Results of output characteristics of unit TEMs of both
electrically serial and parallel structures are shown as follows with respect to a
100 Ω trans-resistor.
All the output I-V data points were fitted using linear fitting algorithm
(embedded in OriginLab) to calculate the open-circuit output voltage, short-circuit
output current and inner resistance of a certain unit TEM. Meanwhile, the output
power data points were fitted using second-order polynomial fitting algorithm
41
(OriginLab) to generate the maximum output power. The calculated results are
summarized in Table 2-3.
Fig. 2-19. Trans-impedance amplifier design to monitor the output current and
voltage of the unit TEM.
42
30 C
50 C
70 C
100 C
10
Output current (mA)
8
6
4
2
0
0
5
10
15
20
Output voltage (mV)
(a)
30 C
50 C
70 C
100 C
60
Output power (W)
50
40
30
20
10
0
0
5
10
15
20
Output voltage (mV)
(b)
Fig. 2-20. Output characteristics of n-type electrically parallel structure unit TEM.
(a) Output current VS output voltage. (b) Output power VS output voltage.
43
2.5
30 C
50 C
70 C
100 C
Output current (mA)
2.0
1.5
1.0
0.5
0.0
0
1
2
3
4
5
6
Output voltage (mV)
(a)
4
30 C
50 C
70 C
100 C
Output power (W)
3
2
1
0
0
1
2
3
4
5
6
Output voltage (mV)
(b)
Fig. 2-21. Output characteristics of p-type electrically parallel structure unit TEM.
(a) Output current VS output voltage. (b) Output power VS output voltage.
44
3.5
30 C
50 C
3.0
70 C
100 C
Output current (mA)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
0
5
10
15
20
25
Output voltage (mV)
(a)
25
30 C
50 C
20
Output power (W)
70 C
100 C
15
10
5
0
0
5
10
15
20
25
Output voltage (mV)
(b)
Fig. 2-22. Output characteristics of electrically serial structure unit TEM. (a)
Output current VS output voltage. (b) Output power VS output voltage.
45
Table 2-3. Calculated results of several parameters with respect to different TEM
structures.
Temperature
difference
(°C)
n-type
parallel
p-type
parallel
serial
30
50
70
100
30
50
70
100
30
50
70
100
Open-circuit
output
voltage
(mV)
5.96±0.04
9.87±0.09
13.67±0.11
19.85±0.15
1.84±0.02
3.04±0.02
4.12±0.02
5.76±0.05
7.32±0.18
12.35±0.19
17.42±0.19
25.04±0.11
Short-circuit
output
current
(mA)
2.92±0.01
4.85±0.02
6.91±0.03
11.68±0.05
0.64±0.003
1.04±0.003
1.46±0.003
2.37±0.01
0.90±0.003
1.58±0.003
2.26±0.003
3.44±0.008
Inner
resistance
(Ω)
2.04±0.02
2.03±0.07
1.98±0.02
1.70±0.01
2.88±0.03
2.92±0.02
2.81±0.01
2.43±0.02
8.06±0.20
7.83±0.12
7.70±0.08
7.29±0.04
Maximum
output
power
(μW)
4.33±0.06
11.98±0.4
23.45±0.9
57.46±2
0.30±0.003
0.79±0.008
1.51±0.02
3.38±0.04
1.64±0.01
4.85±0.03
9.85±0.06
21.23±0.16
For the n-type electrically parallel unit TEM, when the temperature
difference between two boundaries goes up, the open-circuit voltage, short-circuit
current and maximum output power increases, while the inner resistance
decreases to a tiny extent. The n-type material’s Seebeck coefficient under room
temperature region can be calculated using the open-circuit voltage corresponding
to a 30 °C temperature difference as -198.67 ± 1.33 μV/K. Seebeck coefficients
calculated using open-circuit voltage data corresponding to 50°C, 70°C and
100°C temperature differences approximately remain stable.
The resistance of each n-type TE leg is about 0.26 Ω, using the electrical
resistivity/conductivity measured in Section 2.4.2 and considering the dimension
of 2.1 mm×3 mm × 20 mm. The combined resistance of two n-type TE legs is
about 0.13 Ω, which is the ideal case of the inner resistance of the n-type
46
electrically parallel unit TEM. The difference between the ideal case of 0.13 Ω
and the actually measured inner resistance of the corresponding unit TEM (~2 Ω)
is contributed by the contact resistance between the TE legs and the silver inner
connectors and the silver inner connectors themselves, which are made from
cured silver epoxy.
For the p-type electrically parallel unit TEM, the open-circuit voltage,
short-circuit current and maximum output power have the same trends as the ntype case when the temperature difference changes. However, the magnitudes of
all these parameters become significantly smaller. This can be explained by
calculating the p-type material’s Seebeck coefficient under room temperature
region corresponding to 30 °C temperature difference. It is about 61.33 ± 0.67
μV/K, which is approximately one third of the n-type material’s Seebeck
coefficient.
The resistance of each p-type TE leg that makes up the electrically parallel
unit TEM is about 0.25 Ω. The ideal case unit TEM inner resistance is 0.125 Ω.
The difference between the actual measured inner module resistance and the
ideal-case inner resistance is even larger than that of the n-type case. This
difference implies that the contact resistance between the silver inner connectors
and the p-type TE material is larger than that of the n-type case.
The fact that the ideal-case inner resistance of electrically parallel unit
TEM only occupies a small percentage of the actually measured inner resistance
of the unit modules indicates that it is the contact resistance and the silver inner
47
connector resistance that dominate the inner resistance of the modules. The
optimization of the cross-sectional area ratio between the n-type and p-type TE
legs that form the electrically serial unit TEM does not improve the output power
significantly.
For the unit TEM with electrically serial structure, the open-circuit voltage,
short-circuit current and maximum output power also increases as the temperature
difference goes up. The open-circuit output voltage approximately equals to the
summation of the open-circuit output voltages of the n-type and p-type unit TEMs
with electrically parallel structures corresponding to a certain temperature
difference. This is evidence that the fabrication and measurement of the unit
TEMs here is valid to a large extent.
2.7. TEG performance comparison among different TEM structures
The output I-V curves and output power curves of the unit TEMs are
compared among different device structures, as shown in Fig. 23 to 26, with
respect to temperature differences of 30 °C, 50 °C, 70 °C and 100 °C between the
top and bottom boundaries of the unit TEMs.
48
3.0
n parallel
p parallel
serial
Output current (mA)
2.5
2.0
1.5
1.0
0.5
0.0
0
2
4
6
8
Output voltage (mV)
(a)
5
n parallel
p parallel
serial
Output power (W)
4
3
2
1
0
0
2
4
6
8
Output voltage (mV)
(b)
Fig. 2-23. The comparison on output characteristics among different TEM
structures under 30 °C temperature difference. (a) I-V curves. (b) Output power.
49
5
n parallel
p parallel
serial
Output current (mA)
4
3
2
1
0
0
2
4
6
8
10
12
14
Output voltage (mV)
(a)
12
n parallel
p parallel
serial
Output power (W)
10
8
6
4
2
0
0
2
4
6
8
10
12
14
Output voltage (mV)
(b)
Fig. 2-24. The comparison on output characteristics among different TEM
structures under 50 °C temperature difference. (a) I-V curves. (b) Output power.
50
n parallel
p parallel
serial
Output current (mA)
6
4
2
0
0
2
4
6
8
10
12
14
16
18
Output voltage (mV)
(a)
25
n parallel
p parallel
serial
Output power (W)
20
15
10
5
0
0
2
4
6
8
10
12
14
16
18
Output voltage (mV)
(b)
Fig. 2-25. The comparison on output characteristics among different TEM
structures under 70 °C temperature difference. (a) I-V curves. (b) Output power.
51
10
n parallel
p parallel
serial
Output current (mA)
8
6
4
2
0
0
5
10
15
20
25
Output voltage (mV)
(a)
60
n parallel
p parallel
serial
Output power (W)
50
40
30
20
10
0
0
5
10
15
20
25
Output voltage (mV)
(b)
Fig. 2-26. The comparison on output characteristics among different TEM
structures under 100 °C temperature difference. (a) I-V curves. (b) Output power.
52
The comparisons clearly show that the electrically parallel unit TEM made
up of the TE material that has higher ZT value (n-type here) generates the highest
output power. In contrast, the electrically parallel unit TEM made up of the TE
material that has lower ZT value (p-type here) generates the lowest output power.
The output power generated by the conventional electrically serial unit TEM
made up of both types of TE materials is in the middle of the former two cases.
The output power improvement when using the n-type electrically parallel unit
TEM is more than 164%, 147%, 138% and 170%, for each respective temperature
difference, compared to the conventional electrically serial structure.
Even though the maximum output power increases significantly by using
the electrically parallel unit TEM made up of the material that has the higher ZT
value (n-type here), the maximum output power point regarding to the load
resistance decreases, compared to the electrically serial unit TEM.
The comparison here is only for unit TEMs. If TEMs are made up of
dozens of unit TEMs, the output power increase when using the electrically
parallel structure is predicted to be even larger. However, the maximum output
power delivery point with respect to the load resistance is predicted to be even
smaller, which severely limits the applications of the electrically parallel TEM.
Fortunately, this problem can be solved by using a back-end step-up DC-DC
converter, which is discussed in Chapter 5.
53
2.8. Thermoelectric cooler (TEC) performance comparison
The previous section has shown that the electrically parallel unit TEM
made up of the relatively higher ZT material has higher output power, compared
to conventionally electrically serial unit TEM. This implies that the electrically
parallel structure has the potential to be more energy efficient when used as TEG.
It is interesting to investigate whether the electrically parallel unit TEM has the
potential to generate a higher temperature difference when used as TEC.
To carry out this comparison, the unit TEMs were placed in air
environment, leaving both top and bottom boundaries open without any thermal
load. 1 ampere independent current source was used to power the unit TEMs.
Temperatures at both end of the unit TEMs were recorded as time goes on and
compared, as shown in Fig. 2-27.
Temperature difference (C)
100
n parallel
p parallel
serial
80
60
40
20
0
0
100
200
300
400
500
Time (s)
Fig. 2-27. The comparison on the generated temperature difference among different
TEM structures when used as TE coolers.
54
Fig. 2-27 indicates that the electrically parallel unit TEM made up by the
relatively higher ZT value material (n-type here) generated the highest
temperature difference between two ends of the module when used as TEC. The
electrically parallel unit TEM composed of the relatively lower ZT value material
(p-type here) generated the lowest temperature difference. The temperature
difference generated by the conventional electrically serial unit TEM is in the
middle of the former two types of unit TEMs.
2.9. Summary
In this chapter, the experimental observations of electrically parallel
structure unit TEMs are described and compared to traditional electrically serial
structure unit TEMs. The electrically parallel unit TEM has a higher energy
conversion efficiency, when used as both a TEG and a TEC, if the TE material
that has a relatively higher ZT value (n-type here) is used to form the legs. The
observations can be explained from both analytical and numerical perspectives,
which are further introduced in Chapter 3 and 4, respectively.
Even though the inner resistance of the unit TEMs is dominated by the
contact resistance and the silver inner connectors, rather than the TE legs, the
experimental comparisons are still valid, because the fabrication process remains
the same for both types of TE legs.
Additionally, another type of fabrication process to generate TEMs, the
stencil printing process, was also explored, using self-made TE inks, mainly made
from the mixture of the same TE powder used in this chapter and epoxy resins.
55
However, the inner resistance of the electrically serial TE modules was too high
to be characterized. In contrast, electrically parallel TE modules had moderate
inner resistances. The observation here proves that the electrically parallel
structure benefits the applications of TEM made by high resistivity TE materials.
Material property characterization of TE inks involved in the printing process is
not convenient, because of the difficulties to prepare uniform testing TE leg
samples without voids caused by air bubbles. This portion of research is briefly
introduced in Section 7.3.
56
Chapter 3.
ANALYTICAL ANALYSIS OF THE
ELECTRICALLY PARALLEL TEM
3.1. Overview
The traditional TEMs are made of two types of TE materials. For the Π
structure, multilayered stack structure and the roll-up sheet structure, the two
types materials are usually n-type and p-type semiconductor TE materials. For the
uni-leg structure, the metal inner connector can also be considered as a distinct
type of material, compared to the other n-type or p-type of semiconductor
material. The TE legs formed by those two types of materials are connected
electrically in series. If there is a mismatch between the ZT values of the two
types of TE materials, the ZT value of one type of material must be higher than
the other (ZTn>ZTp in Chapter 2). The experimental observations introduced in
the previous chapter indicate that the electrically parallel unit TEM made up of
the TE material that has the higher ZT value (n-type here) shows a higher energy
conversion efficiency, compared to the traditional electrically serial structure.
The observations are explained analytically in this chapter. The energy
efficiency of the traditional electrical serial structure is firstly discussed in
Section 3.2. The energy efficiency and module’s figure-of-merit of the newly
proposed electrically parallel structure are derived in Section 3.3, with and
without considering the wire effects. Carrier driving mechanisms inside TEMs are
discussed in Section 3.4, for both electrically parallel and electrically serial
structure TEMs.
57
3.2. Traditional electrically serial TEM efficiency
TE module’s efficiency is defined as the ratio of the electrical energy
delivered to the external load circuit, to the absorbed energy from the heat source.
Corresponding to electrically serial principle, the maximum possible energy
efficiency of traditional TEM can be depicted as equation (3.1) under the
assumption that the TEM is working under a small temperature gradient [104] and
all material properties are temperature independent.
max 
1  ZTmodule  1
TH  TC

T
TH
1  ZTmodule  C
TH
(3.1)
where TH is the hot side absolute temperature, TC is the cold side temperature, T
is the algebraic mean value of TH and TC , and ZTmodule is the TE module’s
dimensionless figure-of-merit, which equals to
ZTmodule 


 n  T
2
p
 p  p   n n

2

 p2T

 pp 
 n
1 
 p



2
 n n
1 

 pp





2

 n2T

 n n 
 p 
1 

 n 
2
 pp
1 

 n n





2
(3.2)
where
 is the Seebeck coefficient,  is the electrical resistivity, and  is the
thermal conductivity. The subscripts p and n indicate that the corresponding
coefficients belong to the p-type and n-type material, respectively. Equation (3.1)
implies that the higher the module’s figure-of-merit ZTmodule , the higher the
module’s efficiency. From equation (3.2), researchers abstract the figure-of-merit
58
of a certain material as shown in equation (1.1), which is listed out here again for
convenience, as shown in equation (3.3), in order to evaluate a material’s possible
maximum intrinsic efficiency when forming a TEM.
ZTmaterial
2

T

(3.3)
It has to be emphasized that equation (3.3) is valid only for a certain type
of material, rather than the module. It cannot be directly plugged into equation
(3.1), which has been neglected in some of the literatures [4, 44, 105]. Equation
(3.2) indicates that the higher the material figure-of-merit ZTmaterial of a certain
type of material that forms the TEM, the higher the module’s figure-of-merit
ZTmodule , the higher the module’s efficiency. This is the reason why researchers
are continually trying to find better TE materials that have higher ZTmaterial .
In reality, it is almost impossible to find two perfectly matched p-type and
n-type TE materials that have the exact same values of electrical resistivity
(  p   n ), thermal conductivity (  p   n ), and the same absolute values of
Seebeck coefficient (  p   n ) under the same temperature. For the simplest
case of single crystal materials, the effective masses of electrons and holes are
different with respect to p-type and n-type counterparts, resulting in a different
electrical resistivity. For the nanostructured material, the extensive grain
boundaries might scatter electrons and holes at different levels, leading to
unmatched electrical resistivity [106]. For oxide TE materials, most n-type
materials are inferior due to their high thermal conductivities [4], compared to
59
their p-type counterparts. For organic TE materials, it is difficult to dope organic
semiconductors to make them n-type [107] and air stable [47]. For half-Heusler
TE materials, most efforts thus far have concentrated on the n-type half-Heusler
alloys. The search for promising p-type half-Heusler materials that can be coupled
to existing high-performance n-type half-Heusler alloys for high-temperature
thermoelectric power generation has just been initiated in the past decade [108].
All those aforementioned reasons will lead to the mismatch of material properties
between the p-type materials and their n-type counterparts, as shown in Fig.3-1.
Consequently, the module’s figure-of-merit ZTmodule will be impacted by this
mismatch. This can be proved as follows.
Fig. 3-1. The mismatch of material properties between n-type TE materials and
their p-type counterparts.
Assume that the material figure-of-merits of the p-type and n-type
materials that form the TEM under temperature of T are ZTmaterial , p and ZTmaterial ,n ,
60
and
the
TEM
is
working
under
a
small
temperature
gradient
( T  (TH  TC ) / 2  T ). If ZTmaterial , p  ZTmaterial ,n , we can define the attenuation
factor A ( A  1 ) of the module’s figure-of-merit ZTmodule compared to ZTmaterial , p as
equation (3.4), referring to equation (3.2). Similarly, if ZTmaterial ,n  ZTmaterial , p , the
attenuation factor A can be defined as equation (3.5).




A  1   n /  p  / 1   n  n /  p  p
2
A  1   p /  n  / 1   p  p /  n  n
2
2
, when
ZTmaterial , p  ZTmaterial ,n
(3.4)
, when
ZTmaterial ,n  ZTmaterial , p
(3.5)
2
Take the most popular TE material bismuth telluride (Bi2Te3) under room
temperature as an example. If an electrically serial TE module is composed of ptype and n-type materials that have properties described as Table 3-1 at 300 K
[56], the attenuation factor is A  0.76 shown in equation (3.6), compared to the
n-type Bi2Te3, which has the relative higher material figure-of-merit ZTmaterial .
ZTmodule

p 
1



n 
 n2



 n n 
 pp
1 

 n n

2




2
 0.76 
 n2
=0.56
 n n
(3.6)
Table 3-1. Material properties of a pair of thermoelectric materials (Bi2Te3).
Material
Bi2Te3 (p)
Bi2Te3 (n)
Thermal
Electrical
Seebeck
Conductivity
Resistivity Coefficient

 (mΩ∙cm)  (μV/K)
W/(cm∙K)
0.83
156.57
2.09×10-2
0.73
-193.00
2.04×10-2
61
Material figureof-merit
ZTmaterial at 300K
0.42
0.74
The calculation implies that the overall TE generator module’s figure-ofmerit ZTmodule is highly dependent on whether its p-type and n-type materials are
matched well with each other. If there are no existing matched materials with
respect to a certain working temperature, the potential of the material that has the
relative higher material figure-of-merit ZTmaterial will be wasted (by 24% in this
example). If the electrically parallel module structure is used, the module’s figureof-merit ZTmodule can be increased significantly, which will further impact the TE
module’s overall efficiency. The reason is explained in the following section.
3.3. Electrically parallel TEM efficiency
This research proposes an alternative TE module structure where the legs
are connected in parallel both thermally and electrically, as shown in Fig. 3-2.
The legs have to be made from the same type of TE materials (p-type or n-type),
in order to keep the same polarity between both legs. The electrically parallel
TEM’s figure of merit are derived as follows, with and without considering the
wire effects.
A
A
B
(a)
B
(b)
Fig. 3-2. Electrically parallel TE generator unit module where (a) both legs are ptype semiconductor materials (b) both legs are n-type semiconductor materials. The
arrows represent the current directions.
62
3.3.1. When the wire effects are neglected
Assuming that the TEM is under a small temperature gradient and all
material properties (Seebeck coefficient, electrical resistivity and thermal
conductivities) remain constant along the temperature gradient of both legs, (in
other words, the Thomson effect is neglected at this time being), when the unit
TEM is built-up by legs A and B, the equivalent value of the overall inner
resistance RS , Seebeck coefficient
 and thermal conductivity
K of this unit
module are as follows
RS  RA || RB 
RA RB
L

RA  RB S A  S B
A
B
  A B 
A
B


  RA || RB   S
B S A
A B
 RA RB 
1
1
B S A
 A SB
 
K
1
 A S A   B S B 
L
(3.7)
(3.8)
(3.9)
where L is the length of both legs, which is assumed to be the same for both legs
for the sake of fabrication convenience, R is the inner resistance and S is the
cross-sectional area. Then the equivalent total current flowing through the circuit
( T1  T2 ) is
I
 T1  T2 
RS  RL

63
 T1  T2 
RS 1  m 
(3.10)
where m is defined as the ratio between RL and RS ( RL / RS  m ). Therefore the
amount of heat energy QPeltier absorbed at the hot junctions of the two legs through
Peltier effect is
QPeltier   IT1 
 2T1 T1  T2 
RS 1  m 
(3.11)
The heat energy transferred from the hot junctions to the cold junctions through
heat conduction Qh is
Qh  K T1  T2 
(3.12)
The Joule heat generated in the two legs is
QJ  I RS 
2
 2 T1  T2 
RS 1  m 
2
2
(3.13)
The useful power W delivered by the generator unit module to the load resistor is
 2 T1  T2  m
2
W  I RL 
2
RS 1  m 
2
(3.14)
Half of the Joule heat generated by the generator legs returns to the hot
junctions while the other half flows to the cold junctions [109]. The module’s
efficiency equals to the ratio between the useful electrical energy W delivered to
the load resistor RL , and the energy absorbed from the heat source, which equals
to the summation of the Peltier heat QPeltier and the conduction heat Qh , deducted
by the Joule heat returned to the heat source.
64

QPeltier
m
T T
W
m 1
 1 2
1
m

1
1 T T 1
T
1
 Qh  QJ
1
 1 2
2
Z moduleT1 2 T1 m  1
(3.15)
where ZTmodule is the module’s figure-of-merit, which equals to
ZTmodule
B 2
B
 B2  A
x

2
x

A
A
 A2  B
 2T  A2T



KRS  A  A  B 2   B  B 
B
x  1 
x
A
A
  AA 
(3.16)
where x  S A / SB and the material figure-of-merit of the two legs is assumed to
be ZTmaterial , A  ZTmaterial , B .
When the materials that form leg A and B are different (but belong to the
same type, n-type or p-type), it can be proved that the maximum value of the
module’s figure-of-merit can be achieved at x  S A / SB   . This equation is
possible when the cross-section area of the B leg becomes zero. Therefore, leg B
is eliminated. Hence, the module’s figure-of-merit ZTmodule can reach its
maximum value at
ZTmodule 
 A2
T
 AA
(3.17)
which is equal to the material figure-of-merit of leg A.
When the materials that form leg A and B are the same, it can be proved
that the module’s figure-of-merit ZTmodule always remains at the maximum
possible value as equation (3.17), no matter how the ratio of x  S A / SB changes.
65
When the ratio between RL and RS ( RL / RS  m ) is adjusted to realize
 / m  0 , the module’s efficiency shown in equation (3.15) can reach its
highest value, whose expression is the same as equation (3.1).
#14
Electrically Serial
Electrically Parallel
3.5
ZTmodule
3.0
82.65%
#10
#19
2.5
0.42%
#18 / #19
37.77%
2.0
#4
#12
#14 / #15
12.27%
#10 / #11
6.9%
#4 / #5
#12 / #13
1.5
200
300
400
500
600
700
800
900
1000
1100
Temperature (K)
Fig. 3-3. Module’s figure-of-merit increase by using the electrically parallel
structure, compared to the corresponding electrically serial structure, under the
assumption that the involved materials can be made electrically parallel or serial.
When the electrically parallel structure is utilized, the TEM’s figure-ofmerit, when used as TEG, can be the same as the material that has the higher
material figure-of-merit. Therefore, the potential of TE materials will not be
wasted by the mismatch between the two materials that form the two legs of the
unit module, as it would be when using the traditional structure,. The overall
module efficiency will be increased for the proposed electrically parallel structure.
The increases of the module’s figure-of-merit are summarized in Fig. 3-3 if part
66
materials of Table 1-1 are selected to form the TE device. The highest increase
would be 82.65% at the 500 K to 600 K temperature range.
3.3.2. When the wire effects are considered
The derivation process introduced in the former section is under ideal
assumption that the wires that connect the TEM electrodes and the load
electronics have no influence on the module’s performance. In other words, it
assumes that the wires do not conduct heat at all but conduct electric carriers
perfectly, resulting in an arbitrary device area. However, in reality, the wires are
good heat conductor and has finite electric resistivity. When the wire effects are
considered, the electrically parallel structure TEM’s figure-of-merit needs to be
revised.
If the temperature difference mainly falls on the load electronics
As shown in Fig. 3-4, the load electronics is thermally in the middle of the
hot side and cool side of the electrically parallel structure TEM. Meanwhile, all
electrically parallel TE legs can be considered as one leg with a larger crosssectional area. When the TEMs are used under room-temperature region, heat
conducted through the wire can be neglected, because most of the temperature
difference between two boundaries of the TEM can be considered to fall on the
load electronics, which might be composed of complicated electronic components,
such as capacitors, inductors, switches, etc. All those components block the
phonon transmit from the hot side to the cool side through the wire. The
67
equivalent thermal conductivity of the load electronics can be considered as far
larger than the thermal conductivity of the wires.
(a)
(b)
Fig. 3-4. When temperature difference mainly falls on load electronics, where T1>T2.
(a) p-type (b) n-type.
Under this assumption, taking the n-type case as an example, the module’s
thermal conductivity is
K
 w Sw
Lw

 n Sn
Ln

 n Sn
Ln
(3.18)
where the subscript w corresponds to material parameters of wires, subscript n
corresponds to material properties of n-type TE material.  is the thermal
conductivity. L is the length. S is the cross-sectional area.
Meanwhile, the
equivalent inner resistance of the overall module is
R  Rw  Rn 
 w Lw
Sw

 n Ln
Sn
(3.19)
where  is the electrical resistivity. Therefore, the product of the module’s
equivalent inner resistance and the thermal conductivity is
KR 
 n Sn   w Lw
L 

 n n  =n n   w n X
Ln  S w
Sn 
68
(3.20)
where
X
Lw Sn
Ln S w
(3.21)
Therefore, the module’s figure-of-merit is
ZTmodule 
 n 2T
=
 n n   w n X
 n 2T
 

 n n 1  w X 
 n 
(3.22)
where  represents the Seebeck coefficient and  w can be neglected because
 w   n in most cases.
Equation (3.21) and (3.22) imply that as the cross-sectional area of the
electrically parallel structure goes up, X increases, the module’s efficiency
decreases, because of the wire’s resistance effect. When X is designed to be much
smaller than n / w , the denominator of equation (3.22) can be simplified to
n n , resulting an equal efficiency as when the wire effects are neglected and a
higher efficiency compared to that of the electrically serial structure. When X
increases, there should be an upper cross-sectional area limit for the module to
keep a higher efficiency compared to the electrically serial structure.
For the TE materials used in this study, whose material properties are
summarized in Table 2-1, the module’s figure-of-merit corresponding to
electrically serial structure is 40% of the n-type material’s figure-of-merit. The
electrical resistivity of metal wires is about on the order of 10-8 Ω∙m, such as
copper, silver, gold, etc. The electrical resistivity for the n-type TE material used
in the experiment described in Chapter 2 is on the order of 10-5 Ω∙m. Therefore,
69
the ratio between n and  w is about 1000. Therefore, in order to keep a higher
efficiency when the electrically parallel structure is used, the upper limit of X is
around 1500. Considering in the experiment involved in this study, Lw  10Ln ,
Sw  0.02Sn , therefore X  500 , which is far less than the upper limit of 1500.
This is the reason we observed an output power increase of using the n-type
electrically parallel structure TEM.
If the contact resistance between the metal electrodes and the
semiconductor TE material is considered, the upper limit of X can be larger,
because the equivalent electrical resistivity of the TE material n is larger.
For flexible applications where organic flexible TE materials or TE inks
are used under room temperature region, the corresponding electrical resistivity is
much larger, for example 10-3 Ω∙m. Considering the contact resistance, X can be
designed to be 100,000, which provides plenty room to design an electrically
parallel structure TEM with enough cross-sectional device area for applications to
harvest energy from body heat.
If the temperature difference mainly falls on the load electronics
When the TEMs are used under high-temperature regions, the temperature
difference between the two boundaries of the TEM falls on the wires cannot be
ignored. Because most load electronics are place on the cool side of the TEMs.
The worst case is when all the temperature difference falls on the wire, shown in
Fig.3-5, where T1>T2.
70
wire
p
p
wire
(a)
n
n
(b)
Fig. 3-5. When all the temperature difference falls on the wire, where T1>T2. (a) ptype (b) n-type.
Fig.3-5 indicates that the wire can be considered as a leg thermally
connecting the hot side and cool side. Taking the n-type case as an example, the
module is make up by n-type TE material and slightly p-type wires. The n-type
TE legs and the wires are electrically connected in series. The module’s efficiency
can be described using the electrically serial module’s figure-of-merit equation
(3.2). Materials of wires have even lower material’s figure-of-merit. Therefore,
the material property mismatch between the wire and the TE material is even
larger, resulting to an even lower module’s efficiency. The observations of all the
theoretical analyses are summarized in Fig.3-6.
It means the electrically parallel structure TEM is better to be used in
room-temperature region when the load electronics are placed thermally in the
middle of the hot side and the cool side of the TEMs. High TE material electrical
resistivity and contact resistance can increase the maximum device area limit.
Applications such as energy harvesting from body skin using flexible TE
materials are promising to use electrically parallel TEMs.
71
ZT
ZTparallel,n when wire
effects are ignored
ZTn
ZTserial
ZTparallel,n when temperature
difference mainly falls on
load electronics
ZTp
ZTparallel,n when temperature
difference mainly falls on
wires
ZTw
Xmax
Fig. 3-6. Comparisons on the module's figure-of-merit among different module
structures and different assumptions.
In addition, the electrically parallel structure can simplify the fabrication
process of TEM significantly. Researchers have reported that nanostructured TE
materials have higher ZT value. However, the applications of TEM made up of
those advanced materials have suffered from the assembling process of n-type and
p-type nanostructured TE materials when forming traditional electrically serial
structure at the nanometer scale. In contrast, as mentioned before, only one type
of TE material is needed for the newly proposed structure, simplifying the
fabrication process significantly. In the newly proposed structure, the spaces
among the TE module’s legs can be eliminated (i.e. fill factor=1). Therefore, it is
possible to build a simple multilayered structure, shown as Fig. 3-7, where a layer
of TE material (either n-type or p-type) is sandwiched by two layers of electrodes.
This structure would significantly simplify the fabrication process, and further
decrease the cost. The power density and mechanical durability of the device
would also be improved, because of the elimination of the spaces among the TE
72
module legs. In addition, the temperature gradient is still along the cross-plane
direction, which benefits its implementations.
n-type
p-type
(a)
(b)
Fig. 3-7. Sandwich structure of electrically parallel unit TEM, where T1>T2. (a) ptype (b) n-type.
3.4. Carrier driving mechanisms for electrically parallel TEM
The carriers have been observed to move continuously in the electrically
parallel structure TEM in Chapter 2, even though only one type of TE material
(either n-type or p-type) is used. This section reveals the underlying reason behind
the continuous movements, by qualitatively analyzing the carrier driving
mechanisms for the electrically parallel TEM.
Assuming that the metal inner connectors form ohmic contacts with TE
materials, the contact resistance can be ignored. If n-type electrically parallel
TEM is first discussed, the band structure in each TE leg is shown in Fig. 3-8,
where band bendings as a result of metal-semiconductor contacts are ignored,
because under the ohmic contact assumption, it is the body effects that dominate
the carrier movement behaviors throughout the circuit.
73
n-type
Metal
Metal
_
+
Fig. 3-8. Band structure of n-type TE materials under temperature gradient.
In Fig. 3-8, a certain n-type TE material is electrically connected with
metal connectors at the two ends and under open-circuit condition. When the ntype TE leg is under a temperature gradient, the carrier density at the hot end is
higher than the cold side. This means that the chemical potential ξ (defined as the
energy difference between the Fermi level and the band edges) at the hot side is
larger than the cold side, if the bottom edge of the conduction band is selected as
the potential reference. The carriers (electrons) diffuse to the cold side because of
the carrier density gradient, leading to an electrostatic potential V decrease at the
cold side. A drift current driven by the electrostatic potential gradient eventually
balances with the diffusion current driven by the carrier density gradient. This
electrostatic potential biases the whole band structure to make the Fermi level
incline more. The overall open-circuit output voltage Θ of the n-type TE leg is the
electrochemical potential difference between the two ends, which can be
calculated as the product of the Seebeck coefficient and the temperature
74
difference. The Θ is also a summation of the chemical potential difference and the
electrostatic potential difference between its two ends, shown as equation (3.23),
where q is the unit charge. The fact that the temperature gradient and the
electrochemical potential gradient are in the same direction makes the Seebeck
coefficient negative for n-type TE materials.

  T      V
(3.23)
q
Metal
p-type
_
+
Metal
Fig. 3-9. Band structure of p-type TE materials under temperature gradient.
The band structures of p-type TE legs with connections to metal electrodes
are shown in Fig. 3-9 under the open-circuit condition. Similar to the n-type case,
the carriers (holes) eventually reach a balance between the currents driven by the
carrier density gradient and electrostatic potential gradient. The overall output
voltage difference between the two ends is the electrochemical potential
difference Θ, which is a summation of the chemical potential  / q and the
75
electrostatic potential V. The fact that the temperature gradient is in reverse
direction to the electrochemical potential gradient makes the Seebeck coefficient
positive.
For conventional electrically serial TE modules, the band structures are
shown in Fig. 3-10. The carrier driving mechanisms are the same as introduced
above. It has to be emphasized that the carrier flowing mechanisms of TEM do
not depend on p-n junctions, even though there are both types of semiconductor
TE materials in the electrically serial structure. The carriers are driven by the
carrier density variations and balanced with the reversed electrostatic field.
Metal
p-type
+
_
n-type
Metal
+
Metal
_
Fig. 3-10. Band structure of electrically serial TEM under temperature gradient.
3.5. Summary
The theoretical reasons why the electrically parallel structure TEMs have
higher energy conversion efficiency in the experiments introduced in Chapter 2
are discussed in this chapter. For the conventionally electrically serial TEMs,
76
material properties of the two types of semiconductor TE materials that make up
the module are not easily designed as a perfectly match. If there is any mismatch
between the two types of materials, the module’s figure-of-merit is impacted,
leading to a relatively small energy conversion efficiency. However, for the
electrically parallel structure TEMs, there are no such matching puzzles needed to
be solved. When the legs of electrically parallel TEMs are made from the TE
material that has a higher material’s figure-of-merit compared to its counterpart,
the module’s figure-of-merit can be higher relative to the electrically serial
structure, within an upper limit of the device’s area. The electrically parallel
structure also simplifies the fabrication process of the TEMs.
In addition, the carrier driving mechanisms for the electrically parallel
TEM are discussed. Whenever there is a temperature difference across the TE
material, there is a carrier density gradient, leading to a diffusion current, which is
eventually balanced by a drift current driven by aroused electrostatic potential in
reversed direction. This is why the current can flow through the circuit
continuously.
77
Chapter 4.
FINITE ELMENT ANALYSIS OF
ELECTRICALLY PARALLEL TEM
4.1. Overview
The electrically parallel TEM was observed to generate a higher output
power experimentally in Chapter 2, compared to the conventional electrically
serial structure. The reason was discussed analytically in Chapter 3 by comparing
the energy conversion efficiency of both types of TEM structures. However, the
analytical analysis was under extremely simplified assumptions where the
temperature dependencies of the TE material properties were not considered. One
of the advantages of using finite element method (FEM) is the capability of
considering material properties’ temperature dependencies, as introduced in
Chapter 1. Thomson effects can then be involved in the simulation when the
Seebeck coefficient varies with temperature.
Details of FEM analysis of the newly proposed electrically parallel TEM
are introduced in this chapter. The governing equations are first introduced in
Section 4.2. Material properties used in the simulation are then introduced in
Section 4.3. The finite element simulation model is verified in Section 4.4.
Simulation results of the conventional electrically serial TEM and the newly
proposed electrically parallel TEM are described in Section 4.5 and 4.6,
respectively. The simulation results are also compared in Section 4.7.
78
4.2. Governing equations
The equations governing the three-dimensional temperature and electric
potential distributions in TE materials are the energy conservation equation and
charge conservation equations in the absence of an applied magnetic field.
mCm
T
 (T - TJ )   J 2
t
(4.1)
J  0
(4.2)
J      T 
(4.3)
where
Here the vector J is the electric current per unit area; Cm is the heat capacity
with unit of J / ( K  kg ) ;  m is the material density with unit of kg / m3 ; T is the
temperature;  is the thermal conductivity at zero current;   1/  is the
electrical conductivity;  is the electrical resistivity;
 is the Seebeck
coefficient;  is the electrochemical potential. All material properties (  ,  ,
,
etc.) are functions of temperature and introduced in the following section.
4.3. Material properties
The state-of-the-art Skutterudite materials are involved in the simulation
here in this chapter. The p-type [66] and n-type [65] materials’ Seebeck
coefficient, thermal conductivity, electrical conductivity and figure-of-merit are
plotted in Fig. 4-1, 4-2, 4-3 and 4-4, respectively.
79
Absolute Value of Seebeck Coefficient (V/K)
220
200
180
160
140
alfap
|alfan|
120
300
400
500
600
700
800
900
Temperature (K)
Fig. 4-1. Seebeck coefficient of the materials used to carry out the calculation.
kamap
kaman
Thermal Conductivity (mW/(cmK))
20
18
16
14
12
400
500
600
700
800
900
Temperature (K)
Fig. 4-2. Thermal conductivity of the materials used to carry out the calculation.
80
Electrical Conductivity (MS/m)
0.12
0.10
0.08
0.06
sigmap
sigman
0.04
300
400
500
600
700
800
900
Temperature (K)
Fig. 4-3. Electrical conductivity of the material used to carry out the calculation.
2.0
Figure of Merit
1.5
1.0
0.5
ZTp
ZTn
400
500
600
700
800
Temperature (K)
Fig. 4-4. Figure-of-merit of the material used to carry out the calculation.
81
900
4.4. Simulation model verification
The thermoelectric phenomenon is a coupling problem between the heat
field and electric field. COMSOL software was selected because of its powerful
capability of coupling multi-physics fields. When the simulation initially began,
there was no built-in module ready to use. Therefore, the PDE mathematics
interface was chosen. Two types of PDE modules were explored: Coefficient
Form PDE and Weak Form PDE. In recent years, commercially available TEMs
were developed (for example, in COMSOL version 5.0). The simulation results
using the PDE forms were then compared with the built-in thermoelectric
physical module to verify the precision of the self-built PDE simulations. The
simulation results based on a simple TE leg are shown as follows.
4.4.1. Coefficient Form PDE module
Simulation of TE device behaviors using Coefficient Form PDE module
have been frequently reported in the literature [28-30]. The simulation setup based
on the Coefficient Form PDE module is introduced as follows. Two dependent
variables were defined: temperature T and electrochemical potential Θ.
For the Coefficient Form PDE with respect to T, shown in equation (4.4),
ea
 2T
T
 da
   (cT  aT   )   T  aT  f
2
t
t
the coefficient definitions are
c  kamap(T )
f  -( Jp _ x * x  Jp _ y * y  Jp _ z * z) ,
82
(4.4)
a    Jp _ x * alfa (T ),  Jp _ y * alfa (T ),  Jp _ z * alfa (T ) 
(4.5)
where
Jp _ x  -sigmap(T )*(x  alfap(T )*Tx)
Jp _ y  -sigmap(T )*(y  alfap(T )*Ty)
Jp _ z  -sigmap(T )*(z  alfap(T )*Tz)
(4.6)
For the coefficient form PDE with respect to the electrochemical potential
Θ, shown in equation (4.7)
ea
 2

 da
   (c  a   )     a  f
2
t
t
(4.7)
the coefficient definitions are
c  sigmap(T ) ,
f  d ( sigmap (T ) * alfap (T ) * Tx, x)  d ( sigmap (T ) * alfap(T ) * Ty, y )
 d ( sigmap (T ) * alfap(T ) * Tz , z )
(4.8)
Only one TE leg (p-type) is involved in the comparison in this section.
The bottom boundary of the TE leg is defined as the potential reference. Side
boundaries are defined to have convective heat exchange with the ambient
environment, following equation (4.9).
n  (T )   c (
Tbottom  Ttop
2
T)
(4.9)
where n is the outward unit normal vector seen from the inside of a
certain solid domain, Tbottom is the bottom boundary temperature, Ttop is the top
boundary temperature and T is the temperature at the solid boundary. Equation
(4.9) means the ambient temperature is assumed to be the average temperature
83
between the bottom and top boundary temperatures. The convective heat transfer
coefficient  c between the ambient and the module is assumed to be 10 W/(m2∙K).
When the environment temperature is higher than the boundary temperature, heat
is absorbed into the module. When the environment temperature is lower than the
boundary temperature, heat flux flows outwards, as seen from the solid domain.
When the bottom temperature is set to be 340 K and the top temperature is
set to be 330 K, the open-circuit potential distribution along the p-type TE leg is
shown in Fig. 4-5(a). The potential at the top boundary is 3. 45×10-5 V. When the
temperature boundary conditions are reversed, the open-circuit potential
distribution along the leg is shown in Fig. 4-5(b). The potential at the top
boundary is 3.66×10-5 V.
The simulation results are not reasonable. First, the magnitude is only on
the order of 10 μV under 10 K of the temperature difference. However, the ptype leg’s Seebeck coefficient around 300 K is on the order of 100 μV/K, shown
in Fig. 4-1. Multiplying 100 μV/K with 10 K temperature difference, the opencircuit potential difference between two ends of the TE leg should be on the order
of 1 mV theoretically, which doesn’t match with the simulation results calculated
from the Coefficient Form PDE setup. In addition, when the temperature at the
bottom boundary is smaller than that at the top boundary, the potential at the top
boundary should be smaller than that at the bottom for p-type material. This
theoretical prediction does not match with the simulation result either, shown as
Fig. 4-5(b).
84
(a)
(b)
Fig. 4-5. The electrochemical potential distribution along the p-type TE leg under a
10K temperature difference modeled by the Coefficient Form PDE module. (a)
bottom 340 K, top 330 K. (b) bottom 330 K, top 340 K.
4.4.2. Weak Form PDE module
The main idea of the weak form is to turn the differential equation into an
integral equation, so as to lessen the burden on the numerical algorithm in
evaluating derivatives. For many of the different types of physics simulated with
COMSOL Multiphysics, a weak formulation, or weak form, is used behind the
scenes to construct the mathematical model.
For the weak form PDE with respect to T, as shown in equation (4.10)
0   weakV

(4.10)
the weak expression is
weak  test (Tx) *(-kamap(T ) * Tx  Jp _ x * alfap(T ) * T )
test (Ty ) *(-kamap(T ) * Ty  Jp _ y * alfap(T ) * T )
test (Tz ) *(-kamap(T ) * Tz  Jp _ z * alfap(T ) * T )
(4.11)
f  -( Jp _ x * x  Jp _ y * y  Jp _ z * z)
(4.12)
For the weak form PDE with respect to Θ, as shown in equation (4.10),
the weak expression is
85
weak  test (x) *(-sigmap(T ) * x)
test (y ) *(-sigmap(T ) * y )
test (z ) *(-sigmap(T ) * z )
test () * d ( sigmap(T ) * alfap(T ) * Tx, x)
test () * d ( sigmap(T ) * alfap(T ) * Ty, y)
test () * d ( sigmap(T ) * alfap(T ) * Tz, z )
(4.13)
Similar to the exploration using Coefficient Form PDE module, a same
dimension p-type TE leg is modeled. Same boundary conditions are implemented.
When the bottom temperature is set to be 340 K and the top temperature is set to
be 330 K, the top boundary potential is 1.29 mV, with respect to the potential
reference at the bottom boundary of the TE leg, shown in Fig. 4-6(a). When the
bottom temperature is 330 K and the top temperature is 340 K, the potential at the
top boundary is -1.29 mV, shown in Fig. 4-6(b). The magnitude of the opencircuit voltage modeled using the Weak Form PDE module here is reasonable, as
predicted by multiplying the material’s Seebeck coefficient under this temperature
region with the 10 K temperature difference between two ends of the TE leg.
Meanwhile, the temperature gradient and the electrochemical potential gradient
are in opposite directions. This observation is also reasonable for p-type TE
material, where the Seebeck coefficient is positive.
4.4.3. Built-in Thermoelectric module
The COMSOL software also developed a built-in thermoelectric module,
as there has been active research in this area. The single p-type TE leg simulation
results using the Coefficient Form PDE module and the Weak Form PDE module
are compared to the simulation results based on the built-in module, shown in Fig.
4-7, under the same dimensions and boundary conditions.
86
(a)
(b)
Fig. 4-6.The electrochemical potential distribution along the p-type TE leg under a
10K temperature difference and modeled using Weak Form PDE module. (a)
bottom 340 K, top 330 K. (b) bottom 330 K, top 340 K.
(a)
(b)
Fig. 4-7. The electrochemical potential distribution along the p-type TE leg under a
10 K temperature difference and modeled using Weak Form PDE module. (a)
bottom 340 K, top 330 K. (b) bottom 330 K, top 340 K.
The simulation results using the built-in module are approximately the
same as calculated using the Weak Form PDE module. It indicates that the model
building based on the Weak Form PDE is valid. The calculation based on
Coefficient Form PDE module is actually at risk. All the finite element
simulations involved later in this chapter are based on the Weak Form PDE setup.
87
4.5. Modeling of electrically serial TEM
In order to evaluate the performances of the newly proposed electrically
parallel TEM, the traditional electrically serial TEM needs to be characterized
first as a reference. Weak Form PDE module in COMSOL is used to carry out the
simulation. Governing equations have been discussed in Section 4.2. Material
properties have been introduced in Section 4.3. Boundary conditions of all side
boundaries are the same as equation (4.9) in Section 4.4. The geometry setup of
the unit TEM is first introduced in this section. Optimization of the crosssectional area ratio between the unit TEM’s two legs are discussed sequentially.
Finally, the module’s performances are introduced.
4.5.1. Geometry setup of electrically serial unit TEM
The geometry setup of the electrically serial unit TEM is shown in Fig. 48, where the n-type TE leg and p-type TE leg have widths of Wn and Wp,
respectively, while the height (2 mm) and the depth (1.5 mm) of the two TE legs
are identical (the dimensions of the TE legs were based on some popular
commercial TEMs in the market). Therefore, the cross-sectional area ratio
between the two TE legs is Wn/Wp, which will be optimized with respect to the
output energy in order to be compared to the electrically parallel case. It has to be
pointed out that the total cross-sectional area of the n-type and p-type TE legs in
the electrically serial unit TEM is the same as the total cross-sectional area of the
two TE legs that make up the electrically parallel unit TEM, in order to make sure
that the heat energy flowing through the module vertically is approximately the
88
same for both cases. Space between the two legs is 1 mm wide. Metal interconnector and metal wires are assumed to have thickness of 0.1 mm.
Fig. 4-8.Geometry of the electrically serial unit TEM when used as TEG with a load
resistor.
Close circuit condition is simulated, where the open circuit condition is
actually included when the load resistance is close infinite. The metal wires and
the load resistor are represented by three-dimensional physical geometries. The
load resistor is assumed to have dimensions of 1.5 mm×1.5 mm×0.1 mm. As the
electrical conductivity/resistivity of the load resistor changes, the total resistance
of the load resistor changes, and the output characteristics of the unit TEMs can
be investigated. Material properties of the metal inter-connects, electrodes, and
wires are assumed temperature independent. The Seebeck coefficient is -3.5
μV/K. The electrical resistivity is 28.2 nΩ∙m. The thermal conductivity is 205
W/(m∙K). The heat capacity is 0.897 J/(g∙K). The density is 2.7 g/cm3. Any
contact resistance has been ignored.
89
Fig. 4-9. Another option of coupling the SPICE module to consider the load resistor.
The closed circuit condition of the FEM simulation can also be realized
using the coupling electric circuit SPICE simulation in COMSOL, shown as Fig.
4-9, where the load resistor can be directly assigned a resistance value. However,
extremely small values of the load resistor’s resistance cannot be modeled in this
case, possibly because of the discontinuity of the geometries. In order to simulate
the full range from short circuit to open circuit of the output characteristics, the
setup in Fig. 4-9 is not used.
4.5.2. Optimization of the cross-sectional area ratio
The optimization of the cross-sectional area ratio between the n-type and
p-type TE legs can improve the energy conversion efficiency of the TEM. As
introduced above, the height and depth of the two legs are identical. Therefore,
the cross-sectional area ratio between the two legs can be represented by the
90
width ratio Wn/Wp. If this ratio is swept from 0.1 to 1 with a step 0.1, and the
electrical conductivity of the load resistor is swept from 10-10 to 1010 S/m, the
output power is plotted in Fig. 4-10 (where the plot is zoomed in between the
1S/m and 1010 S/m). Fig. 4-10 implies that the best area ratio is Wn/Wp = 0.6,
corresponding to the maximum output power of 110.95 μW and electrical
conductivity of 105.7S/m (considering the load resistor’s dimensions, the load
resistor’s resistance is 0.02 Ω).
Fig. 4-10. The output power as a function of the electrical conductivity of load
resistor and the cross-sectional area ratio Wn/Wp.
The electrical conductivity at 600 K of the materials used in the study here
is around 0.1 and 0.04 MS/m for n-type and p-type materials, respectively,
referring to Fig. 4-3. The thermal conductivity is about 17.5 and 12.5 mW/(cm∙K)
for n-type and p-type materials, respectively, referring to Fig. 4-2. According to
91
analytical expression of the best cross-sectional area ratio, as shown in equation
(2.9),
the
analytical
calculation
results
should
be
around
Sn / S p   p p /  n n  0.53 , which matches relatively well with the numerical
simulation result of around 0.6.
4.5.3. Simulation results of electrically serial unit TEMs
For the electrically serial unit TEM with the best cross-sectional area ratio
of 0.6 between the n-type and p-type TE legs, the electrochemical potential at the
left side boundary of the bottom left metal electrode is set as potential zero. The
surface integration of current density and average electrochemical potential at the
right boundary of the bottom right metal electrode are monitored as the output
characteristics of the module.
From the simulation, three dimensional temperature distribution,
electrochemical potential distribution, current magnitude distribution and current
direction can be easily visualized, with respect to a certain load resistance. When
the electrical conductivity of the load resistor is 105.7S/m (0.02 Ω), the
aforementioned parameters are plotted as the following four figures, respectively,
at the maximum power delivery point. Fig. 4-12 indicates that the potential is not
always increasing from the bottom boundary of the p-leg to the bottom boundary
of the n-leg. In other words, some ability of the TE materials here is wasted to
some extent. In Fig. 4-14, the arrows’ length is in logarithmic relationship with
the actual current density magnitude at each specific location.
92
Fig. 4-11. Temperature distribution of the electrically serial unit TEM, when bottom
temperature is 610 K, the top temperature is 600 K and the load resistance is 105.7
S/m.
Fig. 4-12. The electrochemical potential distribution of the electrically serial unit
TEM, when bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 105.7 S/m.
93
Fig. 4-13. The current density magnitude distribution of the electrically serial unit
TEM, when bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 105.7 S/m.
Fig. 4-14. The current flowing direction of the electrically serial unit TEM, when
bottom temperature is 610 K, the top temperature is 600 K and the load resistance is
105.7 S/m.
94
4.6. Modeling of electrically parallel TEM
The n-type and p-type electrically parallel unit TEMs are also modeled
using the same governing equations, material properties and simulation
environments as Section 4.2. However, the geometry setup is different, compared
to the electrically serial case, which will first be introduced in Section 4.6.1. The
simulation results are also listed out below.
4.6.1. Geometry setup of electrically parallel unit TEM
The geometry of the electrically parallel unit TEM is shown in Fig. 4-15.
The two TE legs are made by the same material (either n-type or p-type) and
assumed to have dimensions of 1.5 mm×1.5 mm×2 mm, based on typical TE leg
dimensions of commercial products. As discussed in Section 3.3, the crosssectional area ratio between the two legs can be arbitrary and does not affect the
maximum energy conversion efficiency. Therefore, the TE legs dimension
definition here can guarantee that the electrically parallel unit TEM has the
highest possible energy conversion efficiency.
Fig. 4-15. Geometry of the electrically parallel unit TEM when used as TEG with a
load resistor.
95
4.6.2. Simulation results of electrically parallel unit TEMs
For the electrically parallel unit TEM, the electrochemical potential at the
left side boundary of the bottom metal inner connector is set as potential zero. The
surface integration of current density and average electrochemical potential at the
right boundary of the top metal inner connector are monitored as the output
characteristics of the module.
When the bottom and top boundary temperatures are 610 K and 600 K, ntype electrically parallel unit TEMs’ temperature and potential distributions are
shown in Fig. 4-16 and 4-17, corresponding to load conductivity of 106.8 S/m,
where the module generates a maximum output power. These two figures indicate
that the temperature gradient and the potential gradient are in the same direction,
as the Seebeck coefficient is negative for the n-type material. The current density
magnitude and direction are shown in Fig. 4-18 and 4-19. The arrows’ length is in
logarithmic relationship with the actual current density magnitude at each specific
location.
With the same boundary temperature conditions, p-type electrically
parallel unit TEMs’ temperature and potential distributions are shown in Fig. 4-20
and 4-21, corresponding to load conductivity of 106.1 S/m, where the module
generates a maximum output power. The temperature gradient and the potential
gradient are in the reverse direction, as the Seebeck coefficient is positive in this
case. The current density magnitude and direction are shown in Fig. 4-22 and 423.
96
Fig. 4-16. Temperature distribution of the n-type electrically parallel unit TEM,
when bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 106.8 S/m.
Fig. 4-17. The electrochemical potential distribution of the n-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 106.8 S/m.
97
Fig. 4-18. The current density magnitude distribution of the n-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 106.8 S/m.
Fig. 4-19. The current flowing direction of the n-type electrically parallel unit TEM,
when bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 106.8 S/m.
98
Fig. 4-20.Temperature distribution of the p-type electrically parallel unit TEM,
when bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 106.1 S/m.
Fig. 4-21. The electrochemical potential distribution of the p-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 106.1 S/m.
99
Fig. 4-22. The current density magnitude distribution of the p-type electrically
parallel unit TEM, when bottom temperature is 610 K, the top temperature is 600 K
and the load resistance is 106.1 S/m.
Fig. 4-23. The current flowing direction of the p-type electrically parallel unit TEM,
when bottom temperature is 610 K, the top temperature is 600 K and the load
resistance is 106.1 S/m.
100
4.7. Comparison among the electrically parallel and serial unit TEMs
The output I-V curves and output power curves of the n-type and p-type
electrically parallel structure unit TEMs are compared to the optimized
electrically serial structure unit TEM, shown in Fig. 4-24. This figure shows that
the maximum output power of the n-type electrically parallel unit TEM is the
highest (0.17 mW), which is 55% higher than the maximum output power of the
electrically serial unit TEM (0.11 mW). On the other hand, the maximum output
power of the p-type electrically parallel unit TEM is the lowest (0.066 mW),
which is 40% lower than the electrically serial case. Meanwhile, the inner
resistance of the n-type electrically parallel unit TEM is the smallest, whereas the
inner resistance of the electrically serial unit TEM is the largest.
4.0
Parallel, n-type, V
Parallel, p-type, V
Serial,V
0.15
Output Voltage (mV)
3.0
Parallel, n-type, W
Parallel, p-type, W
Serial, W
2.5
0.10
2.0
1.5
Output Power (mW)
3.5
0.05
1.0
0.5
0.0
0.00
0.05
0.10
0.15
0.20
0.25
0.00
0.30
Output Current (A)
Fig. 4-24. Output characteristics comparisons among different structured unit
TEMs when the bottom boundary temperature is 610 K and the top boundary
temperature is 600 K.
101
4.8. Summary
The temperature dependencies of material properties that significantly
influence the TEM’s output performances are taken into consideration in this
chapter, by using finite element simulation. For n-type and p-type TE materials
where the ZTn>ZTp, the maximum output power of the n-type electrically parallel
unit TEM is highest, whereas the maximum output power of the p-type
electrically parallel unit TEM is the smallest. The observations here match well
with the experimental observations in Chapter 2 and analytical analysis in
Chapter 3.
Please note that the wire effect is not considered in the numerical
simulation in this chapter. The energy conservation equation does not apply to
wire and load resistor geometries. More numerical simulations are still needed to
be carried out to investigate the wire effects, as well as the device area’s influence
on the TEMs’ energy conversion efficiency.
In addition, it has to be noticed that the inner resistance of the electrically
parallel module is very small, especially for TEM made up of many unit TEMs.
Meanwhile, the output voltage is also small. These two problems can be solved by
back-end DC-DC converter design, as discussed in Chapter 5.
102
Chapter 5.
BACK-END STEP-UP DC-DC CONVERTER
DESIGN FOR ELECTRICALLY PARALLEL TEM
5.1. Overview
It has been proved that the energy conversion efficiency of the electrically
parallel TEMs is higher than conventional electrically serial TEM. The more that
unit TEMs are connected electrically in parallel, the more power provided when
used as TEG. However, while that occurs, the smaller the inner resistance will
become, dramatically limiting the applications of the electrically parallel TEM if
it is directly used to power an electric load. If the inner resistance of the TEM is
far less than the electric load’s inner resistance, the advantages of using energyefficient electrically parallel TEM vanishes. In addition, the output voltage of the
electrically parallel TEM is too small to be directly taken advantage of, and is
even smaller than the start-up voltage of any types of transistors.
Fortunately, the aforementioned problems can be solved by the
involvement of back-end step-up DC-DC converter. It has to be emphasized that
the electrically parallel TEM has huge short-circuit output current, which can
eventually benefit the back-end DC-DC converter design and improve the amount
of power delivered to the load. This claim is proved in this Chapter. There are
generally two types of step-up DC-DC converters, the capacitive type and
inductive type, which are briefly introduced Section 5.2. In this chapter, the
inductive DC-DC converter is used, because it is intrinsically energy lossless.
Inductive step-up DC-DC converter performances serving as back-end circuit of
103
TEMs are discussed in Section 5.3. Self-starting circuit design to realize the
switching function in the DC-DC converter is discussed in Section 5.4.
5.2. Capacitive and inductive step-up DC-DC converters
In order to boost the low input voltage to a high output voltage, capacitors
and inductors are used in a switched mode circuit, resulting in two types of stepup DC-DC converters: the capacitive and the inductive.
For capacitive step-up DC-DC converters, capacitors are the core
components in the circuit. The working principle can be explained briefly as
follows. For a capacitor with capacitance C, the current i flowing through it
equals to the time derivative of the voltage v across it, shown as equation (5.1).
iC
dv
dt
(5.1)
When several capacitors are initially connected electrically in parallel, they can all
be charged by a power source simultaneously. After the voltages inside those
capacitors increase to a certain level, the capacitors are quickly switched to
electrically serial connections. As the voltage across a capacitor cannot change
instantly in time, the output voltage will be as high as the summation of all the
voltages across each capacitor. A relative higher output voltage is realized in this
way.
However, the highest output voltage is limited by the number of capacitors
used in the circuit. In addition, capacitive DC-DC converter can at most store half
of the energy supported by the power source [110]. It is intrinsically energy lossy,
even when all other components in a capacitive step-up DC-DC converter circuit
104
are ideal and lossless. The advantage of capacitive DC-DC converters is that the
implementation of capacitors in IC fabrication process is convenient and costeffective. Consequently, the capacitive DC-DC converters are used most when the
requirements of output power and fabrication cost are both low.
For inductive step-up DC-DC converters, inductors are the core
components. For an inductor with inductance L, the voltage v across the inductor
equals to the time derivative of the current i flowing through it, as shown in
equation (5.2).
vL
di
dt
(5.2)
When an inductor is charged by a power source, the current flowing through it is
increased to a certain level. When the inductor is switched to disconnect with the
power source quickly, as the current through the inductor cannot change instantly
in time, the voltage across the inductor will increase to a high level, resulting in a
high output voltage. This is the fundamental working principle of inductive stepup DC-DC converter. The inductive DC-DC converter is more attractive in the
area of TE technology, because it is intrinsically energy lossless when an ideal
inductor is charged and all other components in the circuit is lossless. Therefore,
the inductive step-up DC-DC converter is adopted as the back-end circuit for
TEMs used as TEG.
5.3. Back-end step-up DC-DC converter performance for the TEM
The output voltage of a TEM (even with traditional electrically serial
structure) is usually lower than the desired value in practical applications,
105
depending on the temperature gradient across the device. As a result, the
switching mode step-up inductive DC-DC converter is desired.
Take the most common boost DC-DC converter as an example, as shown
in Fig. 5-1, where VS and RS are the open-circuit output voltage and inner
resistance of a TEM, L is a conductor, C is a capacitor, R L is a load resistor. SW1
and SW2 are two switches that control the switching mode of the circuit.
RS
VS
SW2
L
C
SW1
RL
Fig. 5-1. Circuit of the switched-mode step-up inductive boost DC-DC converter.
For simplicity, only the Continuous Conduction Mode (CCM) is discussed
here, where the current flowing through the inductor never falls to zero. Under
CCM, there are two phases in each period of the switching mode. The first phase
is the inductor charging phase when SW1 is closed and SW2 is open, with time
duration of ton. In this phase, the inductor L is charged by the TEG, resulting in an
increase of the current flowing through the inductor iL . Simultaneously, the
output capacitor C is discharged through the load resistor R L. The second phase is
the inductor discharging phase when SW1 is open and SW2 is closed. The time
duration in this second phase is toff. During this phase, the inductor L is
discharged into C and RL, leading to a decrease of iL. Meanwhile, C is charged
and RL is powered.
106
The comparison between the back-end DC-DC converter performances
when powered by the conventional electrically serial unit TEM and when
powered by the newly proposed electrically parallel unit TEM are carried out as
follows. Assuming the n-type and p-type materials that form the electrically serial
unit TEM follow material property definitions in Table 3-1, the optimized crosssectional area ratio between the n-type and p-type TE legs is about 1. The
electrically parallel unit TEM is composed by two legs made from the same ntype material, also defined in Table 3-1. All legs are assumed to have the same
dimension, which is 2 mm for both width and depth, and 4 mm for height, as
shown in Fig. 5-2. All parasitic inner resistance of the unit TEMs is ignored.
Therefore, the inner resistance, open circuit voltage, and short circuit current of
the electrically serial unit TEM are 15.6 mΩ, 3.5 mV, and 0.22 A. For the
electrically parallel unit TEM, they are 3.65 mΩ, 1.93 mV, and 0.52 A.
p
n
n
n
4 mm
2 mm
(a)
(b)
Fig. 5-2. A comparison between (a) the traditional electrically serial unit TEM, and
(b) the newly proposed electrically parallel n-type unit TEM.
For the boost step-up DC-DC converter circuit that has L=10 μH, C=1 F,
RL=10 Ω, ton=1.9 ms, and toff=0.1 ms, assuming the switches are ideal (takes zero
107
time to switch and no switching energy loss), the current flowing through the
inductor iL and the output voltage across the load resistor R L are compared
between the two types of structures, shown in Fig. 5-3, simulated using NI
Multisim.
Inductor Current (mA)
Output Voltage (mV)
toff
T
ton
20
15
10
5
0
400
300
200
100
Parallel Structure
Serial Structure
0
0.994
0.996
0.998
1.000
Time (sec)
Fig. 5-3. The comparison between the two unit modules with different structures on
the output voltage and current flowing through the inductor of the back-end step-up
DC-DC converter.
The bottom figure indicates that the current flowing through the inductor
iL is higher, corresponding to the newly proposed electrically parallel structure,
resulting in more energy stored in the inductor L in the inductor charging phase,
following equation (5.3).
1
EL  iL 2 (t ) L
2
108
(5.3)
Consequently, in the inductor discharging phase, more energy is supported to the
load resistor, causing a higher output voltage of the newly proposed electrically
parallel structure, as shown in the upper figure in Fig. 5-3. This higher voltage
also means a high output power and efficiency.
In addition, the electrically parallel unit TEM has a lower inner resistance,
causing a longer time constant

in the inductor charging phase (   L / RS ). This
longer time constant implies that the switching period corresponding to the
electrically parallel unit module can still be larger, allowing more energy to be
stored into the inductor. As a result, there will be an even higher output voltage
and a slower switching frequency. Ultimately, switching energy loss will be
further decreased, considering that the switches in reality are not ideal.
The reason why the electrically parallel TE generator shows a better
performance is because of its larger short-circuit current in the inductor charging
phase. The comparison in Fig. 5-3 is just for the unit TEMs of the traditional
structure and the newly proposed structure. When the whole TE generator module
is constructed based on the unit modules, the newly proposed electrically parallel
TE generator will have an even better performance, because of its even larger
short-circuit current and longer time constant.
5.4. Starter circuit design to toggle the switches
The output voltage of the TE module is too low to directly toggle any
transistor to realize the switching functions of SW1 and SW2, especially the
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newly proposed electrically parallel structure module. Therefore, a starter circuit
is needed if a self-starting step-up DC-DC converter is desired.
The function of SW1 can be realized by a normally-on JFET and a
transformer, shown in Fig. 5-4 [111]. The circuit can only turn on the transistor
for a short period of time. This is the reason why t off was designed to occupy only
5% of the total switching period in Fig. 5-3. Assuming there is no charge on C1
initially, current flowing through the normally on JFET T1 and the primary
winding of the transformer introduces a negative voltage at the second winding of
the transformer. C1 is negatively charged sequentially while the gate voltage of
T1 remains at a high value. As the primary winding current becomes saturated,
the voltage across the secondary winding decreases, resulting in a voltage drop at
the gate of T1. T1 starts to close its channel. The current flowing through the
secondary winding further decreases quickly, which leads to an even deeper gate
voltage drop of T1. Then, T1 is completely shut down, corresponding to toff. At
this instant in time, current flowing through the primary winding is zero. The
voltage across the secondary winding is also zero. The gate voltage of T1 goes up
to a small negative value decided by the voltage of C1, leading to a current
increase in the primary winding. The gate voltage of T1 then goes further up
through the coupling of the transformer. The JFET T1 is quickly turned on again
and remains conducting until the next current saturation happens at the primary
winding. The ton is far bigger than toff, which coincides with the design in Fig. 5-3.
110
Fig. 5-4. Starter circuit design that can realize the function of SW1 in Fig. 5-1.
The function of SW2 can also be realized using the circuit shown in Fig.
5-4. Because SW2 is off for most of the time, the transistor can be selected as a PMOSFET, which can be turned on by the peak negative voltage control signal that
also controls the gate of JFET T1.
5.5. Summary
The problems that electrically parallel TEMs have, which are extremely
small inner resistance and small output voltage, can be solved by using back-end
step-up DC-DC converter.
Through the investigation on an inductive DC-DC converter, the
electrically parallel structure TEM is proved to produce an even higher output
voltage to the electric load, when compared to the traditional electrically serial
structure, leading to higher output power and efficiency. In addition, the new
parallel structure module is capable to work under a slower switching frequency,
resulting in a decreased switching energy loss. Self-starting circuit design to
toggle the switches as expected is theoretically feasible.
111
Chapter 6.
TE ENERGY HARVESTING FROM
PAVEMENT STRUCTURE
6.1. Overview
Electrically parallel TEMs, especially the induced multilayered TEMs,
have the potential to stimulate the applications of TEMs to harvest energy from
naturally existing temperature gradients, because of the convenience and costeffectiveness to fabricate large area devices. Inspired by the advantages of the
newly proposed electrically parallel TEMs, this chapter introduces an innovative
application of TEM to harvest energy from pavement structures.
Aging infrastructures require a proactive strategy to ensure their
functionality and performance. Innovative sensors are needed to develop
intelligent and durable infrastructures. A power supply strategy is among the
crucial components to reduce cost and to ensure the long-term function of these
embedded sensors. Fortunately, a TEM-based energy harvesting system can meet
these requirements and directly collect energy from the temperature gradient
across the pavement structures in situ to power those types of sensors.
Fig. 6-1 shows an example of daily temperature variations across
pavement structures, indicating that the subgrade temperature maintains
approximately at a constant temperature beyond a certain depth (around 80 cm in
this example). This constant temperature implies that the subgrade of the
pavement structure can serve as a heat sink to dissipate the heat absorbed from the
top side of the TEM. A thermal gradient of variable magnitude exists between
112
asphalt concrete layer of the pavement and its subgrade throughout a day, serving
as a potential energy source for electricity generation using TE devices. Even
though there are occasions in which the temperature gradient may be small or
nonexistent, these occasions are a relatively short period of time that do not
dramatically impact the performance of the energy harvester.
Fig. 6-1. Example measured daily temperature variations under pavement [112]
The explorations for this study are introduced as follows. The heat
exchanger at the cold side of the TEM is first optimized, using computer-aided
finite element simulation, as introduced in Section 6.2. In-lab and outdoor
experiments are then introduced in Section 6.3 and Section 6.4, respectively. In
Section 6.5, the amount of energy harvested from pavement structures using the
TE technology is compared among many states in the U.S. by comparing the
average absolute-value temperature gradient across the asphalt concrete layer. The
output density of the TEM is estimated as well.
113
6.2. Computer-aided optimization of aluminum heat changer
As introduced in Section 1.1.4, the heat exchanger design at the cold side
of the TEM is crucial for the performance of the TE energy harvesting system. In
order to generate a large enough output power from the TEM, enough temperature
difference between the upper and lower surface of the module needs to be
maintained. The idea in this study is to thermally connect the lower surface of the
TEM to subgrade soil under the pavement via high thermal conductivity material
(for example, aluminum rod).
To improve heat conduction, this thermal
conductive material needs to be separated by thermal insulating material (such as
foam) from its surrounding pavement environment.
TEM
Heat transfer
compound
layer
Aluminum
plate
Aluminum
rod
Thermal
insulator
Fig. 6-2. Schematic of the TE energy harvesting system.
The schematic of the TE harvesting system design is demonstrated in Fig.
6-2. The system is composed of TEM, heat transfer compound layer, aluminum
plate, aluminum rod and thermal insulator.
114
Although the newly-proposed electrically parallel TEM accommodates the
energy-harvesting from pavements application better than the traditionally
electrically serial TEM, no mature electrically parallel TEM device was fabricated
to handle the large mechanical loads required for that application. Therefore, in
order to prove the concept of the energy harvesting system, commercial
electrically serial TEMs were used instead for this study.
Considering typical pavement structures, the aluminum rod was designed
to be as long as 1 m, in order to make connections to the pavement subgrade. As a
result, the only remaining significant parameter that needs to be optimized in the
energy harvesting system is the length of the thermal insulator. If the insulator
length is too long, aluminum rod and the pavement subgrade soil will not be
contacted sufficiently, weakening the heat exchange at the rod bottom and
consequently decreasing the temperature difference between the upper and lower
TE module surfaces. However, if the insulator length is too short, heat flux from
the upper pavement soil surroundings will interfere with the heat flux within the
aluminum rod, which does not benefit the energy harvesting system, either.
Computer-aided finite element simulation helps to optimize the insulator
length. Material properties and geometry parameters used in the simulation are
listed in Table 6-1. Based on the data in Table 6-1, the insulator length is swept
from 5 cm to 95 cm. The temperature difference between the upper and bottom
side of the TEM can then be calculated. Based on the TEM’s output
characteristics provided by the manufacturer, the TE module’s output power can
then be calculated with respect to the thermal insulator length, shown as Fig. 6-3,
115
zoomed in between 50 cm and 70 cm. According to the figure, the optimum
insulator length is 59 cm, which could produce power of 11.5 mW.
Table 6-1. Parameters and size definition of materials used in FEM simulations.
Material
Aluminum
Plate
Aluminum
Rod
TE module
Thermal
Insulator
Glue
Asphalt
Concrete
Granular
Base
Sub Base
Sub Grade
Density
kg/m3
Width
(x axis)
cm
Length
(y
axis)
cm
Depth
(z
axis)
cm
160
2700
4
4
0.5
900
160
2700
Radius: 0.5
100
2000
0.4
3125
4
0.48
3000
0.04
1000
2000
60
1500
4
4
0.1
1200
1.6
2400
104
104
17.78
1400
1
2080
104
104
30.48
1600
1800
0.8
0.6
1850
1800
104
104
104
104
30
71.74
Heat
Capacity
J/(kg*K)
Thermal
Conductivity
W/(m*K)
900
4
Thickness: 1
11.540
11.535
Output Power (mW)
11.530
11.525
11.520
11.515
11.510
11.505
11.500
50
55
60
65
70
Insulator Length (cm)
Fig. 6-3. TE module’s output power VS thermal insulator length [113].
116
59
An example of thermal field distribution is shown in Fig. 6-4. In this
simulation, the ground temperature was assumed to be 323.15 K.
The
temperature at the deep ground was assumed to be 288.15 K. Fig. 6-4 indicates
that temperature in the upper aluminum rod is lower than the surroundings,
whereas in the lower rod, the situation is reversed. This implies that heat flux
gathers together from the surroundings of the aluminum plate, and then goes
downwards via the high conductivity rod, and eventually dissipates into
surroundings of the bottom aluminum rod.
Fig. 6-4. Temperature distribution across the pavement structure.
6.3. In-lab experiment
The TE energy harvesting system was first tested in the lab, in order to
have a stable environment control. The TEM was designed to sit on top of an
117
asphalt concrete sample and to collect heat energy from the sample’s top
boundary, covered by a piece of black tape.
6.3.1. Experiment setup
Fig. 6-5. Experiment set up in the lab.
The experiment setup was as follows. First, a hole was drilled in the
middle of the asphalt concrete sample, with a diameter of 15 cm and thickness of
10 cm. Aluminum plate and rod, which was covered by a thermal insulator, was
placed through the hole (Fig. 6-5(a)). Sequentially, thermally conductive epoxies
were spread over the upper surface of aluminum plate. Meanwhile, a thin
thermocouple was also placed on top of the surface (Fig. 6-5(b)). Then, a TEM
was installed on the surface of aluminum plate, with the thermally conductive
118
epoxies as the interface (Fig. 6-5(c)). The whole set of equipment was surrounded
by sand, imitating the pavement subground environment. All equipment utilized
in this setup was of the same size as the previous optimization simulation.
In order to systematically analyze the performance of the system, a
comparatively stable heat source is preferred. Therefore, a filament lamp was
utilized to heat the upper surface of the TE module, whose output voltage powers
an energy management circuit, as discussed in Section 6.3.2.
Fig. 6-6. The picture of the entire experiment setup.
The picture of the entire experiment setup is shown in Fig. 6-6. Three
temperature signals (temperatures at TEM upper surface, interface between TEM
and aluminum plate, and aluminum rod bottom) were monitored using software
119
Picolog Recorder and data acquisition device (DAQ) Pico TC-08. LabVIEW
software and data acquisition board NI USB 6251 were also involved in this
system to collect voltage data at the TE module output electrode, capacitor, and
light-emitting diode (LED). The experiment duration was about 150 minutes.
6.3.2. Power management circuit
The aim of a power management circuit is to accumulate the converted
energy into energy storage components, such as super capacitors, which have
extremely long lifespans and can be charged and discharged thousands of times. It
has been reported that a 10 F super capacitor stores enough energy to support mW
consumption applications [114].
The output voltage generated by the TE is too low to directly power any
electrical component, which usually requires a 0.7 V start-up voltage to work.
Consequently, an ultra-low start-up voltage charge pump IC (S-882Z Series,
Seiko) was used to amplify the output voltage, from 300 mV to a voltage higher
than the start-up threshold. The pins of chips are connected as follows:
CS
VIN
VOUT
Charge Pump IC
VSS1
Fig. 6-7. Diagram of the back-end energy management circuit.
120
During the charging cycle, the voltage of the super capacitor keeps
increasing until it reaches the threshold of discharge voltage, from which the
discharge cycle begins. Charges flow from the charged super capacitor to power
the load. The capacitor in this study is 2200 μF. A light-emitting diode (LED)
was used as a load.
6.3.3. Temperature distribution
As shown in Fig. 6-8, the temperature of the TE module upper surface
(blue line in the figure) quickly increased as soon as the heat source (lamp) was
turned on, approaching 70 0C from room temperature. The interface temperature
between the TE module and the aluminum heat collection plate (red line in the
figure) also increased and became stable at 50 °C. A 20 °C temperature difference
was maintained between both sides of the TE module. The temperature at the
bottom of the aluminum heat collection rod did not change significantly,
indicating that heat flux coming from the aluminum plate mostly dissipated into
sand surroundings before it arrived at the bottom of the heat collection aluminum
rod.
The temperature difference between the TEM top surface and the TEM
bottom surface (20 °C) only occupies 40% of the temperature difference between
the TEM top surface and the aluminum rod bottom (50 °C). This implies that
there is still much room to improve the heat exchanger design to further cool
down the temperature at the TEM bottom surface.
121
70
Temperature (C)
60
50
TEM upper surface temperature
40
Interface temperature between TEM
and aluminum plate
30
Aluminum rod bottom temperature
20
-20
0
20
40
60
80
100
120
140
160
Time (min)
Fig. 6-8. Monitored temperature process at different locations in the TE energy
harvesting system.
6.3.4. Electric output of the TE energy harvesting system
Fig. 6-9(a) shows the voltage profiles at the output electrode of the TEM
electrodes, the super capacitor, and the LED. Fig. 6-9(b) zooms in between 120
min to 125 min to show more details of the process. The following work sequence
can be identified from the figures: When the temperature gradient was high
enough for the TE module to generate 300 mV output voltage (the start-up
voltage for the charge pump), the charge pump IC (Seiko, S-882Z) woke up and
produced sufficient voltage to charge the capacitor. This caused the voltage at the
capacitor to increase. Once the voltage in the capacitor reached 2.45 V, the
charge pump IC automatically connected to the output and discharged the
capacitor. Electrical energy stored in the capacitor flew into output pin. A 1.7 V
DC voltage was generated to light up the LED. When the voltage in the capacitor
dropped down to 1.9 V, the charge pump IC disconnected from the output pin.
122
The charge pump IC then turned into an ultra-low power sleeping mode.
Meanwhile, the capacitor was charged again until the next working cycle started.
Voltage (V)
2.5
2.0
Capacitor
Voltage
1.5
LED
Voltage
1.0
TE Module
Output
Voltage
0.5
0.0
-20
0
20
40
60
80
100
120
140
160
Time (min)
(a)
2.4
2.2
Capacitor
Voltage
2.0
Voltage (V)
1.8
LED
Voltage
1.6
1.4
TE Module
Output
Voltage
1.2
1.0
0.8
0.6
0.4
120
121
122
123
124
125
Time (min)
(b)
Fig. 6-9. (a) Voltage profiles at the TE element output electrode, capacitor and LED,
(b) Zoom in between 120 to 125 min.
123
Energy contained in the capacitor is calculated through the following
equation:
1
Ecap   C V 2
2
(6.1)
Each time when the capacitor discharged, its voltage dropped from 2.45 V to 1.9
V. Considering the capacitor’s capacitance used in this circuit is 2200 μF, energy
dissipated from the capacitor is 3.73 mJ per cycle. Assuming the energy
discharging efficiency is 2  50% , which means 50% of energy stored by
capacitor could be transmitted to light the LED, the energy that is used to power
the load is 1.86 mJ in each cycle.
According to the manual of the commercial TEM used in this study, the
output power under 20 0C temperature gradient is about 50 W . Considering that
it takes 1.5 min (i.e. 90 sec) to charge the capacitor, the output energy of TEM per
cycle is 4.5 mJ, resulting in a charging efficiency 1  3.73 / 4.5  82.9% ).
Multiplying the charging efficiency with the discharging efficiency, the TEG
energy harvesting system introduced in this section has the energy efficiency of
about 41.5%.
As the capacitor involved here is only 2200 μF, energy stored in the
capacitor can only power the LED for less than 1 s. A 0.47 F super capacitor was
also tested, where the charge period was up to several hours and the LED could
keep shining for several seconds. Therefore, there exists a tradeoff when choosing
the proper capacitor. If the capacitor has a larger capacitance, the system could be
124
applied to power load that works less frequently but longer. If the capacitance is
smaller, the capacitor charges faster, but with less energy.
6.4. Outdoor experiment
The TE energy harvesting system was also tested outdoors to evaluate the
energy harvested in the field. The back-end energy management circuit is not
involved in this case, in order to reduce the data acquisition failure risk resulting
from the versatile outdoor environments.
In this study, a 1 m-deep hole was drilled into the ground. Then, the whole
TE energy harvesting system was inserted into the hole, as shown in Fig. 6-10.
The hole was then refilled with dry sand to ensure thermal contact between the
bottom part of the aluminum rod and the surrounding soil environment. Moderate
water was introduced into the hole to guarantee high-enough thermal conductivity
of the sand at the bottom of the aluminum rod.
Fig. 6-10. The installation process of the TE energy harvesting system outdoors.
125
6.4.1. TEM is placed on top of the asphalt concrete sample
First, the TE energy harvesting system setup was designed identically to
the case in the lab, where the TEM was placed on top of the same asphalt concrete
sample and collected heat energy from the sample’s upper boundary.
Temperatures of more locations were collected, as shown in Fig. 6-11.
CH 1
CH 7
CH 2
CH 3
20 cm
CH 4
CH 5
100 cm
TE Module
Aluminum
Silicone
Asphalt
Concrete
Foam
CH 6
Fig. 6-11. Locations where temperatures were monitored.
Initially, closed-circuit condition was attempted, where the TEM powered
a 10 Ω load resistor. However, the dew in the outdoor environment impacted the
circuit and data collection. Therefore, open-circuit output voltage of the TEM
was collected instead. All the temperature data and voltage data were collected
using a data acquisition device (DAQ) CR1000 (CAMPBELL Scientific Inc.),
which was powered by a 12 V, 5 Ah lead-acid battery (UB1250). All of the
equipment was covered in a large-enough plastic box, leaving a hole to connect
all the sensor wires through.
126
The data throughout two consecutive sunny summer days (Sep. 16-17,
2015) was recorded. The temperature data is shown in Fig. 6-12. The black curve
is the reference temperature on the DAQ board. During the daytime, the
maximum temperature difference between top (Ch #1) and bottom surfaces (Ch
#2) of the TEM was about 3 °C. The temperatures at the top (Ch #2) and bottom
surfaces (Ch #3) of the aluminum plate were approximately the same, indicating a
good thermal conductivity of the aluminum plate. The inside (Ch #4) of the
thermal insulator had a significantly higher temperature than the outside (Ch #5).
This means that the aluminum rod conducts extensive heat energy downwards to
the bottom of the system. The bottom temperature of the aluminum rod (Ch #6)
remained stable throughout the whole testing period, implying that the aluminum
rod’s length was moderate and that the subgrade of the soil environment served as
a good heat sink. During the nighttime, the temperature difference across the
TEM was nearly zero, leading to a negligible output power.
The open-circuit output voltage with respect to the corresponding
temperature difference between two ends of the TEM is plotted in Fig. 6-13.
Output power is plotted in Fig. 6-14, given the inner resistance of the TEM is
about 10 Ω and assuming the system was working under the maximum power
delivering point where the load resistance matches with the inner resistance of the
TEM. The total output energy during the first day was then calculated as about 8 J
through the integration of Fig. 6-14. This indicates that the average maximum
output power of the system is 92.6 μW. The peak output power is on the order of
mW, shown in Fig. 6-14.
127
Ref.
Ch #1
Ch #2
Ch #3
Ch #4
Ch #5
Ch #6
Ch #7
45
Temperature (C)
40
35
30
25
20
15
10
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Time (day)
Fig. 6-12. Temperature data of two consecutive summer days.
6
mV
T
100
50
5
4
0
3
-50
2
-100
1
-150
0
-200
Temperature Difference (C)
Open Circuit Output Voltage (mV)
150
-1
-250
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Time (day)
Fig. 6-13. Output voltage of the TEM with 10 Ω load resistor. The corresponding
temperature difference between two boundaries of the TEM is also plotted.
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1.4
Output Power
Output Power (mW)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Time (day)
Fig. 6-14. Calculated output power data with time.
6.4.2. TEM is placed beneath the asphalt concrete sample
The asphalt concrete layer of the pavement structure is actually a
promising heat collector, because of its dark color and decent thermal
conductivity (on the order of 1 W/K/m) [115]. The implementation of TEM
beneath the asphalt concrete layer can utilize this natural heat collector, which
might improve the output power of the TE energy harvesting system. In addition,
placing the TEM beneath the asphalt concrete layer hides the TEM, resulting in a
more aesthetically appealing appearance, and a longer service life without
deterioration from the ambient environment. This setup also helps in specific
areas where the powering system needs to be confidential.
In order to take advantage of the heat collected by the asphalt concrete
samples to the largest extent, the bottom surfaces of the asphalt concrete samples
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(diameter of 10 cm, thickness of 6.5 cm) were first painted with silicone heat
transfer compound (MG Chemicals, 860-150G) and then covered by aluminum
foil, as shown in Fig. 6-15.
Fig. 6-15. The bottom heat treatment of the asphalt concrete samples.
Then, the TEMs were placed beneath the asphalt concrete samples and on
top of heat exchangers with silicone heat transfer compound as interface layer to
enhance the heat conduction. As implied by the in-lab and outdoor experimental
observations in Section 6.3.3 and 6.4.1, the heat exchanger design of using
aluminum rods does not seem as efficient as expected. Therefore, in this section,
another type of heat exchanger was explored: a heat sink shown in Fig. 6-16,
buried into the shallow surface of the ground.
The temperature sensor locations are shown in Fig. 6-17 for both TE
energy harvesting systems, based on two types of heat exchangers at the cold side
130
of the TEMs. Open circuit voltages of the two systems were also collected. All
data was recorded using the same DAQ setup as introduced in Section 6.4.1.
Fig. 6-16. Heat sink as a heat exchanger used in control group.
CH #3
CH #1
CH #4
CH #2
CH #5
59 cm
100 cm
CH #6
Fig. 6-17. Temperature monitoring locations.
131
Temperature data of all channels and open-circuit output voltage data were
recorded for about 20 consecutive summer days (from Sep. 23, 2015 to Oct. 13,
2015). The temperature data throughout the full time span is plotted in Fig. 6-18.
Fig. 6-19 zooms in to show the temperature data for the second and third day. In
addition to the collected temperature data, corresponding weather temperature
data in the same period of time in Cleveland, Ohio is also plotted in the two
figures as a reference (downloaded from www.wunderground.com). The opencircuit output voltage data with respect to the two types of heat exchangers is
plotted in Fig. 6-20. Under the assumption that the TEM was working under the
maximum power delivering point where the load resistance and the inner
resistance of the TEM were both equal to 10 Ω, the output power was calculated
and plotted in Fig. 6-21.
Ref
Ch #3
Ch #6
Temperature (C)
50
Ch #1
Ch #4
Ch #2
Ch #5
Weather
40
30
20
10
0
2
4
6
8
10
12
Time (day)
Fig. 6-18. Temperature data of the full time range.
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14
16
18
20
Ref
Ch #3
Ch #6
Temperature (C)
50
Ch #1
Ch #4
Ch #2
Ch #5
Weather
40
30
20
10
2
4
Time (day)
Fig. 6-19. Temperature data zoomed in to the second and third day.
120
With Al System
With Heat Sink
Output Voltage (mV)
100
80
60
40
20
0
-20
-40
0
2
4
6
8
10
12
14
16
18
20
Time (day)
Fig. 6-20. Output voltage comparison between using Al heat exchanger and heat
sink.
133
0.35
With Al System
With Heat Sink
Output power (mW)
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
0
5
10
15
20
Time (day)
Fig. 6-21. Output power comparison between using Al heat exchanger and heat sink.
Fig. 6-18 and 6-19 match well with the trend of weather temperature data,
which implies the collected experiment data is valid. The two figures indicate that
the temperature difference (Ch #4 and #5) across the TEM with aluminum heat
exchanger is smaller than the temperature difference across the TEM with the heat
sink as heat exchanger (Ch #1 and #2), resulting in a smaller output voltage and
power, as shown in Fig. 6-20 and 6-21. It seems that the aluminum heat
exchanging system is not as efficient as the simple heat sink buried into the
shallow surface of the ground.
However, this might not be the case when the two systems are
implemented in real pavement structures. The experiment site in this study was on
grass ground, where the surface temperature of the ground was relatively lower
than the temperature in the field. Heat absorbed from the top boundary of the
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TEM could then easily dissipate into the surface layer of the grass ground.
However, for the real pavement structure, the surface layer might have a high
temperature during the summer daytime, where the aluminum heat exchanger
system might still be more efficient.
For the TE energy harvesting system using the aluminum heat exchanger,
the average output energy in a day is 0.86 J, with respect to testing time span of
about 20 days. The average output power is about 10 μW. Peak output power is
less than 1 mW. If the second day is taken as a sole example, when the weather is
sunny and similar to the weather in Section 6.4.1, the total output energy on that
day is 2.4 J. Average output power is 27 μW. Peak output power is about 0.2
mW. Compared to the data in Section 6.4.1, where the TEMs were placed on top
of the asphalt concrete sample, the output power when the TEMs were placed
beneath the asphalt concrete sample was relatively smaller. This does not
necessarily mean that the asphalt concrete layer of the pavement structure is not a
good heat collector. The asphalt concrete samples used in the experiment in this
study have small diameters, resulting in limited heat energy collected from them.
This might be the reason why the advantages of the placing the TEM beneath the
asphalt concrete samples did not show up in the results. More experiments are still
needed to be carried out in the field, to test the effectiveness of various heat
exchangers.
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6.5. Nationwide evaluation of TEM output energy harvested from pavements
The experiments introduced in previous sections were all carried out on
campus of Case Western Reserve University in Cleveland, Ohio. This section
introduces the comparison of average thermal energy across pavement structures
available for TE energy harvesting among different states in the U.S. The strategy
is to first find the temperature gradient across the asphalt concrete layer of the
pavement structures in each state. Then, the power density generated by TE
energy harvesting system can be evaluated, given the efficiency of the TEMs.
6.5.1. Temperature gradient across asphalt concrete layer of pavements
In order to calculate temperature gradient across the asphalt concrete layer
of pavement structures in each state, temperature data at several given depths
inside the asphalt concrete layer is required. This study utilizes the comprehensive
database collected by the Long Term Pavement Performance (LTPP) program,
composed of long-term historical data in most states, including data on pavement
structures, climate, traffic and pavement performance.
The temperature data within the asphalt concrete layer of pavements was
extracted from table SMP_MRCTEMP_AUTO_HOUR collected by the Seasonal
Monitoring Program (SMP) of the LTPP. It includes hourly temperature data
collected at two individual depths, as shown in Fig. 6-22. The top sensor was
located 25 mm beneath the top surface of the asphalt concrete layer, while the
bottom sensor was placed 25 mm over the bottom boundary of the asphalt
concrete layer.
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Temperature sensors
25 mm
Thickness of
asphalt
concrete layer
25 mm
Fig. 6-22. Temperature sensor locations inside the asphalt concrete layer of the
pavement structure.
First, the thickness of the asphalt concrete layer was extracted from table
TST_AC01_LAYER from the General Information online database, where core
samples of the pavement structures were measured. When many samples close to
each other were measured corresponding to the same testing site, the thickness
data was averaged.
Secondly, the hourly temperature gradient inside the asphalt concrete layer
with respect to each testing site was calculated by dividing the temperature
difference between the upper and lower temperatures, with the thickness of the
asphalt concrete layer subtracted by 50 mm. The temperature gradient value is
positive when the upper temperature is higher than the lower temperature. When
the temperature conditions are reversed, the temperature gradient is negative.
Therefore, the absolute values of the hourly temperature gradient with respect to a
testing location were averaged within a pre-defined evaluation period (a year, or a
month). When there were many testing sites in one state, the calculation results
corresponding to each testing locations were also averaged to represent the state.
When there were many years of data falling in the pre-defined evaluation period,
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the calculation results were also averaged. This is the final data used to be
compared among different states. All the calculations introduced above were
realized using MATLAB. The source scripts are attached in Appendix B.
There are a total of 32 testing locations, but the raw data was taken from
just 26 states, since certain states had multiple testing locations. The testing
locations are highlighted in Fig. 6-23. Some location markers close to each other
are overlapped, such as those in Alabama. Detailed information can also be found
in Table C-1, including the exact latitude and longitude values of each testing
location.
Fig. 6-23. Testing locations of the data involved in the calculations in this study.
The raw data from the online database recorded the thickness changes
resulting from construction projects, such as those deploying new overlay asphalt
concrete layers on top of old layers. In the online database, whenever there was
construction, the thicknesses of new samples were updated, while the temperature
sensors were adjusted to maintain the setup as shown in Fig. 6-22.
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The adjustment of the temperature sensor locations inevitably interrupts
the temperature data collection, leading to data discontinuity. A parameter (Data
Completeness) is defined as the ratio between the accumulated time length when
there is effective data, and the total time length of a certain evaluation period. If
the data completeness is less than 80%, the calculation is considered not
convincing enough.
The calculation results of averaged absolute values of temperature
gradients corresponding to each state within one year are shown in Fig. 6-24,
which roughly indicates that the Southern part and Northeast coast of the U.S.
have relatively small average temperature gradients. For the Southern states, such
as Texas, the ambient temperature is continuously high, leading to little
temperature change at the surface of the pavement. For the Northeast coast states,
the temperature changes mildly, because of their oceanic climate., leading to
small temperature gradients in those areas.
Fig. 6-24 also indicates that the average temperature gradient across the
pavement structure throughout a year is higher in the Western mountain areas,
such as Montana and Colorado, where the air temperature changes violently as
sunshine changes, due to high altitudes. The TE energy harvesting technology fits
best in those high altitude areas.
The averaged absolute values of temperature gradients during winter
(January) and summer (July) are also plotted in Fig. 6-25 and 6-26. For both
months, the comparison among different states roughly maintains the same trend
throughout a year. The magnitude of the averaged absolute values of temperature
139
gradients, when compared between the winter and the summer, indicates that the
summer causes higher temperature gradients compared to the winter. This means
that the TE energy harvesting technology is more effective in summer.
Fig. 6-24. The average temperature gradient across the pavement structure in a
year. The unit of the numbers in the figure is K/m.
Fig. 6-25. The average temperature gradient across the pavement structure in
January. The unit of the numbers in the figure is K/m.
140
Fig. 6-26. The average temperature gradient across the pavement structure in July.
The unit of the numbers in the figure is K/m.
Fig. 6-24, 6-25 and 6-26 only show the cases where the data completeness
is higher than 80%. Other calculation results are shown in Table. C-2, C-3 and C4, for an entire year, January only, and July only, respectively, including standard
deviations when calculating the averaged values of the absolute temperature
gradients and the number of years involved in the calculation.
6.5.2. Output power of TEM harvesting from pavements
The averaged absolute values of temperature gradients of multiple states
throughout a year were calculated and compared in the previous section.
Therefore, the output power densities of the energy harvesting systems can be
evaluated, given the efficiency of the TEMs.
Assuming that the TE materials used in the TEMs have figure-of-merit of
about 1 at room temperature, the module’s figure-of-merit can be as high as 1, if
the newly proposed electrically parallel structure is used. Then, the maximum
module efficiency can be evaluated using equation (3.1), assuming TH=11 °C and
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TC=10 °C, which are around the annual average climate temperature in Cleveland,
Ohio, according to the LTPP database. Calculations show that the maximum
power efficiency ηmax is around 1%.
If the thermal conductivity of the asphalt concrete layer is assumed to be 1
W/(m∙K) [115], assuming the implementation of the TEM does not affect the
temperature gradient across the pavement structures, the heat flux flowing
through the TEM at Ohio is about 77.4 K/m×1W/(m∙K) = 77.4 W/m2. Therefore,
the output power density of the TEM used to harvest energy from the pavement
structure is 77.4 W/m2×1%=0.77 W/m2.
When considering a 1 km-long section of highway with a width of 20 m (6
lanes, each lane is 3.7 m wide), the area is about 20,000 m2, leading to a
significant output power of 15,400 W. If a cost-recovery length is designed to be
10 years, considering the price of electricity to be 10 cents per kW∙h, the electric
energy produced by the TEM has a profit of about $135,000, meaning $6.75/m2.
In other words, if the cost to deploy the TEM can be decreased to $1/m 2,
including the TEM fabrication cost, the energy production through this type of
application can compete with other energy resources. Obviously, there is still a
long way for researchers to catch up with this requirement.
6.6. Summary
The proposal of electrically parallel TEMs can potentially stimulate the
applications of TE technology, because the implementation process can be
extremely simplified if the multilayered electrically parallel TEMs are deployed.
142
The electrically parallel structure would significantly benefit the fabrication of
large-area TEMs. In this chapter, an innovative application of TEM to harvest
energy from pavement structures was introduced.
In-lab experiments showed that the energy harvesting system can
periodically power electric load, proving the feasibility of the concept. Outdoor
experiments showed that peak output power of the TEM was on the order of mW,
which is capable to power some low-energy consumption sensors. These
observations present a promising strategy to power sensors used in long-term
monitoring systems of civil infrastructures. Another observation is that the output
power when the TEM was placed on top of the asphalt concrete sample was more
than when the TEM was placed beneath the asphalt concrete sample. In addition,
two types of heat exchangers were explored: the aluminum rod inserted deeply
into the ground, and the heat sink buried into a shallow layer of the ground. The
former heat exchanger was noticed to be less effective. However, the heat
exchangers still need to be further verified through outdoor experiments in real
pavement environments.
The energy that the TE energy harvesting systems could generate from
pavement structures was compared among many states, by calculating the
averaged absolute values of temperature gradients with respect to each state,
based on LTPP data. The data indicates that the Southern and Northeast coast
states have smaller TE energy resources across the pavement than the Western
mountainous regions. Also, the energy available in the summer is higher than in
the winter. In addition, the power density generated by the TE energy harvesting
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system is estimated to be 0.77 W/m2 in Ohio. When the total cost of deploying
one square meter TEM is decreased to 1 dollar, the energy harvesting system can
compete with other types of energy resources.
144
Chapter 7.
CONCLUSIONS AND SUGGESTIONS FOR
FUTURE RESEARCH
7.1. Conclusions of this study
The development of TE technology has been limited by the conflict
between energy conversion efficiency and cost. The most important conclusion of
this study is that the electrically parallel TE module can not only increase the
module efficiency within a certain device area limit when applied under roomtemperature region, but also decrease the fabrication cost, because of its
simplified device structure. This claim has been verified from experiments
(Chapter 2), analytical analysis (Chapter 3) and finite element numerical
analysis (Chapter 4).
The electrically parallel structure is also predicted to increase the device
life span. Using only one material to form all the TE legs, there is no mismatch
between the thermal expansion rates among TE legs. In addition, for serial
structure, even a single break of the connection inside any part of the module can
lead to the failure of function. However, for electrically parallel structure, a small
break of the junction will not affect the performance significantly. Currents can
still flow through other alternative paths, because they are all in parallel.
Electrically parallel structure TEMs have small inner resistance and
output voltage, even though the output power is higher. Back-end inductive stepup DC-DC converter design can solve this problem, by boosting the small output
voltage to a high-enough level to meet electric load requirements (Chapter 5).
145
When the same inductive DC-DC converter is used, the electrically parallel TEM
can generate a higher output power compared to the conventional electrically
serial TEM, because of a higher short-circuit current. In addition, the time
constant with respect to the electrically parallel structure is longer, indicating a
capability to work under a slower switching frequency, resulting in a decreased
switching energy loss.
The newly proposed electrically parallel structure can still maintain a
cross-plane direction temperature gradient. Meanwhile, the gaps among TE legs
can be completely removed, leading to a multilayered module structure. On the
one hand, the multilayered structure can increase the power density and
mechanical durability. On the other hand, the fabrication or implementation of
such structure is extremely simplified. The device area can be enlarged
conveniently. Many innovative applications of TE technology can be stimulated.
This study proves a concept of using TEM to harvest energy from pavement
structures (Chapter 6). Experiments showed that the strategy is promising in
periodically powering low-energy consumption sensors, in order to monitor civil
infrastructures’ health, such as pavements.
7.2. Suggestions for future research
This study attempts to advance the development of TE technology from an
electrical engineering angle. Despite the innovative efforts and progresses that
have been made, there is still much room in which researchers can push forward
the research on electrically parallel structure TEMs.
146
Firstly, fabrication processes of the TEMs and experiment setups to
characterize material properties and module behaviors are recommended to be
improved, in order to evaluate the performances of the electrically parallel TEMs
more comprehensively.
It has to be pointed out that the fabrication process of the TEMs in this
study was only for comparison purposes between the electrically parallel structure
and electrically serial structure. For future research, better fabrication processes
can be explored, in order to improve the devices’ energy efficiency as much as
possible. For example, TE powders can be prepared using the high-energy ball
milling process to go into nanometer scale. TE legs can be fabricated using hot
pressing technology, or spark plasma sintering (SPS) process, in order to further
decrease the inner electrical resistance. The connections between the TE legs and
metal connecters can be designed to guarantee ohmic contacts by introducing a
metallization layer in between.
Experiment comparisons between the proposed electrically parallel
structure and the traditional electrically serial structure in this present study were
still preliminary, only based on unit TEMs. For future research, entire TEMs
(each is composed of many unit TEMs) with different device areas can be
fabricated. In that case, the comparison on energy conversion efficiency with
respect to a certain device area can be more comprehensive. The module inner
resistance is expected to be much smaller, which might cause difficulties in
designing electric output characterization systems.
147
Meanwhile, the experiment setups of TEM output performance
characterization and TE material property characterization in this study is only
under room temperature and air environment. For future research, the author
recommends to develop more advanced experiment setups to cover a larger
temperature range and maintain a vacuum environment. In addition to electric
output characteristics, other performances can also be compared between the
electrically parallel structure and electrically serial structure, such as the
mechanical properties, durability and reliability.
Secondly, deeper understanding of TE behaviors is still needed through
analytical and numerical modeling. The analysis in this present study was under
the assumption that all material properties (Seebeck coefficient, thermal
conductivity and electrical conductivity) are given. For future research, modeling
of material properties is suggested to be carried out, which could help to
understand the carrier driving mechanisms inside TE materials from firstprinciple perspective. As there are already many efforts on modeling the thermal
conductivity and electrical conductivity, the focus for future research can be on
the modeling of Seebeck coefficient.
Researchers have been dedicated to theoretically model the Seebeck effect
in TE materials since the 1950s [116]. Johnson and Lark-Horovitz [117] evaluated
the Seebeck coefficient of semiconductors through obtaining the Thomson
coefficient, first by following Sommerfeld’s [118] model of thermal and electrical
currents, and then integrating the appropriate Thomson relation. This work was
founded based on thermal equilibrium assumptions, leading to good agreement
148
with experiments within transition and intrinsic ionization temperature ranges
(above room temperature), while there was significant deviation at the impurity
temperature range (i.e. strong ionization temperature range between 78 and 300
K). Frederikse [119] attributed this disagreement at the relatively low temperature
region to the simplified lattice thermal equilibrium assumption. He modified
Johnson--Lark-Horovitz’s calculation by including an additional term inversely
proportional to temperature, to account for the phonon-drag effect (phonons
carrying a thermal current tend to drag electrons from the hot side to the cold
side) at the low temperature region. Price [120] modified Johnson--LarkHorovitz’s modeling by using Onsager’s reciprocal relations [121, 122], resulting
in a Seebeck coefficient expression in terms of electron and hole electrical
conductivities. Loffe [104] described the Seebeck coefficient as the flow of
entropy per unit charge across a junction based on thermodynamic considerations,
and obtained a Seebeck coefficient expression composed of average electron
energy. The most popular method nowadays to predict the Seebeck coefficient is
based on the Boltzmann Transport Equation (BTE), which was first used by Rode
[123], who conducted the calculation for degenerate direct band gap
semiconductor materials. With BTE, good agreements with experiments had been
achieved for various electron concentration levels at room temperature. However,
the theoretical predictions were slightly deviated from experimental results for
higher temperature regions. Another widely used method at for quantum
thermoelectric devices is based on the Non-Equilibrium Green’s Function
(NEGF) [124, 125].
149
Based on all these existing theories, the material properties of TE
materials can be modeled. Combined with the multi-physics model built in this
study, the behaviors of TEM can be evaluated from first-principle perspective. In
order to do that, more characterizations of the TE material properties are
recommended to be carried out, including chemical components, compound
phases, carrier densities, band structures, etc. Then, more precise analytical and
numerical analysis can help to reveal the carrier driving mechanisms.
Finally, more innovative applications of TEMs are suggested to be
investigated, especially for the newly proposed multilayered electrically parallel
TEMs. For example, large-area, wearable and flexible energy harvesting clothes
can be explored using the multilayered TEMs, in order to power wireless sensor
networks that can monitor and process health signals. The electrode materials can
be conductive polymers, such as highly doped polyacetylene. The TE material can
be polymer-based materials, such as poly(3,4-ethylenedioxythiophene) complexed
with polystyrene sulphonic acid (PEDOT:PSS) [126] or tosylate (PEDOT:Tos)
[127]. Once the viscosity of the materials is adjusted appropriately, they can be
sprayed onto large-area flexible substrates, such as normal cotton cloth. The
resulting multilayered TE module can be tailored using laser-cutting machines to
form convenient shapes. Even if the TE module is cracked slightly in the middle,
the output power will not be impacted significantly. Meanwhile, back-end step-up
DC-DC converter circuits are also needed to be designed and implemented, using
wearable and flexible circuit fabrication techniques. The whole system that
150
combines the multilayered TEM and the back-end DC-DC converter needs to be
comprehensively evaluated, to guarantee moderate compatibility.
In order to provide a good instruction for manufacturing flexible
multilayered TEMs, the author explored the stencil printing fabrication process on
flexible substrates, using self-made TE inks and commercial gold inks.
Descriptions of experimental observations are briefly introduced in Section 7.3.
7.3. Stencil printing process to fabricate flexible TEMs
As the development of wearable electronics progresses, the powering issue
has become one the most desperate problems that is waiting to be solved. TE
technology can be a competitive solution because there is a natural temperature
gradient between the human body and the environment, leading to an interesting
topic on the fabrication of TE device on flexible substrates. This section
investigates the stencil printing process to fabricate TE devices.
7.3.1. TE ink preparation
The aforementioned ground p-type and n-type TE powder in Section 2.2
were used as filler particles into an epoxy matrix system to form TE inks. A
vertex mixer was used to make sure they were combined evenly. The TE powderto-epoxy system ratio was 4.5:1, which meets the viscosity requirement of the
later printing process. The epoxy matrix system includes epoxy resin (EPON
Resin 863), hardener (MHHPA) and reaction catalyst (AC-8) with mass ratio of
100:85:1 [73, 75].
151
7.3.2. Screen and stencil design
Mesh screens and stainless steel stencils were designed for printing
electrode and TE inks, respectively. Metal electrodes were printed using
commercial gold ink (Ercon E4464). Screens were designed for both electrically
serial and electrically parallel device structure, as shown in Fig. 7-1. Stencils
were designed for left legs and right legs, as shown in Fig. 7-2. Therefore, there
are two screens and two stencils. TE devices with several aspect ratios were
integrated into one print.
7.3.3. Printing process
The overview of the printing sequences is shown as shown in Fig. 7-3.
After the metal electrodes were printed, they were cured under a temperature of
110 °C for 10 minutes. The TE inks were cured under temperature of 110 °C for
24 hours. The generated device is shown in Fig. 7-4 and Fig. 7-5.
(a)
(b)
Fig. 7-1. Electrode screen designs for (a) electrically serial and (b) parallel TEM
structure.
152
(a)
(b)
Fig. 7-2. Stencil designs for (a) left TE legs and (b) right TE legs.
Screen #1
Screen #2
Stencil #1
Stencil #2
Traditional
electrically serial
TE module
Electrically parallel
TE module (p-type)
Electrically parallel
TE module (n-type)
Fig. 7-3. Printing process for both electrically serial and parallel structure TEM.
153
Fig. 7-4. Printed electrically serial TEM on flexible polyimide substrate.
Fig. 7-5. The rolled-up printed TEM on flexible polyimide substrate.
154
7.3.4. TEM electric output characterization
The output characteristics of the printed TE devices with the electrically
parallel structure were recorded using the same experiment setup as described in
Section 2.6. The results are listed out as follows.
(a)
(b)
Fig. 7-6. Output characteristics of printed TE devices with electrically parallel
structure (n-type).
(a)
(b)
Fig. 7-7. Output characteristics of printed TE devices with electrically parallel
structure (p-type).
The characterization of electrically serial structured TE device is not as
straightforward as the electrically parallel structure, because the inner resistance is
too high. The digital multimeter cannot even measure it directly. Under the
155
assumption that the TEM’s I-V curve is a straight line, then the output
characteristics can be evaluated from the open-circuit voltage and short circuit
current. The latter can be measured using the same experiment setup as Section
2.6. The former can be measured using a voltage follower circuit to increase the
device’s output impedance. These measurements belong to a part of the future
work.
The observations imply that the newly proposed electrically parallel
structure TEM fits in the applications where flexibility is highly required. Because
most flexible TEMs are made from organic TE materials or TE inks, where the
electrical resistivity is extremely high, compared to bulk TE materials. The
electrically parallel structure can reduce the inner resistance of the overall module
that expand the applications of TEMs significantly.
7.3.5. Material property characterization
The characterization on the material properties of the cured TE inks is also
challenging, because it is not easy to prepare homogenous and uniform bulk
samples to be tested using aforementioned methods. Silicone molds were made
using a pre-machined aluminum mold, shown in Fig. 7-8 and Fig. 7-9.
The exploration on how to generate uniform samples without any voids
also belongs to part of the future research. Once uniform samples are collected,
material properties can be measured using the same setup as introduced above.
156
Fig. 7-8. Aluminum reverse mold to make silicone mold.
Fig. 7-9. Silicone mold used to cast TE inks and cured in oven to form test samples.
157
Appendix A. THERMAL FLASH METHOD TO MEASURE
THERAML DIFFUSIVITY
A.1. Theory
The boundary conditions of the thermal flash method are shown in Fig. A1, where one side of a sample (x=0) has a constant incoming heat flux starting
from time zero, while the other side (x=L) connects to a heat sink and therefore
stays at a constant temperature, which is assumed to be 0 for simplicity here. This
problem can be treated as a one-dimensional heat conduction problem.
q0=constant
TE leg
x=0
TL=0
x=L
Fig. A-1. Thermal flash method’s boundary conditions.
When the thermal contact resistance between the sample and the heat
source that generates the constant heat flux is zero, temperature profile at the x=0
position as time goes on can be described using equation (A.1). It is also plotted
in Fig. A-2 when the sample length and the thermal diffusivity are assumed to be
20 mm and 7×10-4 m2/s, respectively. The incoming heat flux is 1 W/m2. The
thermal conductivity is 1 W/(m∙K).
T
x 0

2q  t
k

  1
n 0
n

  n  1 L  
 nL 

ierfc
ierfc 



 t  
 t 


158
(A.1)
0.1
Temperatture (K)
0.01
0.001
1E-4
1E-5
1E-6
Perfect thermal contact
1E-7
1E-11
1E-06
1E-01
1E+04
1E+09
Time (s)
Fig. A-2. Temperature profile for 20 mm sample when the heat flux starts from time
zero and the thermal contact is perfect, where the thermal diffusivity is 7×10-4 m2/s.
The time derivative of the temperature profile at any time is as shown in equation
(A.2).
  n  1 L  
d
q 
 nL 
n 
  
 ierfc 
T  x  0   =   1 
ierfc 
 

dt
k n 0
 t  
 t 

 t 


  n  1 L   
L
 nL 

  n  1  erfc 
 n  erfc 
 

t 
 t   
 t 

(A.2)
A time constant τ is defined as the time span it takes for the temperature profile to
remain as a constant, as described by equation (A.3).
d
T  x  0    0
dt 
t 
159
(A.3)
Then, an analytical relation among the time constant τ, sample length L and
thermal diffusivity  can be described using equation (A.4).

  1
n 0

n
  
  n  1 L  
 nL 

 ierfc 
ierfc 



  
   
  

  n  1 L   
L
 nL 


n

1

erfc


 n  erfc 

   0

 
  
    

(A.4)
When there is thermal contact resistance R, equation (A.1) becomes
T
x 0

2q  t
k

  1
n 0

 L
 qR erfc 
 2 t

n

  n  1 L  
 nL 
ierfc 

  ierfc 
 t  
 t 


  2n  1 L 
  2n  3 L   
 
n 


1
erfc

erfc






 
 
 n 0
 2 t 
 2  t   

(A.5)
The time derivative of the temperature profile with respect to time is
  n  1 L  
d
q 
 nL 
n 
  
 ierfc 
T  x  0   =   1 
ierfc 


dt
k n 0
 t  
 t 

 t 

  n  1 L   
L
 nL 

n

1

erfc


 n  erfc 

 

t 
 t   
 t 

(A.6)

 L
2
 2n  3 L e(2 n3)2 L2 /4t  
n   2n  1 L  (2 n 1) 2 L2 /4 t
 qR 
e L /4 t    1 
e


3
n 0
2  t 3
 2  t 3
 2  t
 
The analytical relation among the time constant τ, sample length L, and thermal
diffusivity  can be described using equation (A.7).
160
q 
 nL
n   
 1  ierfc 

k n 0
 
  
  n  1 L   L 
  n  1 L   

 nL 
  n  1  erfc 
    n  erfc 
 
  ierfc 


  
     
    

2
 2n  3 L e (2 n3)2 L2 /4    0
L
n   2n  1 L  (2 n 1) 2 L2 /4

 qR 
e  L /4    1 
e


3
3
n 0
2  3
 2 
 
 2 
(A.7)
Temperature profile with respect to time, and contact resistance R at x=0
for the 20 mm sample is shown in Fig. A-3, where the thermal diffusivity is 7×104
m2/s. The incoming heat flux is 1 W/m2. The thermal conductivity is 1 W/(m∙K).
This implies that the time constant τ does not change, no matter how the thermal
contact resistance changes. This is the theory foundation of the thermal flash
method, and explains why it has no dependency on thermal contact resistance.
Fig. A-3. Temperature profile for 20 mm sample when the heat flux starts from time
zero and there is thermal contact. The thermal diffusivity is assumed to be 7×10-4
m2/s. The incoming heat flux is 1 W/m2. The thermal conductivity is 1 W/(m∙K).
161
The relation between the time constant τ and the thermal diffusivity a has
been calculated and plotted in Fig. A-4, using equation (A.4) and equation (A.7)
for a sample with 20 mm length. This figure indicates that the relation between
the time constant and the thermal diffusivity does not depend on thermal contact
resistance.
Time constant (s)
10000
1000
100
Pefect contact
R=1E-8 m2K/W
R=1E-4 m2K/W
10
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
2
Thermal diffusivity (m /s)
Fig. A-4. Relation between the time constant and thermal diffusivity for 20 mm
sample. The incoming heat flux is 1 W/m2. The thermal conductivity is 1 W/(m∙K).
Once the time constant is given, the thermal diffusivity can be calculated
for a specific sample with a given length. Time constant can be read from the
voltage profile of the heater that generates the heat flux. The temperature profile
can be related to the experimentally monitored voltage profile as equation (A.8).
It is under the assumption that the heater’s electrical resistivity has a linear
relationship with the temperature at the local temperature region. The data
acquisition device is sensitive enough to capture the potential change.
162
V (t )  V ( ) T (t )  T ( )

V (0)  V ( ) T (0)  T ( )
(A.8)
A.2. Experimental verification of thermal flash method
The thermal flash method is experimentally verified using a known
material under the same experiment setup as described in Section 2.4.3 and
shown in Fig. 2-10. The material used for the verification is aluminum rod
(Multipurpose 6061) with diameter of 1/8 inch (3.175 mm), bought from
McMaster-Carr. The material meets standard ASTM B221 [128]. Its thermal
diffusivity has been measured and reported as 6.4×10-5 m2/s at room temperature
region [129].
Three lengths (1 cm, 2 cm and 3 cm) were tested. Each length was tested
three times. Typical voltage profiles of the heater and its time derivative data are
plotted in Fig. A-5, A-6 and A-7, respectively. The time that the heater starts to
connect to the top end of the sample under test t0, the time that the time derivative
of the smoothed voltage profile becomes zero tτ, the time constant (tτ - t0), and the
calculated corresponding thermal diffusivity a are summarized in Table A-1.
(a)
(b)
Fig. A-5. The voltage profile and its time derivative profile of 1 cm aluminum rod.
163
(a)
(b)
Fig. A-6. The voltage profile and its time derivative profile of the 2 cm aluminum
rod.
(a)
(b)
Fig. A-7. The voltage profile and its time derivative profile of the 3 cm aluminum
rod.
Table A-1. Experiment and calculation result summary of aluminum rod.
Length
(cm)
1
1
1
2
2
2
3
3
3
Test No.
t0 (s)
ta (s)
τ (s)
1
2
3
1
2
3
1
2
3
21.9211
21.77442
21.00105
19.91433
21.54774
20.85438
21.82776
21.08105
20.87438
134.07337
174.14203
199.77665
151.82092
179.49563
182.36911
209.04378
213.25732
197.78322
115.15227
152.36761
178.7756
131.90659
154.94789
161.51473
187.21602
192.17627
176.90884
164
a
(10 m2/s)
1.473
1.207
0.903
4.929
4.250
4.107
7.915
7.898
8.372
-5
Fig. A-5, A-6 and A-7 indicate that the longer the sample, the longer the
time constant τ, the higher the signal-to-noise ratio, and the higher the precision of
the measurement results. The thermal diffusivity measurement error is about 30%
and 25% for 2 cm and 3 cm sample length, respectively. The error may come
from the air ambient of the measurement system and from the foam surrounding
the sample being tested.
A.3. MATLAB scripts
%========================================================
% Author: Guangxi Wu
% The thermal diffusivity calculation for one dimensional sample, whose one
% end is connected to a heat sink (T=0) and the other end has constant income
% heat flux.
%=========================================================
clc;
clear;
%=========================================================
% parameter definition
%=========================================================
% symbolic parameters
% q -> constant income heat flux, [W/m^2]
% alfa -> thermal diffusivity
[m^2/s]
% t -> time
[s]
% k -> thermal conductivity
[W/(m*K)]
% n -> summation index
[1]
% L -> sample length
[m]
% R -> thermal contact resistance [m^2*K/W]
syms q alfa t k n L
assume (q>0 & alfa>0 & k>0 & L>0);
assumeAlso (q, 'real');
assumeAlso (alfa, 'real');
assumeAlso (t, 'real');
assumeAlso (k, 'real');
assumeAlso (L, 'real');
%=========================================================
% 1cm-test 1, alfa=1.473045268786827e-05£¬Equation solved, fsolve stalled.
%=========================================================
time_zero = 21.9211;
time_torr=134.07337;
L=1e-2;
165
TotalFunction=1e-80;
MaxTimes=200;
SmallestStep=1e-50;
InitialPoint=1.468e-5;
options=optimoptions('fsolve','Display','iter','Tolfun',TotalFunction,'MaxFunEvals
',MaxTimes,'TolX',SmallestStep);
%=========================================================
% the case when the thermal contact is perfect
%=========================================================
alfa = fsolve(@(alfa)dT_perfect_contact(alfa,time_torrtime_zero,L),InitialPoint, options);
%=========================================================
% the case when the thermal contact is perfect
%=========================================================
alfa = fsolve(@(alfa)dT_perfect_contact(alfa,time_torrtime_zero,L),InitialPoint, options);
%=========================================================
% the case when there is thermal contact
%=========================================================
%alfa = fsolve(@(alfa)dT_contact_resistance(alfa,time_flattime_zero,L),InitialPoint, options);
function F = dT_perfect_contact(alfa,torr,L)
syms n;
F=double(subs(symsum((-1)^n*(sqrt(alfa/torr)*(ierfc(n*L/sqrt(alfa*torr))ierfc((n+1)*L/sqrt(alfa*torr)))+L/torr*(n*erfc(n*L/sqrt(alfa*torr))(n+1)*erfc((n+1)*L/sqrt(alfa*torr)))),n,0,inf)));
function F = dT_contact_resistance(alfa,torr,q,k,L,R)
syms n;
F=double(subs(q/k*symsum((-1)^n*(sqrt(alfa/torr)*(ierfc(n*L/sqrt(alfa*torr))ierfc((n+1)*L/sqrt(alfa*torr)))+L/torr*(n*erfc(n*L/sqrt(alfa*torr))(n+1)*erfc((n+1)*L/sqrt(alfa*torr)))),n,0,inf)+q*R*(L/2/sqrt(pi*alfa*torr^3)*exp(
-L^2/4/alfa/torr)+symsum((-1)^n*((2*n+1)*L/2/sqrt(pi*alfa*torr^3)*exp((2*n+1)^2*L^2/4/alfa/torr)-(2*n+3)*L/2/sqrt(pi*alfa*torr^3)*exp((2*n+3)^2*L^2/4/alfa/torr)),n,0,inf))));
function y = ierfc (x)
%ERF Error function.
% Y = IERFC(X) is the integral error function for each element of X.
% X must be real. The integral error function is defined as:
% ierfc(x) = exp(-x*x)/sqrt(pi) - x*erfc(x)
% Class support for input X:
% float: double, single
y = -x*erfc(x) + exp(-x*x)/sqrt(pi);
166
Appendix B. MATLAB SCRIPTS TO PROCESS LTPP DATA
B.1. The source code scripts
clc;
clear;
%%=======================================================
%% Import asphalt concrete temperature data.
%%=======================================================
[~, ~, raw] = xlsread('C:\Guangxi Wu\Research\Weather data\LTPP data\Seasonal
Subsurface
Temperature\SMP_MRCTEMP_AUTO_HOUR\01_0101.xlsx','Query','A2:H824
83');
raw(cellfun(@(x) ~isempty(x) && isnumeric(x) && isnan(x),raw)) = [130];
cellVectors = raw(:,[1,2,3,4,5,6,7,8]);
%% Allocate imported array to column variable names
TEMP_SHRP_ID = cellVectors(:,1);
TEMP_STATE_CODE = cellVectors(:,2);
TEMP_CONSTRUCTION_NO = cellVectors(:,3);
TEMP_SMP_DATE = cellVectors(:,4);
TEMP_TEMPERATURE_TIME = cellVectors(:,5);
TEMP_THERM_NO = cellVectors(:,6);
TEMP_AVG_HOUR_TEMPERATURE = cellVectors(:,7);
%TEMP_RECORD_STATUS = cellVectors(:,8);
%% Clear temporary variables
clearvars data raw cellVectors;
%%=======================================================
%% Import asphalt concrete layer thickness data
%%=======================================================
[~, ~, raw] = xlsread('C:\Guangxi Wu\Research\Weather data\LTPP
data\Seasonal Subsurface Temperature\thickness raw
data.xls','Query','A2:N63687');
raw(cellfun(@(x) ~isempty(x) && isnumeric(x) && isnan(x),raw)) = [130];
cellVectors = raw(:,[1,2,3,4,5,6,7,8,9,10,11,12,13,14]);
%% Allocate imported array to column variable names
AC_THICKNESS_SHRP_ID = cellVectors(:,1);
AC_THICKNESS_STATE_CODE = cellVectors(:,2);
%AC_THICKNESS_STATE_CODE_EXP = cellVectors(:,3);
%AC_THICKNESS_FIELD_LAYER_NO = cellVectors(:,4);
%AC_THICKNESS_FIELD_SET = cellVectors(:,5);
%AC_THICKNESS_TEST_NO = cellVectors(:,6);
167
%AC_THICKNESS_TEST_NO_EXP = cellVectors(:,7);
%AC_THICKNESS_LAYER_NO = cellVectors(:,8);
AC_THICKNESS_LOC_NO = cellVectors(:,9);
AC_THICKNESS_CONSTRUCTION_NO = cellVectors(:,10);
AC_THICKNESS_LAYER_DESCRIPTION = cellVectors(:,11);
%AC_THICKNESS_LAYER_DESCRIPTION_EXP = cellVectors(:,12);
AC_THICKNESS_LAYER_THICKNESS = cellVectors(:,13);
%AC_THICKNESS_RECORD_STATUS = cellVectors(:,14);
%% Clear temporary variables
clearvars data raw cellVectors;
%% Import the Location data
[~, ~, raw] = xlsread('C:\Guangxi Wu\Research\Weather data\LTPP data\Seasonal
Subsurface Temperature\General_information.xls','Query','A2:J2515');
raw(cellfun(@(x) ~isempty(x) && isnumeric(x) && isnan(x),raw)) = [130];
cellVectors = raw(:,[1,2,3,4,5,6,7,8,9,10]);
%% Allocate imported array to column variable names
LOCATION_STATE_CODE = cellVectors(:,1);
LOCATION_STATE_CODE_EXP = cellVectors(:,2);
LOCATION_SHRP_ID = cellVectors(:,3);
%LOCATION_RECORD_STATUS = cellVectors(:,4);
LOCATION_LATITUDE = cellVectors(:,5);
LOCATION_LONGITUDE = cellVectors(:,6);
%LOCATION_DATUM = cellVectors(:,7);
%LOCATION_DATUM_EXP = cellVectors(:,8);
%LOCATION_DATUM_OTHER = cellVectors(:,9);
%LOCATION_ELEVATION = cellVectors(:,10);
%% Clear temporary variables
clearvars data raw cellVectors;
%%=======================================================
% Calculate the asphalt concrete thickness with respect to each
% state and each construction number.
%%=======================================================
AC_THICKNESS_DataLength=length(AC_THICKNESS_LAYER_DESCRIPTI
ON);
TEMP_DataLength=length(TEMP_SHRP_ID);
LOCATION_DateLength=length(LOCATION_STATE_CODE);
i=0;
j=0;
168
LOC_TOTAL_NO=0;
LOC_NO='';
Is_Null=0;
Found_Thickness=0;
StateCode=TEMP_STATE_CODE(1);
SHRPID=TEMP_SHRP_ID(1);
ConstructionNo=TEMP_CONSTRUCTION_NO(1);
%State = '';
Cell_NO=0;
Thickness_cell=0;
Thickness_array=0;
Temp=0;
%A=0;
for i=1:TEMP_DataLength
if i==1
for j=1:AC_THICKNESS_DataLength
if strcmpi(StateCode,AC_THICKNESS_STATE_CODE(j)) &&
strcmpi(SHRPID,AC_THICKNESS_SHRP_ID(j)) &&
strcmpi(ConstructionNo,AC_THICKNESS_CONSTRUCTION_NO(j))
Found_Thickness=1;
if strcmpi(AC_THICKNESS_LAYER_THICKNESS(j),'')% if the data
is Null
Is_Null=1;
disp('There is Null value of layer thickess');
continue;
end
if strcmpi(LOC_NO,AC_THICKNESS_LOC_NO(j))
if
strcmpi(AC_THICKNESS_LAYER_DESCRIPTION(j),5)||strcmpi(AC_THICKN
ESS_LAYER_DESCRIPTION(j),6)||strcmpi(AC_THICKNESS_LAYER_DESC
RIPTION(j),7)
continue;
else
Thickness_cell=Thickness_cell+str2double(AC_THICKNESS_LAYER_THICK
NESS(j));
end
elseif Is_Null==1
Is_Null=0;
continue;
169
else
Cell_NO=Cell_NO+1;
LOC_NO = AC_THICKNESS_LOC_NO(j);
Thickness_cell=str2double(AC_THICKNESS_LAYER_THICKNESS(j));
end
Thickness_array(Cell_NO)=Thickness_cell;
end
end
if Found_Thickness==0
disp('No thickness data found at the beginning');
end
TEMP_THICKNESS(i)=mean(Thickness_array);
Cell_NO=0;
Thickness_array=0;
LOC_NO=0;
Thickness_cell=0;
Found_Thickness=0;
continue;
end
if
(strcmpi(StateCode,TEMP_STATE_CODE(i))&&strcmpi(SHRPID,TEMP_SHR
P_ID(i))&&strcmpi(ConstructionNo,TEMP_CONSTRUCTION_NO(i)))
TEMP_THICKNESS(i)=TEMP_THICKNESS(i-1);
else
for j=1:AC_THICKNESS_DataLength
if
strcmpi(TEMP_STATE_CODE(i),AC_THICKNESS_STATE_CODE(j)) &&
strcmpi(TEMP_SHRP_ID(i),AC_THICKNESS_SHRP_ID(j)) &&
strcmpi(TEMP_CONSTRUCTION_NO(i),AC_THICKNESS_CONSTRUCTION
_NO(j))
Found_Thickness=1;
if strcmpi(AC_THICKNESS_LAYER_THICKNESS(j),'')% if the data
is Null
Is_Null=1;
disp('There is Null value of layer thickess');
continue;
end
if strcmpi(LOC_NO,AC_THICKNESS_LOC_NO(j))
if
strcmpi(AC_THICKNESS_LAYER_DESCRIPTION(j),5)||strcmpi(AC_THICKN
ESS_LAYER_DESCRIPTION(j),6)||strcmpi(AC_THICKNESS_LAYER_DESC
RIPTION(j),7)
continue;
else
170
Thickness_cell=Thickness_cell+str2double(AC_THICKNESS_LAYER_THICK
NESS(j));
end
elseif Is_Null==1
Is_Null=0;
continue;
else
Cell_NO=Cell_NO+1;
LOC_NO = AC_THICKNESS_LOC_NO(j);
Thickness_cell=str2double(AC_THICKNESS_LAYER_THICKNESS(j));
end
Thickness_array(Cell_NO)=Thickness_cell;
end
end
if Found_Thickness==0
disp('No thickness data found in the middle');
end
TEMP_THICKNESS(i)=mean(Thickness_array);
Cell_NO=0;
Thickness_array=0;
LOC_NO=0;
Thickness_cell=0;
end
StateCode=TEMP_STATE_CODE(i);
SHRPID=TEMP_SHRP_ID(i);
ConstructionNo=TEMP_CONSTRUCTION_NO(i);
end
%%=======================================================
% Calculate the integration of the temperature gradient across the asphalt
% concrete layer of each state within a specified time span.
%%=======================================================
State_Code=01, SHRP_ID=0101
Start_Year=1995; Start_Month=7; Start_Day=24; Start_Hour=17;
End_Year=1998; End_Month=11; End_Day=17; End_Hour=16;
Date_Flag=0;
Hour_Flag=0;
Temporary_char_array=cell2mat(TEMP_SMP_DATE(1));
Year=0;
171
Month=0;
Day=0;
Hour=0;
Year_ref=Start_Year;
Month_ref=Start_Month;
Day_ref=Start_Day;
Hour_ref=Start_Hour;
Therm_No_ref=1;
End_Year_ref=End_Year;
End_Month_ref=End_Month;
End_Day_ref=End_Day;
End_Hour_ref=End_Hour;
Discontinuous_NO=1;
Discontinuous_Start_Year(Discontinuous_NO,1)=Start_Year;
Discontinuous_Start_Month(Discontinuous_NO,1)=Start_Month;
Discontinuous_Start_Day(Discontinuous_NO,1)=Start_Day;
Discontinuous_Start_Hour(Discontinuous_NO,1)=Start_Hour;
Discontinuous_Start_Row(Discontinuous_NO,1)=1;
Discontinuous_Start(Discontinuous_NO,1)=Start_Year;
Discontinuous_Start(Discontinuous_NO,2)=Start_Month;
Discontinuous_Start(Discontinuous_NO,3)=Start_Day;
Discontinuous_Start(Discontinuous_NO,4)=Start_Hour;
Discontinuous_Start(Discontinuous_NO,5)=1;
Discontinuous_End_Year=0;
Discontinuous_End_Month=0;
Discontinuous_End_Day=0;
Discontinuous_End_Hour=0;
Discontinuous_End_Row=0;
Discontinuous_End=0;
Is_Continuous=0;
Calculated_Hour_NO=0;
Total_Hour_NO=0;
Top_temperature=0;
Bottom_temperature=0;
Integral_absolute_temperature_gradient=0;
Average_temeperature_difference=0;
Temporary_length=0;
172
for i=1:TEMP_DataLength
%% assign the value of Year, Month, Day and Hour. ASCII value of char '0' is
48
Temporary_char_array=cell2mat(TEMP_SMP_DATE(i));
Year=double(Temporary_char_array(1)48)*1000+double(Temporary_char_array(2)48)*100+double(Temporary_char_array(3)48)*10+double(Temporary_char_array(4)-48);
Month=double(Temporary_char_array(6)48)*10+double(Temporary_char_array(7)-48);
Day=double(Temporary_char_array(9)48)*10+double(Temporary_char_array(10)-48);
Temporary_char_array=cell2mat(TEMP_TEMPERATURE_TIME(i));
Hour=double(Temporary_char_array(1)48)*10+double(Temporary_char_array(2)-48);
%% Find out the starting point
if Hour_Flag==0 || Date_Flag==0
if Hour==Start_Hour && Year==Start_Year && Month==Start_Month &&
Day==Start_Day
Hour_Flag=1;
Date_Flag=1;
disp('found matched starting hour');
disp('found matched starting date');
end
end
if Hour_Flag==1 && Date_Flag==1
if TEMP_THICKNESS(i)==0
disp('No thickness data found');
Temporary_char_array=cell2mat(TEMP_SMP_DATE(i-1));
End_Year=double(Temporary_char_array(1)48)*1000+double(Temporary_char_array(2)48)*100+double(Temporary_char_array(3)48)*10+double(Temporary_char_array(4)-48);
End_Month=double(Temporary_char_array(6)48)*10+double(Temporary_char_array(7)-48);
End_Day=double(Temporary_char_array(9)48)*10+double(Temporary_char_array(10)-48);
Temporary_char_array=cell2mat(TEMP_TEMPERATURE_TIME(i-1));
173
End_Hour=double(Temporary_char_array(1)48)*10+double(Temporary_char_array(2)-48);
break;
end
if (Year<End_Year) || ((Year==End_Year) &&
(Month<End_Month))||((Year==End_Year) && (Month==End_Month) &&
(Day<End_Day))||((Year==End_Year) && (Month==End_Month) &&
(Day==End_Day)&&(Hour<=End_Hour))
%% Assign the top temperature
%
Temporary_char_array=cell2mat(TEMP_THERM_NO(i));
%
if double(Temporary_char_array-48)==1
%
Temporary_char_array=cell2mat(TEMP_AVG_HOUR_TEMPERATURE(i));
%
Temporary_length=length(Temporary_char_array);
%
if (Temporary_length==1)&& (Temporary_char_array(1)~=0)
%
Top_temperature=double(Temporary_char_array(1)-48);
%
elseif Temporary_length==2
%
Top_temperature=double(Temporary_char_array(1)48)*10+double(Temporary_char_array(2)-48);
%
elseif (Temporary_length==3) && (Temporary_char_array(1)==45)
%
Top_temperature=(-1)*double(Temporary_char_array(1)48)*10+double(Temporary_char_array(2)-48);
%
end
%
end
if i-1>0
if
str2double(TEMP_THERM_NO(i))<str2double(TEMP_THERM_NO(i-1))
Top_temperature=str2double(TEMP_AVG_HOUR_TEMPERATURE(i));
end
elseif i-1==0
Top_temperature=str2double(TEMP_AVG_HOUR_TEMPERATURE(i));
end
%% Check whether the data is continuous
if Hour==Hour_ref && Year==Year_ref && Month==Month_ref &&
Day==Day_ref
Is_continuous=1;
Temporary_char_array=cell2mat(TEMP_THERM_NO(i));
if double(Temporary_char_array-48)>Therm_No_ref
%% Assign the bottom temperature
Therm_No_ref=double(Temporary_char_array-48);
%
Temporary_char_array=cell2mat(TEMP_AVG_HOUR_TEMPERATURE(i));
%
Temporary_length=length(Temporary_char_array);
174
%
if (Temporary_length==1) && (Temporary_char_array(1)~=0)
%
Bottom_temperature=double(Temporary_char_array(1)-48);
%
elseif Temporary_length==2
%
Bottom_temperature=double(Temporary_char_array(1)48)*10+double(Temporary_char_array(2)-48);
%
elseif (Temporary_length==3) && (Temporary_char_array(1)==45)
%
Bottom_temperature=(-1)*double(Temporary_char_array(1)48)*10+double(Temporary_char_array(2)-48);
%
end
Bottom_temperature=str2double(TEMP_AVG_HOUR_TEMPERATURE(i));
end
elseif Hour==Hour_ref+1 && Year==Year_ref && Month==Month_ref
&& Day==Day_ref
Is_continuous=1;
Therm_No_ref=1;
Calculated_Hour_NO=Calculated_Hour_NO+1;
Integral_absolute_temperature_gradient=Integral_absolute_temperature_gradient
+abs(Top_temperature-Bottom_temperature)/(TEMP_THICKNESS(i-1)-2525)*1000; % in unit of K/m
%disp('normal');
elseif Hour_ref==24 && Hour==1 && Year==Year_ref &&
Month==Month_ref && Day==Day_ref+1
Calculated_Hour_NO=Calculated_Hour_NO+1;
Integral_absolute_temperature_gradient=Integral_absolute_temperature_gradient
+abs(Top_temperature-Bottom_temperature)/(TEMP_THICKNESS(i-1)-2525)*1000;
Is_continuous=1;
Therm_No_ref=1;
%disp('new day');
elseif Hour_ref==24 && Hour==1 && Day==1 && Day_ref==31 &&
(Month_ref==1 ||Month_ref==3 ||Month_ref==5 ||Month_ref==7 ||Month_ref==8
||Month_ref==10 ||Month_ref==12) && Year==Year_ref &&
Month==Month_ref+1
Calculated_Hour_NO=Calculated_Hour_NO+1;
Integral_absolute_temperature_gradient=Integral_absolute_temperature_gradient
+abs(Top_temperature-Bottom_temperature)/(TEMP_THICKNESS(i-1)-2525)*1000;
Is_continuous=1;
Therm_No_ref=1;
disp('new month, 31-day-month just ended');
175
elseif Hour_ref==24 && Hour==1 && Day==1 && Day_ref==30 &&
(Month_ref==4 ||Month_ref==6 ||Month_ref==9 ||Month_ref==11) &&
Year==Year_ref && Month==Month_ref+1
Calculated_Hour_NO=Calculated_Hour_NO+1;
Integral_absolute_temperature_gradient=Integral_absolute_temperature_gradient
+abs(Top_temperature-Bottom_temperature)/(TEMP_THICKNESS(i-1)-2525)*1000;
Is_continuous=1;
Therm_No_ref=1;
disp('new month, 30-day-month just ended');
elseif Hour_ref==24 && Hour==1 && Day==1 && Day_ref==29 &&
Month_ref==2 && Year==Year_ref && Month==Month_ref+1
Calculated_Hour_NO=Calculated_Hour_NO+1;
Integral_absolute_temperature_gradient=Integral_absolute_temperature_gradient
+abs(Top_temperature-Bottom_temperature)/(TEMP_THICKNESS(i-1)-2525)*1000;
Is_continuous=1;
Therm_No_ref=1;
disp('new month, 29-day-month just ended, February');
elseif Hour_ref==24 && Hour==1 && Day==1 && Day_ref==31 &&
Month==1 && Month_ref==12 && Year==Year_ref+1
Calculated_Hour_NO=Calculated_Hour_NO+1;
Integral_absolute_temperature_gradient=Integral_absolute_temperature_gradient
+abs(Top_temperature-Bottom_temperature)/(TEMP_THICKNESS(i-1)-2525)*1000;
Is_continuous=1;
Therm_No_ref=1;
disp('new year');
else
Is_continuous=0;
disp('not continuous');
Discontinuous_NO=Discontinuous_NO+1;
Discontinuous_Start_Year(Discontinuous_NO,1)=Year;
Discontinuous_Start_Month(Discontinuous_NO,1)=Month;
Discontinuous_Start_Day(Discontinuous_NO,1)=Day;
Discontinuous_Start_Hour(Discontinuous_NO,1)=Hour;
Discontinuous_Start_Row(Discontinuous_NO,1)=i;
Discontinuous_Start(Discontinuous_NO,1)=Year;
Discontinuous_Start(Discontinuous_NO,2)=Month;
Discontinuous_Start(Discontinuous_NO,3)=Day;
Discontinuous_Start(Discontinuous_NO,4)=Hour;
176
Discontinuous_Start(Discontinuous_NO,5)=i;
Discontinuous_End_Year(Discontinuous_NO-1,1)=Year_ref;
Discontinuous_End_Month(Discontinuous_NO-1,1)=Month_ref;
Discontinuous_End_Day(Discontinuous_NO-1,1)=Day_ref;
Discontinuous_End_Hour(Discontinuous_NO-1,1)=Hour_ref;
Discontinuous_End_Row(Discontinuous_NO-1,1)=i-1;
Discontinuous_End(Discontinuous_NO-1,1)=Year_ref;
Discontinuous_End(Discontinuous_NO-1,2)=Month_ref;
Discontinuous_End(Discontinuous_NO-1,3)=Day_ref;
Discontinuous_End(Discontinuous_NO-1,4)=Hour_ref;
Discontinuous_End(Discontinuous_NO-1,5)=i-1;
Calculated_Hour_NO=Calculated_Hour_NO+1;
Integral_absolute_temperature_gradient=Integral_absolute_temperature_gradient
+abs(Top_temperature-Bottom_temperature)/(TEMP_THICKNESS(i-1)-2525)*1000;
Therm_No_ref=1;
end
Year_ref=Year;
Month_ref=Month;
Day_ref=Day;
Hour_ref=Hour;
Is_continuous=0;
else
disp('break')
break;
end
end
end
Discontinuous_End_Year(Discontinuous_NO,1)=End_Year;
Discontinuous_End_Month(Discontinuous_NO,1)=End_Month;
Discontinuous_End_Day(Discontinuous_NO,1)=End_Day;
Discontinuous_End_Hour(Discontinuous_NO,1)=End_Hour;
Discontinuous_End_Row(Discontinuous_NO,1)=i;
Discontinuous_End(Discontinuous_NO,1)=End_Year;
Discontinuous_End(Discontinuous_NO,2)=End_Month;
Discontinuous_End(Discontinuous_NO,3)=End_Day;
Discontinuous_End(Discontinuous_NO,4)=End_Hour;
Discontinuous_End(Discontinuous_NO,5)=i;
177
Average_temeperature_difference=Integral_absolute_temperature_gradient/Calcu
lated_Hour_NO;
for i=1:LOCATION_DateLength
if strcmpi(StateCode,LOCATION_STATE_CODE(i)) &&
strcmpi(SHRPID,LOCATION_SHRP_ID(i))
Output_array(1)=num2cell(str2double(StateCode));
Output_array(2)=LOCATION_STATE_CODE_EXP(i);
Output_array(3)=SHRPID;
Output_array(4)=num2cell(str2double(LOCATION_LATITUDE(i)));
Output_array(5)=num2cell(str2double(LOCATION_LONGITUDE(i)));
end
end
Start_Time=datetime([Start_Year,Start_Month,Start_Day]);
End_Time=datetime([End_Year_ref,End_Month_ref,End_Day_ref]);
Time_difference_day=caldiff([Start_Time,End_Time],'days');
Time_difference_day_num=split(Time_difference_day,'days');
Total_Hour_NO = Time_difference_day_num*24+End_Hour_ref-Start_Hour;
Data_Completeness=Calculated_Hour_NO/Total_Hour_NO;
Output_array(6)=num2cell(Start_Year);
Output_array(7)=num2cell(Start_Month);
Output_array(8)=num2cell(Start_Day);
Output_array(9)=num2cell(Start_Hour);
Output_array(10)=num2cell(End_Year_ref);
Output_array(11)=num2cell(End_Month_ref);
Output_array(12)=num2cell(End_Day_ref);
Output_array(13)=num2cell(End_Hour_ref);
Output_array(14)=num2cell(Average_temeperature_difference);
Output_array(15)=num2cell(Calculated_Hour_NO);
Output_array(16)=num2cell(Total_Hour_NO);
Output_array(17)=num2cell(Data_Completeness);
178
B.2. Detailed calculation results
Table B-1. Detailed location information of the data used in this study.
State_Code
1
1
4
4
8
9
10
13
13
16
23
24
27
27
28
30
31
32
33
34
35
36
39
40
46
48
48
49
50
51
51
State_Extension
'Alabama'
'Alabama'
'Arizona'
'Arizona'
'Colorado'
'Connecticut'
'Delaware'
'Georgia'
'Georgia'
'Idaho'
'Maine'
'Maryland'
'Minnesota'
'Minnesota'
'Mississippi'
'Montana'
'Nebraska'
'Nevada'
'New Hampshire'
'New Jersey'
'New Mexico'
'New York'
'Ohio'
'Oklahoma'
'South Dakota'
'Texas'
'Texas'
'Utah'
'Vermont'
'Virginia'
'Virginia'
SHRP_ID
'0101'
'0102'
'0113'
'0114'
'1053'
'1803'
'0102'
'1005'
'1031'
'1010'
'1026'
'1634'
'1028'
'6251'
'1802'
'8129'
'0114'
'0101'
'1001'
'0502'
'1112'
'0801'
'0901'
'4165'
'0804'
'1060'
'1068'
'1001'
'1002'
'0113'
'0114'
179
Latitude
33
33
35
35
39
41
39
33
34
44
45
38
47
47
32
46
40
41
43
40
33
43
40
36
46
29
34
37
44
37
37
Longitude
-85.2814
-85.29572
-114.2802
-114.27134
-108.02639
-72.0273
-75.43874
-83.69992
-84.005
-112.11765
-70.29562
-75.25976
-95.67014
-94.912
-89.42216
-109.12174
-97.61428
-117.00224
-71.51289
-74.54224
-103.51941
-77.92666
-83.07409
-98.2855
-100.40881
-97.05801
-95.58941
-109.58454
-73.17939
-79.36509
-79.36544
Table B-2. Calculation results with respect to a year
State
Code
1
4
8
9
10
13
16
23
24
28
30
31
32
33
34
35
36
39
40
46
48
50
51
Mean of Ave_dT
(K/m)
'Alabama'
62.1188475
'Arizona'
63.54705969
'Colorado'
93.65814964
'Connecticut'
30.56005389
'Delaware'
52.95259563
'Georgia'
28.20694574
'Idaho'
23.35180967
'Maine'
32.71012004
'Maryland'
99.76405044
'Mississippi'
34.45689192
'Montana'
133.4975363
'Nebraska'
42.23043507
'Nevada'
55.79517319
'New Hampshire' 22.74427647
'New Jersey'
88.17728275
'New Mexico'
56.09973485
'New York'
23.80017247
'Ohio'
77.35741359
'Oklahoma'
88.43868078
'South Dakota'
44.19027457
'Texas'
38.02207953
'Vermont'
24.38587829
'Virginia'
66.62196936
State Extension
180
Standard deviation
of Ave_dT
28.80008007
31.87819807
13.77127244
9.773049976
61.87728677
12.07553846
0.879903977
17.52523291
12.53006854
6.016001654
9.005961166
10.41946637
3.379270298
5.78018302
0
0
5.796003496
24.12986489
22.7958199
4.129564956
2.90959622
3.511777785
42.70789018
Years
involved
2
3
2
2
2
3
2
3
2
10
2
3
2
3
1
1
4
4
2
6
5
7
6
Table B-3. Calculation results with respect to January.
State
Code
1
4
8
9
10
13
16
23
24
27
28
30
31
32
33
34
35
36
39
40
46
48
49
50
51
State Extension
'Alabama'
'Arizona'
'Colorado'
'Connecticut'
'Delaware'
'Georgia'
'Idaho'
'Maine'
'Maryland'
'Minnesota'
'Mississippi'
'Montana'
'Nebraska'
'Nevada'
'New Hampshire'
'New Jersey'
'New Mexico'
'New York'
'Ohio'
'Oklahoma'
'South Dakota'
'Texas'
'Utah'
'Vermont'
'Virginia'
Mean of Ave_dT
(K/m)
38.56339163
58.39922224
56.76163939
19.12039765
51.22963173
22.06699423
13.96821479
33.10405027
59.28222918
25.89424958
21.07361752
69.12701726
32.19573276
34.55013292
17.29843258
37.12727695
41.68803862
12.0426336
64.37861084
24.18875403
29.97593621
29.12958168
55.88750466
15.61409472
43.44786372
181
Standard deviation
of Ave_dT
18.72956685
17.58219602
13.36022049
0
62.68512964
10.5144798
3.747623389
4.337494851
14.99328054
6.046540804
3.897686687
0.89853277
8.854336789
5.52164135
4.947859941
0
0.467138064
6.160401061
20.95822694
4.200304832
4.923098327
0.379648875
0
4.113836754
25.10810664
Years
involved
3
5
3
1
2
3
3
2
2
10
2
2
4
4
3
1
2
6
5
2
6
3
1
5
6
Table B-4. Calculation results with respect to July.
State
Code
1
4
8
9
10
13
16
23
24
25
27
28
30
31
32
33
34
35
36
39
40
46
48
49
50
51
Mean of Ave_dT
(K/m)
'Alabama'
67.5157656
'Arizona'
69.20269987
'Colorado'
113.5600756
'Connecticut'
44.58821298
'Delaware'
47.47398085
'Georgia'
44.78313785
'Idaho'
31.05567095
'Maine'
38.5094965
'Maryland'
119.1865718
'Massachusetts'
30.12331202
'Minnesota'
43.84936863
'Mississippi'
30.66350103
'Montana'
154.0426961
'Nebraska'
47.08558312
'Nevada'
61.44688834
'New Hampshire' 26.8284893
'New Jersey'
134.5863789
'New Mexico'
69.40137959
'New York'
35.80869574
'Ohio'
93.13381545
'Oklahoma'
34.53908182
'South Dakota'
55.04267899
'Texas'
45.70218434
'Utah'
87.90720465
'Vermont'
31.01047502
'Virginia'
69.55393518
State Extension
182
Standard deviation
of Ave_dT
23.88474196
55.43323238
13.39479932
0
50.10625167
30.31944956
0
25.33910684
9.017963358
0
6.548448315
8.40451627
45.60053806
15.43718132
19.66556975
6.913865632
0
12.98950879
7.554840416
43.18971223
5.75832488
10.43166033
11.86525143
5.870332057
4.348752927
48.87751864
Years
involved
4
5
2
1
2
4
1
2
2
1
7
2
2
3
3
2
1
3
4
5
2
4
3
2
6
6
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