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36-SAMPLE MEASUREMENT SYSTEM FOR DOPING AND ALLOYING
TRENDS IN NEW THERMOELECTRIC MATERIALS

presented by

Sim Yean Loo

has been accepted towards fulfillment
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Master Electrical and Computer

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6/01 c:/C|FlC/DateDue.p65-p.15

36-SAMPLE MEASUREMENT SYSTEM FOR DOPIN G AND ALLOYING
TRENDS IN NEW THERMOELECTRIC MATERIALS

By

Sim Yean Loo

A THESIS
Submitted to
Michigan State University
In partial fulfillment of the requirements
For the degree of
MASTER OF SCIENCE

Department of Electrical and Computer Engineering

2000

ABSTRACT
36-SAMPLE MEASUREMENT SYSTEM FOR DOPING AND ALLOYING

TRENDS IN NEW THERMOELECTRIC MATERIALS

By

Sim Yean Loo

A computer-control high sample throughput thermoelectric
measurement system is presented in this thesis. The system is designed
to measure 36 samples simultaneously in a single temperature run
(4.2K - 400K) for thermoelectric characterization. Thermoelectric power is
being investigated since it has the largest influence on the thermoelectric
efficiency of a sample. The purpose of this system is to study doping and
alloying trends in new thermoelectric materials in a high-throughput
manner.

The system set-up and wiring process are included in this
document. It further provides valuable technical information for system
utilization. Many significant features of the system, including computer-
control, easy sample mounting, and high sample throughput have made
it a unique system for characterizing thermoelectric materials. Results of
the characterization have been compared to the standard reference data
showing good agreement. Some problems are addressed in this paper

and suggestions for improvements are given.

Dedicated to my parents

iii

ACKNOWLEDGEMENTS

I am very grateful to Dr. Hogan for his guidance and support
throughout my graduate program. He has provided me with the
opportunity to learn a wide array of useful skills and an environment of
continuous learning. I would also like to thank him for his patience and
encouragement when things were not going smoothly. I would like to
thank Dr. Reinhard and Dr. Kanatzidis for taking the time to participate
in my committee. I want to thank Dr. Sangeeta La] and Akiko Kubota for
being supportive and helpful lab colleagues. I would like to thank Aunt
Chim and Uncle Roberto for their kindness and support. Finally, I would
like to thank my fiance, Roger, for his thoughtfulness, support and

patience.

I am also grateful for the financial support of the Office of Naval
Research through grants (N00014—99—1-0623), and (N00014-98—1-0443).

This project would not be possible without their support.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................. x
LIST OF FIGURES ............................................................................... x
Chapter 1
Introduction

Introduction .......................................................................... 1
Chapter 2

History background and theories

2.1

2.2

2.3

2.4

2.5

Introduction .......................................................................... 6
2.1.1 Basic theories .............................................................. 7
2.1.2 Derivation of the formulas .......................................... 12
Theory of thermoelectric devices ........................................... 19
Figure-of—Merit ..................................................................... 23
The efficiency of a thermoelectric generator .......................... 26
Thermoelectric properties of semiconductors ........................ 28

2.5.1 The thermoelectric coefficients of a non-degenerate
semiconductor ............................................................ 28

2.5.2 Electronic conduction in a non-degenerate
semiconductor ........................................................... 3 1

2.5.3 Intrinsic conduction ................................................... 33

2.5.4 Electronic properties of a degenerate conductor .......... 36

2.5.5 Heat conduction by the lattice .................................... 38
2.6 Optimization of carrier concentration ................................... 39
2.7 Material preparation ............................................................ 40

2.7.1 Polychalcogenide flux method ..................................... 41

2.7.2 Flash synthesis ........................................................... 44
2.8 Sample mounting technique ................................................. 44
Chapter 3

Experimental Set-up

3.1 Apparatus ............................................................................ 45
3.1.1 Measurement Unit ...................................................... 45
3.1.1.1 Keithley 7002 High Density Switch System 45
3.1.1.2 Keithley 2400 Digital Source Meter ................ 47
3.1.1.3 Keithley 2182 Nanovoltmeter ......................... 47

3.1.1.4 LakeShore 330 Autotuning Temperature
Controller ...................................................... 48

3.1.1.5 EG&G 7265 DSP (Digital Signal Processor) Lock-

in Amplifier .................................................... 49

3.1.2 Janis Supertran Unit .................................................. 49
3.1.2.1 Cold Finger Cryostat ...................................... 49
3.1.2.2 High efficiency transfer line ............................ 50
3.1.2.3 Radiation shield ............................................. 50

3. 1.2.4 Liquid Nitrogen .............................................. 50

3.1.3 Vacuum Unit .............................................................. 51
3.1.3.1 TURBO-V 7O .................................................. 51
3.1.3.2 TURBO-V 7O CONTROLLER ........................... 51
3.1.3.3 Kurt J. Lesker Multi-Gauge Controller ........... 52

3.1.4 Software Unit .............................................................. 53

3.1.4.1 LabVIEW (Virtual Instrument) Programming .. 53

3.2 Design of the sample stages ................................................. 54
3.3 Preparation for wiring of the sample stage ............................ 63
3.4 Preparation for the measurement: Testing ............................ 69
3.5 Load samples ....................................................................... 81
3.6 Test run ............................................................................... 81
Chapter 4

Results and Discussion

Results and Discussion ........................................................ 83

Chapter 5

Further Improvement

Further Improvement ........................................................... 91

Vii

Chapter 6
Conclusion

Conclusion ........................................................................... 93

viii

LIST OF TABLES

Chapter 1

Table 1.1 Most widely used TE materials’ top performance ............ 3

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

Chapter 3

Figure 3. 1

Figure 3.2

Figure 3.3.1
Figure 3.3.2
Figure 3.4.1

Figure 3.4.2

Figure 3. 5
Figure 3.6

Figure 3.7

LIST OF FIGURES

Closed circuit Seebeck Effect .......................................... 8
Open circuit Seebeck Effect ............................................ 9
Thomson Effect ............................................................. 11
Closed TE circuit ........................................................... 14
Semiconductor based thermocouple .............................. 19
Thermoelectric module .................................................. 20
Thermoelectric Power Generator .................................... 26

Variation of the figure of merit with carrier

concentration ................................................................ 40
Polychalcogenide flux method ....................................... 43
The system set-up ......................................................... 46
Flowchart of the programming ...................................... 55

The top View of the circuit boards and sample stages I .. 58

The top View of the circuit boards and sample stages 11 . 59

The process of assembling the sample stages I .............. 60
The process of assembling the sample stages 11 ............. 61
Stage with all parts assembled ...................................... 62
Heater ........................................................................... 64
Wiring on one sample .................................................... 68

Figure 3.8

Figure 3.9

Figure 3.10
Figure 3.1 1
Figure 3.12
Figure 3.13
Figure 3.14
Figure 3.15

Figure 3.16

Chapter 4

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4. 5

Figure 4.6

Figure 4.7

The inside and outside Views of a 10 pin connector ....... 72

The inside and outside views of a 20 pin connector ....... 73
Wiring on 35 pin connector#l ....................................... 74
Wiring on 35 pin connector#2 ....................................... 75
Wiring on switch card #1a to the connectors ................. 76
Wiring on switch card #1b to the connectors ................. 77
Wiring on switch card #2a to the connectors ................. 78
Wiring on switch card #2b to the connectors ................. 79

Wiring of the four 20-channel relay switch card slots 80

dV/dT plot of sample#15 (Pb/ 81/ Se) for 2.2 periods of the
current pulse ................................................................ 83
dV/dT plot of sample#1 (BizTe3) for 2.2 periods ............. 84
Two runs of sample#15 (Pb / Bi/ Se) near room

temperature .................................................................. 85
Two runs of sample#26 (BizTe3) at room temperature 86
Two runs of sample#32 (BizTes) at room temperature 86
First run of 15 samples (Bi2Te3) at room temperature

range ............................................................................ 87

Second run of 15 samples (B12T e3) at room temperature

range ............................................................................ 88

Xi

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

First run of 4 samples (Pb / Bi/ Se) at room temperature
range ............................................................................ 88
Second run of 4 samples (Pb / Bi/ Se) at room

temperature .................................................................. 89
Comparison between this system’s data (140K—300K) and

data measured in an independent system ..................... 89

Comparison between this system’s data and standard

Tellurex data (1 10K-300K) ............................................ 90

xii

Chapter 1
Introduction

As science has developed and the human’s life is getting more
comfortable than ever, are there still ways to further improve the existing
living style? The answer is always yes. At home, a refrigerator
compresses and condenses a gas (often a chlorofluorocarbon) to maintain
a cold environment for storing food; an air-conditioner is ready to output
cold air when it is turned on and a car is prepared for transporting from
one place to another. However, all these "household" items have their
own disadvantages that people may or may not realize. Possible
improvements include quiet and robust refrigerators that do not produce
environmentally harmful gases, microprocessors able to run at increased
speeds, and a car that can convert the waste heat generated by the
engines into usable power.

The discovery of thennoelectric effects has made a big impact on
these issues. The robustness and high reliability of a thermoelectric (TE)
device, due to its solid-state construction, allows it to be operated under
harsh conditions, for instance under Vibration. In addition, its scalability
has made it available to meet strict application requirements. For
instance, a TE device can be miniaturized to meet compact design
constraints. Thermoelectric devices have no moving parts and are

virtually maintenance free. They can be used in any orientation and in

zero gravity environments. Thus, many have been used in aerospace
application [1].

Scientists have been creating and trying new thermoelectric
materials over many years toward the goal of more efficient energy
conversion. This has been a challenging endeavor as indicated in the
dominance by a single material (Bi2Te3) for near room temperature
applications for over forty years. The greatest cooling efficiency comes
from thermoelectric materials that conduct electricity well but are poor
heat conductors. Unfortunately, there are very few materials that fall into
this category, however recent studies have shown that more
investigations are needed to understand the limits in the thermoelectric
field [2, 3]. Bismuth telluride, BizTe3, was introduced in 1954 [4] and
today can be found in portable beverage coolers that plug into a car’s
cigarette lighter. However, the cooling efficiency and the cost have made
thermoelectric devices less competitive than their compressor based
counterparts.

The unitless figure of merit, ZT, combines a material’s electric and
thermal conductivities with a measure of its capacity to generate
electricity from heat, and as will be shown, represents a material’s
potential in thermoelectric use. After almost 46 years of searching, Bi2Te3
still has the highest ZT. The figure of merit is a temperature dependent
property which peaks at ~1 for BizT€3 near 300K. For a thermoelectric

material to come close to replacing the compressor-based refrigerator

2

near room temperature, it would need a ZT of 4 or 5. Predictions for the
use of thermoelectric systems in automobiles suggest ZT’s of at least 2
are needed [5).

Besides B12TC3, lead telluride and silicon-germaium alloys had
been used during the early years of research. Lead telluride operates well
at high temperature, about 427 C, making it better for power generation.
While silicon-germaium alloys function well at very high temperatures
about 727 C, e. g. Voyager spacecraft launched in 1977 used this
material heated by radioactive sources as a power supply [6]. After a
quarter of a billion device hours, not one of the 1,200 thermoelectric
generators on each Voyager has failed (7]. It has thus, proved the
robustness of thermoelectric device.

Below are the top performance of the most widely used materials
for thermoelectric applications:

Table 1.1 Most widely used TE materials’ top performance

 

Zmax (K'l) Useful Range Tmax (K)

 

 

 

B12T€3 3X10'3 < 500 K 300
PbTe 1.7X10‘3 < 900 K 650
Si-Ge 1X10'3 < 1300 K 1100

 

 

 

 

 

 

In 1993, it was shown that ZT greater than 1 in quantum well

structures were possible [8]. This renewed interest in the field of

thermoelectrics and has recently produced new avenues of research in
thermoelectric quantum structures and new bulk materials.

In the process of making new materials, chemists are very
naturally playing an important role. A group of researchers from the
Chemistry Department at Michigan State University has been notably
active in thermoelectric materials research. The polychalcogenide flux
technique, they developed, allows them to investigate new materials in an
exploratory synthetic approach [9, 10, 11]. After a promising material
has been identified, it can then be more rapidly fabricated through a
flash synthesis. More detail explanation of these material preparation
techniques will be included later in this document.

The rate of sample production with flash synthesis can approach
100 samples per week per investigator. To accommodate such a high
rate, a measurement system has been built with a high sample
throughput. It is used to screen through samples and to determine
general trends in doping and alloying variations. This high throughput
measurement system is the focus of this thesis [12].

The figure of merit is most heavily dependent on the thermoelectric
power (also commonly known as thermopower, or absolute Seebeck
coefficient). If the thermopower of a sample is not promising, or cannot
be maximized to a desired value, then the sample is not a likely
candidate for thermoelectric applications. Thus the high throughput

system described in this thesis has been designed to measure

4

temperature dependent thermopower of 36 samples in a single
measurement run. In this way, we can focus our work on the most
promising materials.

The paper will present the multisample measurement system. It
will first describe the theories and history background. Next, the
experimental setup will be shown. Then, system testing and actual data
collection (result) will be explained. Discussions and analysis of the

result will come before the further improvements and conclusion.

Chapter 2
History background and theories
2.1 Introduction

In early 19th century, Thomas Seebeck and Jean Peltier, first
discovered the phenomena that are the basis of the thermoelectric
effects. In 1821, Seebeck found that an electrical current would flow if a
temperature gradient builds up across the junctions of two dissimilar
conductors connected as shown in Figure 2.1. Thirteen years later,
Peltier learned that passing current through two dissimilar electrical
conductors, caused the absorption or generation of heat at the junction
depending on the direction of current, i.e. one junction is cold while the
other is hot.

Thomson, who was later called Lord Kelvin, realized that there
must be a relationship between Seebeck and Peltier effects and
proceeded to derive the relation. This led him to conclude that a heating
or cooling effect occurs in a homogeneous conductor when an electric
current passes in the direction of a temperature gradient. This is called
the Thomson effect, which completes the three fundamental
thermoelectric effects [13, 14].

The most common thermoelectric device is a thermocouple.
Thermocouple is made up of dissimilar materials, usually metals, with
an electrical joint between the two materials. It utilizes the Seebeck

effect, and is typically used for measuring temperature gradients. Other

6

applications of thermoelectric materials have included generators and
coolers. Altenkirch first derived the basis theory of thermoelectric
generators and refrigerators in 1909 and 191 1. His theory has shown the
challenging part of fabricating such devices with common materials is
that the Peltier cooling is often much less than the Joule heating, which
makes it difficult to utilize the Peltier effect. Furthermore, it was found
that the heat conducted from the hot junctions to the cold junctions
becomes excessive for thermocouples with short length and large cross-
section area (i.e. large thermal conductance). Thus, a compromise must
be made between reducing electrical resistance and increasing thermal
resistance. Semiconductors have been found to make the most efficient
thermoelectric generators and refrigerators. For both applications,
materials with high thermoelectric power, high electrical conductivities
(to minimize Joule heating), and low thermal conductivities (to minimize

heat transfer losses) are required [15, 16, 17].

2.1.1 Basic theories

To further discuss the thermoelectric theory, we should consider
Kelvin relations and their derivation. Kelvin relations are the
relationships of Seebeck effect with Peltier and Thomson effects. The
relation between Seebeck and Peltier effects is very important because
absolute Seebeck coefficient (also known as the thermoelectric power, i.e.

thermopower, or thermal e.m.f. coefficient) which is most easily

7

measured, and Peltier coefficient which determines the cooling capacity

of a thermoelectric refrigerator.

T Material A

Material B

Figure 2.1 Closed circuit Seebeck Effect.

From Seebeck effect, in Figure 2.1, a current, I, flows in the circuit
when a temperature difference, AT, is created. The force that drives this
current can be measured by breaking the circuit and measuring the
voltage, AV, with no current flowing as shown in Figure 2.2. The relative
Seebeck coefficient is defined as the instantaneous rate of change of the
relative Seebeck effect with respect to temperature at a given

temperature. Thus, the relative Seebeck coefficient is

SAB = lim— (1)

Since the Seebeck effect shows that thermoelectric circuit converts
thermal energi into electrical energy, its most common application is in
thermometry. Thermocouples, which are typically composed of
standardized metallic conductors, are used for accurate, sensitive, and

reliable measurements.

Tl Material A

  
    

Material B

+ Material B

Figure 2.2 Open circuit Seebeck Effect.

If in Figure 2.2 a current was forced to flow by placing a battery
across the open terminals, then heat would be absorbed at one junction,
and liberated at the other. This describes the Peltier effect which shows
that reversible heat generation Q is established when a current, I, flows
through a junction between the conductors A and B. This heat
absorption (or generation) is a result of the change in entropy of the
electrical charge carriers as they cross a junction. This heat pumping

also occurs within nonhomogeneous conductor at concentration

gradients or at phase interfaces within multiphase materials. The Peltier

coefficient,
Hw=% (m

is the change in the reversible heat content at the junction of conductors
A and B when unit current flows across it in unit time, where

“AB = 113 - TIA and, HA and H3 are the respective absolute Peltier
coefficients of the conductors. The direction in which current flows
across a junction and the values of HA and 1113 determine whether heat is
liberated or absorbed. For a constant current, the Peltier effect is
proportional to the relative Seebeck coefficient, and at any fixed junction
temperature, it is proportional to the current. These reversible effects are
independent of the shape or dimensions of the junction. This is in
contrast to Joule heating, which is a function of dimensions, does not
require a junction, or change its sign, and is irreversible. Applications of
the Peltier effect include thermoelectric devices for refrigeration and for

power generation.

10

 

Figure 2.3 Thomson Effect.

The Thomson effect is the reversible change of heat content within
any single homogeneous conductor in a temperature gradient when an
electric current passes through it. This may occur in any nonisothermal
segment of a conductor. The Thomson coefficient is the reversible change
of the heat content within a single conductor per unit temperature
gradient per unit current flow. The Thomson effect is a manifestation of
the direction of flow of electrical carriers with respect to a temperature
gradient within a conductor. If current flows in opposite direction to a
thermal gradient, electrons gain potential energy. Likewise, if current
flows in same direction as a thermal gradient, the potential energr of the
electrons is reduced. Figure 2.3 shows that the passage of a current, I,

along a portion of a single homogeneous conductor, over which there is a

ll

temperature difference AT, leads to rate of reversible heat generation AQ

[13). The Thomson coefficient is,

_ . AQ
“3930,73; (3)

2. 1.2 Derivation of the formulas

The Kelvin relations may be derived by applying the laws of
thermodynamics (First Law of Thermodynamics, i.e. energl is always
conserved) to the simple circuit shown in Figure 2.4. A current, I, passes
through this circuit, which consists of conductors A and B with junctions
at temperatures T1 (colder junction) and T 2 (hotter junction). Let T1=T
and T2=T+AT. From the principle of the conservation of energy, the heat
generated must be equal to the consumption of electrical energy. If the
current is small enough, Joule heating may be neglected. The relative
Seebeck effect generated by the temperature difference is EAB. The
relative Seebeck coefficient is dEAB/dT or SAB so the electrical energy is
expressed as

dE
[E = 1 ——AB AT (4)
“‘8 dT

For unit current flow through the circuit,

dE
EA, = #AT = 5,, (AT) (5)

The expressions for Peltier effect at the junctions are: HAB(T+AT) for heat

absorbed at the hotter junction, and -l'IAB(T)for heat liberated at the

12

colder junction. The expressions for Thomson effect within the
conductors are yB(AT) and -yA(AT) for heat absorbed in conductor B and
heat liberated in conductor A respectively [14]. Equating the heat
generated to the consumption of electrical energy for unit current flow in
the circuit gives

5.3mm = mm + AT) — Hum + (y. — y. )AT (6)

Dividing by AT, we get

 

: HAB(T+AT)_HAB(T) +(

S
AB AT

73 — 7A ) (7)

If assume AT approaches zero, Equation 7 can be expressed as

dII
SAB : 07/38 +(7/B ‘7/1) (8)

This is the fundamental thermodynamic theorem for closed
thermoelectric circuits; it shows the energy relationship between the
electrical Seebeck effect and the thermal Peltier and Thomson effects. It
must be emphasized that Equation 8 is derived for closed circuits with

no external electrical sources.

13

T Material A

E T+(AT/ 2)

T+AT

 

T+(AT/ 2)

Figure 2.4 Closed TE circuit

The thermoelectric effects are actually irreversible because of the
Joule heating and heat conduction. However, if we consider the thermal
losses and electrical resistance of the therrnoelement to be very small, we
can neglect the irreversible heat loss and assume the TE circuit is
thermodynamically reversible. Thus, the net change in the entropy, AP

can be assumed zero.

 

This gives
T+AT T T+_ T+_2_

The first two terms of the Equation 9 can be multiplied by AT/ AT to give

14

 

 

 

 

VIMAT+4o+rUATH
AT AT AT
T+7r T+7r

 

As AT approaches zero the difference quotient within the brackets can be

 

replaced by —L(HTAB ], so Equation 10 becomes

 

(1T

If assume AT is very small, then T + AT / 22 T. This gives a more simple

equation

1 ___HAB :LL_Z§; (12)
dT T _ T T

The indicated derivative reduces Equation 12 to

 

 

 

T b _ 1'1
4 “:A_A_ (m)
T2 " T T
which simplifies to
HA8 (ll—1,48
E + — 14
T dT 73 7.. ( )

Equation 14 represents the entropy change at a thermoelectric junction

in a closed circuit because II AB is the change in the heat content of the

junction, and divided by the absolute temperature, is (by the Nernst
definition) the change in entropy of the junction for the given
temperature. From Equation 14, we can rearrange it for the selection of

materials for use in Peltier devices,

15

 

+(7B-7.) (15)

To get the maximum Peltier effect, we set dl'I AB /dT = O. This is used to
obtained the optimum relationship between the two thermal effects as
HAB E(7B'7»\)T (16)

Also, when dIIAB /dT = 0 is applied to Equation 8 we get

S... = (73 —7.)

So, Equation 16 becomes

U... E 5.3T (18)
Note that, SAB = SB - SA
Equation 18 is the first Kelvin relation. This equation is very helpful in
understanding the operation of Peltier devices. It shows why
combinations of therrnoelements with large Peltier effects must be used
for power generation or for refrigeration.

In order to derive the second Kelvin relation, take the

differentiation of Equation 18,

dl'IAB dSAB
—— E S + T— 19
dT ”‘3 dT ( )
from Equation 8 to give
(11]
d—YCWESAB_(yB—y/t) (20)

Equation 19 and Equation 20 are then equated to get

dSAB
dT

T 5—0/3 ‘7/1) (21)

16

rewrite it to

dSAB : (7A ‘73)
(IT ‘ T

(22)
Equation 22 is the second Kelvin relation.

Generally, both of Kelvin’s relations are applicable to all the
materials used in thermoelectric applications though there is an
exception, germanium-copper couple. It appears that the value of the
Peltier coefficient is less than the product of Seebeck coefficient and
temperature.

Seebeck and Peltier coefficients are both defined for junctions
between two conductors while the Thomson coefficient is defined for a

single conductor. We can use Equation 22 to derive the absolute Seebeck

coefficient for a single material,

T T},
=jfldT—j—Bdr (23)
0 T O T

According to the third law of thermodynamics, the Seebeck
coefficient is zero for all junctions at absolute zero temperature. Thus,
the absolute Seebeck coefficient of any material is zero at this
temperature.

From this, the absolute Seebeck coefficient of individual

thermoelements can be found [14].

17

The absolute Seebeck coefficient of a material at very low
temperatures may be determined by joining it to a superconductor. The
latter possess a thermoelectric coefficient of zero while in the
superconducting state (below the superconducting transition
temperature). This procedure has been carried out for pure lead up to 18
K and the Thomson coefficient for lead has been measured between 20 K
and room temperature. Its value in the range between 18 K and 20 K can
be accurately extrapolated. Thus by using Equation 23, the absolute
Seebeck coefficient of lead has been established. The absolute Seebeck
coefficient of any other conductor may then be determined by joining it to
lead. Lead is used because its absolute Seebeck coefficient is relatively
small compare to other thermoelectric elements. Thus, when lead is used
as a reference, the relative Seebeck coefficient of the thermocouple can

be determined easily [13].

18

 

2.2 Theory of thermoelectric devices

 

T1

 

 

 

W/z

 

 

 

 

T2 1 J

 

 

Figure 2.5 Semiconductor based thermocouple.

One of the advantages of thermoelectric generation or refrigeration
is the independence of the efficiency on the capacity of the unit. The
coefficient of performance of a thermoelectric refrigerator can, therefore,
be derived on the basis of the single thermocouple (Figure 2.5). It is
assumed that the heat that flows from heat source to the heat sink is
only through conduction through the branches of the thermocouple. The
thermocouple is connected electrically in series and thermally in parallel.
The number of the thermocouples being connected will affect the power

handling capacity of the converter but not the efficiency.

19

 

 

 

 

 

 

 

 

T21

 

 

 

 

I G\
<— V

Figure 2.6 Thermoelectric module.

If a voltage source is connected across the thermocouple to
conduct a current flow, the thermocouple acts as a heat pump. For
example, if a positive voltage source is applied to the thermocouple
(Figure 2.6), current flows from p to n. In the p-type element, the majority
carriers are holes. The holes flow from the lower plate to the upper plate
carrying charge and heat as they flow. As the holes cross the junction to
recombine with electrons in the upper metal contact, they dissipate heat.
Likewise, heat is absorbed as holes enter at the lower contact. On the
other hand, the electrons in the n—type element flow from the lower plate
to the upper plate (in contrast to the current flow direction). Thus the
electrons also flow from the bottom of the device to the top, also carrying

charge and heat as they flow. As electrons enter the n-type

20

semiconductor from the lower electrode they must absorb some energy
(heat) to enter the conduction band of the semiconductor. As the
electrons enter the upper metal electrode, they must release energy (heat)
to enter the metal [18]. By reversing the current direction, the top metal
electrode is cooled, while the bottom electrode is heated, thus acting as a

heat pump. The total resistance R of the couple is,

R: [PpP +lnpn
A A

p n

 

(24)

The thermal conductance K of the two branches of the thermocouple in

parallel is

K: P P + n n (25)

 

where lis the length, A is the cross-section area, p is the electrical
resistivity and K is the thermal conductivity of an element. The ratio of
lp/Ap and ln/An can be different from one another because the steady—
state condition is unaffected by the shape of branches.

Peltier and Seebeck effects are bulk phenomena, i.e. they depend
on bulk rather than surface properties of the materials. Thus, the
external contact potential has no relationship whatsoever to any
thermoelectric phenomena. When a current, I, flows through a
conductor, it transports heat. As the current passes into another
conductor, the heat transport is different. In the two branches of the

thermocouple, the heat transport from the source to the sink is

21

dT (26a)

qp ZSPTI—KpAp'd—x
q" : _S’IT1 — K" A" g: (26b)
dx

T is absolute temperature. Due to the Joule effect, the rate of heat

generation per unit length in each branch is

 

 

dZT 12p
— A = ” 27a
P P dxz AP ( )
2 [2
«A. :3? j" (27b)
x II

By setting the boundary condition, T=T1 at x=0 and T=T2 at x=lp or In,

 

 

 

We find,
I2 x—l /2 K A T,—T
K)A,d—T:— p,,( p )+ ” ”( ' ') (28a)
’ 'dx Ap lp
2 _ _
K." A" fl: : _ I pn (x l" /2) + I[(1114n(]~2 7]) (28b)
dx A" l"

The combination of Equation26 and Equation 28 gives the rate of heat

 

 

flow at x=0
K A (T —T) 12p 1
=0 =STI— " ” 2 '— ”P (29a)
qp (x ) p [[7 2A1)
_ [2
q" (x 2 0) : _SnT[ _ KHAN ([72 71) __ 26:1,) (29b)

II

Thus, the cooling power qc at the heat source is qc= qp + qn,

1 (30)

qc = (sp —s,,rr,1 —§IZR —K(T2 —T,)

22

where half of the overall Joule heating goes to each junction. The cooling
effect is opposed by Joule heating in the branches and by heat conducted
from the hot junction.

The rate of electrical energy supplied, Win each branch is

I2 1

WP = 5,,1(T,—7])+—h (31a)
- Ap
I2 l

W, = —S,,1(T2 494% (31b)

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. T hus, the power Wsupplied to the couple is given by
W=(Sp —5,,)1(T2 —T,)+12R (32)
The coefficient of performance for refrigerator is defined as the ratio of

qc/ W, which is the net heat absorbed/ applied electric power,

¢_gc__(Sp—snrrlr—érzR—KUZ—Tl) (33)
W (8,, -s,,)I(T2 —T1)+ 12R

 

2.3 Figure-of-Merit
In order to obtain a maximum cooling power, we take dqc/ d1 =0 in
Equation 30, to yield the current for maximum heat absorption

S —S T
Iq=(—L—")_l (34)
R

23

 

The maximum cooling power is then,

( ) _ (sp —S,,)2T12
qC max _ 2R

 

— K(T2 — T1) (35)

Equation 35 shows that if the temperature difference between the
junctions is too large, maximum cooling power will not be achieved. By

setting (qclmax=0, we can find (T2-T1)max,

_ (sp —s,,)2T,2

 

T — T — 36
( 2 l)max ZKR ( )
The figure-of—merit of the thermocouple is
s — s 2
KR
Equation 36 can be rewritten as
1 7
(T2 — TI)max :EZTI- (38)

For a given pair of thermoelectric materials, and for a given hot
and cold junction temperatures, the coefficient of performance is a
function of the current I, the resistance R, and the thermal conductance
K. For a specified cooling capacity, the ratio of length to cross-section
area for an element should rise with the electrical and thermal
conductivities. A balance is then struck between the effects of resistance
heating and thermal conductance. It shows that the coefficient of
performance reaches a maximum value when the dimensions of the

elements obey the rule

24

 

I/2
l A K
H I) :[pp '1 ] (39)

KR = {(K‘ppp )“2 + (K‘npn )“2 F (40)

The figure of merit is

(5,. — S,.>2
imp)“ +(K.p,.)“2}’

The figure of merit, Z, involves the mean values of all the

z: (41)

 

parameters, Seebeck, electrical and thermal conductivities. It is most
convenient to deal with the figure of merit for a single material as

suggested by Equation 37. Thus, Z for a single material is
z = 52 9— (42)
K

o is electrical conductivity and it is equal to l / p.

In general, Z must be regarded as a rather complicated average of
zp and zn. The use of an individual figure of merit as defined in
Equation 39, is justified by the fact that nowadays the values of zp and zn
are never very much different in the thermocouples which are most

suitable for thermoelectric applications.

25

2.4 The efficiency of a thermoelectric generator

W
. //.

T

1

 

 

 

 

 

 

 

 

 

 

R.
W

Figure 2.7 Thermoelectric Power Generator.

 

 

 

 

In Figure 2.7, one junction of a thermocouple is connected to a
source of heat while the other is in thermal contact with a heat sink.
Power is delivered to a load of resistance R1,. The efficiency of the
generator is defined as the ratio of the useful rate of working, Wto the
rate of heat supply, Q from the source. The heat supplied is either
conducted along the branches to the cold junction or used to balance the
Peltier effect at the hot junction. However, half of the Joule heating in the

thermocouple finds its way back to the source. Thus,
Q=K(T2 —T,)+(sp —Snfl‘lI—%IZR (43)

For maximum power output from a given couple the load
resistance R), should be made equal to the generator resistance R. The

useful work is then,

26

 

 

S —S 2T —T 2
W:( p 11:;2 I) (44)

 

Let AT=(T1-T2)/ 2 and TM=(T1+T2)/ 2. Since IRL=IR=(1/ 2)SnpAT,

AT AT _ (Sp -—S,,)2AT2

 

 

 

 

=KT—T+S—SQT+ 45
Q (2 .)(,, ,)(M 2’212 8R ()
i.e. half of the thermoelectric voltage appears across the load. The
efficiency is
W AT
w : — : (4:6)
Q ZTM + g + _4_R_I<_)_
2 (SP — S n)"
The dimensions of the elements should obey Equation 39 giving
AT
(,0 = (47)
AT 4
2TM + — + —
2 Z

Since the efficiency rises with Z this quantity is a figure of merit for
thermoelectric generation as well as for refrigeration.

If Z tends to infinity (p, as given by Equation 47, approaches the
value AT/ (2TM+AT/ 2) which is only half the efficiency of an ideal
thermodynamic machine. The reason is that, when the maximum
efficiency is required, R1, should not be made equal to R. It may be shown
that the maximum efficiency is obtained when

r = (1 +ZTM )“2 (48)
where r denotes the ratio RL/ R. Then

AT
r+1)TM +_A_T_"
r—1 2

(49)

 

(Pm... =

27

Harman has shown that the efficiency of a thermoelectric generator
may be improved by the use of a cascade arrangement. In his system the
same current passes through the thermoelements; for each stage the
number of couples and their dimensions are chosen so that conditions

Equation 39 and Equation 48 are satisfied.

2.5 Thermoelectric properties of semiconductors

The Wiedemann-Franz law states that the thermal to the electrical
conductivity ratio is constant for all metals at a given temperature. Thus,
when the Seebeck coefficient reaches its highest, the metal obtains
maximum figure of merit. However, non-metallic thermocouple can give a
higher differential Seebeck coefficient compared to metallic elements or

compounds.

2.5.1 The thermoelectric coefficients of a non-degenerate
semiconductor

In an insulator, the valence band is completely filled with electrons
and the conduction band is completely empty of electrons. A forbidden
energy gap, commonly known as band gap, separates the two bands. As
the band gap of the insulator is large (23eV), the resistivity is too large
for appreciable current flow, and the figure of merit, Z, is low. A
semiconductor basically has the same band structure as the insulator,

however, with a much smaller band gap (s3eV) and this allow electrons

28

to be excited from the valence band to the conduction band by thermal
generation. An ideal intrinsic semiconductor is a perfect crystal with no
impurities or lattice defects and the charge carriers are only the electron-
hole pairs. As an example, gallium arsenide has a bandgap of 1.42 eV
and an intrinsic carrier concentration of 2.1 x 106 cm‘3 at 300 K. When
the semiconductor is doped with impurities (donors or acceptors),
excitation of electrons from valence band to conduction band will occur
even at relatively low temperatures. This is called an extrinsic
semiconductor. Semiconductors are called n-type when the conduction of
electricity is primarily due to electrons and p-type is due to holes [19].

It is important to introduce the Fermi level here. At absolute zero
temperature, the energy states up to the Fermi level are filled with
electrons and the higher states are empty. For a metal at some finite
temperature, the states are partially filled over a range of energy within
about 2kT of the Fermi level, where k is the Boltzmann’s constant
(8.616 x 10'5 eV/ K). The probability of finding an electron in any given
state is directly proportional to the energy difference between the
corresponding state and the Fermi level.

A junction between an extrinsic semiconductor and an ideal metal
will be considered here. The latter is defined as a metal in which it will be
supposed that all the current carriers travel at the Fermi level of energy.
The absolute thermoelectric coefficients of such a metal are zero. In real

metals, the carriers occupy a small distribution of energies about the

29

 

Fermi level leading to finite, yet small therrnopowers. In equilibrium, the
Fermi level of the metal and semiconductor will align.

Suppose that the Fermi level of a metal is higher than a n-type
semiconductor, then electrons will flow from the metal into the
semiconductor. In order to rise into the conduction band of the latter it is
necessary that an amount of potential energy 4; should be absorbed for a
single electron. C is the Fermi potential and is positive when the Fermi
level lies within the energy band and negative when it lies within the
band gap. In carrying current through the semiconductor the electron
travels with a certain kinetic energy a which is measured from the band
edge. It, therefore, absorbs an amount of energy (s-C) at the junction.
This absorption of energy is the origin of the Peltier cooling effect at metal
to semiconductor junctions, and the Peltier coefficient is, thus, the
average value of this energy change per unit charge. By convention it is
negative for an n—type semiconductor and it is then positive for a p-type
material.

The potential energy of a non-degenerate semiconductor is greater
than 2kT and the average kinetic energy of electrons in the conduction
band is on the order of (3 / 2) Id‘. The average kinetic energy must account
for the relaxation time due to scattering effects of charge carriers. The
average kinetic energy also depends on the density of states since it
varies with energy. Usually, the density of states is proportional to 80-5
and the relaxation time for the charge carriers can be expressed as

30

7 °C 8 (50)

Where A is constant. Then

11,, =—%{[%+Z}T—§} (51)

Szn”:$£(—5-+7t—n] (52)
e 2

Thus, the Kelvin’s relations,

 

where the negative sign applies to n—type material, the positive sign to
p—type material, and n is known as the reduced Fermi potential, equal to
C/kT.

If the carriers are scattered by the acoustical modes of Vibration of
a covalent lattice, A is equal to —1 / 2. If the scattering mode is ionized—
impurities, A is equal to 3 / 2. In many cases, these and other forms of

scattering may be present so an approximation is used to express the

relaxation time as a simple function of the energy.

2.5.2 Electronic conduction in a non-degenerate semiconductor
For an n—type non-degenerate semiconductor, the Seebeck
coefficient can be expressed in terms of the reduced Fermi potential and

the electrical conductivity is

o = neu (53)

Where n is the number of charge carriers per unit volume and ,u is the

drift mobility of the carriers, defined as their average drift velocity in a

31

unit electric field. For a non-degenerate semiconductor the carrier

concentration is given by

* 3/2
n 2 AW) expn (54)

Where h is Planck’s constant and m* is the effective mass of the carriers.
By using this effective mass, rather than the free electron mass m, it is
possible to treat the carriers as of they were free charges, in spite of the
fact that they move in the periodic field of the crystal lattice. The carrier
concentration given by Equation 54 corresponds to 2(21tm*kT/ h2)3/2
electron states located at the edge of the appropriate band though, of
course, in reality the state are spread out over an effectively infinite
range of energies. The quantity 2(215m"‘kT/h2)3/2 is known as the effective
density of states.

Both the charge carriers and the lattice contribute to the
conduction of heat through a semiconductor. Thus, the overall thermal
conductivity is

K = K, + K, (55)
where In is the lattice component of the thermal conductivity and will be
considered in more detail later, and Ke is the electronic component.

The amount of the heat that the charge carriers can conduct
depends on their mean kinetic energy and this is according to their
relative diffusion rates. It may be shown that, for a non-degenerate

conductor, the weighting factor is exactly the same as that employed in

32

 

calculating the Peltier coefficient; the mean kinetic energr is (5 / 2+ MkT

per unit charge. It is thus found that

K,=[§+115] 0T (56)
2 6

2.5.3 Intrinsic Conduction

At a sufficiently high temperature (or for low doping levels), the
concentration of carriers can be dominated by thermally generated (or
intrinsic) electron hole pairs. At these temperatures, the electron and
hole concentrations are almost the same. Under these conditions, a
mixed conduction will occur with both electrons and holes making
significant contributions. The Seebeck coefficient can then be calculated
by

5,0,, +Spc1'p
S = 0' (57)

 

where 0",. and 0",; are the contributions to the electrical conductivity from
the electrons and holes respectively, and an and 01, are calculated
separately for electrons and holes using Equation 53 and the appropriate
substitution of p for n.
The electrical conductivity of a mixed conductor is given by
0' = e(nmun + niuup) (58)
where the electron and hole concentrations, nn and rip respectively are

related by the mass action law

33

 

2nka 3 m,*m,,. m 88
nnnp =4 h2 7 exp —k—T (59)

Suppose that there is temperature-independent extrinsic carrier
concentrations upon which are superimposed concentrations of
intrinsically excited electrons and holes. For simplicity it will be assumed
that the mobilities of electrons and holes are equal. Let the electron and
hole concentrations in a region at temperature Tbe nn and np
respectively. Then for nn electrons travelling to another region at a
temperature T-dT there will be np holes, and thus, according to the

normal electron theory, the kinetic energy transferred must be
[(3— + A)(nn + np )KAT (60)

However, because of the lower temperature of the second region,
dn electrons must recombine with the same number of holes and each
such combination liberates an amount of energy equal to the width of the
forbidden band (assuming no photon emission occurs). Since the kinetic
energy of the carriers is also transferred to the lattice the total heat

transport is
[(%+A)(nn +np)kAT+An{eg +(5+2?\.)kT}] (61)

Now from Equation 61, remembering that (nn-np) must be independent of

temperature,

34

n n 8
An=——”—‘3— —9+3 E (62)
nn+np kT T

Thus, the ratio of the total electronic heat conductivity to the value in

Equation 56 is

n n 8 e
(Ke )total ___ 1+ n p 2 _g_ + 3 _g + 5 + 2K (63)
(Ke )kinetic (3 + Minn + np) kT kT

 

Taking into account the difference between the mobilities of

electrons and holes and including thermal diffusion effects gives:
k2
Ke = {(—3—+ 751)”an + (3+ Ap)npup}:T

(64)
k2
— T
e

 

nnunnpup [89(0)
)

+5+An +A
(nnun+n kT p

pup
where Equation 64 is the energy gap extrapolated to 0 K.

It may be shown that, even in the intrinsic range, the value of the
second term in the Equation 64 for InSb is less than the first term, which
is the kinetic energy contribution. This is because the ratio of the
electron mobility to the hole mobility is about 85. In bismuth telluride,
however, the mobilities of electrons and holes are of the same order and
it is found that, in an intrinsic material, the second term in Equation 64

is an order of magnitude larger than the first term.

35

2.5.4 Electronic properties of a degenerate conductor

There is a higher probability that any of the lower energy states will
be filled when the reduced Fermi potential is greater than -2. Thus,
Fermi-Dirac statistics must be used. For a highly degenerate conductor,
that is when n is greater than 4, simple approximations to the Fermi—
Dirac integrals may be used, but for thermoelectric applications, we are
usually concerned with the intermediate range of partial degeneracy.

If the conductor is partially or completely degenerate, the concept
of an effective density of states breaks down and the carrier

concentration must be expressed as
3/2
4 21tka
n z _[___j F”, (65)

where

Fr = [Emmott (66)
0

4‘ is the reduced kinetic energy of the carriers and is equal to e/k’l‘. The
Fermi distribution function is given by

1
z 7
fom) 1 + EXPIE. - n) (6 )

 

It is usual to express the electrical conductivity directly as

00

*1/2 2
o = 16x/2n;3 e JTeIEISB/Z giggdg (68)

0

36

 

but it is still possible to use Equation 53 provided that it is realized that
the mobility is no longer independent of the Fermi potential, even in the
absence of impurity scattering. In this case the mobility, ,u may be

expressed in terms of the mobility go in non-degenerate material as

J; .Fl/2+,i

 

= - 69
fl 21‘3”») F... “0 ( )
The gamma function is defined as
fly) 2 ny‘l exp(—x)dx (70)
0

When Fermi-Dirac statistics are applicable the Seebeck coefficient is

given by

 

—5— AF
S_k{(2+ ) 3/2+r ‘11} (71)

~ 6 (g + “Fr/2+).

The electronic component of the thermal conductivity may be written as

K 2 LOT (72)

e

where the Lorenz number L is given by

L

 

_e+4)e+4)F....F.... —<%+4>2F’w 1: 2 (73)
_ (%+,1)2F21/2+4 6

When the material is very strongly degenerate, Equations 65, 69, 71, 73

may all be simplified. The appropriate equations in this case are

8 2 *k’1‘3/2
“mi “”1312 i "m (74)

 

37

 

3t/EnA

 

 

= 75
ll 4(§+A)F(§+A)“O ( )
2 3 x
3 e n
2 2
1121(5) (77)
3 6

2.5.5 Heat conduction by the lattice

It is shown that the thermal conductivity could be expressed as the
sum of an electronic component K23 and a lattice component K). The lattice
component, K1, represents the conduction of heat by the lattice Vibrations
of the crystal. In metals K1 is usually negligible in comparison with Ke, but
it provides the sole contribution to the thermal conductivity of an
electrical insulator and it is predominant in most semiconductors.

The thermal vibrations of the lattice may be quantized as phonons
with a mean free path I). As was first shown by Debye, the thermal

conductivity of a dielectric crystal may be expressed in the form

= §cvll (78)

K1
where c is the specific heat per unit volume and v the velocity of sound. If
the vibrations are completely harmonic the value of It must be infinite for
a perfect crystal. However, if the anharmonic nature of the Vibrations is

taken into account It- becomes finite. In the region of the Deybe

temperature and above, the phonons are primarily scattered by collisions

38

 

with other phonons. Their free path length is determined by the
anharmorricity of the thermal vibrations and by their intensity. The
intensity of the vibrations is proportional to the temperature so the
phonon free path and, thus, the thermal conductivity of the lattice are
inversely proportional to the temperature.

At very low temperatures boundary scattering of the phonons
becomes predominant in a good crystal, so that the phonon free path
depends only on the size of the sample. In this range the specific heat
and the thermal conductivity are proportional to T3. The thermal
conductivity reaches a maximum value at a temperature approximately
equal to one twentieth of the Debye temperature.

The value of K1 in the region of the maximum may be limited by
factors other than size of the specimen. Scattering of phonons by
impurities or by lattice defects may be appreciable and, in some
elements, the difference between the atomic weights of the isotopes has
reduced the phonon free path. In an amorphous substance the free path
length remains of the order of the interatomic spacing at all

temperatures.

2.6 Optimization of carrier concentration
Since the Seebeck coefficient and electrical conductivity depend strongly
on the Fermi level (which in turn depends upon the carrier

concentration, the carrier effective mass, and the temperature), it is

39

convenient to express the thermoelectric transport coefficients in terms

of the Fermi energy, EF (conventionally measured from the band edges).

 

 

 

 

 

 

 

Insulatorl Semiconductor [ Metal

Figure 2.8 Variation of the figure of merit with carrier concentration.

On the other hand, thermal conductivity depends weakly on the carrier
concentration and by increasing the carrier concentration, it will thus

give a better figure of merit.

2.7 Material preparation

After the discovery of Seebeck and Peltier effects, many materials
are identified to have interesting thermoelectric properties. In the
beginning, metals and metal alloys were often used for temperature
measurements.

In the late 19408, interest in elemental semiconductors grew, and
in the 1950s, compound semiconductors were heavily investigated.

Among them, chemical compounds and solid solution gave the best and

40

most promising thermoelectric results. To obtain high thermoelectric
efficiency, materials with high carrier concentrations are desired,
however, materials with high doping levels tend to posses low carrier
mobility, which can reduce the thermoelectric efficiency. To achieve a
combination of high carrier concentration and perfect crystalline
structure in a semiconductor is a very difficult task. This leads to
developing better methods for ‘modern’ thermoelectric material
preparation.

In order to facilitate characterization of a material, the material has
to be as free of defects as possible. One way to achieve this goal is to
grow single crystal or polycrystalline ingots with very large grains.

Since the majority of modern thermoelectric materials are solid solutions
or chemical compounds, it is important to understand the process of

preparing these materials from a melt.

2.7.1 Polychalcogenide flux method
The chemical reactions used in the polychalcogenide flux

technique can be described as follows

M + xs -— A29, ——A——)AnMme + Asz
MQ + xs — AZQX —A—)AnMme + A2Qm

where
Asz is the solid solutions (chalcogenide compound)

Q is a chalcogen (S, Se, or Te)
41

M can be group IV or V: Pb, Bi, As
A can be from group I: Li, K, Cs
As examples consider the following reactions used in fabricating
K2Bi8313, and the quaternary K1,25Pb3.5Bl7.258€15
e.g. K28 + B1283 —> KBiessSio + K2B18813

2K2Se + 2 Pb +3B12Se3 +10Se —) K1_25Pb3,5Bi7,253e15

One of the new material preparation techniques is the
polychalcogenide flux technique designed by the Michigan State
University Chemistry group. In Figure 2.9, a chalcogenide compound is
vacuum—sealed in a test tube and heated either in flame or in the
furnace. This allows for low temperature growth (200<T<600 C).
Materials such as Bi2Te3 have traditionally been processed at
temperatures >500 C. This growth technique, thus, allows for lower
temperature growth of new crystal structures, previously unexplored.
After reacting, the molten salt is cooled down at a rate of ~2C / hr. Excess
AzQx is washed away with water or some other polar solvent. The molten
chalcogenide salt provides a medium in which reactants can dissolve
thus accelarating the reaction. The molten salt also provides a medium
for the product of the constituents to recrystallize thus promoting crystal
growth. This method provides the ability to produce a pure form, more
complicated compounds such as ternary or quaternary materials that

would decompose at higher processing temperatures.

42

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43

2.7 .2 Flash synthesis

After a certain type of chalcogenide compound has been produced
from the flux method and shown to have promising thermoelectric
properties, flash synthesis can be used to reproduce this type of
compound in larger quantities. In the flash synthesis technique the
correct element component ratios are used such that there are no excess

reactants after the ingot is formed.

2.8 Sample Mounting Technique

The purpose of this system is to rapidly evaluate a large number of
samples, through thermopower measurements, to gain insight on general
doping and alloying trends. The most promising samples are then
further characterized by measuring electrical conductivity, thermopower,

and thermal conductivity in a 4-sample measurement system [12].

44

Chapter 3
Experimental set-up
3.1 Apparatus
A system that can measure the thermoelectric power of up to 36
samples simultaneously, is presented. The whole system consists of a
Measurement Unit, a Janis Supertran Unit (sub-system), a Vacuum Unit
(sub—system) and a Software Unit, Figure 3.1. The following are the

detailed description for each component in each unit:

3. 1.1 Measurement Unit
3. l. 1. l Keithley 7002 High Density Switch System

The Model 7002 Switch System is a 10—slot mainframe that
supports up to 400 2-pole multiplexer channels or 400 matrix
crosspoints. This is a computer controlled relay bank to connect the
appropriate meter(s) to the desired sample(s). The front panel includes a
unique interactive display of channel status for quick programming.
Scanning speeds of up to 165 channels per second are possible with the
high-density switch cards.

It has nine 20-channel relay switch card slots of which two are
being used in this system. The system is connected to the sample
cryostat, the source meter, six Nanovoltrneters and a Lock-in Amplifier.
By closing the appropriate relays in the 7002, corresponding samples are

selected for measurement.

45

 

 

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3. 1.1.2 Keithley 2400 Digital Source Meter

This meter consists of four instruments in one: a voltage source, a
voltage meter, a current source and current meter. It can source up to 20
watts, allows sourcing and measuring of voltage from +/ -1 uV to +/-200
VDC and current from +/-10pA to +/-1A. It can also automatically
generate sweeps of output voltage or current vs. time.

On board memory of this meter can be used to store measured
data for review or for block transfer to a computer. In this system, it is

used to source current in the 36 sample measurement system

3. 1. 1.3 Keithley 2182 Nanovoltmeter

This meter is capable of 10nV resolution, and averaging multiple
readings for noise reduction. In the 36 sample system, two 2182 meters
are used to measure one sample at a time. One meter measures the
voltage difference (dV), while the other simultaneously measures the
temperature difference (d7). Temperature difference ((17) is measured
using a copper constantan differential thermocouple. The voltage
measured across the differential thermocouple is converted to a

differential temperature reading using a reference thermocouple lookup

table [20].

47

3. 1.1.4 LakeShore 330 Autotuning Temperature Controller

The system is capable of 4.2K to 400K operation and is
temperature controlled using the LakeShore 330 Temperature Controller.
This instrument compares the measured control sensor value to the
desired control set point and minimizes the difference using the standard
Proportional, Integral, Derivative (PID) control. Two heaters setting
provide 25W and 50W maximum and accommodate a variety of cryogenic
systems.

An autotuning algorithm is available, which determines controller
gain (Proportional), reset (Integral), and rate (Derivative) by observing
system time response upon setpoint changes under either P, PI or PID
control.

Limitations to digital control and Autotuning:

1) Any control system is inherently unstable if the sampling rate
(frequency) is not greater than twice the system bandwidth (inverse of
system time constant). Known as the Nyquist criterion

2) Autotuning requires system time response measured as a result of a
change in temperature setpoint. Several points on this response curve
must be measured to determine PID parameters.

LakeShore simplified the input of the rate time constant to
correspond to a percentage of the reset time constant, i.e., 0 to 200%. So

in manual mode with RATE set to 100%, any change in RESET causes

48

the controller to automatically calculate the RESET time constant and

set the RATE time constant at 1 / 8 of the RESET time constant.

3. 1. 1.5 EG&G 7265 DSP (Digital Signal Processor) Lock-in Amplifier
This instrument has dual capability:
1. It can recover signals in the presence of an overwhelming noise
background;

2. It can provide high-resolution measurements of relatively clean
signals over several orders of magnitude and frequency.

It can function as: AC signal recovery instrument, vector voltmeter,
phase meter, spectrum analyzer, transient recorder, precision oscillator,
frequency meter and noise measurement unit. Its signal recovery mode is
the default mode on power—up. Its signal channel input can be used for
either single-ended or differential voltage mode operation, or single-ended
current mode operation.

In voltage mode, AC and DC coupling is available, also the input
may be switched between PET and bipolar devices. In current mode, two
conversion gains are available. In both modes, the input connector shells

may be either floated via 1k ohm resistor or grounded.

3. 1.2 Janis Supertran Unit
3. 1.2. 1 Cold Finger Cryostat

This is the part of the system that interfaces with samples. It
includes a copper cold finger with tapped mounting holes, heater and

thermometer for monitoring and regulating the temperature. The system

49

 

is designed to operate with either liquid nitrogen or liquid helium as the
working cryogen. As part of this thesis, this sample stage was designed
and submitted to the Physics Machine Shop for fabrication. It was

subsequently gold plated for surface stability.

3.1.2.2 High efficiency transfer line

The Janis Supertran transfer line combines vacuum insulation
with multilayer superinsulation to provide low cryogen losses during
transfer. A needle valve flow regulator is built-in to the transfer line. One
end of the transfer line is inserted into the cryogen storage container (we
use a liquid nitrogen tank here), while the other end is inserted into the

cold finger cryostat.

3. 1.2.3 Radiation shield

This shield, usually fabricated from polished aluminum tubing, is
mounted to a thermal anchor on the cold finger cryostat. It intercepts
room temperature radiation, thereby reducing the heat load on the
sample. This helps the system achieve lower sample temperatures and

minimizes temperature gradients.

3. 1.2.4 Liquid Nitrogen
The liquid nitrogen cools the samples and provides a temperature-

controlled environment for obtaining temperature dependent

50

measurements. There is a temperature sensor (silicon diode) in the base
of the cryostat that connects to the LakeShore 330 temperature
controller. The sensor provides accurate temperature measurements

(< lOmK accuracy) and feedback control to the temperature controller.
Typical measurement runs are from 77K to 400K. The cryostat is also

capable of liquid helium use for 4.2K to 400K operation.

3. 1.3 Vacuum Unit
The system needs to have a vacuum environment to prevent icing

and heat loss through convection.

3.1.3.1 TURBO-V 7O
Turbo-molecular pump has KF 40 NW high vacuum flange for high
and ultra—high vacuum. The pumping action is obtained through a high

speed turbine (max. 75000 rpm) driven by 3-phase electric motor.

3.1.3.2 TURBO-V 70 CONTROLLER

The controller drives the Turbo-V 70 pump during the starting
phase by controlling the voltage and current with respect to the speed
reached by the pump. The controller is a solid-state frequency converter
that is driven by a single chip microcomputer and is composed of:
* Power transformer

* Front panel display and keyboard

51

* Rear panel with input/ output connectors
* PCB including: power supply and 3-phase output, analog and

input/ output section, microprocessor and digital section, display and
keyboard circuits.

The power supply converts the single-phase (50-60 Hz) AC mains
supply into a 3-phase, low voltage, medium frequency output which is
required to power the Turbo-V pump. The microcomputer generates the
variable output frequency and controls the 3-phase output voltage
according to the on board software and the gas load condition of the
pump. It manages signals from sensors, input/ output connection
information to be displayed, and gives outputs for a fully automatic
operation. A non-volatile RAM is used to store pump operating
parameters.

The vaccum station is turned on by pressing the "Start" key of the
controller. The controller starts the rough pump followed by the turbo
pump automatically. The vacuum level can be monitored with the multi-

gauge controller described below.

3.1.3.3 Kurt J. Lesker Multi-Gauge Controller

It is used to control and read the pressure of the sample chamber.
Plug—in Boards: 1) T/ C gauge, 2) Bayard-Alpert and 3) RS232 Control
and output. The thermocouple gauge board can monitor up to four

thermocouple gauges. These gauges are capable of measuring from

atmospheric pressure down to 1.0 x 10‘3 Torr. Below this pressure, a

52

Bayard-Alpert ion gauge is used. This ion gauge has a tungsten filament
and can measure pressures in the 10'4 to 10'9 Torr range. The ion gauge
should always be turned off before removing the cryostat to avoid

burning out the filament and contaminating the gauge.

3. 1.4 Software Unit

A very significant feature of this system is the computer-control. By
connecting GPIB cables to each instrument, it provides channels for
communicating between the computer and the instruments. A graphical
programming language was used for system control and data acquisition

and was developed in LabVIEW®.

3. 1.4. 1 LabVIEW (Virtual Instrument) Programming

LabVIEW is a program development environment, much like
modern C or BASIC development environments, and National
Instruments LabWindows/CVI. However, LabVIEW is different from those
applications in one important respect. Other programming systems use
text-based commands to create lines of codes, while LabVIEW uses a
graphical programming language, G, to create programs in block diagram
form. A graphical icon within the program represents a subroutine, and
data is passed in an out of these subroutines by connecting graphical
wires between icons. LabVIEW is a general-purpose programming

system, but it includes libraries for data acquisition, GPIB and serial

53

instrument control, data analysis, data presentation and data storage.
LabVIEW programs are called virtual instruments (Vls) because their
appearance and operation can imitate actual instruments. Figure 3.2 is

the flowchart of the system’s programming.

3.2 Design of the sample stages

The following set of figures show the details of this system,

including drawings used in fabricating various parts of the sample stage.

54

 

Start File Initialization (creation)
F ilename for 32 samples

\L

Instrument reset and initialization
e.g. *rst; system: preset; *clr

 

 

 

 

t

start current source
oscillating

 

 

 

 

     

go to setpoint (temperature)
Is it stable?

 

> 330 temperature controller '

 

  

Yes

4
trigger all 6 N anovoltmeters
simultaneously (3 samples are
measured at a time)
to collect 4.2 periods

‘ of current source oscillation
/ ‘ \l/

 

 

 

 

 

 

 

 

/ Read all data save to file

 

 

 

._ \1/

g Calculate linear (fit) and convert to dV/dT

I \ l l

Switc to the Save data to these 3 files
I next 3 amples J/

 

 

 

    
     

 

 

 

Are all sample measured?
, flYes
\
\ Switch to the next sample
\ , measure 2-probe electrical conductivity

Are all sample measured?

Temperature ' crement \/

or decrement Yes

 

 

 

 

 
 
  

 

No

 

Is temperature > Stop temperature?

   

 

Set range to 100V on 2182‘s
and turn off 2400 output —>-

Figure 3.2 Flowchart of the programming

 

 

 

55

 

Figure 3.3.1 and 3.3.2 show the top View of the circuit boards and
sample stages of this system.

Figure 3.3. 1(a) A 1.7" diameter circuit board with 76 holes (each
hole is 0.035" diameter) distributed into four groups. Each hole has been
soldered to a 0.4" length gold plated electrical pin. The four larger holes
are the bolt positions.

Figure 3.3. l(b) A 1.7" diameter circuit board with 76 smaller holes
(each hole is 0.067" diameter) and each hole will be soldered to a socket.

Figure 3.3. l(c) A 1.5" diameter circuit board with two rings of 36
holes each. It is placed under the 36-arm-spring for support purposes
and each spring arm is soldered to the circuit board.

Figure 3.3. l(d) Support stage to hold the 36 springs to the proper.
It is slightly larger than the pin and socket circuit boards. It will combine
with the circuit board #b.

Figure 3.3.2(e) is a spring with 36 arms. The springs were
originally connected by a ring of metal at the center of the spring
assembly. This provided proper alignment while mounting the springs to
a circuit board. After mounting, the inner metal ring was removed in
order to produce 36 individual arms. The spring arm provides a flexible
capacity to hold the sample in place during the measurement and
accommodates samples of varying sizes.

Figure 3.3.2 (f) Stage that is bolted on the cryostat cold head.

56

Figure 3.3.2 (g) Sample holder stage with 36 dimples to hold each
sample in place.

Figure 3.3.2 (h) Radiation shield.

Figure 3.4.1 and 3.4.2 show the brief process of how the whole
sample stage is assembled.

In Figure 3.4.1(a, b), one side of the pin-circuit-board is soldered
with 76 quad-twisted wires which are connected to the cryostat. The
other side of the board is where the pins make contact (plug-in) with the
76 sockets. The quad-twisted wires are fed through the 4 holes of the
sample stage #f. Sample stage #f is bolted to the cold head of the
cryostat. These wires are soldered to the pins of 3 connectors inside the
cryostat.

In Figure 3.4.1(c) and 3.4.2(d), the circuit board #b is combined
with the support stage #d. The wiring of this circuit board will be
explained later. The sample holder stage #g is placed on the stage #f and
the combined stage #b and #d are placed on the top of the stage #g.

In Figure 3.4.2(e), part of the stage is assembled.

In Figure 3.4.2(f), solder was forced through the holes of the spring
to make a robust contact with the circuit board #0. Part #c and #e are
bolted to the top of the stage #d. Figure 3.5 is the top and side View of

the stages after all parts are assembled.

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Tab to accommodate
the common end of a
differential thermocouple.

 

Top View of sample stage showing 36 samples near
the perimeter, and 76 electrical pins closer to the center.

Radiation
Shield

 

 

 

1 J \ Cryostat
L/ cold head

Figure 3.5 Stage with all parts assembled. The top and side View.

62

3.3 Preparation for wiring of the sample stage

Two types of lead were used to measure the thermopower of each

sample: the temperature leads (thermocouples) and the voltage leads.

S = dV/dT

A l K temperature drop is created across the sample using a

surface mount resistor as a heater on each of the 36 springs.

1) Temperature lead (Thermocouples)

2)

3)

36 lengths of 5cm (0.003" diameter, Teflon insulated) copper and
constantan wires were prepared. Both ends of each wire were scraped
to remove the insulation and 36 pairs of copper-constantan
thermocouples were made by spark welding the wires together.
Voltage lead

36 lengths of 5cm (0.003" diameter, Teflon insulated) copper wires
were prepared. Both ends were scraped to remove the insulation
Heater

36 surface mount resistors were used as heaters to create the
temperature gradient, AT, across each sample. These AT heaters were
mounted near the end of each spring arm. Two copper wires (0.003"
diameter, Teflon insulated) were soldered on each resistor, as shown

in Figure 3.6(a).

63

 

 

 

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470x90

 

 

 

 

(C)

Figure 3. 6 Heater

The temperature gradient should be created across the sample, while one
end of the sample remains at the sample stage temperature. To avoid
changes in the sample stage temperature, only half of AT heaters (every
other one) are heated at one time. Each of these two clusters consists of
18 resistors formed by the parallel connection of two groups of 9 series
connected resistors. Figure 3.6(b) shows how two resistors are connected
and Figure 3.6(c) shows the series combination of nine resistors per
group. The two clusters share a common ground, however current is
selected to pass through only one cluster at a time. Each surface mount
resistor is 470 Q, thus, the resistance per cluster is

R = 9*470/2 = 2115 ohms
If current, I = 7 mA is supplied we get,

V = I*R 2 14.8 V

By doing this simple calculation, we can set the limit on the voltage
across these clusters. With this AT heater configuration (two clusters of
two groups each) the widest range of power from the current source is

available .

3.3 Wiring the sample stage

With so many sample positions, it was essential to organize the
wiring into smaller tasks. The following eight steps were used in wiring
the sample stage.

Step1: Mounting the AT heaters on springs, Figure 3.6(d).

65

The AT heaters were mounted on the spring in the following layered order
Spring > Stycast epoxy > paper > Stycast epoxy > resistor > Stycast epoxy
Stycast epoxy gives good thermal conduction but poor electrical
conduction. It, thus, allows the heat from the resistor to conduct to the
sample while preventing electrical shorting of the resistor through the
spring. Paper was used to assure a physical separation between the AT
resistors and the spring was maintained while the epoxy dried. Kapton
tape is used to tape down the wires on the spring to make the wires more
stable in position and provide some strain relief for the wires.

Step2: All voltage and temperature leads (wires) were each soldered to the
appropriate socket on the circuit board. 36 copper wires (for CW) and 36
copper wires (from copper-constantan thermocouple) were soldered to the
sockets.

Step3: All wires were fed through the stage#d. This was very challenging
as many wires were broken during this step. To help, groups of wires
were twist-tied together and then slowly fed through each hole (in the
stage Figure 3.3. l(d)).

Step4: Sparking the Constantan wire of the Thermocouples.

To reduce the number of wires traveling up the cryostat, the differential
thermocouples were fabricated using one common junction thermally
connected to the sample stage. This was assembled in the following
manner: After all wires were fed through the stage, the ends of each

constantan wire were sparked together in a single bundle. However, it is

66

pretty hard to make a big joint out of 36 wires, so smaller groups were
sparked together electrically joined using constantan wires. A single
constantan wire was then connected to this large bundle and used to
form the common junction by spark welding it to a copper wire. All AT
measurements were made by measuring the voltage between this
common copper wire and one of the 36 copper wires from the
thermocouple attached to the end of a spring (as described in Step 2).
To further describe the sparking process: 1) A few constantan
wires were twisted together; 2) A small constantan foil was folded over
the twisted wires, leaving the ends sticking out of the foil; 3) The end
wires were sparked causing them to melt back to the foil and form a
strong joint. All of these small joints were wrapped with Kapton tape to
prevent electrical shorts to the copper stage. They were further hidden
between the support stage and the spring circuit board to protect them
from mechanical disturbances.
Step5: Bolt down the spring to the support stage with a Teflon sheet in
between.
Step6: With all the wires sticking out, start to tape down each
thermocouple and voltage lead to their corresponding spring. This is an
important part because wrong wiring will result in testing the wrong

sample.

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Step7: Mount the thermocouple on very end of each spring arm.
Thermocouple is mounted in the following order

Spring > Stycast epoxy > paper > Stycast epoxy > Thermocouple > Stycast
epoxy

Step8: Mount the voltage leads.

Voltage leads will be soldered on each spring arm. Figure 3.7 shows the

wiring on one sample.

3.4 Preparation for the measurement: Testing

For this section, several figures are included to give a better View of
how the wiring and testing work. Figure 3.8 — 3.1 1 show the wiring of
different connectors which are plugged into the cryostat. Figure 3.12 —
3.15 show the wiring on four switch cards that are inserted to the 7 002
switch system. Figure 3.16 shows the interconnection between the
switch cards and other instruments.
Step1: A multimeter was used to test continuity between the leads at the
instruments and the pins at the sample stage, to make sure there were
no electrical shorts to the ground.
Step2: The voltage contacts were tested by checking continuity between
the individual sockets and the corresponding spring contact.
Step3: The thermocouples could not be checked with the same methods
used for the voltage leads because all thermocouples are jointed to a

common point. Instead the thermocouples were checked by measuring

69

the resistance of each differential thermocouple. The resistance of all the
thermocouple leads was found to be similar.

Step4: After testing the wiring on the spring and socket, it was plugged
in to the stage. Care was taken to match each group of sockets to the
corresponding pin-group.

Step5: Continuity was then tested between each spring contact and the
cryostat’s connector pins.

Step6: The 4 cable connectors (including the connector from the
temperature controller) were then plugged into the cryostat. Further
testing the connection between the meters and the stage.

Step7: All 2182 nanovoltmeters were then turned on and monitored as
the appropriate relay closures in 7002 were made. With no temperature
gradient, the AT readings where found to be on the order of 0.001mV.
Step8: The voltage leads were tested by closing the appropriate contacts
in the 7002 switching system, unplugging the 2182 connectors and
testing continuity between the 2182 connector pins and the
corresponding spring. The continuity was monitored as the relay in the
7002 switching system was opened. With the relay closed, continuity
between the 2182 connector and ground was also tested (to verify an
open circuit condition with no sample present).

Step9: Finally the differential thermocouples were also tested by closing
the appropriate contacts in the 7002 and monitoring the voltage from the

corresponding differential thermocouple while gently warming the spring

70

(by placing a finger on it). The AT voltages were observed to rapidly
increase while touching the spring, and subsequently decrease upon

removing the finger.

71

Inside View of the 10 pin connector

   
   
  

red

add

(9 red/ye whi/blk whi
blk

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Outside View of the 10 pin connector

   
     
      
 

   

e red
6 6
Wm whi/blk red/ye

blk

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red I+

ye V+

whi 1-

blk V-
Heater Output:
High - red / ye
Low - whi/blk

Figure 3.8 The inside and outside views of a 10 pin connector.
It connects the temperature controller to the cryostat, reads
and controls the temperature sensor which is mounted in the
base of the cryostat.

72

Inside View of the 20 holes connector

  
 

Q? Z: ERIE?

browb

 

C - B19 (Short to heater low,
common point for two groups of heaters)
L - C19 (heater reisistor)
J - D 19 (heater reisistor)
N - C15
S - D9
Q - A19 (Short to six 2182 meters’ ground,
physically ground to sample stage)
Figure 3.9 Inside and outside views of a 20 pin connector.
It provides connection to the heater and extra pins to the cryostat.

73

Inside View of the 35 hole connector

 

Color of the wire

Letter on the connector
blk - black

blu - blue

brow— brown

gr - green

org - orange

red - red

whi - white

ye - yellow

Figure 3.10 Wiring on 35 pin connector# 1.
It connects samples’ lead to the switch system and meters.

74

Inside View of the 35 hole connector

 

Color of the wire

Letter on the connector
blk — black

blu - blue

brow- brown

gr - green
org - orange
red - red
whi - white
ye - yellow

Figure 3.11 Wiring on 35 pin connector#2.
It connects samples’ lead to the switch system and meters.

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80

3.5 Load samples

Samples dimensions from 3x3x7mm to 4x4x9mm can be
accommodated in this system. Samples received with dimensions larger
than these were cut into smaller pieces by using a diamond saw.
Samples are easily mounted by slowly lifting the spring arm with a pair
of tweezers while placing the sample under the spring. The spring arm
thus holds the sample in place. Silver or gold paste can then be used for

improved electrical and thermal contact to the spring and sample stage.

3.6 Test run

Reference materials of bismuth telluride Bi2Te3, and lead bismuth
selenide Pb / Bi/ Se, were first measured. These samples were received
from industrial collaborators, and have been characterized in
independent systems. While at room temperature, the source current
from the 2400 meter was adjusted to create a temperature drop of ~1 K
across the samples.

The samples were then prepared for temperature dependent
measurements by loading them into the cryostat vacuum chamber. The
bolts were then tightened and all electrical connectors plugged into the
cryostat before turning on the vacuum pump. The cryogenic transfer line
was then inserted into the cryostat. After releasing all pressure on the
liquid nitrogen storage tank, the other end of the transfer line was

inserted approximately 8 inches into the dewer (not far enough to touch

81

the liquid nitrogen). The valve on the transfer line was then opened to
allow dry nitrogen gas to purge the transfer line of any moisture that
might be in the line. This is an essential step to assure that ice does not
form in the transfer line and clog it. Typically the first two or three data
points are monitored to adjust the cryogen flow through the transfer line,
however, since the system is computer-controlled, by entering the
desired parameters, e. g. the temperature range, the pulse height, the

period and etc, it can operate independently until the run is over.

82

Chapter 4
Results and Discussion
Each thermopower data point (at a given temperature) is obtained
by fitting (linear) over 600lpoints of dV vs. d’I‘ data as shown in
Figure 4.1. The two complete loops that fall on top of one another in this
figure correspond to two periods of current through the AT heater

resistor for this sample.

 

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50:

 

 

40:

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Voltage gradient, dV (uV)

 

10:

 

 

 

 

O . L l 1 le . . . . . . l . . . l 14 . m; .
-l.6 -1.4 -l.2 -1 -O.8 -O.6 -O.4 -O.2
Temperature gradient, dT (K)

 

Figure 4.1 dV/dT plot of sample#15 (Pb / Bi/ Se) for 2.2 periods
of the current pulse.

Figure 4.1 shows the dV/ dT plotting for Pb / Bi/ Se. The
thermopower of the sample is the slope of dV/dT. Since the slope is
negative, the thermopower is negative and thus the sample is n-type. For

the indicated temperature gradient of approximately 1.35 K, the sample

83

voltage of nearly 50 (N was measured, giving a thermopower of

approximately —37 uV/ K at this temperature.

300

N
01
O

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Voltage gradient, dV (uV)
S E?
o o

 

01
O

 

O
-1.6 -1.4 -1.2 -1 -O.8 -O.6 -O.4 —O.2

Temperature gradient, dT (K)

Figure 4.2 dV/dT plot of sample#1 (BizTCs) for 2.2 periods.

Similar measurements on n-type Bi2Te3 are shown in Figure 4.2. In
this case, the slope of the data indicate a thermopower of approximately
—217 uV/ K in excellent agreement with measurements from independent
systems.

The looping observed in Figures 4.1, and 4.2 occurs due to a
temperature difference between the location of the thermocouple and
voltage leads. While the thermocouple and voltage leads have been
placed as closely together as possible, there is some separation across

which small gradients could exist. As this system is used for screening

84

many samples, an accuracy of i20% is adequate and such small looping
is acceptable. In comparison, Figure 4.2 has a much smaller looping
indicating the sample dependence of this effect. Often the looping
problem can be corrected by increasing the pulsing period. This is
because the longer the period, the closer the system will come to

reaching steady-state.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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296 298 300 302 304 306

Temperature (K)

Figure 4.3 Two runs of sample#15 (Pb/ Bi/ Se) near room
temperature.

The repeatability of thermopower measurements was investigated
as shown in Figures 4.3, 4.4, and 4.5. Figure 4.3 shows repeatability
within 1.25%. Figure 4.4 indicates repeatability of better than 0.2%, and

Figure 4.5 shows approximately 1.7% repeatability.

85

 

 

 

 

 

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296 298 300 302 304 306

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Figure 4.4 Two runs of sample#26 (Bi2Te3) at room temperature.

 

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Thermoelectric Power, (uV/ K)

 

 

 

 

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296 298 300 302 304 306
Temperature (K)

Figure 4.5 Two runs of sample#32 (BizTes) at room temperature.

86

Figures 4.3-4.5 show higher thermopower in the second run. This
might due to unstable vacuum. After replacing the rubber O—ring with a
copper plate for better sealing, the results are more consistent. This can
be seen in Figures 4.6—4.9.

Figures 4.6—4.9 show the results of the first and second runs of 19
samples. Among them are 15 samples of bismuth telluride and 4
samples of lead bismuth selenide. The first and second runs gave very
consistent results. The standard value of thermopower for BlgTCs at room
temperature is about —220 uV/K. It is obvious that some of the samples
did not give the correct thermopower values. Further explanation will be
discussed. The results for lead bismuth sellenide have more deviation.

—160

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ti:
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Thermoelectric Power,

i'o
oo
o

——s—_

 

—300
298 300 302 304 306 308

Temperature (K)

Figure 4.6 First run of 15 samples (B12T63) at room temperature
range.

87

—160

Thermoelectric Power, (uV / K)
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—300
296 298 300 302 304 306 308

Temperature (K)

Figure 4.7 Second run of 15 samples (Bi2Te3) at room
temperature range.

Thermoelectric Power, (uV/ K)

 

296 298 300 302 304 306
Temperature (K)

Figure 4.8 First run of 4 samples (Pb /Bi / Se) at room temperature
range.

88

 

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to

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-42

-46

Thermoelectric Power, (uV/ K)

 

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296 298 300 302 304 306

Temperature (K)

Figure 4.9 Second run of 4 samples (Pb / Bi/Se) at room temperature.

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Thermoelectric Power, (uV/ K)

 

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50 100 150 200 250 300 350

Temperature (K)

Figure 4.10 Comparison between this system’s data (l4OK—300K)

and data measured in an independent system.

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 4.11 Comparison between this system’s data and standard
Tellurex data (110K-300K)

Figure 4.10 and 4.11 are the plots including the reference data for
these samples. In Figure 4.10, except #32, the other samples show good
agreement with the reference data. All samples shown above indicate n-
type behavior. This system has also been utilized in characterizing p-type
samples giving dV/ d’l‘ plots similar to Figures 4.1 and 4.2, but with
positive slopes.

Improper linear fitting in the software is suspected to have caused
some bad data points as shown in Figure 4.11. Low temperature dV/ dT
plots have also shown increased noise potentially due to thermal
contractions of the spring contacts and resulting degradation of the
interface between sample and spring contact.

Images in this thesis are presented in color.

90

Chapter 5
Further Improvement
The system was designed to characterize 36 samples
simultaneously but during the building process, many of the sample
locations had problems caused by broken wires, bad thermocouples, or
shorting to ground. The remaining positions have shown good results.
The experience of building this system has been invaluable, particularly
for identifying areas for further improvements including:

1) Type of wires — The wires that are used for voltage leads and
thermocouples are formvar insulated and they are not suitable for
high temperature measurement. Polyimide insulated wires can be
considered since they can operate at a relatively high temperature,
about 220C (473K). Gold wire was used in the original design for
voltage but it was replaced by copper wire due to its brittleness.
Though, gold wire will have low loss in electrical conduction. A
redesign of the sample stage may be possible to better handle this
fragile gold wire.

2) Wiring on stage — As shown in the wiring figures, wiring all 36
thermocouples, 36 voltage leads and 36 surface mount resistors on
a stage which is less than 2” diameter is not an easy job. Since all
the wires are exposed, it is very easy to break the wires during the

wiring process or even when loading the samples. Thus, a stage

91

with hidden wires, such as in flexible circuit boards, will be one of

our considerations in building the next stage.

3) Thermocouple — thermocouples, which are used in this system are

4)

5)

sparked welded. The joint of each thermocouple may be different
and thus posses different resistance. Thermocouple junction
quality is suspected as a reason for the deviation among samples
of the same material. For our next revision, we might purchase
pre-fabricated thermocouples.

Labview programming — communication between computer and
system did not always go smoothly. Since the system consists of 10
instruments, a slight delay on one of the meters might cause the
whole system to lock up. Thus, improved communications and
error handling would help to provide smooth measurement runs.
2-probe electrical conductivity — The system is also designed to add
in more features in the future. 2-probe electrical conductivity
measurements will be included in the run to better evaluate the

sample quality.

92

Chapter 6
Conclusion

A high sample throughput computer-control measurement system
has been presented for characterizing the thermoelectric power of up to
36 samples in a single temperature run (4.2K - 400K). This will greatly
increase the number of samples being characterized and thus speed up
the exploration in the field of thermoelectrics.

Many significant features of the system, including computer-
control, easy sample mounting, and high sample throughput have made
it a unique system for characterizing thermoelectric materials. We are
not aware of anyone in the nation with such a capability. For
comparison, a separate system in the same laboratory has been
configured to measure up to 4 samples in a single run. The system
described in this thesis can accommodate more than 5 times this
number of samples. When investigating new thermoelectric materials,
the use of this system can provide a broad perspective of sample
variations with doping and alloying. It is, therefore, a good starting point
in searching for new samples before proceeding with more exhaustive

characterization techniques.

93

[ll

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

REFERENCES

Ferrotec America Corporation: “Technical Reference For Ferrotec
Thermoelectric Cooling Modules.” [Online] Available
http: / /www.ferrotec—america.com/3ref.htm (1998).

T. C. Harman, P. J. Taylor, D. L. Spears, M.P. Walsh,
“Thermoelectric Quantum-Dot Superlattices with High ZT,” Journal
of Electronic Materials, vol. 29, no. 1 (2000), pp. L1—L4.

P. J. Lin—Chung, T. L. Reinecke, “Thermoelectric figure of merit of

composite superlattice systems,” Physical Review B, vol. 51, no. 19
(1995), pp. 13244-13248.

Thermoelectric Refrigeration,” British Journal of Applied Physics, vol.
5 (1954), pp. 386-390.

D. T. Morelli, “Advanced Thermoelectric Materials and Systems for
Automotives Applications in the Next Millennium,” Meeting of the
Materials Research Society, San Francisco (1997).

Corinna Wu, “A Silent Cool,” Science News Online, [Online] Available
http: / / www.sciencenews.org / sn_arc97 / 9_6__97 / bob 1.htm (l 997).

[Online] Available http: / / vraptor. jpl.nasa. gov / voyager / voyagerhtml
(2000).

L. D. Hick, T. C. Harman, M. S. Dresselhaus, Applied Physics Letter,
vol. 63, no. 3230 (1993).

M. Kanatzidis, et al, “Thermoelectric Materials: Solid State
Synthesis,” Naval Res. Rev. vol. 48, no. 4 (1996).

[10] Duck-Young Chung, et al, “Complex Chalcogenides as Approach,”

Bull. Korean Chem Soc., vol. 19, no. 12 (1998), pp. 1283-1293.

[1 l] Duck-Young Chung, T. Hogan, “CsBi4Te6: A High-Performance

Thermoelectric Material for Low-Temperature Applications,” Science,
vol. 287 (2000), pp. 1024-1027.

[12] T. Hogan, N. Ghelani, S. Loo, “Measurement System for Doping and

Alloying Trends in New Thermoelectric Materials,” Eighteenth
International Conference on Thermoelectrics Proceedings, pp. 671 -
674, 1999.

94

[13] H. J. Goldsmid, Applications of Thermoelectricity, Methuen
Monograph, London (1960).

[14] D. M. Rowe, “Rowe’s chapter title,” Chapter I in CRC Handbook of
Thermoelectrics, CRC press, Inc. (1994).

[15] N. E. Lindenblad, “Thermoelectric Heat Pump,” (1958), pp. 802-806.

[16] J. R. Andersen, “Thermoelectric Air Conditioner for Submarines,”
RCA Review, (1961), pp.292-304.

[17] F. D. Rosi, E. F. Hockings, N. E. Lindenblad, “Semiconducting
Materials for Thermoelectric Power Generation,” RCA Review, (1961),
pp. 82-121.

[18] [Online] Available, Tellurex, “An Introduction to Thermoelectrics,”
www.tellurex.com (2000).

 

[19] Ben G., Streetman, Solid State Electronic Devices, 4th edition,
Prentice-Hall, Inc (1995).

[20] The Temperature Handbook, 21st century edition, Omega
Engineering, Inc (1999).

95

 

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