SCANNING PROBE MEASUREMENT SYSTEM FOR ROOM TEMPERATURE
THERMOPOWER
By
Marvell Mukongolo

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Electrical and Computer Engineering
2011

ABSTRACT
SCANNING PROBE MEASUREMENT SYSTEM FOR ROOM TEMPERATURE
THERMOPOWER
By
Marvell Mukongolo

The development of new and established materials for use in thermoelectric devices, and
the development of new measurement techniques for the advancement of research in the field are
major initiatives of thermoelectrics research at Michigan State University. To achieve this,
measurement systems created for this research have to be accurate and as well as diverse in their
capabilities. A new measurement system with scanning probe capabilities has been developed to
measure thermopower at room temperature. The degree of homogeneity of bulk thermoelectrical
materials can be obtained with thermopower measurements due to the fact that the thermopower
of a semiconductor is related to the concentration of impurities in the material. Devices made of
inhomogeneous or segmented materials are known to have increased efficiency compared to
devices with homogeneous composition. The ability to characterize in-homogeneity in devices
adds a new dimension to the type of research that can be achieved. This thesis presents an
introduction to the room temperature thermopower scanning probe. The system is designed to
operate in an open air, room temperature environment. The system is fully automated with
LabVIEW software used for control and data collection purposes. Reference materials were used
to verify the systems accuracy. A study of segmented p-type materials composed of Bi2Te3LASTT (Ag(Pb1-xSnx)mSbTe2+m) and n-type materials composed of Bi2Te3-LAST
(AgPbmSbTe2+m) is also be presented.

ACKNOWLEDGEMENTS
I would like to take this opportunity to thank Dr. Timothy Hogan, for his unwavering
support, guidance and encouragement throughout the years I have had the opportunity to be his
student. Being a part of his research group has given me valuable experience and has helped me
reach greater heights in my pursuit of knowledge.
I would to thank Dr. Chun-I Wu and Dr. Jonathan D’Angelo, for their guidance and
mentorship throughout my research. I will forever be grateful for the mentorship I received from
these two gentlemen.
I would like to thank Dr. Donnie Reinhard and Dr. Virginia Ayres for taking the time to
review my thesis and serve on my thesis committee.
I would like to thank Dr. Percy Pierre and Dr. Barbara O’Kelly for their guidance in
helping me attend graduate school and their support while I was in graduate school.
Finally, I would like to thank my mother, brother and sister for providing me the
necessary motivation to succeed in my endeavors.

iii

TABLE OF CONTENTS
LIST OF TABLES ......................................................................................................................... vi
LIST OF FIGURES ...................................................................................................................... vii
Key to Symbols ............................................................................................................................... x
Chapter 1: Introduction to Thermoelectrics .................................................................................... 1
1.1 Introduction ........................................................................................................................... 1
Chapter 2: Thermoelectric Principles ............................................................................................. 3
2.1 Introduction ........................................................................................................................... 3
2.2 Seebeck Effect ....................................................................................................................... 4
2.2.2 Seebeck Effect in Insulators, Semiconductors, and Metals ........................................... 5
2.2.3 The Seebeck Effect and Metals ................................................................................... 10
2.3 Peltier Effect ....................................................................................................................... 12
2.4 Thomson Effect .................................................................................................................. 13
2.5 Electrical Conductivity........................................................................................................ 14
2.6 Thermal conductivity ......................................................................................................... 14
2.7 A Good Thermoelectric ...................................................................................................... 15
2.8 Thermocouples ................................................................................................................... 17
2.8.2 Reference Junctions ...................................................................................................... 18
2.8.3 Ice Bath Reference........................................................................................................ 18
2.8.4 Practical Thermocouple Circuits .................................................................................. 19
2.9 Thermoelectric Devices....................................................................................................... 21
Chapter 3: The Room Temperature Thermopower Scanning Probe ............................................ 23
3.1 Introduction ......................................................................................................................... 23
3.2 History ................................................................................................................................. 23
3.3 Room Temperature Thermopower Scanning Probe ............................................................ 26
3.3.1 Objectives ..................................................................................................................... 26
3.3.2 X-Y-Z Translation Stage and Motors ........................................................................... 27
3.3.3 Measuring Equipment................................................................................................... 31
3.3.4 Probe ............................................................................................................................. 33
iv

3.3.5 LabVIEW Program Overview ...................................................................................... 33
3.4 Thermopower Calculation Techniques ............................................................................... 37
3.4.1 Pulsed technique for measuring thermopower ............................................................ 39
3.4.2 Method of Measuring Thermopower Using Direct ∆T Measurements ........................ 43
3.4.3 Thermocouple Method for Measuring Thermopower .................................................. 47
Chapter 4: Reference measurements ............................................................................................. 49
4.1 Introduction ......................................................................................................................... 49
4.2 Bi2Te3 Reference Measurements ........................................................................................ 50
4.3 Constantan ........................................................................................................................... 52
4.4 Low thermopower material measurements ......................................................................... 56
4.5 Error Analysis ..................................................................................................................... 56

Chapter 5: Measurements of segmented thermoelectric bulk material composed of Bi2Te3 and
LAST/LASTT. .............................................................................................................................. 66
5.1 Introduction: ........................................................................................................................ 66
5.2 PECS ................................................................................................................................... 67
5.3 LAST/LASTT ..................................................................................................................... 67
5.3.1 Preparation of LAST/LASTT ....................................................................................... 68
5.4 Preparation of Bi2Te3.......................................................................................................... 69
5.5 Scanning Probe Measurements ........................................................................................... 72
Chapter 6: Conclusion and Future Work ...................................................................................... 80
6.1 Conclusions ......................................................................................................................... 80
6.2 Future Work ........................................................................................................................ 80
Appendix A ................................................................................................................................... 83
Bibliography ................................................................................................................................. 86

v

LIST OF TABLES
Table 2-1: Seebeck coefficients of various metals ……………………………………………...11
Table 2-2: Bi2Te3 alloys…………….…………………………………………………………...16
Table 4.1: The coefficients for the fit of the thermopower constantan ………………..………..53
Table 5.1: EDS analysis of area 1 in SEM image of LAST/Bi2Te3 sample…………………….75
Table 5.2: EDS analysis of area 2 in SEM image of LAST/Bi2Te3 sample…………………….75
Table 5.3: EDS analysis of area 1 in SEM image of LASTT/Bi2Te3 sample…………………...78
Table 5.4: EDS analysis of area 2 in SEM image of LASTT/Bi2Te3 sample…………………...78
Table A-1: Material composition of thermocouples and their temperature ranges……………...83
Table A-2: Coefficients of the calibration equation for voltage as a function of temperature
(eq.2.22) for type-T thermocouples……………………………………………………. 83
Table A-3: Coefficients of the calibration equation for temperature as a function of voltage
(eq.2.23) for type-T thermocouples……………………………………………….….... 84

vi

LIST OF FIGURES
Figure 2.1: The Seebeck Effect……………………………………………………………………5
Figure 2.2: Ideal Insulator…………………………………………………………………………7
Figure 2.3: Metal………………………………………………………………………………..…9
Figure 2.4: Peltier Effect…………………………………………………………………………12
Figure 2.5: Thomson Effect……………………………………………………………………...13
Figure 2.6: Thermocouple………………………………………………………………………. 17
Figure 2.7: Thermocouple Circuit with reference junction……………………………………. 18
Figure 2.8: Thermocouple Circuit with RTD as reference ……………………………………...19
Figure 3.1: Schematic diagram of apparatus for calculating thermopower using a method similar
to the Wheatstone bridge circuit……………………………………………………….. 25
Figure 3.2 UCN5804B Stepper Motor Driver………………………………………………….. 29
Figure 3.3 National Instruments USB-6501schematic…………………………………………. 30
Figure 3.4: X-Y-Z Three Motor Control Circuit layout ………………………………………. 31
Figure 3.5: Data Collection equipment…………………………………………………………. 32
Figure 3.6: Scanning probe design……………………………………………………………… 33
Figure 3.7: LabVIEW software flow chart………………………………………………………36
Figure 3.8: LabView user interface…………………………………………………………….. 37
Figure 3.9: Scatter plot of V1/(V2-V1) data……………………………………………………..38
Figure 3.10: Scatter plot of V1/(V2-V1) data with linear fit…………………………………….39
Figure 3.11: Pulsed Technique measurement diagram…………………………………………..40
Figure 3.12: An illustration of Method of Measuring Thermopower Using Direct ∆T
Measurements…………………………………………………………………………... 44
Figure 3.13: Voltage/∆T data of constantan sample with the Cu contribution not yet removed..46
Figure 3.14: Corrected Constantan Thermopower Data…………………………………………46
Figure 3.15: An illustration of the Thermocouple Voltage Measurements Method for Calculating
Thermopower using copper-constantan thermocouples…………………………………48

vii

Figure 4.1: N-type Bi2Te3 reference measurement……...............................................................51
Figure 4.2: P-type Bi2Te3 reference measurement………………………………………………52
Figure 4.3: The thermopower of constantan from 290K to 680K……………………………….54
Figure 4.4: cylindrical piece of constantan………………………………………………………54
Figure 4.5: Constantan Thermopower Data…………………………………………………….. 55
Figure 4.6: Constantan measurement errors……………………………………………………. 55
Figure 4.7: The expected values of ∆T vs. V2 –V1………………………………………………57
Figure 4.8: Expected values of V1 and V2 for Cu .……………………………………………... 58
Figure 4.9: Expected and measured values of V1 and V2 for Cu………….…………..…………59
Figure 4.10: Expected and measured values of V1 and V2 for constantan...……………...……. 60
Figure 4.11: Measured values of V1 and V2 for constantan…………………………………….. 61
Figure 4.12: Expected values of V1 and V2 for nickel….……………………………………..... 62
Figure 4.13: Expected and Measured values of V1 and V2 for nickel..……………………….... 63
Figure 4.14: Nickel thermopower data ……………..………………………………………….. 64
Figure 4.15: Measured values of V1 and V2 for nickel…………………………………………. 65
Figure 5.1: PECS system at MSU………………………………………………………………..67
Figure 5.2: Temperature and Pressure profiles for LAST/LASTT PECS processing………….. 68
Figure 5.3: LASTT coin after PECS processing…………………………………………………69
Figure 5.4: Bi2Te3 powder placed on top of PECS processed LAST/LASTT material………... 70
Figure 5.5: Finished PECS processed Bi2Te3 and LAST……………………………….……….71
Figure 5.6: Optical microscope image of Bi2Te3 and LAST surface after processing………… 71
Figure 5.7: LAST/Bi2Te3 scan across the center of the sample (as shown in the inset)….……..72

viii

Figure 5.8: LAST/Bi2Te3 scan at 1mm behind the first scan at the center of the sample……….73
Figure 5.9: SEM surface image of LAST/Bi2Te3 sample……………………………………… 74
Figure 5.10: LASTT/Bi2Te3 scan across the center of the sample………………………………76
Figure 5.11: LASTT/Bi2Te3 scan at 1mm behind the first scan …………………………...…...77
Figure 5.12: SEM surface image of LASTT/Bi2Te3 sample…………………………………….77

ix

Key to Symbols
Symbol

Discription

Eav
S

Average energy

kB

Boltzmann’s constant {1.38 × 10

ζ

η
σ

Chemical potential
Coefficient of performance for cooling applications
Concentration of free electrons
Concentration of free holes
Density of states
Efficiency of a thermoelectric generator
Electrical conductivity

σc

The electrical conductivities of carriers in the conduction band

σv
E

The electrical conductivities of carriers in the valence band

q

Elementary charge {1.602 × 10

EFO
ZT
U
L
λ

Fermi energy at 0K

τo
µ
τ
T

Mean scattering time

φ
n
p
N

Absolute Seebeck coefficient
-23

5

(J/K) = 8.616 × 10- (eV/K)}

Electron energy
-19

C}

Figure of merit
Internal energy
Lorenz number
Mean free path

κ

Mobility
Relaxation time
Temperature
Thermal conductivity

τm

Thomson coefficient

x

Chapter 1: Introduction to Thermoelectrics
1.1 Introduction
Due to advancements in technology and a greater demand for energy by the global
population, there has never been a greater need for complementary energy sources and
alternatives to fossil fuel than there is today. There is an impending crisis looming due to the fact
that more and more countries are becoming developed nations, while the world’s supplies of
developed energy sources are being depleted at an alarming rate. Considering the fact that the
world’s population is set to increase by three billion within a life time, the need to develop
alternative sources to diversify the world’s energy supply has never been greater. A larger
population, higher demand and depleting resources will likely lead to social unrest in the near
future if this crisis is not averted. The solution to this problem is very clear; efficient renewable
energy sources have to be found in order to avoid a global energy crisis.
Since the discovery of the Seebeck effect in the early 19th century, thermoelectrics (TE)
research has focused in part on using electric transport phenomena as a basis for energy
production. For years, researchers studying TEs have searched for ways to efficiently use the
advantages that solid state devices provide. These devices are silent, scalable and require no
moving parts. It is important to note that thermoelectrics is not viewed as a solution to the
dependence on fossil fuels, but with increased efficiency TEs can be a component in a wide
range of alternative energy technologies designed to help meet the greater demand from energy,
improve the efficiency of energy use, bring diversity to the world’s energy supply, and reduce
environmental pollution.
The Electronic Materials Characterization and Pulsed Laser Deposition Lab at Michigan
State University is one group in a collaborative effort between the Electrical and Computer
1

Engineering, Chemical Engineering and Material Science, Chemistry, Mechanical Engineering,
and Physics and Astronomy departments as well as other universities to develop new
thermoelectric materials. At the same time new measuring techniques are being developed in the
lab to further advance research in this field.
Greater understanding of TE materials requires various transport measurement techniques.
As part of this research a new measurement system has been developed to measure thermopower
(or absolute Seebeck coefficient) in an open air, room temperature environment. This system
allows for scanning probe capabilities for greater characterization abilities. The thermopower of
a semiconductor is related to the concentration of impurities, using this information an indication
of the degree of homogeneity of a sample can be obtained by measuring the thermopower from
point to point on the surface of a sample. Inhomogeneous TE devices have been known to
increase the efficiency of these devices and this concept will be discussed in further detail in later
chapters. This system can also help gain insight into doping effects near metal contacts.

2

Chapter 2: Thermoelectric Principles
2.1 Introduction
Thermoelectric devices can be used in cooling applications when electric energy is
supplied to the device or in power generation applications when heat energy is supplied to the
device. For cooling applications the coefficient of performance (φ) is defined as the heat flow
into the cold side of the thermoelectric cooler over the electric power supplied to the device. For
power generation the efficiency of the device (η) is defined as the electrical power output from
the module over the heat flow into the hot side of the device. As a generator, thermoelectrics can
utilize waste heat to help improve the efficiency of existing energy sources and help to minimize
adverse environmental impact. TE devices, however, have not reached a level of development
where they are efficient enough to replace mechanical electric generators or to compete with
devices such as compressor based refrigerators. The quality of a thermoelectric material depends
on the material properties of electrical conductivity (σ), thermal conductivity (κ), absolute
Seebeck coefficient (S) and temperature (T) through a figure of merit, ZT. A higher ZT results in
a higher efficiency material, and maximizing the figure of merit requires a large absolute
Seebeck coefficient, high electrical conductivity, and low thermal conductivity. The equation for
ZT is: [1]

ܼܶ ൌ

ఙௌ మ
఑

·ܶ

(2.1)

1

For comparison, a freon based refrigerator has a coefficient of performance (φ) of 1.4 . To
achieve this with a TE device operating near room temperature would require a ZT of 4-5 [2].
Bismuth telluride (Bi2Te3) is one of the oldest and best known TE materials, with a ZT of ~1 at
1

Detailed explanation of Coefficient of Performance and Ideal efficiency in section 2.9

3

room temperature when properly doped and alloyed with Bi2Se3 (for n-type materials) or Sb2Te3
(for p-type materials). One can see the lengths researchers still have to go to find TE materials
that can rival devices currently in use.
Maximizing the ZT of a sample requires knowledge of the transport characteristics of the
material. To have a high thermopower a material should only have a single type of carrier (ptype or n-type), with a low carrier concentration. Unfortunately low carrier concentrations result
in low electric conductivity [1]. Finding a balance between the three transport characteristics is
one of the challenges facing researchers trying to optimize TE materials to achieve higher ZT
values.
This chapter will give an in-depth explanation into the principles of thermoelectrics.

2.2 Seebeck Effect
In 1821, Thomas Seebeck discovered the first known thermoelectric phenomenon. The
equation for the absolute Seebeck coefficient is simply

ܵൌ

ௗ௏
ௗ்

(µV/K)

(2.2)

The sign of S represents the potential of the cold side with respect to the hot side. Both electrons
and holes diffuse from the hot side to the cold side of the sample, thus n-type samples which
have a majority of electrons yield negative thermopower voltage while p-type samples, having a
majority of holes yield positive thermopower voltages. Figure 2.1 shows an example of this
where a temperature gradient maintained across a homogeneous conductor without an external
flow of current causes electrons to diffuse to the area with lower energy states (colder side). The
accumulation of electrons on the cold side results in a voltage difference [4].

4

Hot

Temperature ∆T

Cold

Voltage ∆V
Hot

+
+
+

- Cold
-

Figure 2.1: (For interpretation of the references to color in this and all other figures, the reader is
referred to the electronic version of this thesis.)The absolute Seebeck Effect [4]
The potential difference ∆V across the conductor due to a temperature gradient ∆T is the
thermopower (or absolute Seebeck coefficient) of the sample. The term Seebeck effect is
applicable when there is a closed loop of two dissimilar materials with a presence of a
temperature difference between the two junctions. The net Seebeck coefficient of the loop is
considered to be the difference between the absolute Seebeck coefficients of the two materials
that make up the loop [5].

2.2.2 Seebeck Effect in Insulators, Semiconductors, and Metals [5]
The Seebeck coefficient usually depends on carrier densities, the energy of states
available to carriers, and the interactions of the carriers with one another and with the
environment around them. These reasons make computations of the Seebeck coefficient very
complex. One way the Seebeck coefficient can be derived is by considering an open circuit with
no current flow. States occupied by charged carriers yield no net current when a system is in

5

thermal equilibrium. Thermal and potential gradients drive carriers to unoccupied states
generating a net flow. This flow is opposed by scattering events which return the carriers to an
equilibrium state. The relaxation time (τ) characterizes this re-equilibrium. The electric current
density for an x directed flow influenced by an electric field –∂V/∂x and temperature gradient
∂T/∂x is as follows:
ି௤ డ௏

‫ܬ‬௡ ൌ ‫ܰܧ݀ ׬‬ሺ‫ ܧ‬ሻ݂ሺ‫ ܧ‬ሻሾ1 െ ݂ሺ‫ ܧ‬ሻሿሾ‫ ݒ‬ଶ ሺ‫ ܧ‬ሻ߬ሿ ቂቀ
௞

ಳ்

ൌ ‫ܧ݀ ׬‬σሺ‫ ܧ‬ሻ ቂቀെ

డ௏
డ௫

డ௫

ாି఍ డ்

ቁെቀ

ாି఍ డ்

௞ಳ ் మ డ௫

ቁቃ

ቁെቀ

௤் డ௫

ቁቃ

(2.3)

Where N(E) is the density of states, v(E) is the carrier velocity, ݂(E) = 1/{exp[(E-ζ)/kBT]+1} is
the Fermi distribution function for carriers of energy E and σ(E) is the energy dependent
electrical conductivity, q is the charge of the current carriers (-1.602x10

-19

C for electrons), kB is

Boltzmann’s constant and ζ is the chemical potential. From equation 2.3, the Seebeck coefficient
can be obtained when there is an open circuit (Jn = 0).
ିଵ ‫ ׬‬ௗሺாሻఙሺாሻሾாି఍ሿ
∆ܶ
௤்
‫ ׬‬ௗሺாሻఙሺாሻ

∆ܸ ൌ ቀ ቁ
ିଵ

‫ ؠ‬ቀ ቁ ‫ۃ‬ሾ‫ ܧ‬െ ߞሿ‫ۄ‬σሺ୉ሻ ∆ܶ
௤்

(2.4)

Equation 2.4 shows the potential drop across a material in response to a temperature gradient.
The Seebeck voltage ∆V is proportional to the average of E – ζ with respect to σ(E), this is
defined by ‫ۃ‬ሾ‫ ܧ‬െ ߞሿ‫ۄ‬σሺ୉ሻ .
6

For insulators the Seebeck coefficient is usually greater than kB/|q|=86µV/K (|q| denotes
the absolute value of the charge of an electron) and in some cases this can be as much as 1mV/K.
Conversely in metals, the carrier density is a significant fraction of the density of thermally
available states, which explains the low value of the Seebeck coefficient in electrical conductors
(usually under 10µV/K). To have a better understanding of the reason behind this difference in
Seebeck coefficients it is useful to rewrite equation 2.2 as
௞

ಳ
ܵ ൌ ቀ|௤|ቁ

‫ۃ‬ாି఍‫ۄ‬഑ሺಶሻ
௞ಳ ்

(2.5)

The entropy of a system of N carriers is (U– ζN)/T, U being the systems internal energy. Adding
a carrier changes this to (∆U- ζ)/T, ∆U=E is equal to the change in the systems internal energy.
Without kB, equation 2.3 can be described as “the average change of the entropy of a system
upon the addition of a carrier of energy E weighted by that carrier’s contribution to the dc
conductivity divided by qT”. With kB in the formula, kB/q appears as the natural unit with which
to measure the Seebeck coefficients magnitude.

Figure 2.2: Ideal Insulator [5]
7

Illustrated in Figure 2.2 is an ideal intrinsic insulator with the chemical potential near the center
of the energy gap between the valence and conduction bands. Most states in the valence band are
filled and holes are the charge carriers that populate this band. Most states in the conduction
band are empty, with electrons populating this band. The Seebeck coefficient can be written as a
weighted average due to holes in the valence band and electrons in the conduction band the
following way:

ܵൌ

௞ಳ

|௤|

‫ۃ‬఍ିா‫ۄ‬ೇ

ቂቀ

௞ಳ ்

ቁ ቀఙ

ఙೇ

ೇ ାఙ಴

ቁെቀ

‫ۃ‬ாି఍‫ۄ‬಴
௞ಳ ்

ቁ ቀఙ

ఙ಴

಴ ାఙೇ

ቁቃ

(2.6)

where σv and σc represent the electrical conductivities of carriers in the valence and conduction
bands respectively. Customarily the energies of valence and conduction band states are written
relative to their respective band edges, Ec and Ev: E = Ec – εc and E = Ev – εv. Equation 2.6
becomes
௞ಳ

ܵൌ
where ‫ܣ‬௏ ൌ

|௤|

‫ۃ‬ఌೇ ‫ۄ‬ఙೇ ሺாሻ
௞ಳ ்

఍ିாೇ

ቂቀ

௞ಳ ்

and ‫ܣ‬஼ ൌ

൅ ‫ܣ‬௏ ቁ ቀ
‫ۃ‬ఌ಴ ‫ۄ‬ఙ಴ ሺாሻ
௞ಳ ்

ఙೇ

ఙೇ ାఙ಴

ா ି఍

ቁ െ ቀ ௞಴ ் ൅ ‫ܣ‬஼ ቁ ቀఙ
ಳ

ఙ಴

಴ ାఙೇ

ቁቃ

(2.7)

.

Most of the time one of the two terms inside the square brackets in equation 2.7 dominates the
other. The Seebeck coefficient then becomes very large, >>kB/q, since (ζ-Ev) and (Ec-ζ) are
usually much larger than kBT. At higher temperatures this Seebeck coefficient falls with
increasing temperature in proportion to 1/kBT.

8

Figure 2.3: Metal [5]
Figure 2.3 shows the lack of a band gap in metals with the chemical potential of a metal residing
within the band of states occupied by carriers. In this case the energy of the carriers can be
expressed as E = ζ+ε, where ε is the energy of the valence or conduction band states. For this
particular case the product of the factors that involve Fermi functions, f(E)[1-f(E)], in equation
2.4, can be approximated as a Gaussian function of ε that has peaked at about ε=0 with a width
comparable to kBT. The Seebeck coefficient for metals can then be represented as

ܵൌ

಍

మ

మ
ିଵ ‫ ׬‬ௗఌேሺ஖ାகሻୣ୶୮ ሾି൬మౡా ౐൰ ሿ௩ ሺ஖ାகሻதக
ቀ ቁ
మ
௤்
಍
൰ ሿ௩ మ ሺ஖ାகሻத
‫ ׬‬ௗఌேሺ஖ାகሻୣ୶୮ ሾି൬

(2.8)

మౡా ౐

“Since the principle contribution of both integrals in equation 2.8 occurs at ε <kBT, S must be
small, <kB/|q|.” Evaluating equation 2.8 shows the Seebeck coefficient for metals vanishes at
absolute zero, rises proportionally with temperature, and is very small.
ଵ

|ܵ| ൎ ቀ ቁ
|௤|்

డ ୪୬ൣேሺாሻ௩ మ ሺாሻ൧
డா

9

ቚ ሺ݇஻ ܶሻଶ
஖

௞

௞ಳ ்

ಳ
ൎ ቀ|௤|ቁ ቀ

஖

ቁ

(2.9)

The typical chemical potential for metals is 1eV, while the value of kBT is usually 0.027eV,
using equation 2.9, at 300K the Seebeck coefficient is only a few micro volts per Kelvin.

2.2.3 The Seebeck Effect and Metals [4]
For a metal with parabolic energy bands, the average energy, Eav, per electron is:

‫ܧ‬௔௩ ሺܶሻ ൌ

ଷ

ହ

‫ܧ‬ிை ൤1 ൅

ହగమ ௞ಳ ் ଶ
ଵଶ

ቀ

ாಷೀ

ቁ ൨

(2.10)

where EFO is the Fermi energy at 0 K. From this equation it can be seen that when the
temperature is elevated, the average energy per electron also increases. This leads to the more
energetic electrons on the hot end diffusing toward the cold region until a potential difference ∆V
is built up which prevents further diffusion. For an electron to diffuse from the hot end to the
cold end of a conductor the electron has to do work against the potential difference ∆V across
that conductor which amounts to q∆V. This work decreases the average energy of the electron by
∆Eav, from Eav(hot) to Eav(cold):

‫∆ݍ‬V ൌ ‫ܧ‬௔௩ ሺܶ ൅ ∆ܶሻ െ ‫ܧ‬௔௩ ሺܶሻ
Substituting equation 2.10 into Eav gives
ଷ

ହ

‫ܧ‬ிை ൤1 ൅

ହగమ ௞ಳ ሺ்ା∆்ሻ ଶ
ଵଶ

ቀ

ாಷೀ

ቁ ൨െ
10

ଷ

ହ

‫ܧ‬ிை ൤1 ൅

ହగమ ௞ಳ ் ଶ
ଵଶ

ቀ

ாಷೀ

ቁ ൨

2

Expanding (T+∆T), replacing ∆T with δT and neglecting δT gives
ଷ

‫ ܸߜݍ‬ൌ ቂ ‫ܧ‬ிை
ହ

ହగమ ௞ಳ మ ଶ்ఋ்
ாಷೀ మ

ଵଶ

ቃ

Finally using equation 2.2 the Seebeck coefficient of metals is,

ܵൌ

గమ ௞ಳ మ ்
ଶ௤ாಷೀ

(V/K)

(2.11)

It should be noted that this equation was derived with the assumption that the conduction
electrons in the metal behave as if they were “free”. Also the electron energy E = K.E. =
2

1/2me*v and the effective electron mass me* are assumed to be constant with the velocity equal
to the Fermi velocity. The final assumption is that higher energy electrons have greater mean
speeds and longer mean free paths (λ) so they diffuse from the hot to cold ends of the conductors.
These assumptions only apply to “normal” metals, such as aluminum, potassium, sodium, etc.
Table 2-1 shows the Seebeck coefficients of various metals.
Table 2-1: Seebeck coefficients of various metals [4]
-1

Metal

S at 0°C (µV K )

Na
K
Al
Mg
Pb
Pd
Pt
Mo
Li
Cu
Ag

-1.6
-1.3
-1.15
-9
-4.45
4.47
14
1.7
1.38

-1

S at 27°C (µV K )
-5
-12.5
-1.8
-1.3
-9.99
-5.28
5.57
1.84
1.51

11

2.3 Peltier Effect [6]
Discovered by Jean Peltier in 1834, the Peltier Effect is a phenomenon in which heat is
liberated or absorbed when an electric current passes through an in interface between two
dissimilar conductors. The Peltier Effect is dependent on junctions between thermoelements
where bulk materials are required for this phenomenon to take place.

Cold reservoir
Tcold

n

p

Thot

I

Figure 2.4: Peltier Effect [6]
The temperature rises or falls at the interface of the two dissimilar metals based on electric
current going up or down a potential gradient. When the two metals are joined together there is a
potential difference between them, known as the Peltier Coefficient, ΠAB. The amount of heat
that is liberated or absorbed per unit time is proportional to the current applied; this relationship
is given by the equation
12

ܳ ൌ ߎ · ‫( ܫ‬W)

(2.13)

Since it is linearly dependent on current, heating or cooling at the junction is reversible by
changing the current direction. In 1857 Lord Kelvin derived the relationship between the
Seebeck and Peltier coefficients through a third effect called Thomson effect.
ߎ ൌ ܶ · ܵ (V/K)

(2.14)

2.4 Thomson Effect [7]
The third of the thermoelectric phenomena is the Thomson Effect. Discovered in 1854 by
the British physicist William Thomson later dubbed Lord Kelvin. He showed for current flowing
in a homogeneous conductor along an imposed temperature gradient, a reversible process of heat
production (or absorption) along the conductor exists. The Thomson Effect is characterized by
the Thomson coefficient τm, which is very significant theoretically because it is used to complete
the thermodynamic theory of thermoelectricity.

T1

T2 + ΔT

e-

Figure 2.5: Thomson Effect [7]
The quantity of heat generated per unit time can be expressed as

݀ܳ ൌ ሺ߬௠ ‫ܫ‬
13

ୢ୘
ୢ୶

ሻdx

(2.15)

where dT/dx is a temperature gradient along the homogeneous conductor carrying a current I in
the x-direction with dx being a unit length. The direction of the current relative to the
temperature gradient and the sign of τm determines whether heat is absorbed or liberated (i.e. if
current flows in the direction in the direction of rising temperature and τm>0 then heat is
liberated).

2.5 Electrical Conductivity[8]
In semiconductors charged particles (electrons and holes) move under the influence of
electric fields. This movement creates drift current inside the semiconductor. The magnitude of
the electrical conductivity is proportional to the density of the charge carriers in the material.

‫ܬ‬ௗ௥௜௙௧ ൌ ߪ‫ܧ‬௢
ቊ
ߪ ൌ ‫ݍ‬ሺ ௡ · ݊ ൅ ߤ௣ · ‫݌‬ሻ

(2.16)

Where
σ = electrical conductivity (S/m)
Eo = electric field
n and p = carrier concentrations
µ = mobility
q= elementary charge (+1.602E-19)

2.6 Thermal conductivity [1]
Thermal conductivity is a measure of ability of a material to conduct heat. The total
value of thermal conductivity κ takes into account the phonons traveling through the lattice

14

(κLattice) and electrons and holes transporting heat (κElectronic) can conduct heat through a
material. Equation 2.17 shows this,

ߢ ்௢௧௔௟ ൌ ߢா௟௘௖௧௥௢௡௜௖ ൅ ߢ௅௔௧௧௜௖௘ (Wm-1K-1)

(2.17)

The Wiedemann-Franz Law states that the ratio of the electronic contribution to κ and
electrical conductivity (σ) of a metal is proportional to the temperature. This is shown in equation
2.18,
఑

ఙ

ൌ ‫( ܶ · ܮ‬W

-1

K )

(2.18)

where

κ= thermal conductivity (W/m·K)
σ = electrical conductivity (S/m)
-8

-2

L = Lorenz number = 2.45x10 (W K

)

T = Temperature (K)

2.7 A Good Thermoelectric [9]
While doing research in thermoelectrics, one looks for materials with a figure of merit
(ZT) near 1 or higher at some temperature. Materials used in power generation have their peak
ZT values at high temperatures, while materials used in refrigiration have their peak ZT at low
temperatures. High ZT materials typically have the following properties: low thermal
conductivity (κLattice= 0.5 – 1.0 W/m·K), high mobilities for the electrons and holes (µ > 1000
2

cm /V·s), at least four equivalent band minima (be multivalley), and posses a large density of
states effective masses.
15

For applications near or at room temperature Bi2Te3 is the best known TE material. For
p-type samples it is alloyed with Sb2Te3, and for n-type samples it is alloyed with Bi2Se3. Table
2-2 shows several Bi2Te3 based materials with comparable room temperature ZT values.

Table 2-2: Bi2Te3 alloys

Material

ZT

Type

Bi24Sb68Te142Se6

0.96

p

Bi0.5Sb1.5Te3.13

0.9

p

(Sb2Te3)72(Bi2Te3)25(Sb2Se3)3

1.02

p

Bi1.75Sb0.25Te3.13

0.66

n

(Sb2Te3)5(Bi2Te3)90(Sb2Se3)5

0.96

n

(p-type and n-type materials can be formed with variations of the mole fraction of Te)
The structure of Bi2Te3 is stacked in a five-layer sequence (Te-Bi-Te-Bi-Te), with
hexagonal symmetry. This sequence repeats so two Te layers are adjacent on the boundaries of
these units. Bi2Se3, Sb2Te3, Bi2Te2Se, and other related compounds share this crystal structure.
Other known attributes to Bi2Te3 are: both valence and conduction bands have six equivalent
extrema, the energy bands are non parabolic and the effective masses are temperature dependent.
Finally Bi2Te3 is usually alloyed with Sb2Te3 to reduce thermal conductivity causing an increase
in its energy gap from 0.15 eV to 0.25 eV.
16

2.8 Thermocouples [10]
Thermocouples are commonly made of metals and utilize the Seebeck effect to measure
the potential difference between two dissimilar metals, which in turn can be converted into a
temperature. If there is a temperature gradient along the path of a wire, then there exists a
potential across the wire. With dissimilar metals electrically joined at one end, the difference in
the potentials across each wire is measured as the thermocouple voltage.

Cu

High
Low

Cu

Tt
Material P

Tj
2

Tt
Material N

Figure 2.6: Thermocouple
The relationship between the Seebeck coefficient, ∆V and ∆T in thermocouples can be derived
using equation 2.2. The ∆V due to the Seebeck effect is given by:
்

୘

∆ܸ ൌ ‫ ׬‬ೕሺS୔ െ S୒ ሻ݀ܶ ൌ ‫ ׬‬ೕሺS୔୒ ሻ݀ܶ
୘
୘
೟

೟

(2.19)

Where Tt is the temperature at the voltmeter terminals and Tj is the temperature at the junction of
the two dissimilar metals. As you can see from the above equation the net voltage (∆V) of metals
with equal Seebeck coefficients is zero. The relationship between the three components of
equation (2.19) makes it possible to have various types of thermocouples, making it possible to
use materials compatible with high or low temperature applications.

17

2.8.2 Reference Junctions
Thermocouples using two dissimilar wires only indicate temperature differences; in order
to measure the absolute temperature a reference junction is required as shown in Figure 2.7
where Tr represents the temperature of the reference junction, and Tj is the thermocouple
junction temperature.

Tr
T1
High
Low

Cu

2
Material P

Cu
T5

4

Tj
3

Material N

Figure 2.7: Thermocouple circuit with a reference junction

2.8.3 Ice Bath Reference
The National Institute of Standards and Technology (NIST) has developed tables for
temperature values versus thermocouple voltage. This was done for a variety of standard
thermocouples (Type: C, E, J, K, M, N, T). Using an ice bath (0 ºC) reference junction, reference
tables have been generated for standard thermocouples.
Polynomial fits to the reference data are often used to conveniently convert between
temperature and voltage for each thermocouple. To solve for voltage as a function of
temperature the following polynomial curve fit is commonly used,

ܸ଴௥ ൌ ‫ܨ‬ሺܶ௥ ሻ ൌ ܾ଴ ൅ ܾଵ ܶ௥ ൅ ܾଶ ܶ௥ଶ ൅ … ൅ ܾ௡ ܶ௥௡

18

(2.20)

For temperature as a function of voltage the following polynomial curve fit is used,
௠
ଶ
ܶ଴௥ ൌ ‫ܩ‬ሺܸ଴௥ ሻ ൌ ܿ଴ ൅ ܿଵ ܸ଴௥ ൅ ܿଶ ܸ଴௥ ൅ . . . ൅ܿ௠ ܸ଴௥

(2.21)

The coefficients for (2.20) and (2.21) are shown in Tables A-2 and A-3 of appendix A.

2.8.4 Practical Thermocouple Circuits
In a thermocouple circuit it may not be convenient to maintain an ice bath. Another
method is to maintain the reference junction at an arbitrary, but known, temperature. This allows
for the flexibility of only needing a simple temperature measurement device (i.e. resistance
temperature detector (RTD) or temperature sensor diode) to find a reference temperature instead
of devising a way to create an environment at 0°C (ice-bath).

Tr
T1
High
Low

2

Cu

Tj

Material P

Cu
4
RTD

T5

3
Material N

Figure 2.8: Thermocouple Circuit with RTD as reference.
To find the absolute temperature with a thermocouple using an arbitrary reference temperature,
the value of the voltage at the terminals of the voltmeter and can be determined by integration as
shown in equation (2.22).
்

்

்

்

V୫ୣୟୱ୳୰ୣୢ ൌ ‫ ׬‬ೝ ܵ஼௨ · ݀ܶ ൅ ‫ ׬‬ೕ ܵே ݀ܶ ൅ ‫ ׬‬ೝ ܵ௉ ݀ܶ ൅ ‫ ׬‬భ ܵ஼௨ · ݀ܶ
்
்
்
்
ఱ

ೝ

ೕ

19

ೝ

(2.22)

The first and fourth integrals in (2.22) account for the voltages developed by temperature
gradients in the lead wires from the voltmeter. Since these wires have materials with the same
thermopower (i.e. copper), it is assumed that the voltage developed is the same (i.e. T1 = T5) and
the two integrals cancel each other. The next step is to determine the temperature at Tr by an
independent method. Since Tr ≠ 0ºC the standard thermocouple calibration data cannot be
applied directly to equation (2.22). In this scenario let Vrj be the voltage generated between Tr
and Tj, which is also the voltage shown in equation (2.22).
்

ܸ௥௝ ൌ ‫ ׬‬ೕ ܵ௉ே ݀ܶ
்

(2.23)

ೝ

This can also be written as

ܸ௥௝ ൌ ‫ ׬‬ೕ ܵ௉ே ݀ܶ ൅ ‫ ׬‬ೝ ܵ௉ே ݀ܶ െ ‫ ׬‬ೝ ܵ௉ே ݀ܶ
଴
଴
்
்

்

்

ೝ

ൌ ‫ ׬‬ೕ ܵ௉ே ݀ܶ െ ‫ ׬‬ೝ ܵ௉ே ݀ܶ
଴
଴
்

்

where
்

(2.24)

்

(2.25)

ܸ଴௥ ൌ ‫ ׬‬ೝሺܵ௉ே ሻ݀ܶ
଴
ܸ଴௝ ൌ ‫ ׬‬ೕሺܵ௉ே ሻ݀ܶ
଴

V0j is the voltage of a thermocouple with Tr = 0°C and its measuring junction at Tj. V0r is the
voltage of a thermocouple with Tr= 0°C and its measuring junction at Tr. Vrj is measured by the

20

voltmeter, V0r can be calculated by using the value of the temperature measured independently
by an RTD, diode, or other temperature sensor in equation (2.20). Finally with these two values
the V0j can be calculated as

ܸ଴௝ ൌ ܸ௥௝ ൅ ܸ
௢௥

(2.26)

Using NIST data V0j can be converted to a temperature using the following polynomial.
ଶ
௠
ܶ௝ ൌ ‫ܩ‬൫ܸ௢௝ ൯ ൌ ܿ଴ ൅ ܿଵ ܸ଴௝ ൅ ܿଶ ܸ଴௝ ൅ . . . ൅ܿ௠ ܸ଴௝

(2.27)

2.9 Thermoelectric Devices
Thermoelectric devices are made of many couples wired electrically in series and
thermally in parallel, consisting of n-type and p-type thermoelectric elements in pairs.
Thermoelectric generators power externally connected electric loads, by converting the heat flow
through the device into electricity. The heat flow acts as a driver of electric current and the
temperature gradient provides the voltage (V= S·∆T). At any given operating point, the product
of the current and voltage determine the power output from the thermoelectric generator.
Conversely, for Peltier coolers the power is supplied externally by a dc power supply. The power
supply drives an external current (I) and heat flow (Q), thereby cooling the top surface due to the
Peltier effect (Q=S·T·I). For both devices heat flow through the device must be maintained by
appropriate heat exchangers [1]. The efficiency of a Peltier cooler can be quantified by the
coefficient of performance (which is the net heat absorbed/applied electric power) [3]:

ߔൌ

21

ொ೎

ூ·௏

(2.28)

where I·V is the electric power supplied to the module. The efficiency of a thermoelectric
generator can be defined as the power delivered to a load resistance R by the heat supply Q
which must be supplied to maintain a temperature gradient across the module [5].

ߟൌ

ூమ ோ
ொ

(2.29)

Impedance matching between the resistive load and the internal resistance of the thermoelectric
generator is needed in order to have maximum power output.

\

22

Chapter 3: The Room Temperature Thermopower Scanning Probe
3.1 Introduction
In the Electronic Materials Transport Characterization and Pulsed Laser Deposition
Laboratory, most of the measurement instruments are custom built with a specific goal in mind
as far as performance is concerned. The main focus of TE research is to find ways to increase the
ZT of materials as well as to identify new materials with promising properties for further
research. It is important that data collected by our measurement systems is accurate and at the
same time it is also important to the research that there is diversity in the capabilities of the
measurement systems in the lab. Cross correlation of measurements of the same property taken
on various systems helps to validate accuracy of the results. To build these systems one has to
be knowledgeable of the governing principles behind thermoelectrics as well as posses skills in
electrical and computer engineering. With these measurement systems the level of understanding
of the transport characteristics of various TE materials can be achieved which leads to
progressively better devices being produced. In this chapter the Room Temperature
Thermopower Scanning Probe will be introduced. This chapter will provide detailed
explanations about the design of the system.

3.2 History
Scanning probe microscopy is a method of microscopy in which an image is formed
using a physical probe to scan the surface of a sample. An image of the surface of a sample is
created by moving the probe over the surface of the sample and recording the probe to surface
interaction as a function of position. This concept can also be applied when measuring
thermopower. In some cases using multiple materials to create a TE sample can be advantageous
when it comes to increasing the ZT of the sample.

23

The first systems of this kind were developed to “obtain an indication of the degree of
homogeneity of a sample by the measuring of the variation of Seebeck coefficient from point to
point” [11]. The apparatus by Cowles and Dauncey presented in 1962 showed a method of rapid
scanning of the Seebeck coefficient of semiconductors. In their method a sample was placed on a
metal heat sink, a heated probe was lowered on top of the sample creating a temperature gradient
immediately below the probe. The temperature gradient was measured by two chromel-alumel
thermocouples, one on the probe tip and the other inside the heat sink. The voltage across the
sample was measured by the chromel wire. The ratio of the voltage across the sample to the
difference between the voltages at the two thermocouples was determined directly. That ratio
was equal to the Seebeck coefficients of the chromel-sample junction to the chromel-alumel
thermocouples. Their circuit obtained this value using the ratio of an adjustable resistance to a
fixed resistance, similar to a wheat stone bridge circuit. The heat sink was attached to a
microscope stage whose slides permitted movement in the X-Y directions, while the probes
movement was in the Z direction. There was no indication that these movements were motorized.
In 1986 Goldsmid [12] presented an improvement to Cowles and Dauncey’s system by
creating a simpler circuit requiring only a single balancing operation. Like the previous apparatus
the probe and heat sink have the same design, the only difference being the thermocouple used in
this case is a copper-constantan thermocouple. The voltage generated by the sample due to the
temperature gradient is applied across three resisters (R1, R2, R3) in series. The voltage generated
at the junctions of the copper-constantan thermocouples is applied between one end of resistor
R1 and a null detector which is connected to the sliding contact of the potentiometer. The sliding
contact is adjusted until the null detector indicates a balance bridge. If this balance is reached

24

when the resistance of the potentiometer winding is between the slider and the connection to R1
is xR2, then;

ܴଵ ൅ ‫ܴݔ‬ଶ
ܵ଴ ∆ܶ ܵ଴
ൌ
ൌ
ܴଵ ൅ ܴଶ ൅ ܴଷ
ܵ∆ܶ
ܵ
∆T being the temperature difference, S0 is the Seebeck coefficient of the copper-constantan
thermocouple and S is the required Seebeck coefficient of the semiconductor against copper.
This technique is illustrated in Figure 3.1.

Figure 3.1: Schematic diagram of apparatus for calculating thermopower using a method similar
to the Wheatstone bridge circuit [12].
25

In recent years technological improvements have made it possible for greater resolution
(up to 10µm) by similar apparatuses. In their study of functionally graded materials Platzek et.al
created the “Seebeck Scanning Microprobe” [13]. The probe is mounted on a three-dimensional
micro-positioning system. The system is fully automated; the measurements of the Seebeck
coefficient and the position of system are the synchronized by a computer. The probe is heated
to create a 3-4 K temperature difference and two copper-constantan thermocouples are used to
measure the temperature of the probe (T1) and temperature of the heat sink (T0). Two voltages
are measured between the Cu-Cu (V1) connections and the constantan-constantan (V2)
connections. Using these voltages the Seebeck coefficient of the sample was solved in the
following manner,

ܵ௦ ൌ

௏భ

௏మ ି௏భ

ሺܵ஼௨ െ ܵ஼௨ே௜ ሻ ൅ ܵ஼௨

(3.1)

This apparatus showed a two-dimensional image of the Seebeck coefficient of the surface of the
sample. This thesis work focuses on the development of a similar system for characterization of
materials and couples fabricated at MSU.

3.3 Room Temperature Thermopower Scanning Probe

3.3.1 Objectives
Using LabVIEW software, the thermopower scanning probe simultaneously measures the
voltage across a TE sample and the temperature between a copper probe touching the top surface
of the sample and a heat sink beneath the sample. The voltage across the sample will be
generated by heating the probe tip to a temperature between 5 – 10oC above the temperature of
the heat sink. The thermopower scanning probe uses copper-constantan thermocouples to
26

measure the temperature of the probe and the heat sink as well as the voltage across the sample.
Using these measurements the system determines the thermopower of the sample at specific
points such that a thermopower profile for the sample can be measured. The system can be
programmed to move vertically and horizontally with respect to the surface of the samples,
which allows for greater automation of the measurement.

3.3.2 X-Y-Z Translation Stage and Motors
The thermopower scanning probe is mounted on an X-Y-Z translation stage in order to
give it 3-dimensional movement. This allows for scanning in both horizontal and vertical
directions with respect to the surface of the samples. The movement is controlled by stepper
motors mounted on the stage. The range of motion is 5/8 inches on each axis. The 12 Volt-DC
stepper motors are mounted inside the frame of the stage.
Figure 3.2 shows the UCN5804B stepper motor driver used to control the stepper motors.
This driver has a simple design which requires only two digital signals; directional control and
step input. In this case that digital high-low signal is provided by the National Instruments USB6501and a LabVIEW program was created to provide a user interface to control the motor using
this digital I/O device.
LabVIEW stands for Laboratory Virtual Instrumentation Engineering Workbench and is
a software package provided by National Instruments, Inc. This is a graphical programming
language that can be used for instrument control, and for data acquisition and analysis. A virtual
instrument (VI) is a software routine (or subroutine) that provides an interactive user interface
such that software could be programmed to operate similar to the front panel of the instrument it
controls. The first step in programming the VI for this stepper motor operation is to calculate the

27

number of pulses required to move the stage the desired distance. In this case the stepper motor
is bipolar, with each step amounting to1.8 degrees, which equals 200 steps per revolution. The
stepper motors are attached to the micrometers of an X-Y-Z stage which rotate to move each axis
of the stage. One full rotation amounts to one millimeter of travel, which equals 200 steps by the
stepper motor. In the VI, the user provides a desired distance and a subroutine calculates how
many steps that distance would require. Once the number of steps required is calculated, this
value is used as the number of iterations for a loop. Within the loop, two calls to the digital
acquisition VI (or subroutine) are fed a high and low command. Figure 3.3 shows a diagram of
the digital I/O device and its connection to the stepper motor driver in Figure 3.2. Figure 3.4
shows the layout for a circuit with three drivers which control the automation of the scanning
probe. The directional control signal is sent out simultaneously with the step input signal. This
works by sending both signals as one package similar to a modulation of signals, where the
directional signal acts an envelope for the step inputs carrier signal. There are two directions,
each with a high or low value (i.e. left=high, right=low). Once a high or low command is
specified, then that direction is sent along with the step input signal.

28

Motor
Motor

12V supply

12V Supply

1
1
1

Pull Up
Pull Up
Resistor
Resistor

a1

b1

2
2
2

UCN5804B
UCN5804B
Stepper
Stepper
Motor Driver
Motor Driver

a2

3
33

5
1

15
6

Directional
Control
14

a3

b3

a4

b4

14
7

a1

12

5

b1

11
a2

b2

13
8
12
5

11
6

Step
Input

7
7
3

10

a3

b3

a4

b4

8
8
4

Directional
Control

13

6
6
2

16
5

15

b2

4
4
4

5V
Supply

16

10
7

9

9

8

GND
0

Figure 3.2 UCN5804B Stepper Motor Driver [14]

29

Step
Input

5V supply

TTL Signal

P0.0
P0.1
P0.2
P0.3
P0.4
P0.5
P0.6
P0.7

Figure 3.3 National Instruments USB-6501 schematic [15]

30

12V Supply

Ground
5v supply

Motor Controller

Figure 3.4: X-Y-Z Three Motor Control Printed Circuit Board Layout

3.3.3 Measuring Equipment
Keithley Instruments 2400 Digital Source Meter
This meter has four capabilities: current source, current meter, voltage source and voltage
meter. As a source it can supply up to 20 watts of power. For voltage measurements and sourcing
it ranges from ±1µV to ±200VDC. For current measurements and sources it ranges from ±10pA
to ±1A. It can take readings at a high rate of speed and has on board data storage. It is connected
to the computer via a General Purpose Interface Bus (GPIB) connection. In this application the
Keithley Instruments 2400 source meter provides current to heat up the probe.

31

Keithley Instruments 2002 Digital Multimeter
This meter is used only for voltage measurements and provides a resolution ±1µVon the
lowest scale setting. This meter contains an optional built in card which allows for ten input
channels for measurements, and allows for high speed switching between these channels. The
meter has on board data storage for measurement collection and averaging; it is also connected to
a computer via GPIB connection. For this system, the 2002 is used to measure thermocouple
voltages which range from ±1µV to a few millivolts.

Figure 3.5: Data collection equipment

32

3.3.4 Probe
A 1” long cone shaped piece of copper with a ¼” diameter is used as the probe. The
copper-constantan thermocouple is inserted into the probe through 1mm diameter hole and
spark welded to the probe on the sharp end. A nickel chromium wire wound around the probe is
used as a heater when current is passed through it, as shown in Figure 3.6. The copper probe
and nickel chromium wire are separated by a silicone encapsulate.

Figure 3.6: Scanning probe design

3.3.5 LabVIEW Program Overview
LabVIEW is a development environment similar to C and BASIC programming
languages, but it differs from its counter parts with its graphical language, “G”, where structures
of block diagrams and icons are graphically wired together to build the code. This software is
commonly used for data acquisition, instrument control, image analysis, data storage, data

33

analysis, and industrial automation. Subroutines are represented by graphical icons, which are
connected by wires for data transmission.
The scanning probe system is fully controlled via PC by LabVIEW. In one program, the
movement of the X-Y-Z stage and instrument instruction can be controlled, as well as data
collection. Figure 3.7 shows the program flowchart and Figure 3.8 shows the user interface of the
LabVIEW program. Some of the more important components of the software can be summarized
as follows:
•

At room temperature it takes 50-70 seconds for 500 mA of current to heat the
probe to a temperature where a satisfactory temperature difference develops
between the stage and the probe.

•

The system is programmed to begin when the sample is placed on the stage and
the probe is touching the top surface of the sample. Beginning the measurements
this way takes away the need to measure the distance the probe needs to move up
and down to establish a connection with the sample. One way to make sure a
connection between the sample and probe is made is to look at the voltage
measurements. The voltage readings decline in a steady slope when there is a
temperature gradient and conductivity between the probe, sample and stage. If a
connection at one of those three points is broken there will be significant noise in
the voltage measurements.

•

For the motor control, the total distance is the length across the sample in the
direction the measurements are taken (i.e. Y-axis). The shift distance is the
distance between measurements in the Y direction, the total number of
measurements in the Y direction is the total distance divided by the shift distance.
34

The in/out distance is the distance to move the probe in the X direction to begin a
new scan at a different location on the sample. The number of measurements has
to be specified so the system can repeat the process for a specified number of
locations.

35

Figure 3.7: LabVIEW software flow chart
36

Figure 3.8: LabView user interface.

3.4 Thermopower Calculation Techniques
To determine the thermopower of the sample, measurements of the voltage across the
sample and the temperature gradient between hot and cold sides of the sample are taken at a high
sampling rate. Temperature measurements can be done directly by measuring thermocouple
voltages for the hot and cold sides of the sample and calculating a temperature difference. About
100-300 data points are taken for each measurement point and a fit of this data is made. Figure
37

3.9 and 3.10 show this graphically, where Figure 3.9 is the data taken and Figure 3.10 is the
linear fit of the data.

-4

10
x 10

-4

-2.9

Constantan Thermopower Data
Thermopower Data

-3
-3.1
-3.2

V1

-3.3
-3.4
-3.5
-3.6
-3.7
-3.8
-3.9

4

4.2

4.4

4.6

4.8

5

V2-V1

Figure 3.9: Scatter plot of V1/(V2-V1) data.

38

5.2

5.4
x 10 -4
10
-4

Figure 3.10: Scatter plot of V1/(V2-V1) data with linear fit.

3.4.1 Pulsed technique for measuring thermopower [16]
One method used to measure thermopower is a pulsed technique where two
thermocouples are used to measure the thermopower in a homogeneous bulk material [16]. The
mounting configuration is shown in Figure 3.11 for type-T thermocouples.

39

Heater
Thot

Cu
CuNi

+

V1

+

V3

-

Tcold

Cu
CuNi

+
-

V2

Figure 3.11: Pulsed technique measurement diagram.

In the above figure three voltage measurements are taken with two thermocouples. The
thermocouples are copper (Cu) -constantan (CuNi). An RTD provides the heat for the hot side of
the sample. The thermopower is measured by supplying pulsed heat across the sample (the RTD
is turned on and of periodically). Over time the difference in temperature across the sample will
maintain a stable periodic function with a constant offset. This method allows for a 1K difference
between the hot side and cold side temperature, this temperature gradient and the voltage across
the sample are used to calculate the thermopower of the sample. The advantage behind
measuring thermopower with this technique is it eliminates any unknown temperature gradients
along the measuring wires by using the slope of many data points in the calculation of
thermopower, and ignoring the y-axis offset. This method also eliminates any D.C. offsets that
might exist in the measurement meters. The calculation of thermopower using this method can
be shown mathematically as:
்

்

்

ܸଵ ൌ ‫ ்׬‬ಹ ܵ஼௨ ሺܶሻ݀ܶ ൅ ‫ ்׬‬ೃ ܵ஼௨ே௜ ሺܶሻ݀ܶ ൌ ‫ ்׬‬ಹሾܵ஼௨ ሺܶሻ݀ܶ െ ܵ஼௨ே௜ ሺܶሻሿ݀ܶ
ೃ

ಹ

ೃ

40

(3.6)

்

்

்

ܸଶ ൌ ‫ ்׬‬಴ ܵ஼௨ ሺܶሻ݀ܶ ൅ ‫ ்׬‬ೃ ܵ஼௨ே௜ ሺܶሻ݀ܶ ൌ ‫ ்׬‬಴ሾܵ஼௨ ሺܶሻ݀ܶ െ ܵ஼௨ே௜ ሺܶሻሿ݀ܶ
ೃ

಴

ೃ

்

்

ܸଵ െ ܸଶ ൌ ‫ ்׬‬ಹሾܵ஼௨ ሺܶሻ݀ܶ െ ܵ஼௨ே௜ ሺܶሻሿ݀ܶ െ ‫ ்׬‬಴ሾܵ஼௨ ሺܶሻ݀ܶ െ ܵ஼௨ே௜ ሺܶሻሿ݀ܶ
ೃ

ೃ

்ಹ

்ೃ

்಴

்ೃ

଴

଴

଴

଴

(3.7)

(3.8)

்ಹ

ൌ න ்ܵ஼ ሺܶሻ݀ܶ െ න ்ܵ஼ ሺܶሻ݀ܶ െ න ்ܵ஼ ሺܶሻ݀ܶ െ න ்ܵ஼ ሺܶሻ݀ܶ ൌ න ்ܵ஼ ሺܶሻ݀ܶ
்಴

்

ಹ
‫்ܵ ்׬‬஼ ሺܶሻ݀ܶ ൎ ்ܵ஼ ሺܶ஺௏ீ ሻ · ሺܶு െ ܶ஼ ሻ, (TAVG= average temperature)
಴

ܶு െ ܶ஼ ‫ܶ ا‬஺௏ீ ‫ؠ‬

(3.9)

ܶଵ ൅ ܶଶ
2

՜ ܵௌ௔௠௣௟௘ ሺܶு ሻ ൎ ܵௌ௔௠௣௟௘ ሺܶ஼ ሻ and ܵ஼௨ே௜ ሺܶு ሻ ൎ ܵ஼௨ே௜ ሺܶ௖ ሻ

(3.10)

ܵௌ௔௠௣௟௘ ሺܶሻ ܽ݊݀ ܵ஼௨ே௜ ሺܶு ሻ are constant over ∆T.
ܸଵ െ ܸଶ ൌ ்ܵ஼ ሺܶு െ ܶ஼ ሻ ൌ ்ܵ஼ ሺܶ஺௏ீ ሻ · ∆ܶ

(3.11)

The difference between V1 and V2 in this technique equals the thermopower of the
thermocouples used multiplied by the temperature gradient between the two thermocouples. In
the technique V1 and V2 provide the temperature gradient needed to calculate thermopower of the
sample, to solve for the voltage difference you need a third voltage measurement V3, which is
derived as follows:
்

்

்

ܸଷ ൌ ‫ ்׬‬ಹ ܵ஼௨ே௜ ሺܶሻ݀ܶ ൅ ‫ ்׬‬಴ ܵௌ௔௠௣௟௘ ሺܶሻ݀ܶ ൅ ‫ ்׬‬ೃ ܵ஼௨ே௜ ሺܶሻ݀ܶ
ೃ

ಹ

಴

41

(3.12)

்ಹ

்ೃ

଴

଴

்ೃ

்಴

଴

଴

்ಹ

ൌ න ܵ஼௨ே௜ ሺܶሻ݀ܶ െ න ܵ஼௨ே௜ ሺܶሻ݀ܶ െ න ܵௌ௔௠௣௟௘ ሺܶሻ݀ܶ ൅ න ܵ஼௨ே௜ ሺܶሻ݀ܶ െ න ܵ஼௨ே௜ ሺܶሻ݀ܶ
்಴

்ಹ

்ಹ

ൌ െ න ܵௌ௔௠௣௟௘ ሺܶሻ݀ܶ ൅ න ܵ஼௨ே௜ ሺܶሻ݀ܶ
்಴

்಴

when ܶு െ ܶ஼ ‫ܶ ا‬஺௏ீ ‫ؠ‬

்భ ା ்మ
ଶ

՜ ்ܵ஼ ሺܶு ሻ ൎ ்ܵ஼ ሺܶ஼ ሻ, ்ܵ஼ ሺܶு ሻ is a constant. Assuming the

sample thermopower and platinum thermopower are constant over a small temperature gradient
then
ܸଷ= [ܵ஼௨ே௜ ሺܶ஺௏ீ ሻ െ ܵௌ௔௠௣௟௘ ሺܶ஺௏ீ ሻሿ · ∆ܶ

(3.13)

Finally to solve for the thermopower of a sample, (3.8) is used in (3.13) to give,
ܵௌ௔௠௣௟௘ ሺܶ஺௏ீ ሻ ൌ ܵ஼௨ே௜ ሺܶ஺௏ீ ሻ െ

ܸଷ
ܸଷ
ൌ ܵ஼௨ே௜ ሺܶ஺௏ீ ሻ െ
ܸ െ ܸଶ
∆ܶ
൬ ଵ
൰
்ܵ஼ ሺܶ஺௏ீ ሻ
௏

య
ൌ ܵ஼௨ே௜ ሺܶ஺௏ீ ሻ െ ௏ ି௏ · ்ܵ஼ ሺܶ஺௏ீ ሻ
భ

(3.14)

మ

V3 and (V1-V2) are non-linear functions by themselves but they have a linear relation to each
other. When ܶு െ ܶ஼ ‫ܶ ا‬஺௏ீ ‫ؠ‬

்భ ା ்మ
ଶ

՜ ܵௌ௔௠௣௟௘ ሺܶሻis constant, thus the slope

∆௏
∆்

is constant.

In this technique V3 and (V1-V2) are plotted against each other which results in a linear function.
The thermopower is calculated by taking 200-300 data points for V3 and (V1-V2), taking the best
fit of the linear function and finding the slope of that linear function.

42

As stated before the advantage of this method, is it eliminates spurious voltages caused
by unknown temperature gradients along the measuring wires. This method is used in various
measurements systems and provides accurate thermopower measurements from room
temperature to very high temperatures. The disadvantage to this method is it requires the sample
being measured to have homogeneous composition in order to have accurate measurements. This
can be problematic when samples are inhomogeneous, i.e. samples made of segmented material.
The following sections will present methods for measuring thermopower, which allow for
measurements of homogeneous and inhomogeneous bulk TE material.

3.4.2 Method of Measuring Thermopower Using Direct ∆T Measurements
In this technique direct voltage measurements are taken by a probe and separate
temperature measurements are taken for the temperature gradient. Since only one meter is used
to take both measurements, the meter needs to be able to switch between two measurements very
quickly. This method does not provide instantaneously corresponding voltage and temperature
measurements as the pulsed technique, but the high speed switching between the two
measurement ports provides reasonable measurements that are comparable to those found using
multiple meters to collect instantaneous voltage and temperature gradient data.
The two voltages taken are the voltage across the sample and the voltage of the copperconstantan thermocouple. Using the procedure outlined in section 2.8.4, the thermocouple
voltage is converted to the hot side temperature. The cold side temperature is measured by a
resistance temperature detector (RTD), which is attached to the heat sink. The difference
between the hot and cold side temperatures is the value of ∆T. For this technique, the slope of
the data is what determines the value of the thermopower. Taking over 100 ∆V/∆T data points, a
thermopower measurement for a single point is made where the probe tip touches the surface of
43

the samples. Over time the heat from the probe permeates the sample from the point of contact
between the probe and the sample. Taking many measurements from a single point of contact
shows the gradual decline in temperature and voltage as the sample absorbs the heat from the
probe. A linear fit to the ∆V vs. ∆T data then gives a slope that is a Seebeck voltage of the
copper to sample junction. The thermopower of the sample is then determined by removing the
contribution from the copper leads.

CuNi

Cu

+

+

- VCu2 +

V2

V1

Cu
Cu
- VCu1 +

RTD

Thot
Vsample
+

Tcold

Figure 3.12: An illustration of the Method of Measuring Thermopower Using Direct ∆T
Measurements
One disadvantage to this method is the inability to properly analyze high inaccuracies for
lower thermopower samples. This can be explained by breaking down the voltage measurement
of the sample; illustrated in Figure 3.12. Using Kirchhoff’s voltage law the expression for the
voltages in the loop is as follows:

ܸ௠௘௔௦௨௥௘ௗ െ ܸ஼௨ଵ െ ܸ௦௔௠௣௟௘ ൅ ܸ஼௨ଶ ൌ 0
44

(3.15)

The voltages in equation (3.15) can be written in terms of the thermopower and temperature
using equation (2.2). This leads to an expression for the voltage measured by the volt meter.
்೎

ܸ௠௘௔௦௨௥௘ௗ ൌ න ܵ஼௨ଵ ݀‫ ݐ‬൅ න
்೚

்ಹ

்೎

்

்೚

ܵ௦௔௠௣௟௘ ݀‫ ݐ‬൅ න ܵ஼௨ଶ ݀‫ݐ‬
்ಹ

்

ൌ ‫ ்׬‬ಹ ܵ௦௔௠௣௟௘ ݀‫ ݐ‬൅ ‫ ்׬‬಴ ܵ஼௨ ݀‫ݐ‬
಴

ಹ

(3.16)

The voltage due to the copper wires can be written as:
்ಹ

െ න ܵ஼௨ ݀‫ݐ‬
்಴

This leads to the following equation for the voltage measured by the meter.
ܸ௠௘௔௦௨௥௘ௗ ൌ ܵ௦௔௠௣௟௘ ሺ߂ܶሻ െ ܵ஼௨ ሺ߂ܶሻ

(3.17)

The true voltage across the sample is given by the following expression.
ܵ௦௔௠௣௟௘ ሺ߂ܶሻ ൌ ܸ௠௘௔௦௨௥௘ௗ ൅ ܵ஼௨ ሺ߂ܶሻ

(3.18)

This voltage takes into account the added contribution of the Cu leads∗.
The measurements in Figure 3.13 show the value of Vmeasured for a reference sample of
constantan (-39.5µV/K at 300K). The measurements range from -31µV/K to -33µV/K and
Figure 3.14 show the measured thermopower values for constantan after correction for the
copper leads. These thermopower values range from -28µV/K to -31µV/K, which differ from the
reference value by 20%-26% respectively. It is important to note that these errors are less
pronounced when the samples thermopower is higher that ±100µV/K. These large errors can

∗

The thermopower of Cu is 1.97µV at room temperature.
45

lead to unreliable measurements for samples with smaller thermopower. Also it can be very time
consuming and inefficient to calculate how much the addition of the copper connection wires
thermopower affects the overall data.
0

Vmeasured/ΔT (µV/K)

-5

1

2

3

4

5

6

7

8

9

-10
-15
-20
-25
-30
-35
-40

Order of Measurements

Figure 3.13: Voltage/∆T data of constantan sample with the Cu contribution not yet removed.

Constantan Thermopower(µV/K)

0
-5

1

2

3

4

5

6

7

8

-10
-15
-20
-25
-30
-35
-40

Order of Measurements

Figure 3.14: Corrected constantan thermopower data.

46

9

While using this method finding the cause of measurement errors was very difficult. The
issue did not become apparent until a different method was attempted. This method will be
introduced in the following section and measurement results will be presented in chapter 4.

3.4.3 Thermocouple Method for Measuring Thermopower
To investigate improvements to the accuracy of the system the RTD used to measure the
base temperature was replaced with a copper-constantan thermocouple. Similar to the method
presented in [13], two copper-constantan thermocouples were used to measure the hot and cold
side temperatures. Using equations the following equations

ܸଵ ൌ ሺܵ௦ െ ܵ஼௨ ሻ · ሺܶଵ െ ܶ଴ ሻ

(3.2)

ܸଶ ൌ ሺܵ௦ െ ܵ஼௨ே௜ ሻ · ሺܶଵ െ ܶ଴ ሻ

(3.3)

ሺௌೞ ିௌ಴ೠ ሻ·ሺ்భ ି்బ ሻ
ሺௌೞ ିௌ಴ೠಿ೔ ሻ·ሺ்భ ି்బ ሻିሺௌೞ ିௌ಴ೠ ሻ·ሺ்భ ି்బ ሻ

ܵ௦ ൌ

௏భ

௏మ ି௏భ

ൌ

௏భ

௏మ ି௏భ

ሺܵ஼௨ െ ܵ஼௨ே௜ ሻ ൅ ܵ஼௨

The thermopower of the sample can be solved directly using the slope of V1/(V2 -V1) as shown in
Figure 3.15, and the thermopower of constantan and copper. This also helps eliminate errors that
can be created by erroneous temperature measurements. The measurement results using this
method will be presented in chapters four and five.

47

CuNi
+

+

Cu

V2

V1

Cu
Thot
Vsample
+

Tcold

CuNi

Figure 3.15: An illustration of the Thermocouple Voltage Measurements Method for Calculating
Thermopower using copper-constantan thermocouples.

48

Chapter 4: Reference measurements
4.1 Introduction
To test that the system is operating as desired, thermopower values of various metals and
alloys were used as references. The ideal material for reference measurements are high purity
metals or alloys with thermopower values that remain constant over time regardless of the
method of which the material was formed. For example the thermopower values of Cu, Pb and Pt
have been known for decades, if measurements of a high purity sample made of one these metals
is taken with various systems in labs across the country, a result matching published data would
be considered reliable since these materials have been used as standard reference materials in
research. Another good candidate for reference measurements is the alloy constantan, which will
be explored further in a later section. Using well known thermoelectric materials (i.e. Si-Ge,
PbTe) as reference material is an unreliable method of checking the accuracy of a system since
there can be significant variation in the properties of the samples even when made by the same
process. There are no standard reference materials for high thermopower materials even though
Bi2Te3 has recently come into consideration to be named as a standard reference material [17].
The following criterion for acceptable standard reference materials was developed by NIST [18]:
•

First it was determined that the material should be able to achieve long term stability and
be homogenous, for reproduction at a large scale.

•

The standard reference material should be able to have a thermopower value regularly
measured in the field (between 25µV/K and 400µV/K).

•

A thermoelectric standard reference material should be reasonably available to the
research community as far as cost is concerned.

49

•

Lastly a standard reference material has to be able to be used in the future for
development of reference materials for broader and different temperature ranges.

Most thermoelectric materials are tailor made with specific optimizations in mind, i.e. doping
concentration, annealing time, etc. Even though thermoelectric materials might not be useful as
reference samples for absolute thermopower measurements, they can be useful in measuring the
polarity of a material due to their high thermopower values. The polarity of the voltage
measurement of a sample is the indicator that shows if the sample is n-type or p-type.

4.2 Bi2Te3 Reference Measurements
Bi2Te3 samples from the Tellurex Corporation were used to check if the system would
produce a voltage measurement with the proper polarity. Samples with dimensions of 5mm ×
5mm × 2mm were used to check for n-type and p-type polarity. For the n-type measurement, a
single point on the surface of the sample was measured. The resulting slope of V1/(V2-V1) was
negative indicating that the sample was indeed n-type, and the magnitude was reasonable for
these samples as shown in Figure 4.1.

50

Figure 4.1: N-type Bi2Te3 reference measurement.
Likewise for the p-type sample, the resulting slope of V1/(V2-V1) was positive indicating that the
sample was p-type and the value of the thermopower was 220µV/K which is in good agreement
with high quality p-type Bi2Te3 materials.

51

Figure 4.2: P-type Bi2Te3 reference measurement.

4.3 Constantan
Constantan is an alloy composed of 55% Cu and 45% Ni, it is a suitable material for
reference measurements in this system because it is commonly fabricated, reproducible, and is
stable in time. Constantan is an n-type material, with a thermopower of -39.5µV/K at room
temperature. A fit for the thermopower of constantan was determined for a wide temperature
range using the thermopower of a type T thermocouple and Cu [16]. The thermopower of a type
T thermocouple is the difference between the thermopower of Cu and constantan. The
thermopower of Cu was published by Roberts [19]; the literature also provided a thermopower
scale for temperatures ranging from room temperature to 900K. The thermopower of
thermocouples can be calculated by using data provided by NIST for thermocouple voltages
52

versus temperature for a wide range of thermocouple types. Table 4.1 shows the ninth order
polynomial coefficients for the fit of the thermopower of constantan over a wide temperature
range and Figure 4.3 shows the thermopower data from 290K to 680K.
Table 4.1: The coefficients for the fit of the thermopower of constantan [16]
Y=
8
9
M0+M1*x+….+M8*x +M9*x
-996.557
M0
13.94639
M1
-0.08016
M2
0.000223
M3
-2.45E-07
M4
-2.18E-10
M5
9.67E-13
M6
-1.12E-15
M7
5.38E-19
M8
-7.47E-23
M9
0.999999984
R

53

Constantan Thermopower
-35

Thermopower (uV/K)

-40

-45

-50

-55

-60
250

300

350

400

450
500
Temperature(K)

550

600

650

700

Figure 4.3: The thermopower of constantan from 290K to 680K.
An 8.1mm diameter × 3.1mm thick cylindrical piece of 99.999% pure constantan was used as a
reference sample (see Figure 4.4).

Figure 4.4: cylindrical piece of constantan.
Figure 4.5 shows ten measurements of constantan using the thermopower scanning probe.

54

Constantan Thermopower(µV/K)

0
1

-5

2

3

4

5

6

7

8

9

10

-10
-15
-20
-25
-30
-35
-40

Order of Measurements

Figure 4.5: Constantan thermopower data.
The measurements range from -31µV/K to -33µV/K, with the average being -32.458µV/K. This
corresponds to an error between 20%-15% from the reference -39.5µV/K, with the average error
of the ten measurements being 17.94%.

20
19
18

% Error

17
16
15
14
13
12
11
10
0

1

2

3

4

5

6

7

8

Order of Measurements

Figure 4.6: Constantan measurement errors.

55

9

10

Using the method presented in section 3.4.4 the thermopower of constantan fell reliably
within the range presented in Figure 4.5. These measurements for constantan are important
because they help to show the limits of accuracy of this system.

4.4 Low thermopower material measurements
Metals such as Cu and Pb were measured and the error between measured thermopower
values and expected values was substantially larger than the error found for the constantan
measurements. Cu has a room temperature thermopower value of 1.97µV/K and Pb has a room
temperature thermopower of -1.05µV/K [19]. When the thermopower of these two metals were
measured using the thermopower scanning probe, a measurable thermopower could not be
detected. Lower thermopower values of a sample correlated to higher the measurement error
while using this method to measure thermopower.

4.5 Error Analysis
To begin to understand the errors in these measurements, the key components of this
measurement technique have to be explained in detail. As stated in the previous chapter the two
voltages are defined as

ܸଵ െ ܸ஼௨ଵ െ ܸ௦௔௠௣௟௘ ൅ ܸ஼௨ଶ ൌ 0 and
ܸଶ െ ܸ஼௨ே௜ଵ െ ܸ௦௔௠௣௟௘ ൅ ܸ஼௨ே௜ଶ ൌ 0
As shown in section 3.4.3, these equations can be represented the following way

ܸଵ ൌ ܵ௦ · ሺ∆ܶሻ െ ܵ஼௨ · ሺ∆ܶሻ
ܸଶ ൌ ܵ௦ · ሺ∆ܶሻ െ ܵ஼௨ே௜ · ሺ∆ܶሻ

56

This results to the following representation which will be used for the remainder of this thesis:

ܸଵ ൌ ሺܵ௦ െ ܵ஼௨ ሻ · ሺܶଵ െ ܶ଴ ሻ
ܸଶ ൌ ሺܵ௦ െ ܵ஼௨ே௜ ሻ · ሺܶଵ െ ܶ଴ ሻ
From the above equation the temperature gradient is calculated in the following manner

ܸଶ െ ܸଵ ൌ ሺܵ௦ െ ܵ஼௨ே௜ ሻ · ሺܶଵ െ ܶ଴ ሻ െ ሺܵ௦ െ ܵ஼௨ ሻ · ሺܶଵ െ ܶ଴ ሻ
∆ܶ ൌ

௏మ ି௏భ

ሺௌ಴ೠ ିௌ಴ೠಿ೔ ሻ

(4.1)

Using the above equation for the temperature gradient, the expected values of ∆T can be
calculated for V2 – V1 values (as shown in Figure 4.7).

Figure 4.7: The expected values of ∆T vs. V2 –V1.
57

While doing reference measurements, the samples with the largest percent errors from the
expected values were those with low thermopower values. The source of this error can be
explained using the thermopower of copper and constantan and the above equations for V2 and
V1.To begin, the expected values of copper can be calculated in the following manner.

ܸଵ ൌ ሺ1.97ߤܸ/‫ ܭ‬െ ܵ஼௨ ሻ · ሺܶଵ െ ܶ଴ ሻ
ܸଶ ൌ ሺ1.97ߤܸ/‫ ܭ‬െ ܵ஼௨ே௜ ሻ · ሺܶଵ െ ܶ଴ ሻ
For the range of ∆T values shown in Figure 4.7, the corresponding values of V2 and V1 are
shown in Figure 4.8.

Figure 4.8: Expected values of V1 and V2 for Cu
58

When a copper sample was measured using the thermopower scanning probe the measured value
had a very high error with respect to its expected value. Looking closer at the data, the voltage
values for V1 and V2 were offset in a negative direction with respect to their expected values.
This offset was equal in magnitude for both V1 and V2 as shown in Figure 4.9.

Figure 4.9: Expected and measured values of V1 and V2 for Cu.

The expected value of V1 value is zero but for all measurements the values of V1 and V2 are
offset from 200µV to 160µV in the negative direction with respect to their expected values.
Although it might seem that the offset is decreasing, this does not mean that the error can be
reduced with a decreasing temperature gradient since the calculation of the temperature gradient
59

depends on V2 –V1. Figure 4.9 shows a snapshot of the voltage measurements at a ∆T between 8
and 10K. Using the same procedure used to calculate the expected value of copper, the expected
values of V1 and V2 for constantan are shown in Figure 4.10.

Figure 4.10: Expected and measured values of V1 and V2 for constantan.

The offset for constantan was shifted to more positive voltages than expected (Figure 4.10),
while the offset for the copper sample was to more negative voltages than expected (Figure 4.9).
In Figure 4.11 it can be seen that the magnitude of the offset correlates with the increase in
voltage magnitude; as the temperature gradient increases the magnitudes of the measured
voltages for V1 and V2 increase. Figure 4.11 shows the 100 V1 and V2 measurements used to
60

calculate each thermopower values in Figure 4.5. This data shows the effect of the temperature
gradient to the voltage magnitude. The initial measurements were done while the probe was cool,
which led to a smaller temperature gradient. The probe was heated with a specific amount of
current for a short amount of time, lowered to the surface of the sample and these measurements
were taken. Some measurements were taken consecutively, repeating the same process after a
short break which caused the probe temperature to rise; as a result some measurements had
higher temperature gradients than others.

-6

Measured V1 and V2 values for constantan

200 10

-6

v1_1
v2_1
v2_2
v1_2
v1_3
v2_3
v1_4
v2_4
v1_5
v2_5
v1_6
v2_6
v1_7
v2_7
v1_8
v2_8
v1_9
v2_9
v1_10
v2_10

100 10

0

0 10

-6

-100 10

-6

-200 10

-6

-300 10

-6

-400 10

-6

-500 10

-6

-600 10

0

20

40

60

80

100

120

Order of Measurements

Figure 4.11: Measured values of V1 and V2 for constantan.

These two measurements show the major source of errors using this technique. For
samples with thermopower values near those of constantan and copper, there was an error
61

created by an offset in voltage. This error is less pronounced for constantan due to the fact that
the offset did not greatly affect the magnitude of V1 which is used to determine the thermopower
as (V1/V2 –V1). For samples with thermopower values closer to copper the offset has a large
effect in the magnitude of V1 which accounts for the large errors.

In the previous examples the thermopower of the samples were either equal copper or
constantan where either V1, or V2 was expected to equal zero respectively. To investigate a
reference material with a thermopower between that of copper and constantan, a nickel sample
was prepared. Nickel has a room temperature thermopower of -19.5µV/K [20]; the expected
values of V1 and V2 for nickel are shown in Figure 4.12.

Figure 4.12: Expected values of V1 and V2 for nickel.
62

Figure 4.12 shows the values of V1 and V2 diverge as the temperature gradient gets larger.
Measurements of a nickel sample showed the values of V1 and V2 were equal in magnitude.
Unlike the other samples where one slope of a particular voltage grew larger than the other, for
nickel which has a room temperature thermopower value approximately halfway between copper
and constantan the values of V1 and V2 are almost equal in magnitude and their magnitudes
increasing equally to each other with a rising temperature gradient. This makes it possible for
equation 4.1 to be used to calculate an accurate temperature gradient for samples with
thermopower values in a similar range. From the measured values of nickel there were no
noticeable offsets from the expected voltage values (shown in Figure 4.13).

Figure 4.13: Expected and measured values of V1 and V2 for nickel.
63

Figure 4.14 shows ten measurements of the thermopower of nickel ranging from -24.763µV/K to
-22.0445µV/K with an average thermopower value of -23.2µV/K.

0

Nickel Thermopower (µK/K)

1

2

3

4

5

6

7

8

9

-5
-10
-15
-20
-25
-30

Order of Measurements

Figure 4.14: Nickel thermopower data.

The corresponding V1 and V2 measurements for these values are shown in Figure 4.15.

64

Measured V1 and V2 values for Nickel

300 10

-6

200 10

-6

100 10

-6

0 10

v1_1
v2_1
v1_2
v2_2
v1_3
v2_3
v1_4
v2_4
v1_5
v2_5
v1_6
v2_6
v1_7
v2_7
v1_8
v2_8
v1_9
v2_9

0

-100 10

-6

-200 10

-6

-300 10

-6

0

20

40

60

80

100

120

Order of Measurements

Figure 4.15: Measured values of V1 and V2 for nickel

In conclusion while analyzing the voltage measurements used to calculate the
thermopower of reference samples, the source of errors between measured and expected results
was found to be an offset in the magnitude of the voltages. This offset was largest for constantan
and copper. The error was greatest in samples with relatively small thermopower due to the fact
that V1 was greatly shifted from its expected value, causing a greater error in the V1/(V2 –V1)
slope which is used to calculate the thermopower of a sample. These measurements also showed
that V2 –V1 is a reliable method of measuring the temperature gradient across the samples.

65

Chapter 5: Measurements of segmented thermoelectric bulk material
composed of Bi2Te3 and LAST/LASTT.
5.1 Introduction:
Devices such as thermoelectric generators operate over large temperature gradients, but
the materials used to create these devices have limited efficiency due to the fact that their peak
ZT is restricted to a small temperature range. To maximize the average ZT over the hot to cold
side temperature range, segmentation of the thermoelectric legs can be used. In this case, two or
more n-type materials are joined to form the n-type legs, and likewise two or more p-type
materials are joined to form the p-type legs. Such a configuration allows for larger temperature
gradients by combining lower melting point materials with higher melting point materials. The
larger hot to cold side temperature gradients also improves the efficiency of thermoelectric
generators since they are Carnot efficiency limited. For smaller temperature gradients
segmentation based on a single material system with minor compositional variation (doping,
alloying) can also be used [21].
In this chapter segmented legs for thermoelectric devices using n and p-type Bi2Te3 and
LAST (lead-antimony-silver-tellurium) and LASTT (lead-antimony-silver-tin-tellurium) are
presented. Bi2Te3 is a well known thermoelectric material which has a peak ZT of ~1.0 at room
temperature. LAST and LASTT are n-type and p-type materials respectively with peak ZT
values near 700 K. Each material was in powder form and PECS processing was used to form the
segmented samples. The following sections will document this process and the measurements
taken by the room temperature thermopower scanning probe of these samples.

66

5.2 PECS
Both samples were made using Pulsed Electric Current Sintering (PECS). Also known as
Spark Plasma Sintering, this method uses a pulsed DC current to heat the powder sample by
Joule heating. High heating and cooling rates can be used since this method allows a direct way
of heating. This allows for densification over grain grow promoting diffusion mechanisms,
growth
maintaining the intrinsic properties of nano powders in their fully dense products. Temperature
he
nano-powders
gradients inside the sample should be minimized in order to permit homogenous sintering
behavior [22].

Figure 5.1: PECS system at MSU
MSU.

5.3 LAST/LASTT
LAST is an n-type semiconductor with a chemical formula of AgPbmSbTe2+m, while
LASTT is a p-type semiconductor with a chemical formula of Ag(Pb1-xSnx)mSbTe2+m [23]. In
type

67

recent years LAST was considered a material of interest because of its high ZT value compared
to other TE materials. LAST exhibits desirable properties such as isotropic morphology, high
crystal symmetry, low thermal conductivity and controllable carrier concentration [24]. LASTT
has been reported to exhibit high performance p-type TE properties, such as a ZT~1.45 at 630 K.
A sample with the composition Ag0.5Pb6Sn2Sb0.2Te10 had a reported electrical conductivity of
1000 S/cm and a thermopower of roughly 50µV/K at room temperature [25].

5.3.1 Preparation of LAST/LASTT
Due to their desirable properties at high temperatures, LAST and LASTT were used as a
hot side material for the n and p-type segmented samples. Each material was in powder form
before PECS processing. Approximately 3g of LAST and LASTT powder was used to fill a
12.7mm diameter graphite die. They were placed separately inside the PECS system and
processed in an argon environment at a maximum temperature of 550°C and pressure of 60MPa.
The following profile was used during the PECS process:

20

20

Figure 5.2: Temperature and pressure profiles for LAST/LASTT PECS processing.
68

Figure 5.3 shows the finished sample after PECS processing. The LASTT and LAST billets were
approximately 2.5mm thick after pressing.

Figure 5.3: LASTT coin after PECS processing.

5.4 Preparation of Bi2Te3
Bi2Te3 was used as the material for the cold side of the segmented sample. The
preparation process began with 5mm × 5mm × 2mm cubes of n and p-type Bi2Te3 from the
Tellurex Corporation. The cubes were crushed into powders using a mechanical mortar and
pestle, and 3g for both the n-type and p-type were prepared by sieving through a 53µm sieve.
The powder was placed in a 12.7mm diameter graphite die with the already PECS processed
LAST/LASTT samples inside, as illustrated in Figure 5.4.

69

Bi2Te3

LAST/LASTT

Figure 5.4: Bi2Te3 powder placed on top of PECS processed LAST/LASTT material.

The Bi2Te3 powder was processed at a gradually increase of temperature to a maximum
temperature of 430°C. The processing began with an initial increase in temperature from room
temperature to 110°C at a rate of 40°C/min, followed by a 10 minute hold at 110°C. Then the
temperature was increased to 410°C at a rate of 60°C/min. Finally at a rate of 5°C/min the
temperature was increased to 430°C. Throughout this process the pressure stayed constant at
40MPa. At 430°C, the pressure was increased to 50 MPa and the temperature remained at 430°C
for a period of 20 minutes. At the end of that twenty minute period, the system gradually cooled
down using the previously stated process in reverse, from 430°C to room temperature. Figure 5.5
shows the merged Bi2Te3 and LAST material after PECS processing.

70

Bi2Te3 - LAST

LAST

Bi2Te3

Figure 5.5: Finished PECS processed Bi2Te3 and LAST.

After excess graphite material was polished off the surface, the samples were cut into two
rectangular pieces. Figure 5.6 is an image from an optical microscope, showing a distinction
between the two materials after processing.

Figure 5.6: Optical microscope image of Bi2Te3 and LAST surface after processing.

71

5.5 Scanning Probe Measurements
The thermopower scanning probes was used to take several scans of the two segmented
leg samples. For the n-type Bi2Te3/LAST material the surface scan distance was 5mm across in
the Y-direction. The system was programmed to measure in 0.5mm increments. After a
completed scan, the system moved a distance on 1mm in the X direction and another scan
initiated in the Y direction.

0

Bi2Te3

Thermopower (µV/K)

-50

-100

-150

LAST
-200

-250
-1

0

1

2

3

4

5

6

Position (mm)

Figure 5.7: LAST/Bi2Te3 scan across the center of the sample (as shown in the inset).

Figure 5.7 shows the LAST material has a high thermopower (approximately -200µV/K).
The thermopower scan shows a clear demarcation between the LAST material and the Bi2Te3
based material at approximately 2.8mm. The measurements also show a significantly lower

72

thermopower for the Bi2Te3 sample than expected based on the results from Figure 4.1. The
solid Bi2Te3 cubes used to create the powder for this sample had a thermopower slightly less
than -200µV/K, this scan shows that this thermopower dropped to ~-50µV/K. The cause of this
can be the Bi2Te3 cubes were not properly crushed into powder form. Also this can be a side
effect of using previously processed material in this procedure. This was the case for both n and
p-type Bi2Te3material, as will be shown in the following figures.

0

Bi2Te3

Thermopower (µV/K)

-50

-100

-150

LAST
-200

-250
-1

0

1

2

3

4

5

6

Position (mm)

Figure 5.8: LAST/Bi2Te3 scan at 1mm behind the first scan at the center of the sample.

Figure 5.8 shows the second scan 1mm behind the origin. This scan shows agreement in
measurements with the scan at the origin for the first 2mm, but between 2mm and 2.5 mm there
was a dramatic drop in thermopower values. This is possibly due to a mixture in materials during
73

the fusion of the two different alloys. The two measurements also shows towards the outer edges
of the Bi2Te3 material, the scans show a consistent drop in thermopower, which can mean the
sample becomes more metallic at this point. Electro-dispersive X-ray spectroscopy (EDS)
analysis of the samples surface was done to verify which materials were in each half of the
sample. Table 5.1 shows area 1 is predominantly Bi and Te. While the analysis for area two
shows the two prominent elements were Te and Pb.

Area 1

Area 2
1 mm

Figure 5.9: SEM surface image of LAST/Bi2Te3 sample.

74

Table 5.1: EDS analysis of area 1 in SEM image of LAST/Bi2Te3 sample.

Element Weight Atomic
%
%
BiM

47.11

34.85

SbL

0.56

0.71

TeL

50.97

61.76

SeK

1.36

2.67

Table 5.2: EDS analysis of area 2 in SEM image of LAST/Bi2Te3 sample.

Element Weight Atomic
%
%
PbM

50.62

35.45

AgL

4.76

6.4

SbL

2.59

3.08

TeL

40.62

46.18

For the p-type Bi2Te3/LASTT material the surface scan distance was 3mm as shown in
Figure 5.10. The system scanned at 0.5mm increments, when this scan was complete the system
moved a distance on 1mm in the X direction and another scan taken. The measurements for
LASTT were between 50µV/K and 65µV/K, which is comparable to the values presented in
literature [26]. Similar to the n-type Bi2Te3 in the LAST/ Bi2Te3 sample, the thermopower of the
p-type Bi2Te3 material was significantly lower than the expected ~200µV/K. In this case the
thermopower values for the p-type Bi2Te3 material were between 60-70µV/K. Unlike the
75

LAST/Bi2Te3 sample, in this LASTT/Bi2Te3 sample there are no clear distinctions between the
two materials as shown in Figures 5.10 and 5.11.

70

Bi2Te3

Thermopower (µV/K)

65

60

55

50
-0.5

LASTT

0

0.5

1

1.5

2

2.5

3

Position (mm)

Figure 5.10: LASTT/Bi2Te3 scan across the center of the sample.

76

3.5

64

62

Thermopower (µV/K)

Bi2Te3
60

58

LASTT
56

54
-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Position (mm)

Figure 5.11: LASTT/Bi2Te3 scan at 1mm behind the first scan.

Area 1

Area 2
1 mm

Figure 5.12: SEM surface image of LASTT/Bi2Te3 sample.

77

Table 5.3: EDS analysis of area 1 in SEM image of LASTT/Bi2Te3 sample.

Element

Weight Atomic
%
%

PbM

25.23

15.11

AgL

1.91

2.2

SnL

19.69

20.58

SbL

2.62

2.67

TeL

47.99

46.66

Table 5.4: EDS analysis of area 2 in SEM image of LASTT/Bi2Te3 sample.

Element Weight Atomic
%
%
BiM

12.07

7.18

SbL

27.56

28.15

TeL

56.02

54.6

SeK

3.23

5.1

Using measurements of the TE materials composed of n-type LAST and Bi2TE3 and the
p-type LASTT and Bi2TE3, the thermopower scanning probe showed a roll this type of system
can have in TE research. For the n-type LAST and Bi2TE3 material, the results showed relative
agreement between the expected and measured results for the LAST material. The measured
78

thermopower values of LAST were higher in magnitude than their expected values; it is
suspected this is due to increased doping. In the EDS results shown in Table 5.2, Ag and Sb
show a 2:1 relationship instead of a 0.8:1 relationship. This might be the cause of the increase in
magnitude for the thermopower of the LAST material. For the n-type Bi2TE3 material the
measured thermopower values were drastically lower than their expected value, the method of
which this material was processed is suspected to be the reason behind the drop in thermopower
values. For the p-type LASTT and Bi2TE3 material, the LASTT material showed close
agreement between measured and expected thermopower values. The p-type Bi2TE3 material in
this sample also showed a drastic drop in magnitude between measured and expected values,
similar to the n-type Bi2TE3 material. These initial measurements showed the potential this
system has in expanding future TE research, with greater improvement to automation and
resolution future generations of this system will be able to provide better insight into this type of
research.

79

Chapter 6: Conclusion and Future Work
6.1 Conclusions
A new scanning probe system has been presented for better characterization of
thermoelectric materials. The system allows for characterization of the surface of a sample in
two dimensions. Using the Seebeck coefficient, the degree of homogeneity of a sample can be
attained by taking measurements from point to point across the surface of a sample. This
information gives researches greater insight into the composition of specific samples, where
other measurement methods only allow for single thermopower measurements of homogeneous
samples. Reference measurements were taken to show the system operates as desired for high
thermopower samples. The system was used in a study of segmented thermoelectric materials
composed of n and p-type Bi2Te3 and LAST/LASTT to show the systems value in future
research of inhomogeneous samples.
6.2 Future Work
From the onset of this project the intent was to build a scanning probe system that would
be able to measure thermopower at room temperature and create a two dimensional
characterization of a sample. As a prototype the system was successfully built and programmed
to work as it was originally intended. Over the course of the research various issues with the
design and programming developed that showed areas that can be improved in the overall design
of the system. Moving forward in order to build on the work presented in this thesis and improve
the capabilities of the system the following improvements are advised:

1.

Motors – The three stepper motors used by the system required at least 12V- 2.5A to
work properly. These motors give off a considerable amount of heat after being on for a
short amount of time. This presents a few problems that will have to be addressed. The
80

system was not tested for a prolonged period of time because it was unclear what kind of
damage this amount of heat would do to the motors and circuitry. Also this heat is
transported through the motor mounts into the translation stage. Since these
measurements are dependent on the temperature around the sample remaining constant,
any ambient heat given off by the stage and the motors can cause inaccuracies in the
measurements. If the system is to be operational for a prolonged period of time, the
amount of heat given off by the motors has to be addressed.

2.

Probe - Another issue that needs to be addressed is the resolution of the probe. The true
resolution of the probe was not quantified in these initial tests of the system. Moving
forward a better understanding of the probes resolution can lead to greater surface
characterization. One area that can be studied is the interaction at the interface of
thermoelectric materials and metal contacts in devices. With a finer resolution the
thermopower scanning probe would be able to show the effects of bonding metals and
thermoelectric material. Thermoelectric devices use metals such as stainless steel to
separate n and p-type thermoelectric material and to act as electrical connections. This
system can be used to study any doping that occurs to the thermoelectric materials when
they are bonded with the metal interconnects.

81

Appendix

82

Appendix A
Table A-1: Material composition of thermocouples and their temperature ranges [26]
Type
B
E
J
K
N
R
S
T

Positive element
Platinum(70%),Rhodium(30%)
Nickel(90%), Chromium(10%)
Iron
Nickel(90%), Chromium(10%)
Ni(84.4%), Cr(14.2%),Si(1.4%)
Platinum(87%),Rhodium(13%)
Platinum(90%),Rhodium(10%)
Copper

Negative element
Platinum(94%),Rhodium(6%)
Constantan: Nickel(55%), Copper(45%)
Constantan: Nickel(55%), Copper(45%)
Ni(95%), Al(2%), Mn(2%),Si(1%)
Ni(95%), Si(4.4%),Mn(0.15%)
Platinum
Platinum
Constantan: Nickel(55%), Copper(45%)

Temperature Range ( C )
800 to 1700
0 to 900
0 to 750
0 to 1250
500 to 1000
0 to 1450
0 to 1450
0 to 350

Table A-2: Coefficients of the calibration equation for voltage as a function of temperature
(eq.2.20) for type-T thermocouples [26]

b0
b1
b2
b3
b4
b5
b6
b7
b8

0°C ≤ T ≤ 400°C
0
3.8748106364E-02
3.329222788E-05
2.0618243404E-07
-2.1882256846E-09
1.0996880928E-11
-3.0815758772E-14
4.5479135290E-17
-2.7512901673E-20

83

Table A-3: Coefficients of the calibration equation for temperature as a function of voltage
(eq.2.21) for type-T thermocouples [26]

c0
c1
c2
c3
c4
c5
c6
c7

0mV ≤ E0j ≤ 20.872mV
0
2.5928E+01
-7.602961E-01
4.637791E-02
-2.165394E-03
6.048144E-05
-7.293422E-07
0

84

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