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TRANSPORT CHARACTERIZATION OF NEW HIGH
TEMPERATURE QUATERNARY THERMOELECTRIC
MATERIALS AND DEVICES

presented by

SIM YEAN LOO

has been accepted towards fulﬁllment
of the requirements for the

 

 

PhD. degree in Electrical Engineem
//:——_——
/ assay——

 

Majot MoT‘essor’s Signature
5% 4/03

Date

 

MSU is an Affirmative Action/Equal Opportunity Institution

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DATE DUE

DATE DUE

DATE DUE

 

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6/01 c:/ClRC/Dat90ue.p65op. 15

 

 

TRANSPORT CHARACTERIZATION OF NEW HIGH TEMPERATURE
QUATERNARY THERMOELECTRIC MATERIALS AND DEVICES

By

Sim Yean Loo

A DISSERTATION

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

DOCTOR OF PHILOSOPHY
Department of Electrical and Computer Engineering

2003

ABSTRACT

TRANSPORT CHARACTERIZATION OF NEW HIGH TEMPERATURE
QUATERNARY THERMOELECTRIC MATERIALS AND DEVICES

By

Sim Yean Loo

A new computer-controlled high temperature thermoelectric transport
measurement system was built for investigating new high temperature quaternary
thermoelectric materials and devices. Such thermoelectric materials are desirable for
power generation applications — converting thermal energy to electricity. Some of the
advantages of thermoelectric devices include no moving parts, solid-state construction,
environmentally friendliness, and high reliability. An increasing concern of environment
and awareness of limited resources has made waste heat recovery an urgent global issue.

The high temperature thermoelectric system is computer-controlled by
LabVIEWTM programming with extensive PID temperature control. It can be used to
characterize the thermoelectric power (S) and electrical conductivity (0) of electronic
materials in a broad temperature range (80-8OOK). The ﬁgure of merit, ZT (= Szo’l‘lx), is
used to deﬁne the efﬁciency of thermoelectric materials. The measured power factor
(820) can be used to identify good candidates for thermoelectric applications. Some of
the new quaternary materials exhibit power factor larger than 30 uW/KZ-cm in a wide
temperature range of 300-6OOK. Since these materials are expected to have very low
thermal conductivity at high temperatures, a ZT of approaching or larger than 1 at high
temperatures can be achieved. Three of the best thermoelectric materials: bismuth

telluride alloys, lead telluride alloys and silicon-germanium, have a ZT of ~1 at their

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optimum temperatures. The experimental results also reveal the new quaternary materials
as narrow-band gap semiconductors with metallic behavior.

The theory behind thermoelectric materials will be reviewed; this includes the
search of materials with large band degeneracy or high anisotropy, the parameters that
can enhance the B-factor, and the coefﬁcient of performance as well as the efﬁciency of
the thermoelectric devices. The structural design and automated features of the
measurement system will be presented. The technique of material/device characterization
will be discussed as well as the results of investigations on new quaternary materials and

devices constructed with these materials.

Dedicated to my sweet husband, Roger Booth. '

 

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ACKNOWLEDGEMENTS

This research would not have been possible without the patience and guidance of
my advisor, Dr. Tim Hogan. He has contributed a signiﬁcant amount of time to introduce
many students, including me, to the world of scientiﬁc research. It has been a great
experience working for Dr. Hogan and I value everything that I have learned in this lab,
not just the spirit of research, but also the working manner, attitude and ethics. I would
also like to thank all the people with whom I have worked in the thermoelectric project,

including Duck-Young Chung, Kuei-Fang Hsu, Sangeeta La], Daniel Bilc and etc.

I would like to thank Dr. Mercouri Kanatzidis, Dr. Tim Grotjohn and Dr. Don
Reinhard for taking the time to review my thesis, attending my presentation and
contributing to some helpful discussions. I would like to thank Dr. Eldon Case for
assisting in the material science aspect of thermoelectrics investigation. I also feel

grateful for all the wonderful lab colleagues I have worked with.

At last, but not the least, I would like to thank my husband, Roger Booth, my
parents, my parents in-law, and my aunt Chim and uncle Roberto for all their support

throughout the years.

I am also grateful for the financial support of the Ofﬁce of Naval Research and

DARPA through grants NOOOl4-Ol-l-O728.

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................... vi
LIST OF FIGURES ......................................................................................................... x
Chapter 1
Introduction
Introduction .................................................................................................... 1
Chapter 2
Background
2.1.1 What is thermoelectrics? ................................................................................ 3
2.1.2 Why thermoelectrics? .................................................................................... 8
2.1.3 How does a thermoelectric device work? ...................................................... 9
2.2 Why there is renewed interest in recent years ....................................................... 13
2.2.1 Transport theory: Optimizing ZT — the B factor ........................................... 14
2.2.2 New materials and material synthesis techniques ......................................... 18
2.2.3 Modern technologies ..................................................................................... 19
2.3 Enhancing ZT ........................................................................................................ 19
2.3.1 Minimizing thermal conductivity ................................................................. 21
2.3.2 Properties of good TE materials ................................................................... 23
2.4 What is being done at MSU and other places ........................................................ 23
2.4.1 Bismuth Telluride ......................................................................................... 24

2.4.2 II-IV Semiconductors (PbS, PbSe, and PbTe) .............................................. 26

2.4.3 Si-Ge ........................................................................................................... 27
2.4.4 Bismuth Antimony ........................................................................................ 28
2.4.5 Skutterudites ................................................................................................. 29
2.4.6 Clathrates ...................................................................................................... 30
2.4.7 Half-Heusler Alloys ...................................................................................... 32
2.4.8 TAGS ........................................................................................................... 33
2.4.9 Chalcogenides — CsBi4Te6 ............................................................................ 34
2.4.10 Cubic —AngBiQ3 (Q = S, Se, Te) ................................................................ 35
2.4.11 Quantum Well (Superlattice Structure) ........................................................ 36
2.4.12 Quantum Dots ............................................................................................... 37
2.5 Techniques of characterization .............................................................................. 39
2.5.1 For Materials ............................................................................................... 39
2.5.1.1 Steady-state Technique ........................................................................... 39
2.5.1.2 Harman Technique .................................................................................. 41
2.5.1.3 Pulse Tehcnique ...................................................................................... 49
2.5.1.4 High temperature transport probe ........................................................... 59
2.5.1.5 Parallel thermal conductance (I’TC) technique ....................................... 61
2.5.1.6 Low temperature 4-sample thermoelectric measurement system ........... 62
2.5.2 For Modules ............................................................................................... 64
2.5.2.1 Thermal conductance measurement ........................................................ 64
2.5.2.2 Modiﬁed Harman Technique .................................................................. 67

Chapter 3

Module/prototype Design

3.1 Background of TE generation ................................................................................ 71
3.2 Choice of TE materials for module fabrication ..................................................... 72
3.3 Construction of the thermoelectric module ............................................................ 73
3.4 Segmented TE modules ......................................................................................... 76
Chapter 4

High temperature measurement system

4.1 System set-up and design ....................................................................................... 79
4.2 Mounting and running ............................................................................................ 84
4.3 Measurement method ............................................................................................. 87
4.4 Software Control - PID .......................................................................................... 89

4.4.1 Introduction to P11) in Temperature control ................................................. 89

4.4.2 Tuning the LakeShore 330 Temperature controller ...................................... 94
4.5 Sample mounting procedures ................................................................................. 98
4.6 High temperature operating procedures ................................................................ 103
4.7 Thermal loss calculation ....................................................................................... 117
Chapter 5

Experimental Results of the system

5.1 Experimental Results ............................................................................................ 128

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Chapter 6

Simulations and experimental results of the module

6.1 Simulations .......................................................................................................... 164
6.2 Module Testing ................................................................................................. 169
Chapter 7

Conclusion/Future Work ................................................................................................ 174
Appendix A .......................................................................................................... 178
Appendix B .......................................................................................................... 193
Appendix C .......................................................................................................... 194
Appendix D .......................................................................................................... 195
Appendix E .......................................................................................................... 196
Reference .......................................................................................................... 203

LIST OF TABLES

Chapter 2
Table 2.1 Z of three typical TE materials ...................................................................... 14
Table 2.2 Energy band gap of some good TE materials ............................................... 16
Table 2.3 The best TE materials at T=300K ................................................................. 26
Chapter 3
Table 3.1 Performance of various types of electrical power generators ....................... 72
Table 3.2 Some properties of the most widely used TE Materials ............................... 73
Chapter 4

Table 4.1 The electrical resistivity and thermal conductivity of some metals and alloys
at room temperature. .................................................................................... 118

Table 4.2 The electrical resistivity and thermal conductivity of some metals and alloys

at 800K ......................................................................................................... 1 18
Table 4.3 The thermal conductance of each wire at 300K ........................................... 119
Table 4.4 The thermal conductance of each wire at 800K ........................................... 124
Chapter 5

Table 5.1 The electrical resistivity and thermal conductivity of some metals and alloys

at room temperature. .................................................................................... 135
Table 5.2 Error percentage calculation of the sample KF2229R1D. ........................... 136
Table 5.3 The EDS result for surface of the cubic materials KF2229R1D. ................ 138

 

 

 

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Table 5.4 The EDS result for inside of the cubic materials KF2229R1D. .................. 138

Table 5.5 Error percentage calculation of the molybdenum HT thermopower
measurement with the Reference. ................................................................ 143

Table 5.6 Error percentage calculation of the molybdenum HT resistivity measurement
with the Reference. ...................................................................................... 144

Table 5.7 Error percentage calculation of the NIST stainless steel HT electrical

conductivity measurement with the Reference. ........................................... 145
Chapter 6
Table 6.1 The performance parameters obtained from simulation. ............................. 166
Table 6.2 The experimental result of the open circuit test. .......................................... 172
Table 6.3 The experimental result of the short circuit test ........................................... 172
Table 6.4 The determined ZT of the module from the two tests. ................................. 172

Chapter 2
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9
Figure 2.10

Figure 2.11

Figure 2.12
Figure 2.13
Figure 2.14
Figure 2.15
Figure 2.16
Figure 2.17
Figure 2.18
Figure 2.19

Figure 2.20

LIST OF FIGURES

Seebeck Effect ......................................................................................... 4

Peltier Effect ............................................................................................ 5

Thomson Effect ........................................................................................ 6

TE module (couple) for Cooling ............................................................. 10
TE module for Power Generation ........................................................... 12
Density of states for different dimensionalities ...................................... 17
The variation of Figure of Merit ZT with carrier concentration ............. 21
ZT of some best TE materials ................................................................. 24
The crystal structure of bismuth telluride ............................................... 25
The crystal structure of lead telluride ..................................................... 27

Schematic illustrating the unit cell of the unﬁlled skutterudite crystal

structure ................................................................................................... 29
The crystal structure of Clathrates ........................................................... 32
The crystal structure of Half-Heusler alloy ............................................ 33
The crystal structure of CsBi4Te6 ........................................................... 35
Stead-State Technique ............................................................................ 40
Cylindrical sample connecting to a circuit .............................................. 42
Harman technique circuit ........................................................................ 47
Pulse Technique experimental set-up ..................................................... 50
The periodic waveform of the heater current .......................................... 52
The waveform of the temperature gradient across the sample ............... 58

Figure 2.21
Figure 2.22
Figure 2.23
Figure 2.24
Figure 2.25
Figure 2.26
Figure 2.27
Figure 2.28

Figure 2.29

High Temperature Transport Probe Sample Stage ................................. 60

Sample holder with sample ..................................................................... 62
Sample conﬁguration in 4-sample system .............................................. 63
The plot of temperature gradient vs. time of two samples ...................... 64
The plot of dV vs. dT curve of two samples ........................................... 64
Short circuited TE module with p and n-legs ......................................... 65
Open circuited TE module with p and n-legs ......................................... 66
The current that is applied to the sample vs. time ................................... 69
The voltage across the sample vs. time ................................................... 7O

Chapter 3

Figure 3.1

Figure 3.2

Figure 3.3

The range of output power provided by TE generators with different fuel
sources ..................................................................................................... 71
TB module consists of a p- and n-type leg, an electrically connected metal
strip and a ceramic for better thermal contact ......................................... 74

The combinations of various TE materials at the unicouples ................. 78

xiv

Chapter 4

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5
Figure 4.6
Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10
Figure 4.11
Figure 4.12

Figure 4.13

Figure 4.14

Wiring diagram of connector B as seen from the outside of the connector.
TC. is the upper side of the two thermocouple that are mounted on the
sample, TC- is the bottom thermocouple ................................................ 80
Wiring diagram of connector TC as seen from the outside of the
connector. This connector contains the heater and sensor leads to the
temperature controller. ............................................................................ 81
The wiring diagram of the Lake Shore 330 temperature controller sensor
Channel B connector in the rear panel .................................................... 82

Heater Output of the rear panel of Lake Shore 330 temperature controller

........................................................................................................... 82
The set-up of the high temperature system ............................................. 83
The design of the sample stage ............................................................... 84
The sample mounting conﬁguration ....................................................... 85

The photo of the sample mounting conﬁguration in the early development

of the system ........................................................................................... 85
The photo of the sample mounting conﬁguration now ........................... 86
A close view of the sample mounting conﬁguration now ..... 86
The slope of W vs. dT curve ................................................................... 87
The temperature gradient vs. time plot ................................................... 87

The dV vs. dT curve and the temperature gradient plot when the
temperature is not stable ......................................................................... 88

Signals from an On-Off temperature controller ...................................... 90

 

 

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Figure 4.16

Figure 4.17

Figure 4.18

Figure 4.19

Figure 4.20

Figure 4.21

Figure 4.22

Figure 4.23

Figure 4.24

Figure 4.25

Figure 4.26

Figure 4.27

Figure 4.28

Figure 4.29

Proportional temperature controller ........................................................ 91
Proportional + Derivative temperature controller ................................... 92
Proportional + Integral + Derivative temperature controller .................. 93

A snapshot of LabVIEW display on the system temperature with P, I, D =
50, 0, 0 ..................................................................................................... 95

A snapshot of LabVIEW display on the sensor (system) temperature with

P, I, D = 40, 4, 59. The system stabilize at 310 K .................................. 96
System stabilize at 330K ......................................................................... 97
The transition between temperatures ...................................................... 98

The HT heater and the positive current lead are mounted on top of the
sample with silver paint ......................................................................... 101
The top thermocouple is held with Kapton tape and the bottom
thermocouple is mounted on the sample with silver paint ..................... 102
The leads separation is measured between the mid-points of contacts and
edges of the contacts .............................................................................. 103
PowerFactor_Manual.vi ......................................................................... 104
After the measurement, the values are displayed in
PowerFactor_Manual.vi ......................................................................... 106
At room temperature, the value of M0 is displayed in Thermopower slope
ﬁt.vi ........................................................................................................ 107
High Temp_Aprl6.vi ............................................................................. 108

At 530K, the value of M0 is displayed in Thermopower slope ﬁt.vi 110

Figure 4.30

Figure 4.31

Figure 4.32

Figure 4.33

Figure 4.34

Figure 4.35

Figure 4.36

Figure 4.37

Figure 4.38

Figure 4.39

Figure 4.40

Figure 4.41

Figure 4.42

Figure 4.43

Figure 4.44

The transition between temperatures during the temperature dependent
measurement .......................................................................................... 1 10
Distorted plots due to temperature instability ........................................ 111
Reset the PID values to 100, 0, 0. The white vertical line indicated when
the PID was changed .............................................................................. 112
The amplitude of the oscillation decreases ............................................ 113

The PID is reset to 150, 0, 0 and it then sustains a constant amplitude

oscillation ............................................................................................... 1 13
The magniﬁed view of the oscillation ................................................... 114
Calculate the period, period=116s ......................................................... 114

After the new PID: 50,8,29 is entered, the system stables at the set point
less than 10 minutes ............................................................................... 115

The instability occurs due to the large heater current that is applied to the

sample .................................................................................................... l 16
Looping occurs due to the instability of the system .............................. 116
Various ways of heat transfer from the sample ..................................... 117
The thermal conductivity of Crzo N130 ................................................... 121

The comparison between the Reference and 4-sample system
measurement in thermal conductivity of constantan ............................. 122
Use the curve ﬁt equation in Figure 3 to extrapolate the thermal
conductivity of constantan at 800K ....................................................... 123

Thermal conductivity of Copper ............................................................ 123

 

 

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Chapter 5

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Thermal conductance of Copper, assuming a temperature gradient of 1K

.......................................................................................................... 124

The electrical conductivity and thermopower of AgongmeoggBioozTelz

.......................................................................................................... 128
Electrical conductivity and thermopower of BizTe3. ............................. 129
Electrical conductivity and thermopower of AgojgpwabTCzo ............. 130
Electrical conductivity and thermopower of Ago,7nglngTezo ............. 131
The comparison of the thermopower of bismuth telluride between 4-
sample system and hi gh-temperature system ......................................... 133

The comparison of the electrical conductivity of bismuth telluride between
4-sample system and hi gh-temperature system ..................................... 133
The comparison of the thermopower of Constantan between 4-sample
system and hi gh-temperature system to the literature values ................ 134
The comparison of the electrical conductivity and thermopower of cubic
material KF2229R1D between 4-sample system and high-temperature
system (Oct. 25) ..................................................................................... 136
The comparison of the electrical conductivity and thermopower of cubic
material KF2229R1D between 4-sample system and high-temperature
system (Oct. 26) ..................................................................................... 137
The power factor comparison between the two runs (Oct. 25 & 26) of

KF2229R1D ........................................................................................... 139

 

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Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

Figure 5.16

Figure 5.17

Figure 5.18

Figure 5.19

Figure 5.20

The comparison of the electrical conductivity and thermopower of cubic
material KF2229R1C between 4-sample system and high-temperature
system .................................................................................................... 140
The comparison of the thermopower of molybdenum between the

I
reference (POIIOCk [Erron Bookmark not deﬁned.

]) and hi gh-temperature system
(before the temperature controller is properly tuned). ........................... 141
The comparison of the thermopower of molybdenum between the
reference and hi gh-temperature system (after the temperature controller is
properly tuned) ....................................................................................... 142
The comparison between the reference and measured electrical resistivity
of Mo ...................................................................................................... 143
The comparison of the electrical conductivity of NIST 1461 stainless steel
between the reference (NIST) and high-temperature system ................ 144
Electrical conductivity of Agog4PblngTezo and the sample ID is
KF2242R2 with A, B and C sections ..................................................... 146
Thermopower of Agog4Pb138bTezo and the sample ID is KF2242R2 with
A, B and C sections ................................................................................ 147
Power factor of Agog4PblngTezo and the sample ID is KF2242R2 with A,
B and C sections ..................................................................................... 147
KP series materials are grown as ingot and cut to different sections for
measurement .......................................................................................... 148

The total thermal conductivity of KF2242R2A from the 4-sample system

in Hogan’s lab ........................................................................................ 149

Figure 5.21

Figure 5.22

Figure 5.23

Figure 5.24

Figure 5.25

Figure 5.26

Figure 5.27

Figure 5.28

Figure 5.29

Figure 5.30

Figure 5.31

The electronic thermal conductivity of KF2242R2A calculated from the
electrical conductivity and with two different Lorentz numbers ........... 150
The lattice thermal conductivity of KF2242R2A is calculated from
subtractions of electronic thermal conductivity from the total thermal
conductivity. These data are calculated through the equations of the sixth
polynomial ﬁt of the electronic thermal conductivity and the fourth
polynomial ﬁt of the total thermal conductivity .................................... 151
The lattice thermal conductivity of KF2242R2A with curve ﬁt till 700K

.......................................................................................................... 152
The total thermal conductivity of KF2242R2A with two different Lorentz
number ................................................................................................... 153
The estimated ZT of KF2242R2A with two different Lorentz number. 153
The electrical conductivity and thermopower of KF2242R2A .............. 155
The electrical conductivity of sample KF2242R3C Ago_36Pb133bT620 with
repeated runs .......................................................................................... 156
The thermopower of sample KF2242R3C AgogéPblngTezo with repeated
runs ......................................................................................................... 157
An oxide layer formed on the surface of sample KF2242R3C
Ago_36PblngTezo after running in high temperature .............................. 157
Crack lines occurred on the surface of sample KF2242R3C
AgogéPblngTezo after running in high temperature .............................. 158
The copper plate coated with tellurium (left) and a clean copper plate

(right) ..................................................................................................... 158

Figure 5.32

Figure 5.33

Figure 5.34

The Thermopower of cubic materials with various composition of silver
.......................................................................................................... 160
The electrical conductivity of cubic materials with various composition of
silver ....................................................................................................... 161
The power factor of cubic materials with various composition of silver

.......................................................................................................... 162

Chapter 6
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5

Figure 6.6

Figure 6.7

Simulated ZT of the module vs. temperature ......................................... 166
Heat ﬂow through the module vs. current output. ................................. 167
Efﬁciency of the module vs. Current Output ......................................... 167
Power output of the module vs. efﬁciency ............................................ 168
Power output of the module vs. temperature gradient ........................... 168

Single couple TE module with n-type cubic material, Ago_32Pb138bTezo,
and a p-type cubic material, AgogSnSbuTeg ........................................ 171
The capture image displayed the temperature gradient across the sample

vs. time ................................................................................................... 171

 

 

 

 

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Chapter 1 Introduction

New perspectives on thermoelectric research are explored at Michigan State
University through collaborations among the Electrical Engineering, Chemistry and
Physics departments. My role in this research has been in developing a new transport
measurement system and module design/prototype that will be compatible with the newly
discovered thermoelectric materials. A new computer-controlled thermoelectric
measurement system is built to characterize the electrical and thermal properties of new
thermoelectric materials, primarily at high temperatures (up to 800K). Thermoelectric
research at high temperatures is desirable since materials with high thermoelectric
efﬁciency at high temperatures have potential applications in power generation. Using
this system, we can study the new materials’ properties over a very broad temperature
range. Quaternary cubic materials are the main focus in this investigation. Knowledge in
chemistry (6. g. chemical structure in doping and alloying, crystallography and etc.) and
physics (e. g. band gap calculation, band diagram and etc.) is required to understand why
the materials have such properties.

The uniqueness of this research includes the thermoelectric properties of new high
temperature quaternary cubic materials obtained for the ﬁrst time through this high
temperature measurement system. The development of this measurement system as part
of this research has further allowed for the investigation of thermoelectric properties for
other materials not included in this work, primarily at high temperatures. Since these
measurements will give the ﬁrst insight of the thermoelectric properties of new materials,
the system is an important tool used to investigate these new materials. This high

temperature TE measurement system is specially designed to measure small geometry

 

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bulk samples and some of the unique features of this system include computer-control
through LabVIEWTM programming. Through such programming, routes to temperature
stabilization and control have been investigated. This has also allowed for the collection
of large number of data points in the experiments. These features have overcome some
of the limitations found among the few existing high temperature TE measurement
systems.

A broad and detailed background of thermoelectricity is introduced in the ﬁrst
part of the thesis. This section includes the theoretical background of thermoelectrics, the
transport theory relating to thermoelectrics, the investigation of old and new
thermoelectric materials and the various techniques of material/module characterization.
The next section gives a description of the new high temperature system, including the
structural design, and automated features, especially in temperature control of the system.
The experimental results will be presented and a detailed investigation on the new
quaternary cubic materials will be discussed based on the experimental results. Finally, a
thermoelectric module will be fabricated with these types of materials and the

performance of this module will be discussed.

 

 

 

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Chapter 2 Background

Thermoelectric (TE) materials have been investigated ever since the discovery of
thermoelectric effects in the 18003. Their lightweight, lack of moving parts and
environmental friendliness are just some of the advantages of TE devices. However, the
low efﬁciency of TE devices has made them less viable as commercial devices. The
search for high efﬁciency TE materials lies in discovering materials with a high ﬁgure of
merit, ZT [1]. The ﬁgure of merit includes the thermoelectric power (Absolute Seebeck
Coefﬁcient) (S), electrical conductivity (0) and thermal conductivity (K) of the sample,
while T is the absolute temperature. Z has unit of UK thus ZT is a unitless quantity. The
higher the ZT, the better the material for TB applications.
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2.1.1 What is Thermoelectrics?

Therrnoelectrics is the study of the conversion between thermal and electrical
energy. There are three thermoelectric effects associated with it. The ﬁrst thermoelectric
phenomenon was discovered in 1823 by Seebeck. He found that when heat was applied
to one of the junctions of two dissimilar metals, when connected in a closed loop
conﬁguration as shown in Figure 2.1 a), he would measure a deflection on his
galvanometer. Seebeck thought it was a magnetic effect and pursued a derivation to
explain this phenomenon. He had investigated a large number of materials, including

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coefﬁcient, S, and electrical conductivity, 0'. Although, he had pursued the wrong

direction, he did gather a lot of useful information for many materials.

Material A Material A

  

Material B

Material B Material B

a) b)

Figure 2.1 Seebeck Effect.

With the discovery of Faraday’s Law, the magnetic ﬁeld measured by Seebeck
was better understood to be caused by a current ﬂowing in the closed loop of Figure 2.1
a). This was later veriﬁed by a corresponding open circuit voltage when the loop was
broken as shown in Figure 2.1 b). The relative Seebeck coefﬁcient is expressed as the

voltage, V0 divided by the temperature gradient, AT = (Th-TC),

V

_ 0

S
AB AT (2.)

 

The Seebeck voltage is also known as Seebeck electromotive force, emf. The
application of the Seebeck effect is a thermocouple. A thermocouple is a device which
converts thermal energy to electric energy. It is made up of two dissimilar conductors and
when the junctions are in different temperatures, a Seebeck emf or voltage is produced.
The amount of electric energy produced can be used to measure temperature. When a
reference temperature is used, the temperature difference, and consequently the emf of a

thermocouple, becomes a function of the temperature of the measuring junction. This

 

 

El‘v‘s,

Pr.
Ag

and

Con.

 

functional dependence permits the establishment of lookup tables, curves or mathematic
relationships for a speciﬁc type of thermocouple.

About 12 years after the discovery of Seebeck, Jean Peltier discovered the second
effect which shows a temperature gradient across the junctions of two dissimilar metals

when a current, I, is applied.

Heat Released

MaterialB

 

Figure 2.2 Peltier Effect.

Figure 2.2 shows the Peltier effect. The heat ﬂow (dQ/dt, energy per unit time)
away from the junction was found to be proportional to the current, I with the

proportionality constant, H, deﬁned as the Peltier coefﬁcient

_ dQ
AB (11‘ . I (3.)

Unfortunately, these fascinating discoveries were neglected since the
electromagnetic phenomena were also discovered and developed around the same time,
and had caught the attention of many scientists during that period.

Some twenty years passed before interest in direct thermal to electric energy

conversion found renewed interest following the further development of

 

 

 

 

"J

IT

 

 

 

ier

[hr

in

thermodynamics. In 1851, Thomson had discovered a third effect, which described how a
single homogeneous metal could release or absorb heat depending on the direction of the
current ﬂow in the presence of a temperature gradient on it. To restate this phenomena
[2], if the electrons move along the increasing temperature gradient (from cold to hot),
the material will absorb the energy (heat) and the potential energy of the electrons is
increased. If the electrons move along the same direction as the gradient (from hot to
cold), the material will give up the energy (heat) and the potential energy of the electrons

is decreased.

AQ

 

Figure 2.3 Thomson Effect.

Figure 2.3 shows the Thomson effect which describes the development of a
temperature gradient, AT, along the length of a single material when current, I, flows
through the sample. A corresponding absorption or emission of heat, AQ, is proportional
to the product of the current and temperature gradient, with the proportionality constant,

Yr. deﬁned as the Thomson coefﬁcient

 

 

 

 

It"

I‘LL”

 

31',

 

 

7 -—AQ
T I-AT (4')

Thus, a net heat flow in a single homogeneous conductor per unit volume per unit
time is
AQ=12R—yToAT-I (5.)
where I is the current density, R is the electrical resistance of the conductor. The ﬁrst
term on the right side is the irreversible Joule heating and the second term is the
reversible Thomson effect. The sign of the second term is positive if heat is absorbed and

negative is heat is liberated.

Thomson further derived a relationship between the Seebeck and Peltier effects,
H AB = SABT (6-)

and also related the Seebeck effect to Thomson effect,

71

T

where S is the absolute thermoelectric power of a single conductor. Equations 6 and 7
also known as the Kelvin relations and the Seebeck effect of a thermocouple can be

expressed as

SAB =S

(8-)

GIN
GIN

Equation 8 shows that the Seebeck effect or thermoelectric power of a thermocouple can

be expressed as the algebraic sum of the absolute thermoelectric power of each of the

individual elements. This result is crucial because it allows one to predict the properties
of a thermocouple if the thermoelectric properties of the individual element are known.
There are three ways to better visualize the thermoelectric power of a material.
One way is to consider the Thomson effect, which describes the reversible heat change
and is related to the current and emfs in the conductor along the temperature gradient, this
property of the material is called the absolute thermoelectric power. Another way is to
consider a thermocouple made of a superconductor and the sample of interest. Since
superconductors show no thermoelectric effects below their transition temperatures,
usually at very low temperatures (<21K), the observed thermoelectric effect of this
thermocouple at these temperatures must be only by the sample of interest. Greater
accuracy can then be found for a given reference material (such as lead, or platinum) by
forming a junction between the reference material and a superconductor, and measuring
the junction at temperatures below the transition temperature of the superconductor. The
data for the reference material that was obtained over a wide temperature range can then
be shifted to align with the low temperature data for a more accurate reference material
data set. This calibrated reference material can then be used to form a junction with other

unknown samples, and determine their thermopower.

2.1.2 Why Thermoelectric?

The uniqueness and advantages of thermoelectric devices has been reviewed [3]
over many years. For cooling applications, much effort has been made toward replacing
existing compressor-based devices with thermoelectric devices. However, there are many

other applications where TE devices are the best choice.

 

 

 

Cor

 

 

 

The advantages of TE devices are:
1. No moving parts — less maintenance required
2. Solid-state construction — can operated under harsh conditions, e. g. under
vibration
3. Environmentally friendly
4. Scalability — light weight, small size devices
5. Act as a converter — can be a cooler or a power generator
6. Can be operated in any orientation and in zero gravity environment
7. Low electronic signature (noise)

8. High reliability, and long lifetime

2.1.3 How Does A Thermoelectric Device Work?

Thermoelectric devices can consist of a single couple (or commonly known as a
thermocouple) as shown in Figure 2.4, or many such couples connected together. Most
TE devices consist of a p and an n-type material forming the couple since this
conﬁguration gives the best performance.

The gray strips at the top and bottom of the device shown in Figure 2.4 are the
metal connections. This couple is connected electrically in series and thermally in
parallel. To distinguish between the efﬁciency of a thermoelectric generator and a
thermoelectric cooler, the efﬁciency of a cooler is titled the coefﬁcient of performance
(COP), 4’, while the efﬁciency of a generator is titled efﬁciency, 77. Since TE devices can
be scaled without loss of efﬁciency, the coefﬁcient of performance (COP) of a TB cooler

can be derived on the basis of a single TE couple.

 

 

 

 

 

 

 

Figure 2.4 TB module (couple) for Cooling.

In Figure 2.4, when current ﬂows from n to p-type material, both carriers ﬂow
from the top to the bottom plates, carrying heat with them. This has made the top plate an
active cooling area and the bottom plate a heat source. Reverse the direction of current
will result the cooling in the bottom plate and heat flow from the bottom to the top. This
construction utilizes the Peltier effect and thus, is often called Peltier cooling.

The cooling effect is offset only in equilibrium between them by the Joule heating
(12R) and by heat conducted from the hot junction. It shows that half of the overall Joule

heating goes to each junction. The rate of absorption of heat from the source is

1 2
Q = SpnTcI — 21 R — KAT (9,,

and AT = Th- Tc

10

Part of the potential difference applied to the couple is employed in overcoming
the resistance of the branches and part is used to balance the Seebeck voltage resulting
from the temperature difference between the junctions. Thus, the power W supplied to the

couple is given by
W = SWAT] + 12R (10,)

After some derivations [4], the coefﬁcient of performance, ¢, for a TB cooler is

deﬁned as the ratio of W, which is

_ SpnTCI —%IZR - KAT
— SWAT] + 12R (“9

 

The maximum COP is determined by taking the derivative of equation (11) with respect
to current I - setting equal to zero and solving for [max

_ SWAT 1

"m" _ R 1+er -1 (12')

 

then inserting 1m, into (1 1) gives,

¢ _ TM(,/1+ZTM —1)__1_
m" _ Art/17%; +1) 2 “3"

 

where TM = (Th+Tc)/2

In Figure 2.5, the TB couple is electrically connected to a load on one end and
when heat is applied to the other end, electrons in the n-type, and holes in the p-type legs
preferentially flow from the top (higher energy) plate to the bottom (lower energy) plate.

A current, I, is thus induced and the structure works as a power generation device.

11

 

 

US

Heat Applied
I I I i

 

 

 

 

 

 

 

 

_’

I

Power Generation

Figure 2.5 TB module for Power Generation.

The heat supplied is either conducted along the branches to the cold junction or
used to balance the Peltier effect at the hot junction. Since the Joule heating is distributed

throughout each of the n and p legs, one half of it ﬂows back to the source. Thus,
AT
_ 1 2
Q— KAT+SW[TM +—2 —-2—1 R (1,)

The Peltier effect is not associated with the nature of the contact between the two
conductors, i.e. it is not related to “contact potential”. The Peltier effect is different from
the Joule heating in that Joule heating varies as the square of the current and directly as
the electrical resistance of the conductor (12R). Moreover, Joule heating is a function of

dimensions of the conductor and does not require a junction of dissimilar materials. Also,

12

 

 

 

OJ

Bl
1h:

in

f0.

1

[En

in contrast to Peltier effect, Joule heating does not change its sign when the direction of
the current is reversed since it is an irreversible phenomenon.
For maximum power output from a given couple the load resistance RL should be

made equal to the generator resistance R. The useful work is then,

 

 

 

51,3137“2
W = (15.)
4R
since half of the thermoelectric voltage appears across the load. The efﬁciency is
77 _ AT
AT 4RK (16.)
ZTM + -——- + 2
2
pa

More detail derivations for the COP of TE cooler and efﬁciency of power generator can

be found in various sources [5, 6].

2.2 Why there is renewed interest in recent years

At room temperature, the best bulk TE material is Bismuth Telluride alloys where
BizTe3 which was suggested by Goldsmid [7] about four decades ago. ZT is about 1 for
this material at room temperature (its optimum temperature). Much effort and
investigation had been directed toward optimizing the properties of bismuth telluride
alloys but there has been only modest progress in finding a bulk material with higher ZT.
The highest ZT in any bulk TE materials at about room temperature is 1.14 for p-type
(BizTe3)o,25(Ssze3)o,72(Sb28e3)o,o3 alloy [8]. Table 2.1 shows three typical TE materials
for different temperature ranges. All of them have a ZT of about 1 at their optimum

temperature:

13

 

 

 

 

Zmax (K-l) Useful Range
BizTes 3x103 < 500 K
PbTe 1.7x10'3 < 900 K
Si-Ge 1x10-3 < 1300 K

 

 

 

 

 

Table 2.1 Z of three typical TE materials.

Materials with ZT of about 4 or 5 are needed in order for a TE cooler to compete
with the compressor-based refrigerator while ZT of 2 is predicted for thermoelectric
systems to be useful in many applications such as automobiles and shipboard use.

A renewed interest in recent years follows the availability of new fabrication
techniques, and the development of new theories predicting large increases in the

efﬁciencies might be possible through quantum conﬁnement.

2.2.1 Transport Theory: Optimizing Z T — the B factor

In 1993, Hicks and Dresselhaus [9] had shown that preparing material with
superlattice (SL) structure should enhance ZT. They also suggested a B parameter in
calculations to evaluate the effect of anisotropy on the ﬁgure of merit. This paper had
delivered new prospective in TE research and suggested that more investigation could be
done in searching for new TE materials.

The B parameter was ﬁrst introduced by Chasmar and Stratton [10]. For bulk

semiconductors, ZT is directly proportional to the B parameter and BBC, which is the

energy gap divided by the thermal energy. ZT = F(B, BEG), where B = llkT

1 2kg 3’2 k 2
B: .Im m m —B—-
73ﬂ2( h) j x y rent“. (17.)

 

14

where m is the effective mass of the carriers (electrons or holes) in the x, y, or z direction,

and ,ux is the carrier mobility along the transport direction, x, and y is the degeneracy of

the bands for the carriers (electrons or holes) in the material. A high B factor translates to
a high ﬁgure of merit, ZT.

This formula shows that highly anisotropic materials can be utilized to improve
efﬁciencies if the highest mobility direction (the x-direction) can be chosen to correspond
to the electrical current ﬂow direction, while the effective masses of the other two
directions are large. However, exploiting an anisotropic mass may run counter to attempts
to increase the B factor through the band degeneracy term, 7.

Large band degeneracy can be obtained in materials where the band minima
(conduction band) or the band maxima (valence band) is located in the Brillouin zone at
points of low symmetry. This condition is generally found in highly symmetric crystal
structures (i.e.: cubic) that contain a large number of atoms in the unit cell. Because of
the requirement for high symmetry in the crystal structure, highly anisotropic effective
masses of the carriers are not found in such materials. Thus attempts to increase the B
factor through the y term are generally in contrast with attempts to increase the B factor
through exploiting the anisotropic mass. For instance, BizTe3 has a band degeneracy of
y = 6 as ellipsoidal band extrema.

Thus, in order to increase the value of Z, large effective masses, high carrier
mobility and low lattice thermal conductivity is necessary. The value of ZT increases with
BEG until BEG ~ 10. So for good thermoelectric materials, the optimal value of BEG

should be about 10, i.e. semiconductors with an energy gap of 10 kT [11]. The energy

15

 

('0

EL

 

gap can be obtained from appropriate band structure calculations. Table 2.2 shows the

energy bandgap and the BEG values of some typical TE materials.

 

 

 

 

 

 

Materials Eg (eV) TM(K) Eg/kBTM
BizTe3 0.16 300 9.7
PbTe 0.5 650 8.9
AngTez 0.3 650 5.4
GeTe 0.4 700 6.6
Si-Ge 0.7 1 100 7.4

 

 

 

 

 

 

Table 2.2 Energy band gap of some good TE materials.

In the Boltzmann transport theory, thermopower can be expressed in the Mott

equation [12]

nszT dln 0(E)|
S = ' (18.)
3e dE IN,

 

0(E) is the electrical conductivity and it is a function of Fermi energy, Ef. For bulk
materials, if the electronic scattering is independent of energy, 0(E) is simply

proportional to the density of states (DOS) at E = E]. The Mott equation shows us that S
is a measure of the variation in 0(E) above and below the Fermi surface, speciﬁcally
through the derivative of the natural log of 0(E). Since the thermopower is a measure of
the asymmetry in electronic structure and scattering rates near the Fermi level, ﬁnding
materials with electrical conductivities that have strong asymmetrical energy dependence
in a small energy interval (a few kT) near Efis a way to approach high thermopower.
Subsequently, this has lead to searching for complex structures and composition

compounds. Furthermore, it has led to fabricating materials with 2D, 1D and 0D

16

structures due to the large value in dln 0( E )/dE as can be seen through the density of

states for each of these conditions (shown in Figure 2.6 below).

 

 

 

 

 

n (e) n (e) n (s) n (s)
301k (3D) 7 E Quantum WeIIED)E Quantum WireKD)E QranturnDot (0D) E

Figure 2.6 Density of states for different dimensionalities.

Another factor to achieve high ZT values is to have high mobility. As for a direct
gap semiconductor, the conduction and valence bands are at the same point in k—space,
this leads to small effective masses, thus high mobility. This is not desired for TB
materials, because small effective masses will reduce the B factor. Actually, an indirect
bandgap will be a better TE material.

We assume a quality factor, Qf and it is depended on the degeneracy, effective

masses and mobility,

Qf : ywlmxmymz [air

The best quality factor in semiconductors are achieved by silicon and germanium.
These two elements are nonpolar because all atoms are alike, so the bonding is purely

covalent. It is now important to introduce the concept of electronegativity, X, it is a

17

C

 

number which indicates an atom’s tendency to take an electron away from another atom
or to donate to the other atom.

In a binary solid composed of atoms A and B, an electronegativity difference of
this compound is AX = XA-XB. If this compound is a solid composed of cations and
anions, it means that the atoms wish to trade electrons. In this case the solid is ionic and
polar. Optical phonons tend to create long-range electric ﬁelds that scatter the electron
strongly. Polar scattering by phonon makes a signiﬁcant contribution to limiting the
mobility of electrons. Silicon and germanium have high mobility because they lack polar
scattering. They do have carriers scattered by optical phonons through other interactions,
such as the deformation potential.

Slack [13] indicated that, for any TE materials composed of two or more
elements, high mobility is achieved by having all of the atoms with similar values of
electronegativity. Then the value of AX is small and the bonding is largely covalent. The
small amount of ionic bonding means that polar scattering is weak and the mobilities
should be large. This is the case for bismuth telluride, which has <AX> = 0.30. Here XBi
=2.02 and X11, =2.40 and the average value of <AX> is found by averaging the number of

bonds of different types.

2.2.2 New Materials and Material Synthesis Techniques

Progress in material synthesis methods, especially the advent in structure
determination by x-ray diffraction [3], has been advanced in recent years and the new or
improved synthesis techniques allow much more complex materials to be studied for TB

applications. The polychalcogenide flux technique [14], which has been developed at

18

Michigan State University, has produced a large number of new and interesting TE
materials [15, 16].

As reducing material dimensions will enhance the ZT, various chemical or
physical deposition methods are developed to grow thin ﬁlm and very encouraging
results have been reported [17]. The combination of revised theories and the development
of fabrication methods has helped in deﬁning the path to search for higher efﬁciency TE

materials.

2.2.3 Modern Technologies

All the above factors have, in a way, made this a good time to look for better TE
materials, i.e. materials with high efﬁciency (high 27‘). If new TE materials with high
efﬁciency can be found and the fabrication cost is reasonable, the cooling industries will
not be the only party beneﬁting. Other industries like IC fabrication will enjoy the more
advanced active cooling since heat dissipation problem will be more signiﬁcant in the
coming century. To be able to use the waste heat from various sources including the

internal combustion engine will make the current automobiles more efﬁcient.

2.3 Enhancing ZT

In order to enhance the ZT of materials, either the Power Factor (S 20') of the
materials should be increased or the thermal conductivity should be reduced, or both
based on equation (1.). Increasing the Power Factor would seem like a better approach
since the thermopower has more inﬂuence upon the ZT (ZT oc SZ). However, for simple

materials, increasing thermopower will lead to a simultaneous decrease in the electrical

19

conductivity. An increase in the electrical conductivity will results in increase to the
electronic contribution in the thermal conductivity due to the Wiedeman-Franz (VVF) law.
Based on the WF law, for metal and metal alloys, the ratio of the thermal conductivity to
electrical conductivity is a constant. So it is difﬁcult to reduce one while increasing the
other. In semiconductors, the ratio of the thermal conductivity to electrical conductivity
has a higher value than the metals due to its lower electrical conductivity. However, Ioffe
[18] showed that alloying the semiconductors could reduce this ratio.

In Section 2.2.1, we have described how large asymmetry electronic structure
would give high thermopower based on transport theory. Generally if thermopower
increases, so does the resistivity. This can be seen in the Mott equation (equation 18)

when the substitution for E p/(kT) is made,

 

 

=-l%lll%~si+lnl’i:)i

while 0' = ’13 ,U , where n is the carrier concentration, e is the charge of electron, and

p. is the mobility. For traditional materials, the best compromise has been found in narrow
gap, heavily doped (~ 1019 /cm3) semiconductors. Figure 2.7 shows the variation of

Figure of Merit, ZT, with carrier concentration.

20

5‘5.)

16

11"
*1

 

 

 

 

 

 

 

Insulatorl Semiconductor I Metal

Figure 2.7 The variation of Figure of Merit ZT with carrier concentration

2.3.1 Minimizing Thermal Conductivity
Many researchers have also investigated avenues toward reducing the thermal
conductivity of materials. Thermal conductivity of a semiconductor has two main

components: the lattice (phonon) component (K1) and electronic component (Kc),

K = Kc + K, . The electronic thermal conductivity is IQ = Lo‘T, where L is the Lorentz

number, 0 is the electrical conductivity, and T is temperature. In semiconductors, the
Lorentz number L varies with the level of doping, reduced Fermi energy, 6 = Ep/kT,
reduced energy band gap Eg/kT and the particular carrier scattering mechanisms.

Since the electronic thermal conductivity varies with the electrical conductivity,
and in many semiconductors, K) is much greater than Kg, it will be more effective to
reduce the lattice contribution. These are some of the ways to approach minimizing K1:

1. The concept of “phonon glass electron crystal” (PGEC), which was suggested by

Slack [13], is supported by various experimental results [25, 26, 27, 29, 30]. A

proposed way for a material to exhibit PGEC behavior is for the material to

21

contain cages (or tunnels) in its crystal structure, in which atoms are allowed to
“rattle”. This situation produces a phonon damping effect that results in dramatic
reduction of the solid’s lattice thermal conductivity. It can be pictured as a loosely
bound atom with a large thermal parameter scatters phonons much more strongly
than electrons thus permitting a glass-like thermal conductivity to coexist with the
high electron mobilities found in a crystal [19].

. Another way is using compounds made from heavy elements such as antimony,
bismuth, tellurium or lead. This is because high atomic masses can reduce the
atomic vibrations frequencies (maintain in lower frequencies range, i.e. it has
lower energy). So this large non-periodic mass ﬂuctuation is introduced in the
crystal lattice to lower the thermal conductivity. Unfortunately, low vibration
frequencies also raise the electrical resistivity.

Selenium, tellurium and antimony have another advantages in TE: they have a
high value of polarizability. Compounds made with them have a large dielectric
constant, thus a long scattering time. This contributed to strong screening of
impurities, which increases the mobility. Atoms and ions with large atomic
number have low thermal conductivity and high dielectric constant.

. Having large number of atoms (N) in the unit cell or using alloys to prepare
materials with complex structure. Since large N lowers the fraction of vibrational
modes (phonons) that carry heat efﬁciently (the acoustic modes) to UN. Large
unit cell has larger lattice period and this will provide short mean free path-length

for the heat carrying phonons.

22

4. The disorder of random atomic substitution in an alloy can also scatter the

phonons, which reduces the thermal conductivity.

2.3.2 Properties of Good TE materials

Kanatzidis [19] has summarized that the best semiconductors for TB application

have the following characteristics:

1.

electronic bands near the Fermi level with many valleys preferably away
from the Brillouin zone boundaries. This requires high symmetry. (TS,
Tu)

elements with large atomic number and large spin-orbit coupling. (I K)
compositions with more than two elements (i.e. ternary, quaternary
compounds) (I K)

low average electronegativity difference between elements. (Tu)

large unit cell size. (i K)

energy gap equal to about 10 kT, where T is the operating temperature of

the TB. For room temp operation this should be 0 < Eg <0.3 eV. (TS)

2.4 What is being done at MSU and other places

One way to categorize the TB research area is by the material type: uniform bulk

materials and compositionally modulated ﬁlms. Bulk materials can often be fabricated in

large quantities using traditional methods such as direct solidiﬁcation from a melt. While

to produce modulated materials might require rather sophisticated process like chemical

vapor deposition. Both types of materials have their own difﬁculties in fabrication

23

process and in optimizing their TE properties. To establish the goals for materials made
at MSU and by the TE scientiﬁc community, Figure 2.8 shows some of the best TE

materials which are currently under investigation.

 

 

3 . +TlgBiTe6 +8181)
+Zn48b3 Mir p—TeAgGeSb
+PbTe 'r’rCeFemCow SI)“

2-5 E +ceqrezcusu1‘ ﬂ—YbﬂmCOJSbV
_ —t—TAGS-85 4!— Eu Co Sb Ge
0.42 4 11.37 0.5
2 ; +SiGe (n—type) +CsBi4Te6
t —°—Ba Ni Co su --n~-Bi Te
03 0(5 3% 12 2 3
’ +BizTeq/Sb2T61 SL

 

 

 

 

 

l

800
Temperature (K)

 

Figure 2.8 ZT of some best TE materials. (Images in this dissertation are presented in
color.)

Bulk materials (Other locations than MSU)
2.4.1 Bismuth Telluride

Bismuth telluride is the most important TE material and it has the best Z T at room
temperature. It is used in all devices that operate at or near to room temperature. This
included all present reﬁigeration devices. It is usually alloyed with szTeg, which has the
same crystal structure. Alloying with szTe3 can reduce the thermal conductivity to as

low as K = 1 W/mK. This low thermal conductivity is the main contribution in achieving

24

high ZT. Both n- and p-type materials have equally good properties. A single junction can
cool down to a temperature of about 212 K if T), = 300K. In practice, a single device
cools slightly less than this ideal limit. However, a device with four to ﬁve stages can
cool to well below 200K from room temperature.

Although, BizTe3 is often considered as a rhombohedric structure, it is easier to
represent this structure as a layered crystal with hexagonal symmetry. The layers are
stacked in a ﬁve-layer sequence (Te-Bi-Te-Bi-Te), which repeats itself; so two Te layers
are adjacent on the boundaries of these units. Figure 2.9 shows the crystal structure of

bismuth telluride.

 

Figure 2.9 The crystal structure of bismuth telluride (Small circle indicates the bismuth
atom and large circle indicates the tellurium atom).

Both conduction and valence bands have six equivalent minima. The ellipsoids

are canted away from symmetry axes. The energy bands are nonparabolic, and the

25

effective masses are temperature dependent. A transport model is complicated due to the
anisotropy and the nonparabolic, nonellipsoidal energy bands.

The energy band gap of pure BizTe3 is 0.16 eV [20], but this value increases when
alloyed with szTe3, and the device material has a gap of about 0.25 eV. Table 2.3 shows
the different composition of bismuth telluride alloys. The composition of the commercial
bismuth telluride alloys remain company secret as unknown doping is introduced to the

compounds to optimize the properties.

 

 

 

 

 

 

Material 2 (10‘3 K") 21‘ Type
Bi24Sb6gTe1428e6 3.2 0.96 p
Bio,5Sb1.5Te3,13 3.0 0.90 p
(szTe3)72(B12Te3)25(SbZSe3)3 3.4 1.02 p
Bi 1 ~75Sbr),25Te3_13 2.2 0.66 n
(szTe3)5(Bi2Te3)90(Sb28e3)5 3.2 0.96 n

 

 

 

 

 

 

Table 2.3 The best TE materials at T=300K

2.4.2 IV-VI Semiconductors (PbS, PbSe, and PbTe)

PbS, PbSe, and PbTe all have NaCl structure. PbTe is a good TE material around
700K so it is used in TE generators. PbTe is a semiconductor with a small energy gap. At
low temperature the gap is 0.19 eV. The gap increases with increasing temperature and
equals 0.31 eV at T = 300K [11]. The standard alloy is PbHSnxTe. The best alloy is
when x = 0.25, which has ZT > 1 near 800K. PbTe can be alloyed with a few tenths of
1% of sodium to make a p-type TE. Figure 2.10 shows the crystal structure of lead

telluride.

26

N

 

Figure 2.10 The crystal structure of lead telluride (Small circle indicates lead atom and
large circle indicates tellurium atom).

2.4.3 Si-Ge

Silicon germanium alloys were ﬁrst used in space in the SNAP-10A nuclear
reactor and have been the exclusive choice for radioisotope thermoelectric generators
launched by the US. since 1976. The operating temperature of the SiGe device can be up
to 1300K without signiﬁcant degradation. Satellites and space stations are often powered
by thermonuclear TE generators. A spherical radioactive core serves as a source of heat.
It is clad with layers of TE. Power is generated by the outward flow of heat. The inner
layer is the warmest and uses Si-Ge alloys. The next layer uses PbTe for n-type and
TAGS for p-types elements. B12T63 is used for the last layer, near 300K.

The best mixture is Sio,7Geo,3. The p and n-type SiGe can be produced by
introducing boron and phosphorus doping respectively. The best n-type SiGe has a ZT of
0.9 at around 1200K. The best p-type SiGe has lower ZT of 0.5 at 1200K. The thermal
expansion and mechanical strength considerations are critical to the design of the high

temperature devices. Therefore these properties of SiGe alloys are studied to reduce the

27

stresses occur in the devices [21]. The thermal expansion of SiGe alloys range from 4 to

snot/K in temperature 300-1400 K.

2.4.4 Bismuth Antimony

Bismuth has rhombohedral structure and is a semimetal with a carrier
concentration of about 10'8/cm'3. In pure form it has a small but equal number of
electrons and holes. A semimetal is due to band overlaps. The conduction band in one
part of the Brillouin zone overlaps the valence band in another part. There are six electron
ellipsoids, so the material is multivalley.

Alloying bismuth with group IV elements has introduced addition of donors or
acceptors and this is expected to modify the band structure of bismuth as well as change
the carrier concentration. However, the addition of group V elements can be expected to
modify the band structure without destroying the equality of electron and hole
concentration. Therefore, antimony is chosen due to it is similar to Bi and they form
complete range of solid solutions [22]. Alloying with antimony raises the chemical
potential and the hole pockets disappear. Then the material is n-type with a small energy
gap between the chemical potential in the electron band and the top of the valence band.
In this sense it becomes a narrow-gap semiconductor. The highest ZT is 0.6 and it is
reached with 10-15% of Sb alloying with Bi. There is also a magnetotherrnoelectric
effect. Some types of TE behavior are induced, or improved, by the application of
magnetic ﬁeld. In most cases, the application of magnetic ﬁeld can make modest

improvement in ZT for poor-TE materials but has no effect on materials that have high

28

ZT. Bi-Sb alloys are the exception to this general behavior. Magnetic ﬁelds can double

the value of ZT to where it can achieve ZT >1 [23] (See Figure 2.8).

2.4.5 Skutterudites

Skutterudites are one of the families of compounds that are of great interest for
thermoelectric applications. Skutterudite is a naturally occurring mineral, CoAs3, ﬁrst
found in Skutterud, Norway. The structure is cubic and contains 32 atoms per unit cubic
cell as shown in Figure 2.11. It poses an open, or cage-like, structure. When atoms are
placed into the interstitial voids, or cages, of these materials, the lattice thermal

conductivity can be substantially reduced compared to that of unﬁlled Skutterudites.

o Antimony
- Cobalt

 

 

 

§
§\

 

 

 

 

 

 

 

 

 

Ecr—
g h

 

 

 

 

 

"ii

 

 

 

 

 

 

 

 

 

 

‘r
1\
'\
\
\
\
\
\
\
I
I
l
'
I
is;

 

 

 

 

 

Figure 2.11 Schematic illustrating the unit cell of the unﬁlled Skutterudite crystal
structure [24].

29

Skutterudite materials meet the basic conditions for having high ZT values. These
include a large unit cell, heavy constituent atom masses, low electronegativity differences
between the constituent atoms, and large carrier mobilities [25]. Skutterudites can form
covalent structures with low coordination numbers for the constituent atoms and can thus
incorporate atoms in the relatively large voids formed in the lattice. The concept of
phonon-glass electron-single-crystal says that heavy atoms should be introduced into the
voids to lower the thermal conductivity of the sample. The basic families of these binary
compounds are CoP3, CoAs3, CoSb3 and etc. Ytterbium Skutterudites (ZT~1 at 600K) and
Eu-ﬁlled CoSb3-based Skutterudites (ZT > 1 at 700K) have been showed to have very

high ZI‘ [26, 27].

2.4.6 Clathrates

Clathrates are also called gas hydrates. Hydrates were discovered in 1810 by Sir
Humphrey Davy, and were considered to be a laboratory curiosity. In the 1930s clathrate
formation turned out to be a major problem, clogging pipelines during transportation of
gas under cold conditions. Clathrates are crystalline solids which look like ice, and which
occur when water molecules form a cage-like structure around smaller 'guest molecules'.
The most common guest molecules are methane, ethane, propane, isobutane, normal
butane, nitrogen, carbon dioxide and hydrogen sulﬁde, of which methane occurs most
abundantly in natural hydrates. In Clathrates, water crystallizes in the cubic system, rather
than in the hexagonal structure of normal ice. Several different hydrate structures are
known with one structure, known as Structure 1, being the most common. In this structure

the cages are arranged in body-centered packing; the unit cell contains 46 molecules of

30

water and up to eight molecules of methane [(CH.;). 5.75(H20)], but not all cages are
occupied [28].

The cage-like structure can also formed by group IV elements, for instance, X3E46
where E is a group IV element and X is an atom in the voids (cages), formed by E. Nolas
et a1. [29, 30] have shown reduction of thermal conductivity in polycrystalline Ge (ZT > 1
at > 700K) and Sn clathrates with the voids ﬁlled with alkali-metal atoms. These
materials have replaced the traditional alloy phonon scattering, which predominantly
scatters the highest frequency phonons, by a much lower frequency “rattle” scattering.
The highest frequency phonons have very low or zero group velocity and thus contribute
little to the total thermal conductivity. The low frequency phonons have the highest group
velocity and contribute most to thermal conductivity. This has explained why the
impurities, alkali-metal atoms in this case, produce such signiﬁcant reduction in thermal
conductivity. Moreover, the high Seebeck coefﬁcient and electrical conductivity of
clathrate materials have made them of growing interest as potential thermoelectric
materials.

The difference between Skutterudites and Clathrates systems is that in the
Skutterudites, the voids are present in the structure whether or not the “guest” atoms are

present. Figure 2.12 shows the crystal structure of Clathrates.

31

 

Figure 2.12 The crystal structure of Clathrates (Small circle indicates GaSi atom and large
circle indicates Ba atom).

2.4.7 Half-Heusler Alloys

Half-Heusler alloys are cubic materials (MgAgAs type) wih the general formula
MNiSn where M is a group IV transition metal (Ti, Zr or Hf). Half- Heusler is formed by
removing the Ni atoms on one of the two Ni sublattices of the full Heusler alloys MNiZSn
and replacing them by an ordered lattice of vacancies.

Full Heusler alloys are metals but half-Heuslers alloys are intermetallics. It has a
small gap in the density of states and a substantially semiconducting character. These
materials exhibit a high negative thermopower (-40 to -250 [IV/K) and low electrical
resistivity values (0.1-8 m 52cm). However, the thermal conductivity is rather high
(~10 W/mK). Transport properties of Ti-based half-Heusler compounds ( TiNiSnHbe)
are investigated by Tritt’s group [31]. It showed that by introducing very small amount of

Sb doping to TiNiSn compounds, the electrical resisitivity can be reduced signiﬁcantly.

32

Uher et a1. [32] have shown that the transport properties of the half-Heusler compounds
can be manipulated by annealing, isostructural alloying and doping. The thermal
conductivity of some half-Heusler compounds can be reduced through these methods.

Figure 2.13 shows the crystal structure of half-heusler alloy.

ONi

 

Figure 2.13 The crystal structure of Half-Heusler alloy.

2.4.8 TAGS

In the early 19608, lead telluride, PbTe, was the standard material for TB
application in space power supplies at high temperature. The n-type PbTe has very good

stability and mechanical properties but the p-type PbTe has a number of weaknesses. This

33

has led to various studies in different doping on PbTe in order to improve the p-type
materials. This is how TAGS materials were discovered.

AngTez is a good TE by itself because it has low thermal conductivity. This is
caused by silver ion disordering, as occurs in AgI and similar compounds. These four
elements produce an excellent p-type TE at high temperature. They are usually
represented as GeTe alloyed with AngTez. The best TE materials have 10—20% of
AngTez.

Basic TAGS-type materials have general formula of (AngTe2)1.,,(GeTe)x where
T is tellurium, A is antimony, G is germanium and S is silver. Two of the famous
materials are TAGS-80 and TAGS-85 [33], 80% and 85% of GeTe respectively.
Actually, TAGS-80 (ZT~1.85 at 800K) exhibits better TE properties than TAGS—85
(ZT~1.35 at 700K) but the mechanical and stability problems of this composition has

made TAGS-85 a preferable choice.

New materials in MSU
2.4.9 Chalcogenides - CsBiaTeg

One of the successful cases in creating new materials through the
polychalcogenide ﬂux technique is CSBI4T66. Since B-KzBigSelg has shown promising
TE properties and low thermal conductivity [34], there was an attempt to make the Te
analog of this material with Cs. CsBiaTe6 was formed instead of the expected CSzB13T613
and it exhibits a new structure.

The alkali metals (e. g. K and Cs) play an important role in lowering the thermal

conductivity. In Figure 2.14, Cs’r ions lie between the [Bi4Te6] layer and they undergo

34

“rattling” to reduce the thermal conductivity. When doped appropriately, this material
exhibits a high ZT below room temperature. CsBi4Te6 doped with various percentages of
SbI3 have shown some trend in power factor measurement. The sample doped with
0.05% of Sb13 has the maximum ZT of about 0.8 at 225 K [35]. This material is air and
water stable and melts without decomposition at 545 C. The crystals grow with long
needle-like morphology. The direction of rapid growth along the needle axis is also the

direction of the maximum TE performance.

 

 

 

Q
O 0
O . . o v il ‘v
.3 re a ’ ,
e 9 8 e 9 a.
O E. g E. 3. “ ‘3 9
9 ’ g .1-
“.ﬁ. - ' i J. r ‘ cs ‘iﬁﬂ‘ a"
wsersggwwgrhi'ab he} 3 nan-riﬂ-
° “ I 'g-wg— '
9
%X
Z

Figure 2.14 The crystal structure of CsBi4Te6 (Small gray circle indicates tellurium atom,
small black circle indicates bismuth atom and large circle indicates Cs atom)

2.4.10 Cubic - AngBi03 (Q = S, Se, Te)

The AngBng class of compounds and their solid solution members are related to
the NaCl structure type (or cubic structure), where Ag, Pb and Bi atoms are statistically
disordered on the Na site and Q atoms occupy the Cl site [36]. These compounds were
synthesized by combining the elements in appropriate ratio and heating under static

vacuum at high temperature for days.

35

 

 

 

These materials are narrow band gap semiconductors with band gaps in the range
of 0.6 to 0.28 eV. Their electrical conductivity is in the range of 70-400 S/cm,
thermopower is from —40 to -160 uV/K (n-type) and they have extremely low thermal
conductivity (<1.3 W/mK). The compounds AngB1T63, AngBiSe3 and
AngBiTeusSeozs and AngBiTezse were investigated.

More recently, the TB properties of this type of material have been enhanced and

some of the measurement results are shown in the preliminary section.

Modulated materials
2.4.11 Quantum Well (Superlattice Structure)

When bulk TE materials seem to reach its limit in optimizing ZT, revised
transport theory as stated in section 2.2.1 has suggested fabrication of 2D and 1D TE
materials. A breakthrough was reached [17] when a p-type BizTe3/Sb2Te3 SL structure
with ZT of 2.4 was fabricated and a temperature gradient of 32.2 K was measured from
the device made by this material. The enhancement is achieved by controlling the
transport of phonons and electrons in the SL. The SL structures are produced with
various layer thickness, some are as small as 10 A, using a low-temperature growth
chemical vapor deposition (CVD) process [37, 38]. The thickness of the heterojunction
layers inﬂuences the mobility of the samples. Materials with similar cross and in-plane
mobilities as well as low thermal conductivity are chosen and ZT values were measured
in devices using the Harman technique.

A QW is composed of a semiconductor with a narrow band gap sandwiched

between two materials with larger band gaps. This conﬁguration is called a type I

36

quantum well. Electrons and holes have their lowest energy states in the middle material
and are usually conﬁned to this region. Conducting particles such as electrons or holes
are created in semiconductors by deliberately adding impurities that donate these carriers.
In bulk 3D materials, the impurities scatter the carriers and impede their motion. In a
QW, one can put the impurities in the barrier materials, so the conducting layer is free of
impurities. Then the carriers in this layer have no impurities to limit their mobility. There
are still phonons, but they are ineffective scatterers at low temperatures. This
arrangement of impurities is called modulation doping.

Very high mobilities can be achieved in QW’s by modulation doping. The hope is
that a similar enhancement can be achieved for the Seebeck coefﬁcient. However, in
devices one will need to move bulk heat, which means that a multiple QW structure is
desired. The fabrication cost of such devices is much higher than for bulk homogeneous

materials and it is a challenge to fabricate homogenous QW structures.

2.4.12 Quantum Dots

Quantum dot superlattice (QDSL) structures have been investigated for
application in thermoelectrics. This structure has a delta-function distribution of density
of states and discrete energy levels due to three-dimensional quantum conﬁnements. A
test device that is made by PbSeTe/PbTe QDSL (grown by molecular beam epitaxy
(MBE)) showed very large temperature gradients across the device [39]. This enhanced
TE device performance and is believed to be almost entirely due to a high density of
quantum nanodots with essentially 100% PbSe composition embedded in a 3D slab

matrix of PbTe. The maximum temperature gradient for this device is 43.7 K. It is higher

37

than the previous reported value of 32.2 K for similar single one leg BizTe3/Sb2Te3 SL
[17] (cross-plane current ﬂow of SL and no QD) for an equivalent hot junction

temperature.

38

‘

 

C l

 

2.5 Techniques of Characterization

Transport measurement of TE materials has been the main focus in the primary
stage of my research. It is important to know the various properties of TE materials for
they will tell us how good such materials are in TE performance, and help us to
understand the materials to a level that we can improve upon them and develop them into
devices.

After identifying materials with good TE properties, the investigation will be
brought to the next stage — TE module/prototype fabrication.

Some of the characterization techniques will be reviewed followed by the set-up

of the measurement system constructed for this research.

2.5.1 For Materials
Various techniques have been developed to measure the electrical and thermal
properties of materials. Studying the advantages and disadvantages of these methods

helps to design a better measurement system.

2.5.1.1 Steady-State Technique

The Steady-State method [40] is widely used for thermal conductivity
measurements at low temperatures where the heat radiated from the sample is much
smaller than the heat transported through the sample. Figure 2.15 shows the mounting

conﬁguration of this method.

39

 

 

 

Heat Sink

 

 

 

T1

 

NIX\

 

// T2

 

 

 

 

 

Source T”

 

Figure 2.15 Stead-State Technique.

If all the heat supplied to the source Q (= aq/BT) is conducted along a sample of
uniform cross section A and distance L between two thermocouples, then at any point, the

thermal conductivity,

Q - 0L
K (T) = —— (20.)
A . BT
and the mean conductivity between points 1 and 2 separated by a distance L is
Q - L
K(T) = — (21.)

A - AT
where AT is Tz-Tl
If the sample has high electrical conductivity, then the length of the sample should
be sufﬁciently greater than the diameter. This helps to create a larger temperature
gradient across the sample. For low conductivity materials, equilibrium times become

very long so l/A ratio should be small.

40

The disadvantage of this technique is it requires a relatively long time for
temperature stabilization and this long waiting time might also affect the precision of the

measurement.

2.5.1.2 Harman Technique

The most common methods to measure thermal conductivity are the comparison
method [41] and the absolute method [42]. In both methods, it is difﬁcult to eliminate
unnecessary heat transfer to the sample, especially in the case of small sample of low
thermal conductivity. Therefore, Harman technique is introduced attempt to solve this
problem.

Harman Technique [43] is a measurement of thermal conductivity by utilization
of the Peltier effect. This measurement allows calculation of thermopower, thermal
conductivity and electrical resistivity. A special feature of this method is that ZT is given
in terms of the ratio of two voltages. Even though this method has been tested at 300K
only, it should be able to be tested on low thermal conductivity materials of small
dimension up to 1000K. The theory of this measurement is explained below, followed by
descriptions of the experimental methods used.

1. Theory

41

¥
’—

=U2
‘ go >———":. 4

Ta Ta

 

 

 

 

(m) I I (m)

 

Figure 2.16 Cylindrical sample connecting to a circuit.

The basic circuit for this technique is in Figure 2.16. With direct current in the
circuit, three principal phenomena will occur: Peltier effect, Joule heating and thermal
conduction. Before the current is applied, it is assumed that there is no temperature
gradient across the sample. By applying a current, I, through the sample, a temperature
gradient is induced as caused by the Peltier heating at one end of the sample, and a
subsequent Peltier cooling at the other end of the sample. Assuming it is a p-type
material, the current is carrying heat from the cold junction (2 = - U2) at temperature TC
to the hot junction (2 = U2) at temperature Th. The lead wires are maintained at the
ambient temperature Ta.

The formal solution of this measurement can be derived in two parts. In the ﬁrst
part, the temperature distribution in a homogeneous cylinder satisfying appropriate
boundary conditions is derived. In the second part, the energy balance at each junction (2
= i U2) is obtained, and the resulting equations combined to obtain the desired relation

between the thermoelectric quantities.

i. Derivation of the temperature distribution

The continuity equation for the total energy ﬂux, u, in steady-state is

42

V- II =0 (22.)

Energy ﬂux is the rate at which energy passes through a ﬁxed boundary per unit
cross sectional area per unit time. The common unit is J/(mzs). From the consideration of

irreversible thermodynamics, u is given for isotropic materials by
u = (0LT+A)j- KVT (23.)

Otis the thermopower, j is the current density, K is the thermal conductivity and the

 

gradient of electrochemical potential, A, is
V A=-jp-0t VT (24.)
p is the electrical resistivity. If substituting (20) and (21) in (19) yields
jzp-Tj -V or = V - («V T) (25.)
where V - j = 0, assuming charge concentration is stationary.

Under the conditions that the gradients of or, K, p are small

V 2T =-j2p/K (26.)
Equation 23 is the heat equation with uniform Joule heating in the sample, assuming the
resistivity is independent of temperature.

In order to obtain a solution of the heat equation, we next consider the boundary
conditions of this circuit. The sample is in right circular cylindrical shape with length L,
radius a, and the lead-in wires are assumed to have sufﬁciently small cross section so that
radiation loss may be neglected. The radiation ﬂux oe(T‘-Ta4) is approximate to
408T 3(T—Ta) where o is the Stefan-Boltzmann constant, e is the surface emissivity and

T = (T).+Tc)/2. The energy ﬂux in the neighborhood of the junction is assumed parallel to

the cylindrical axis. This yields the following boundary conditions:

43

T(r,—L/2) = T, (27.)

 

 

 

 

T(r, L/ 2) = T, (28.)
aT(a, z)
‘ “[7] = hind. Z) 7' Ta] (29.)
in cylindrical coordinate gives
air 1 8T air
V2T= +— — + =—'2 /K
(0%] rt») (fizz) J ,0 (30')
By applying the boundary conditions (27-29) to the solution of equation 23, one obtains
T(r, z) — Ta
__ °° 2y T, —Tc sinh/InZ +(T—T _ jzp cosh/Inz
,z, (zine)2 + y2 2 sinh 2,, /2 “ 2,} cosh 2,,L/ 2 (31.)

10(2"r)+j2pa [[1 r2]+1

Joana) 2h 2 -27

where h = 4057”, y: ha/Kand 2,. is a solution of mam/La): mam).
In order that the approximation be accurate to 1%, it is necessary for T and T0 not

to deviate from T(avg) by more than 1/3 of 1%.

ii. Energy Balance at the Junctions

The total energy enters the sample at z = -U2, is the sum of the energy current

entering the sample and the radiation from the face of the sample. Thus the total energy,

Us. is

Use = 277Ius(r,—L/2)rdr+7za2h(Tc —Ta) (3,)
0

Combining equations 31 and 32 will result in equation 33, detail derivation can be found

in Harman [43],

1(a, —am)T = (Km + K,)(T,, —T,)
+m(a+ L/3)h(Th -TC)/2+ IZARC

(
— [(1/24) + (L2 /180a2) + (a2 /48L2) - 2aA/L][7ra2h(Th —Tc)]2
KSAT

 

In equation 33, if the thermopower of the sample and lead wires, as well as the
thermal conductivity of the lead wire are known. Thermal conductivity of the sample can
be determined (calculated) from this equation, assuming we can measure the values of
current, cold and hot temperature, dimension and emissivity.

Actually the emissivity can be obtained from equation 33 through measuring two
samples with identical properties but different dimensions.

The factor involving contact resistance is eliminated experimentally by carrying

out measurements for both directions of current.

11. Experimental Method
i. Measurement of Thermopower

Figure 2.16 shows material (m) in contact with sample (s). Point 1 and 4 are at the
ambient temperature Ta and points 2 and 3 are at the temperature Tc and T). respectively.

The thermopower of the sample (3) relative to the material (m) is

45

33.)

 

 

Si

SE

ii.

the

[he

V4 " V1

a — a = lim ——
5 ’" (Th—Tc)—)0 Th _ T (34')
C
If the material (m) is chromel, then equation 30 becomes
V V _
as = -—a— = i ii + achr (35)
AT AT
If the material (m) is alumel, then equation 30 becomes
a, _ Va _ Var-alt: +
s — _ — aalu (36.)
AT AT
Va is the absolute Seebeck potential of the sample and Vow," is the thermal emf of a

chromel-sample-chromel circuit. If the material (m) is alumel, then let the notation
changes from ‘chr’ to ‘alu’. Since these materials are used for thermocouples, their
absolute thermopowers can be found from the literature. Thus, the thermopower of the
sample can be easily obtained from measuring the voltage and temperature across the

sample.

ii. Measurement of electrical resistivity and contact resistance

The measurement requires 8 wires attached to the sample as shown in Figure 2.17
The cylindrical sample is nickel plated on both ends and soldered to a chromel-alumel
thermocouple and a copper current lead on each end. Two alumel wires are attached to

the sample as voltage leads with a spacing of L’.

46

 

CO

13;

V0}

 

 

 

 

 

 

 

 

 

Figure 2.17. Harman technique circuit.

If the potential difference between the ends of the sample is Vp+ Vc and the

between points A and B is Vp’ when applying a current I, then the resistivity of the

sample can be determined,

Vém 2
p :
IL'
where a is the radius of the sample.
The total contact resistance is
: Vp + VC _ pL
C I naz

where L is the length of the sample.

iii. Measurement of thermopower and thermal conductivity

(37.)

(38.)

With the same conﬁguration of the sample, thermopower and thermal

conductivity can be obtained by addition of voltage method.

When a current is applying across the sample, a potential VT exists. This potential

is the sum of the IR drop due to sample resistance, the contact resistance and the Seebeck

voltage of the sample and the lead wires.

47

AI

sample is

Where V;
current 2
directior
mm"ersi
the total

dissimil.

Combi n:

Equal] 0n

At steady-state, the total voltage across the two alumel leads on the ends of the

sample is determined by the usual dc null method in the two current directions,

+ V, (alu)* = +Vp + Vc + VH,“ + V," (alu) (39,)
- Vr (aluY = -Vp - V. - Vast. + Va. (01“) (40.)

The total voltage across the chromel leads in the two current directions is

+ V7 (Chr)+ = +Vp + Vc + Vwchr + V," (Chr) (41.)
— V]r (chr)‘ = —Vp — VC - Va“, + V," (chr) (42,)

where V1(alu)+ is the total dc voltage across the two alumel leads in the plus direction of
current and VT (alu)' is the total dc voltage across the two alumel leads in the minus
direction of current; so on for chromel leads. V)” is a voltage across the sample which is
irreversible with current and hence temperature gradient. It is less than a few percent of
the total voltage and is believed to be due to unequal Joule heating in the vicinity of two
dissimilar material junctions.

Equalize equations 35 and 36 gives

 

 

Va— I — Va- hr
achr _ aalu : chr-alu : auAT C (43.)
Combining equations 39 and 40 to obtain
VT (alu)+ + V, (alu)'
Va—alu : Va — Valu : 2 _ (Vp + Vc) (44.)
Equation 44 becomes

48

 

W

«I.-

the

=i VT(alu)+ +VT (alu)"

 

 

Va 2 — (Vp + VC) + aamAT (45.)
Similarly,
V (chr)+ +V (chr)’
Va 2 It T 2 T — (Vp + VC) + achrAT (46)

The thermopower of the sample is thus

 

 

Va
a =—" 47
‘ AT ‘ °’
and the thermal conductivity is
_ asIT L
K- AT .rtaz (48')

where T is the average temperature. As we know Z: Ci/Kp, and by substituting the

equations 38, 47 and 48, the ﬁgure of merit Z can be determined from a ratio of two

 

voltages,
Z - Va
_ — (49.)
vp T
2.5.1.3 Pulse Technique

Pulse technique is a method for measurement of thermoelectric power and
thermal conductivity simultaneously at low temperatures [44]. It is very similar to the

steady-state technique but doesn’t require a long waiting time. This is an AC method

49

used to avoid rapid temperature drift; the heat current, which is used to create a thermal
gradient across the sample, is pulsed with a square wave.

This method will produce piecewise exponential signals for the temperature
gradient and voltage across the sample. These signals are used to obtain the thermopower

and thermal conductivity of sample.

 

 

 

 

 

 

 

Cu Heat Source
Au-Fe Chrorml
"DC .
Mangamn
Heater
Sarrple
Contact Pins
\+_;>a éggo

 

 

 

 

 

Figure 2.18 Pulse Technique experimental set-up.

The high speed of this technique also allows the accumulation of a high density of
data points. For long pulse times, this method reaches steady-state where it is the same as
the technique described in section 2.5.1.1. For shorter pulse times this method does not
reach steady-state temperature gradient and the thermal conductivity of the sample should
be extracted from the data as discussed below.

Figure 2.18 has shown the measurement set—up of the pulse technique, a sample
with thermal conductance, K, is sandwiched between a heat source with T1( t) and a heat
bath with Tom. When a current is applied to the sample, the heat equation can be written

as

50

 

 

Q' = C(T.)T'1 = 1200120) -- KIT. —T.) (50.)

where Q is the amount of heat per unit time accumulated at the heat source, C( T) ) is the
heat capacity of the heat source and R( T1) is the resistance of the heater. The amount of
heat is balanced between the current dissipated by the heater and heat conducted by the
sample.

The temperature difference, AT = ( T1 —T0), is usually made small with respect to
the mean temperature, T = (T) +To)/2, so the thermal conductance can be considered as a
function of mean temperature. If the bath temperature stays constant and a constant
current la is applied through the heater, after a sufﬁcient long time, a steady state is
reached and thus T1 = 0 and the thermal conductance becomes

12R(T,)

K(T)= T _T
I 0

(51.)

If the bath temperature is let to drift slowly, and a periodic square-wave current

with period 2 is applied thought the resistance,

{0 if t mod 22'<7'
1(t)=

10 if t mod 2722' (52')

then the system will no longer reach steady state and the temperature T) of the heat
source will also be an oscillating function of time. Figure 2.19 shows the periodic
waveform of the current supplied to the sample. The condition t mod 21: gives the
remainder after t is divided by 21:. The mathematics equations that will be performed now

will further explain how the technique is used to obtain the conductance K as a function

51

 

 

of temperature from the amplitude of the measured signal T), if the C( T) and R( T) are

known. The heat equation needed to be solved in this case.

I

10 ——

 

 

 

 

 

 

 

 

‘L' 21: 3t 4': t

Figure 2.19 The periodic waveform of the heater current.

Some assumptions needed to be made to solve the heat equation. Since AT is
small, we can approximate T1 to To, and we can assume C( T), R( T) and K( T) to be
constant. To can be considered to be constant as far as the bath temperature drift slowly. If
the drift is slow compared to the time scale that is used to modulate the current, then it is
possible to solve the heat equation.

Equation 50 becomes

- R K
TI :EIZ(I)_E(T1_T0) (53.)
Subtracting both sides by To , gives
. . R K .
7]"To=Elz(t)-Eai—T0)—To (54.)

Equation 54 can be written as

52

 

 

d K R -
— AT +—AT=—12t—Tt
dt( ) C C () ()0

Equation 55 is a linear ﬁrst order differential equation and can be expressed as
d K
——(AT) + —AT 2 f(t)
dz C
where
R .
fa) = E12(t) — T0

If we let f( t) = 0, equation 56 becomes

1(AT) = —£AT
dt C

rearrange equation 58 gives

L(AT) =—£dt
AT C

Integrating both sides in equation 59 gives
K K
ln(AT) = —_[—dt + cl = ———-t +cl
C C

01'

K K
——t+c1 ——I
AT=e C =c0nst.*e C

where C) is the integration constant and const.= ec‘ . Combining equation 61 and 56

gives

K K K
§;{ATeC ]=ec (%(AT)+%AT)=eC f(t)

53

(55.)

(56.)

(57.)

(58.)

(59.)

(60.)

(61.)

(62.)

Integrating equation 62 gives

£1 £1 5., R 2 .
C zjec f(t)dt=_[ec (El (t)-To(t)]dt (63.)

K
- t—egtj‘ — 221 (t)dt — [C e To (t)dt + c2 (6.”
If we let I = t), then
1‘ —r,) R ICEU-t') . —fttl
AT = We -——-12(t)dt- :Ie T0(t)dt + cze (65.)
0 0
The second term in equation 65 can be approximated by
I] K

I K K

‘ —(I—-t,). C - —("’I) C ° ‘ _—II

Iec Tamra-ERG)“ =—' T0(t1)_T0(0)e C (66.)
0

o
if we assume To varies very slowly with time and it can be considered as a constant but

still include the limits of the integration (an adiabatic approximation). The ﬁrst term in

equation 65 then becomes

K("‘ ‘1)

:IeCU—ti)512t()dt=—:%tj-O-e dr+j1§ eC dt (67.)
0

0

37 5(1—11) 47 2 fin-I.)
+IO-ec dt+IIOeC dt+...
31

I

K
—(I"11)

+ J12(t,)-eC dt

lei

 

54

I . . . . .
[i] is the integer part of tl/Z'and I) 18 In term of 7'. For t) mod 27'< 7', equation 67
T

becomes
Rt1 50*!) RI' Jim-I)
-—jeC ‘12(r)dr=_[ 9‘ 12mm
C 0 C 0
K K K K
R C —(t -21) —(I-r) —(I —4r) ———(I-3r)
=EEI§ ‘3 Cl ‘6 C! +6 l -e Cl +... (68.)

. I
Since t1 = II modr + [4} {This equation can be understood better by giving an example,
I

la ’1 = 235 and 7': 5s, so 23 =3 + 47' }, taking the factor (t, mod 2) out from the right side

of equation gives

K

Rtl T—(tl—t) 2
—Ie C I (t)dt=
C 0

R _.... . ail-2) an). Ali-lei

— Ice 6
(69.)

55

T .

In equation 70, the alternating addition and subtraction terms will cancel each other and

only the last two terms will remain. Multiplying the numerator and denominator by

K
—-——r
1+ e C will give

 

 

 

 

( .5 .5, )
l—e C 1+e C
R:1 l(’;-) R lalmod r)
—[e C '12(r)dr=—I§e C K
C0 K 1+e—Er (71.)
k /
R'1 450.4) 2 R 2 Jciulmod r) l—eCCzr
EIB I “XII—E108 T
0 1+e C
K I,
— - 7 72.
R 2 imam n l—e CH ( ’
= 0 if
1+e C

For t) mod 272 7', equation 67 becomes

’1 ill-t
Eje 6‘ )12(t)dt
C0

56

a.) are)

taking the factor I) mod Tout from the right side of equation 73 gives

Eje%("_”12(t)dt :21; 1+e—CWd ”
0
e—zla—zlle-i-la-l)Malia—irieaia-it)--.

In equation 74, the alternating addition and subtraction terms will cancel each other and

only the last two terms will remain. Multiplying the numerator and denominator with

if
1+e C will give

 

K In 2'
IT,l T—EUITH 2 R 2 ”Lé'UImOd 7) 1+8 (:[1]
Etie I (tﬂt—EIO l—e 1 —%¢- (75.)
+8

Combining equations 66, 72 and 75 and substituting into equation 65 gives

57

T

—K! C . . —Kr
AT=AT(0)e C _K To(t)—T0(0)e C

“H
K —— r
—(tmod7') l—e C T

e C ——'—

 

K if tmod27'<7
———7'
1+e C
+513. (76.)
K K _:[L],
—<modr) 1+ ’ .
—e C! e_K 1ftmod2727'
1+e—CT

K

The solution has a saw-tooth waveform as shown in Figure 2.20.

 

 

Figure 2.20 The waveform of the temperature gradient across the sample.

The maxima occur at t = n“: with n even and the minima with n odd. If t = n: then

7 mod 1: = 0 and 7[t/1:] = t. The temperature gradient is obtained by taking the difference

between the maximum and minimum curves,

58

 

R 1— C 1+ C
Army—E13 e K —1 e
-(-) -(—)
1+ 2 C T 1+ 6 C T
R (77.)
K 2'
= —15 tanh —
K 2C
Rewrite the equation will let us obtain the thermal conductance
K = R I: tanh(ﬂ) (78.)
Ar”, 26

K can be solved by numerical iteration if all the other parameters are known as a function

temperature. If the heat capacity, C, is unknown, then a similar derivation from equation

will obtain

 

 

C _ 2R I 2 1
(3T / at) pp 0 -(£)r (79')
1+ e C
For the case when 1: is much greater than the system relaxation time C/K, then
tanh(K‘r/2C) ~ 1, so the thermal conductance becomes
R 2
K = AT 10 (80.)
pp

This is the same result one achieves for the steady-state technique described in section

2.5.1.1.

2.5.1.4 High Temperature Transport Probe

This system is developed to measure the power factor of material as a function of

temperature over a range of 80-7OOK [45]. The system is considered as a high

59

temperature probe, consists of two stainless steel half cylinders which are bolted together
and separated by a thin sheet of machinable ceramic, Macor. A 100 Watt heater is
inserted into each half cylinder. Each heater is independently controlled to establish

T +AT/2 and T—AT/Z. On the top faces of the half-cylinders are thick quartz substrates
which are attached with silver paint. The sample is mounted laterally across the surfaces
of the substrates with silver paint. Type K thermocouples are attached at each end of the
sample while two platinum wires are attached just inside each of the sample ends. Figure

2.21 shows the sample stage of this system.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cross-Sectional View
High Terrperatme Pmbe
TOP “cw \I-m
H _ Shield
Quartz A
a “ ° Substrates
Stainless Steel
Half-Cylinders
“2 \Camidge
/ Haters
_ Wires Insulator
\
Cerarrn'c Multibore
Tubes
('IC, current and heater leads)
Base

 

 

 

Figure 2.21 High Temperature Transport Probe Sample Stage.

A possible disadvantage of this sample conﬁguration, is that the sample is

mounted laterally on the surface, where for thicker samples, an additional temperature

60

gradient can occur from the top surface of the sample to the bottom of the sample. This

might affect the accuracy of the measurement.

2.5.1.5 Parallel Thermal Conductance (PTC) Technique

This method is also a variation of steady-state technique [46]. It is developed in
order to measure the thermal conductivity of small samples. Most other measurement
technique requires mounting a heater, a differential thermocouple (or two single ended
thermocouples) to the sample. If the sample is very small, the mounting job becomes
difﬁcult and if the sample is fragile, it might be too weak to support the weight of the
heater.

In the PTC method, a sample holder or stage is made to support the small sample.
A heater and thermocouples are mounted on the support post and the sample is simply
attached to the post with paste. This method consists of three steps. Step1 is to measure
the preliminary thermal conductance of the sample holder itself, which determines the
base line or background thermal conduction and losses associated with the sample stage.
Step 2 is to measure the thermal conductance of the whole system after attaching the
sample to the sample stage. The parallel thermal conductance can be obtained after
subtracting the value of Step 2 from Step 1. The last step is to disconnect the sample from
the base (but not from the sample holder hat) and measure the thermal conductance. If we
subtract this value from step 1, we can determine the radiation losses due to the sample
itself. A 0.5 correction factor is introduced for the estimated radiation losses. Figure 2.22

shows the sample conﬁguration of PFC technique.

61

 

Heater /§'

Differential 3 /\
'Iherrmcouple Post Sample

K
I %

Figure 2.22 Sample holder with sample.

 

 

 

 

 

 

 

 

 

 

 

 

 

2.5.1.6 Low-Temperature 4-sample Thermoelectric Measurement System

This automated system is a well-established low-temperature (80-400K)
thermoelectric measurement system that is developed in our lab [47]. The system is
capable to measure the thermopower, electrical conductivity and thermal conductivity of
four samples simultaneously.

The measurement method and sample conﬁguration (shown in Figure 2.23) are
variation of the pulse technique. A copper — constantan differential thermocouple is used
for measuring the temperature gradient, and thermally connected to the sample using GE
varnish. A surface mount resistor (470 S2) is used to periodically heat one end of the
sample to establish a temperature gradient of < 1K between the thermocouples on the
sample. Two copper wires act as voltage leads and are soldered to the sample with
indium. A ten-minute period (2.2 cycle) of oscillation was chosen and the temperature
gradient was observed to reach steady state within half of the period, as shown in

Figure 2.24. In this condition, the peak-to-peak value was used to determine the

62

temperature gradient across the sample, and along with the measured power supplied to

the heater, and the sample dimensions, the thermal conductivity was found.

I

HT Heater

J W

 
 

 

 

 

 

 

Figure 2.23 Sample conﬁguration in 4-samp1e system.

This pulse technique also gives the opportunity to determine the thermopower by
simultaneously measuring the voltage, W, and ﬁnding the slope of the (W vs. dT curve as

shown in Figure 2.25. The ﬁnal measurement of electrical conductivity is measured by

both ac and dc techniques.

The 4-sample system in our lab is used in the steady state mode where the

temperature gradient reaches steady state during the current pulse.

63

l> sim_plot1

E'e_§¢‘ Wit EXCELEEQE lisbﬁ_
inhabit ‘ Font

 

 

 

 

 

Figure 2.25 The plot of dV vs. dT curve of two samples.

64

2.5.2 For Modules

Another way to determine the ﬁgure of merit of materials is to characterize a
module that is made up of these materials. The advantage of such method is that the
measurement includes all the contact resistances of the module and it tells the actual
performance of the module as a device. Since the contact resistances are included in the
overall device performance, there is signiﬁcant effort will be made to investigate

reducing the contact resistances to these materials.

2.5.2.1 Thermal Conductance Measurement

This is a method for determining the ZT from thermal conductance measurements
on a thermoelement that is connected in parallel with a metallic wire [48].

The thermal conductance K of a sample, in the absence of an electric ﬁeld (E = O)

is KE=0 and under zero current ﬂow (I = 0) is K1=o, it can be found that
KEzo : K1=o(1+ ZT) (81.)

where z is the ﬁgure of merit of a single element.

 

\

 

 

 

 

 

Figure 2.26 Short circuited TE module with p and n-legs.

65

This concept can also be applied to a module. Figure 2.26 shows short circuit in a
module where the voltage is zero, i.e. the electric ﬁeld is zero. Equation 14 can be also

expressed as
Q = KAT + SpnThI — % 12R (8;)
The short circuit heat flow is

Qshort = KpnAT + SpnThI _ % IzRModule (83-)

where RModuk is the resistance of the p and n-legs plus the contact resistance.

\

 

 

 

 

Figure 2.27 Open circuited TE module with p and n-legs.

Figure 2.27 shows an open circuit module where there is no current flow and the

heat flow from the top to the bottom of the module is
Qapen = K ”AT (84.)

When a temperature gradient is created across the module, there will be a flow of
current. It will lead to heat transfer through Peltier effect. The current is equal to
(5,...)AT/(Rmm) and the Peltier heat ﬂow is (5,... fur/(12mm. ). Substitute I in equation

83 with (SpnMT/(Rmoduk). The short circuit equation is then

66

52 52
&'£ = KP" +—£n—-[Th —1AT) = Kpn +—‘En_TM (85.)
AT R 2 Rmodule

mod ule

where TM is the mean temperature. Comparing equations 84 and 85 gives

Kpn.E=0 : K (1+ ZT) (86.)

pn.l=0
or

K*=(KP+K,,)(1+ZT) (87.)
where Kp and K. are the separate thermal conductances of the branches, thus

(Sp -S,,)2

ZT =
(RModule )(Kp + Kn) (88.)

 

Equations 49 and 55 are identical if S,., R,. and K,. are all zero.
If we assume that the conductor n is a metal with S,.=O and the product R,.K,. will
have the known value LT, where L is the experimentally determined Lorentz number. K,

from equation 55 can be eliminated and the equation becomes

K 1 KpRn

P

= +
K*—Kp —LT/Rn z T szT (89-)

P

 

 

 

Thus, sz can be found as the intercept on the ordinate axis of the linear plot of

K
” against Rn. This plot is obtained from measurements of the thermal
K * —Kp - LT / R,I

 

conductance Kp in the open-circuit condition and K * for various values of the parallel

electrical resistance R". The Seebeck coefficient Sp can be determined from the SIOpe

Kip/Sp 2T of the plot.

67

By measuring the thermal conductance of the module with its input leads
separated and then joined together, the ZT of the module can be determined. This method

can be applied to whole modules as well as to individual thermocouples.

2.5.2.2 Modified Harman Technique

Continuing from the work of Harman , a modified technique is developed [49] by
utilizing only the voltage components in the measurement. When an electrical current, I,
is applied to a TB device, a signiﬁcant device Seebeck voltage, Va, will be added. Thus,

the total voltage across a TB device is

VT

otal = Va + Vp
where Va=S *AT, V,,=I*R. Equation 49 has shown that the ﬁgure of merit of a TE
material or module can be obtained from the ratio of the Seebeck voltage to the Ohmic
voltage. This technique is feasible only if these two voltage components can be
distinguished. Va term can be proportionally larger for small currents and it can easily be
non—zero even when there is no current ﬂow.

The quantity of V10”), I and AT can be measured, but it is not easy to separate the
two voltages V0, and V9 The Harman method resolves these two voltages by creating a
bipolar AC current and sending this current through the sample. At a sufﬁciently high
frequency (10’s to 100’s of Hertz), a temperature gradient can not be established across

the sample, however, the Ohmic voltage can change sign with the alternating current,

thus, Vp reverses polarity but Va does not.

68

Figure 2.28 shows when a current is applied to a sample, the voltage across is
shown in Figure 2.29. The voltage rises instantaneously to Vp and then asymptotically to
VTotal at steady state. As the current is tum off, the voltage drops instantaneously to V0

and decay exponentially to zero.

02 Efrem (A)

 

0.15 _

0.1 __

0.05 __

 

 

 

 

10203040506070801'Ime(s)

Figure 2.28 The current that is applied to the sample vs. time.

69

Volta (V)
0.4 r 99

V00
0.3 _ / T"

0.2 _

 

0.1 __

__ Va
0 \

10203040506070801'Irm(s)

 

 

 

 

Figure 2.29 The voltage across the sample vs. time.

70

Chapter 3 Module/prototype Design

From the engineering point of view, the research will not seem completed until a
TB module or prototype is actually built and shown to be operational. The synthesis and
the transport characterization tell the properties of the individual materials used, but they
do not give the necessary insight on how the device will perform after it is fully

assembled.

3.1 Background of TE Generation

Figure 3.1 shows the range of output power provided by TE generators with
various fuel sources. The magnitude of the power ranges from nanowatts generated in
miniature thermocouple arrays to the megawatts in nuclear reactor-powered generators

for the outer space applications.

 

 

 

 

 

Medical
Dynamic Space
Cardiac
Micro Pacemaker Military _ OTec Sp-100
Chip H 7 HH
-9 -

10 1o 10 1o 3'10 i 11(31021103104105106
1 l l l l I I IWatts
[ Waste Heat ]

I Isotopic l
I Fossil Fuel I

 

Figure 3. l The range of output power provided by TE generators with different fuel
sources. (Sp-100 is a space subsystem)

71

The TE materials which perform well at high temperatures are usually developed
into power generation applications where large temperature gradients are utilized for
improved efﬁciencies. Every TE material has its Optimum operating temperature. For the
cubic materials studied is this project, the optimum operating temperatures are around
600-800 K. TE materials are often fabricated by either directional crystallization from a
melt or pressed powder metallurgy. Each manufacturing method has its own particular
advantages and sometimes, each leg in a TB module is fabricated by different methods.

Table 3.1 shows the performance of various types of electrical power generators.

 

 

 

 

 

 

 

 

Types of Electrical Power Efﬁciency Output Maintenance
Generators (%) (W/lb) interval (h)
Central station steam plant 2040 50 5000
Airplane piston engine 30 1000 50
Automobile engine 15 1000 30

Boeing 707 jet engine 20 2000 50

Fuel cell 60 7 5000

Solar cell 8 1.5 Very reliable
Thermoelectric generator 5 0.8 70,000
(MHW)

 

 

 

 

 

 

Table 3. 1 Performance of various types of electrical power generators.

3.2 Choice of TE Materials for Module Fabrication

Bismuth telluride, lead telluride and silicon-germanium alloys are the most widely
used materials for power generation. As shown in Figure 2.8, each material has its own
range of useful operating temperatures due to its ﬁgure of merit, ZT. Bismuth telluride
operates well between room temperatures to 250-300°C and has the best ZT among these

materials. Lead telluride has a lower value of ZT and its operating temperatures are

72

between room temperature to 600°C. Silicon-germanium has the lowest ZT among the
three and its operating temperature is around 1000°C. All three materials have relatively

different characteristics that are important to the construction and operation of practical

TE power generators. Table 3.2 shows some of the properties of these materials [50]:

 

 

 

TE Materials Density (g/cm) Thermal expansion Tensile strength
coefficient mo‘5 c (lb/in’z)

Si-Ge alloys 3-3.5 5 3000-5000

Bi-Te and Pb-Te 75-875 18 2000

alloys

 

 

 

 

 

 

Table 3. 2 Some properties of the most widely used TE Materials.

3.3 Construction of the Thermoelectric Module

The high reliability of TE modules is due to their solid-state construction and
lacks of moving parts. The mean time between failure (MTBF) is typically greater than
200,000 hours. However, sometimes, a good construction design of the whole TE module
system is a more important issue than the “natural robustness” of the module itself. The
following are some of the important factors in constructing a good, reliable TE module

[50, 51, 52]:

1) Mechanical Design

Most of the thermoelectric modules have higher compression strength than shear
or tensile strength. Some of the modules can even survive compressive loads of up to
1000 psi. Therefore, the mechanical design of any thermoelectric system must ensure that

only compressive loads are applied to the modules.

73

Ceramic
Metal Strip

   

//

\\<\

 

 

 

 

 

 

 

 

 

l l

Figure 3. 2 TE module consists of a p- and n-type leg, an electrically connected metal
strip and a ceramic for better thermal contact.

2) Contact

Good electrical contact must be formed between the TE materials and the metal
strips since high contact resistance contributes to a signiﬁcant Ohmic loss that will result
in low device efﬁciency. On the other hand, poor thermal contact to the heat sink will
result in overheating of the TB module, which will also signiﬁcantly reduce the
performance. All interfaces between the system components must be ﬂat, parallel and
free of debris to minimize thermal resistance. High conductivity thermal interface
materials, e. g. alumina or other ceramics, are often used to ensure good contact between
surfaces.
a) Solder
The most common way to form contact with low temperature TE materials, e.g., bismuth
tellurides are soldering. The types of solders deﬁne their speciﬁc operating temperatures
and must be selected carefully so as to avoid elements that might poison the TE materials,
for instance, copper ions are known to rapidly diffuse into TE materials and change their

properties. In some cases a diffusion barrier between the TB materials and the solder or

74

contacts is used. Introducing a flux prior to soldering might be a solution for some TE

materials that do not bond well with solder directly.

b) Metallurgical bonding

Metallurgical bonding is often used as contact electrodes, however, metallic bonding is
restricted to certain operating conditions where diffusion of the materials is negligible.
The thermal expansion, chemical and physical properties of the materials used for
contacts are also important considerations in building a module. Some of the examples
are: tungsten and silicon alloys form very good bonding with silicon-germanium alloys,
using graphite as a barrier layer between the tungsten and silicon-germanium alloys can
extend the operating temperatures; Iron bonds well with lead telluride and nickel is used

as a barrier to prevent the diffusion of iron into lead tellurides.

c) Pressure contact

Electrical and thermal losses across the mechanical interfaces are usually minimized by
using spring-loaded pressed contacts. In fact, many of the high temperature TE modules
are conﬁgured with pressure-contacts alone and no solder used. The TE materials are
held together by spring-load pressed contacts. This helps to avoid difﬁculties associated
with differences in the coefﬁcients of thermal expansion between contacts and the TB
materials.

d) Conductive paint

The alternative way for connecting TE materials is the use of conductive paint or paste.

For instance, silver paint or platinum paint have offered very good electrical contacts.

75

Sometimes, a combination of conductive paint and pressure contact are obtained for

better module construction.

3) Moisture/Oxidation

Moisture and oxygen in the air can corrode some TE materials. In this case it is
important to seal the TE materials (of the modules) with an epoxy or coating material that
can prevent oxidation without signiﬁcantly degrading the module efﬁciency. Often power
generators such as those that use bismuth telluride and lead telluride are evacuated,
sealed, and back-ﬁlled with an inert gas in order to minimize material degradation at high
temperatures. At low temperature, effective moisture seals are often installed. For
instance, ﬂexible foam insulating tapes or sheet materials or silicone rubber RTV are
relatively good moisture seals. At high temperatures, silicon-germanium alloys are quite
insensitive to their operating environment. Oxides will form on the surface of the
materials but it will not affect the properties of the materials so scaling is not required for
this type of materials. Sometimes, a silicon nitride coating is employed to prevent

sublimation for extended operating temperatures over 1000 °C.

3.4 Segmented TE Modules

A segmented TE module consists of multiple layers of different TE materials. In a
stacked conﬁguration, individual modules made with different materials are stacked.
Another conﬁguration is also possible, called a unicouple, where different TE materials
are stacked in direct contact with each other (or separated by a thin barrier layer).

Segmentation can provide a wider operating temperature range for the module. One of

76

the examples of a segmented TE unicouples is shown in Figure 3.3 below [53]. The
unicouple includes a combination of state-of-art TE materials including BizTe3 and novel
materials based on Skutterudites made in the Jet Propulsion Lab (IPL) is shown in Figure
3.3. Each section of one leg has the same current and heat ﬂow, and the geometry of the
legs must be optimized to maintain the desired temperature proﬁle. This optimization is
mainly due to differences in thermal conductivity. The segmented unicouple is expected
to operate between 300 and about 975 K with a projected thermal to electrical efﬁciency
of up to 15%.

The segmentation can be adjusted to accommodate various hot side temperatures
depending on the speciﬁc application requirement. Various techniques and materials have
been investigated to develop better bonding between the TB segments and to the metallic
contacts. Calculations based on typical material properties show that a low contact
resistance of less than about 20 u.Qcm2, is required to keep the efﬁciency from being
signiﬁcantly degraded by the contact resistance.

Both the n- and p-segrnented legs are fabricated by hot-pressing the various TE
materials separated by thin metallic foils. Nickel and niobium metallic powders were
added on the top of the legs during the hot-pressing. The electrical contact resistance was
measured by a four probe technique up to the predicted optimum temperatures. One
voltage probe is located at one end of the sample while the second probe can move along
the sample. The variations of the electrical contact resistance was recorded as a function
of the distance of the moving probe to the ﬁxed probe.

Electrical contact resistance lower than 5 1.1.Qcm2 have been obtained for each of

the junctions at its projected operating temperature. For the p- and n-type samples with

77

Ni as the top metallic segment, even though, the interfaces showed good bonding, lateral

cracks are observed within the Skutterudite materials in the region adjacent to Ni. This is

probably due to the relative large difference between the thermal expansion of Ni,

13.3x10'6/K, and to those for p-CeFeasblz and n-CoSb3, 7.5 and 6.36x10'6/K,

respectively. On the other hand, the samples with Nb as the metallic contact, did not

show cracks since the coefﬁcient of thermal expansion of Nb is 7.1x10'6/K and is a much

better match to the samples.

 

 

 

 

97 K

5 Ni
p-CeFe48b12

675K B—Zmes

475K P-

300K p-Bio.4Sb1.6Te3

 

 

 

 

 

 

 

 

 

 

 

 

 

Power Out

Ni

n-CoSb12

n-Bi2Te2.95$eo.05

 

 

 

Figure 3. 3 The combinations of various TE materials at the unicouples.

78

Chapter 4 High temperature measurement system
4.1 System set-up and design

A new thermoelectric measurement system is presented to characterize the
properties of new materials, primarily at high temperatures (up to 800K) where materials
for power generation applications are typically operated. This computer-controlled
system was designed to measure the thermoelectric power through a slope measurement
technique, also called the pulse technique, and electrical conductivity in the standard
four—probe conﬁguration. Here we present the design and computer-controlled features of
this measurement system, and its use in studying the properties of new materials over a
very broad temperature range (80-800K).

The system consists of a Cryo Industries cryostat chamber, a Varian Turbo-V 70
Controller unit, a temperature controller (Lake Shore 330), a source meter (Keithley
2400), four nanovoltmeters (Keithley 2182) and a computer. The LakeShore 330
temperature controller is tuned by adjusting the Gain (Proportional), Reset (Integral) and
Rate (Derivative) of the controller, and settings can vary from sample to sample.

The Varian Turbo-V 70 Controller is a microprocessor-controlled, solid-state
frequency converter with self-di agnostic and self-protection features. The controller is
composed of a power transformer, front panel display and keypad, rear panel with
input/output connectors and a PCB that includes the power supply, 3-phase output, A/D
section and other controls. This unit monitors the operation of a rough pump and a
minuteman turbomolecular-dry pump (Turbo-V 70LP pump). The controller drives the
pumps during starting phase by controlling the voltage and current with respect to the

speed of the pump. The turbo-pump is rated to 1.5 x10'9 Torr and the rotational speed is

79

75,000 rpm. Due to the flanges that are used, the system can only be pumped to
5x10'5 Torr at around 700K. However, this is a sufﬁcient vacuum level for the
experimental purposes.

The cryostat chamber is a Cryo Industries continuous flow cryogenic system. A
flexible stainless steel transfer line is connected to the cryostat with the other end into a
liquid nitrogen storage dewar. The sample stage on the end of the cold ﬁnger is custom
designed. The cryostat contains three 20-pin connectors and they are labeled as A, B and
TC. In this system, only connectors B and TC are used. The wiring diagrams of the two
connectors are shown in Figures 4.1 and 4.2. Connector B has bundled all the wires from
the source and voltmeters while Connector TC has connected a cable from the

temperature controller to the heater and sensor of the cryostat.

O ”O

 

W-

V.

TC+ (constantan)

TC+ (chromel) also short to V4-
TC- (constantan)

TC- (chromel) also short to V-
1+

1-

Heater+

Heater-

     

KOID g OROD

JOTO osoE
ooo

         
 

w=e<wruoug

 

 

 

Figure 4. 1 Wiring diagram of connector B as seen from the outside of the connector. TC,
is the upper side of the two thermocouple that are mounted on the sample, TC- is the
bottom thermocouple.

80

 

M heater white (LO)

L heater yellow (HI)
K heater black (LO)

J heater red (HI)

E sensor 1+

F sensor V+

G sensor V-

H sensor 1-

 

 

 

 

Figure 4. 2 Wiring diagram of connector TC as seen from the outside of the connector.
This connector contains the heater and sensor leads to the temperature controller.

The Lake Shore 330 Temperature Controller is a microprocessor-based
instrument with digital control of a variable current output. The sensor for this controller
is a 10082 Platinum resistor. The controller has dual sensor inputs and contains isolated
current sources which allow true 4-wire sensor readings. It can store up to 21 sensor
calibration curves. It has autotuning (PID) control as well as zone modes which can store
up to 10 temperature ranges. Figure 4.3 and 4.4 show the sensor and heater connectors on
the rear of the instrument. The wiring labels in Figure 4.3 and 4.4 correspond to the
wiring labels in Figure 4.2. There are two pairs of heaters: label W and label UK at the
connector TC. The temperature controller is usually connected by either pair of the heater

and each pair has a 5052 resistor, if they are connected in parallel, the heater output is

2552.

81

 

Figure 4. 3 The wiring diagram of the Lake Shore 330 temperature controller sensor
Channel B connector in the rear panel.

Heater Output
HI L0 GND

©©©

Figure 4. 4 Heater Output of the rear panel of Lake Shore 330 temperature controller.

The Keithley 2400 Source Meter is a dc power supply with a built-in multimeter.
It has 0.012% accuracy with 5V2-di git resolution. The source voltage is from SuV to
210V and it can measure luV to 211V; the source current is from 50pA to 1.05A and it
can measure 10pA to 1.055A. It can measure resistance from 1001152 to 211MS2 and the
maximum source power is 22W. This meter can deliver 520 readings per second over the
GPIB cable connecting it to the computer.

The Keithley 2182 Nanovoltmeter is a 7V2-digit high-performance digital
nanovoltrneter. It is a low noise and high speed device with 15 nV peak-to-peak noise at

1 second response time and 40-50 nV peak-to-peak noise at 60 ms response time. The

82

meter can measure voltages from 10 nV to 12 V. The meter also has two trigger link
cables for sending and receiving trigger pulses to initiate data collection.

All of the instruments that were introduced are controlled by LabVIEW
programming. The communication between the measurement instruments and the
computer is through GPIB address cables. Figure 4.5 shows the set-up of the high

temperature system.

 

Figure 4. 5 The set-up of the high temperature system

Figure 4.6 shows the different views of the sample stage. The stage and the heat
shroud are made with OFHC (Oxygen Free High Conductivity) copper and nickel/ gold

plated on the surface. The stage screws onto the cold ﬁnger of the cryostat while the heat

83

shroud screws onto the stage. The sample is mounted on the stage with conductive paint,

and the heat shroud is used to reduce the radiation heat loss.

 

 

 

 

 

Side view ofthe heat shroud

Topviewofdreheatshrorxi

Hill @

 

 

 

 

 

 

 

 

Side view of the stage Top view of the stage

Figure 4. 6 The design of the sample stage.

4.2 Mounting and Running

Figure 4.7 shows the sample conﬁguration on the stage. The pulse technique is
used to periodically heat one end of the sample through a high temperature heater
(100 W) to establish a temperature gradient of less than 1K. The high temperature heater

is a 500 S2 Platinum RTD from Omega and it is ceramic encased. The temperature rating

84

is from —50 to 600 °C. The temperature and voltage gradients of the sample are measured
by two single ended thermocouples (TC). In the early stage of the development of this
system, the thermocouple was made of 0.001” diameter bare copper and constantan

wires, as shown in Figure 4.8.

HT Heater

 

Figure 4. 7 The sample mounting conﬁguration.

 

Figure 4. 8 The photo of the sample mounting conﬁguration in the early development of
the system.

85

The reference temperature of the thermocouples was located at the connectors, where the
temperature is near room temperature. This location of the reference temperature has
caused some inconvenience in replacing the new thermocouples. Therefore, a more
recent wiring conﬁguration is used, where the reference temperature locates at the sample
stage, Figure 4.9 and 4.10. The heater and current leads are all 0.001” diameter bared

copper wires. Bared wires are fed through ﬁberglass sleeves for electrical insulation.

 

Figure 4. 9 The photo of the sample mounting conﬁguration now.

 

Figure 4. 10 A close view of the sample mounting conﬁguration now.

86

4.3 Measurement Method

The voltage (dV ) and temperature (dT ) gradients are measured simultaneously.
The slope of (IV vs. dT curve gives the thermopower as shown in Figure 4.11. Figure 4.12
shows the steady-state plot of the temperature gradient, dT as the sample is periodically
heated. The electrical conductivity, 0, of the sample is measured by a four probe

conﬁguration, 0 = U(R-A) where L is the probe spacing, R is the resistance and A is the

cross-section area of the sample.

 

Figure 4. 11 The slope of W vs. dT curve Figure 4. 12 The temperature
gradient vs. time plot.

The heater and all the leads are mounted to the sample with conductive paint.
Several different paints are used including F'elco® 16031 silver paint, high temperature
silver paint, SPI# 05006-AB carbon paint and SP1# 04990-AB platinum paint. Silver

paint works very well although it was not found suitable to some samples at high

87

temperatures. The high temperature silver paint was found to evaporate at high
temperature and coat the sample surfaces. Carbon paint is the most inert paint but the
contact resistance is too high and it is not suitable for electrical conductivity
measurements. Platinum paint forms the best contact to the sample, but it has to go
through a certain process of curing and the cost is very high. Furthermore, as the
temperature is increased, the platinum paint can easily lift off the sample surfaces,
causing lost contact of leads.

In addition to the challenges in choosing the right contact pastes, temperature
stabilization at high temperatures is the most challenging task for this system. Figure 4.13
shows that when the temperature is not stable, the dV vs. dT curve and the temperature
gradient plot will be distorted and thus the thermopower measurement will not be

accurate.

 

Figure 4. 13 The dV vs. dT curve and the temperature gradient plot when the temperature
is not stable.

88

4.4 Software Control - PID

The PID control algorithm [54] is the most widely used automatic control
technique in industries and it is the basis for many advanced control algorithms and
strategies. PID control is a simple form of feedback. Feedback is a very powerful concept
with many useful properties, e. g. reducing the effects of disturbances, creating robust
linear relations, following commands with high ﬁdelity, and establishing robustness to
process variations. But there is some risk of instability, and for the control loop to work
properly, the PID loop must be properly tuned.

The PID control algorithm comprises three elements: Proportional (P) - also
known as Gain, Integral (I) - also known as Automatic Reset or simply Reset, and
Derivative (D) - also known as Rate

The algorithm is normally available in several combinations of these elements:

. Proportional only
0 Proportional and Integral
o Proportional, Integral, and Derivative

o Proportional and Derivative

4.4.1 Introduction to PID in Temperature Control
4.4.1.1 Proportional Control

A proportional controller attempts to perform better than the On-Off type
controller by applying power, W, to the heater in proportion to the difference in

temperature between the system and the set-point,

W = Px(TS —T0)

89

where P is the proportional gain of the controller, T5 is the set-point (or set temperature)
and To is the system temperature (actual temperature). As the gain is increased the system
responds faster to changes in set-point but becomes progressively underdamped and

eventually unstable.

 

\
\
\
150 r X I
I

 

Temperatme (°C)
1 l I l
\

l
I
\
\‘\“
\ ~\\
\
I
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I,
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1m \\ ’1’] \\>‘\\" ’1”,
§
.1 mm 11 Si
oi.
1 1 1 I11 L11
0 300 600 900 1200 1500

Time (s)

Figure 4. 14 Signals from an On-Off temperature controller.

The top portion of Figure 4.14 shows the set temperature (solid line) and the
actual temperature (dashed line), the bottom line shows the control signal of a typical on-
off controller. Figure 4.15 shows the set temperature (solid line) and the actual

temperature (dashed line) signals of a controller with proportional control only.

90

 

 

 

 

 

 

 

 

 

S3
g 150
g {’1le /
.','/ Increasin 'n
100 gga’
1 ______________ i"
1111111111111111111
0 300 600 900 1200 1500
Time(s)

Figure 4. 15 Proportional temperature controller.

4-4- 1.2 Proportional + Derivative Control

The stability and overshoot problems that arise when a proportional controller is

used at high gain can be eliminated by adding a term proportional to the time'derivative

of the error signal,

W = Px((TS -T0)+Dxdit(TS —T0))

This technique is known as PD control. The value of the damping constant, D,

c a1“) be adjusted to achieve a critically damped response to changes in the set-point
I:
e11‘1I>erature. Too little damping will result in overshoot and ringing, too much will cause

a
1') unnecessarily slow response. Figure 4.16 shows the signals from a PD temperature

C on
t1‘Oller.

91

 

 

 

 

 

 

 

 

20° —
0v _
g 150 _ liming damping
is ._
100
111|111JI11|111|111
0 300 600 900 1200 1500
Time (s)

Figure 4. 16 Proportional + Derivative temperature controller.

Proportional + Integral + Derivative Control

4-4. 1 .3
Even though PD control deals with the overshoot and ringing problems associated

Wi th proportional control, it can not eliminate the steady-state error. Fortunately it is

DOSSible to solve this problem by using relatively low gain and adding an integral term to

the Control function,
d

' here I, the integral gain parameter is sometimes known as the controller reset level.

92

 

 

 

 

 

 

 

9 r ”””
g 150+—
100
1111111l111|111|111
0 300 600 900 1200 1500
Ture(s)

Figure 4. 17 Proportional + Integral + Derivative temperature controller.

This form of function is known as proportional-integral-differential, or PID,
control. The effect of the integral term is to change the heater power until the time-
averaged value of the temperature error is zero. The method works quite well but
complicates the mathematical analysis slightly because the system is now third-order.
Fi gure 4.17 shows the signals from a PID temperature controller.

4-4- l -4 Conslusion in PID Control

The PID control algorithm does not "know" the correct output to bring the process
t . . . . . .
O the setpornt. It merely continues to move the output in the direction which should

thQVe the process toward the setpoint. The algorithm must have feedback (process

I)";
6&3 urement) to perform.

The PID algorithm must be "tuned" for the particular process loop. Without such

tLl -
I) l “g, it will not be able to function. The tuning is based on the dynamics of the process
re
8 Don se.

93

4.4.2 Tunning the LakeShore 330 Temperature Controller
There are various PID tuning methods and every system has its most suitable
tuning method. We have adapted the tuning procedures from the LakeShore Model 330
Autotunin g Temperature Controller User’s Manual [55] for our high temperature system.
The procedures are stated in the following paragraphs. Further reading in the Controller
User’s Manual is recommended.
Step 1: Give a set temperature, e. g. let the set temperature be 310K. Turn off both
Reset (I) and Rate (D). Enter a nominal gain of 50 by adjusting value of P and verify that
the heater turns on. If the heater does not turn on, then increase the gain setting until it
t urns on; and wait to let the system stabilize. One should expect the controller to stabilize
at some point below the set point (typically a few Kelvin below). As seen in Figure 4.18,
the System stabilized at 305 K.

Step 2: Increase the gain by a factor of two until the system temperature begins to
080i 1 late. Adjust the gain for small sustained oscillations. For example, if the oscillation
EuTlI>litude decreases with time, increase the gain. However, if the oscillation amplitude

i n‘-"I"E=ases with time, decrease the gain.

In this case, when the gain was increased from 50 to 100 (50x2), the temperature
osci l l ated with a decreasing amplitude. Thus, the gain was further increased to 150. The
t.3'l11136rature then started to oscillate with increasing amplitude. These two settings helped

to determine where the possible value of gain would be. At a gain setting of 120, the

S 3’
Stem oscillated with a constant amplitude.

94

5 Temp_controller_sim3.vi

 

 

Fi gure 4. 18 A snapshot of LabVIEW display on the system temperature with P, I, D =
5 0. 0, 0

Then the period of these oscillations is measured to determine the correct setting
for reset (I). In this case the period of oscillation is 235 seconds so I and D can be
detel‘rnined as:
I = max. reset value/Period = 999/235 = 4 since the maximum value of I in the
3 3 0 Controller is 999.

D = Period/4 = 235/4 = 59. Depending on the system, a setting of D = Period/8
mi ght have a better effect. Also, depending on the system, the gain should be reduced by
a. fae t()r of two to three when this is used. After some iterations, let P(new) = P(old)/3 =

120,3 =40

95

Step 3: Re-enter the new values for P,I,D = 40, 4, 59 until the temperature again
stabilizes.
Figure 4.19 shows a snapshot of LabVIEW display on the sensor (system)
temperature with P, I, D of 40, 4, 59. The system eventually stabilize at 310 K.
Figure 4.20 shows another set temperature, T=330K with the same PID and it took less

than 15 nrinutes to stabilize at desired temperature.

5 Temp_controller_sim3.vi
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I igul‘e 4. 19 A snapshot of LabVIEW display on the sensor (system) temperature with P,
’ D = 40, 4, 59. The system stabilize at 310 K.

96

5 Tenrp_controller_sim 3.vi

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Figure 4. 20 System stabilize at 330K.

Figure 4.21 shows the temperature transition between 550K to 560K and the

syStem stabilize at 560K within 20 minutes.

97

5 Temp_cor1troller_sim3.vi

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Figure 4. 21 The transition between temperatures.

4‘5 Sample Mounting Procedures
This section mainly addresses sample mounting procedures. This is not the only
Way to mount a sample but it can act as a guide. Alternative methods can be used as long
as they result in the same outcome.
1 - When new samples arrive in the lab, record the material composition, the ID
numbers, the person who made them and the date of receipt in the lab logbook.
2 ~ Prepare a “Sample Run Sheet” for each sample, record the geometry, the

appearance and any preliminary tests that were taken on the sample. The

98

geometry of the sample can be measured by the digital calipers or by a
microscope and micrometer. If using the microscope, the micrometer scale is not
1:1, so one should remember to include the micrometer magnifying scale in
calculation of the actual measurement. The magnifying scale is posted on the
microscope. Occasionally, when the sample has an irregular shape, a hand-sketch
is helpful and should be included on the run sheet. Recording the appearance of
the sample is important because it allows comparison of the appearance before
and after the run. For instance, discoloration might be observed after the run for
some samples and it will be helpful to have taken notes before mounting. Other
observations, for example, cracks on samples, needle-like surface and etc, are also
important to record since this information can be critical in the future. If the
sample is measured in the room temperature four-point probe system, also record
the electrical conductivity value at room temperature. If the sample has a
rectangular shape, it is necessary to measure all four faces to verify the
homogeneity of the sample.

It is necessary to clean the sample prior mounting. Acetone is used to clean the
surface. Next, the surface of the sample needs to be scraped in order to remove
any possible oxide layer. Depending on the sample, polishing on a sand paper
might be helpful too. Again, clean the surface of sample with acetone.

After cleaning the sample, it is ready to be mounted on the sample stage. Make
sure the stage is clean and contains no leftover silver paint from the previous run.
The dry silver paint can be removed by scraping with a razor blade, followed by

acetone cleaning.

99

5. The sample is mounted on the sample stage with silver paint. Remember to shake
the silver paint very well before using it. Shake the bottle laterally so that the
paint does not splash against the cap, or alternatively stir the silver paint with a
clean wooden stir stick. Open the cap and use the wire holder tool to take some
silver paint (only a small drop is needed) from the brush and paint it on the stage.
Mount the sample by sliding on the paint so that there are no air bubbles between
the sample and the stage.

6. Allow 1-2 hours for the silver paint to dry. Sometimes, the drying time can take
longer due to the humidity in the room. Then proceed on mounting the positive
current lead and the HT heater on top of the sample with silver paint. It is often
helpful to bend wires into place before applying silver paste so to avoid having to
hold the wire in place while drying. Connect the HT heater with Cu wire leads
after the paint is dry. Figure 4.22 shows the HT heater and positive current lead
are mounted on top of the sample.

7. Place the HT stage underneath the microscope for mounting the thermocouple
leads. Two single-ended chromel-constantan thermocouples are mounted on the
side of the sample with silver paint. After mounting, remember to measure the

separation between leads under the microscope.

100

   

Figure 4. 22 The HT heater and the positive current lead are mounted on top of the
sample with silver paint.

8. Again, before mounting the thermocouple with silver paste, bend the wires into
place before. Kapton tape can be used to hold the wire in place when putting the
silver paint on. Remember to remove the Kapton tape only after the silver paint is
completely dry, or else, wires can be pulled away as removing the tape. Figure
4.23 shows the top thermocouple is held with Kapton tape while the bottom
thermocouple is mounted on the sample with silver paint. Remember to make as
small contact point of silver paint as possible on the thermocouple and add more
when necessary. Large contact point can result in difﬁculty in measuring the
accurate lead separation and small deviation in lead separation will cause a large

change in electrical conductivity measurement.

101

9. The leads separation is measured between the mid-points and the edges of the
silver contacts as shown in Figure 4.24. But only the mid-point to mid-point leads
separation is used in the electrical conductivity measurement.

10. When ﬁnished mounting, arrange all the bare wires so that they do not touch each
other nor the radiation shield that is about to be placed on. Check the wiring

connection by using the multi-meter before and after placing the shield on.

 

F i gure 4. 23 The top thermocouple is held with Kapton tape and the bottom thermocouple
l S mounted on the sample with silver paint.

102

 

Mid-point to mid-point
leads separation

 

 

 

 

Figure 4. 24 The leads separation is measured between the mid-points of contacts and
edges of the contacts.

_I
.

High Temperature Operating Procedures

Ensure that the chamber o-ring is clean and lightly lubricated with high vacuum
grease to seal appropriately. Also, inspect the o-ring groves on the sealing faces
for cleanliness. Place the cryostat into the chamber and plug-in all connectors,
verify the temperature controller reads the correct temperature (nominal room
temp approx 24°C or 297K).

Turn on the dry pump vacuum system by pressing the “start” button. The rough
pump will start ﬁrst and then the turbo pump will automatically turn on when
certain vacuum level is reached (usually around 10'3 Torr). Notice that the pump
speed increase till 75 krpm. If it does not reach 75 krprn, stop the pump to detect
possible leaks. It takes 1.5-2 hours for the system to reach vacuum level of 10'5

Torr at room temperature once the pump speed reaches 75 krpm.

103

3. A so-called “manual run” can be operated. The manual run does not include the
automated temperature control software. In Nanowire computer, under
C:\Program Files\National Instruments\LabVIEW 6\user.lib, in “Tim’s Programs
old” library, choose “PowerFactor_Manual.vi”, the program will pop up as seen
in Figure 4.25. This program will control the thermopower and electrical
conductivity measurements. This is a quick check on the room temperature

measurement as well as verify the wiring connections are ﬁne.

El
Iii

{it PawerFaclor»Manual.vi

11115

n

,.

w
I I
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.-

 

 

Figure 4. 25 PowerFactor_Manual.vi

4. In “PowerFactor_Manual.vi”, enter the geometry of the sample, dT and dV probe

5.

spacing are the probe spacing of the thermocouples and voltage leads. In our case,
these two values are the same because the two single—ended thermocouples are
also used as voltage leads. The number of reading per period is default to 300 but
it can be changed depending on your needs. The dT resistor current is the amount
of current supply to the heater resistor for heat pulsing. For metals, a higher
current is required, for instance 30-50 mA, for typical sample dimensions to
create a temperature gradient of less than 1K. For semiconductors of typical
sample dimensions, a heater current of 5-10 mA is sufﬁcient. The dT resistor
pulse period is default to 180 seconds and can be adjusted depends on the steady-
state condition. The ﬁrst step of this program is by using the pulse technique,
construct a heat pulse and measure the voltage and temperature gradient across
the sample simultaneously. To develop the temperature gradient across the
sample, a platinum resistor was used. The second step is to measure the electrical
conductivity by ﬂowing an appropriate current (generally lOmA) through the
sample and measuring the resulting voltage gradient. There are two ﬁts for the
thermopower values and will be discussed later in this section.

The “PowerFactor_Manual.vi” is designed to construct a 2.2 temperature gradient
period per data point. So the program run time per data point is about 2.2 x pulse
period. In this case, 2.2 x 180 = 6.6 minutes. Also, including the delay time and
electrical conductivity measurement, it will take about 10-12 rrrinutes per data

point.

105

6. When running this program, it is also recommended to open another program
“Thermopower slope ﬁt.vi”. This program will display the temperature gradient
of the sample and allows checking if steady-state condition is met.

7. When the run is ﬁnished, the display is on Figure 4.26. The “Thermopower slope
ﬁt.vi” is on Figure 4.27. If the values look ﬁne, then continue with the

temperature dependent measurements.

1) Powerfuctor Manualm '

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Figure 4. 26 After the measurement, the values are displayed in PowerFactor_Manual.vi

8. Since different samples have different heat capacity and emissivity, the

temperature controlling parameters, PID, needed to be tuned for each sample.

106

9. Choose the ‘”I‘emp_controller_sim3.vi” to display the temperature of the system
verses time. The “330 TUNE PID_sim.vi” allows changing the PID setting
manually.

l? Thermopower slope lit.vi

EIeEdtQpaateIoolsQowser-ph

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Figure 4. 27 At room temperature, the value of M0 is displayed in Thermopower slope
ﬁt.vi

10. Please refer to Section 4.4.2 Tunning the LakeShore 330 Temperature Controller
in how to tune the PID of the high temperature system.

11. When the PID system is tuned, saved the new PID setting to “330 Init.vi”.
Remember right click on the mouse in Data Operations, select “Make Current
Values Default” and saved the changes.

12. “High Temp_Aprl6.vi” is the automatic run with temperature ranges and the
display can be seen in Figure 4.28. This program measures and saves data to a ﬁle

as a function of temperatures.

107

 

 

 

Figure 4. 28 High Temp_Aprl6.vi

13. “Temp_controller_sim3.vi” can be run simultaneously with the “High
Temp_Aprl6.vi”.

14. Most of the time, once the P11) is properly tuned for the system at around 310K or
higher, the PID is usually good till 700K. Sometimes, temperature instabilities
might occur during the run. Then, the system needs to be re-tuned by following
the tuning procedures previously described. An example is shown in the last part
of this section.

In measuring the thermopower, the dT vs. dV curve must be ﬁt and the slope
extracted from the data. In this software, there are two types of curve ﬁtting routines

used. In ﬁt#1 the regions where the dT data are rapidly changing in time are not used, but

108

an upper and lower region of the dT vs. dV data are independently ﬁt and an average of
the ﬁts between the upper and lower slopes/arrays is calculated. Fit#2 is the linear ﬁt to
the overall SIOpe/array of data.

Figure 4.26 shows the result of the manual run of the molybdenum sample. The
difference between the two thermopower curve fits is due to the looping that occurred in
the plot. The 100ping is usually caused by unstable temperatures but it also can be caused
by the difference in cooling and heating rate across the sample and on the quality of the
thermal interface between the sample and the cryostat sample stage. When looping is not
apparent in the data, then ﬁt#2 is less susceptible, noise in the data and will give a better
result than ﬁt #1. In Figure 4.29, the shape of the slope has changed due to temperature

instabilies. Fit#1 is now a much better ﬁt than ﬁt#2.

Figure 4.30 shows the transition between temperatures during the automated
temperature measurement. It is obvious that small oscillations have occurred and this has
affected the measurement. Figure 4.31 shows the distortions in the temperature gradient

plot and slope caused by the oscillation of the temperatures.

109

5 Thermopower slope lit.vi

 

 

 

Figure 4. 30 The transition between temperatures during the temperature dependent
measurement.

110

l) lhcrmopowur slope Iit.vi

 

 

Figure 4. 31 Distorted plots due to temperature instability.

When distorted waveforms are observed, the system has to be re-tuned for better
temperature stabilization. Try to choose a reasonable value for P so oscillation will occur.
In this case, the PID was set to 100, 0, 0 with a new P value that is twice the old P value.
Remember to do the tuning in the beginning of the next set temperature. If the amplitude
of the oscillation decreases, change the P to a higher value, like 150. In Figure 4.32, a

white straight line indicated when the PID is changed to 100, 0, 0.

111

5 Temp_controller_sim3.v1'

ﬁle Edit Qperate Idols Erowse \Mndow lielp

 

 

Figure 4. 32 Reset the PID values to 100, 0, O. The white vertical line indicated when the
PID was changed.

After the PID was tuned to 100, 0, 0, the oscillation occurred but with a
decreasing amplitude in time as shown in Figure 4.33. Now, re-tune the PID to 150, 0, 0,
this will allow more power to the controller. In Figure 4.34, the system obtains
oscillations with constant amplitude. The plot is then magniﬁed so the period of
oscillation can be determined since this will be used to determine the I and D values.

Figures 4.35 and 4.36 have shown the different magniﬁcations of the waveform.

112

5‘ Temp_ controller sim3.vi

fie Edit Qperate Tools Erowse V_V_indow Help

 

 

 

 

Figure 4. 34 The PID is reset to 150, 0, 0 and it then sustains a constant amplitude
oscillation.

113

5 Temp_controller_sim3.vi '
Elle Edit Qperate Iools Erowse ﬂindow Help
-@[E 13pt Application Fo

 

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1%.
l

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?-'

it""jrrjt'vr‘

 

 

Figure 4. 36 Calculate the period, period=116s.

114

The period was calculated to be 116 second and thus the new PID is 50, 8, 29.
With the new PID values and the system stablizes at the set temperature at 535K as

shown in Figure 4.37. The stabilization process was less than 10 minutes.

5 Temp_r.ontroller_sim3.vi ]:IIEHEI

_E-

Elle Ed1t Qperate Iools Erowse Window lielp lj

 

 

Figure 4. 37 After the new PID: 50,8,29 is entered, the system stables at the set point less

than 10 minutes.

Once the system is stable at the set temperature, the measurement can be

continued. As an example, in a measurement for this study, a temperature oscillation was

observed as in Figure 4.38. This temperature oscillation is affect by the heat pulse from

the HT heater that is mounted on the top of the sample. Since the sample that is being

measured is a metal, molybdenum, a larger heater current is required to create a sufﬁcient

temperature gradient. Even though the temperature deviation is only + /- 0.2 K, it is

enough to create looping in the measurement as shown in Figure 4.39.

115

5 Temp_controller_sim3.vi

_E_ile Edit—goerate Iools Erowse ﬂindow Eelp

 

 

 

sample.

 

 

Figure 4. 39. Looping occurs due to the instability of the system.

116

4.7 Thermal Loss Calculation

Heat is transported in three ways [56]: Conduction, convection and radiation.
Thus, heat losses through these three ways are often considered when one is measuring
the thermal conductivity of a specimen. This section also explains why the thermal
conductivity measurement is not considered in the high temperature system.

Heat loss calculations at room temperature and at 800K through conduction,
convection and radiation will be performed in this section. Figure 4.40 shows the

different paths of heat loss in the high temperature sample conﬁguration.

Conduction ----—>
Convection N
R l' .

 

 

 

 

Figure 4. 40 Various ways of heat transfer from the sample.

4.7.1 Conduction

The equation for heat conduction is

117

A
Qcond : K.(Ywh — To ) T

and the thermal conductance is equal to K? .

There are three 25 um diameter copper wires, two 25 um constantan wires and two
25pm chromel wires required in the HT system and all these wires are connected to
thicker (50um diameter) copper wires with silver paint. Table 4.1 and 4.2 are the

electrical and thermal properties of various metals and alloys.

 

 

 

 

 

 

 

Material Electrical Resistivity Thermal Conductivity
(10'8 S2m) @3OOK (W/m-K) @3OOK
Copper (Cu) 1.725 [57] 401 [57]
Nickel (Ni) 7.2 [57] 90.7 [57]
Chromium (Cr) 12.7 [57] 93.7 [57]
Constantan (Ni45Cu55) 52 [58] 19.5 [58]
Chrome] (Ni90Cr10) 70.6 [58] 19 [58]

 

 

 

Table 4. l The electrical resistivity and thermal conductivity of some metals and alloys at
room temperature.

 

 

 

 

 

Material Electrical Resistivity Thermal Conductivity
(10‘8 $2111) @8OOK (W/m-K) @800K
Copper (Cu) 5.262 [57] 366 [57]
Nickel (Ni) 35.5 [57] 67.6 [57]
Chromium (Cr) 34.6 [57] 71.3 [57]

 

 

 

 

 

Table 4. 2 The electrical resistivity and thermal conductivity of some metals and alloys at
800K.

At room temperature (300K), the thermal conductance for each copper wire (3 cm long)

is 401*1r*(12.5p.)2/0.03 = 6.56 uW/K

118

For three Cu wires, the thermal conductance is 19.68 uW/K. Similar calculations

can be applied to other metal wires. Table 4.3 shows the result of the thermal

conductance of each wire at 300K.

 

 

 

 

Material (3 cm long) Thermal Conductance Total Thermal
(uW/ K) @300K Conductance (uW/ K)
Copper (Cu) 6.56 6.56*3 = 19.68
Constantan (Ni45Cu55) 0.319 O.3l9*2 = 0.638
Chromel (Ni90Cr10) 0.31 0.3 1 *2 = 0.62
Total 20.938

 

 

 

 

 

 

Table 4. 3 The thermal conductance of each wire at 300K.

Since the thermal and electrical properties of chrome] at high temperatures were

not found in the literature, a simple method can be used to estimate the values based on

the available properties of nickel.

This method is called Nordheim rule [59], and is used to predict the resistivity of
an alloy. The Nordheim rule relates the alloy resistivity, pang, (in this case, chromel), to

the atomic fraction X of the solute atoms (Nickel) in a solid solution.
palloy :pmatrix +CX(1—X)

where C is the Nordheim coefﬁcient. There is an important assumption in this rule which
is that the alloying does not signiﬁcantly vary the number of conduction electrons per
atom in the alloy. Even though, it is only true for the alloys with the same valency, i.e.
from the same column in the Periodic chart, it still gives very good prediction for dilute

alloys. In this case, we consider chromel to be a dilute alloy since the impurity

(Chromium) is only 10%.

119

In order to ﬁnd the thermal conductivity value of Chromel at 800K, the Nordheim
coefﬁcient can be determined from the room temperature values by assuming the
Nordheim coefﬁcient is constant between these temperature ranges. At 300K, the
resistivity of Chromel is 70.6x10'8 82m, nickel is 7.21108 Qm and Chrome] has the
composition of 90% nickel and 10% Chromium. So the equation becomes

70.6x10'8= 7.2x10‘8 + C(O.l)(1-0.1)

C = 7.04x10'8 am
Once C is found, the high temperature value for the resistivity is

p.,,,.,,,,., = 35.5x10'8 + 7.04x10'8 x(O.l)(1-0.l)

= 9.886x10'7S2m

The thermal conductivity of Chromel at 800K can be found from the Wiedemann-
Franz-Lorenz Law, which gives

K(hromel = 0714

= TU pchromel

= 800*2.44x10'8,9.886x10'7

= 19.745 W/m K

This value is very similar to the nickel alloys ngocrzo as shown in Figure 4.41
and it shows that the estimation is pretty good.

The experimental value of thermal conductivity of Constantan from 80—400K is
shown in Figure 4.42 and the 800K value was obtained by extrapolating from the curve
ﬁt as shown in Figure 4.43. The thermal conductivity at 800K is about 130 W/m K. If

using the Nordheim rule, we obtained about 119 W/mK. Figure 4.44 shows the

120

temperature dependent thermal conductivity57 of copper. For a temperature gradient of

l K, the thermal conductance of copper is shown in Figure 4.45.

 

 

   
 

24 IIIUIFITIIIIIIIVIIITYIIllilitrﬁlllliii
T ,

22 L l—e—Thermaloonductivity(W/m K)| :
Q »
g : i
g 20 - -
é" . ‘
.2 - -
g . x=2o.41 @800K .
C _ -.
O __ J
3 16 — -
m - d
E - ..
B _ -1
E 14 _— j

12 j 0 ——y=8.0179+0.015478x R=0.99912 j

10 iIrrrrlrrrrlrrnnlrrrrlrrrrlrrrrlrrrrlrrrl-

 

 

 

200 300 400 500 600 700 800 900 1000
Temperature (K)

Figure 4. 41 The thermal conductivity of Crzo N130.

121

 

40 I I I I I I I I I l I I I I l I I I r] I I I I

 

 
 

 

 

 

I —e— 4-sample system I
a 35 . 0 CRC Handbook ‘2
X »- -
E 30 :- j
5 : 1
P: :. i
:2 25 - ~
J—J b -l
8 '- -l
U 1— _.
8 20 C :
0 I I
E 15 _- j
E - .
S—
E Z 2
1— 10 1‘. ‘.
5 ’- g
1- -1
t :
0 p 1 1 1 1 I 1 1 1 1 l 1 1 1 1 I 1 1 1 1 L 1 1 L ‘
0

1 00 200 300 400 500
Temperature (K)

Figure 4. 42 The comparison between the Reference and 4-sample system measurement
in thermal conductivity of constantan.

122

Thermal Conductivity (th K)

Figure 4. 43 Use the curve ﬁt equation in Figure 4.42 to extrapolate the thermal

140

120

100

80

60

40

20

 

 

IirrTIIIlIIIIIII'IIIrIII'III

 

 

 

 

 

200 400 600 800
Temperature (K)

conductivity of constantan at 800K.

Thermal conductivity (th K)

430

420

410

400

390

380

370

360

350

‘
§ 11LL11111111111111111111111

 

II—IIIIIIIlrIjIIrIII'IIII'IWFI'IIIIIIII—I

 

I I a l I I I l I I I I I I I l I I I I I I I

 

I 0 Thermal conductivity (W/mK)CRC

111l111l11111111111Q11

Llullllllllllllllllllllllllllllll ll

 

 

O

200 400 600 800 1000
Temperature (K)

Figure 4. 44 Thermal conductivity of Copper

123

1200

It-

 

 

 

 

 

7.2 _ r I I I I r r I I I I I r I r I I I r I I l I 1

7 : o l 0 Thermal Conductance (pW/K) I 1

g? I I
3 ' .
in L o L
g 6.6 _ o .
g : o :
3 6-4 : ° 1
C ,. O a
3 . .
g P d
.05.) 6 " o —.
'- ' :
5-8 :- o :
5.6 '- 1 1 1 I J 1 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 -

0 200 400 600 800 1 000 1 200

Temperature (K)

Figure 4. 45 Thermal conductance of Copper, assuming a temperature gradient of 1K.

Table 4.4 has listed the thermal conductance of each wire at 800K. The total

thermal conductance of all wires at 300K and 800K are very similar, in the range of

 

 

 

 

 

11W! K.
Material (3 cm long) Thermal Thermal Total Thermal
Conductivity Conductance Conductance
(W/m K) @800K (uW/ K) (uW/ K)
@800K
Copper (Cu) 366 5.98 5.98*3 = 17.94
Constantan (Ni45Cu55) 130.84 2.127 2.127*2 = 4.254
Chromel (Ni90Cr10) 19.745 0.323 0.323*2 = 0.646
Total 22.84

 

 

 

 

 

 

Table 4. 4 The thermal conductance of each wire at 800K.

124

 

 

 

fro r

whe

is th

molt

 

coef
The

is 29

4.7.2 Convection
At low pressure (< 10” Torr), the gas molecules generally travel from one place
to another without colliding with other molecules. These gas molecules will transfer heat
from a surface at temperature T), to a parallel surface at Tc at a rate Q per unit area, thus
e... = aF—l i—P-(T. —T.)
y —l 87: MT
where y is the ratio of Cp/Cv, Cp is the speciﬁc heat capacity at constant pressure and Cv
is the speciﬁc heat capacity at constant volume. P is pressure in Torr and M is the
molecule weight of the gas, a is an accommodation coefﬁcient related to individual
coefﬁcients. For dirty surfaces, a approaches a maximum value of l. R is the gas constant
The speciﬁc heat capacity, Cp of nitrogen is 1.04 J/gK and the molar heat capacity of N2
is 29.124 J/mol K.
For most measurements, pressures in the range below 10‘5 Torr are sufﬁcient to make
Qcom, negligible. In our case, assume a is l and the residual gas is nitrogen (atomic weight
is 14), the pressure is 10'5 Torr and at 300K,
Rum'v: Cp-Cv= 8.3143 J/mol K
So for nitrogen C, = 29.124-8.3143 = 20.8097 J/mol K
7: 29.124/20.8097 ~ 1.4

At 300K, assume Th-Tc = 1K

 

1.4+1 8.3143 10‘5 X13332 (l)

= 1x

Q“""’ 1.4—1 87: ,/14*2*300
= 157.7 uW/mz
= 15.77 nW/cm2

125

 

 

 

At

So

Thu

4.7.

0f 11

radi

SBCO

 

near

1001

an it

are]

Asst

[Emu

At 8(

At 800K, QW,, = 96.58 uW/mz = 9.658 nW/ cm2

So for a one centimeter square surface area, the heat loss is only in nano watts range.

Thus, at high enough vacuum, heat convection can be neglected.

4.7.3 Radiation

A black body has a surface emissivity of 1. It means that this body will absorb all
of the thermal radiation to it. When this body is heated up, it will emit all the thermal
radiation it has. At some temperature, T, a black body emits radiant energy, E = 07” per
second per unit area, where dis the Stefan constant, 5.7x10'8 W/m2 K4. At temperature
near absolute zero, such losses are small but they become more signiﬁcant at above
100K.

Surface emissivity, c, is the relative errrissive power of a body compare to that of
an ideal blackbody.

If the emissivities are equal for the shield and the sample, and their temperatures
are Tshieid and Tsample. The radiation heat loss is

Qrad = f; (Tszmple — Tszietd )

Assume a sample with an e of 1, and the sample temperature is 301K and shield

temperature is 300K. So

_ 5.7*10’8x1

Q.,.,— 2_1 (3014-3004)

= 6.1868 W/mz
= 618.68 pW/cmz

At 800K, the radiation becomes

126

 

 

 

me.

me.

_ 5.7*10‘8x1

4_ 4
2-1 (800 799)

Qrad

 

= 116.5 W/rn2
= 11.65 mW/cm2
So for a one centimeter square surface area, the heat loss through radiation
becomes very large and it is difﬁcult to eliminate this loss in thermal conductivity
measurement at high temperature. It is for this reason that thermal conductivity

measurements have not been pursued in this high temperature system.

127

 

 

 

(3h

appr
decr
poi r
exhi

Flgi

Chapter 5 Experimental Results

The high temperature system is designed to investigate cubic materials which
perform well at high temperatures. The result of one of the ﬁrst samples received by the
lab is shown in Figure 5.1. This cubic material, Agogpb]0813038310ng812, exhibits
electrical conductivity of about 700 S/cm and a thermopower value of —150 uV/K at
room temperature (300K). The negative value of thermopower indicates that it is an
n-type semiconductor material. The thermoelectric power value at high temperatures has
approached -300 pV/K which is very encouraging, while the electrical conductivity
decreases with temperature. This is indicative of metallic behavior. The sudden turning
point of the thermopower measurement at 680K was unexpected. Though some materials
exhibit a minimum or maximum in the thermopower values, the curve showed in

Figure 5.1 was not symmetric about the peak as would normally be expected.

 

 

 

 

 

 

 

 

 

 

700 .I I I I I I I I I I I I I I l I I I I I I I I I q -150
"o. I
- o 0 Electrical Conductivity (S/cm)| .
. . . .
600 - ° 0. 1 .
_ o . o Thermopowermvmﬂ ,
E I o . J -200
o
5; 500 — ° 0. i 3‘
i o ' : ‘3”
E l’ o .. .. 0
ti r <—— o 0 ~ U
a 400 - '0. i g
g b 00 .. j '1
<3 I o 0. - 450 ’t;
8 _ o .0 ’ I 3
g 300 :- 00 O... 1
3 ’ 0° "In ° 2
: 000 o O. o .
200 — °°°Oooo I
: 0O 0C! - -m0
' OO 0" 0° 3
100 P 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 L 1
300 400 500 600 700 800

Temperature (K)

Figure 5. l The electrical conductivity and thermopower of AgongmeosgBiomTelz

128

 

 

 

 

Dan
Inn-

abc

 

 

 

 

 

 

40m 1. I I I r I I I I I l I I I T l I I I I—I I I I I I If I I I '100
. . , ‘l
3500 E 0 Electrical Condictivity (S/cm) ‘j 120
I o O o Thermopower (uV/K) «
,_. 3000 _— j
E: i ° - -140 _,
a 2500 ’— ° , g
é“ : 0 j g
g 0 8 - -160 "D
g 2000 _— I 0 - g
C .. " -1
8 : 2 o 0 0 ‘ €
:‘3 1500 T (._._ o - -180 g
‘5 r 0 8 0 I
3.3 i 8 o 3 o .
LlJ 1000 r o a - -200
E 8 ° ‘
500* 0000800000 :
: .0. .. _220
o .- 1 1 1 1 I 1 1 1 L I 1 1 1 1 I 1 1 1 1 I L 1 1 1 I 1 1 1 1 4
O 1 00 200 300 400 500 600

Temperature (K)

Figure 5. 2 Electrical conductivity and thermopower of BizTe3.

A standard material, bismuth telluride, was measured in the system again to verify
the performance of the system. In Figure 5.2, the measured values of bismuth telluride
agree very well with the reference data. A sample of a third material, Ago_7ng138bTezo,
was mounted and tested but the turning point was still observed where it was not
expected, and it happened at the same temperature as seen in Figure 5.1. This indicated a
problem with the measurement, either in the system or the sample mounting, at that
particular temperature. Figure 5.3 shows a repeated measurement to conﬁrm that the
turning point did not appear randomly. Again there is an upturn in the data for the points
above approximately 660K, however based on measurements for the B12TC3 reference

material (Figure 5.2) it is expected that the results on this sample are accurate for the

129

 

 

 

30

abt

bis

ten

da

I‘a‘

thi

300-660K range in Figure 5.3. Further investigations were necessary for the data points
above this temperature range.

This material has a higher composition of lead and tellurium and did not contain
bismuth. It has higher values of electrical conductivity and thermopower at room

temperature compared to the AgongioSboggBiomTei2.

 

 

 

 

 

 

10m L I I I I l I I I I I I Wﬁ I l I' I I I l I I I I -100
a o Thermopower (pV/K) -
1- . ..
g 800 __ g. 0 Electrical Conductivity (S/cm) .
5:) i- . Q . 7 " "15°
9 r- 8 O 4 ‘1
. «—
Q 600 — o o . 3
3 . 0
2 - ., ° . a
. O .. .
8 o 0 . 200 g
E ” 0 1 :5
g 400 ~ 9 0 °.. ——> . §
8 r .0 0 ‘ "’
UJ . 98 . .
. 0809000.8 O - -250
200 - 009 -
. Recomeogooggoo
. .0 .
, “I." 1
0 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 _m0
300 400 500 600 700 800

Temperature (K)

Figure 5. 3 Electrical conductivity and thermopower of Ago_7ng138bTezo

After some investigation, it was discovered that the problem associated with the
data above 660K came from the type of thermocouple used in the measurement. The type
T thermocouples (copper-constantan TC) that were used in these measurements are not
rated for high temperature applications, and the polynomial used for converting the
thermocouple voltage to a temperature was valid only up to 660 K. The temperature

gradient across the sample is determined by comparing the voltage drop across the

130

Sill

M.

Fig

L

EX;

IIIiII|

 

 

r

.L...\.rt..\ \CTJCt:C(2KCL :WL..-M71:

|_
1W

 

 

sample to the derivative (dV/dT) of the absolute voltage drop of the thermocouple. The
dV/dT curve of the type T thermocouples has a sharp drop above 660K.

Type K thermocouples (Chromel-Alumel thermocouples) were used next and
Figure 5.4 shows one of the results of a sample mounting with this type of thermocouple.
Examination of the dV/dT curve of the type K thermocouple, however, is not very
smooth, which can cause large errors in the dT value if the temperature is slightly
unstable. In Figure 5.4, the sample has the same composition as the sample in Figure 5.3,
AgoqublngTezo, though; the electrical conductivity is much higher (about 1000 S/cm)

for the latter material.

 

 

 

 

   
 

50m T I I I I I I I I I I I I I I I I I I I I I I I I I I I I l I I I I l I I I I q o
i- l 0 Electrical Conductivity (S/cm) I j
P o d
» °\\ 0 Thermopower corrected for leads (uV/K) I" -50
4000 - I
,. O
A O ‘
E ’ a
u . q 400
«2; . °° . g
,2; 3000 - o . g
a ~ q, ~ 0
u ,. O “ '150 D
g o . g
C b -
8 P % d ’1
d t
76 200° C <—— ~ -200 §
0 q
E i- Q) . V
E L o°o
LU .-
10“) -
0 '- 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1

 

 

 

100 200 300 400 500 600 700 800
Temperature (K)

0

Figure 5. 4 Electrical conductivity and thermopower of AgmnglngTezo

131

 

der
Tel
sys
10v.
funi

ofb

gapl

 

tEmw

One thing that needs to be noted is that the PID temperature control of this system
was not properly tuned yet. Therefore, the type K thermocouple was not suitable for use
then.

Finally, a Type E TC (Chromel-Constantan) was used for its very smooth
derivative curve. Figure 5.5, 5.6 and 5.7 are results of the reference samples - Bismuth
Telluride and constantan foil. The ﬁgures show the comparison between the 4-sample
system and the high temperature system. The 4-sample system [60] is a well-established
low temperature (80400 K) TE measurement system in the lab. It is used to verify the
functionality of the high temperature system. In Figure 5.5, the maximum thermopower
of bismuth telluride is -227 uV/K at 390K. According to Goldsmid [61], the energy band
gap, Eg, can be determined from the maximum thermopower value and the corresponding
temperature,

Eg=2xexSmmex

From Figure 5.5, Eg = 2 x e x 227 x 390

= 0.177 eV

This band gap value agrees very well with the literature values of 0.17 eV [62].

132

 

 

Fi

SYSt

. LQ
Ecx \ \zth .ICCL t... E: \
p U . U

 

 

 

 

 

 

 

 

 

-w p I I I I I I I I I I I r 1 I I I I I I l r I I f I I I I I d
l' A "
100 i ”A A Thermoelectric Power (4-sample) .
I AA 0 HT Thermopower (pV/K) :
A
F‘ I. A "
g -120 _- AA 1
g. " AA .
T: l- A -
m -140 - ‘5 —
E ' 9, .
D. ' A -
u " .
E -160 - ..
U " d
2 " -l
Q)
E -180 '- J
.. . .
-200 _ .0 .‘i
: ’. ,
-Qo ~ .' “
I not. 2
-240 '- 1 1 1 1 I L 1 1 1 I 1 4 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 d
0 100 200 300 400 500 600

Temperature (K)

Figure 5. 5 The comparison of the thermopower of bismuth telluride between 4-sample
system and hi gh-temperature system.

45(1)

 

I r I I I I l I I I I l I I I I I I I I I I I I I I

 

4000 A dc Electrical Conmctivity (cl-sample)

0 HT Electrical Conductivity (S/cm)

3500

A
A
A
A
A
3000 AA
A
A
2500 AA
A
A
A

32

20(1)

Electrical Conductivity (Sim)

1500

1000

111I1111I1111I1111I1111I11111111LI1111

IIII[IIIIlIrIIIIIITTTjIIIIIIIIIIIIlIIIIJ

 

 

 

500 l l I l I 1 J l

 

O
—L
O
O
N
O
O

300 400 500 600
Temperature (K)

Figure 5. 6 The comparison of the electrical conductivity of bismuth telluride between 4-
sample system and hi gh-temperature system

133

 

W11

an

duc

 

In Figure 5.7, Constantan (CussNi45 alloy) foil was measured in the system and
was compared with the literature values. Negative thermopower values indicate that it is
an n-type alloy. The small disagreement occurred at higher temperatures which might be
due to the shape and/or purity of the sample — voltage and temperature gradient
(distribution) across a foil might be slightly different than those across a wire. The error
percentage of this measurement can be obtained from

Error% = (Reference — Measured)/Reference

The error percentage of the HT Constantan thermopower measurement is shown

in Table 5.1. The overall error percentage of this measurement falls between 5-8%.

 

I I I I l I I I I I I I I I I I I I I I I I I I l I I I I l I I I I I I I I I

  
    

 

A Reference from literature

      

 

 

 

 

 

-10 1 o 4-sample system (pV/K) .2
: :1 HT Thermopower (yV/K) ;
- , q
ix: -2o :- -1
a . .
T: 3 Constantan wire 1
“3’ ’3’ 1' / (from literature) 4
8 : \_ I
o - d
E -40 - ‘ —
U . . .
m ‘- .‘ CI
5 _ -l
o - l
E '50 I 1
(D r. .
.c: _ .
l.— _ .i
’60 i' Constantan foil 1
E (measured data) 3
l- u .
-70 _- ‘1 D gt
_m h 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 u

0 100 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 7 The comparison of the thermopower of Constantan between 4-sample system
and hi gh-temperature system to the literature values.

134

 

Ta?

rne.
th

coni

C0llt
ther
'Ihe
Sysu

Sam}

 

[hes

 

 

 

 

Temperature Reference TEP Measured TEP Error %
(K) 31le (EV/K)
302 - 41 - 43.207 5.38%
502 -54.72 -57.654 5.24%
649 -61.13 -65.99 7.95%

 

 

 

 

 

 

Table 5. 1 Error percentage calculation of the HT Constantan thermopower measurement.

Cubic materials are the main focus when the high temperature system is ready for
measurement. Silver paste was used as an electrically and thermally conductive adhesive.
In one case, however, the surface of the sample showed a change in which the
composition of the sample was found to be more silver rich after the run, than before the
run. To eliminate the possibility that the excess silver was from the silver paste, other
conductive pastes were used. Figure 5.8 shows the electrical conductivity and
thermopower data of the cubic sample KF2229R1D (Ago-gzpblgstezo) from 300-700K.
The result agreed very well with the 4-sample system and the percentage error of the HT
system measurement for this sample is in Table 5.2. However, the properties of the
sample changed after it was heated to 780K. Figure 5.9 shows the change of properties as

the sample was measured from 760K to 300K.

135

 

 

  
   

   
   

 

 

 

 

70m '- I I I I I I I I I I I T r I I I I I I I I I j I—T l I I I I I I I I I I I I I Fl 0
0 HT Electrical Conductivity (S/cm)
60m -_ 1:1 4-sarnple system Electrical Condlctivity (S/cm) -50
: 0 HT Thermoelectric Power (pV/K)
A c I 4-sample system Thermoelectric Power (yV/K)
E 5000 - -100
t-g - -i
to - 3
v _ (1)
g - 3
,5 4000 _- - -150 8
s l 0
e . . §
8 3000 — _ -200 A
re ’ i E
:3. . o __, : 3
§ 2000 _ . - -250
in ’ 3
. ° 2
1000 : o - -300
0 ° ° . . 3
o
0 1 1 L 1 1 I o 9 1 _50
O 100 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 8 The comparison of the electrical conductivity and thermopower of cubic
material KF2229R1D between 4-sample system and high-temperature system (Oct. 25)

 

 

 

Temperature 4-sample system High T system Error %
(K) S (uV/K) o (S/cm) S (pV/K) o (S/cm) S (pV/K) o (S/cm)
320 -l70.36 956.59 -l63.37 960.13 4.1% 0.37%
400 - 204.52 587.77 - 201.22 640.86 1.6% 8.3%

 

 

 

 

 

 

 

 

 

Table 5. 2 Error percentage calculation of the sample KF2229R1D.

136

 

 

anal
com

Effec

 

sum
frOm
from
Sui-fa
tern

felarj

 

   

 

    
   
    
  

 

 

 

 

80m P I I I I I I I I I I I I I I r I I I I I I I I I I T T I I l’ I I I T I I I I I o
l.
: 0 HT Electrical Conductivity (S/cm)
7000 : :1 4-sample system Electrical Conchctivty (S/cm) 50
HT Thermopower (uV/K)
,_. 6000 _- 4-sample system Thermoelectric Power (pV/K)
g : " 400 —{
Q. 5000 ' I 3
s : . 3
. _ -i 0
t5 . — -150 P
g 4000 f " g
s - 3 9
g: 3000 :‘ . . j -200 ‘3
E I o ——> «
cu - O .
1000 _— -
h ° ° 0 o J -300
r o
o L 1 1 1 1 14 1 1 1 I 1 1 1 1 J L 1 J 1 L 1 1 1 1 I 1 1 1 1 I 1 101% 9 O1 o1 o1 1 d

1 00 200 300 400 500 600 700 800
Temperature (K)

0

Figure 5. 9 The comparison of the electrical conductivity and thermopower of cubic
material KF2229R1D between 4-sample system and hi gh-temperature system (Oct. 26).
The scanning electron microscopy (SEM), energy dispersive spectrometry (EDS)
analysis showed that the sample surface included excess silver as well as copper. An EDS
comparison between the inside and the surface of the sample shows that it was a surface
effect instead of total reaction throughout the whole sample. The EDS results are
summarized in Table 5.3 and 5.4. It was believed that the extra silver might have come
from the silver paint or that some of the other elements in the sample were evaporated
from the surface layers at the high temperatures leaving the sample silver rich on the
surface. For example, if tellurium was evaporated from the surface at the high
temperatures, this would leave the samples surface with less tellurium, and with higher

relative compositions of all other elements. In either case, the excess composition of

137

 

sil

the

thou
diff].
layer
indie

felea

 

silver might have changed the measured voltages at the surface of the sample and caused

the electrical conductivity to increase and thermopower to decrease.

 

 

 

 

 

 

 

 

 

Element Atom% Element Wt. % Wt. % Error
Te 45.4 36.6 +/- 0.4
Pb 44.3 57.9 +/- 1.4
Ag 3.6 2.4 +/- 0.2
Cu 2.9 1.2 +/- 0.1

 

Table 5. 3 The EDS result for surface of the cubic materials KF2229R1D [63].

 

 

 

 

 

 

 

 

 

Element Atom% Element Wt. % Wt. % Error
Te 49.8 38.6 +/- 0.8
Pb 48.2 60.6 +/- 8.1
Ag 0.3 0.2 +/- 0.2
Cu 0.3 0.1 +/- 0.4

 

 

 

Table 5. 4 The EDS result for inside of the cubic materials KF2229R1D [64].

It was rather difﬁcult to determine where the copper elements came from. Even
though the sample stage is made of OFHC copper, it is nickel/gold plated and it is
difﬁcult for the copper ions to penetrate into the sample through the nickel and gold
layer. Furthermore, the change of color of the stainless steel bolts was observed, this is an
indication of alloy annealing at high temperature. It is not known if elemental copper was

released from the stainless steel during the annealing process.

138

 

Figr
KF2

 

DOW]
diffe
Figu

 

 

 

 

 

 

21 I I I I l I I I I I I I I I l I I I I I j I I f
. 0 ° ° 0 o b 0 Power factor Oct25
: of" o 0 Power factor_0ct26 .
20.5 - c’o -
. O .-
0
§ ' o o
g 20 - ' -
LL 0
B
s - ° . -
a. 19.5 - ° -
. Q .
O
19 - ° -
. o .
18.5 '- 1 1 1 1 l 1 1 1 1 l 1 1 1 1 I 1 1 1 L l 1 1
300 400 500 600 700 800
Temperature (K)

Figure 5. 10 The power factor comparison between the two runs (Oct. 25 & 26) of
KF2229R1D.

Even though the thermopower and electrical conductivity values of KF2229R1D
are different before and after heating to high temperatures, Figure 5.10 shows that the
power factor appears the same. Another sample from the same ingot of KF2229R1D but
different section is measured and similar surface composition problem occurred.
Figure 5.11 shows the comparison of the 4-sample and high temperature system in

electrical conductivity and thermopower of sample, KF2229R1C, from 300K to 700K.

139

 

 

    
 

 

 

 

 

 

 

60m . I I I I I I I I I l I I I I I ,' I I I I I I I I I I I I I l I I I I j I I I j . O
. O 4-sample Electrical Conductivity (S/cm)
; in HT Electrical Conductivity (S/cm) 50
5000 -
A ’ O 4-sarnple Thermoelectric Power (pV/K)
g E I HT Thermoelectric Power (pV/K) 400 g
‘3 4000 — . g
é‘ " ‘ a
13 E - -150 §
3 ~ ‘ '3
E 3000 e I n‘
O r- .. U
9 t ~ -200 g
.8 . I ; _,
b _ .l e
E 2000 . J <
Lu P . j '250 3
1 000 r I _ {”0
_ 'l
. u u 1
1- n 1
o 1 1_1 1 L 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 L 1 1 1 1 l 1 1 1 1 -50
0 1 00 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 11 The comparison of the electrical conductivity and thermopower of cubic
material KF2229R1C between 4-sample system and high-temperature system [65].

After this experience, all stainless steel bolts were replaced with titanium bolts.
The use of different paint for mounting, such as carbon and platinum paints, was also
investigated. As has been stated in the experimental set-up section, silver paint was still
determined to be the most suitable paint as long as the measurement is not on a cubic
sample at more than 700K.

As a conclusion, most of these cubic materials have metallic—like electrical
conductivity and the conductivity becomes constant at high temperatures while the
thermopower values linearly increase as the temperature increases. Due to the high
thermopower at high temperature, these compounds have great potential in TE power

generation applications.

140

lﬁgu
(Pol
tline

were
aﬁer
th at L

pech

 

More reference materials were measured in the high temperature system to verify
its performance. Figure 5.12 shows the thermopower measurement of 99.9% purity
molybdenum and it agreed very well with the reference data found in Pollock [2]. This
measurement was taken before the PID temperature controller was properly tuned so

there were not many data points.

 

 

 

20 I I I I I I fI—r I I I I I I ﬁr I I I I I I I I I I r I I I I I I I I I I I
. 7 .l
- 1 Reference Mo from Pollock -
’ :1 HT Thermoelectric Power (uV/K) '
F 1 ‘ -l
15 - e
A _ u a q
E
> " ‘ .
3;
L - It
a. 10 - -
.0 l- d
a - ° -
g - u
to 11
IE 5 '- ‘ -l
. I21 .1
E1
0 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1

 

 

 

1 00 200 300 400 500 600 700 800 900
Temperature (K)

Figure 5. 12 The comparison of the thermopower of molybdenum between the reference
(Pollock [2]) and hi gh-temperature system (before the temperature controller is properly
tuned).

After the temperature controller was properly tuned, large amount of data points
were collected in each run. Figure 5.13 has shown another measurement of molybdenum
after the proper tuning, the measured values agree very well with the reference, except

that at lower temperatures, small deviation is shown. Table 5.5 shows the error

percentage of HT system measurement for molybdenum. The deviation might results in

141

 

FiguI
(Pol
tUne

 

different purity between the sample and the reference. The discontinued data between
550-580K is due to unexpected electronic noise during the thermopower measurement, so

those data has been removed.

 

20 I I I I I I I I I 1 I I I I l I I I I I I I I I l I I I I l I I I I

- 1 Reference Mo from Pollock

1

u HT Thermoelectric Power ‘

15*-

1141

l

10-

Thermoelectric Power (uViK)

 

 

 

o llllIllllIllllIlllJIlllllllllILlI1L

200 300 400 500 600 700 800 900
Temperature (K)

 

Figure 5. 13 The comparison of the thermopower of molybdenum between the reference
(Pollock [2]) and hi gh-temperature system (after the temperature controller is properly
tuned).

142

 

 

 

 

 

 

 

 

 

Temperature (K) Reference TEP Measured TEP Error %
(NV/K) (RV/K)
400 8.52 6.973 18.16%
500 11.12 9.6987 12.78%
600 13.27 12.496 5.8%
700 14.94 14.821 0.8%

 

Table 5. 5 Error percentage calculation of the molybdenum HT thermopower
measurement with the Reference.

The HT measured electrical resistivity data of molybdenum was also compared

with the reference in Figure 5.14 and they agree very well as shown in Table 5.6.

 

2.5 10‘

l I I I I I I I— '

 

—6— Reference Electrical Resistivity

-0— HT Resistivity (n ohm m)

 

210‘

Electrical Resistivity (n ohm m)

5000

 

 

 

 

200 400 600 800

Temperature (K)

10m

Figure 5. 14 The comparison between the reference [57] and measured electrical

resistivity of M0.

143

 

 

T2

wi

Clnnbvrw n-.. -1.

 

Fm

b

bent

 

 

 

 

 

 

 

 

 

 

Temperature (K) Reference resistivity Measured resistivity Error %
(n S2 m) (n 82 m)
400 8020 8140.9 1.5%
500 10600 10708 1.02%
600 13100 13439 2.58%
700 15800 161 16 2%

 

 

 

Table 5. 6 Error percentage calculation of the molybdenum HT resistivity measurement

with the Reference.

 

1.8104 .

1.6104

1.4104

Electrical Conductivity (S/cm)

III'IIIIrIleIITI

 

8000 ‘

 

 

—9— NIST Ref.

121 BOO-561K
O 31 0-480K
o

 

A 320-700-560K

490-7OM, 310-7mK

 

 

.111111111111111111

 

O

200 400

600 800

Temperature (K)

Figure 5. 15 The comparison of the electrical conductivity of NIST 1461 stainless steel
between the reference (NIST [66]) and high-temperature system.

144

 

T (K) c(S/cm) at 400 (K) Error% o(S/cm) at 700 (K) Error%

 

 

 

 

 

 

 

 

 

 

 

Reference 1 1299 ---- 9569.4 ----
Runl (320-700- 11611 2.76% 9721.1 1.58%
560K)

Run2 (600-560K) ---- ---_ ---- ----
Run3 (310-480K) 1 1516 1.92% ---- ---- '
Run4 (490-700, 1 1535 2.08% 9753.9 1.93%

310-700K)

 

Table 5. 7 Error percentage calculation of the NIST stainless steel HT electrical
conductivity measurement with the Reference.

Figure 5.15 shows the NIST 1461 Stainless steel measured in high temperature
system and it agreed very well with the NIST standard data. Refer to Table 5.7 for error
percentage calculation.

Figure 5.16, 5.17 and 5.18 show the measurement results of another series of
cubic material, the composition is Ago,g4Pb13SbTe20. The sample was grown in ingot and
was cut to three different sections (See Figure 5.19). Figure 5.16 shows the electrical
conductivity of the three sections. The samples have metallic behavior since the
conductivities reduce as the temperature increases. Section A was measured in 4-sample
system from 80-4OOK and it was measured in HT from 300K to 700K. The two
measurement agreed very well as shown in Figure 5.16. Section B was measured in HT
system before the temperature controller is properly tuned so the data points were less
than the other two sections that were measured after the tuning. Figure 5.17 shows the
thermopower of the three samples. The thermopower values increase linearly with
temperature until around 600-700K. The power factors of the three samples are shown in

Figure 5.18. The power factors of sections B and C are obtained from the curve fits of the

145

electrical conductivities and thermopowers plots. The EDS analysis of these samples can

be found in Appendix A [67].

 

4
110 TIIIIIIIIIIITIIIIIIITIﬁI[IﬁIIlIIII'IIII

 

 

O
- a O KF2242R2A '
~ %- - KF2242R28 -
8000 ~ g A KF2242R2C -

6000

40(1)

Electrical Conductivity (Slcm)

20C!)

 

 

 

l l l l

0 1 00 200 300 400 500 600 700 800
Temperature (K)

 

Figure 5. 16 Electrical conductivity of Ago_g4Pb13SbTe20 and the sample ID is KF2242R2
with A, B and C sections.

146

 

 

 

 

 

 

 

 

o ._ I I I I I I I I I I I I I I I I—I I I I I I I I I I W—FI I I I I I I I I I I .
l. O KF2242R2A ‘
-50 L I KF2242R28 J
E A KF2242RZC 1
7 ‘l
S r I
>3 -1oo - -
a I j
3 .. .
O
Q_ .. .l
.g -150 — -
8 _ I j
E -200 —
(D ,. .1
.C
F. " d
I :
-wo 1 1 J 1 I 11 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 14 I1 1 1 1 I1 1 1 1
0 1 00 200 300 400 500 600 700 800

Temperature (K)

Figure 5. l7 Thermopower of Ago,g4Pb13SbTezo and the sample ID is KF2242R2 with A,
B and C sections.

.5
C

 

I I I l I I I I I I I I I I I I I I I

O KF2242R2A
I KF2242R28
A KF2242R2C

 

35

 

30

25

20

POWBI' Factor

15

10

0‘1

 

 

 

O

 

.4
§ 111111111I1111I1111I1111I1111I1111l11

o IIrIIIrIITIIIIIIIIIII—III'IIIIIIIIIITIWI

200 400 600 800
Temperature (K)

Figure 5. 18 Power factor of Ago.g4Pb13SbTe20 and the sample ID is KF2242R2 with A, B
and C sections.

147

 

 

Figure 5. 19 KF series materials are grown as ingot and cut to different sections for
measurement.

The high temperature system only measures the power factor of materials, as
explained in the experimental set-up chapter that why high temperature thermal
conductivity measurement was not considered. In order to estimate the figure of merit of
a material, a theoretical calculation is included here to roughly derive the thermal
conductivity of the materials based on the existing HT data and 4-sample (low-
temperature) measured thermal conductivity data.

The electrical conductivity can be expressed as
0' = me2 (2') / me
and the electronic thermal conductivity is
Kc = LOT = :akz /e2)0T

(TXEZ‘Z') — (ET)2
k’fz(z')2

 

where if = and of is a pure number and L = ﬂkZ/ez) is the Lorentz

number. For a non-degenerate semiconductor, the relaxation time is 2': at?“ so
_ 5 5
(2') _ an3 - s) / F(E)

(2E) = akin-g- - s) / 1‘03)

148

2 2
(2E >= asz I‘(%— s)/I‘(%)
Since 171+x)=x17x), so of = g-s, where s is the scattering parameter and for various

scattering mechanisms, the 5 value is different. For scattering by the acoustical modes,

s = 1/2 (of = 2), and for ionized impurities scattering s = -3/2 (.27 = 4).

For a fully degenerate semiconductor (metal), a better approximation is used to

obtain the Lorentz number, please see Appendix B for more information [68]. We have
2 2
<T><EZT> — (E7) = §7z2k2T2(r)
so of = l/31't2 =3.289 and L = 2.44x10'8 VZ/KZ. If a semiconductor which is degenerately

doped but not fully degenerate, we can assume a of = 2.15 and thus L = 1.596x10'8 VZIKZ.

For the cubic materials, the latter Lorentz number is more suitable for calculating
the electronic contribution of the thermal conductivity. However, since the materials are
very highly doped, both Lorentz numbers are used for calculation comparisons.

Figure 5.20 shows the total thermal conductivity of sample KF2242R2A
measured in 4-sample system from 80-400K. Figure 5.21 shows the calculated electronic
thermal conductivity based on the measured electrical conductivity values measured from
the 4-sample and HT systems. Equation is used for this calculation. Since the total
thermal conductivity is known from 80-400K. We can approximate the lattice term for

both L values as shown in Figure 5.22.

149

 

 

 

 

 

 

 

6 h I I I I I I I I I I I I 1 T I I I I I I I I I I I I I I I I I I I I j I I I I .-

i- 0 cl

I o [‘9‘ Thermal Conductivity (W/mEK) | :

5.5 :- -_

.- -l

g " d

E 5 r 1

a - ‘

2‘ L d

E 4.5 _ j

H i- d
U

8 : I

S 4 _ "

u . 1

E C I

E 3.5 - -

0..) i- d

5 I 2

a L ~

‘6 3 ’- _.

+- : :

2.5 :- 2.

2 '- 1 1 1 1 I 1 1 1 1 I 1 L1 1 I 1 l_1 1 I 1 1 1 11L 1 1 1 1 I 1 1 1 1 I 1 1 1 1 d

50 1 00 1 50 200 250 300 350 400 450

Temperature (K)

Figure 5. 20 The total thermal conductivity of KF2242R2A from the 4—sample system in
Hogan’s lab.

 

 

 

 

2.5 I I I I I I I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I r I
L 0 Electronic thermal conductivity (L=2.44e-8) -
r I Electronic thermal conductivity (L=1.5966-8) ‘
A ’- 7 d
X
E 2 . .
g . .
.2? ’ -
E - -r
ti 1 5 ._ _
3 I
U h a
C
o b d
U .- q
a _ .
5 " .
2 '- .
C _ u
0
.3 .. .l
2 0.5 — J
LU )- d
1- cl
0 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1

 

 

 

0 1 00 200 300 400 500 600 700 800
Temperature (K)

Figure 5. 21 The electronic thermal conductivity of KF2242R2A calculated from the
electrical conductivity and with two different Lorentz numbers.

150

 

 

 

 

 

 

4.5 .. I I rw I r I r I I I I I I I I I I I I I—T I I I I I I I I I ﬂ I I I I Iﬁ d
: . o Lattice thermal conductivity (L=2.44e-8) :
4 :_ I I Lattice thermal conductivity (L=1 .5969-8) ;
5? I ' 3
g . I .
3 3-5 : ° I '2
2.. - O - .t
3 3 f o I 2
E b . d
o . ° - .
U _, o .. q
E 2.5 - o I. ‘
E I o I Z
a.) P O - . -
5 _ o I. .
E ‘ ° ' d
S '- 0 o ... :
1.5 '- 0 o O _
: O O O o O :
r 0000000 ~
1 I. 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 L 1 1 1 1 1

50 100 150 200 250 300 350 400 450

Temperature (K)

Figure 5. 22 The lattice thermal conductivity of KF2242R2A is calculated from
subtractions of electronic thermal conductivity from the total thermal conductivity. These
data are calculated through the equations of the sixth polynomial ﬁt of the electronic
thermal conductivity and the fourth polynomial fit of the total thermal conductivity.

The two basic scattering mechanisms in conduction are the lattice scattering and
impurity scattering. Lattice scattering is when the carriers scattered by vibration of lattice.
This vibration results from the temperature. Thus, as the temperature increases, lattice
scattering is dominant and causes the carriers’ mobility decrease. Impurity scattering, on
the other hand, is dominant at low temperature. At low temperature, the thermal motion is
low and the carriers have lower mobilities so they are more likely to be scattered by
charged ions (impurities) than with greater momentum carriers.

In Figure 5.23, the lattice thermal conductivities are assumed to be constant at
high temperatures because lattice scattering is dominant. Once the lattice thermal

conductivities are predicted, the electronic thermal conductivities can be added to obtain

151

the total thermal conductivities as shown in Figure 5.24. Finally, the ZT of the material

can be estimated as shown in Figure 5.25.

 

 

 

     
 

 

 

 

4.5 I. I I I I I I I I I I I I I I I I I I I T r r I I l I ﬁ I I I I I I I l I I I I
. . 1
I I —6— Lattice thermal conductivity (L=2.449-8) I
4 - x -I— Lattice thermal conductivity (L=1.596e-8) -
9 I I
g _ ..
g 3.5 r 1
.3“ C 2
g 1- d
8 3 : :
u

c - .
o - .
o ,_ ..
E 2'5 : Added po'nts for better curve fit :
(T, r at higr temperatures ‘
5 I 1
.3 2 : 1
g _ J
_1 _ .
1 .5 :' -45 ~-~. :
l- ..
1 h 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 L I 1 1 1 1 1 1 1 1 ‘

0 1 00 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 23 The lattice thermal conductivity of KF2242R2A with curve ﬁt till 700K.

152

 

 

 

 

 

 

 

5.5 .- I I I I l I I I I I I I fr I I I I I l I I I I l I I I I l I I I rj r I I I ..
: —9—Total thermal conductivity (L=2.44e-8) ;
5 _— -I-Total thermal conductivity (LL-1.59698) :
2‘ C :
E 4.5 _- j
g, : :
g 4 I- E
‘5 E 3
E 3.5 - .4
o » .
U r- -r
B : :
E 3 — _
OJ P .1
g : :
g 2.5 ’— J
r— : :
15 b 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 11 I 1 1 1 1 L 1 1 1 1 I 1 1 1 1 1 1 ‘

O 1 00 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 24 The total thermal conductivity of KF2242R2A with two different Lorentz

 

 

 

 

 

 

 

number.
1 I I r I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
* o ZT(L=2.449-8) ‘
* -I—ZT(L=1.596e-8) ‘
l- o ‘
0.8 *- _
l- u
g; 0.6 - _
U " -l
a.)
an . -l
~§ _ d
g 0.4 " -l
0.2 - "
t J
r -r
P
0 4 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 J 1 1 14 I 1 1 1 1 I 1 1 1 1.1
0 1 00 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 25 The estimated ZT of KF2242R2A with two different Lorentz number.

153

In some of the latter materials, we have observed a change of electrical
conductivity and thermopower as the sample is measured from 300 to 700K in a step of
10K versus measurements on the same sample from 700 to 300K. The electrical
conductivity decreases as the thermopower increases as shown in Figure 5.26. Two
hypotheses were made: the ﬁrst hypothesis is that there might be oxide growth on the
surface of the sample. Even though the sample is measured under relatively high vacuum
(5x10'5 Torr). There is still signiﬁcantly large amount of particles inside the chamber.
Taking the equation from Ohring [69],

Number of molecules that strike an element of surface per unit time and area is

 

(I) = 3.513><1022 «5%: molecule/cmz-sec

where P is pressure in Torr, M is the mass of gas molecules and T is temperature in K.
For our case, at 700K, vacuum is 5x10'S Torr, the number of oxygen molecules (02) that
strike an element of surface per unit time and area is (molecule weight for 02 is 16 x 2 =

32g)

5><10’5

432x700

= 1.17 x1016 oxygen molecules/ cmz-sec

(I) = 3.513x1022 x

The second hypothesis is that rnicrocracks might appear inside the materials. This

is a whole new area of research to investigate the material science of cubic materials.

154

JI———

 

 

 

 

 

 

 

 

 

 

 

25m I I I I l I I I I 7' I I I I T I I I I l I T -100
. 0 Electrical Condrctivity (S/cm)
. Enema I i I?
h o n d
E 2000 _ 0 Burn :1 TEP (uV/K) q 450
1- un J
% " 00 “an I
V r- -‘ '4
g I O Dunn " a
“+3 1500 - 0 DD ‘ '200 g
3 " 0 an " O
'o
E " 0 an ‘ o
O . 0 t1 111 . g
0 ' ooo UBSEU ' (“a
S 1000 - 0C) 333% - 450 ”:2
'C " o -
.. _ o a ,
E _ °oo $Emll I 3
UJ _ °°o° ‘
500 — 0033008 ~ -300
~ 99 r
: 883938.060 ‘
O P 1 1 I 1 1 1 I 1 1 1 I 1 1 1 1 I 1 1.I _350
300 400 500 600 700

Temperature (K)

Figure 5. 26 The electrical conductivity and thermopower of KF2242R2A.

A sample with more silver composition KF2242R3C, Ago,86Pb138bTezo, was
measured with the electrical conductivity and thermopower shown in Figures 5.27 and
5.28. The sample has been measured repeatedly as to show consistency. The electrical
conductivity data repeated very well. The magnitude of the thermopower values
decreases a bit after one cycle but it remained same values after that. After the
measurement, the sample was observed under the microscope. Figure 5.29 shows a layer
of thin ﬁlm is formed on the surface of the material. Figure 5.30 shows crack lines appear
on the surface of the sample, this might explain the deviation in thermopower data. Since
the electrical conductivity measurement did not change, it is believed that the cracks have
affected the sample thermal conduction only. It is suspected that the cracks on the sample

are due to the difference in thermal expansion between the sample itself and the sample

155

stage. The thermal expansion coefﬁcient of a sample with similar composition was
measured using TMA (Therrnomechanical Analyzer) and it gives about 21.4 urn/(m °C)
[70]. It is compares with the thermal expansion coefﬁcient of copper at 16 urn/(m °C).

In addition to the thermal expansion problem, some evidence also suggests that
elements might have evaporated from the sample. As shown in Figure 5.31, after the high
temperature run with the sample KF2242R3C, the copper plate used to mount the sensor
had a grayish coating on the surface. Only one face of the copper plate changed color,
this indicates a coating on the plate, as opposed to an alloying. EDS analysis shows that
the surface of the copper plate was coated with tellurium [71] and this is one of the main
components of the sample. However, this was not observed before so not all cubic

materials will evaporate elements.

 

 

 

 

 

 

 

 

 

2000 I I I I T I T I T I I I I I I I I I I I I I I 1
'. 0 Ju n95 (31 O-400-34OK) ‘
" . . l3 Jun66 (340-700, 350-44OK) '
L 6 A June12 (320-380K) -
. 0a 0 June1 4 (350-7OOK, 31 0460K)
n 1500 - 00' "9--June16 _
g _ O .' - II— Ju net 7 (490-700K-580K)
k7,- WU --I- June19 (590-635K) -
3% " ' '
3a l Ii .
3 i”
g 1 000 - 'un '-
8 h '.u '
‘16 ..
g 'l
U
9 ' .4
“J 500 - a
l i
o 1 1 1 4 J 1 1 1 1 I 1 1 1 1 L 1 1 1 4 I 1 1 1 1
300 400 500 600 700 800

Temperature (K)

Figure 5. 27 The electrical conductivity of sample KF2242R3C Ago.36Pb13$bTe20 with
repeated runs.

156

 

 

 

 

 

 

 

'100 L I I I I l I I I l I T I—Ii I l I I I I I I I I I
_ o JuneS(310-400-340K)
[ u Jun96(340-700,350-440K)
, A June12(320-380K)
-150 a‘. o June14(350-700K, 310-460K)
. 0.6 --e--June16
r- l - II—June17(490—700K-580K)
A ~ III a— June19 (590-635K)
>5. . I...
i -200 _ '- -
a " ‘
g b
a - l
g - J
a -250 _— j
I:
p.— _ q
. .
-300 r -
_350 l l l l l l
300 800

 

Temperatue (K)

Figure 5. 28 The thermopower of sample KF2242R3C Ago,36PblngTe/zo with repeated
runs.

 

Figure 5. 29 A layer of thin ﬁlm formed on the surface of sample KF2242R3C
Ago_36PblngTe20 after running in high temperature.

157

 

Figure 5. 30 Crack lines occurred on the surface of sample KF2242R3C Ago_g(,PbingTezo
after running in high temperature.

 

Figure 5. 31 The copper plate coated with tellurium (left) and a clean copper plate (right).

Figure 5.31, 5.32, and 5.33 show the thermopower, electrical conductivity, and
the power factor of cubic materials with various composition of silver. This allows us to
determine the best properties of the cubic materials among various composition of silver.
For this series of cubic materials, the sample that contains the most silver has the best
properties (the highest power factor). Some of the samples labeled “ﬁt” indicates those
power factor plots were generated from curve ﬁts of the thermopower and electrical

conductivity measurements. This was done because some of the measurements were

158

taken before the system was properly tuned and having fewer data points made it difﬁcult
to determine the trends of the power factor.
In Figure 5.32 or some of the previous thermopower plots, the thermopower
values of some samples stayed constant between 660-700K. At ﬁrst, it appears to be a
turning point but it is not as deﬁned as expected. Further investigation on the energy band
gap of the cubic material gives some information on how to interpolate the shape of the
thermopower. Appendix D shows the bandgap of a cubic sample AnglngTezo to be
0.26 eV at room temperature (300K). If we assume a constant energy bandgap from
room temperature to high temperatures and use the same calculation that was performed
to estimate the bandgap of bismuth telluride earlier in this chapter, assuming the turning
point occurs at 650K, we get,
0.26eV=2ex650xSmax
Smax ~ - 200 uV/K
The estimated maximum thermpower does not fall into the range of the measured
thermopower. The measured thermopower plots suggested maximum thermopower
should be larger than ~25011V/K. If we assume a higher Tm = 700K or 800K, the Smax
value will be even lower.
If we take another approach, taking the sample Ago,36Pb13$bTezo as example, if
the turning point really occurs and the estimated bandgap will be
Eg=2ex680x350

Eg ~ 0.476 eV

159

 

 

  
 
 
  

 

 

 

 

 

 

50 h r I I I I I I I I I I I I I I I I I I I I I I I l I I I I l I I I I I I I I I-
: o AngbmeTe20 :
0 _— A Ag Pb SbTe C 1
_ 0.82 13 20 ‘
g ‘50 E Ago_&Pb1aSbTe20D _:
>1 E AgomemeTezoA 3
g -100 E AgosapbreSbTezoB E
E : AgopuwaSbTezoC :
.2 _'_ _‘
.3 -150 _ AgoaePbIBSbTezo _
2 -

a I 3
E -200 _— '
B - I
.C - ..
I— - ..
'250 : t
{”0 j q
C -<
-350 *1 1 1 1 I 1 1 1 1 I 141_;1_I 1 1 I I I 1 1 1 LL4J_I 1 I 1 1 1 1 1 1

0 1 00 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 32 The Thermopower of cubic materials with various composition of silver.

160

 

 

 
  
 
   
   
 

 

    

 

 

 

1104 IIIIIITrVIIIIIIIIIIIIIIIIIIWIIIIIIUII—I
_ 9° 0 Ago. 78Pb1 BSbTezo
_ oo A Ag Pb SbTe C
1 082 13 20
8000 h
E . o Ago'aszmeTe20 D
E _ - o Age-“waSbTezo A
E. 6000 _ o Ago‘memeTezo B
:3 _ o A Ago'uwaSbTezo c
E » 0 Ag Pb SbTe -
D 0.86 18 20
o r .
E 4000 r- -
E r- 4
U
2 P _
LU
2000 — -
O 1 1 1 1 I 1 1 1 L I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 A...‘
0 l 00 200 300 400 500 600 700 800

Temperature (K)

Figure 5. 33 The electrical conductivity of cubic materials with various composition of
silver.

If this is true, it suggests that this sample exhibits increasing bandgap with increasing
temperatures. This property can be found in PbTe and since cubic materials are mainly
PbTe derivation. Further investigation on the change of bandgap vs. temperatures will be

helpful.

16]

50

40

30

Power Factor

20

10

Figure 5. 34 The power factor of cubic materials with various composition of silver.

 

0.73

 

 

 

Pb 1 8SbTe20

 

A AgmuPbmeTe20 A

 
  
   

 

 

11907813018313Te20 (fit) A AgoﬁwaSbTezo 3 (fit)
I I I 1 I I I . .
; Ago_82waSbTe,‘,o C (fit) I AgomemeTez0 C (fit)
I. .
_ AgomemeTe20 D (trt) AgomewaTezo
C ‘ 111. ’6» l
_ Q‘AMI '3 ; a ‘5 ..
: ‘ ”‘" 1
In“, if“ '51:; -‘ u
L I‘ .‘ “::.-.' ..’C.|
L111."111111411I1111I1111ILLL1L1111I11L1‘
0 100 300 400 500 600 700 800

Temperature (K)

162

Chapter 6 Simulation and Experimental Results of the Module

Theoretical simulations of the device’s performance can be obtained by utilizing
the results from the 4-sample and hi gh-temperature measurement systems. TE modules
for low temperature applications, i.e. for cooling purpose, have been investigated [72]
and models for the high temperature modules are being developed.

Before building a TB module, some performance simulations are needed to
estimate the best pairing of p- and n-type legs for the device. MathCAD® simulation was
used to determine the module’s ZT, TE efﬁciency, and maximum power output of a TB
module. Most of the important parameters for the simulations can be obtained from the
transport measurements of each material individually.

The performance of a TB power generator depends on the hot side temperature,

Th, the temperature difference between the hot and cold ends, AT, and the Figure of merit

of the materials, ZT. The efﬁciency of a single—couple TE generator without contact

resistance is given by

 

Of

 

,7 =_ #77. ,
' I(#+1)2/ZTH+(#+1)-m/ZJ

A TE module made up of an n-type cubic material, Ago_82PblngTezo, and a p-type
cubic material, AgogSnSbHTeg, was fabricated. Both samples have similar thermoelectric
efﬁciency. The n-type cubic materials have been heavily investigated as discussed in
Chapter 5. The optimized material was not used to fabricate the module because

optimized p-type material has not yet been discovered. Therefore, the n-type sample that

163

'0
.4
I

was used in building the module was selected to match the ZT of the p-type samples that

we have. The following sections compare experimental and simulated results.

6.1 Simulations

MathCAD® software was used to simulate the TB modules performance. The
code and results from these calculations can be found in Appendix E.

Since these two materials have been characterized by measurements from the low
and high temperature systems, the thermoelectric properties are taken directly from
experimental results. These properties are then used in simulation to determine the
performance of the TB module, and ﬁnally compared to experimental results. A list of
important parameters used in the simulation of the TB module are given below:

Sp( T): Temperature dependent thermopower of p-type material (pV/K)
S,,( T): Temperature dependent thermopower of n-type material
SM( T): Temperature dependent thermopower of the TB module

pp( T): Temperature dependent resistivity of p-type material (£2 cm)
,0,.( T): Temperature dependent resistivity of n-type material

RM T): Temperature dependent internal resistance of TE module (S2)
Ream: Contact resistance of TE module

RM( T): Total TE module resistance

RL( T): Load resistance

191T): Temperature dependent thermal conductivity of p-type material (W/m K)
K,,( T): Temperature dependent thermal conductivity of n-type material
KM( T): Temperature dependent thermal conductance of TE module

IL: Load current (A)
V0€( T): Open circuit voltage (V)

Ap and A,. are the surface area of p and n-type materials respectively (m2)
LP and L,. are the length of p and n-type materials respectively (m)

770: Carnot efﬁciency (%)
77: TB module efﬁciency or conversion efﬁciency

164

We: Electrical output power (W)
Qh: Thermal power input (W)

AT: Temperature gradient
T). and Tc are the hot side and cold side temperatures respectively
TM: The mean temperature

Important Equations: (these are the general equations, unit conversion is not included)

AT=n—T

T+T
TM: h2r‘

 

3,, (T) = |S, (T)| +

 

p. (T) + ppm]... LP

 

RM (T) = Rim (T) + Rm
KM (T) = (x, (T) * A" + KP (T) * Ap )* LP

 

 

AT
”r:T WezleRL
h
77—we
Q1.
12*
thSM(T)*IL*AT+KM(T)*AT— EMU?

Assume a constant temperature gradient, constant module contact resistance of 3
m. Table 6.1 shows the performance parameters obtained from the simulation. A
conversion efﬁciency of 3.6% is obtained for a ﬁxed temperature gradient of 200K,
Th=500K and Tc=300K. Figure 6.1 shows the simulated ZT of the module vs.
temperatures. The ZT is 0.5 at 500K. The simulation was done only till 500K because the
module is suppose to operate less than 550K since the p-type sample will melt above this
temperature. Figure 6.2 shows the heat flow through the module with temperature
gradient of 100K and 200K vs. current output. It veriﬁes that higher temperature gradient

will give larger heat ﬂow.

165

 

Performance Parameters Simulation Results

 

 

 

Open circuit voltage, V0c (V) 0.064
Load current, IL (A) 2.148
Load voltage, VL (V) 0.028

 

Total internal resistance, Rim (9) 0.017

 

Electrical output power, We (W) 0.06

 

Conversion efﬁciency, 1] (%) 3.6
Input thermal power, Qh (W) 1.662

 

 

 

 

 

Table 6. 1 The performance parameters obtained from simulation.

 

 

 

 

 

.0526, l l
0.4 - -
Z( T ) -T
0.2 - 2
.4295 -10" 3, I 1
0 200 400 600
.80, T .5001

Figure 6. 1 Simulated ZT of the module vs. temperature.

Figure 6.3 shows that the efﬁciency also increases as the temperature gradient
increases. Figure 6.4 and 6.5 show the power output of the module vs. efﬁciency and

temperature gradient.

166

 

 

 

 

.1322, 2 I
1 — -
Qh(100,1)
..... l — .i"o”- -—
.0775. 0.5 l
0 5 10
.0. I .10,

Figure 6. 2 Heat flow through the module vs. current output.

 

 

 

 

.0.016.. 002 I
T] h( 200.1) N
71 h( 100,1)
0.01 — _
-3 ""-¢l---\---s -----
.5.017-10 10,005 ”I

O I 1.101
Figure 6. 3 Efﬁciency of the module vs. Current Output.

167

 

L0°06J0.08 I I I

0.06

w e(AT) 0.04

 

0.02

 

 

   

 

0 0.01 0.02 0.03 0.04
.0. n h( AT,1) .0038.

Figure 6. 4 Power output of the module vs. efﬁciency.

 

0.06 '-

 

 

 

 

 

w e(AT) 0.04 -
0.02 —
50.1 0 ‘ I I
0 50 100 150 200
.01 AT I.200.

Figure 6. 5 Power output of the module vs. temperature gradient.

168

6.2 Module Testing

Figure 6.6 shows the TB module made of an n-type cubic material,
Agogzpblgstezo, and a p-type cubic material, Ago.9SnSb1_lTe3. The p and n-type samples
are sandwiched between two alumina plates with nickel traces. The samples are soldered
to the bottom plate with a standard tin-lead solder. If the sample does not bond with
solder easily it is helpful to nickel plate the ends of the sample allowing the solder to
bond. The samples are bonded to the top plate with platinum paste since the top plate is
exposed to high temperatures where standard tin-lead solder would melt. The total
resistance including the contact resistance of the module was tested to be about 0.1 Q by
a handheld multimeter. Unfortunately, the p-type sample was broken laterally during the
process of mounting the module onto the cryostat. Although the platinum paste gives
very good electrical contact, the paste becomes ﬂaky after it is dried and the mechanical
bonding is weakened. It was clear from this experience, that the solder bond was stronger
than the bond of the platinum paste, as one might expect. After this, one of the broken
pieces of the p-type sample was reoriented (to match the length of the n-type leg) and
used as the p-type leg of the module and the samples were connected to the t0p plate
using silver paste. The total module resistance then became approximately 0.2 52
indicating an increase in contact resistance. During the re-assembly of this module, the
same sample preparation (polishing and nickel plating) was followed as in the ﬁrst
assembly.

The thermal conductance measurement technique, which is described in Section
2.5.2.1, was used to characterize the module, in the same HT system. The module was

mounted on the sample stage with silver paste and the system was maintained in a

169

 

vacuum environment of 10’5 Torr with the temperature of the sample stage held constant
at 300K. Two sin gle-ended Chromel-Constantan thermocouples were used to monitor the
temperature gradient across the module. A platinum RTD was used as a heater and
mounted on top of the module to establish the desired temperature gradient. The pulse
technique was used to obtain the temperature gradient. Two voltage leads were added to
the RTD heater to measure the power applied to the heater. The temperature of the
sample stage was maintained at 300K with some flow of liquid nitrogen through the
cryostat. The PID temperature control was easily tuned to maintain a constant
temperature.

First, the thermal conductance of the open-circuit module was measured with
various source currents (or temperature gradients). Then the thermal conductance of the
short-circuit module was measured. Each of the bottom nickel traces was soldered to a
thick copper wire (1 mm diameter) and these wires were connected to one of the pins in
the connector A (which was not used before). In open-circuit condition, just leaving the
two pins unconnected. In short-circuit condition, simply shorted these two pins from
outside. Figure 6.7 show the capture image displayed the temperature gradient across the

sample vs. time. Table 6.2 and 6.3 show the results of the Open and short circuit tests.

Thermal conductance is K = 1%- , where Q is the power supplied to the heater.

170

 

Figure 6. 6 Single couple TE module with n-type cubic material, Ag0.32Pb13$bTe20, and a
p-type cubic material, Ag0,9SnSb1_1Te3.

 
    

 

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7.62E-3
Delta T (K) TWO!
(32,005+0 I 300-00
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I243.77E-3

 

 

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time.

Figure 6. 7 The capture image displayed the temperature gradient across the sample vs.

 

 

 

 

 

 

Source current Temperature Power Supplied Thermal

(mA) Gradient (K) to Heater (W) Conductance (W/K)
10 9.38 0.05744 6.1237

20 42.199 0.2573 6.097

30 118.71 0.71726 6.042

37 220.7 1.3625 6.174

 

 

 

 

Table 6. 2 The experimental result of the open circuit test.

 

 

 

 

 

 

Source current Temperature Power Supplied Thermal

(mA) Gradient (K) to Heater (W) Conductance (W/K)
10 9.36 0.057344 6.1265

20 41.8843 0.25705 6.1372

30 117.6757 0.7164 6.088

37 219.238 1.359 6.199

 

 

 

 

Table 6. 3 The experimental result of the short circuit test.

Using equation 81, the ZT of the module can be determined:

 

 

 

 

 

 

Source current Determined
(mA) Module ZT
10 4.57 x 10*r
20 0.0066

30 0.00761

37 0.004

 

 

 

Table 6. 4 The determined ZT of the module from the two tests.

The experimental results for ZT do not agree with the simulated ZT as shown in

172

Figure 6.1 of 0.15 at 300K. This is because the simulation value is based on ideal case
where contact resistance is not included in the calculations. A later simulation included
the effect of a 3 milliohm contact resistance; however, the actual contact resistance is
much higher than this value. Since the module is characterized through an open and short

circuit method, the accuracy of this experiment was suspected to be affected by the non-

 

 

ideal short circuit measurement. In addition, the simulated ZT is calculated at an average
temperature, however the actual module operates over a temperature gradient.
Improvement of the contact resistance to these new materials is an area of study presently

being investigated along with variable load measurements on these modules.

173

 

Chapter 7 Conclusion/Future Work

A high temperature thermoelectric transport measurement system has been
successfully built and new quaternary cubic materials have been characterized. Various
reference materials, including bismuth telluride, Constantan, molybdenum, and NIST
1461 stainless steel have been measured in the HT system to verify the accuracy of the
system. Since some variation is expected between the reference samples that were
measured and the reference samples that were shown in the literature, the error
percentage calculation is subjective to each material. Overall measurements show a very
low error percentage of < 3% in electrical conductivity measurement. A slightly higher
error percentage of 5-8% (for Constantan) and 6-18% (for Molybdenum) are observed for
thermopower measurements.

On some samples, it was observed that after the HT measurement a thin grayish
ﬁlm formed on the surface of material. In some measurements of the new cubic materials,
the repeatability between runs was also a challenge and it was suspected that these
samples underwent elemental redistribution and/or evaporation of elements from the
material at the high temperatures used in the measurement. The evidence of this
hypothesis came from the SEM/EDS analysis, collected on samples before and after the
temperature dependent measurements, which indicated a change in the surface
composition. Further EDS analysis on copper taps placed near the samples showed ﬁlms
deposited on the copper tabs included a tellurium component (one of the constituent
elements of the new materials). In some of the cases, when changes in electrical
conductivity and thermopower were observed between runs, the power factor remained

the same. This suggests that the redistribution of elements near the surface of the

174

 

 

materials has not signiﬁcantly changed the thermoelectric efﬁciencies of these samples.
Cracks were also observed after the HT measurement in some cubic materials. The
coefﬁcient of thermal expansion (CTE) between the sample (2111an K) and the copper
(16umlm K) stage is signiﬁcant, however, for a reference sample of molybdenum
(6um/m K) the measurement did not experience difﬁculties. Further investigations on
the cause of such cracking are needed to better understand these materials.

The results of the investigations show that the higher the silver composition of the
compounds Agbe13SbTezo with x = 0.78, 0.82, 0.84 and 0.86, the higher the power
factor. Some of thermopower values of these cubic materials have reached saturation at
around 650-700K, these phenomena was suspected to be associated with the
characteristic of increasing bandgap with increasing temperature. Goldsmid’s Sm Tmax
estimates were used to calculate the bandgap of this material based on the thermopower
measurement. The estimates were not accurate and this suggests that Goldsmid’s method
cannot be applied to all materials.

Experimental results have helped to further understand these novel materials and
to determine the doping trends in order to achieve pr0perty optimization. In general, these
new cubic materials are all n-type semiconductors with metallic electrical conductivity
behavior indicating these are degenerately doped semiconductors. Some of the power
factors reach > 30p.W/K2 cm in a large temperature range of 300-600K.

A prototype TE module based on these new materials has been presented along
with performance measurements of the overall module. Both p and n-type cubic samples
are used to construct the module. Since the properties of the p-type cubic materials are

not optimized, an n-type cubic sample was selected to match the ZT of the p-type sample.

175

Both of these samples have a maximum ZT of 0.5 at 500K. The module was fabricated
and later tested using the open and shorted circuit technique. The measured ZT of the
module did not match with the estimation. The main difﬁculty in the module fabrication
is in obtaining low contact resistances. In addition, the simulated ZT was based on the
ideal case where ZT was estimated at the average module temperature but the actual
module was operated with a temperature gradient rather than a ﬁxed temperature. More
investigation of various materials for making low resistance electrical and thermal
contacts to these materials, as well as further investigations of material preparation are
recommended for future studies.

Some of the suggestions for further improvement on this HT system include
different sample mounting conﬁguration, different design of cryostat, replacement of the
sample stage material as well as the shield material, adding an extra thermocouple on the
stage. A different sample mounting conﬁguration might require a redesign of the sample
stage, one of the ideas is using spring-loaded pressure contact instead of conductive paste
contact, however, since most of the samples are small in sizes, extra care must be taken in
designing the contact tips/areas. The spring-loaded contact might also help eliminate
problems associated with the difference in thermal expansion between the sample and the
stage. Since it was suspected that oxide was form on the surface of the samples, an idea is
to replace the existing single inlet cryostat with a two inlets cryostat. This allows
continuously ﬂushing the chamber with nitrogen gas while pumping the system to
vacuum. Replacement of the OFHC copper stage and shield with another more inert
metals or alloys or ceramics might help reduce the maintenance effort. Although, the

OFHC copper stage is nickel/gold plated on the surface, the high operating temperatures

176

and constant cooling and heating process in the measurement caused the coating to
degrade. The addition of an extra thermocouple on the stage will help determine the
contact quality between the sample and the base. This would help to investigate the
quality of the thermal interface between the module and the cryostat sample stage. High
thermal resistance at this interface would lead to inaccuracies in the module
characterization. Continuous improvement in the software, especially in the PID
temperature controller implementation, can make the system function more efﬁciently

and more reliably.

177

EDS ANALYSIS FROM SEM IMAGING

Fri NOV 08 16:35:25 2002

KF2229R l C

Refit _Sb-L' _Sb-L" _Cu-L' _Cu-L" _Ni-L' _Ni—L" _Zn-L' _Zn-L" _Fe-L' _Fe-L"

Refit _Ni-L _Fe-L
Filter Fit Method

Chi-sqd = 118.49 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (1-Sigma) Counts (l-Sigma)
Te-L 0.30336 +/- 0.00361 75389 +/- 896
Sb-L 0.00358 +/- 0.00157 911 +/- 399
Pb-L 0.66727 +/- 0.01676 23727 +/- 596
Cu-L 0.00555 +/- 0.00053 1021 +/— 97
Ni-L 0.00000 +/— 0.00001 0 +/- 0
Zn-L 0.00413 +/- 0.00039 1120 +/- 105
Ag-L 0.01610 +/- 0.00145 4775 +/- 431
Fe-L 0.00000 +/- 0.00001 0 +/- O
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.=
Number of Iterations = 4

Element

k-ratio Z A

(calc.l
Te-L 0.260 0.97 l
Sb-L 0.003 0.94 l
Pb-L 0.571 1.04 1
Cu-L 0.005 0.83 3
Ni-L 0.000 0.78 2
Zn-L 0.004 0.82 3
Ag-L 0.014 0.90 1
Fe-L 0.000 0.80 3
Total

Figure A. l The EDS analysis of the surface of the sample KF2229R1C after the High

Temperature (HT) measurement.

APPENDIX A

20 kV Take-off

P‘OIJF‘HIJF‘H

F

178

Atom

43.
0.
46.

OOKDQOCDHGSD

OONNOUJ

Angle=30.00 deg

d9

ONI—‘Ol—‘UINh

Element Wt % Err.
Wt % (l-Sigma
35.1 +/- 0.

0.4 +/- 0.
59.9 +/- 1.

1.5 +/- 0.

0.0 +/- 0.

1.1 +/- 0.

1.9 +/- 0.

0.0 +/- 0.
100.0

Fri Nov 08 16:38:35 2002
KF2229R1C-unscmped

Refit _Sb-L' _Sb-L" _Cu-L' _Cu-L" _Ni-L' _Ni-L" _Zn-L' _Zn-L" _Fe-L' _Fe-L"

Refit _Ni-L _
Filter Fit Method

Fe-L

Chi-sqd = 115.24 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (1-Sigma) Counts (1-Sigma)
Te-L 0.29474 +/- 0.00363 71715 +/- 884
Sb-L 0.00162 +/- 0.00159 402 +/- 396
Pb-L 0.67365 +/— 0.01695 23453 +/— 590
Cu-L 0.00815 +/- 0.00057 1467 +/- 103
Ni-L 0.00000 +/- 0.00001 0 +/- 0
Zn-L 0.00725 +/- 0.00042 1923 +/- 111
Ag—L 0.01459 +/- 0.00146 4237 +/- 425
Fe-L 0.00000 +/- 0.00001 0 +/- O
Adjustment Factors K L M
Z—Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.- 20 RV Take-off

Angle=30.00 deg
Number of Iterations = 4

k-ratio Z A F Atom % Element Wt % Err.
Element (calc.) Wt t (l-Sigma)
Te-L 0.250 0.97 1.39 1.00 41.6 33.8 +/- 0.4
Sb-L 0.001 0.95 1.47 1.00 0.2 0.2 +/- 0.2
Pb-L 0.571 1.05 1.00 1.00 45.5 60.1 +/- 1.5
Cu-L 0.007 0.83 3.83 1.00 5.4 2.2 +/- 0.2
Ni-L 0.000 0.78 2.59 1.00 0.0 0.0 +/- 0.0
Zn-L 0.006 0.83 3.80 1.00 4.6 1.9 +/- 0.1
Ag-L 0.012 0.90 1.59 0.99 2.6 1.8 +/— 0.2
Fe—L 0.000 0.80 3.22 1.00 0.0 0.0 +/- 0.0
Total 100 0 100.0

Figure A. 2 The EDS analysis of another surface of the sample KF2229R1C after the
High Temperature (HT) measurement.

179

 

Wed Dec 11 19:54:34 2002
KF2229R1C-center

Refit _Ag-L' _Ag-L" _Cu—L' _Cu-L" _Cu-K' _Cu-K" _Zn-K' _Zn-K"
Refit _Pb-L" _Cu-L _Cu-K _Zn-K
Filter Fit Method

 

Chi-sqd = 2.87 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (l-Sigma) Counts (l-Sigma)
C -K --- --- 790 +/- 43
Pb-M --- --- 41466 +/- 427
Te-L 0.37568 +/- 0.00808 17056 +/- 367
Pb-L 0.61855 +/- 0.09056 683 +/- 100
Ag-L 0.00576 +/- 0.00198 339 +/- 116
Cu-L --- --- 0 +/- 0
Cu-K 0.00000 +/- 0.00001 0 +/- 0
Zn-K 0.00000 +/- 0.00001 0 +/- 0
Adjustment Factors K L M
Z—Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.= 15 kV Take-off Angle=30.00 deg
Number of Iterations = 4

Element k—ratio Z A F Atom

% Element Wt % Err.
(calc.) Wt % (l-Sigma)
Te-L 0.340 0.96 1.23 1.00 52.0 40.3 +/- 0.
Pb-L 0.560 1.05 1.00 1.00 47.0 59.1 +/- 8 7
Ag-L 0.005 0.89 1.36 0.99 1.0 0.6 +/- 0 2
Cu-K 0.000 0.75 1.05 0.99 0.0 0.0 +/- 0 0
Zn-K 0.000 0.75 1.04 0.99 0.0 0.0 +/- 0 0
Total 100.0 100.0

Figure A. 3 The EDS analysis inside the sample KF2229R1C after the High Temperature
(HT) measurement.

180

Fri NOV 08 16:31:28 2002

KF2229R1D

Refit _Sb-L‘ _Sb-L" _Cu-L' _Cu—L" _Ni—L' _Ni-L" _Zn-L' _Zn-L" _Fe-L' _Fe-L"
Refit _Ni-L _Fe-L
Filter Fit Method
Chi-sqd = 143.89
Standardless Analysis

Livetime = 100.0 Sec.

Element Relative Error Net Error
k-ratio (l-Sigma) Counts (l-Sigma)
Te-L 0.31916 +/— 0.00345 92516 +/— 1000
Sb-L 0.00579 +/- 0.00150 1716 +/- 445
Pb—L 0.64590 +/- 0.01519 26788 +/- 630
Cu-L 0.00420 +/- 0.00049 900 +/- 106
Ni-L 0.00000 +/- 0.00001 0 +/- 0
Zn-L 0.00452 +/- 0.00036 1429 +/- 115
Ag-L 0.02042 +/- 0.00144 7065 +/- 497
Fe-L 0.00000 +/- 0.00001 0 +/- 0
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.=
Number of Iterations = 4

20 kv Take-off Angle=30.00 deg

Element k-ratio Z A F Atom % Element Wt % Err.

- (calc.) Wt % (l-Sigma
Te-L 0.272 0.97 1 38 1.00 45.4 36.6 +/- 0.4
Sb-L 0.005 0.94 1 45 1.00 0.9 0.7 +/- 0.2
Pb-L 0.551 1.05 1.00 1.00 44.3 57.9 +/- 1.4
Cu-L 0.004 0.83 3.95 1.00 2.9 1.2 +/- 0.1
Ni-L 0.000 0.78 2.65 1.00 0.0 0.0 +/- 0.0
Zn-L 0.004 0.82 3.85 1.00 3.0 1.2 +/- 0.1
Ag-L 0.017 0.90 1.57 0.99 3.6 2.4 +/- 0.2
Fe-L 0.000 0.80 3 29 1.00 0.0 0.0 +/- 0.0
Total 100.0 100.0

Figure A. 4 The EDS analysis on the surface of the sample KF2229R1D after the High
Temperature (HT) measurement.

181

Wed Dec 11 19:59:43 2002

KF2229R1D-center

Refit _Ag-L' ‘Ag-L" _Cu-L' _Cu-L" _Cu-K' _Cu-K" _Zn—K' _Zn-K"
Refit _Pb—L' _Pb-L"
Filter Fit Method

Chi-sqd = 2.98 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (1-Sigma) Counts (l-Sigma)
C -K --- --- 1054 +/- 49
Pb-M --- --- 43251 +/~ 436
Te-L 0.35727 +/- 0.00774 17267 +/- 374
Pb-L 0.63125 +/- 0.08422 742 +/- 99
Ag-L 0.00170 +/- 0.00189 107 +/- 119
Cu-L --- ~-- 261 +/- 54
Cu-K 0.00173 +/- 0.00540 24 +/— 77
Zn-K 0.00805 +/- 0.00708 83 +/- 73
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.
Number of Iterations = 4

15 kV Take-off Angle=30.00 deg

k-ratio Z A F Atom % Element Wt % Err.
Element (calc.) Wt % (l-Sigma)
Te-L 0.325 0.96 1.24 1.00 49.8 38.6 +/- 0.8
Pb—L 0.574 1.05 1.00 1.00 48.2 60.6 +/- 8.1
Ag-L 0.002 0.89 1.37 0.99 0.3 0.2 +/- 0.2
Cu-K 0.002 0.76 1.05 0.99 0.3 0.1 +/- 0.4
Zn-K 0.007 0.75 1.04 0.99 1.4 0.6 +/- 0.5
Total 100.0 100.0

Figure A. 5 The EDS analysis inside the sample KF2229R1D after the High Temperature
(HT) measurement.

182

Wed Apr 16 19:57:42 2003
KF2242R2Agbeforerun

Refit _o -K' _0 -K" _Cu-K' _Cu—K" _Sb-L' _Sb-L" _Ag-L' _Ag-L"
Refit _0 -K
Filter Fit Method

Chi-sqd = 6.03 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (l-Sigma) Counts (l-Sigma)
O -K --- —-- 0 +/— 0
C -K --- --- 2608 +/- 79
Cu-K 0.00157 +/- 0.00157 145 +/— 145
Te-L 0.30124 +/- 0.00406 57733 +/- 779
Sb-L 0.00551 +/- 0.00178 1082 +/- 350
Pb-L 0.68854 +/- 0.01904 18552 +/- 513
Ag-L 0.00313 +/- 0.00085 720 +/— 195
Pb-M --- --- 128199 +/- 739
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.
Number of Iterations = 4

20 kV Take-off Angle=33.81 deg

Element k-ratio Z A F Atom % Element Wt % Err.
(calc.) Wt % (l-Sigma)
Cu-K 0.001 0.78 1.09 0.97 0.3 0.1 +/- 0.1
Te-L 0.268 0.96 1.37 1.00 46.6 35.3 +/- 0.5
Sb-L 0.005 0.93 1.44 1.00 0.9 0.7 +/- 0.2
Pb-L 0.613 1.03 1.00 1.00 51.6 63.5 +/- 1.8
Ag-L 0.003 0 89 1.55 0.99 0.6 0.4 +/- 0.1
Total 100.0 100.0

Figure A. 6 The EDS analysis of the sample KFZZ42R2A before the High Temperature
(HT) measurement.

183

Sat May 31 10:40:53 2003

KF2242R2A_after_run

Refit _0 -K'
Refit _Ag—L'
Filter Fit Method

Error

8 (l-Sigma)

+/- 99

+/- 968

+/- 1017

+/- 680

+/— 78

+/- 192

+/- 448

+/- 505

L M
0000 0.00000
0000 1.00000

Atom

46.
50.
0.
0.
l.

Chi-sqd = 7.46 Livetime = 100.0 Sec.

Standardless Analysis

Element Relative Error Net

k-ratio (l-Sigma) Count

C -K --- --- 4118
Pb-M . —-- --- 220117
Te-L 0.30514 +/- 0.00326 95051
Pb-L 0.67974 +/- 0.01553 29769
O -K --- -—- 192
Cu-K 0.00289 +/— 0.00128 432
Sb-L 0.00372 +/- 0.00141 1185
Ag-L 0.00852 +/- 0.00135 3184

Adjustment Factors K
Z-Balance: 0.00000 0.0
Shell: 1.00000 1.0

PROZA Correction Acc.Volt.: 20 kV Take—off

Number of Iterations = 4

Element k—ratio Z A F

(calc.)

Te-L 0.271 0.96 1.37 1.00
Pb-L 0.604 1.03 1.00 1.00
Cu-K 0.003 0.78 1.09 0.97
Sb-L 0.003 0.94 1.43 1.00
Ag-L 0.008 0.89 1.55 0.99
Total

Figure A. 7 The EDS analysis of the sample KF2242R2A after the High Temperature

(HT) measurement.

184

100.

0 -K" _Cu-K' _Cu-K" _Sb-L' _Sb-L"

Angle=33.81 deg

0030\me 01°

Element Wt % Err.

1

Wt
35.
62.
0.
0.
1.
00.

OOthNQsld’

(l-Sigma
+/- 0.
+/— 1.
+/- 0.
+/- 0.
+/- 0.

NJN14¢bb

 

7

 

Sat May 31 10:53:05 2003

KF2242R2A_after_run_

Refit _Cu-K'
Refit _Pb-L" _o -K"
Filter Fit Method
Chi-sqd = 6.46

Element Relative
k—ratio
C -K —--
Pb-M -—-
Te-L 0.35745 +/
Pb-L 0.58209 +/
O -K ---
Cu—K 0.00298 +/
Sb-L 0.00724 +/
Ag-L 0.05024 +/
In-L ---

Adjustment Factors
Z-Balance:
Shell:

PROZA Correction Acc.Volt.

Number of Iterations

Element k-ratio
(calc.)
Te-L 0.310
Pb-L 0.504
Cu-K 0.003
Sb-L 0.006
Ag-L 0.044
Total

3

OOOl-‘O

Z

Livetime
Standardless Analysis

Cu-K" _Sb-L' _Sb-L"

= 100.0 Sec.
Error Net Error
(1—Sigma) Counts (1-Sigma)
--- 4472 +/- 104
--- 157176 +/- 857
0.00436 94001 +/- 1146
0.01082 21522 +/- 400
--- 1260 +/- 77
0.00147 377 +/- 186
0.00240 1949 +/- 646
0.00203 15860 +/- 641
--- 41863 +/- 933
K L M
0.00000 0.00000 0.00000
1.00000 1.00000 1.00000
= 20 kV Take—off Angle=33.81 deg
4
A F Atom % Element Wt % Err.
Wt % (l-Sigma
.97 1.33 1.00 49.6 40.1 +/- 0.5
.05 1.00 1.00 40.4 53.1 +/- 1.0
.79 1.09 0.98 0.5 0.2 +/- 0.1
.94 1.40 1.00 1.1 0.8 +/- 0.3
.90 1.47 0.99 8.4 5.7 +/- 0.2
100.0 100.0

Figure A. 8 The EDS analysis of another surface of sample KF2242R2A after the High
Temperature (HT) measurement.

185

Wed Dec 11 19:42:39 2002

KF2242R2B

Refit _Ag-L' _Ag-L" _Cu-L' _Cu-L" _Cu-K' _Cu-K“ _Zn-K' _Zn-K"
Refit _Pb-L" _Cu-K

Filter Fit Method

Chi-sqd = 3.13 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (l—Sigma) Counts (l-Sigma)
C -K --- --- 979 +/- 49
Pb-M --- --- 48727 +/— 465
Te-L 0.38190 +/- 0.00768 19836 +/— 399
Pb-L 0.61115 +/- 0.08233 772 +/- 104
Ag-L 0.00091 +/- 0.00189 61 +/- 128
Cu-L --- --- 183 +/- 54
Cu-K 0.00000 +/- 0.00001 0 il- 0
Zn-K 0.00605 +/- 0.00704 67 +/- 78
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.
Number of Iterations = 4

15 kV Take-off

Angle=30.00 deg

k-ratio Z A F Atom % Element Wt % Err.
Element (calc.) Wt 1r (l-Sigma)
Te-L 0.347 0.96 1.23 1.00 52.5 40.9 +/- 0.8
Pb-L 0.555 1.06 1.00 1.00 46.3 58.6 +/- 7.9
Ag-L 0.001 0.89 1.36 0.99 0.2 0.1 +/- 0.2
Cu-K 0.000 0.76 1.05 0.99 0.0 0.0 +/- 0.0
Zn-K 0.005 0.75 1.04 0.99 1.1 0.4 +/- 0.5
Total 100.0 100.0

Figure A. 9 The EDS analysis of the sample KF2242R2B before the High Temperature
(HT) measurement.

186

 

Tue Dec 17 11:19:15 2002

KF2242R2B_1

Refit _Sb-L' _Sb-L" _Ag—L' _Ag-L"
Filter Fit Method

Chi-sqd = 2.80 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (l-Sigma) Counts (l-Sigma)
Pb-M 0.64743 +/- 0.00373 172381 +/- 994
Te—L 0.33912 +/- 0.00400 76380 +/- 902
Sb-L 0.00758 +/- 0.00175 1746 +/- 402
Ag-L 0.00587 +/- 0.00084 1577 +/- 225
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.:

20 kV Take-off Angle=30.00 deg
Number of Iterations = 5

Element k-ratio z A F Atom % Element Wt % Err.

(calc.) Wt % (l-Sigma

Pb-M 0.554 1.02 1.06 1.00 47.6 59.7 +/- 0.3

Te-L 0.290 0.96 1.38 1.00 50.1 38.7 +/- 0.5

Sb-L 0.006 0.94 1.46 1.00 1.2 0.9 +/- 0.2

A —L 0.005 0.89 1.58 0.99 1.1 0.7 +/- 0.1

g 100.0 100.0

Total

Figure A. 10 The EDS analysis of the sample KF2242RZB after the High Temperature
(HT) measurement.

187

 

Tue Dec 17 11:26:53 2002

KF2242R2B_2

Refit _Sb-L' _Sb-L" _Ag-L' _Ag-L" _Cu-K' _Cu-K"
Filter Fit Method

Chi-sqd = 2.38 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (l-Sigma) Counts (l-Sigma)
Pb-M 0.65292 +/- 0.00353 206180 +/- 1116
Te—L 0.33817 +/- 0.00369 90336 +/- 987
Sb-L 0.00203 +/- 0.00160 554 +/— 438
Ag-L 0.00328 +/- 0.00077 1046 +/- 245
Cu-K 0.00360 +/- 0.00138 472 +/- 181
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.: 20 kV Take-off Angle=30.00 deg
Number of Iterations = 5

Element k-ratio Z A F Atom % Element Wt % Err.
(calc.) Wt % (l—Sigma
Pb-h‘ 0.560 1.02 1.06 1.00 48.2 60.4 +/- 0.3
Te-L 0.290 0.96 1.39 1.00 50.2 38.7 +/- 0.4
Sb—I. 0.002 0.94 1.46 1.00 0.3 0.2 +/- 0.2
Ag_L 0.003 0.89 1.59 0.99 0.6 0.4 +/- 0.1
Cu-l( 0.003 0.79 1.10 0.97 0.7 0.3 +/- 0.1
Tbml 100.0 100.0

Figure A. 11 The EDS analysis of another surface of sample KF2242R2B after the High
Temperature (HT) measurement.

188

Mon Mar 17 16:46:39 2003

KF2242r20 (ﬁrst one) .

Refit _0 -x' _0 -K" _Ag-L' _Ag-L" _Sb-L' _Sb-L"
Refit _O -K

Filter Fit Method

Chi-sqd = 6.17 Livetime = 60.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (l-Sigma) Counts (1-Sigma)
C -K --- --- 2125 +/- 73
O —K --- --- 0 +/- 0
Ag-L 0.00432 +/- 0.00091 881 +/- 185
Sb-L 0.00725 +/- 0.00190 1320 +/- 346
Te-L 0.31777 +/- 0.00431 57097 +/— 775
Pb-L --- --- 34364 +/- 623
Pb-M 0.67066 +/- 0.00438 122606 +/- 801
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 . 1.00000 1.00000

PROZA Correction Acc.Volt.: 25 kV Take-off Angle=30.98
Number of Iterations = 5

Element k-ratio Z A F Atom % Element
(calc.) Wt %
A£-I. 0.004 0.90 1.78 0.99 0.9 0.6
Sb-L 0.006 0.94 1.63 1.00 1.2 0.9
Te-L 0.260 0.97 1.53 1.00 49.9 38.5
Pb-M 0.548 1.02 1.08 1.00 48.0 60.1
Total 100.0 100.0

deg

Wt % Err.
(l-Sigma)
+/- 0.1
+/- 0.2
+/- 0.5
+/- 0.4

Figure A. 12 The EDS analysis of sample KF2242R2C before the High Temperature

(HT) measurement.

189

Thu Apr 10 19:26:39 2003

KF2242R2C_postrun

Refit _Sb-L' _Sb-L" _O -K' _O -K"
Refit _Ag-L' _Ag-L"
Filter Fit Method
Chi-sqd = 7.06 Livetime = 100.0 Sec.
Standardless Analysis
Element Relative Error Net Error
k-ratio (1-Sigma) Counts (1-Sigma)
Ag-L 0.01261 +/- 0.00093 3049 +/— 226
Sb-L 0.00531 +/- 0.00185 1095 +/- 381
Te-L 0.34519 +/- 0.00424 69528 +/— 855
Pb-M 0.63689 +/- 0.00381 155765 +/- 932
C -K --- --- 3076 +/- 86
O -K --- --- 123 +/- 65
Pb-L --- --— 21484 +/- 546
Adjustment Factors K L M
Z-Balance: 0.00000 0.00000 0.00000
Shell: 1.00000 1.00000 1.00000

PROZA Correction Acc.Volt.
Number of Iterations = 5

20 kV Take-off

Angle=33.81 deg

Element k-ratio Z
(calc.)
Ag_1‘ 0.011 0.90
Sb_1‘ 0.005 0.94
Te—I. 0.298 0.97
Pb-M 0.550 1.02
Tom]

A

1.52
1.41
1.35
1.06

F

0.99
1.00
1.00
1.00

Atom

2

0
50
46
100

% Element Wt

.2
.8
.0
.9
.0

1

Wt %
1.5
0.6

38.8

59.1

00.0

% Err.

(1-Sigmal

+/~
+/-
+/-
+/-

0

0
0
0

.1

2
.5
.4

Figure A. 13 The EDS analysis of sample KF2242R2C after the High Temperature (HT)

measurement.

190

Thu Apr 10 19:31:46 2003

KF2242R2C_postrun__2

Refit Ag-L' _Ag-L" _Sb-L' _Sb—L" _0 -K' _0 -K"

Filter—Fit Method
Chi—sqd = 6.65

Standardless Analysis

Element Relative
k-ratio
Ag-L 0.00399
Sb-L 0.00299
Te-L 0.34566
Pb-M 0.64736
C -K ---
O -K ---
Pb-L ---

Adjustment Factors
Z-Balance:
Shell:

Error
(l-Sigma)

+/- 0.
+/— O.
+/- 0.
+/- 0.

00091
00189
00434
00392

0.00000
1.00000

Livetime = 100.0 Sec.

Net
Counts
920
589
66475
151165
2694

21225

+/-
+/-
+/-
+/-
+/-
+/-
+/-

L

0.00000
1.00000

PROZA Correction Acc.Volt.: 20 kV Take-off

Number of Iterations

Element k-ratio

(calc.)
Ag-Ia 0.003
Sb-I. 0.003
Te-L 0.300
Pb-M 0.561
Total

= 5
Z

0.89
0.94
0.96
1.02

A

1.53
1.41
1.35
1.06

F

0.99
1.00
1.00
1.00

Atom

0.
0.
50.
48.
100.

Error

(1-Sigma)

211
371
834
915

83

64
546

M
0.00000
1.00000

Angle=33.81 deg

0P

ONMUTQ

Element
Wt %
0.5
0.3
39.0
60.2
100.0

Wt % Err.
(l-Sigma)
+/— 0.1
+/- 0.2
+/- 0.5
+/- 0.4

Figure A. 14 The EDS analysis of another surface of sample KF2242R2C before the
High Temperature (HT) measurement.

191

 

.Aob 8:558 55 6888 82m 838 BE. 2 .< 0.53m

m 3.3 ”one... ween 8:88 2: ”085. 33
02.3.9” 6&3 b0 83,—. >oM on Bw§o>wenee$oo<

H - 32d 8&8

 

8v . 0N >3.

 

CD

51 l

 

 

 

 

3U

UOSCUO

 

 

 

:0 ﬁ
Ooowd

 

 

 

z<sz 659:

192

APPENDIX B

For a fully degenerate semiconductor, a better approximation to obtain <‘t'>, <Et> and
<EZT> can be obtained from the equation

.3
2

3
<z'>=—EF 2

°° a

IzE —f°—dE
0 35

A better approximation

— I¢(E)%fl::dE is used and expanding 01E) in powers of (E-Ep), we get

¢(E) = ¢(Ep ) + (E - EF )¢'(EF ) + %(E - Ep)2¢"(Ep)+
On integrating, we can obtain the values
1°

dE = —1
BE

 

0

 

E—E °dE=0
y 03E

 

E—E 2 °dE=———k2T2

So, we have

 

_oo afo _ Z: 2 n
£¢(E)8E dE—¢(E,.)+ 6 (kT) ¢ (E,)+....

Applying this approximations to <z>, <E2 z>, <Ez>2 and we get

(TXEZT) — (Er)2 = §n2k2T2(z')2

193

APPENDIX C

THERMOMECHANICAL ANALYZER

0N

 

-0

AOL ﬂange.
ow- ow. . 8- . 8..

 

 

 

0.2513025
0.8.2

 

 

é.
Vt
(010) aﬁueqo uogsuewgq

es.

 

on

 

«99 8.53st ”Ema cam
03 E5 “.2280
So. r<mmmmwwm¥e_9...uo ”0:”.

838» 3832 08558

83 s 28 v “8522

as 85+ 5%

<2... gamma? No.38

194

APPENDIX D

Energy Band Gap Measurement

 

1611)

15.00 b

14.0) 7

13.00 5

12(1) "

(2)8

11.(X) ‘

10.0) "

9.00 “'

 

 

 

 

 

800 l l l l I l l

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
E (eV)

The Energy bandgap (= 0.26 eV) is obtained through the room temperature optical
measurement. The composition of this sample is Ang1ngTe20.

195

APPENDIX E

MathCAD Simulation codes

T := 80.. 500
The Properties of KF2229R1C (n-type)
s n(T) :=- 17.192+ 0.085565-T— 0.0026058121- 4.7082-106-1'3- 2.801210%4
0 “(7) := 9345.7- 59.93am. 0.1898412- 000034152913.~ 3.384710'7-T4- 13493101015
Knm :=4.9247_ 0.010908T+ 1.136410512- 12814-10913

Dimensions of A and L are in meters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 cum
A n := 00027-00028 Ln := .0036 2 nm := s n('1‘) .
Kn(T)
-24.728 0 I ' 3 1-104 1 1
5.60210
Sn”) 0,,(T) 5000- -
- 212.41 -300 1 1 488.263 0 1 1
0 200 400 600 0 200 400 600
80. T 500. ,80. T 500
4.124 5 ' ' 0.512 1 I I
4 no .—
x (T) -10 _ .—
n Zn(T)-10 -'I‘ 0.5
3 — —
2.152 2 4 I 6.644103 0 1
0 200 400 600 0 200 400 600
80. T .500 80 T 500

196

 

 

The Properties of D0066a__0118 (p-type)
s (T) := 6.2407 + 0.35449-T
p
6 pm := 1096.3 - 0.5133-T - 0.0028289-1‘2 + 3.7148-10'6-13
x pm := 0.93438 + 0.0031056-T — 7.6469-10'6-1'2 + 1.0122-10'8-13

Dimensions of A and L are in meters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A := 002-0033 L := 0.0036 0 (T)
P P ,_ 2 P
2pm .- 3 pm -
K (T)
P
181486200 I I 1.039103 1200 I
1000 — —
spa) 100— 5 op(T) 800- -
600 _ -
34.6 0 I I 596.775 400 I
0 200 400 600 500
80. T 500 .80. T 800
1.841. 2 I I -.0-546 1 I l
“pm 1-5 ‘ ‘ zp(T).1o' 1% 0.5 -
-3
1.139. 1 I I 8.73610 0 I
0 200 400 600 0 200 400 600
80. T 500 .80. T

197

Resistivity is in ohm cm

 

 

 

 

 

 

A A
n P
Yn=— Y :=— pn(T):=
L n p L p o 11
0.003 I r
R n(T) :=
0.002 "' -
p n(T)
0.001 " ‘ .-
R p(T) .—
0 1 1
0 200 400 600
T
The properties of the Module

3 Mm :=| s n(T) M s p(T)|
R mm := R n(T) + R pm

K M(T) == Kn(T)'Y n+ Kp(T)'Y p

2 -12
SM(T) -10

Z(T) z:
KMm-R 1.1T)

 

198

1
OP(T)

 

P p(T) ==

p n(T)~0.01

 

Yn

p p(T)-0.01

 

Yp

 

 

 

 

 

0.526 ' ' ' '
0.4 r ‘
Z(T) -T
0.2 — ‘
4.295103 1 1 1
0 100 200 300 400 500
.80 T 500
The unit of the load current is in Am;
-3
R cont := 3-10
AT := 0.. 200
R (T) :=R- T)+R
M "“( “0‘“ 1:: 0,.1.. 10
T h := 500
AT
TM<Th,AT> := Th- _2—

Q h(AT,I) := (s M<TM(Th,AT>>-10'6>%-<Th - AT) + K M(TM(Th,AT))-(AT)

_ (%)Z-R M(TM(T h,AT>)

 

2

199

 

 

 

 

 

.1822, 2 l
1.5 "' —
Qh(200,1)
011100.11 '
..... 1 L 'i..-"- _
.0775, 0.5 l
0 5 10
,0, I .10.
.1822, 2 l l 1

 

 

 

 

Q 1,110.10)
0.5 — ’1'. —
$0
,0 096, 0 l I 1
0 50 100 150 200
1.0.. AT .200,

200

 

Open circuit voltage, Voc
-6
V 0c(AT) := s M(TM<Th,AT)) -10 -AT

R L := R M(300)
Electrical Output Power, We
(3 M(T M<T h,AT)) -AT)2-10’12-R L

(RL+RM(TM(Th,AT)))2

 

w 6(AT) :=

Efﬁciency
W 6( AT)

For ﬁxed temperature gradient of 200K

0 1.10121):

VOC(200) =0.064

Load current Load voltage

—— =2.l48

 

RL

Total internal resistance
R M(T M(500,200)) = 0.017
w e(200) = 0.06

n h(200,2.6) = 0.036
Q h(200,2.6) =1.662

201

 

.0039. 0'04

71 h( 200,1) 0.03

n h( 100.1)

0.02

 

41013 0.01

 

 

O

202

.10..

[1]
[2]

[3]

[4]

[5]

[6]

[7]

[8]

[91

[10]

[11]

[12]

[13]

[14]

[15]

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207

 

 

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