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305; LIBRARY
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This is to certify that the

thesis entitled

CHARACTERIZATION OF NOVEL
THERMOELECTRIC MATERIALS

presented by

Nishant A. Gheiani

has been accepted towards fulfillment
of the requirements for

Masters degree in Electrical Eng

_ V
Major professor

Date 0 ‘7Z3/01

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

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6’01 c-JCIRC/DateOuopes-pts

 

CHARACTERIZATION OF NOVEL THERMOELECTRIC
MATERIALS

By

Nishant Ghelani

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

2001

ABSTRACT
CHARACTERIZATION OF NOVEL THERMOELECTRIC MATERIALS
By

Nishant Ghelani

During the last decade there has been a worldwide search for new materials with
higher thermoelectric figures-of-merit and attempts to improve the thermoelectric
properties of the known compounds. It is anticipated that the successful development of
such materials will lead to new fields of application for thermoelectric devices and
related technologies based on bulk crystals and on films. However, the improvement of
thermoelectric materials requires a detailed knowledge of all the factors that determine
their properties.

Recent advances in synthesis techniques have greatly increased the rate of
fabrication of new electronic materials. The polychalcogenide flux technique for instance,
has produced a variety of new and interesting thermoelectric materials. With existing
charge transport characterization systems, it would be difficult to measure samples at
such a rate, therefore a new 4-sample measurement system has been designed. Special
features of the 4-sample system include simultaneous measurement of electrical
conductivity, thermoelectric power, and thermal conductivity.

This system has been successfully used to characterize several new thermoelectric
materials (including some of the above-mentioned compounds) and reference materials

exhibiting a wide range of thermal conductivities.

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my advisor, Dr. Tim Hogan. This
work wouldn’t have been possible without his guidance, constant encouragement and
continuing support. Time and again, his inspiring efforts and knowledge have helped
resolve a number of project-related issues, providing me a better technical understanding
of certain key concepts. I would also like to thank my committee members, Dr. Reinhard
and Dr. Kanatzidis for their valuable comments on the project.

Many thanks and good wishes go to my research colleagues Sim Loo, Sangeeta
Lal and Akiko Kubota for their advice, support and friendship. I cannot forget the
contributions of my senior research colleagues in Dr. Kanatzidis’s group, especially the
materials fabrication processes. Camaraderie between us has helped working as a team
and made my research an enjoyable, satisfying experience.

Finally I would like to express my gratitude to my parents and family members

for their patience, unconditional support and confidence in my abilities.

iii

TABLE OF CONTENTS
List of Tables
List of Figures
Chapter 1
1.1 Introduction
1.2 Objectives
1.3 Thesis Outline
Chapter 2
2.1 Historical Background
2.2 Thermoelectric effects
2.3 Figure-of-merit
2.4 Factors affecting ZT
2.5 Optimization of ZT
2.6 Current exploratory materials research
Chapter 3
3.1 Measurement of thermal conductivity
3.1 .1 Steady-state technique
3.1.2 30) technique
3.1.3 Harman technqique
3.1.4 Angstrom’s technique

3.1.5 Maldonado’s pulse technique

iv

vi

vii

ll

15

28

35

39

41

42

45

48

50

 

3.2 Experimental Setup
3.3 Preparation of differential thermocouples/heaters
Chapter 4
4.1 Equipment/Instrumentation
4.1.1 Continuous flow cryostat system
4.1.2 Vacuum system
4.1.3 Data Acquisition Instrumentation
4.2 4-sample system mounting assembly
4.3 System assembly
4.4 Remote Operation
4.4.1 Programming details
4.4.2 Experimental procedure
Chapter 5
5.1 Standard Materials

5.2 New Materials

5.2.1 Ternary and Quaternary alkali metal bismuth chalcogenides

5.2.2 Quaternary bismuth selenides

5.2.3 Cubic semiconducting quaternary chalcogenides

Chapter 6
6.1 Conclusion
6.2 Recommendations

References

58

61

64

65

65

69

73

74

77

79

87

9O

94

97

117

119

121

LIST OF TABLES

1.1 Introduction 1
Table 1.1: Thermoelectric properties of n -— type PbTe and BizTe3 3
6 Conclusion 117

Table 6.1: Physical and transport properties for members of different
Systems 118

vi

LIST OF FIGURES

Figure 2.1 Thermodynamic circuit for the relative Seebeck coefficient
Figure 2.2 Thermodynamic circuit for the Peltier effect

Figure 2.3 Thermodynamic circuit for the Thomson effect

Figure 2.4 Thermocouple for heat pumping or generation

Figure 2.5 Intrinsic and extrinsic semiconductors

Figure 2.6 Thermal conductivity and the different scattering processes
Figure 2.7 Three phonons interaction

Figure 2.8 Seebeck Coefficient behavior for different types of materials
Figure 2.9 Seebeck measurement showing a maximum at the point A

Figure 2.10 Semiconductor carrier concentration as a function of
Temperature

Figure 2.11 Schematic Representation of the PGEC concept

Figure 3.1 Schematic Arrangement for the Steady State Technique
Figure 3.2. Schematic arrangement in 3a) Technique

Figure 3.3. Schematic Arrangement for Harman’s Method

Figure 3.4. Schematic Arrangement for Angstrom’s Method
Figure 3.5. Schematic arrangement for the Pulse technique

Figure 3.6. Typical AT data collected

Figure 3.7. Differential Thermocouple Preparation

Figure 4.1 Sample mounting stage

Figure 4.2 Circuit board (a) top view (b) bottom view

vii

10

ll

17

21

22

26

27

27

37

41

43

46

48

57

58

63

71

72

Figure 4.3
Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 5.1.

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6.

Figure 5.7

Figure 5.8

Plug-in board (a) top view (b) front view
Radiation shield (a) front view (b) top view

Schematic diagram of system assembly

Four-sample measurement flow diagram

Thermal conductivity and thermoelectric power measurement
flow diagram

Electrical conductivity measurement flow diagram

Thermal conductivity of a NIST stainless steel sample

Electrical and Thermal conductivity of a NIST stainless steel
sample

The solid lines indicate the variation in thermal conductivity
due to change in the measured spacing of the thermocouple
probes

BizTe3 sample from Marlow Industries, Inc. Radiation
effects were investigated at the higher temperatures by
changing the temperature gradients

Electrical Resistivity and Thermopower for BizTe3

The structure of (A) CsBi4.bexTe6 (x = 0.3)

and (B) CsBi4Te6.ySey (y = 0.3) viewed down the b-axis.
Open circles are Te atoms, gray ones Bi atoms, black
ones Cs atoms, and striped ones Sb atoms (A) or Se
atoms (B). The widths of the [Bi4Te5] slabs are showna).

Variable temperature conductivity and thermopower data
for CSBI3_6Sbo_4T66_

Conductivity and thermopower data for a
CsBi4Te5,ZSeo,3 sample

viii

72

73

74

81

84

86

87

88

89

89

9O

91

92

93

Figure 5.9

Figure 5.10

Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

Figure 5.16

Figure 5.17

Figure 5.18

Figure 5.19

Figure 5.20

Figure 5.21
Figure 5.22

Figure 5.23

Figure 5.24

Figure 5.25

Thermal conductivity of a CsBi4Te4gSe12 sample

CsBi3.4Sb0.6Te6 sample

Variable Temperature Conductivity and Thermopower
data for a RbSmBi11$e21 polycrystalline ingot

Conductivity and Thermopower for Cst4Bi1 [Se21

Variable Temperature Thermal Conductivity data
Variable Temperature Thermopower data for KanBiQn+2
(Q = Te, Se)

Variable Temperature Thermal conductivity for KanBiQn+2
(Q= Te, 86)

Variable Temperature Thermoelectric power of Ag/Pb/Q/Te
(Q = Bi, Sb)

Thermal Conductivity data for Ag/Pb/Q/T e ( Q = Bi, Sb)
Ingots

Electrical Conductivity of Ag/Pb/Bi/Te ingots
indicating metallic behavior

Thermal conductivity data for a AnglngTezo ingot

Electrical Conductivity and Thermopower data for
AnglsSbTCzo

Experimental and Extrapolated ZT values for AnglngTezo
Thermal Conductivity of a Anglgstezo Ingot

Electrical Conductivity and Thermopower data for
Anglgstezo

Figure — of — merit ZT of a Anglgstezo ingot

Variable temperature thermal conductivity data for
Anglsstezo

ix

93

94

95

96

97

99

100

101

102

102

104

104

105

106

107

107

108

Figure 5.26

Figure 5.27

Figure 5.28

Figure 5.29

Figure 5.30

Figure 5.31

Figure 5.32

Figure 5.33

Figure 5.34

Figure 5.35

Figure 5.36

Figure 5.37

Electrical conductivity and thermoelectric power
data for Anglgstezo

Figure — of — merit ZT (considering dc conductivity)
0f Anglgstezo

Thermal conductivity data along different axes for a
AnglngTezo sample

DC conductivity and thermopower along different
axes for Anglgstezo

Thermal conductivity along different axes for AnglngTezo

DC Conductivity and thermoelectric power for AnglngTezo
Figure — of - merit variation with different axes for
Angjgstezo

Variable temperature thermal conductivity data for
Ag5Pb8b6Tel3

DC conductivity and thermoelectric power for Ag6PbSb6Te13

Variable temperature thermal conductivity for a
Ang16SbTelg sample

DC conductivity and thermoelectric power for Angléstelg

Figure — of — merit ZT for AnglGSbTelg

109

109

110

111

111

112

112

114

114

115

115

116

Chapter 1
1.1 Introduction

The truly remarkable pictures of the rings of Saturn transmitted to Earth from the
Voyagers 1 and 2 spacecraft captured the imagination of people throughout the world. No
less remarkable is the source of electrical power, which enabled the information to be
transmitted from the spacecrafi afier more than a decade into its mission and from over
1.5 billion miles in space.

The power source is not a solar cell as one might at first think. The craft is too far
away from the sun to receive sufficient light energy to power the transmitters. On-board
power is provided by an RTG (radioisotope thermoelectric generator) which utilizes the
Seebeck“) effect in converting the heat from a radioactive heat source directly into
electrical energy. The Seebeck effect and the reverse phenomenon, the Peltierm effect,
are principal components in Thermoelectrics — the science and technology associated with
thermoelectric generation and refrigeration.

In attempting to make practical use of thermoelectric generation, the quantity
which is of great interest to us is the efficiency for a given temperature difference
between the source of heat and the sink. In applying thermoelectric refrigeration, we
require the highest coefficient of performance for a given temperature difference. In both
cases the performance, under the optimum operating conditions, can be expressed in
terms of a figure of merit. It is perhaps, not surprising that it is the same figure of merit
that applies both for thermoelectric generation and for refrigeration. This figure of merit

Z for a single material may be written as

Z=Szo/1c (H)

where S is the Seebeck coefficient expressed in volts per degree, or more often in
microvolts per degree IIVK'l , o the electrical conductivity expressed in S/cm and K is the
thermal conductivity usually expressed in W/mK. The unit of Z is UK. At a given
absolute temperature T, since Z may vary with T, a useful non-dimensional figure-of-
merit is ZT. Thus research on materials for thermoelectric applications is aimed at
obtaining the highest values for Z.

Although the properties favorable for thermoelectric applications were well
known, the important advantages offered by Seebeck’s mineral semiconductors were
overlooked with the attention of researchers focussed on metals and metal alloys. In these
materials the ratio of the thermal conductivity to electrical conductivity is a constant
(Wiedemann — Franz — Lorenz law) and it is not possible to reduce one while increasing
the other. Consequently, the metals best suited are those with the highest Seebeck
coefficients. Most metals possess Seebeck coefficients of 10uV/K or less, giving
associated generating efficiencies of a fraction of 1 %, which are not economical as a
source of electrical power. Research into compound semiconductors for possible
transistor applications in the 19505 resulted in new materials with substantially improved
thermoelectric properties and in 1956, Ioffe and his co— workers (3) demonstrated that the
ratio could be decreased if the thermoelectric material is alloyed with an isomorphous
element or compound. Spurred on by possible military applications, a tremendous survey
of materials was undertaken, particularly at the RCA laboratories in the US, which

resulted in the discovery of a few semiconductors with ZT approaching 1.5. Currently

established thermoelectric materials conveniently fall into three categories depending
upon their temperature range of operation. Bismuth telluride and it’s alloys have the
highest figures-of—merit, are extensively employed in refrigeration, and have a maximum
operating temperature of around 450 K. Alloys based on lead telluride have the next
highest figures — of — merit with silicon germanium alloys having the lowest. Lead
telluride and silicon germanium are used in generator applications with upper operating
temperatures of around 1000 K and 1300 K, respectively. The material of reference in
any TE research is bismuth telluride and it’s alloys. Extensive use of bismuth-antimony
telluride and bismuth antimony alloys tends to confirm that Bi plays a decisive role in the
enhancement of thermoelectric properties. It is important to note that its contribution is
not well understood at the present time. There is great effort for developing new
compounds that could surpass the properties of bismuth telluride that has led the market

for the last 30 years.

Table 1.1: Thermoelectric properties of n — type PbTe and BizTe3

 

Compound Tmax (K) o (S/cm) S(uV/K) 1c(W/mK) ZT Mp (°C) Ref.

 

BizTe3 300 800-1000 i210 1.4-1.6 0.8-1.1 585 *

 

PbTe 650 360 -180 1.1 0.7 1197 31

 

 

 

 

 

 

 

 

 

 

*Data provided by Marlow Industries Inc.

During the last decade there has been a worldwide search for new materials with
higher thermoelectric figures-of—merit and attempts to improve the thermoelectric

properties of the known compounds. It is anticipated that the successful development of

such materials will lead to new fields of application for thermoelectric devices and
related technologies based on bulk crystals and on films. However, the improvement of
thermoelectric materials requires a detailed knowledge of all the factors that determine
their properties. This study investigates thermoelectric properties of materials by careful
measurement of the quantities which occur in the figure-of—merit, i.e., the electrical
conductivity 0', thermoelectric power S, and thermal conductivity K.
1.2 Objective

The main objective of this work is to investigate several new electronic materials,
which have shown promising characteristics for thermoelectric applications. To
accommodate the large number of samples required for doping and alloying studies, the
most promising samples obtained after screening through a high throughput
thermoelectric power measurement system“) are fully characterized in a 4—sample

measurement system“)

. Special features of the 4 — sample system include simultaneous
measurement of electrical conductivity, thermoelectric power, and thermal conductivity.
This work primarily concentrates on thermoelectric materials measurement in the 4—
sample system.

Specific objectives are:

0 To design and implement the charge transport characterization system for
simultaneous measurements of electrical conductivity, thermoelectric power and
thermal conductivity as a function of temperature.

0 To characterize several standard, commercially available materials in order to

evaluate the working of the system.

0 To investigate thermoelectric properties of novel thermoelectric materials.

1.3 Thesis outline
The main body of the thesis is divided in six chapters, which include the following:
Chapter 2 begins with a historical background of thermoelectrics, discussing
thermoelectric phenomena and factors affecting the thermoelectric figure-of-merit.
Chapter 3 reviews different thermal conductivity measurement techniques, with merits
and demerits. It provides a detailed explanation of the slow-ac technique, which has been
implemented in this research. Chapter 4 specifies equipment and instrumentation
specifications as well as programming details involved in the design of the charge
transport characterization system. Chapter 5 presents the characterization results obtained
for standard materials and novel thermoelectric materials. Chapter 6 summarizes the
results, identifying a few promising candidates for further research, on the basis of
collected data. Chapter 7 discusses future research work and possible improvements in

system operation.

.amflq

Chapter 2
Thermoelectric Phenomena
2.1 Historical Background

In 1823 Seebeck reported the results of experiments in which a galvanometer was
deflected if placed in the vicinity of a closed loop, formed from two dissimilar
conductors, when one of the junctions was heated. Seebeck erroneously concluded that
the interaction was a magnetic phenomenon and, in pursuing this line of thought,
attempted to relate the Earth’s magnetism to the temperature difference between the
equator and the poles. Nevertheless, he did investigate the phenomenon in a large number
of materials, including some we now call semiconductors, and arranged them in order of
the product So, where S is the Seebeck coefficient and o the electrical conductivity. The
Seebeck coefficient is expressed in volts per degree, or more often in microvolts per
degree uVK'l. With the benefit of hindsight it is apparent from Seebeck’s account that
the phenomenon observed was caused by an electric current flowing in the circuit and
that he had discovered the so-called thermoelectric effects.

Some 12 years later, a complementary effect was discovered by Peltier, who
observed temperature changes in the vicinity of the junction between dissimilar
conductors when a current is passed. The true nature of the Peltier effect was however,
explained by Lenzw) in 1838. He concluded that, depending upon the direction of the
current flow, heat is absorbed or generated at a junction between two conductors, and
demonstrated this by freezing water at a bismuth-junction and melting ice by reversing

the direction of current flow.

The Seebeck effect and the reverse phenomenon, the Peltier effect, are the
principal elements of Therrnoelectrics - the science and technology associated with
thermoelectric generation and refiigeration.

In 1851‘” W. Thomson established a relationship between the Seebeck and Peltier
coefficients and predicted the existence of a third thermoelectric effect, the Thomson
effect, which he subsequently observed experimentally. This effect relates to the heating
or cooling in a single homogeneous conductor when a current passes along it in the
presence of a temperature gradient. In 1909“” and 1911 Altenkirch gave a satisfactory
theory of thermoelectric generation and refrigeration and showed that good
thermoelectric materials should possess large Seebeck coefficients with low thermal
conductivity to retain the heat at the junction and low electrical resistance to minimize
Joule heating. These desirable parameters were embodied in a so-called figure-of-merit
Z, where Z = 820' / K where K is the thermal conductivity and the unit of Z is UK. At a
given absolute temperature T, since Z may vary with T, a useful non-dimensional figure-
of-merit is ZT.

2.2 Thermoelectric Effects

An electrical potential is generated within an isolated conducting material that is
subjected to a temperature gradient; this is the absolute Seebeck efiect, ASE. The absolute
Seebeck coefficient, ASC, is defined as the instantaneous rate of change of the ASE with
respect to temperature at a given temperature: ASC = [d(ASE)/dT]T. The simplest way in
which this phenomenon is used is to form a thermocouple composed of two dissimilar
conductors, or therrno-elements, by electrically joining one set of their ends. The

application of a temperature difference, or gradient, between the ends of this device will

produce a voltage across its unpaired terminals, that is a function of the temperature
distribution. The resulting voltage is the relative Seebeck emf, RSE. It results only from
the difference between the internal potentials, or ASEs, within the individual conductors
of which it is composed. The relative Seebeck coefficient, RSC, is the instantaneous rate
of change of the RSE with temperature at a given temperature:

RSC = [d(RSE)/dT]T.

A

T- T+AT

B

Figure 2.1. Thermodynamic circuit for the relative Seebeck coefficient.

The Seebeck effect does not arise as a result of the junction of dissimilar
materials, nor is it directly affected by the Thomson or the Peltier effects; the latter two
thermal effects are present only when current flows in a thermoelectric circuit and are not
voltages. These responses are in contrast to that of the relative Seebeck effect, which
exists as long as the temperature gradient is maintained, regardless of whether current
flows or not. The greatest application of the Seebeck effect is in thermoelectric
thermometry. Thermocouples composed of standardized metallic conductors are widely
used for the accurate, sensitive, and reliable measurement and/or control of temperature.

Peltier showed that heat is absorbed or liberated when a current crosses an

interface between two different conductors; see Figure 2.2. The Peltier effect is the

reversible change in the heat content at an interface between dissimilar conductors that

results from the flow of current through it.

/

T1 -AT T1 +AT

\

Figure 2.2: Thermodynamic circuit for the Peltier effect .(9)

The Peltier coefficient, TCAB, 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. The
direction in which current flows across a junction and the values of TEA and RB determine
whether heat is liberated or absorbed.

Heat absorbed at the hotter junction = rtAg (T + AT ) (2.1)
Heat liberated at the colder junction = -1tAg (T) (2.2)
These reversible effects are independent of the shape or dimensions of the junction.

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 non-isothermal 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 coefficient is not a voltage,

although, like the Peltier effect, it can be expressed in energy units involving volts.

 

Figure 2.3: Thermodynamic circuit for the Thomson Effectm).
Figure 2.3 shows that the passage of a current I along a portion of a single

homogeneous conductor, over which there is a temperature difference AT, leads to a rate

of reversible heat generation AQ. The Thomson coefficient 7 is defined by

_ . AQ
Y—Aly—r’lom (23)

The Thomson effect is a manifestation of the direction of flow of electrical carriers with
respect to a temperature gradient within a conductor. These absorb energy (heat) flowing
in a direction opposite to a thermal gradient, increasing their potential energy; and, when
flowing in the same direction as a thermal gradient, they liberate heat, decreasing their
potential energy. Thomson, later Lord Kelvin, realized that a relation should exist

between the Seebeck and Peltier effects and proceeded to derive these relations from

 

thermodynamical arguments.

Relation 12 Sab = RAB /T (2.4)

Relation 2: d8” = Y“ '7” (2.5)
dT T

10

Both of Kelvin ’s laws have been confirmed, within experimental error, for a
number of thermocouple materials. However, it has been reported that relation (1) is not
strictly obeyed for a germanium — copper thermocouple. It appears that the value of the
Peltier coefficient is less than the product ST.

2.3 Figure - of - merit

In order to obtain an expression for the conversion efficiency of a thermoelectric
device, the rather idealized thermocouple shown in Figure 2.4 is considered.

The thermocouple consists of a positive (p ) and negative ( n ) branch (thermoelement) to
which are attached metallic conductors A , B , and C of negligible electrical resistance.

The branches are of length L,, and Ln and of cross — section area Ap and An where
in general, the ratios Lp / Ap and L.1 / An are different from one another. An important
assumption is that heat is transferred from the heat source at B to the heat sink at AC
solely by conduction along the branches of the thermocouple.

It should be clear that the connection of any number of such couples, electrically

 

HEAT SOURCE
B T
//////////L

 

1/////// T2///////A
A HEAT SINK C

 

 

 

 

 

 

Figure 2.4. Thermocouple for heat pumping or generation

in series and thermally in parallel, affects the power handling capacity of the convertor

but not it’s efficiency.

11

The thermocouple can be used in two ways. If a voltage source is connected
across A and C so that an electric current is driven through the couple, it acts as a heat
pump (or, more specifically, if A is negative and C is positive, as a refrigerator). Heat is
pumped from the source at an absolute temperature T1 to the heat sink at temperature T2
by means of the Peltier effect. Alternatively, if a resistive load is placed across A and C,
the supply of heat at B and it’s removal at AC causes an electric current to flow around
the circuit due to the Seebeck effect; in other words, the thermocouple acts as a generator.

It is important to realize that, although the Peltier and Seebeck effects require
junctions between the therrnoelements for their manifestation, they are essentially bulk
phenomena, i.e., they depend on bulk rather than surface properties of the materials.
Thus, when an electric current flows through a conductor it transports heat, which reveals
itself in the Peltier effect when it has to be liberated or absorbed as the current passes into
another conductor in which the heat transported is different. Thus, in the two branches,
the heat transported from the source to the sink is

dT

qp=SpIT—KpApE— (2'6)
dT
q”:_S"IT_K"A"71x_ (2.7)

in the two branches respectively, where S is the absolute Seebeck coefficient, 1 is the
current, K is the thermal conductivity, and dT/dx is the temperature gradient. The rate of
heat generation per unit length within each branch, due to the Joule effect, is I2 p / A,
where p is the electrical resistivity, which is the reciprocal of the electrical conductivity

0'. This heat generation implies that the temperature gradient is non-uniform, where

12

12
_K A (127‘ 2- pp (2.8)

 

2
_K A d2T -1 P» (2.9)

 

For the present purposes, it is assumed that the Seebeck coefficient is independent
of temperature, which means that the Thomson effect is absent. Setting the boundary
condition that T = T, at x = 0 (i.e., at the heat source) and also setting T = T2 at x = LP or

L, (i.e., at the heat sink), Equation (2.8,2.9) can be solved to find

 

 

 

 

-I2 x—L /2 x A T —T
KpAp£= pp( p )+ p p( 2 l) (2.10)
dx A, L,
2
— — /2 T —T
KnAnij—‘z I pn(x Ln )+KnAn( 2 I) (2.11)
dx A, L,

Equations (2.6, 2.7, 2.10, 2.11) can be combined to obtain the rate of heat flow, q,,

and q", at x = 0 and then, if qp and q,, are added at x = 0, the cooling power qc of the

heat source is obtained.

qc=(Sp—Sn)ITl—K(T2—Tl)—IZR/2 (2.12)

where the thermal conductance of the branches in parallel is

K A A
K: P P+Kn n (213)

L Ln

P

13

and the electrical resistance of the two branches in series is

R = LPpP + ann

A, A,

 

(2.14)

Equation (2.12) reveals the interesting result (often assumed without proof) that
half the Joule heating (12R / 2) arrives at the heat source while, presumably, the other half
tums up at the heat sink. (11)

When Equation (2.12) is inspected, it is seen that the Peltier cooling

term (Sp —Su )IT varies linearly with the electric current 1, whereas, the Joule heating

term varies as the square of the current. This means that there must be a particular current
1., at which the cooling power reaches its maximum value. This current is easily found by
setting dqc / dt = 0 which occurs when

(Sp -Sn)T1
I, = R (2.15)

 

and the maximum cooling power is then

(Sp —Sn)2T12
2R

 

(qc)max = -'K(T2 -T1) (2-16)

This equation reveals that a positive cooling effect cannot be achieved if the temperature
difference between the junctions is too great . The figure — of — merit of the thermocouple

is defined as

2
(Sp-Sn)
KR

z = (2.17)

Sometimes use can be made of the dimensionless figure—of—merit ZT instead of Z

and it becomes clear that, in seeking new thermoelectric materials, one should be looking

14

for values of ZT of the order of unity or greater. It is apparent that the figure—of—merit Z,
as defined by Equation (2.17), is a characteristic not of a pair of materials, but, rather, of
a particular couple, since it includes terms that involve the relative dimensions of the
thermoelements. For a given pair of materials, the highest value of Z is reached when the
product RK is minimized. Of course, R rises and K falls as the ratio of length to cross-
sectional area increases, and indeed, a thermocouple can be designed for a given cooling
power and electric current by altering the ratio in both arms. For maximum efficiency, the
Seebeck (and Peltier) coefficients are required to be large and have opposite signs in the
two materials. In addition, the thermal conductivity and electrical resistivity should be
low. In other words, the reversible thermoelectric effects should dominate over the
irreversible effects of heat conduction and Joule heating.

Actually, Equation (2.17) is rather cumbersome when attempting to find a good
thermoelectric material, be it p — type or n — type, since it involves the properties of both
thermoelements. It is for this reason that the figure—of—merit of a single material is

encountered, defined as

2

z — S“ (218)

pm _ '
pp,nKp,n

 

It is through the Thomson relations that the figure-of-merit can be written for each
material.
2.4 Factors affecting ZT

As observed, the figure—of—merit is proportional to the square of the Seebeck

coefficient S, to the electrical conductivity 0' and to the inverse of the thermal

conductivity K. It is important to note that these three parameters are not independent and

15

their values are determined by the details of their electronic structure, and by the
scattering and the number of charge carriers. Therefore, by modifying one property, one
can adversely affect the other in the wrong direction. Usually when increasing the
electrical conductivity the Seebeck coefficient decreases, and vice versa. Therefore, a
subtle equilibrium must be found in order to achieve optimization. The thermal
conductivity must be decreased, while increasing or keeping constant the two other
parameters. This can be achieved by doping, and/or by preparing solid solutions.
0 Electrical Conductivity o

A semiconductor normally exhibits thermally activated electrical conductivity that
increases with rising temperature. Metals have very high electrical conductivity, typically
above 2000 S/cm that decreases as the temperature increases. Instead, non-degenerate
semiconductors exhibit a conductivity that rises with temperature, but the magnitude is
much lower than for a metal, and typically in the range of 10's to 2000 S/cm depending
on the band gap. Insulators have conductivity typically less than 10'7 S/cm.
(a) Intrinsic Semiconductors

If a semiconductor does not have impurities, its energy diagram can be
represented as shown in Figure 2.5(a). As the temperature increases, electrons from the
valence band are excited to the conduction band where they can move freely. As they
leave the valence band, holes are created and left behind. Under the action of an electric
field, the holes move in the opposite direction of the electrons present in the conduction

band. This creates an electric conduction that can be written as ('2)

o = 60 exp[-Eg / 2kgT] (2.19)

16

where 0'0 is the limit of the conductivity at high temperature, E3 is the band gap, kg the
Boltzmann constant, and T the absolute temperature. It is important to note that for
industrial applications, extrinsic semiconductors are used because their conductivity can
be precisely controlled through doping. In practice, many semiconducting materials are

extrinsic since they are either naturally or intentionally doped.

 

 

 

 

 

 

 

 

Conduction
Impurity
Energy ‘I—
GantF... . . . . Level
Valence
Band

   

Figure 2.5 (a) Intrinsic and (b) Extrinsic Semiconductor

(b) Extrinsic Semiconductors
The values of the conductivity can be greatly increased by the addition of
small controlled amount of impurities in the pure semiconductor. The band diagram can
be represented as in Figure 2.5(b). Impurity levels have been created in the forbidden
energy gap by addition of these dopants. Two cases are then possible.
0 If the impurity added has one electron less than the element in the system that it
replaces, the later will provide the missing electron for the partial covalent bond
(Figure 2.6(a)) leaving a moving hole behind. We therefore obtain a p — type doped

material and the conductivity is equal to 0' = 0'0 exp[-Ep / ka] where 0'0 is the limit of

17

the conductivity at high temperature, and E, the energy level of the impurity added
relative to the edge of the valence band.

0 In the case where the element added has one electron in excess, this electron will
move freely in the crystal since it cannot be integrated in covalent bonding, see
(Figure 2.6(b)). The system is then said to be 11 — type, and o = 0'0 exp[-En / ka]
where E. is the energy level, relative to the conduction band, of the impurity having
one electron in excess.

The electrical conduction can also be expressed as a function of the mobility
which is a proportional coefficient between the average drift velocity vd of the charge
distribution and the applied field EX”)

0' = Nellfl + Peup V (2.20)

where N and P are respectively the number of electrons and holes moving in the system

expressed in number/cm3, and It“ and up the mobility of the negative and positive charge

carriers expressed in cm2 / V-sec.

0 Thermal Conductivity (K)

The value of the thermal conductivity of a compound plays a decisive role in its
possible use as a thermoelectric material. Because the value of ZT is inversely
proportional to the thermal conductivity, a low value of thermal conduction is
advantageous. The thermal conductivity of a material is mainly the sum of two
components: the lattice (phonons) component K], and the electronic component Kc.

x=a+m Q2n

18

In this equation, we have neglected the bipolar contribution that is due to the
simultaneous movement of electrons and related holes, only important in the intrinsic
region of the semiconductor.

For an intrinsic undoped semiconductor, the thermal conduction will be mainly due to
the lattice contribution. As electrons (or holes) are added to the system, the electronic
contribution rises since the electrons (or holes) act as carriers of heat. Nevertheless, they
also serve as scattering centers for the phonons that will diminish the mean free path of
the heat carriers, and as a consequence diminish the thermal conductivity. It is
understandable that predictions on the evolution of the thermal conductivity are therefore
challenging since the addition of a dopant has a double effect on K.

(a) Electronic Thermal Conductivity

This contribution, due to electrons (or holes) that carry heat in the system, is
insignificant at very low doping level but becomes more important as the number of
charge carriers increase. The electronic participation of the thermal conductivity is given
by the Wiedemann — Franz law as a fimction of the electrical conductivity, 0', the
absolute temperature, T, and the Lorenz factor, L0, in the approximation where only one

band contributes to the transport propertiesm)

k 2
x, =[i] LooT (2.22)
e

The Lorenz factor is dependent upon the scattering mechanisms that occur in the
system, and upon the level of doping. It has a wide range of variation: from a value of 2
in the case where an acoustic scattering mechanism is dominant, to a value of 4 for a

ionized impurity scattering mechanism.(1 1)

19

(b) Lattice Thermal Conductivity

In a crystal, atoms can vibrate around their positions and give rise to standing or
traveling vibrational waves through the lattice. These normal modes of vibrations have
characteristic frequencies. Phonons are defined as the quanta of excitation of these
normal modes of lattice vibrations. In the presence of a temperature gradient, the phonon
distribution deviate from the equilibrium and a flow of heat is generated.

The lattice thermal conductivity follows a T3 law at very low temperatures, and a T'1
law at temperatures higher than the Debye temperature. Umklapp three—phonon
scattering, and boundary scattering mechanismm) can explain these dependencies. A
three phonon interaction is created by the anharmonic nature of the crystal potential and
can be simply described in Figure 2.7(a), where two longitudinal phonons, represented by
wave vectors ql and qz interact to produce a third one (q3). In terms of conservation of
energy, this is described as: (1)3 = (01 + (02. The conservation of the momentum gives us
q] + q2 = q3 (normal process). In fact, the phonon momentum can be changed in some
cases and we have the new expression:

q1 + q2 = Q3 + G (2.23)
where G is the reciprocal lattice vector as shown in Figure 2.7(b).

If G = 0, the phonon momentum is conserved. The flow of phonons will continue
independently of the temperature. Since the mean free path stays unchanged, no thermal
resistance is created. In the case of G at O, the mean free path is altered and a thermal
resistance is created. This generates a maximum in the thermal conductivity at the

boundary between the T3 and the 1/1‘ dependence (see Figure 2.6).

20

Leibfried and Schlomann (1954)“5) derived the following equations that can
account for the behavior of the lattice thermal conductivity as a function of the

temperatue, if we assume that an Umklapp process takes place :

KI = K0f(@D /T) (2.24)
At high temperature, T > OD, f (90 / T) = OD / T (2.25)
T 3 9
While, when T < OD, f (OD / T) = [—] exp[—D] (2.26)
OD bT

To this effect, we must add the boundary scattering, at low temperatures, and the
exponential rise of the lattice thermal conductivity (in Eq. 2.26) is changed to a T3 law.
The prediction given by the UT law at high temperature (from Eq. 2.25) is in good
agreement with the experimental values if the volume and pressure are kept constants.
Using these equations, we can justify the T3 rise of the thermal conductivity by

considering Eq. 2.25 and the UT at higher temperature from the Eq. 2.26.

 

v ' ‘7' I v v ' vii ''''''''''''''
D Q ‘
_ 1

_Z‘ e ° Umklapp + Impurity ecetterlng':
.5 0 1H dependence :
s E - -
U l- e
c I
0 ° 0 -
2‘: . 0 Beundery scattering 1

. ‘
E o e T' dependence

. C
.2 F. e .e ‘
P b . . 1
. .

 

 

 

Temperature (K)

Figure 2.6. Thermal conductivity and the different scattering processes involved.

21

(c) Radiative losses
This important phenomenon is common to all materials. Phonons passing through a

material will give rise to thermal radiation. The contribution due to this effect was

formalized by Genzelfwl

Ky

<12 qz

<11

 

 

 

cl3

 

Figure 2.7. Three phonons interaction. (a) Normal process and (b) Umklapp process

Kphotons = [139}301121‘30'-‘ (227)

where 0'0 is the Stefan — Boltzmann constant, 11 is the refractive index of the material and
or the absorption coefficient. The radiative losses follow a T3 law as seen in Eq. 2.27.
Bhandari and Rowe pointed out that this contribution is appreciable for tellurium,
selenium and the lead chalcogenides. Therefore, we can expect to find this part in the
measurement of the materials presented in this dissertation.
During the analysis of the thermal conductivity data, the phonon contribution

needs to be subtracted since the value of Kphotons depends on the shape of the samples

22

measured and is not an intrinsic property of the material. In order to obtain K of a certain

sample without the photon contribution, the following methodology should be adopted:

1. The electronic contribution is calculated using the Wiedemann — Franz law and
subtracted from the experimentally measured thermal conductivity. Let us call the

remaining thermal conductivity contribution K’.

N

. At high temperature, typically greater than 150 K, a 1/T fit is applied to the appropriate
part of the K’ plot. The difference between the fit and K’ gives the radiative
contribution Kphomns.

3. K1 is then obtained by keeping the values of K’ at low temperature and by using the
value given by the fit at higher temperature.

4. The total thermal conductivity without the contribution from radiative losses is then
obtained by adding the lattice and the electronic contribution.

5. In order to verify that the rise in the original plot of the thermal conductivity at high

temperature is due to radiative losses, Kphomns is plotted against T3 .

(d) Seebeck Coefficient (S )

When new compound is synthesized, one of the first properties measured is the
Seebeck coefficient since it is squared in the equation for ZT. It is a relatively simple
measurement that can be done on semiconductors and it gives also other valuable
information about the material such as its class (metal, insulator, semiconductor), its

doping state (n-type, p-type), and sometimes its energy gap.

23

The plot of Figure 2.8 shows the behavior of S for different types of materials as a
function of temperature. For a metal, S decreases as the temperature decreases in

accordance with the relation between S and T:

S z [£1231] (2.28)
eEF
where e is the charge of the carrier and BF the Fermi level. The value of kB/e being
approximately 87 ItV/K. This equation shows that S must be much smaller than 87 uV/K,
since for a metal the transport takes place within kgT of the Fermi level. On the contrary,
for a semiconductor, the absolute value of S increases as the temperature decreases based

on Eq. 2.29. In the case where only one type of carrier is present, a value greater than 87

uV/K is expected.

.. ‘2‘ .. a. _E_.
S~ eT ~( e 1(2kBT)] (229)

Finally, among other possible behaviors, some narrow band gap semiconductors
can exhibit a combination of metallic and semiconductor behavior. The thermopower in
this case may be reminiscent of either a metal or a semiconductor, or may even be nearly
temperature independent depending on the size of the gap and the degree of doping.

When measuring the Seebeck coefficient, a temperature gradient is applied to a
material, establishing cold (Tc) and hot (Th) sides. The electrons move from (Th) to (Tc)
because electrons at (Th) have higher kinetic energy than those on the cold side. In an

open circuit configuration, the flow of carriers from (Th) to (Tc) creates a charge build-up

24

at (Tc), and an electric field is established from (Tc) to (Th) in order to avoid more
charging at (Tc). Thus, a voltage difference, AV, is measurable between (Th) and (Tc). If
the material is n — doped, the measured voltage is negative at (Tc) relative to (Th) for
which S is defined as negative. In the case of a p — type compound, a similar flow is
generated with holes moving from (Th) to (Tc) and (Tc) will be positive relative to (Th),
and the sign of S is positive. Seebeck measurement is an effective, fast and easy method
to determine the type of majority carriers.

Ofien, because of the existence of two different regions (extrinsic and intrinsic), S
does not vary linearly. As the temperature rises, extrinsic carriers are excited from
impurity states. This allows the gap between the Fermi level and the appropriate band to
increase, which enhances the absolute value of the Seebeck coefficient. As soon as the
temperature is large enough, carriers coming from impurities reach a saturation level and
electron — hole pairs across the band gap are excited (intrinsic region). This creates
opposite carriers and therefore S decreases, due to the fact that S is the sum of the
contribution due to the electrons and the contribution due to the holes.

_ oes, +o,,S,,
0, +6,

S

 

(2.30)

If we plot S as function of temperature (See Figure 2.9) the Seebeck coefficient
passes through a maximum. The energy gap can then be estimated based on Eq. 2.3 107)
Eg ~ 2eSmameax (2.31)
For wide band gap materials, Tmax is greater than 150 °C, which is beyond our systems
measurement capability, and therefore, this method of calculating Eg only works for

narrow gap semiconductors.

25

 

0 Charge Carrier Concentration

The carrier concentration is defined as the number of charge carriers of a certain type
per unit volume. This concentration shows different properties for different materials. For
metals, n is independent of the temperature which explains the decrease of the
conductivity that follows the behavior of the mobility due to the increase in the scattering
probability. For semiconductors, n is a function of the temperature and increases
exponentially as T increases. A typical plot of the carrier concentration as a function of
temperature is shown in Fig 2.10. Three distinct regions are present. At low temperature
(high Tl), only few carriers are excited to the conduction bands. As the temperature
increases thermal excitation allows more transitions until a saturation plateau is reached
(called exhaustion). When the temperature is increased further, the intrinsic carriers are

excited and we observe a large increase of n.

 

 

 

     
  
      

AA
A
AAAAA
a
AA
A AA I
AAA 1
AAA ‘
eOe AAA -
.e e. .
e 0 . 1
e" .."O :
e 1
e. 000° 1
0. 00°000° :
o oo .
oO°°°

 

Seebeck Coeffrcrent ( uV/K )
a 8 8 8 8 8 8 8 8

0100200300400500600700800
Terrperature(K)

Figure 2.8. Seebeck Coefficient behavior for different types of materials

26

 

VI'V'IVVV'IVV'IIVIVUVIV'vrTi"

200 '-

>
..;
i
II

350, Smx= 165 )

r
- IIALLJLAJAJAAA

150

"V'I'VVIVU fl
‘1...

S(p.V/K)

V
O

100 _-

AILJALA

b

t 0

- O

D I
AAl‘AAl-AAJA-llAJAllA-ljllI AA

50 ‘ ‘
260 280 300 320 340 360 380 400 420
Temperature ( K)

 

 

 

Figure 2.9. Seebeck measurement showing a maximum at the point A

It is important to try to obtain a large temperature range for the exhaustion part, making

the device performance stable over large temperature range.

 

 

 

Log n _ _
Intrrnsrc
Slope = -€, / 2k
Saturation
Slope = -€/k
\ or -e/2k
1 / T

Figure 2.10. Carrier Concentration for a semiconductor as a function of
temperature

27

 

The figure — of — merit is a function of the Fermi energy. The Fermi energy is in
turn a function of the carrier concentration, carrier effective mass and the temperature.
Nevertheless, the thermal conductivity depends little on n, at least until a certain level.
The Seebeck coefficient is a function of 1/ 1n (11). Therefore, it is the conductivity and
Seebeck coefficient that can be optimized by controlling the carrier concentration
introduced as impurities.

It has been demonstrated that for an intrinsic semiconductor the product NP is a
constant (N and P being the concentration of electrons and holes respectively). Therefore
when introducing one type of carrier in the system, the concentration of the other type is

adjusted to keep the product constant.

3 E
NP = {21:11:}: ] {mcmh’w2 exru[k 2]] (2.32)
B

For extrinsic semiconductors, optimization of the transport properties is reached

 

 

for a certain number of charge carriers; if more charge carriers are added, the properties
of the material deteriorate. For small band gap semiconductors, 11 should be in the range
of 1018 to 1020 cm'3. If the carrier concentration is too high then the electronic part of the

thermal conductivity would increase considerably which is undesirable.

2.5 Optimization of ZT

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”). Since the thermal conductivity depends only weakly on the

carrier concentration (11) the general effect of an increase in carrier concentration would

28

 

manifest itself in the figure—of—merit, through the power factor S26. Consider a single
band (either an electron or hole band) with the usual parabolic density—of—states
distribution and assume that the carriers obey classical statistics. The Seebeck coefficient

can then be expressed as
- k3
S=+—(5/2+s—E) (2.33)
e

The sign i refers to the contributions from holes and electrons, respectively and E, = ( Ef/
kgT ) is the reduced Fermi energy, k3 is the Boltzmann’s constant, T the absolute
temperature, and 3 refers to the scattering parameter. It is assumed that the carrier
relaxation time can be expressed in terms of the carrier energy in a simple way, i.e., t is
proportional to Es.

The electrical conductivity is given by

0' = new (2.34)

where 11c is the carrier mobility in the low carrier concentration limit . The carrier

concentration is related to the reduced Fermi energy by the equation

n = 2(2zzm‘k,T/h2)3’2 exp;
(2.35)

The thermal conductivity is written as the sum of lattice and electronic components i.e.,

K = KL + Kc
(2.36)

Evidently E affects the thermal conductivity only through the electronic contribution Kg.

29

In addition,

1:, = L0(kB /e)2oT (2.37)

Where the dimensionless quantity L0 is referred to as the Lorenz factor. In the limit of

low carrier concentration it can be shown that “3)

L0 = (5 / 2 + s)
(2.38)
When the following parameters are introduced:
F = EL(’—"—)3’2, G = (21rmk,,T/h2)3’2 (2.39)
K L m

The thermoelectric figure — of — merit can, after some rearrangement, be expressed as
k 2
z = (5/2 + s —r:)2 /[{2-LFGexp§}" + (5/2+ rm
e
(2.40)

0 Optimum Fermi Level

The figure — of — merit varies with the Fermi level and the optimum value of E which

maximizes Z is obtained by setting dZ/dfi = 0. This givesm)

2

50p, +4(5/2+s)iFGTexp§0p, = %+ s
e (2.41)
f... = -‘— + s
2 (2.42)
In general, the lattice contribution to the thermal conductivity is large. Neglecting the
second term in the above equation, which amounts to neglecting Kc, gives:

When the electron scattering is by acoustic phonons and ionized impurities the

scattering parameter s takes the values of —1/2 and 3/2, respectively, with corresponding

30

5,0,” values of 0 and 2. Including the electronic thermal conductivity will amount to a
reduction in fiopt. Obviously, the thermoelectric material has to be doped heavily to obtain
Fermi levels well within the bands.

0 Optimum Seebeck Coefficient

Setting dZ/da = 0 gives,

opt

= fl[1+(xe /K,)] = —172[1+(K, /K’,)]flV /K
e (2.43)

The results predicted by this model are not unrealistic. A more rigorous
theoretical model can be formulated which takes into account several important features

that characterize a thermoelectric semiconductorm’)

, viz., the presence of several
equivalent valleys in the conducting band, with or without intervalley electron scattering,
minority carrier effects, and possible deviations from the parabolic E — k relationship.
The use of classical statistics in describing the behavior of the carriers is justified
only in the limit of low carrier concentration. As the thermoelectric material is heavily
doped, Fermi—Dirac statistics must be employed. The expressions for the Seebeck

coefficient and the Lorenz factor then take the form”)

S = ifi-(S- 8) (2.44)
e

where

5 = (S+5/2)F3+3/2(6)
(3+3/2)Fr+1/2(§)

 

(2.45)

= (S+ 7/2)F..572(€) _52 (2.46)
o (3+3/2)Fr+1/2(§)

Fr(§) are the Fermi integrals.The electrical conductivity is given by 0' = 0’08, where

 

o, = 2(2rrm‘k3 T/hz )3” euc (2.47)

31

and e = F,,,,,(§)/(s + 1 / 2) (2.48)

These equations enable the dimensionless thermoelectric figure—of—merit to be expressed

33,

27 = (ti-g)2 /[L0 + {-E-HkB /e)2 )"1 (2.49)
L

It is convenient to work with the dimensionless quantity, 0", referred to as the reduced
electrical conductivity, where

o" = (0' / mm, /e)2 (2.50)

The dimensionless figure — of — merit is then given byus)

 

_ 2
ZT = M (2.51)

La +1/a

In addition
0' = 13F..u2(§)/(S +1/ 2)! (252)
3/2 2
with ,6 = 20"“), k8 A' (2.53)
eh

A’ = T5’2m’3’2p/KL (2.54)

The dependence of the Fermi level on carrier concentration is now given by

n =-4;(2m‘k.T/h2>”2 Fore) (2.55)

J—

The parameters A' and B are referred to as the material parameters, since for a
given scattering mechanism and Fermi level, the figure—of—merit depends on the physical

properties of the material only through these parameters.

32

o Minimizing the Thermal Conductivity

Good Thermoelectric materials require a low thermal conductivity to prevent a
significant portion of the heat from flowing down the temperature gradient. Most of the
thermal conductivity studies that relate to thermoelectric materials have dealt primarily
with the question of reducing the thermal conductivity without resulting in an adverse
effect on the electrical power factor. However, there are considerable problems in
achieving this objective. As the thermoelectric semiconductors are heavily doped, a
significant contribution to thermal conductivity arises from the electrons (or holes). Thus,
the fact that a significant Kg is invariably present needs to be taken in any thermal
conductivity minimization program.
0 Alloy Disorder

A reduction in lattice thermal conductivity can be achieved in several ways. Any
mechanism that scatters phonons more effectively than electrons (or holes) is likely to
enhance the electrical to thermal conductivity ratio. Among the important scattering
mechanisms that tend to reduce the phonon mean free path are scattering by other
phonons, lattice defects, electrons and holes, and grain boundaries. One of the most
thoroughly understood mechanisms related to defect scattering is based upon mass—
difference scattering. Reduction of the phonon mean free path in solid solutions is
analyzed in terms of mass—difference scattering with an associated phonon relaxation

time.
1;}, = Fw2g(a))/6N (2.58)

where I‘ is a measure of the strength of the scattering, and is given by

33

Mi 2
Rial—7) (2.59)

f,- is the fractional concentration of the impurity of mass, M), and M— is the mean atomic
mass. For the Debye model g((t)) cc (02 and the Rayleigh expression is obtained
1;; = £20m“ Muir: (2.60)

(20 = V/ N is the average atomic volume, v,- is the average sound velocity, and 0) refers to
the phonon fiequency. This method of reducing KL is useful in alloys where the atomic
masses of the components differ considerably.
o Scattering by Charge Carriers

Heavy doping of the thermoelectric material necessitates a detailed investigation
of the role of carriers as (1) agents aiding the flow of heat down the temperature gradient,
and (2) scattering centers for the phonons, thereby opposing the flow of heat. For some
doping levels the two contributions can be comparable. Ziman investigated the scattering

of phonons by carriers and obtained the relaxation time”),

 

_1 _ ezmakBT z—ln 1+exp(t|r+z/2)

_ 2.61
pa 21:714va l+exp(\|I-z/2)]} ( )

where z = hw/kT and

v = hzmz /8m'v,§k,r + m‘vfikBT — E, /kBT (2.62)

Here 8 is the strength of the electron — phonon interaction and Er is the F errni energy.
The velocity, vL, refers to the average phonon velocity and the various other parameters

have their usual meanings.

34

o Scattering by Grain Boundaries

Crystal dimensions may limit the phonon mean free path. A mean free path (lb)
can be defined which is related to the crystal size; Ib = 1.12 D,“” for a specimen with
square cross - section of side D. Earlier accounts of boundary scattering portrayed it as a
low—temperature phenomenon. However, in highly disordered materials, boundary
scattering may become significant at high temperatures. A high degree of disorder
effectively scatters short—wavelength phonons with the net heat conduction being
primarily due to long—wavelength phonons. These may then be scattered effectively by

grain boundaries and result in significant reduction in thermal conductivity.

2.6 Current Exploratory Materials Research

The subject of thermoelectric materials is now a growing and active field

primarily due to several new concepts and also because of a recognized need.(2°)’(2”

Although there are many different avenues taken by different groups around the world,

(22)

here we discuss our approach to new thermoelectric materials, exploring complex

chalcogenide materials using newly developed solid state synthetic techniques for these
systemsm)

An efficient thermoelectric device is fabricated from two materials, one n — type
and the other a p — type conductor. Each material is separately chosen to optimize the
figure — of - merit ZT, where Z = (120' / K; T is the temperature, or the thermopower, o
the electrical conductivity, and K the thermal conductivity. All three of these properties
are determined by the details of the electronic structure and scattering of charge carriers

(11)

(as described earlier) and thus are not independently controllable parameters. K has a

35

contribution from K1, the phonon thermal conductivity as well as the carrier thermal
conductivity, Kc. In order to carry a heat flux of reasonable magnitude, moderate to high
carrier densities are needed (small band semiconductors with carrier densities of 10'8 -
1019 / cm3 to metals at 1023 / cm3). When the carrier densities approach 1023 / cm3, Ke is
usually much greater than iq. Because cancellations in thermoelectric power can occur
when both electrons and holes are dominant one needs materials with preferably one type
of carrier. The material used in commercial devices today is Bi2.,,Sb,‘Te3.ySey alloy
(thermopower of i 220 ltV/K) and it’s ZT value at room temperature is ~ 0.9—1.0.
Improving device performance means improving ZT or increasing S while keeping
moderate to large carrier densities of one carrier type.

We seek to identify new materials with higher degree of merit than those
available today. Boltzmann transport theory provides a general understanding of the

thermopower that is expressed in the Mott equation:

n2 k,2r amour)
s =— | _
3 e (11? 5‘51

 

(2.63)

o(E) is the electrical conductivity determined by a function of band filling or Fermi
energy , Ep. If the electron scattering is independent of energy, then 0(E) is just
proportional to the density of states at E. In the general case, S is a measure of the
difference in o(E) above and below the Fermi surface, specifically through the
logarithmic derivative of o with E. Since the thermopower of a material is a measure of
the asymmetry in electronic structure and scattering rates near the Fermi level, we desire

to produce complexities in either or both in a small energy interval (a few kgT) near Ep.

36

Structural and compositional complexity can result in corresponding complexities
in the electronic structure, which may produce the required asymmetry in C(13) to obtain
large therrnopowers. The phonon contribution to the thermal conductivity can also be
lowered by such structural complexity, by choosing heavy elements as components of the
material and by choosing combinations of elements that normally make moderate to weak
chemical bonds.

A significant development is the emergence of materials that conduct electricity

like a crystalline solid but conduct heat like a glass.

Crystalline Semiconductor Lattice

 

Rattling Ions

Figure 2.11 Schematic Representation of the PGEC concept

tal”(24)’ (25) and often

Such a material has been coined a “phonon glass electron crys
features cages (or tunnels) in it’s crystal structure inside which reside atoms small enough

to “rattle”, as shown in the schematic Figure 2.11.

37

As observed in the figure, the crystalline semiconducting framework of the
material has cages, or tunnels in which electropositive or neutral atoms, with weak bonds
to the framework, reside. The weak interactions give rise to soft phonon modes due to
“rattling” type motions, which scatter the thermal phonons travelling through the
material. This situation produces a phonon damping effect that results in dramatic
reduction of the solid ’s lattice thermal conductivity. If the atomic orbitals of the rattling
ions do not participate in the electronic structure near the Fermi level, the mobility of
carriers throughout the rest of the structure may not be substantially affected, potentially
giving rise to high electrical conductivity as well as thermopower. The classes of
chalcogenide materials characterized in this project fall under this description.

We know that heavy atoms are desirable since they tend to give rise to low
frequency phonons, which help slow down heat transfer through a material leading to low
thermal conductivity. The fact that BizTe3 is the best material known to date suggests that
it combine many of the necessary features for high figure -of—merit. Thus, one of
research directions that we could explore, would be, more complex chalcogenides of

bismuth. These complex chalcogenidesm)

would, most likely, have a low lattice thermal
conductivity. This is because a structure with a large unit cell is expected for such
materials, which would decrease the acoustic phonon mode velocities that are responsible

for the transfer of heat in materials.

38

Chapter 3
3.1 Measurement of Thermal Conductivity

Thermal conductivity measurements can be carried out using a variety of
techniques including the steady state technique, the 3m technique“), the Harman
technique“) and the pulse technique”). There are similarities between the measurement of
thermal conductivity and the electrical conductivity measurement. In the electrical
conductivity measurement, a pre-determined amount of current is confined to flow
through the sample while the resulting voltage developed across the sample is measured.
For thermal conductivity, a pre-determined amount of heat flow is confined to flow
through the sample while the resulting temperature gradient established across the sample
is measured. Both measurements usually use a four-probe configuration to alleviate errors
caused by contact resistances. In determining the electrical conductivity of a
semiconductor one can usually assume that the electric current passes only through the
specimen or sample. Especially, for low frequency measurements, it is relatively easy to
confine the current to flow through the sample by using high electrical conductivity leads
coated with very low electrical conductivity materials such as varnish. However, in a
thermal conductivity measurement there is always a possibility of heat transfer through
the surrounding medium. If this medium is air, heat may be passed by conduction,
convection, and radiation; even if the sample is held in a high vacuum, heat may still be
transferred by radiation. At pressures below 10" Torr, the heat transfer per unit area due

to convection between two parallel surfaces held at temperatures To and T1 is

 

- bor+l
ans —_—_1\[:;Epm(ln-TO) (3-1)

39

where a = Cp / CV, R8 is the gas constant (8.31 J .K'l.mole"), P is pressure in Torr, M... is
the molecular weight of the gas, and b is an accomodation coefficient related to the two
surfaces. For dirty surfaces, b approaches a maximum value of l.

The various wires used for making thermal and electrical connections to the
sample act as thermal conduction paths diverting heat from flowing through the sample at

a rate

9.... = 8% AT (32)

where Kis the thermal conductivity in (W/cm-K) of the wire, A is the cross-sectional area

of the wire in cmz, L is the length of the wire in cm and AT is the temperature gradient
across the wire.
Radiative losses follow a T 4 dependence such that per unit surface area heat

transfer is given as
Qar =9—e (Ti-r?) (3.3)
2 — e

where e is the emissivity of the sample and the surrounding shield which are assumed
equal, g is the Stefan-Boltzmann constant (5.67 x 10'8 W.m'2.K"’), T0 is the temperature
of the surroundings of the sample, and Ts is the temperature of the sample. The
combination of these losses increases the difficulty of this measurement. In order to make
the lateral heat losses relatively small, it is best to use a short sample with a large cross-
sectional area.

It seems worthwhile to summarize the various methods of thermal conductivity
measurement and discuss their advantages and disadvantages. The first choice lies

between the static and dynamic methods. In the former it is only after equilibrium has

40

been reached that measurements are made. This condition assists in the achievement of a
high degree of accuracy but, particularly for poor thermal conductors, the attainment of
equilibrium can be a lengthy process. Thus, the total time involved in measurements on a
sample at several different temperatures may be very great. In contrast, by using a
dynamic method in which the thermal gradients are observed as a function of time, a
wide range of temperature may be covered more rapidly and in rather more detail than is
possible with a static method.

Several contemporary static/dynamic methods have been discussed and evaluated
in the following section.

3.1.1 Steady State Technique

 

 

 

 

28:? r.
T1
“A” Sample
T2

 

Heat source
T3

 

 

 

Figure 3.1 Schematic Arrangement for the Steady State Technique.

For this measurement, the sample, with cross-sectional area A, is connected to a stage

at a reference temperature To. At the other end of the sample, a heater is attached as

41

shown in Figure 2.1 and raised to the temperature T3. The thermal conductivity of the

sample is

 

Q L
K:— 3.4
40.4.) ‘ ’

Where Q is the heat flow through the sample, L is the distance between temperature

sensors at T2 and T1. Assuming all leakage paths are negligible Q is the power supplied

to the heater. This configuration has been used for high accuracy measurements by
including a radiation shield surrounding the sample and establishing the same
temperature profile along the shield as exists along the sample. This helps to minimize
the radiative losses by making To z T,. With this technique, the time for each data point
can take from 2 to 6 hours which is mostly spent waiting for temperature stabilization.

Generally samples 1-2 mm in diameter by 1-2 cm in length or larger are measured.

3.1.2 30) Technique

A novel and interesting technique developed originally for glasses and other
amorphous solids“) has been extended to the measurement of thermal properties of thin
films and bulk materials. This is similar to the hot wire techniques in that a single
element is used both as a heater and a thermometer. The difference is that the

measurements are made in the frequency rather than the time domain.

42

 

 

 

Nichrome
I Layer used as
heater/thermo-
I meter

 

SAMPLE

 

 

 

Figure 3.2. Schematic arrangement in 3(1) Technique

A thin layer of Nichrome / insulator is first deposited on the sample to a thickness
of about 100 A followed by 5000 A of silver. The width of the metal film is made small

with respect to the wavelength of the diffusive thermal wave either by photolithography
or with a shadow mask during deposition. This leads to a cylindrical thermal diffusive

wave with an amplitude, AT, equal to

w
AT = EEC-K00”) (3.5)

Where W is the power generated by the metal film, L is the length of the film, K is the

thermal conductivity of the sample, K0 is the zeroth-order modified Bessel function, r is

the radial distance from the line source of heat, and 10.). is the thermal penetration depth

during one cycle of the ac power heating. For llhrl << 1, this can be approximated as

43

AT:l llrr-I-)—+1uz—0.5772-llnto—fl (3.6)
me 2 r2 2 4

Since the power is proportional to the current squared, this ac heating is at twice the
frequency of the current source. For small temperature variations, the temperature
dependence of the resistance of the metal film, dR/dT gives rise to a third harmonic
voltage equal to

dR
V =I— T+AT/2 3.7
3 dT( ) ( )

Measuring this third harmonic voltage at two different frequencies, f1 and f2, yields a

thermal conductivity

V3ln-fl
fr dR

K = 47‘LR2(V3,1 we)?

 

(3.8)

where R is the average resistance of the metal line, V is the voltage across the line at the
fundamental fi'equency, 00,V3,1 is the voltage at the third harmonic for frequency
f 1, and V3,; is the voltage at the third harmonic for frequency f 2.

In the 30) technique, only the surface within the thermal penetration depth from
the heater — thermometer is involved in the radiation error. Small sample geometry is
another advantage of this technique. The size of the sample need only be large enough to
accommodate the metal line and electrical contact pads. To avoid reflections, the
thickness of the sample should be greater than five times the width of the metal line.
Also, this technique provides very rapid data collection. Several temperature cycles of the
metal line are sufficient, requiring only seconds per data point.

However, depositing and patterning the metal heater — thermometer, especially for

small thermal penetration depths could be difficult for small samples. Also, for higher

44

electrical conductivity samples, some of the current expected to pass through the metal
line could be shunted through the sample.
3.1.3 Harman’s Technique

In Harman’s method a temperature gradient along the sample is established by
means of the Peltier effect. When an electric current is passed through the sample, held
between metallic contacts, there is heating at one end and cooling at the other. If the
current is small enough, the Joule heating effect may be neglected.

In a practical apparatus as shown in Figure 3.3, copper leads and chromel -
alumel thermocouples are soldered to the ends of the sample under measurement. A pair
of alumel probes are also attached (e.g. by spot welding) to the surface of the sample.
Two measurements are required in this technique. An ac measurement to determine
sample resistivity and contact resistance is done first, followed by a dc measurement
which makes use of the Peltier effect.

The resistivity of the sample is measured using V) as

P’Yim2
I L'

 

(3.9)

where r is the radius of cross-section of the sample. Then, using the resistivity of the
sample along with the full-length dimension, L, and either V2 or V3, the contact
resistance can be measured.

The contact resistance is

R.= $713, (3.10)

45

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l V 2
F L >1
\
9 Sample i j
/\
<— L' —>
4 3
—. V] .___
5 6
. V2 C
e V3 %

 

 

7 8
1, 2 — Copper current leads
3,4 - Alumel leads

5,6 — Chromel leads of thermocouples
7,8 — Alumel leads of thermocouples

Figure 3.3. Schematic Arrangement for Harman’s Method
Where V; = V3 = Vp + Vc,and Vp = voltage across the entire sample due to the resistivity
of the sample, and Vc = voltage due to contact resistance at the ends of the sample. This is
followed by a dc measurement. At each end of the sample there is a junction
between the copper leads and the sample. Therefore, with dc current flowing through the
junctions, the Peltier effect will cause heat to be absorbed at one end while it is generated
at the other, and a temperature gradient is established across the sample. This gradient
will continue to increase until the thermal conduction through the sample balances with

the heat generation and absorption at the junctions.

46

v; = Vp+ Vc + (Sch,- 5,) AT+ V,” (3.11)

Vz' = -V,, - VC - (563,- S3) AT + V,” (3.12)
where V; corresponds to a positive supple voltage (V), and V2' is for a negative supply
voltage. The quantity (Sch, - S3) AT is the Seebeck voltage generated by the temperature
gradient AT, and Vi” is an irreversible offset voltage caused, in part, by unequal Joule
heating at the junctions. Similarly,

V} = Vp+ VC+ (Sam-S.) AT+ V... (3.13)

V3' = -Vp - Vc- (Salu’ s) AT+ Virr (3-14)
where the therm0power of the alumel leads has replaced that for the chromel leads used

in equations (3.11) and (3.12). Then the temperature gradient is

 

AT=(Vz+-Vz')- (Vg-Vgl (3.15)
2(Schr'salu)

Values of (Sch, - Salu) versus temperature can be found in the literature, and the
thermopower of the sample is

S,=1/AT[V2'-V2+/2 +Vp+ Vc]+Sch, (3.16)
At this point, the resistivity and thermopower of the sample has been determined. As
previously mentioned, the Peltier heating and cooling at the two junctions must balance
with the thermal conduction through the sample in steady state. If it is assumed that the
thermal conductance of the lead wires, the thermopower of the current leads, and the

radiative heat transfer are small, then

K: -' (3.17)

 

47

The figure — of — merit can be obtained directly from this measurement as

= S3AT

VPT

Z

 

(3.18)This is a

powerful technique since all three parameters are simultaneouly measured. One difficulty
is the number of wires that must be attached to the sample, eight in all. For small
samples, this can be very difficult.

3.1.4 Angstrom’s Technique
T2

Sample T‘

 

Copper Bar

Figure 3.4. Schematic Arrangement for Angstrom’s Method

Originally developed in 1861‘”, this technique is based on the fact that if a heat
source, whose temperature varies sinusoidally with time, is located at one end (x = 0) of a
semi-infinite radiating rod these temperature oscillations will propagate along the rod

with a velocity V = (0/ )6 where a) is the angular frequency and ,B the phase shift per unit

length.

48

A sinusoidal current is sourced through the heater wrapped on the copper bar. This
causes a sine shaped heat wave to travel through the sample, reflecting off the upper end.
The heater current is adjusted so the reflected heat wave decays practically to zero
amplitude before reaching the T1 thermocouple. The thermocouple voltages are

V1 =A cos(at) + C) (3.19)
V2 = Bcos(at -,B) + C2 (3.20)
for T1 and T2 respectively, where A and B are the relative amplitudes of the heat wave at
the ends of the sample, (0 is the frequency of the heat wave, [3 is the phase difference
between the ends of the sample. C, and C2 are temperature variables. The thermal
diffusivity can be measured as

2 2
(01 (01 (3.21)

21n2[2—A) Zflz
B

Thus calculations from the amplitude ratio A/B and from the phase difference [3

should independently agree. The thermal conductivity is then calculated as
K = D.C,,. 6 (3.22)

The major disadvantage of this technique is the need for multiple measurements on a
single sample to obtain the thermal conductivity. One measurement is required to
determine the density, 6, of the material, while another determines the specific heat, CI)
The thermal diffusivity is then measured as described in the figure and the thermal
conductivity calculated from these three measured values. The advantage of this
technique is that each of these measurements can be obtained with relatively high

accuracy and without long wait times for temperature stabilization.

49

. Maldonado’s Pulse Technique“)

A method similar to the steady state technique is the pulse technique. Here the heater is
pulsed while the temperature gradient across the sample is monitored. This arrangement
can also be used as a steady state technique by turning on the heater and waiting for
temperature stabilization. With a sample of thermal conductance K between the heat

source at T1(t) and the copper stage at To(t), the amount of heat per unit time at the heater,
Q is
Q = C(T.)T'. = R(T.)12(t>— K0. —T.> (3.23)
where C(T1) and MD) are the heat capacity and resistance of the heater respectively, and
I( t) is the current through the heater. Varying this current as a square wave of period of
period 2 rsuch that
I(t) = 0 if tmod2r < r (3.24)
= 10 iftmoer >= 1'
yields a non steady — state condition. With a small temperature gradient, AT, the
following assumptions are made
C(T1)~ C(To) = C (3.25)
R (T1) ~ R(To) = R
K(T1)~ K(To) = K
Then equation (3.23) can be linearized by the adiabatic approximation that the

temperature of the copper stage, To, is nearly constant. This gives

n—To 7120—30: —T.)-To (3.26)

50

 

where T0 was subtracted from both sides. This is a linear first order differential equation

that can be written as

W) 5 -
dz +CAT g(t) (3.27)
R 2 ‘
where g(t)=EI (t)—To(t)

If g(t) = 0 , then equation (3.27) becomes

M = _£ AT (3.28)
dt C
or _d_(A_n = -Edt
dt C
Integrating both sides gives
ln(AT) = —I-I:dt+cl (3.29)
C

where c, is an integration constant. Taking the exponential of both sides yields

iMC, _K

AT = e C = Ar7 (3.30)

Using this with equation (3.28), the following can be written

dI Me?" I K K
=e?'[i(—AQ+£ATI=eFf(r) (3.31)

dr dt C

K K 5, .
Thus ATeC =Iec g12(t)dt—Iec To(t)dt+cz (3.32)

Where C2 is an integration constant. Evaluating this at an ordinary time, t = t, gives

51

 

—K

" liq—r 1' . —Kr,—r
AT(tl)=C2eC '+%_II’(t)eC( )dt—IYMtyC )dt (3.33)
o 0

Assuming To varies slowly with time, the last term can be approximated by

1 :—K1

ITO (t)e C dt ~£[To (tl)— T0(0)eC I (3.34)

0 K

The integral containing the 12(t) term can be solved by inserting (3.24) for the current.
Then the integral becomes

1' r Zr

—K -K
—(-) —(~) K(-)
5 120).»6"r dt=5 0.eC"' dt+ R Ioze 6'” dt
C C C
0 0

I

(3.35)

31 41 t,

-K -K
—(.- —(.—) —(. )
+R O.eC I dt+£ 102eC ' t dt+£ I2 (t1)eC t t dt
+C C C

21 31 t
[*3]
Where I:-t'—:I is the integer value of t) divided by T, and I( t) ) is the value of I at t = t, which
1'

is zero or [20 for t1m0d2r < r and (1m0d2‘l' > = 1 respectively. For the first case, equation

(3.35) becomes

Rtl "Kt )
—il—f
— IzteC dt=
.l (1
0

-K —K —K -K
—(r, —21) —E—(r, -r) —6—(r, ~41) ?(tl —3t)
C — e + e - e

(3.36)
R

C’“ ‘C’ Kari.) AH)

52

. ’—<r mode . . . . . .
Pullmg out e C ' on the right srde of this equation leaves the integer portion of t1

times t in each exponent. Therefore (3.35) becomes
R " ‘—K(r.—t)

—I12(t)e C dt=

C 0

-aHe~ err» errm errm
R _.—C]£(tlmod1) e T _e T +8 T —e T +....

(3.37)

Where the second of the last term can be reduced to 1. Simplifying gives

—(’1 0d

—I1 (t)eC =

_ —Kr — r —Kr
R .e.. —flv —-i —il —t4> _.
—Io2eCl eCT —C’ +e —eCT +.. +1 eC
(3.38)

Because of the alternating addition and subtraction of exponential quantities, a

cancellation of all but two of these terms can be obtained by multiplying the numerator

—K
and denominator by 1+ e C , which gives

 

Rt] 2 :EKUITT) — 2 -: ..—
C II (t)e dt—k—Ioe i.

(3.39)

53

If t1m0d2‘t >= 1:, the final term in (3.36) would change to

-C—(de)

—I12(Jec

—(r.-2rJ 365mm“? e—(r.—4r) 1550.41)
102 C eC —e —e +....

'6“ K JJJJJ- JJJJJ

(3.40)
Giving (3.41)
gtIfiayj'” dt=
_, W— m... :5 s—J -—JJ MJJJ _—«—;-mJJ }

—K
Multiplying the numerator and denominator by l + e C gives

’ .. 1J2]
—:Ilz(t)ec(t_t)dt=02§12J1—e%(tlmm) EFT—J J
1+e—C—r I

 

 

(3.42)

54

Using equations (3.39), (3.42), and (3.34) in (3.33) gives

Am) = AT(0)e(_%) — %[TO (I) - To (0)e[%} I

V r

e
2

 

l-e

 

 

-K i [m]
_ .. . _( J
{c} °" 1__e_c__
1+4?)r >
[%}"‘°“‘ 1+e[%}[ml

1+e[%}

where [t / 1:] is the integer part of t / 1:.

 

J

If tmod21< 1'

IftmodZTZ 2'

(3.43)

 

Since the maxima occur at t = m for even integer values of n and the minima for odd

integer values of n, the peak to peak amplitude of the temperature gradient can be found

by subtracting a curve through the minima from a curve through the maxima. At the

maximums and minimums, t

 

 

= nt, (t mod 1') = O, and zit/2'] = t giving

RIo l—e C 1+e C
AT W = :5, —1+_i,
l+eC l+eC
R102 Kr
———tanh _
K 2C
Or, rearranging,
AT”, 2C

55

(3.44)

(3.45)

(3.46)

With the addition of two extra leads, the thermopower of the sample can be measured
simultaneously. When K1: / 2C << 1, then the steady state limit is reached and

_ R1:
AT

PP

K
(3.47)
To obtain thermal conductivity, this should be multiplied by the geometry factor of length
over cross-sectional area of the sample.

This technique obtains the thermal conductivity with a single measurement run. Also,
the pulse technique affords more rapid data acquisition than obtainable with a steady state
technique. However, should the user wish to take measurements using the steady state
technique, no change to this measurement configuration is required. Only a software
change to the time dependence of the heat current is needed changing it from a pulse
function to a step function. The addition of two voltage probes to simultaneously extract
thermopower data for the sample provides full characterization of the thermoelectric
properties of the sample more rapidly.

Thus, this technique provides more rapid data acquisition than the steady state
technique, while having the ability to measure the steady state value for comparison. It
uses fewer sample leads than needed for the Harman technique, does not pass current
directly through the sample as in the Harman technique, obtains thermal conductivity
values in a single measurement run as opposed to the two runs required in the
Angstrom’s technique, and gives both thermal conductivity and thermopower data from a
single run. For these reasons, the pulse technique was chosen over the others described

above.

56

 

In a practical apparatus as shown in Figure 3.5., a surface mount resistor ( 470 Q ) is
used to periodically heat one end of the sample to establish a measured temperature

gradient of approximately 1 K.

{J
VCoppa
ii

 

 

 

\\ \

 

Figure 3.5. Schematic arrangement for the Pulse technique.

Typically a 12-13 minute period of oscillation is chosen and the temperature gradient
is observed to reach steady state within half of the period, as shown for B12T63 in Figure
3.6. In this condition the peak — to — peak value is used in determining the thermal
conductivity. As mentioned earlier, this pulse technique gives the opportunity to

determine the thermoelectric power by simultaneously measuring the voltage,AV,

indicated in Figure 3.6 and finding the slope of the AV v/s AT curve.

57

 

 

-5
510 v I v v v I v w 1 I v v v I I v v I v v v I v v v I v v v
p u

: I > I

410'5 - q
, C) 4
’ < o C

.5

0

UI
rj

A

v
I"
v
A
v
A
v

##1 L4 4

 

 

 

 

E

a:

c»

g

>

2

a

3

g * <> 0 0
o o

h '5 <> 1

g 210 - C, —
O

E

‘6

g 110"" -

E

D

o L l

 

 

 

 

 

 

800 1000 1200 1400
Time (s)

Figure 3.6. Typical AT data collected.

The final measurement of electrical conductivity is carried out using ac and dc

techniques after the thermal conductivity and thermoelectric power are measured“)

3.2 Experimental Setup

Typical steps in sample characterization are listed below:
0 Sample Mounting
0 Sample Loading in the Cryostat
0 Data acquisition

In step one, the amount of time required per sample can be somewhat reduced with
large sample geometries, and through appropriate engineering of the sample stage. The
greatest efficiencies in sample mounting, however, generally come through practice. The

procedure for mounting a sample to the measurement stage is outlined below:

58

. One end of the sample is attached to a copper stage with gold or silver paste. The
copper stages are permanently mounted to the gold — plated measurement stage
using silver paste.

. The heater is attached to the other end with gold or silver paste. The heater is a
470 (2 surface mount resistor with copper leads soldered at the ends. It is coated
with StycastTM Epoxy and wrapped with a piece of aluminum foil. The aluminum
foil increases the emissivity of the heater to reduce the radiative losses and the
Stycast epoxy provides electrical isolation.

. A copper-constantan differential thermocouple is used for measuring the
temperature gradient, AT. The thermocouples are electrically isolated from the
sample and thermally connected to the sample using Stycast epoxy to attach them
on the surface of small copper plates, as shown in Figure 3.5. The copper plates
holding the thermocouples are then attached to the sample with gold/silver paste
such that they are roughly equi-distant from the sample ends.

. The voltage leads are then gold — pasted to the sample through the copper plates.
This helps to assure that the voltage and temperature gradients are measured at the
same locations on the sample for accurate thermoelectric power measurements.

. The current leads are then attached to the sample (the positive lead is attached on
the top surface of the sample along with the heater using gold/silver paste, while
the negative lead is permanently attached to one of the walls of the measurement
stage) for electrical conductivity measurements. Heat conduction losses through
the electrical connections are minimized by using long leads (~ 15 cm) wrapped

around a glass tube.

59

 

Electrical isolation of the differential thermocouple is then determined by
measuring the resistance between the copper stage and each end of the differential
thermocouple.

Electrical connection of the sample voltage leads should also be checked for
continuity at this time.

Careful testing of each contact is imperative in order to avoid measurement errors.
Thus, a substantial amount of time is devoted to contact testing and evaluation.
Next the gold - plated copper heat radiation shield is placed on the stage taking
care not to touch the wires connected to the sample. The shield helps to provide
isothermal conditions around the sample.

Step two includes loading the sample stage into the cryostat, evacuating the

sample chamber, testing contacts, and cooling the samples to the starting temperature.

A brief procedure outlining the same is described below:

1.

The assembled stage and shield are connected to the end of the cryostat through
the circuit board permanently fixed at the end.
Then a second heat shield and the outer vacuum can are placed on the cryostat.
The contact resistances are measured again at the point where the wires from the
sample stage connect to the instrumentation.
The cryostat is then evacuated to approximately 10'6 Torr to minimize thermal
losses caused by heat convection.

Step Three : Data Acquisition

A brief PRERUN is carried out to verify all connections and obtain room

temperature values.

60

If the PRERUN results look good, the samples are cooled with liquid nitrogen
through a transfer line.

The actual RUN software begins data acquisition once the samples are cooled to
the desired temperature. Further details on the measurement have been provided
in chapter 4.

At the end of the run, the software will automatically reset the instruments and the

samples can be removed when the cryostat reaches room temperature.

When removing the differential thermocouple and voltage leads, care is taken to

avoid breaking the wires. Acetone is generally used to remove the gold—pasted and

varnished connections from the sample. The wires and copper stage are then carefully

cleaned with methanol and acetone for the next run.

3.3 Preparation of Differential Thermocouples / Heaters

Differential Thermocouples

Typical steps in thermocouple preparation are:

1.

Cut 2 small pieces of copper wire (Formvar insulated, 48 gauge, about 25};
diameter) 15 cm in length, and a constantan wire (25“ diameter, bare) 10 cm in
length. Scrape the ends of the copper wires.

Attach the wires to a piece of KaptonTM tape, with a pair of tweezers. Care should
be taken to avoid kink formation in the wires, which could affect conduction.
Stick the Kapton tape (along with the wires) to a small glass tube, with the wire

ends out of the tape. See Figure 3.7.

61

4. Gently twist one end of each copper wire around the constantan wire, with
tweezers (use of blunt tweezers is recommended, to avoid wire breaking).

5. Spark-weld the copper-constantan wire junctions to make permanent contact.

6. After soldering the other end of the copper wires to pin receptacles, you should
observe a resistance of, typically 90-150 9 between the ends, considering the wire
dimensions and the quality of the spark-welded contact.

The differential thermocouple is ready for temperature measurement.

0 Heaters

Typical steps in preparation of heaters are:

1. Cut two pieces of copper wire (Formvar insulated, 48 gauge, about 25}; diameter)
15 cm in length, and scrape the ends to make contact

2. Wrap the copper wires around a small glass tube and stick them with Kapton tape,

leaving the ends out of the tape.

3. Solder one end of each wire to the terminals of a 470 (2 surface mount resistor.

4. Take a copper plate, roughly the size of the surface mount resistor, and attach a
piece of paper (delicate task wipers / tissues) to it’s surface with StycastTM Epoxy.

5. Place the surface mount resistor with the soldered terminals, on the paper; Cover
the resistor (especially the terminals) entirely with epoxy, in order to electrically
insulate the terminals.

6. Measure the resistance between the other two ends of the wires after curing the
epoxy for a few hours. A resistance around 470 Q would mean the heater is ready

for operation.

62

Glass tube

I Conner wires

    

 

 

 

I:

 

 

 

 

 

 

 

l

Kapton tape Constantan wire /4— —>
90 - 150 Q

 

Figure 3.7. Differential Thermocouple Preparation

63

Chapter 4
System Assembly and Operation
4.1 Equipment l Instrumentation
This section describes the features of the charge transport measurement system,
especially those relevant to thermoelectric measurements. It includes descriptions of the
continuous flow research cryostat system, gas/vacuum system, data acquisition
instrumentation, and the sample mounting assembly used in the experiments.
4.1.1 Continuous flow cryostat system
The Janis Research Supertran (ST) system is a continuous flow research cryostat
that has been used for experiments in the temperature range from 80K to 400K. Special
features of the ST-lOO include:
0 High temperature operation capability (up to 475K).
0 Optical vacuum shroud.
0 Optical radiation shield used to intercept room temperature radiation.
0 Three blank feedthrough ports, used to make electrical connections to the
sample stage, with appropriate connectors.
- One lO-pin electrical feedthrough.
0 Silicon diode temperature sensor, calibrated for use with a Lakeshore 330
temperature controller.

0 6” super-insulated cryogen transfer line.

64

4.1.2 Vacuum system
The vacuum system includes a Leybold TRIVAC® B rotary vane vacuum pump operated
along with a Leybold TURBOVAC turbomolecular pump featuring grease-lubricated
bearings. Features of the rotary vane pump include :
0 Pumping speed of 1.6 m3.h’l
o Built-in oil pump; pressure lubricated sliding bearings
A TURBOTRONIK frequency converter is required for the operation of the
TURBOVAC. The turbomolecular pump includes the following features:
0 Ultimate pressure 8 x 10'9 mbar
0 Nominal speed — 72,000 rpm
4.1.3 Data Acquisition Instrumentation

The data acquisition equipment includes the following:

0 Model 2182 Keithley Nanovoltrneter

The model 2182 Keithley Nanovoltrneter is a 7.5 digit high — performance digital
nanovoltrneter. Special features of the nanovoltrneter include:

0 Dual channels for measuring voltage and temperature

0 Synchronization to line

0 Direct reading of ratio

0 Built — in thermocouple linearization and cold reference junction

0 Low noise at high speeds
The 4 - sample characterization system currently employs four 2182’s, two samples are
measured simultaneously with each sample using two nanovoltrneters, measuring voltage

and temperature gradients respectively.

65

o Keithley Model 2400 SourceMeter®

The Model 2400 SourceMeter combines a precise, low — noise, highly stable DC
power supply with a low noise, highly repeatable, high — impedance multi-meter which
incorporates the following features:

0 0.012 % basic measurement accuracy, 0.035 % basic source accuracy with 5-1/2

digit resolution.1000 readings/second at 4-1/2 digits via GPIB.

0 Voltage source/measure range: i luV - i 200V DC.

0 Current source/measure range: iIOpA - i 1A.Concurrent measurements of all

three functions over the remote interface

0 Source-measure sweep capabilities (linear and logarithmic staircase sweeps).

o 22W, 4-quadrant source and sink operation.

- Trigger—link interface to Keithley series 7000 switching hardware.

0 IEEE-488 and R8232 interfaces.

The 4—sample characterization system currently employs one model 2400
SourceMeter to source current/voltage through the surface mount resistance heater for
thermal conductivity and thermopower measurements. By controlling switch closures in
the Keithley 7002 (described below), this meter is also used to source current and/or

voltage to the sample stage for do electrical conductivity measurements.

0 LakeShore 330 Autotuning Temperature Controller

The Lakeshore 330 Temperature controller is a rrricroprocessor based instrument with

digital control of a variable current output. The controller has been used along with a

66

silicon diode temperature sensor for accurate temperature control. Relevant features of
the controller include:
0 Control stability of i 25mK at 300K.
0 Temperature Accuracy: i 80mK at 300K with silicon diode sensors.
0 10 user-defmed temperature zone storage capability with separate PID and
heater range settings for each zone.
0 Autotuning capability, which utilizes information, gathered during setpoint
changes to optimize control parameters.
0 Setpoint setting resolution: 0.01K < 200K, 0.1K 2 200K.
0 15-bit heater setting resolution with 25W and 50W output ranges.
- EG&G 7265 DSP (Digital Signal Processor) Lock-In Amplifier
The EG&G lock-in amplifier has been employed to perform AC electrical
conductivity measurements, with the following features:
0 Oscillator frequency range: 0.001Hz — 250kHz with absolute accuracy 25ppm
+ 30qu. Amplitude range: luV-SV with luv-1.25mV resolution.
0 Signal channel voltage sensitivity: 2nV-1V full-scale in 1-2-5 sequence with
dynamic reserve capability > 100dB
4» Output time constant: lOus —- lOOks.
0 Single reference mode AC gain limit: 90dB
Currently, AC conductivity measurements are performed in single reference mode at
100Hz oscillator frequency (which has been found to provide best results by trial and
error) with a time constant of 100ms, 1V signal channel sensitivity with corresponding

dynamic reserve 6dB and an input signal limit of 3V. It seems worthwhile to mention that

67

an input signal limit of 5V was considered unacceptable after inaccurate conductivity
measurements, possibly due to signal input overload.
o Keithley 7002 High Density Switch System
The Model 7002 Switch System is a lO-slot mainframe that supports up to 400 2-
pole multiplexer channels or 400 matrix cross-points. Other relevant features include:

0 Channel cross-talk: < -65dB @ lMHz(50(2 load)

0 Path isolation: > 1020 Q, < SOpF path-to-path

0 IEEE command execution time: < 8 ms + Relay settle time(automatically

selected by the mainfi'ame)

The 4-sample system uses two 7012-8 4 x 10 matrix cards, One 7013-8 20-
channel isolated switch card, and two special purpose 7168 8-channel nanovolt scanner
cards installed in the 7002 mainframe. The nanovolt scanner cards have extremely low
contact potentials (<30nV), in comparison to the general purpose 7012-S as well as 7013-
S cards (<500nV), making them ideal for the nano-voltmeter connections.

For wiring details, see appendix A.
o Keithley 2002 Multimeter

The 4-sample system currently uses a model 2002 multimeter for accurate voltage
measurements across the heater resistors. The multimeter has extremely versatile
functionality, among other important features, which are: ’

0 DC voltage measurement range: 200mV-1000V with normal accuracy lOnV-

lOOuV and input resistance > lOOGQ.

0 Data collection rate: up to 2000 readings/second at 4.5 digits of resolution,

and 215 readings/second at 6.5 digits.

68

0 Memory storage capacity: 850 readings at 4.5 digits or up to 250 time-

stamped readings at 6.5 digits.

4.2 4 — sample system Mounting Assembly
Typical thermal conductivity measurement systems incorporate one or two sample

positions, and often are able to measure one sample property in a single temperature
sweep. This system is unique in that four samples are characterized in a single
temperature sweep through the simultaneous measurements of electrical conductivity,
thermoelectric power, and thermal conductivity. The system mounting configuration
incorporates the following components:
0 Sample mounting stage

The sample mounting stage consists of gold plated OFHC copper, with a separate
chamber for each of the four samples, as shown in Figure 4.1. For clarity, the radiation
shield, which surrounds the sample stage is not shown in the figure.
0 Circuit Boards

The above figure shows two views of the circuit board, with 40 tapped holes, each of
diameter 0.038”. Gold plated printed circuit brass pins (0.024” pin diameter) with 0.035"
mounting hole diameter, are soldered to each hole. The remaining 4 holes have been
provided to bolt the circuit board to the bottom of the mounting stage. The pins mate with
0.062” diameter receptacles soldered to another circuit board, which is attached to a plug

— in board permanently fixed to one end of the cryostat.

69

0 Plug - In Board

Figure 4.3 shows the plug — in board, which consists of gold plated OFHC copper,
and has another circuit board (with receptacles soldered to each hole) attached to it’s
bottom as indicated. Thus, the mounting stage can be conveniently disconnected from the
plug - in board whenever required.

Electrical contact between the mounting stage and the instrumentation is made with
the help of:

0 larger diameter copper wires (quad twisted and duo twisted) which connect the

plug — in board to the 19 — pin connectors situated outside the dipstick, and
0 two 19 — cables which, in turn, carry signals from the connectors to the
instrumentation through the switch system.

0 Radiation Shield

Figure 4.4 shows the radiation shield, which is also OFHC copper gold-plated in
order to minimize radiative losses during the measurement. It also serves as a protective
cover for the samples mounted on the stage within.
0 Bread - Board modules

Bread — board modules are bolted at one of the sidewalls of each chamber of the
mounting stage. Printed circuit pins (described earlier) are soldered to 8 holes (0.037”
diameter) and mate with receptacles to which are soldered, the wires from each sample.
Larger diameter quad—twisted and duo—twisted copper wires are soldered to the mounting
holes of the pins, and pass through a hollow cavity to the bottom of the sample stage,

where they are attached to the circuit board (bolted to the stage).

70

-- - 0.156"

a 2.000"

 

 

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00.116" through

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Fl
1.781"

(b)
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0.063"

I l j - L 1
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§;
——-—:£>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a 1.438"
a 1.875" (c)
(— 62.000"

 

 

 

 

 

 

 

 

 

 

00.116" through

 

 

a 0.250"
oounterbore
0.250" deep

Figure 4.1 Sample mounting stage (a) top view (b) front view (0) bottom view

71

 

(a) (b)
Figure 4.2 Circuit board (a) top view (b) bottom view

(a)

 

 

 

 

 

 

 

 

 

(b)

Figure 4.3 Plug-in board (a) top view (b) front view

72

.__ 2.145" —--~

 

 

1.906"

 

 

 

 

 

0.750.. I

 

a 0.116" through center . a 2.145"

a 2.003"

 

Figure 4.4 Radiation shield (a) front view (b) top view

4.3 System Assembly

The 4 — sample characterization system has been assembled as shown in figure 4.5.
Remote operation is accomplished with the help of a GPIB interface between the
computer and the instrumentation. A pair of 19 — pin coaxial cables is used to connect the
instrumentation to the sample mounting stage through 19 — pin connectors mounted on
the cryostat. Smaller diameter wires (25}; thick) are used to make connections to the
individual samples, thus minimizing conduction losses through the wires which become

important particularly in thermal conductivity measurements.

73

Convective losses are minimized by high — vacuum (of the order 10'5 Torr)
operation. Currently the system is utilized for measurements in the temperature range
80K-400K, using liquid nitrogen, which is transferred from the nitrogen storage container
to the cold finger cryostat with a multi-layer super-insulated transfer line, however, it is

fully compatible with 4.2K-400K operation with the use of liquid helium.

D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l ' l Liquid
A I
, Nitrogen
GPIB interface
Temperature 2002 1 9-pin
CODU'OHCI' Multimeter coaxial cable
2182 2182
Nanovoltrneter Nanovoltrneter
7002 High-Density Switch
System
I 1 I l

2182 2182 ’
Nanovoltrneter Nanovoltrneter
2400 7265
SourceMeter Lock-In

 

 

 

 

Vacuum
system

Cryostat

Nitrogen Tank

Figure 4.5 Schematic diagram of system assembly

Remote Operation

The 4 — sample measurement system is fully computer — controlled and

implemented in LabVIEWNSJ.

74

System automation demanded an extensive

programming effort involving instrumentation set-up, initialization, data acquisition, and
subsequent data processing to obtain the final values of the desired measurement
quantities.

The following algorithm enlists the steps carried out through LabVIEW to obtain
the desired measurements. The user enters the sample specifications and other
measurement parameters (sample dimensions, temperature range of measurement, heater
pulse period, heater current, oscillator frequency and voltage, etc.) in the 4 — sample run
new VI'. The operation of the 4-sample run new V1 can be described in 4 steps as
explained below:

Make Files

This step involves making files for each sample at the beginning of a given
measurement run. Each sample file stores information about the sample including sample
dimensions, description, and the measurements taken during the sample run.
1. Initialize Instruments

As the name suggests, this step involves instrument initialization to the desired
measurement parameters before each measurement run. For instance, the 2400
SourceMeter initialization sets the required trigger, digital filter, compliance, display
resolution, interlocking, measurement range, measurement speed, and output
configuration specifications as desired by the user. A similar initialization procedure is
followed for each instrument involved in the measurement.

2. For each temperature range, measure each sample

 

' VI — virtual instrument: consists of an interactive user interface, a data-flow diagram that serves as the
source code, and icon connections that set up the VI so that it can be called from higher-level V15.

75

This step involves the actual data acquisition and measurement operation for every

sample over each specified temperature range. This step can be subdivided into the

following steps executed in that order.

The source-meter outputs a repeating current pulse with the desired pulse
height and period while the Temperature controller waits for temperature
stabilization at the desired set-point.

When the condition for temperature stabilization is satisfied over the pre-
programmed period of time, data acquistion for the first 2 samples begins.
Four 2182 nano-voltmeters are employed to collect dV and dT data through
the differential thermocouples and voltage leads at regular intervals of time
for a little over 2 pulse periods. Also, the 2002 multi-meter measures the
voltage across the heaters, which is used for heater power calculations. The
dV and dT data undergo a number of calculations (see flowchart) in various
VIs which ultimately obtain values of thermal conductivity and thermopower.
A similar process repeats to characterize the other 2 samples.

The system obtains 4 — probe electrical conductivity measurements using the
2182 nano-voltmeter and 2400 SourceMeter (for DC measurements) and the
7265 Lock -— In Amplifier (for AC measurements).

The results are saved to the pre-initialized files and plotted as a function of

temperature.

3. Set Instruments to Safe Conditions

On completion of all measurements for all temperature ranges, the instruments are

reset to safe conditions (maximum ranges, zero output, etc.).

76

4.4.1 Programming Details

Labview programming has been employed to automate system operation. A brief
description of the V15 (virtual instruments) is given below:
0 The Read VIs

As the name suggests, the Read VIs obtain/read data from various instruments.
0 The Write VIs

As the name suggests, the Write VIs write data (SCPI commands, for instance) to
various instruments, thus programming them to perform the desired operation.
- Initialization VIs

The Initialization VIs initialize each instrument before a measurement run, to the
required measurement parameters. Every instrument has its own set of initialization
commands which, when integrated together, set the instrument in the programmed mode
of operation.
0 2400 New Pulse VI

The 2400 New Pulse VI initiates a new current pulse with the desired magnitude and
period as specified by the user. This VI configures the trigger scheme, trigger count,
delay, and other sourcemeter parameters as part of the current pulse generation

procedure.

- Tempctrl VI

The Tempctrl VI, in conjunction with the 330ReadT VI, monitors the

temperature at the sample stage. PID parameters for ten temperature zones were loaded

77

into the 330 Temperature Controller’s memory during initialization. These parameters
are automatically accessed when the corresponding temperature range is entered. The
system starts data acquisition only after the sample temperature stabilizes within a pre-
programmed deviation value about the set-point for a pre-programmed period of time.
0 7002 Switcher VI

The 7002 Switcher VI controls the operation of the 7002 Switch system.
Depending on the sample position and the type of measurement required, it selects a
combination of the necessary switch closures (in other words, the instruments to be used
for the measurement) from a text file containing combinations for all possible
measurements, and outputs the same to the 7002 Switch system.
0 Kappa Arrays VI

The Kappa Arrays VI collects dV and dT data from the 2182 NanoVoltmeters
and calculates appropriate time stamps to output arrays of dT (temperature gradient),
dT/dt (time differential of temperature gradient) as well as max’s in dT/dt. It also reads
data from the 2002 multi-meter in order to calculate the power supplied to the surface
mount resistors used to generate the temperature gradients.
0 Kappa 2a VI

The Kappa 2a VI evaluates the best fit to the output arrays of the Kappa Arrays
VI in order to calculate the average maximum temperature gradient as a function of time,
for two samples at a time. Temperature stability is evaluated in this subroutine by
comparing the slopes of the measured temperature gradients to user specified max/min
slope criterion for the dT arrays. Using the temperature gradient, sample dimensions, and

the heater power, it then calculates the thermal conductivity and thermopower.

78

0 Electrical Conductivity VI

The Electrical Conductivity VI controls the operation of the 2400 SourceMeter,
2182 NanoVoltmeter, as well as the 7265 Lock-In Amplifier to evaluate the DC /AC
electrical conductivity of the specified samples. This V1 is executed afier completion of
the thermal conductivity and thermopower measurements while current pulsing through
the dT heaters is set to zero.

0 Plots VI

The Plots VI displays the measured quantities (thermal conductivity,
thermopower, and electrical conductivity) as a function of temperature. These plots are
updated afier each temperature, for in-situ monitoring of measurement progress.

4.4.2 Experimental Procedure

The experimental procedure has been explained with the help of flow diagrams,
indicating the order of execution for measurements.

Figure 4.6 is a flow diagram indicating the overall system operation for the entire
characterization run which includes all measurements over different temperature ranges.
The flow diagram in Figure 4.7 explains the thermal conductivity and thermoelectric
power measurement technique, including the necessary calculations involved. Figure 4.8
is a flow diagram summarizing the steps involved in AC and DC electrical conductivity
measurements.

As indicated in Figure 4.6, the thermal conductivity and thermoelectric power
measurements are first taken, followed by electrical conductivity measurements. Typical
rim times for complete 4-sample characterization from 80K-400K at 5K steps are about

70-80 hours, depending on the heater pulse period and temperature stabilization.

79

Accept User Input
and make Files

I

Initialize Instruments to
Known conditions
1
Start Temp = T1
Stop Temp = T2
Temp Step = T

 

 

 

 

 

 

 

 

 

 

 

63 +

Goto Setpoint Temperature;
Generate new pulse of specified
period and magnitude;

 

 

 

 

 

 

 

 

Y J.

 

Based on user input, determine the sample
positions that require a temperature gradient for

 

 

 

measurement

 

 

 

 

 

__> (A)

Perform the necessary switch .
Please see Fig 4.7
closures and measure K and TEP ' for details
Perform AC and DC conductivity _, Please see Fig 4.8
Measurements for details

 

 

 

 

(«b

80

 

 

Set new Start
temp, Stop

temp and

 

 

Plot data a

 

 

 

 

   

  
      
   
     
    

 

Have we
reached stop Set new
temperature ? SCtPOInt

 

 

 

Is there another
temperature
range ?

l N

 

 

Set Instruments to safe
conditions (maximum ranges,
zero output, etc.)

 

 

(A): For 4 samples, there could be 16 possible combinations of thermal
conductivity / thermopower measurements, depending on the user specified
measurement requirements.

Figure 4.6 Four-sample measurement flow diagram.

81

 

Based on measurement and

the necessary switch closures

 

sample #, determine and perform

 

 

 

l-

I

Turn on the current to the
heater resistor

Collect 1 50 sample
temperature gradient and
sample voltage data points
in time t = 1/2(pulse period)
into Array# 1 [A1]

Measure current, I], and
the voltage, V1, of the
heater resistor

Measure temperature T1

I

Turn off the current to the

time t = l/2(pulse period) into

heater resistor

Collect 1 50 sample
temperature gradient and
sample voltage data points in
Array # 2 [A2]

Measure temperature T2

I

Turn on the current to the
heater resistor

Collect 150 sample points
in time t = l/2(pulse period)
into Array # 3 [A3]

l

Measure current, 12, and
the voltage, V2, of the
heater resistor

Measure temperature T3

\\

/
/

 

82

®

 

Turn off the current to the
heater resistor

Collect 150 sample
temperature gradient and
sample voltage data points in
time t = l/z(pulse period) into
Array # 4 [A4]

Measure Temperature T4

 

l

 

Maxl=Maximumof[A1];
[A1]’ = d/dt [A1];

Maxl’ = Maximum of [A1]’;
Min2 = Minimum of [A2];
[A21’ = d/dt [A2];

Min2’ = Minimum of [A2]’;
Max3 = Maximum of [A3];
[A3]’ = d/dt [A3];

Max3’ = Maximum of [A3]’;
Min4 = Minimum of [A4];
[A4]’ = d/dt [A4];

Min4’ = Minimum of [A4]’;
T = mean (T1, T2, T3, T4);

I = mean (11, 12);

V = mean (V1, V2);

dT Power, P = V.I ;

 

 

 

l

 

 

Calculate the Best Linear fit, slopes, and
intercepts of:
Max 1 -Max3; Min2-Min4;

 

   

Is Max/Min

 

 

 

slope criterion
satisfied?

     

Compute dT (V), using the
difference in slopes and
intercepts of:

Maxl-Max3; Min2-Min4;

l

Compute the corresponding
dT(K) using pre-programmed
fitting routine dV/dT

l

L: Thermal probe spacing;
A: Cr ross - sectional area;

_P_L
dTA

 

 

 

 

 

 

 

 

 

K:

 

 

 

l

Calculate a linear fit to dV v/s dT(volts) for
rising and falling arrays ;

TEP = mean (product of slopes of the fits
and the fitting routine);

 

 

 

 

Figure 4.7 Thermal conductivity and thermoelectric power measurement flow diagram.

84

   

  

Is AC
conductivity

 

   
     
 

to be
measured?

l

 

Perform the necessary switch closures;
Set Lock — In amplifier source voltage

 

 

 

and fi'equency;

 

Collect user — specified # of signal
magnitude and phase readings

 

 

 

l

 

 

Compute the following:

Mean Magnitude R, (V);

Mean Phase 6, (degrees);

Real component of R, i.e. RcosO (V);
Imaginary component of R, i.e. RsinG (V);

Mean real and imaginary components of R;

Standard deviations of real and imaginary

 

 

magnitude and phase;

 

Switch to ac current sensing mode

 

 

 

l

 

Compute current sensitivity using signal
threshold detection and comparison;

 

 

 

J

Block 1

 

 

Collect user -— specified # of signal magnitude and

phase readings and execute block 1

 

 

85

Q)
1

Obtain actual signal
conductance Z (magnitude,
phase) by magnitude division
and phase subtraction from
previously calculated values

l

Convert Z to rectangular form
(ZcosG, ZsinO); Compute AC
conductivity using the real
component of Z in the formula:
Z .L
0'“ = -—
A

L: Electrical probe spacing
A: Cross-sectional area

5‘ {5)

Perform the necessary switch closures for DC
conductivity;

Source user specified current/voltage;

Measure sourced current, and voltage drop
across the sample in user specified # of readings

l

Invert the sign of the sourced quantity and
measure sourced current, and voltage drop
across the sample in user specified # of readings

1

Using average current and voltage values
over both cycles, compute DC conductance
and conductivity with the appropriate sample
dimensions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

STOP

Figure 4.8 Electrical conductivity measurement flow diagram

 

86

Chapter 5
Results and Discussion
0 5.1 Standard Materials

In testing the 4-sample system, a NIST 1461 stainless steel thermal conductivity
reference was used. The sample was cut to a 3mm x 3mm x 10mm geometry and
mounted to the sample stage using the above-mentioned procedure (see chapter 3).
Results of our measurements are shown in Figure 5.1 and Figure 5.2 indicating good
agreement with the NIST data. Some increase in the measured data at higher

temperatures is assumed to be caused by radiation losses (indicated in Figure 5.1).

 

18 T'fiI—riii'fii‘Ith'II"I'I'V'IVIUVIUI

o MSU Electronic Materials Lab 0
15 t ‘NISTData o °°°°°

14-

A A l A A

12-

10-

Thermal Conductivity (W/m-K)

 

 

I Alain-AA

350 400 450

l

 

6 AAAAIAA111441LIALAALAA

50 100 150 200 250 300
Temperature (K)

 

Figure 5 . 1. Thermal conductivity of a NIST stainless steel sample

It is interesting to note the dashed lines in Figure 5.2 where using the dimension
of ps from Figure 3.5 yields the lower dashed line, while (ps + 25) gives the upper dashed
line. For this sample 5 ~ 0.75 mm and ps ~ 6 mm. The plotted data use the midpoint

measurement (ps + 8), and show good agreement with the NIST data. As a second

87

reference a Corning PyrexTM 7740 glass sample, cut to a 5mm x 5mm x 6mm geometry
was mounted, and tested, with results as shown in figure 5.3. As observed, the plotted
data agree best with previously reported values“), when the average of the probe

separations or center-to-inside edge is used.

 

 

 

 

 

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so 100 150 200 250 300 350

Temperature (K)

Figure 5.2 Electrical and Thermal conductivity of a NIST stainless steel sample

Figures 5.4 and 5.5 show measurements of a BizTe3 sample from Marlow
Industries, Inc. in good agreement with Marlow data. The effects of radiative losses were
experimentally investigated by measuring the thermal conductivity using different
temperature gradients across the sample. These radiative contributions are clearly
indicated in Figure 5.4 as seen by the increasing measured thermal conductivity with

increases in the temperature gradient across the sample.

88

 

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0IAILiJJAJIAAAIIllnLLer—AAIAAAAIAAALIALAA
50 100 150 200 250 300 350 400 450

Temperature (K)

Figure 5.3 The solid lines indicate the variation in thermal conductivity due to

change in the measured spacing of the thermocouple probes

 

    
    

 

 

3_ . ......,..-...-.-.-rfi-.......f.-‘
I Bi Te from Marlow Industries 1
2 3

2.8 - -
5.4 2.6 _- j
v 2.4 1 J
n; I '
~33 2 2 t Indication of .
3 ‘ . Radiative losses.
2 F 1
o 2 '_ ~12K l
U . / . 1
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1.6 r
. . ‘- Marlow Data,
b 1
l 4 A A A A l A A A A l A A A A l A A A A I A A A A l A A H l A A A A

 

50 100 150 200 250 300 350 400
Temperature (K)

Figure 5.4 BizTe3 sample from Marlow Industries, Inc. Radiation effects were
investigated at the higher temperatures by changing the temperature gradients.

89

 

1,8 r..., in. ....T..v.....,..rT..... -80
aha Bi 2Te3 from Marlow Industries ‘

1.5 .. Don : Marlow Data 5" - -100
' an o ‘

14 - ”an ‘—’ o ° 1 -120

H
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Resistivity (mil-cm)
.0 .
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A ac resistivity

by Ari) ramod otnoelaouneql

 

 

 

 

0.6

04"- o‘fiOfiz‘,A

' : . «czar
I .80. 5 r

0.2 LaAAAA-.r...An....n-..-r-...1.--. _240
50 100 150 200 250 300 350 400

Temperature (K)

Figure 5.5 Electrical Resistivity and Thermopower for BizTe3.

5.2 New Materials

0 5.2.1 Ternary and Quaternary alkali metal bismuth chalcogenides

To meet the necessity for the design of a practical thermoelectric device, both p-
and n-type materials are required and the best materials currently being used in
thermoelectric applications are Bi2.bexTe3 and BizTe3.,Sey for p- and n-type materials,
respectively. We are currently examining the same type of chemical manipulation on
CsBi4Te6 to achieve both p- and n-type behavior. Additionally, a reduced thermal
conductivity may be expected from the mass fluctuation caused by introducing Sb and
Se, into CsBi4Te6. In this paper we present preliminary results obtained from oriented
ingot samples‘z) of CsBi4.,beTe6 and CsBi4Te6.,Sey. It should be noted that the

production of such ingots has not been optimized and they most likely contain

90

imperfections and micro-cracks. This of course can affect critically the electrical

conductivity of the sample, yet it does not significantly influence the thermopower.

    

88i wide, 23 IA.

 

 

 

 

 

B', t .
0.0.8.8..,Oro 0".
3 is “3*"

108i wide, 29 A

Figure 5.6. The structure of (A) CsBi4.,Sb,Te6 (x = 0.3) and (B) CsBi4Te5.ySey

(y = 0.3) viewed down the b-axis. Open circles are Te atoms, gray ones Bi

atoms, black ones Cs atoms, and striped ones Sb atoms (A) or Se atoms (B).

The widths of the [Bum] slabs are showna).
Tranport Measurements

All CsBi4.,beTe5 (x < 0.8) solid solutions showed p-type behavior with the

maximum thermopower of ~150 uV/K at different temperatures. The thermopower data
for all materials appear to be very dependent upon temperature and show a maximum
between 250 and 350 K, see Figure 5.7. The CsBiMSbMTeé ingot sample showed 600

S/cm and 150 pV/K at room temperature and the maximum power factor of

13.4 uW/cm-K was obtained at 275 K. Based on the maximum values of S, the band gap

91

of CsBi4.be,Te5 and CsBi4Te¢5.ySey can be estimated from the formula Eg ~ 2(SmaxXTmax)

to be 0.081 and 0.084 eV respectivelya).

 

 

 

 

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350 :- 0” -j 90

300 . r n . 1 . A g. L. r . . r . . . . A L. . . 1 r . . . ' 80

100 150 200 250 300 350 400

Temperature (K)

Figure 5.7 Variable temperature conductivity and thermopower data for
CSBi3.6Sb0.4Te6.

The CsBi4Te¢5.,Sey sample showed a similar maximum in the thermopower at
~140 uV/K at 300 K. The electrical conductivity at room temperature was ~300 S/cm and
showed a metal like dependence, Figure 5.8. Hall measurements are planned to obtain
further insights into these samples such as carrier concentrations and mobilities.

Low thermal conductivity is shown for a CsBi4Te4_gSe1,2 sample in Figure 5.9.
Room temperature thermal conductivity of this sample is ~ 0.9 W/m-K, quite lower than
that of BizTe3 (~ 1.6 W/m-K at room temperature). Figure 5.10 shows thermal
conductivity measurements on a CsBi3.4Sb0.6Te6 sample with a room temperature value of

~ 1.8W/m-K.

92

 

§§§

DC Electrical Conductivity (S/cm)

 

 

 

 

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50 100 150 200 250 300 350 400

Temperature (K)

Figure 5.8 Conductivity and thermopower data for a CsBi4Te5,ZSeo,3 sample.

 

 

 

 

 

5 ""l""l"'rrfifi'Tl—""l'"'I""
CSBI4T64£SG12 l
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50 100 150 200 250 300 350 400

Temperature (K)

Figure 5.9 Thermal conductivity of a CsBi4Te4,38e1,2 sample.

93

 

 

 

 

 

[ .
. CsBr3‘4Sb0‘6Te6 :
4 " -
A r
E r
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’.-..r..4.r..LA_A.+AI AAA—LA .4..;.
50 100 150 200 250 300 350 400
Temperature (K)

Figure 5.10 CsBi3.4Sb0.6Te6 sample.

5.2.2 Quaternary Bismuth Selenides A1.,M4.,Biu+,Se21 (A = K, Rb, Cs; M = Sn, Pb)
Crystals of RbSn4BinSe21 and Cst4Bi118e21 were prepared by direct

combination of alkali selenide, Bi28e3, Sn (or Pb), and Se at 800°C. These selenides are
n-type narrow band gap semiconductorsm with moderate electrical conductivity and
thermopower as indicated in our measurements.
Transport Measurements

The temperature dependence of electrical conductivity and thermopower of
RbSn4Bi11Se21 and Cst4BinSe21 were measured on polycrystalline ingots, see Figure
5.11 and 5.12. Rb1.xSn4.xBiu+xSe21 has higher electrical conductivity with values starting
around 450 S/cm at 75K and falling to 180 S/cm at 400K In comparison, the Pb

compound is slightly less conductive with an electrical conductivity of 260 S/cm at 75 K

94

and 170 S/cm at 400 K for Csl.be4.xBin+xSe2.. The variable temperature thermopower
data of polycrystalline ingots of Rb1.xSn4- Biu+xSe21 and Csl.be4.xBi11+xSezl show a
negative, nearly linear dependence. With rising temperature the Seebeck coefficient

decreases from —14 uV/K at 75K to -72 uV/K at 400K for Rb1.xSn4.xBin+xSe2| and

Csl.be4.,Bi1 1+,Se21, respectively.

 

 

 

 

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1 JAAAIAAAAIAAAAIAAALIAAAAl-A-ALLAAAJAA

 

50 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.11 Variable Temperature Conductivity and Thermopower data
for a RbSn4Bi1 ISe21 polycrystalline ingot.

The negative values indicate n-type behavior with electrons as the dominant charge
carriers. The thermal conductivity vs. temperature plot is shown in Figure 5 .13. Both
samples possess a very low thermal conductivity around 1 W/m-K at room temperature.
Cs]- Pb4.xBi1 1+xSe21 exhibits unusual temperature dependence, its thermal conductivity is
increasing linear with rising temperature what might be caused by radiation losses at

higher temperatures.

95

 

      
   

 

 

 

700.""l""l"1* ----.......--.,-..-,..-.‘ .10
I .. , :
: ...... Cst‘BI11Sez1 J _20
’e‘ 6°° T ---- 3 g
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100 ’ A LL‘ A A A A l A A A A l A A A A l A A A l A A l A A A l A A A A .90

50 100 1 50 200 250 300 350 400 450
Temperature (K)

Figure 5.12 Conductivity and Thermopower for Cst4Bi118e21.

The very low thermal conductivity of these compounds may be attributed to the
extensive disorder of the metal atoms in the anionic framework, the large unit cells, the
low crystal symmetry and the “rattling” of the alkali ions in the tunnels of the
chalcogenide framework. The observed thermal conductivity values are among the
lowest reported for materials with a potential thermoelectric application. Optimized
BizTe3 has a thermal conductivity of ~1.5 W/m-K, which is about 50% higher than the
thermal conductivity these compounds.

Although the observed electrical conductivity and thermopower of
A1.xM4.xBiu+xSe21 are relatively low, their very low thermal conductivity makes them

interesting for further investigations in order to increase their thermoelectric power.

96

 

 

 

 

 

2.5 ‘ ' V ‘ F ' ' ' V 1 ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I V r' '

Q . o 0st Bi Se .

2 __ 4 11 21 .4

g C . RbSn 4311 18921 -

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2 15 . .

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g - W o °°

l- d

0 (15 - .

15 t

l

o AAAAlAAAJILAAAJAAAALAAAAIAAAAlAAAAlAAJJ1

50 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.13 Variable Temperature Thermal Conductivity data.

5.2.3 Cubic Semiconducting Quaternary Chalcogenides AmBanszn

In the search for better thermoelectric materials, a new family of quartemary
chalcogenide compounds exhibiting promising thermoelectric properties has been
synthesized and characterized. The first compound discovered belonging to this family of
compounds of general formula AmBananm (where A is K or Ag, B is Pb or Sn, M is
Bi or Sb, and Q is Te, Se, or S) was KPbBiTe; using the flux method“) by Dr. Chung.
These materials possess the NaCl crystal structure type with A, B and M disordered on
the Na+ cationic sites and Q on the Cl' anionic positions. Such disorder is particularly
attractive for TB materials because mass fluctuation in the crystal will decrease the mean

free path of the phonons and therefore, the thermal conductivity.

97

In the general formula AmBananm, m and n can theoretically have any values
allowing a continuous range of stoichiometry. This is true as long as the elements that are
used for A, B, M, or Q have a valence charge of +1, +2, +3 and —2 respectively, verifying
the following charge neutrality equation:

m(charge of A) + n(charge of B) + m(charge of M) + (2m+n)(charge of Q) = 0

Any deviation from this rule will lead to compounds with different structure types
and different properties. Several members of the family of compounds studied in this
research have already been reported in the literature, TAGS, for instance. TAGS are well
known for their thermoelectric properties and can also be seen as members of the broad
family AmBananm by writing them as Ag1.xG<3,,Sb1.,,Te2(1rmJr and replacing l-x by m
and x by n. We then obtain the general formula AgmGenSmee2m+n which is identical to
the one studied in this research. Compounds belonging to this system were used for

power generation.

0 Synthesis of A.,,B..M..,Q2mm compounds
Binary compounds were prepared according to the reaction below“):
nPbQ + (m/2)Bi2Q3 + (m/2)K2Q —> KmenBimQ2m+n
Stoichiometric amounts of KZQ, Bi2Q3 and PbQ are mixed under nitrogen atmosphere in
vacuum, and the mixture is heated at high temperatures in order to synthesize the

different compounds.

98

0 Transport Properties

0 K/Pb/Bi/Q ( Q = Te, Se) system
Seebeck Coefficient measurements on pressed pellets of members of the KanBiQn+2 (Q
= Te, Se) system showed that all the compounds characterized were n - type, indicating

that the majority carriers are electrons.

 

 

 

 

 

 

 

 

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o mama“
A . KPbBITe
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A

T: r 0 D
O I A D
§-1oo - o -
o . .
-= l
f- ,

-150

50

100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.14 Variable Temperature Thermopower data for KanBiQn+2 (Q = Te, Se)

Selected values of the Seebeck coefficient are —92 uV/K for KszBiSe4 at 320K
and -101 uV/K for KszBiTe4 at 400K. The materials show narrow band — gap
semiconductor behavior.Thermal Conductivity data for these compounds is as shown in
figure 5.15.The thermal conductivity values of KszBiTe4 and KszBiSe4 were measured
to be ~ 1.46 W/m-K and ~ 1.03 W/m-K respectively at room temperature. The thermal

conductivity plots of these two compounds also indicate a possible radiative contribution

99

to the values observed. Correction for the same would bring the thermal conductivity to
values lower than the ones reported. These values are very low and encouraging for TE
applications. KPbgBiTelo also emerges as a promising TE material with a room

temperature thermal conductivity of ~ 2.0 W/m-K, which is in agreement with previously

 

 

 

 

 

reported values“)
5 '"'IfifirT1'#'I""I""""'l'"fi""

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5 1 ' o o o o o 0 ° ° A "
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A

 

 

 

200 250 300 350 400 450
Temperature (K)

0 AAAAlAAAA
50 100 150

Figure 5.15 Variable Temperature Thermal conductivity for KanBiQn+2 (Q=
Te, Se)

0 Ag/Pb/Q/Te ( Q = Bi, Sb) system

Thermoelectric power measurements indicate (as shown in the Figure 5.16) that all
the compounds are n—type with electrons as the majority charge carriers. Clearly,
Ang3SbTe5 emerges as a very promising TE material with a room temperature
thermoelectric power of ~ -230 uV/K, a little higher than that of BizTe3 (~-220 uV/K) at
room temperature. The Seebeck coefficient appears to be increasing even as we go

beyond 400K, indicating possible high — temperature applications.

100

 

 

 

 

 

 

 

 

 

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_ A A A ‘ . ‘ ‘ :
o o o o A ‘ .
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300 -_ 0 Ang3$bTe5 .'
I A AngBiTe3 ‘
-350 P A A A A l A A A A l A A A A l A A A A 1 A4 LA 14‘ A4 L A A A A l A A A A‘

50 100 150 200 250 300 350 400 450

Temperature (K)

Figure 5.16 Variable Temperature Thermoelectric power of Ag/Pb/Q/T e (Q = Bi, Sb)

The measured Seebeck coefficient for AngBiTe3 is slightly lower than
previously reported values“). However, the measurements were made on different
samples of the same compound. Thus, doping variations in the form of a concentration
gradient along the sample length could possibly lead to different values being measured
for the two samples.

Thermal conductivity data (see Figure 5.17) indicates very low (hence promising)
values, especially for AngBiTe3 (~ 0.74 W/m'K at RT) and Ang3SbTe5 (~ 1.0675
W/m-K). The data shows evidence of possible radiative losses, especially for
Ang3BiTe5. Electrical conductivity measurements indicate low values (~ 50 S/cm) for

these compounds with the exception of AngBiTe3 and Ang3BiTes as shown in Figure

101

5.18. Based on the above measurements, the figure — of — merit ZT reaches a maximum

of 0.039 at 400K for Ang3BiTes and 0.016 at 320K for AngBiTe3.

 

 

 

 

 

 

 

 

 

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0 A A A A l A A A A l A A A A l A A A A l A A A A l A A A A I PL AJ_L A A A L.
50 100 1 50 200 250 300 350 400 450
Temperature (K)

Figure 5.17 Thermal Conductivity data for Ag/Pb/QfTe ( Q = Bi, Sb) ingots.

 

 

 

 

600 V'V'Ui'vri'r'fi'rrrtv"'I""I I '
' “b o AngBrTe ‘
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1m AA AAIAAAA_AI AAA A l l l l l

 

 

 

50 100 150 200 250 300 350 400 450
Temperature (K)

 

Figure 5.18 Electrical Conductivity of Ag/Pb/Bi/Te ingots indicating metallic behavior.

102

o Ag/Pble/Te system with increased silver / lead content
0 Synthesis
The following is the procedure of the synthesis of these compounds”):
step 1: synthesis from elements of Ag(0.1294 g), Pb (4.4755 g), Sb(0.1461 g) and
Te(3.0624 g) and in the molar ratio of Ag:Pb:Sb:Te = l:18:1:20. These elements are
loaded in a 9 mm quartz tube and in the sequence of Ag, Pb, Sb and Te, respectively,
from the bottom of the tube and finally the tube is sealed under the vacuum below
10'4 bar.
step 2: The tube is put in the furnace and heating at 900°C for 3 days and cooling to 50°C
for 15 hrs.
step 3: The ingot is sliced into A, B, C, D, E, F and G parts with the thickness ~0.3 cm
for each sample.
The "A" sample is fiom the top of the ingot.
The "F" sample is from the bottom of the ingot.
0 Transport Measurements

An extensive amount of data has been obtained for this system, including
anisotropy and annealing effect measurements. A number of samples of the same type
(but synthesized in a different manner and at different times) have been characterized
with promising results.

Figures 5.19 and 5.20 show measurements of a Anglgstezo ingot. Two

measurement runs have been carried out for the sample, since it cracked at the comers

while cutting, making it difficult to determine the dimensions with accuracy.

103

 

As observed, the thermal conductivity doesn’t seem to vary with the measurement

run, except at lower temperatures.

 

 

 

 

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50 100 150 200 250 300 350 400 450

Temperature (K)

Figure 5.19 Thermal conductivity data for a Anglgstezo ingot

 

é

 

: AngmeTe20 Ingot 4 (Bottom) . 0
@5000 _- ‘____ First run data ‘ —|
Q . “Dug ‘ 3
a - ‘ ‘3”
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0 .A..-...A-------Aul----1AUA ......... -400

 

 

 

50 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.20 Electrical Conductivity and Thermopower data for Anglgstezo

104

 

The sample appears very promising with a room temperature thermal conductivity
of ~1.9 W/m°K (and decreasing further), Seebeck coefficient ~ -170 uV/K (increasing
further) and dc electrical conductivity ~ 900 S/cm. Based on the first run measurements,

the projected ZT reaches a value of ~ 0.95 at 600K (see Figure 5.21)

 

vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

1 P AngnSbTemlngoMmottom)
0.8 r
0.6;
0.4 1

0.2 '-

 

 

 

LJ-A AAAA‘An-A

0 100 200 300 400 500 600 700
Temperature (K)

Figure 5.21 Experimental and Extrapolated ZT values for AngmeTezo

High temperature measurements must be taken to confirm the extrapolation.
Annealing and Thermal Cycling Effects

Various samples have been subjected to an annealing treatment, in which we
characterize the sample from 80K to 400K, anneal the system at 400K for about 12 hours,
and then take measurements from 400K to 80K. Another cycle of data collection is
carried out to observe changes, if any, in the measured values. Investigations of this type
have been made with interesting results.

Figures 5.22 and 5.23 show thermal conductivity measurements on another

AngmeTezo sample before and afier the annealing treatment. The thermal conductivity

105

seems to drop marginally after the heat treatment. The Seebeck coefficient, on the other
hand, increases. Electrical conductivity seems to be most substantially affected,
decreasing by about 200 S/cm at room temperature after annealing. It is interesting to

note the rapid decrease in electrical conductivity of the pre — annealed sample beyond

 

 

 

 

 

325K.
4 ' ' ‘ ' l ' ' ' ' l ' ' ' ' T ' ' ‘ ‘ l V T V V I r ‘ ' ' I ' ' ' ' I 'fifi '
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50 100 150 200 250 300 350 400 450

Temperature (K)

Figure 5.22 Thermal Conductivity of a Ang1gstezo Ingot
The sample has a room temperature Seebeck coefficient of about ~ -300 uV/K (pre —
annealed), which is sufficiently higher than that of BizTe3, and a thermal conductivity of
~ 1.8 W/m-K at room temperature, a little higher than that of BizTe3. The heat treatment
shifts the ZTmax point by 70K, while increasing its value a little over the pre — anneal

value (see Figure 5.24). Some images in this section are presented in color.

106

 

   
  
 

 

 

800_'*"I""l""l""l""r""l""1""
. Pre-anneal -
A 700 .- AngmeTezo Ingot (Bottom) any“ m - _100
E i ‘ '5]
2 ' -
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.3‘ : ~ -200 8
.E 500 .- ‘ 5'?
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a 400 .' ( 4 ”U
8 ; i -300 o
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g t ”In °° °°° . 4331*: 'ch : ‘E‘
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m ' °W°.. ‘ ‘ "is, ' i v
100 '0 dc conductivity 5-9'.~;,. "*“f“e.u. mermurg
:: esteem. Mm- . . 5,,

 

so 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.23 Electrical Conductivity and Thermopower data for Anglgstezo

05 ""l""l""l""l""l""l""I""'

 

t AngwaTem lngot1 (Bottom) ;
0.4 L . -‘
I m l
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" °°°°° / " "
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I a: ‘
o h A A
50 1 00 1 50 200 250 300 350 400 450
Temperature (K)

       

LALul-AA‘L-‘A-IM I

 

 

Figure 5.24 Figure — of — merit ZT of a AngnSbTezo Ingot

107

Similar trends are observed in another sample from the same ingot, although
different values are obtained. We observe a slight decrease in electrical conductivity with
annealing, while the thermopower magnitude increases a little over it’s pre — annealed
value (see Figure 5.26).

The thermal conductivity decreases a little during the 400K - 80K measurement
run afier the annealing, and drops further during the 80K — 400K measurement run

beyond 225K as indicated in Figure 5.25.

 

 
   

4.5 'fi'I""I""I""I""r'**'fivvvrvvvv

L 1
. 'o AnglsSchm lngot( Bottom) -

A 4 I- . 1

=2 t 019; o Pnrannam ‘

At : c 'Q, o Poetanneal )

E35 - " .. (4OOK-12hrs) j

E , 0:3 oh I

g: L 623;: 1

£3 3 . dh° ° 55?} .

G : O %.

825'

"a ' : °°

E 1

fig 2 r 9 .
E

 

 

   

 

L5 ‘ " ‘ "
50 100 150 200 250 300
Temperature (K)

350 400 450

Figure 5.25 Variable temperature thermal conductivity data for AnglngTezo

108

 

   
 

 

 

 

2000........... ..........................'-50
_ "‘" Agl’bmeTe20 Ingot l (Bottom) fi’mnw :
")Sl'dfiflea ‘
E ' - -100 :1
a 1500 ' . g
b ' -' -150 8
'5 . _‘
"3 : s
D F ' B-
E 1000 - -. -200 g;
' 4 o
2 1 a
g - a
“E r250 e
3 500 - ‘ <
a 1 5
, d -300
. 0 dc conductivity
.0 ac conductivity " "
0 A A A A I A A l A A A A IA_A A I l I I A A A A ‘350
50 100 150 200 250 300 350 400 450

Temperature (K)

Figure 5.26 Electrical conductivity and thermoelectric power data for AnglngTezo

 

 

 

0.5 ‘V'l""""'l""I""I""I""I"".
; Ang‘BSbTezo lngott (Bottom) 1
L .

. O
: 83,-” :
0.3 .- o ab.0000 -.
it: : o . :
0.2 ' 0 ZT (dc) pre-anneal j
0 ZT (dc) post-anneal 1
n d
'. 33“ :
0.1 _ 69f. .

a”.
‘1‘ I I I I I

 

50100150200250300350400450
Temperature (K)

Figure 5.27 Figure - of - merit ZT ( considering dcconductivity) of AnglngTezo

109

We observe a significant enhancement in the figure - of — merit for the post -
annealed sample (~ around 0.4 maximum).

Anisotropy Effects

Another interesting property investigated was the anisotropy of these compounds.
The samples have been characterized, with the temperature gradient along and
perpendicular to the crystal growth axes, with some interesting results.

Figures 5.28 and 5.29 show measurements of a AnglngTezo sample from
another ingot. There is a noticeable decrease in thermal conductivity along the growth
direction (about 0.2 W/mK at room temperature). We observe a sharp decrease in
electrical conductivity perpendicular to the growth axes, while the thermopower
magnitude increases substantially (almost by -100uV/K at room temperature) to ~
SOOuV/K at 400K.

Measurements for another AnglngTezo sample cut from the same ingot (but
from the middle of the ingot) are shown in Figures 5.30 and 5.31. We observe opposite
behavior in thermal conductivity of this sample (it is higher along the growth direction),
thermopower magnitude (which also increases sharply along the growth direction) and

electrical conductivity (which is lower along the grth direction).

110

 

 

 

 

 

 

 

3 "j'U""U""I'f"I""I""l""l""
Agl’busw‘ezo Ingot 2 (top) .
Q 0 Perpendicular to Growth direction
E 2.5 - 0 Parallel to Growth Direction '
E ' ‘
i? ' i
*5 0am, ‘
a 2 ’ 1
2 ’ mm ‘
Ti : OW :
g 1.5 " 4‘- -i
y I
1 A A A A I A A A I A A A A I A AAA—A I A A A A I A A A A I A A A A I A A A

 

50 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.28 Thermal conductivity data along different axes for a AnglngTezo sample

 

 

 

 

 

 

 

 

 

 

 

 

r"'I""U""U'Tr“—I""I""I‘firri"" 0
A 560 : Agpbnsorczoingoiz (Top) 0 Conductivity (Perpendicular) I
g : ' Conductivity (Parallel)
a 480 '- ‘A‘ -100
v : a ‘A. A Thermopower (Perpendicular) . 5!
g ' 'A°A “‘A e Thermo r (Parallel) G
.2 400 I: 0. AA “A‘ pom a
. ' . o
‘3 32 0 -_ - -200 %
E - i g:
8 = - °
240 _- ‘ o“
g . - -300 g
g 160 f - €<
m I . 3
I i
0 ' r
' A A A A I A A A A I A U A I A A A A I A A A A I A A J4 I A A A AAI A A A A -500
50 1 00 1 50 200 250 300 350 400 450

Temperature (K)

Figure 5.29 dc conductivity and thermopower along different axes for AngmeTezo

111

 

 

 

 

 

 

 

3 "*'I""I'*"l""l""I""I""I""
. AngmeTc20 Ingot 2 (Middle) .
O Perpendicular to Growth Direction
g 2.5 - . 0 Parallel to Growth Direction '
i i '
a . Moo
:5 ' @0000
T5 2 - 000 -
3 . W i
0 .
Ti ' ‘
E - a
.5 1.5 L' '
1 A A A A I A ALA L A A A A I A A A A4 A AJAI A A A A I A A A A I A A A A i
50 1 00 1 50 200 250 300 350 400 450

Temperature (K)

Figure 5.30 Thermal conductivity along different axes for AnglngTezo

 

 

 

 

 

 

 

2500 ' *fi ' T ' '—f ‘ I ' ' ‘ ' I ‘ ' ' ' I ' ' ' ' I ' ' ' ‘ I ' ' ' ' I ' ' ' ' ‘
I ASPb"SbT¢201"80t2 (Middle 0 Conductivity(Perpendicular) ; o

’5‘ » - Conductivity(Parallel) .
o ' . _‘
@2000 ' Macao“ A Thermopower(Perpendicular) : 8'
Q . a. “MMAMAA ‘ Thermopower(ParaIlel) . .100 3
22 ' i. Moo : o
' m
§1500 ~ “a. M ‘ §
.0 b A“‘ AMA ___’ .: .200 0-0
C ’ 0o “‘A Wm ' (:9

8 ’ O ‘5‘ AAAA 1
. 0° 5“ A ‘ t
S 1000 - 000 “‘A ‘ g
's. b 000 “‘A‘ q _300 CD
4- ' <—— 000 5“. q ’1
g : 0000 M...“ : t<
500 '- ‘e ‘A - \
8 . COMM mm.“ : -400 25

i W i

o A A A A 1+1 A A I A A A A I A LA AJ A A A A I A LA A_I A A A A I A A A A -500
50 1 00 1 50 200 250 300 350 400 450
Temperature (K)

Figure 5.31 DC Conductivity and thermoelectric power for Anglgstezo

112

 

 

 

 

0.5 '-"Iv'v'l""I*"'I""r"f'I""I"" 0-5
: A ZT(ac)Perpendicular 0 ZT(dc)Perpendicular
_ 0 ZT(ac)Parallel A ZT(dc)Parallel .
0.4 - ' - 0.4
, . J
Ang SbTe Ingot 2 (Middle)
II 20 '
i 5333:;
b ‘ I
A 0.3 - fix“ - 0.3
8 I at“ I E
E . r!” . (I;
0.2 " f M " 0.2 v
b A AMAAA ‘
b J omoowaéxnoo MMAwOOO ‘
' MM 000° °° 00000000 '
. MM6 0 .
0.1 - 6038300000 - 0.1
l e
0 AA. 1 1AA... AAALAAAAIAAA lAAAAJAAA. o

 

 

 

200 250 300 350 400 450
Temperature (K)

50 100 150

Figure 5.32 Figure — of — merit variation with different axes for AnglngTezo

Figure - of — merit calculations reveal, quite understandably a marked difference
in ZT values for measurements along the different axes, with a ZTmax ~ 0.38 at 375K
along the growth axes.

Further investigations of this nature would provide a better understanding of the
material, especially the doping profile variations across the ingot. Another interesting
observation is the variation in the measured values for samples cut at different levels
from the same ingot. We observe better thermoelectric properties for samples cut from
the bottom of the ingot, as compared to the ones out from the top, suggesting a possible
doping concentration gradient along the grth axes.

Another promising system from the same family of compounds is the
Ag6PbSb6Te13 system with thermoelectric properties as shown in Figures 5.33 and 5.34.

The thermal conductivity is unusually low in this material (~ 0.75 at RT), which is

113

promising for thermoelectric applications. Electrical conductivity is about 95 S/cm while
the thermoelectric power is high, ~280 uV/K at room temperature indicating p — type
conduction. The figure — of - merit is about 0.42 at 400K and increasing with

temperature.

 

2 fivv'vvvv'vvvr'vvvv‘vvvv'ffirvv'vvvv'vv

» Agbl’bSbéTc”

_
M
I
1
A I A A A A I A A A A

 

Thermal Conductivity (W/m-K)
O
1,. .—

 

 

AAAAIAAAAIAAAAIAAAAIAAAAIAA—A—‘IAL_A_AIAA_AA

0
50 100 150 200 250 300 350 400 450
Temperature (K)

 

Figure 5.33 Variable temperature thermal conductivity data for Ag6PbSb6Tel3

 

 

400 ffi 'j I V I V ' V I V ' ' ' I ' ' ' ' I V V ‘ ' I ' ' ' ' I V ' ' V ‘ 400

E 350 :- .‘kgfil’bSbéTe'3 :
2 : 1 350 .5!
a 300 ’- : o
‘3 5 5 300 g
2: 250 - . ._
8 1 I 8
'0 : l ‘3.
8 200 .- - 250 n
U . 1 g
'3 1 . g
.0 150 "' i a
58 E - 200 E":
53 100 :- . <
0 ~ 1 7?:
-o ; . 150 V

50 _- :

 

 

 

0 100
50 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.34 DC conductivity and thermoelectric power for Ag6PbSb6Te13

114

Figures 5.35 and 5.36 show thermoelectric measurements of another compound of the

same system, AngmeTeig.

 

4 'V'V'VV 'VT' V V U 'j I V V ' V ' ' V ' tv' ' I V V V‘ 'Vfi‘rfii

Ang SbTe
I6 is

to s»

01 (a) GI

I I I I
I A A

Thermal Conductivity (W/m-K)

N
j

 

b

b

 

 

L A A A l A A A A l L L A A

 

1 AAAAIAAAAIAAJAIAAAAIAAAAJAAAAIAAAAIAAAA

50 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.35 Variable temperature thermal conductivity for a Ang16SbTC|3

 

 

 

 

 

2000 - 0
E I
o I-
@1600 ‘1”?
a ’ 1 a
.2 3
§ . ~-200a>
131200 ‘ 9’
C , 2.
O _ O
o c?
§ “3003
'= 800 51
3 - E
LU
8 “4003

400- 1

. L W-soo

50 100 150 200 250 300 350 400 450
Temperature (K)

Figure 5.36 DC conductivity and thermoelectric power for AngmeTelg

115

Reasonably high values of electrical conductivity (~7OO S/cm) and thermoelectric
power (~ -190 uV/K ) at room temperature are reported for the compound AngmeTelg.

The figure — of — merit ZT reaches a value of 0.5 at 400K(Figure 5 .37).

 

0.6 V V V V I V V V V I V V V V ‘l V V V V I V V V V I V V V V I V V V V I V V V V
I

Ang SbTe
16 II ‘
0.5 " " a

0.4 .-

A 14 1444A A A A

no.3

0.2

V IV V V

0.1

 

V V V V I V V V

 

 

I A-Alfl-ALIAAAAI AA-IAAAA

200 250 300 350 400 450
Temperature (K)

ALA; LA. I

o A A
50 100 150

 

Figure 5.37 Figure — of - merit ZT for Ang16SbT€13

116

Chapter 6
6.1 Conclusion

The primary objective of this research was to design and assemble a charge
transport characterization system and investigate thermoelectric properties of several new
materials by simultaneous measurements of electrical conductivity, thermoelectric power
and thermal conductivity. This objective has been realized by taking a number of
different measurements, as described in the preceding chapters. A slow ac technique,
similar to the one developed by Maldonadoz, has been successfully implemented for
thermoelectric measurements in the LabVIEWTM programming environment. Typical run
times for 4 samples from 80K — 400K in 5K steps are about 3 — 4 days, depending on
pulse period and temperature stabilization.

System reliability and performance has been evaluated by characterization of
several standard, commercially available materials (stainless steel, Pyrex® glass and
bismuth telluride). Results of these measurements are in good agreement with reference
data, indicating successful implementation of the system.

Several material systems of the general formula AmBanszn (where A is K or
Ag, B is Pb or Sn, M is Bi or Sb, and Q is Te, Se, or S) have been characterized and
studied. Table 6.1 summarizes the physicochemical and transport properties of the most
promising members of the system. The temperature dependence of the Seebeck
coefficient for most of the compounds indicates that these are narrow band—gap
semiconductors, one of the requirements that a material must follow in order to be a
viable TE material at or below room temperature. If the band gap is too large, the

conductivity will be too low; conversely; if the band gap is too small, minority carriers

117

can be created that adversely affect the Seebeck coefficient. Most members of the system
show a metallic temperature dependence of conductivity, which decreases with increase
in temperature. The thermal conductivity is quite low, especially in the Ag/Pb/Q/Te (Q =
Bi,Sb) system where high Seebeck coefficients (typically 200 uV/K at room temperature)

are simultaneously exhibited.

Table 6.1 Physical and transport properties for members of different systems

 

 

 

 

 

 

Compound SRT cm KRT l5g (eV)3 ZTRT
(uV/K) (S/cm) (W/mK)

Anglsstezo -155 946 1.99 ~ 0.3 0.35

AngwaTeig -l71 708 2.19 ~ 0.3 0.3

Ag5PbSb6Te|3 285 100 0.81 ~ 0.3 0.3

Ang3BiTes -80 400 2.7 ~ 0.28 0.028

AngBiTe; -40 203 0.74 ~ 0.28 0.013

 

 

 

 

 

 

 

 

Quaternary Bismuth Selenides A1-xM4-xBin+xSe2. (A = K, Rb, Cs; M = Sn, Pb)
have also been characterized, with interesting results. These compounds possess room
temperature thermal conductivities of ~1 W/mK, which is lower than that of BizTe3.
Although the electrical conductivity and thermoelectric power are moderate, further
investigations could lead to more promising results.

Ternary and quaternary alkali metal bismuth chalcogenides, especially the

Cs/Bi/T e system and their solid solutions, exhibit promising thermoelectric properties.

 

2 Please see Ref. 3 (chapter 3)

118

All CsBi1-bexTe6 (x < 0.8) showed p—type behavior with a maximum thermoelectric
power of ~150uV/K at different temperatures. The thermoelectric power data appear to
be very dependent on temperature and show a maximum between 250K and 350K.

Although optimum levels have not yet been reached, we believe additional
improvements in TE performance in these materials are possible with further exploration
of doping agents and solid solutions. Band structure calculations for these compounds
should provide firrther insight into their electronic properties.
6.2 Recommendations

The information obtained during this research has contributed to a better
understanding of several new thermoelectric materials, however, a few improvements in
the measurement technique would help produce better results. For instance, a better
fitting routine to the temperature gradient calculations would improve measurement
accuracy and reliability. In particular, a fitting routine that is not as susceptible to noise in
the AT data would be an improvement. A few results have indicated possible radiation
losses, particularly at temperatures beyond 300K, affecting thermal conductivity
measurements. Minimization of these effects could be achieved by providing isothermal
conditions around the sample with the help of another radiation shield, which maintains a
temperature profile identical to that across the measured sample. Alternatively, additional
investigations of radiation losses as a function of temperature gradient may lead to a
method of extrapolation to zero temperature gradients where the radiation losses are zero.

Sample mounting for complete characterization turns out to be a lengthy process,
affecting system throughput to a certain extent. Simplification in the mounting

method/configuration (easily installable point contact thermocouples, for instance) for

 

3 Band gap data from research collaborators

119

faster sample mounting would substantially improve the rate of sample characterization.
Good thermal contact of the sample with the stage is an essential requirement for accurate
measurements. The present methodology includes the use of gold paste in order to meet
the requirement. An alternative method would be to solder the sample directly to the
stage (using solders like woods metal, or indium for instance), possibly decreasing
thermal resistance at the junction. Other improvements within the software might include
saving to the data files, the standard deviation of measurements such that error bars could
be incorporated in the data plots. The thermoelectric power is currently obtained by
fitting the AV vs. AT data, which occasionally exhibits some looping due to a temperature
difference between the locations of where AT and AV are measured. An improvement in

the fitting of this data could improve the accuracy of the thermopower measurements.

120

REFERENCES

121

10.

11.

12.

13.

14.

15.

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H. J. Goldsmid, “Conversion Efficiency and Figure-of-merit”, in CRC Handbook of
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T. M. Tritt., M.G. Kanatzidis, et al, Thermoelectric Materials — New Directions and
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7. K. Fang, Private Communication.

125

 

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