SILICON-BASED SEMIMETALS AND SEMICONDUCTORS
FOR THERMOELECTRIC APPLICATIONS
By
Hui Sun

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Materials Science and Engineering - Doctor of Philosophy
2013

ABSTRACT
SILICON-BASED SEMIMETALS AND SEMICONDUCTORS
FOR THERMOELECTRIC APPLICATIONS
By
Hui Sun
The direct conversion between heat and electricity can be achieved by thermoelectric devices.
Thus, thermoelectricity is considered as not only an environmentally friendly substitute for
compressor-based refrigerators but also a promising energy solution to harvest waste heat.
State-of-the-art thermoelectric materials are often comprised of expensive tellurium or
germanium elements and hence are hardly suitable for mass production. The silicon-based
thermoelectrics, e.g. semimetallic CoSi and semiconducting β-FeSi2 materials we study here, are
composed of abundant elements in nature. They are also chemically stable, non-toxic, and
mechanically robust. Despite the above benefits, they exhibit relatively lower efficiencies
compared to state-of-the-art materials. In this dissertation, we have intended to understand the
thermal and electrical transport in these materials and enhance their thermoelectric performance.
CoSi possesses one of the highest power factors among thermoelectrics due to the sharp
features around the Fermi level in its electronic density of states. In order to improve the
performance, the effects of p-type dopants, isoelectronic substitutions, n-type dopants, and
double doping were systematically studied for arc-melted CoSi samples. The results show that
p-type dopants like iron and gallium and n-type dopants like nickel and palladium deteriorate the

electrical properties due to the introduction of excess holes and electrons, respectively. Boron
and platinum have very limited solubility in CoSi and the segregated impurity phases at grain
boundaries are helpful to improve the electrical properties. The isoelectronic substitutions
influence the power factor slightly; however, they result in a drastic decrease in the lattice
thermal conductivity and hence an enhancement in the figure of merit. In addition, CoSi samples
prepared by powder processing were investigated to further reduce the lattice thermal
conductivity. Unfortunately, all the consolidated samples show worse performance than the
arc-melted CoSi.
β-FeSi2 is one of the most cost-efficient thermoelectric materials. Its thermoelectric
performance can be tuned by cobalt doping and the highest figure of merit is close to 0.4 at 1000
K. Grain size reduction was also used to reduce the lattice thermal conductivity. However, no
improvement has been obtained yet. SiC nanoparticles were dispersed into β-FeSi2 matrix to
form a composite structure. With addition of the nanoparticles, the thermal conductivity is
slightly decreased associated with a decrease in the power factor. Although the figure of merit is
less than that of some Te-based materials, β-FeSi2-based thermoelectrics may be suitable in
large-scale applications where material abundance and cost are concerns.

DEDICATION
To my loving wife Chengling Gu, wish our love to be eternal.
To my cute son You You, wish you full of happiness and vitality.
To my dear parents, who support me and believe me every single day.

iv

ACKNOWLEDGMENTS

I am deeply grateful to my advisor Dr. Donald Morelli who gave me this opportunity to
conduct the research. Under his guidance, I recognize that doing research is delightful and
encouraging. I would also like to thank my committee members Drs. S. D. Mahanti, Jeff
Sakamoto, and Wei Lai for their suggestions during my Ph. D. study. Many thanks go to my
former colleagues Drs. Chen (Kevin) Zhou, Chang Liu and Eric Skoug. They taught me a lot of
experimental and data analyzing skills. I also appreciate my current lab-mates Dr. Vijayabarathi
Ponnambalam, Xu Lu, Steve Boona, Gloria Lehr and Minyoung Jeong for their helpful
discussion and cooperation.
I would also like to acknowledge the funding agency. This work is sponsored as part of the
Center for Revolutionary Materials for Solid State Energy Conversion (RMSSEC), an Energy
Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Energy
Sciences under Award Number DE-SC0001054. I would like to sincerely thank my collaborators
who are connected with me through the RMSSEC platform: Drs. Melanie Kirkham, Harry Meyer,
and Edgar Lara-Curzio at Oak Ridge National Laboratory, Dr. Ivan Blum and Prof. David
Seidman at Northwestern University, and Ed Timm, Prof. Harold Schock, Xiaofeng Fan and Prof.
Eldon Case at Michigan State University. The use of testing facility equipment in the Electrical
and Computer Engineering Department at Michigan State University is also highly appreciated.
v

TABLE OF CONTENTS

LIST OF TABLES ························································································· viii
LIST OF FIGURES ························································································· ix

Chapter 1 Introduction to Thermoelectricity ····························································· 1
1.1 Energy Issues and Thermoelectricity ································································· 1
1.2 Thermoelectric Efficiency ·············································································· 3
1.3 Enhancement of the Figure of Merit ·································································· 6
1.4 Motivation for the Current Work ····································································· 16

Chapter 2 Sample Preparation and Characterization ··················································· 18
2.1 Sample Synthesis ······················································································· 18
2.2 Phase Identification and Microstructure Analysis ·················································· 20
2.3 Electrical and Thermal Transport Properties Measurements ······································ 21
2.4 Carrier Concentration and Mobility Measurements ················································ 24

Chapter 3 P-type Dopant Effects on the Thermoelectric Properties of CoSi ························ 26
3.1 Background and Motivation ·········································································· 26
3.2 CoSi1-xGax Alloys ····················································································· 27
3.3 CoSi1-xBx Alloys ······················································································· 39
3.4 Summary································································································· 51

Chapter 4 Isoelectronic Substitution Effects on the Thermoelectric Properties of CoSi··········· 53
4.1 Background and Motivation ·········································································· 53
4.2 Co1-xRhxSi0.98B0.02 Alloys ·········································································· 54
4.3 CoSi0.98-xGexB0.02 Alloys············································································ 69
4.4 Summary································································································· 77

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Chapter 5 N-type and Double Doping Effects on the Thermoelectric Properties of CoSi········· 79
5.1 Background and Motivation ·········································································· 79
5.2 Ni-, Pd- and Pt-substituted CoSi Alloys ····························································· 80
5.3 Co1-x-yFexNiySi Alloys ··············································································· 93
5.4 Summary································································································· 99

Chapter 6 CoSi Samples Prepared by Powder Processing ··········································· 102
6.1 Background and Motivation ········································································ 102
6.2 Ball Milling, Consolidation and Thermoelectric Properties ···································· 104
6.3 Summary······························································································· 116

Chapter 7 High-temperature Thermoelectric Materials based on β-FeSi2 ························· 118
7.1 Background and Motivation ········································································ 118
7.2 Co-doped β-FeSi2 Materials ········································································ 119
7.3 β-FeSi2 with Reduced Grain Size and Composites with SiC Inclusions ······················ 128
7.4 Summary······························································································· 136

Chapter 8 Conclusions and Future Work······························································· 139
BIBLIOGRAPHY ························································································ 142

vii

LIST OF TABLES

Table 1 Room-temperature Hall results for CoSi1-xGax alloys with x = 0.00, 0.01 and 0.05. ···· 30

Table 2 Parameters used in the two-parabolic-band calculations for the Seebeck coefficient and
the Hall coefficient at room temperature. (me is the electron rest mass) ····························· 34

Table 3 Surface chemical composition (at. %) analyzed by Scanning Auger Nanoprobe. ········ 43

Table 4 Chemical composition (at. %) determined by atom-probe tomography. ··················· 44

Table 5 Values used in the Debye approximation for CoSi and Co1-xRhxSi0.98B0.02 samples.·· 67

Table 6 Chemical compositions (at. %) of bright and dark regions of CoSi and Pt-substituted
samples in Figure 47. ······················································································· 83

Table 7 Room-temperature carrier concentration, mobility, Seebeck coefficient, reduced Fermi
level and effective mass of Ni-doped CoSi samples. ··················································· 89

Table 8 CoSi samples with various preparation conditions. ········································· 105

Table 9 Hall results of PECS and Arc-melted samples at 80 and 300 K. ·························· 110

Table 10 Chemical compositions (at. %) of the grey region and the black region phases for
samples in Figure 81. ····················································································· 134

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LIST OF FIGURES

Figure 1 Thermoelectric unicouple for power generation (left) and thermoelectric cooling (right).
For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation. ································································ 2

Figure 2 (a) Maximum conversion efficiency for power generation, and (b) coefficient of
performance for refrigeration as a function of hot side temperature with various dimensionless
figure of merit for the unicouple. The cold side temperature is maintained at 300 K and 278 K for
(a) and (b), respectively.····················································································· 4

Figure 3 Dimensionless figure of merit vs. temperature for bulk materials investigated over the
past decades: (1) 0.9CePd2.95+0.1CePt3 [7]; (2) Bi2Te3 [8]; (3) AgPb18SbTe20 [9]; (4)
Yb0.19Co4Sb12 [10]; (5) PbTe+0.055mol%PbI2 [11]; (6) PbTe+4mol%SrTe+2mol%Na [12]; (7)
Ba8Ga16Ge30 [13]; (8) Hf0.6Zr0.4NiSn0.98Sb0.02 [14]; (9) Yb14MnSb11 [15]; (10) n-type
Si0.8Ge0.2 [16]. ······························································································· 5

Figure 4 The Seebeck coefficient, electrical conductivity and power factor as a function of the
carrier concentration for a partially or completely degenerate semiconductor. ······················ 9

Figure 5 Thermal conductivity of Si-Ge alloys as a function of Ge fraction in Si at room
temperature (reproduced from [22]). ····································································· 10

Figure 6 Schematic electronic density of states for materials with various dimensions
(reproduced from [38]). 3D: bulk crystalline materials; 2D: quantum wells; 1D: nanowires or
nanotubes; 0D: quantum dots. ············································································· 13

ix

Figure 7 Calculated electronic density of states for RuAl2 (left) with TiSi2 structure and Fe2VAl
(right) with BiF3 structure (reproduced from [44]). The Fermi level is indicated by the dashed
line at zero energy. ·························································································· 15

Figure 8 Calculated electronic density of states for CoSi with B20 cubic structure (reproduced
from [45]). The Fermi level is indicated by the dashed line at zero energy. ························· 16

Figure 9 The arc-melted CoSi and FeSi2 button-like ingots. The parallelepipeds on the right of
each ingot are the typical shapes for transport properties measurements. ··························· 18

Figure 10 Schematic sample mounting for low temperature simultaneous measurements of the
electrical resistivity, the Seebeck coefficient and the thermal conductivity.························· 22

Figure 11 The scheme of low-temperature Hall coefficient measurement. ·························· 24

Figure 12 B20 cubic structure of CoSi: larger yellow spheres are Co atoms and smaller blue
spheres are Si atoms. ······················································································· 26

Figure 13 Lattice constant of CoSi1-xGax alloys with various Ga concentration. ·················· 28

Figure 14 Electrical resistivity of (a) CoSi1-xGax alloys with various x and (b) as a function of
Ga concentration at 80 K and 300 K, respectively. ····················································· 29

Figure 15 Temperature dependence of (a) Hall carrier concentration (calculated with Equation
(21)) and (b) Hall mobility for Ga-doped CoSi alloys.················································· 31

Figure 16 Seebeck coefficients of Ga-doped CoSi alloys with various Ga concentrations as a
function of temperature. ···················································································· 32

x

Figure 17 Calculated room-temperature Seebeck coefficients (blue squares) and Hall coefficients
(pink circles) as a function of the hole concentration for a p-type doped CoSi using the
two-parabolic-band model. ················································································ 35

Figure 18 Temperature dependence of (a) the thermal conductivity and (b) the lattice thermal
conductivity for Ga-doped CoSi alloys with various Ga concentrations. The inset in (b) is the
lattice thermal conductivity as a function of Ga concentration.······································· 37

Figure 19 Dimensionless figure of merit as a function of temperature for Ga-doped CoSi alloys
with various x. ······························································································· 38

Figure 20 (a) XRD patterns of B-substituted CoSi alloys with various x and (b) magnified region
for the x = 0.10 sample with 2θ ranging from 33 to 42 degrees, as indicated by the red dashed
box in (a). CoB peaks are indicated based on PDF #03-065-2596.··································· 40

Figure 21 Lattice constant of CoSi1-xBx alloys as a function of B concentration. ················· 41

Figure 22 SEM and Auger B map images: (a) and (c) are SEM images of x = 0.02 and 0.10
samples; (b) and (d) are B maps of x = 0.02 and 0.10 samples, respectively. The B distribution is
marked by the green color. ················································································· 42

Figure 23 Temperature dependence of the electrical resistivity of CoSi1-xBx samples. ··········· 45

Figure 24 Hall results for CoSi1-xBx samples as a function of temperature: (a) Hall carrier
concentration; and (b) Hall mobility. ····································································· 46

Figure 25 Reported electrical resistivity of CoSi (solid lines) and the resistivity of our
CoSi0.98B0.02 sample (grey dashed line). Data is from [58], [57], [69], [54], [62], [70], and [71]
in chronological order. P represents polycrystalline samples and S single crystals.················ 47

Figure 26 Temperature dependence of the Seebeck coefficient of CoSi1-xBx samples. ··········· 49
xi

Figure 27 Temperature dependence of the power factor of CoSi1-xBx samples. The dashed line
represents the power factor of the state-of-the-art Bi2Te3 material [73]. ···························· 49

Figure 28 Temperature dependence of (a) the thermal conductivity and (b) the lattice thermal
conductivity of CoSi1-xBx samples. ······································································ 50

Figure 29 (a) XRD patterns of the CoSi and Co1-xRhxSi0.98B0.02 samples with various Rh
concentrations. (b) Lattice constant as a function of the Rh concentration. Closed circles
represent Co1-xRhxSi0.98B0.02 samples and the open square represents CoSi. ···················· 55

Figure 30 Electrical resistivity of CoSi and Co1-xRhxSi0.98B0.02 samples vs. temperature. ····· 56

Figure 31 Seebeck coefficient of CoSi and Co1-xRhxSi0.98B0.02 as a function of temperature. · 57

Figure 32 Hall results for CoSi and Co1-xRhxSi0.98B0.02 samples as a function of temperature:
(a) Hall carrier concentration; and (b) Hall mobility. ·················································· 58

Figure 33 Power factor of CoSi and Co1-xRhxSi0.98B0.02 samples vs. temperature. ·············· 59

Figure 34 Temperature dependence of thermal conductivity of CoSi and Co1-xRhxSi0.98B0.02
samples. ······································································································ 60

Figure 35 Lattice thermal conductivity of CoSi and Co1-xRhxSi0.98B0.02 samples as a function
of temperature. Solid curves are the calculated results using the Debye approximation. The inset
is the lattice thermal conductivity as a function of Rh concentration. ······························· 61

Figure 36 Grain size distribution of polycrystalline CoSi1-xBx samples in Figure 22. ············ 63

xii

Figure 37 Temperature dependence of ZT of CoSi and Co1-xRhxSi0.98B0.02 samples. ··········· 69

Figure 38 (a) XRD patterns and (b) Lattice constant as a function of the Ge concentration for
CoSi0.98-xGexB0.02 alloys. ················································································ 70

Figure 39 Electrical resistivity as a function of temperature for CoSi0.98-xGexB0.02 samples. ·· 72

Figure 40 Seebeck coefficient as a function of temperature for CoSi0.98-xGexB0.02 samples.··· 72

Figure 41 Temperature dependence of the power factor of CoSi0.98-xGexB0.02 samples. ········ 73

Figure 42 Temperature dependence of the thermal conductivity of CoSi0.98-xGexB0.02 samples.
················································································································· 73

Figure 43 Lattice thermal conductivity and Debye approximation results with different grain
sizes as a function of temperature for the CoSi0.93Ge0.05B0.02 sample. ···························· 74

Figure 44 Experimental lattice thermal conductivity and calculated curves for 5 mol% Ga and 5
mol% Ge substituted CoSi samples. ······································································ 75

Figure 45 Temperature dependence of ZT of CoSi0.98-xGexB0.02 samples. ························ 76

Figure 46 XRD patterns of (a) Ni-, Pd-, and Pt-substituted CoSi samples and (b) 1 mol%, 2
mol%, and 5 mol% Pt-substituted CoSi samples.······················································· 81

Figure 47 BSE images of (a) CoSi, (b) 1 mol% Pt, (c) 2 mol% Pt, and (d) 5 mol% Pt samples. · 82

xiii

Figure 48 Temperature dependence of the electrical resistivity of (a) Ni- and Pd-doped CoSi
samples and (b) Pt-substituted CoSi samples. ··························································· 84

Figure 49 Hall results of n-type doped samples: (a) electron concentration and (b) mobility. The
solid lines designated “N+A” are fits using a combination of neutral impurity and acoustic
phonon scattering.··························································································· 85

Figure 50 Reciprocal neutral impurity scattering mobility as a function of Ni concentration. ··· 86

Figure 51 Hall results of Pt-substituted samples: (a) carrier concentration and (b) mobility. ····· 88

Figure 52 Temperature dependence of the Seebeck coefficient of Ni-, Pd-, and Pt-substituted
CoSi samples. Solid lines are a guide to the eye. ······················································· 90

Figure 53 Power factor as a function of temperature for Ni-, Pd-, and Pt-substituted CoSi
samples. Solid lines are a guide to the eye. ······························································ 91

Figure 54 Temperature dependence of the thermal conductivity of Ni-, Pd-, and Pt-substituted
CoSi samples. Solid lines are a guide to the eye. ······················································· 92

Figure 55 Temperature dependence of the electrical resistivity of Co1-x-yFexNiySi alloys. ······ 93

Figure 56 Hall results for Co1-x-yFexNiySi alloys: (a) carrier concentration and (b) mobility. ·· 94

Figure 57 Temperature dependence of the Seebeck coefficient of Co1-x-yFexNiySi samples. ··· 95

Figure 58 Temperature dependence of the power factor of Co1-x-yFexNiySi samples. ············ 97

xiv

Figure 59 Temperature dependence of ZT of Co1-x-yFexNiySi samples. ···························· 99

Figure 60 Lattice thermal conductivity of CoSi samples with various grain sizes. From top to
bottom: 30 μm, 1 μm, 500 nm, 100 nm, 20 nm and κmin, respectively.···························· 103

Figure 61 XRD patterns of the arc-melted CoSi, 100-minute ball-milled CoSi powders, and
PECS-1 CoSi sample. ···················································································· 106

Figure 62 SEM fracture surface images of the PECS-1 (left) and HP (right) CoSi samples. ··· 107

Figure 63 Temperature dependence of the electrical resistivity of PECS and HP samples. ····· 108

Figure 64 Room-temperature electrical resistivity as a function of porosity for PECS and HP
CoSi samples. The dashed line is a guide to the eye. ················································· 108

Figure 65 Temperature dependence of the Seebeck coefficient of PECS and HP samples. ····· 109

Figure 66 Temperature dependence of the Seebeck coefficient of Arc-melted, HP, and HP-0.5
mol% Ni samples. ························································································· 111

Figure 67 Temperature dependence of (a) the thermal conductivity and (b) the lattice thermal
conductivity of PECS and HP CoSi samples. ························································· 114

Figure 68 Room-temperature lattice thermal conductivity as a function of porosity for PECS and
HP CoSi samples. The dashed line is a guide to the eye. ············································ 115

Figure 69 Temperature dependence of ZT of PECS and HP samples. ····························· 116

xv

Figure 70 XRD patterns of (a) β-FeSi2 and PDF #01-071-0642; and (b) Co-doped β-FeSi2
materials. ··································································································· 120

Figure 71 Electrical resistivity of Co-doped β-FeSi2 samples vs. reciprocal temperature. The
solid curves are only a guide to the eye. ······························································· 121

Figure 72 Temperature dependence of the Seebeck coefficient of Co-doped β-FeSi2 samples.
Solid lines are a guide to the eye. ······································································· 123

Figure 73 Temperature dependence of the power factor of Co-doped β-FeSi2 samples. Solid lines
are a guide to the eye. ···················································································· 124

Figure 74 High-temperature thermal conductivity measurements for Co-doped β-FeSi2: (a)
thermal diffusivity and (b) specific heat capacity. Dashed line in (b) is the Dulong-Petit value.
··············································································································· 125

Figure 75 Temperature dependence of the thermal conductivity of Co-doped β-FeSi2 samples.
··············································································································· 126

Figure 76 Temperature dependence of ZT of Co-doped β-FeSi2 samples. ························ 127

Figure 77 XRD patterns of the control, the powders ball-milled for 1.5 hours and the reduced
grain size samples. ························································································ 129

Figure 78 SEM images of (a) 1.5-hour ball-milled Fe0.92Co0.08Si2 powders; (b) fracture surface
of the control sample; and (c) fracture surface of the reduced grain size sample. ················ 130

Figure 79 Thermoelectric properties of the control and the reduced grain size samples. ········ 131

xvi

Figure 80 XRD patterns of β-Fe0.92Co0.08Si2 - SiC composites. ·································· 132

Figure 81 BSE images of (a) the control sample; (b) 1 wt.% SiC; (c) 3 wt.% SiC and (d) 5 wt.%
SiC composites. ··························································································· 133

Figure 82 Thermoelectric properties of the control sample and the SiC composites. ············ 135

xvii

Chapter 1 Introduction to Thermoelectricity

1.1 Energy Issues and Thermoelectricity
In the near future, humankind may potentially suffer from a shortage in energy, since the
demand for energy is continuously escalating while the traditional energy sources like fossil fuels
are being exhausted rapidly. Moreover, the greenhouse effect due to the combustion of fossil
fuels can also play a vital role in global warming and climate change [1]. All these concerns
impel researchers to address these challenges by two means: either developing renewable energy
sources such as solar, wind and geothermal energy, or increasing current energy utilization
efficiency.
Among various approaches to promote efficiency, thermoelectric effects are capable of
achieving direct conversion between waste heat and electricity and thus have attracted
considerable attention for energy recovery. The concept of thermoelectricity can be traced back
to 1821, when Thomas Seebeck discovered that a temperature difference between the joints of
two dissimilar metals could induce an electromagnetic effect in the loop [2]. Afterward in 1834,
Jean-Charles Peltier identified the inverse effect, demonstrating a heating or cooling
phenomenon at the junctions of two different conductors when an electric current was applied [2].
Both findings are named after their discoverers as the Seebeck effect and the Peltier effect,
respectively. Based on the above two effects, a thermoelectric unicouple composed of p- and
n-type semiconductors and metal connectors can be established as shown in Figure 1. If the
upper side of the couple is exposed to a heat source and the lower side is fixed to a heat sink (see
1

Figure 1 left), the ho charge ca
ot
arriers, name the holes in the p-le and electr
ely,
s
eg
rons in the n
n-leg,
will diffu down to the cold sid and a diff
use
de
ferential vol
ltage can be developed a
across the co
ouple
via the S
Seebeck effec On the co
ct.
ontrary, if an electric cu
n
urrent is applied through the couple from
h
the n-leg to the p-le (see Figu 1 right), the charge carriers wil absorb the heat at the top
g
eg
ure
ll
e
junctions and release the heat at t bottom o
s
e
the
ones by the P
Peltier effect
t.

Figure 1 Thermoelec
ctric unicoup for power generation (left) and th
ple
n
hermoelectri cooling (right).
ic
For inter
rpretation of the referenc to color in this and a other figu
f
ces
all
ures, the rea
ader is referr to
red
the electr
ronic version of this diss
n
sertation.
The f
former effec is capable of creating a thermoel
ct
e
g
lectric devic to produc electric po
ce
ce
ower.
This kind of thermoelectric pow generator can be use to exploit the waste heat produc in
d
wer
ed
t
ced
power pl
lants or auto
omotive exha to enha
aust
ance vehicle fuel efficien Additio
ncy.
onally, the P
Peltier
effect ca give rise to a ther
an
e
rmoelectric refrigerator and air co
onditioning. Many of other
advantag also ma
ges
ake these th
hermoelectri devices highly attra
ic
active: they are solid state
y
equipmen without vibrating par and thus a quiet and reliable; th do not r
nt
v
rts
are
hey
require the u of
use
harmful r
refrigerants and therefor are not de
re
etrimental to the environm [3]. It is also prom
ment
mising
to combi a therm
ine
moelectric po
ower genera
ator with a solar absorb to conve solar the
ber
ert
ermal
energy in electricit [4]. Despi all the be
nto
ty
ite
enefits demo
onstrated abo
ove, the most successfu and
ul
2

important applications of thermoelectric devices in the past were merely focused on radioisotope
thermoelectric generators for deep space exploration and small-scale modules for localized
heating and cooling [3]. It is not simple to transfer these devices towards large-scale applications
due to the conflict between high manufacturing costs and low conversion efficiencies.

1.2 Thermoelectric Efficiency
Based on the thermoelectric unicouple illustrated in Figure 1 and given that the geometry of
the p- and n-legs complies with a certain rule [5], the highest conversion efficiency of a power
generator can be obtained as [6]:

ηmax =

1 + Z pnT − 1
Th − Tc
⋅
Th
1 + Z pnT + Tc / Th

(1)

and the maximum coefficient of performance (COP) for refrigeration can be expressed as [5]:

COPmax =

1 + Z pnT − 1 1
T
⋅
−
Th − Tc 1 + Z pnT + 1 2

(2)

where in both cases Th is the absolute temperature of the hot side, Tc is the cold side absolute
temperature, T is the average of Th and Tc, and Zpn is a parameter dependent on the p- and
n-type semiconductors. The expression of Zpn is shown as follows [5]:

Z pn =

2
S pn

⎧⎛ κ
⎪ p
⎨⎜
⎜
⎪ σp
⎩⎝

1/ 2

⎞
⎟
⎟
⎠

3

1/ 2 ⎫

⎛κ ⎞
+⎜ n ⎟
⎝σn ⎠

⎪
⎬
⎪
⎭

2

(3)

(a)

0.8
ZpnT = infinity

ηmax

0.6

ZpnT = 10

0.4

ZpnT = 3
0.2
ZpnT = 1
0.0
300

500

700

900

1100

1300

Th (K)
(b)

20

ZpnT = 1
ZpnT = 3

COPmax

16

ZpnT = 10

12

ZpnT = infinity
8
4
0
295

300

305

310
315
Th (K)

320

325

330

Figure 2 (a) Maximum conversion efficiency for power generation, and (b) coefficient of
performance for refrigeration as a function of hot side temperature with various dimensionless
figure of merit for the unicouple. The cold side temperature is maintained at 300 K and 278 K for
(a) and (b), respectively.
where Spn is the differential Seebeck coefficient of p- and n-type semiconductors, κ is the
thermal conductivity and σ is the electrical conductivity. It can be seen that both the efficiency
and COP increase with the increase of Zpn, and thus it is called the thermoelectric figure of merit

4

for the unicouple. The figure of merit itself has dimensions of the reciprocal absolute temperature.
For simplicity, the dimensionless figure of merit ZpnT is generally used. In order to show the
relationship between the efficiencies and the dimensionless figure of merit intuitively, the
detailed values of ηmax and COPmax at various ZpnT values are presented in Figure 2 (assuming
temperature-independent ZpnT).
2.5

6

2.0
3
7

ZT

1.5
4
2

1.0

8

9

5

10

0.5
1
0.0
0

200

400

600

800

1000

1200

1400

T (K)
Figure 3 Dimensionless figure of merit vs. temperature for bulk materials investigated over the
past decades: (1) 0.9CePd2.95+0.1CePt3 [7]; (2) Bi2Te3 [8]; (3) AgPb18SbTe20 [9]; (4)
Yb0.19Co4Sb12 [10]; (5) PbTe+0.055mol%PbI2 [11]; (6) PbTe+4mol%SrTe+2mol%Na [12]; (7)
Ba8Ga16Ge30 [13]; (8) Hf0.6Zr0.4NiSn0.98Sb0.02 [14]; (9) Yb14MnSb11 [15]; (10) n-type
Si0.8Ge0.2 [16].
However, the dimensionless figure of merit for the thermoelectric unicouple does not provide
instructive information about the selection of p- and n-type materials. Assuming that the two
types of materials show the same values of the absolute Seebeck coefficient (considering that the

5

Seebeck coefficients for p- and n-type materials show opposite signs), the thermal conductivity
and the electrical conductivity, ZpnT now can be simplified to the material dimensionless figure
of merit ZT where Z is expressed as:

Z=

S 2σ

κ

(4)

In realistic cases, the two types of materials possess comparable transport properties and thus the
individual ZT value determines the device efficiency. The foremost mission for thermoelectricity
is to seek both p- and n-type materials with high ZT values.
In spite of decades of research, only a few materials exhibit ZT values greater than unity (see
Figure 3). This frustrated development of thermoelectric materials has caused the device
efficiency to lag far behind that required for practical applications. The reasons for the
difficulties to seek high ZT materials and the methods to increase the figure of merit for a given
material are the foci in the next section.

1.3 Enhancement of the Figure of Merit
Since the figure of merit is determined by the material’s physical properties as shown in
Equation (4), a straightforward idea to obtain high ZT materials is to increase both the Seebeck
coefficient and electrical conductivity whereas reduce the thermal conductivity. However, all
these properties are interrelated and thus we can hardly tune each property separately. Another
key problem is the conflicting change between these thermoelectric properties. For instance, the
thermal conductivity of a material is generally the sum of a lattice contribution (κl) and an

6

electronic component (κe) as shown in Equation (5):

κ = κl + κe

(5)

The contribution of the charge carriers to the thermal conductivity is proportional to the electrical
conductivity through the Wiedemann-Franz law [17]:

κ e = Lσ T
where L =

π2 ⎛k ⎞

2

2

-2

−8
⎜ ⎟ ≈ 2.45 × 10 J K
3 ⎝e⎠

-2

C

(6)

for free electrons and is called the Lorenz number.

Therefore the increasing thermal conductivity cancels out the benefit of an increase in the
electrical conductivity. On the other hand, the Seebeck coefficient usually drops off with the
rising electrical conductivity. The extreme examples are the insulators and metals: the former
may show very large Seebeck coefficients but they are also poor conductors; the latter are
usually good electrical conductors but their Seebeck coefficients approach zero. For the
intermediate materials, namely, semiconductors and semimetals, the electrical properties are
more suitable for good thermoelectrics.
The partially and completely degenerate semiconductors are employed here to give a
quantitative explanation of the interrelationship between the Seebeck coefficient and the
electrical conductivity. The carrier concentration (n) for this class of materials can be expressed
as [18]:

4 ⎛ 2π m*kT
n=
⎜
π ⎜ h2
⎝
*

⎞
⎟
⎟
⎠

3/ 2

F1/ 2 (η )

(7)

where m is the charge carrier effective mass, k is the Boltzmann constant, h is the Planck

7

constant and Fr(η) is the Fermi-Dirac integral shown as:
∞

Fr (η ) = ∫ ε r f (ε ) dε
0

(8)

1
f (ε ) =
1 + exp(ε − η )

in which f(ε) is the Fermi-Dirac distribution function, ε = E/kT is the reduced kinetic energy of
carriers and η = Ef/kT is the reduced Fermi level and usually greater than -2 for partial
degeneracy. The electrical conductivity and the Seebeck coefficient are expressed as [18]:

σ=

16 2π m*1/ 2 e 2 ∞
3h3

∫0 τ e ( E ) E

3/ 2

df ( E )
dE
dE

⎡⎛ 5
⎤
⎞
⎢ ⎜ 2 + λ ⎟ F3 / 2 + λ (η )
⎥
k
⎠
S = m ⎢⎝
−η ⎥
e ⎢⎛ 3
⎞
⎥
+ λ ⎟ F1/ 2 + λ (η )
⎢⎜ 2
⎥
⎠
⎣⎝
⎦

(9)

(10)

where e is the elementary electronic charge, τe is the charge carrier relaxation time and can be
λ

approximated as τe = τ0E where λ is a constant and τ0 is a constant pre-factor [19]. The
definition of λ in (10) is the same as it is in (9), representing the carrier scattering parameter. The
values of λ are usually taken as -1/2 for acoustic phonon-carrier scattering and 3/2 for carriers
scattered by ionized impurities. In our discussion, it is more convenient to explain the electrical
conductivity with the carrier concentration (n) and mobility (μ) as:

σ = neμ
The corresponding carrier mobility based on (11) can be deduced from (7) and (9) as:

8

(11)

2

S σ
S
σ

18

10

19

20

10
10
Carrier concentration n (cm-3)

21

10

Figure 4 The Seebeck coefficient, electrical conductivity and power factor as a function of the
carrier concentration for a partially or completely degenerate semiconductor.

μ=
=

2eτ 0

(η )
⎛3
⎞F
(kT )λ ⎜ + λ ⎟ 1/ 2 + λ
⎝2
⎠ F1/ 2 (η )
3m
*

F
(η )
⋅ 1/ 2 + λ
⋅ μ0
⎛3
⎞ F1/ 2 (η )
2Γ ⎜ + λ ⎟
⎝2
⎠

π

(12)

and μ0 is given as [19]:

μ0 =

4eτ 0

⎛5
⎞
Γ ⎜ + λ ⎟ (kT )λ
⎠
3m* π ⎝ 2

(13)

where Γ(x) is the Gamma function. The expression of μ0 is exactly the same as the carrier
mobility for a non-degenerate material and it is independent of Fermi level, whereas the mobility
for a degenerate material is Fermi-level dependent. Assuming that the material is kept at a certain
temperature and its effective mass is proportional to the electron rest mass, meanwhile provided

9

that μ0 is a constant, then the carrier-concentration-dependent Seebeck coefficient can be
calculated according to (7) and (10) and the electrical conductivity can also be determined by (7),
(11) and (12) for given values of λ and η. In both cases, the carrier scattering process is assumed
to be dominated by acoustic phonons and thus λ is taken as -1/2. As shown in Figure 4, the
2

calculation presents that a saturated S σ, namely the highest thermoelectric power factor, can be
obtained by tuning the carrier concentration for a given material. This modification of electrical
properties is typically achieved by replacing some host atoms with dopants and the obtained
materials are usually heavily doped semiconductors.
1.6
1.4

κ (W/cm K)

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

20

40

60

80

100

Ge fraction, %
Figure 5 Thermal conductivity of Si-Ge alloys as a function of Ge fraction in Si at room
temperature (reproduced from [22]).
Returning to the expressions (4) and (5), one can contemplate two methods to increase ZT:
either enhancing the power factor or reducing the thermal conductivity, especially the isolated
lattice part. Fortunately, doping not only benefits the electrical properties, but also helps reduce
10

the lattice thermal conductivity. Two ways to reduce the lattice thermal conductivity, i.e. alloying
and doping, have long been established. Both the methods introduce impurity atoms into the
lattice. The phonons can be strongly scattered due to the mass and size differences between host
and impurity atoms [20]. The thermal conductivity reduction by forming solid solutions has been
extensively studied for many materials systems such as Si-Ge alloys [21], III-V alloys [22], and
Bi2Te3-xSex and Bi2-xSbxTe3 alloys [23]. The effect of solid solution formation on the thermal
conductivity for Si-Ge alloys is illustrated in Figure 5.
Another effective way to reduce the thermal conductivity is to extend the complexity of the
unit cell for a parent crystal structure. This idea is based on the following expression [24]:

κl =

BMV 1/ 3θ 3
n 2 / 3γ 2T

(14)

where B is a constant, M is the average atomic mass, V is the average volume per atom, θ is the
Debye temperature, T is the absolute temperature, γ is the Grüneisen parameter and n is the
number of atoms per primitive unit cell. The lattice thermal conductivity decreases as the number
of atoms in the unit cell grows. This idea has been proven quite successful when taking the
layered Zintl compounds (e.g. SrZn2Sb2) and diamond-like group IV materials (e.g. Si) as the
parent crystal structures. A material with much lower thermal conductivity like SrZnSb2 can be
obtained from the former [25]; and the latter can be expanded to I-III-VI2 (n=4), I2-IV-VI3 (n=6)
and I3-V-VI4 (n=8) compounds, showing reduced thermal conductivity with increasing number
of atoms [26]. Moreover, the complex unit cell may also bring about some unconventional
thermal properties. For instance, the AgSbTe2 material (deduced from the PbTe structure)

11

exhibits extremely low thermal conductivity [27]. The reduction also likely stems from the
enhanced anharmonicity in the crystal lattice. A larger Grüneisen parameter represents a stronger
anharmonicity in the lattice and thus a lower thermal conductivity as is seen in Equation (14).
Nowadays, a new class of materials with cage-like structures has also attracted much
research interest. These materials possess an open crystal framework and thus they show
relatively low thermal conductivity themselves. The so-called “rattling” atoms, like rare earth
and alkaline earth atoms, can be introduced into the voids of these compounds and thus to scatter
the phonons more intensively. On the other hand, the crystalline framework itself can provide for
good electrical conduction. The above benefits result in ZT values greater than one for these
materials, including filled skutterudites and clathrates [28,29].
With the occurrence of nanotechnology, we have witnessed an increasing number of studies
on low dimensional thermoelectric materials. In 1993, Hicks and Dresselhaus theoretically
predicted that the figure of merit could be enhanced significantly in 2D quantum well structure
due to the quantum confinement effect of electrons [30]. This concept has been proven to
successfully enhance ZT close to 2.5 for thin film superlattices [31]. Although the thin film
materials exhibit alluring ZT values, the chemical and physical stability, fabrication difficulties
and manufacturing cost prevent their large-scale application. On the contrary, bulk
nanostructured materials are more suitable to be mass produced. The 3D nanocomposites and
nanogranular materials have been synthesized to take advantage of numerous interfaces within
the materials to reduce the thermal conductivity [32-34]. Generally speaking, the increase of
interfaces will also cause a decrease in electrical conductivity [35,36]. The total enhancement
12

stems from the more intensive reduction of thermal conductivity than electrical conductivity.
However, one must keep in mind that it is unrealistic to infinitely minimize the thermal
conductivity because the phonon mean free path of a given material cannot be shorter than its
interatomic spacing. The “minimal” thermal conductivity [37] eventually constrains the
enhancement of the figure of merit by only reducing the denominator in Equation (4). Therefore,
this limitation reminds us to consider the other way to increase ZT, namely finding out
approaches to enhance the power factor.
2D

1D

0D

Density of States

3D

E
Figure 6 Schematic electronic density of states for materials with various dimensions
(reproduced from [38]). 3D: bulk crystalline materials; 2D: quantum wells; 1D: nanowires or
nanotubes; 0D: quantum dots.
As mentioned above, quantum confinement effects are beneficial to the thermoelectric
performance and the improvement can be attributed to an enhanced power factor [30]. The
enhancement originates from the unique electronic structure of the low dimensional materials as
sketched in Figure 6 [38]. In a simple point of view, the Seebeck coefficient can be understood
by the Mott equation [39]:

13

S=

π 2k 2T ⎛ d ln σ ( E ) ⎞
3e

⎜
⎝

dE

⎟
⎠

(15)
E = Ef

Provided that the scattering of electrons is independent of energy, then the energy-dependent
electrical conductivity is proportional only to the electronic density of states. In the above case,
the Seebeck coefficient is the result of the varying rate of the density of states at the Fermi level.
As can be seen in Figure 6, abrupt changes can appear in the density of states for low
dimensional materials, resulting in rapid variation near the Fermi level and leading to a larger
Seebeck coefficient. Usually, the above assumption is too brief and the detailed Mott equation
can explain the Seebeck coefficient more clearly as follows [40]:

S=

π 2 k 2T ⎛ d ln g ( E ) d ln v 2 ( E ) d ln τ ( E ) ⎞
3e

⎜
⎜
⎝

dE

+

dE

+

dE

⎟
⎟
⎠ E = Ef

(16)

where g is the density of states, v is the average electron drift velocity and τ is the electron
relaxation time. The third term in Equation (16) implies that the Seebeck coefficient can be also
changed by altering the electron scattering mechanism [41].
In 1996, Mahan and Sofo suggested that a high power factor should take place in any system
where sharp discontinuities appear in the material’s density of states [42]. The interpretation of
their theory is that materials with the similar electronic density of states as low dimensional ones
are most likely to exhibit high power factors no matter what length scale they belong to [43].
This boosted theoretical and experimental studies on seeking high power factor bulk materials.
After decades of research, such materials with the unique electronic structure do exist. For
instance, the d electrons of transition metals are prone to hybridize with the s or p electrons of
14

5

10
Density of States (states/eV)

Density of States (states/eV)

RuAl2
4
3
2
1

Fe2VAl

8
6
4
2
0

0
-10

-5

0

-10

5

-5

0

5

Energy (eV)

Energy (eV)

Figure 7 Calculated electronic density of states for RuAl2 (left) with TiSi2 structure and Fe2VAl
(right) with BiF3 structure (reproduced from [44]). The Fermi level is indicated by the dashed
line at zero energy.
main group elements, leading to two unique types of density of states in the compounds
composed of them. The first type is termed as hybridization gap and the materials are categorized
as narrow-band semiconductors (e.g. RuAl2). The second one is called pseudo gap because the
small overlap between the valence and the conduction bands results in a low density of states at
the “gap” (e.g. Fe2VAl). As shown in Figure 7, the densities of states for the two examples both
present sharp peaks near the Fermi level [44]. Therefore, one is likely to obtain high power
factors for these materials. In general, the position of the Fermi level is not optimized to achieve
the highest power factor. The theoretical calculations provide an insightful suggestion that we
can improve the electronic properties by tuning the Fermi level to a suitable position where the
variation of the density of states is severe.

15

1.4 Motivation for the Current Work
In the main project, the semimetallic CoSi system is selected as our research object. This
material is promising for near-room-temperature thermoelectric applications. The theoretical
electronic structure calculations also showed the same feature around the Fermi level for CoSi
[45,46] as that for Fe2VAl, as can be seen in Figure 8. The unique density of states results in a
quite large Seebeck coefficient even though its electrical conductivity behaves more like a metal.
Since the Fermi level of CoSi is located around the pseudo gap, it should be possible to achieve a
higher power factor by tuning its position. We hope to understand the underlying science of the
enhancement of the power factor through this investigation and apply the results to other
materials systems.

Density of States (states/eV)

15

10

5

0
-1

-0.5

0

0.5

1

Energy (eV)
Figure 8 Calculated electronic density of states for CoSi with B20 cubic structure (reproduced
from [45]). The Fermi level is indicated by the dashed line at zero energy.

16

A general approach to adjust the Fermi level is dopant substitution for host atoms. The
elements beside both Co and Si in the Periodic Table are candidates for substitutions. In the
following text, Chapters 3-5 mainly focus on the substitution effects on the thermoelectric
properties of arc-melted CoSi alloys. The materials with chemical formulas like Co1-xMxSi or
CoSi1-xMx (M = substitution elements) were investigated.
In Chapter 6, the research turns to the preparation of CoSi samples by powder processing.
The effects of powder processing under different synthesis conditions were explored. Finally in
Chapter 7, another system β-FeSi2 was studied as a low-cost high-temperature (around 1000 K)
thermoelectric material. Its electrical properties could be appropriately tuned by Co doping. In
addition, the efforts to prepare nano-grained samples and composite structures are also presented.

17

Chapter 2 Sample Preparation and Characterization

2.1 Sample Synthesis
The samples in the present work were usually prepared by arc melting the stoichiometric
quantities of high purity elements such as Co (99.95%, Alfa Aesar), Si (99.9999%, Alfa Aesar)
and the necessary substitution elements on a water-cooled copper hearth under flowing argon.
The ingots were flipped and re-melted typically five times to encourage homogeneity. Since a
rapid cooling process at an estimated rate of tens of Kelvins per second occurs after melting, the
sample tends to crack or crumble once it is completely cooled. To avoid this problem, one should
turn over the ingot promptly to re-melt it when it is still hot. The ingots were then sealed in
quartz ampoules under vacuum (~ 10

-5

o

Torr) and annealed at 900 C for several days. The arc

melting process for FeSi2 ingots is the same as CoSi. However, the phase obtained from the melt
is a mixture of metallic FeSi and α-FeSi2 phases instead of the semiconducting β-FeSi2
according to the Fe-Si phase diagram [47]. Therefore, additional processing for these materials is
required. The obtained button-like CoSi and FeSi2 samples are shown in Figure 9.
FeSi2
CoSi

1 cm
Figure 9 The arc-melted CoSi and FeSi2 button-like ingots. The parallelepipeds on the right of
each ingot are the typical shapes for transport properties measurements.
18

o

In order to form the β-FeSi2 phase, it is necessary to anneal the ingots under 955 C [47].
However, there are always cracks inside the samples and thus an appropriate section cannot be
obtained for transport property measurements. In this case, powder processing was employed to
prepare high-quality samples. The standard synthesis procedure is to pulverize the arc-melted
FeSi2 ingots for 30 minutes, press the powders under a pressure of 30 MPa and at a temperature
o

o

of 1150 C for 8 minutes to form a dense disk, and finally anneal the sealed pellet at 800 C for
100 hours. All the ingot pulverization was completed with an 8004 tungsten carbide vial set in a
SPEX SamplePrep 8000M high-energy ball mill. The densification was achieved using a Pulsed
Electric Current Sintering (PECS) system from Thermal Technology LLC under argon
atmosphere. To minimize oxidation, the vial set was sealed in an argon-filled glove box with
Parafilm® M barrier film before milling and the powders were also loaded in a glove box and
transferred to the PECS system quickly.
The PECS process, also sometimes referred to as spark-plasma sintering, is a
pressure-assisted current-activated consolidation technique. This method has been reported to be
useful to attain high density samples in a shorter time compared to the traditional hot pressing
o

[48]. Another distinction is that an extremely fast heating rate of about 2000 C/min can be
achieved in this system [49]. Recent studies on the sintering mechanisms showed that the pulsing
had little effect on the sintering, while the thermal activation only stemmed from the direct
current in the form of Joule heating [50]. Some researchers claimed that PECS was beneficial to
the thermoelectric properties improvement [51,52]. The grain growth can be suppressed due to
the fast heating and consolidation process [53]. Therefore, it is possible to obtain nano-grained
19

materials, the structures of which are promising for low lattice thermal conductivity. In our work,
the influences of ball milling and PECS on the thermoelectric properties of CoSi and β-FeSi2
samples are investigated. The PECS conditions like temperature, pressure, and ramp rate as well
as the ball milling time are the controllable parameters and can be optimized to attain fine
microstructures and enhance the thermoelectric performance. The detailed differences between
sample preparations will be elucidated in the subsequent chapters where it is necessary.

2.2 Phase Identification and Microstructure Analysis
The phase and crystal structure were generally determined by powder X-ray diffraction
(XRD) using a Rigaku Miniflex II desktop X-ray diffractometer with Cu Kα (wavelength =
0.154187 nm) radiation at Michigan State University (MSU). The powders were obtained by
crushing a portion of each sample with a set of agate mortar and pestle. The XRD patterns were
evaluated using a Jade 9.0 software package, which includes a JCPDS XRD database. Some of
the samples were also characterized at Oak Ridge National Laboratory (ORNL) using a
PANalytical X’pert Pro diffractometer with Cu Kα radiation, as independent studies to determine
the phase purity.
The microstructures were observed using a JEOL JSM-7500F field-emission scanning
electron microscope (SEM) at the MSU Center for Advanced Microscopy. The chemical
compositions of certain samples were determined by energy dispersive X-ray spectroscopy
(EDS). However, EDS is not sensitive to the light elements, so light element (e.g. B) evaluation
was carried out by a physical electronic scanning Auger Nanoprobe (model Phi 680) at ORNL.
20

The backscattered electron (BSE) imaging was selected to distinguish impurity phases from the
majority especially when there is a large atomic weight difference between phases. A phase with
a larger atomic number (Z-contrast) is usually brighter in color than the lighter one.

2.3 Electrical and Thermal Transport Properties Measurements
The electrical and thermal transport properties measurements are divided to two portions: the
low-temperature measurements from 80 K to room temperature (300 K) and the measurements
above room temperature, or high-temperature measurements.
For low-temperature measurements, a sample shape of rectangular parallelepiped is required.
Generally speaking, the arc-melted samples were sectioned to typical dimensions of 2.5×2.5×7
3

3

mm and the PECS samples to 2.5×2.5×10 mm (see Figure 9) with a Buehler IsoMet low speed
-5

diamond saw. The measurements were carried out under vacuum (< 10

Torr) in a Janis model

ST-100 cryostat cooled by liquid nitrogen. Figure 10 shows the sample mounting scheme for the
cryostat measurement: two thin copper strips were fixed along the length of the sample. One end
of the sample was fixed to a copper base and the other to an 800 Ω resistive heater.
Copper-constantan thermocouples were soldered directly to the strips. All connections to the
sample were implemented using a silver-based epoxy.
Electrical resistivity was obtained using a four-probe DC technique. The two copper leads of
the thermocouples acted as the voltage probes, measuring the voltage drop (VS) when an electric
current (IS) was applied through the sample. The resistivity (ρ) is calculated as:

21

IH
VH
resistive
heater
constantan

sample

IS

cop
pper
ΔT
Δ
VS & ΔV
co
opper strip

screw ho
ole

copp base
per
Figure 10 Schematic sample mo
0
c
ounting for low tempera
ature simultaneous mea
asurements o the
of
electrical resistivity, the Seebeck coefficient and the therm conduct
l
k
mal
tivity.

ρ=

VS s
⋅
IS l

(17)

is
sectional are and l is the probe sepa
ea
aration betw
ween the therm
mocouples. After
where s i the cross-s
measurin the resisti
ng
ivity, the hea was activ
ater
vated by ene
ergizing it w another current. A st
with
teady
temperatu differenc (ΔT) was established between the probes afte a certain t
ure
ce
s
d
e
er
time (genera 5
ally
minutes). The Seebe coefficie (S) was then calcula
eck
ent
ated using t induced Seebeck vo
the
oltage
(ΔV) as:
S=

ΔV
ΔT

(18)

The therm conduct
mal
tivity (κ) wa obtained based on a steady-state condition p
as
e
provided tha the
at
22

power generated by the heater was totally conducted through the sample to the copper base:

κ=

VH I H l
⋅
ΔT s

(19)

where IH is the electric current through the heater and VH is the heater voltage. All the above
data was automatically collected by a LabVIEW program.
The high-temperature electrical resistivity and Seebeck coefficient were simultaneously
measured by a commercial ULVAC ZEM-3 system under low-pressure helium atmosphere. This
system can carry out measurements from room temperature to 1100 K. The sample geometry and
the electrical resistivity measurement are the same as those used in the cryostat. To measure the
Seebeck coefficient, three different temperature differences were created and the corresponding
voltages were recorded to plot a line of the Seebeck voltage versus the temperature difference.
The slope of the line and the contribution of the type-R thermocouples were summed to
determine the material’s Seebeck coefficient.
The high-temperature thermal conductivity was obtained based on the thermal diffusivity (D),
specific heat capacity (Cp) and sample density (d) measurements as:

κ = D ⋅ Cp ⋅ d

(20)

The thermal diffusivity and the specific heat capacity were measured using a commercial
Netzsch LFA-457 laser flash system (300–1373 K) and a Netzsch DSC-200 F3 system (300–873
K), respectively. Samples used in thermal diffusivity measurements had thin disk geometry with
a thickness of 1-2 mm and a diameter of 12.7 mm. The room-temperature sample density was
determined by Archimedes method with ethanol as a medium.

23

2.4 Carr Concent
rier
tration and Mobility M
Measuremen
nts
The c
carrier conce
entration was determined based on a one-band as
d
ssumption as follows:

RH =

1
ne

(21)

where RH is the Hal coefficien n is the c
ll
nt,
carrier conce
entration and e is the el
d
lementary ch
harge
(positive for holes and nega
s
ative for e
electrons). T
The low-te
emperature Hall coeffi
icient
measurem
ments (60-300 K) were carried ou in a Quan
e
ut
ntum Desig Versalab system with the
gn
h
Electrica Transport Option (ETO under he
al
O)
elium atmosp
phere. Thin rectangular plate sampl of
les
3

typical di
imensions of 2×7×0.5 m were us Silver le
mm
sed.
eads of diam
meter 0.127 m were atta
mm
ached
to the sam with a silver-filled adhesive. Th sample m
mple
he
mounting sch
heme is show in Figure 11.
wn
VH
B

jx
Ey

Ix
z
sample
e
silver leads
s

silver-filled adhesi
ive

x
t: t
thickness

y
Figure 11 The schem of low-tem
me
mperature H coefficie measurem
Hall
ent
ment.
As sh
hown above when an e
e,
electric curre (Ix) pass through the sample along the le
ent
ses
ength
and a ma
agnetic field (B) is appli perpendi
d
ied
icular to the sample plan carriers a driven b the
ne,
are
by

24

Lorentz force to one side of the sample and a balanced transverse electric field (Ey) as well as a
Hall voltage (VH) is finally established. The Hall coefficient shows a relationship with the Hall
voltage as:

RH =

Ey

V t
= H
jx B I x B

(22)

where t is the sample thickness and jx is the corresponding current density of Ix. The ETO
program recorded the virtual Hall resistances (defined by VH/Ix) induced by different magnetic
fields (-3 to 3 Tesla) at each temperature. Then the Hall coefficient at a given temperature was
calculated from the slope of the Hall resistance versus the magnetic field curve. The ETO
simultaneously measured the electrical resistivity (ρ) through a four-probe DC technique as well.
The carrier mobility (μ) was eventually obtained from the Hall coefficient and the electrical
resistivity as:

μ=

25

RH

ρ

(23)

Chapter 3 P-type Dopant Effects on the Thermoelectric Properties of CoSi

3.1 Background and Motivation
Intrinsic CoSi is a diamagnetic semimetal with excess electrons dominating the transport
properties [54]. This material crystallizes in the B20 cubic structure (space group P213) with a
3

lattice constant of 4.443 Å and a theoretical density of 6.59 g/cm [55]. The unit cell contains
four Co atoms and four Si atoms, as shown in Figure 12. Each Co (or Si) atom is coordinated by
seven Si (or Co) atoms with one nearest Si (or Co) atom at 2.286 Å, three second nearest Si (or
Co) atoms at 2.329 Å, and three third nearest Si (or Co) atoms at 2.469 Å. The nearest Co-Co
and Si-Si distances are 2.727 Å and 2.750 Å, respectively. The former distance is larger than the
Co-Co single-bond length (2.46±0.01 Å) proposed by Pauling [56], suggesting weak or no bonds
between Co atoms.

Figure 12 B20 cubic structure of CoSi: larger yellow spheres are Co atoms and smaller blue
spheres are Si atoms.

26

In the past decades, substitutions on both Co and Si sites for CoSi have been extensively
studied, showing that the neighboring elements in the Periodic Table have considerably good
solubility in this material. In general, it is much easier for the materials with the same B20
crystal structure such as MnSi, FeSi and CoGe to form a solid solution with CoSi [57-59].
Among them, FeSi can even form a continuous solid solution with CoSi [58] while the solubility
limit for Ge is as high as 67 mol% [59]. On the other hand, the materials with dissimilar crystal
structures show lower solubility limit. For instance, the solubility limit for Al in CoSi is between
20 and 30 mol% because CoAl shows another cubic structure (space group Pm 3 m) [60] while
the solubility limit for Ni is even lower (about 17 mol%) since NiSi is stable with an
orthorhombic B31 structure (space group Pnma) [61].
The thermoelectric properties of Fe-doped and Al-doped CoSi alloys have been
systematically studied [58,60,62]. Neither of them was beneficial to the thermoelectric
performance. However, another p-type dopant, boron (B), was reported to be helpful to enhance
the power factor [63]. The study on B substitution was not comprehensive because only one
sample with 0.5 mol% B doping was prepared and the reason for the enhancement was not clear
[63]. In this chapter, the possible p-type dopants like Ga and B were investigated, and the effects
of these p-type dopants on the thermoelectric properties are clarified.

3.2 CoSi1-xGax Alloys
The Ga-doped CoSi samples were all prepared by arc melting. Since Ga has a very low
melting point (302.9 K) as well as high vapor pressure, it readily vaporizes compared to Co and
27

Si during melting. Therefore, the prepared samples always lost some Ga (the weight loss of the
ingot was no more than 1%) and the chemical formula only represents the nominal composition.
The elements like In and B in the same column as Ga were also attempted. The preparation of
CoSi1-xInx alloys was not successful because In only agglomerated at the bottom of the ingot.
The results for CoSi1-xBx alloys will be discussed in section 3.3.
The XRD patterns for CoSi1-xGax alloys with x ranging from 0 to 0.20 only show a CoSi
single phase. Figure 13 shows the calculated lattice constant for CoSi1-xGax alloys. The linear
relation between the lattice constant and the composition suggests the successful formation of
solid solutions according to Vegard’s law [60]. The solubility limit for Ga in CoSi has not been
reached and is more than 20 mol%.

Lattice Constant (Å)

4.48

4.47

4.46

4.45

4.44
0

0.05

0.1
0.15
Ga concentration, x

0.2

0.25

Figure 13 Lattice constant of CoSi1-xGax alloys with various Ga concentration.

28

(a)

0.0007

x=0.00
x=0.01
x=0.05
x=0.10
x=0.15
x=0.20

0.0006

ρ (Ω cm)

0.0005
0.0004
0.0003
0.0002
0.0001
0
50

100

150

200

250

300

350

T (K)
(b)

0.0007
80 K

0.0006

300 K

ρ (Ω cm)

0.0005
0.0004
0.0003
0.0002
0.0001
0
0

0.05

0.1

0.15

0.2

Ga concentration, x
Figure 14 Electrical resistivity of (a) CoSi1-xGax alloys with various x and (b) as a function of
Ga concentration at 80 K and 300 K, respectively.

29

Figure 14 displays the electrical resistivity of CoSi1-xGax samples. All the resistivity curves
show a metallic behavior with a positive temperature coefficient. The resistivity first increases
with the increasing Ga concentration up to 10 mol% and then decreases with the further increase
of Ga as shown in Figure 14(b). This trend can be ascribed to a two-band conduction model as
will be discussed below. All the Ga-doped samples show larger resistivity than the pure CoSi
over the entire temperature range except for the x = 0.01 sample. This sample exhibits a little
lower resistivity near room temperature compared to CoSi, while it still shows higher resistivity
at lower temperature.
Table 1 Room-temperature Hall results for CoSi1-xGax alloys with x = 0.00, 0.01 and 0.05.
Sample

x = 0.00

20

Hall carrier concentration (10

-0.00479

4.30

13.0

69.5

2 -1 -1

Hall mobility (cm V s )

-0.0145

3.78

-3

cm )

x = 0.05

-0.0165

3 -1

Hall coefficient (cm C )

x = 0.01

65.5

11.5

The room-temperature Hall results for the x = 0.00, 0.01 and 0.05 samples are listed in Table
1 and the temperature dependence of the Hall carrier concentration as well as the Hall mobility is
shown in Figure 15. The Hall coefficients for samples with x ≥ 0.10 are too small to be
21

determined, suggesting extremely high carrier concentrations (more than 2×10

-3

cm ) in these

samples. Figure 16 shows the temperature-dependent Seebeck coefficient for all Ga-doped
samples. The pure CoSi sample shows negative Seebeck coefficients over the entire temperature

30

(a)

1.00E+22

Carrier Concentration (cm-3)

x=0.00
x=0.01
x=0.05

1.00E+21

1.00E+20
50

100

150

200

250

300

350

T (K)
(b)

1000
x=0.00
x=0.01
x=0.05
μ (cm2/Vs)

100

10

1
50

100

150

200

250

300

350

T (K)
Figure 15 Temperature dependence of (a) Hall carrier concentration (calculated with Equation
(21)) and (b) Hall mobility for Ga-doped CoSi alloys.

31

60
40
20

S (μV/K)

0
-20
x=0.00
-40

x=0.01
x=0.05

-60

x=0.10
x=0.15

-80

x=0.20

-100
50

100

150

200

250

300

350

T (K)
Figure 16 Seebeck coefficients of Ga-doped CoSi alloys with various Ga concentrations as a
function of temperature.
range, while the Seebeck coefficients of the x = 0.01 sample are positive below 120 K and
become negative at higher temperature. All the other samples doped with more Ga show positive
Seebeck coefficients over the investigated temperature range. Generally, the Seebeck coefficient
has the same sign as the Hall coefficient, indicating the type of dominant carriers, i.e. negative
for electron dominating and positive for hole dominating. However, a contradiction is observed
for the 5% Ga-doped sample. This sample shows positive Seebeck coefficients from 80 K to
room temperature, whereas its Hall coefficients are always negative at the corresponding
temperature. This phenomenon as well as the change of the resistivity is a clear indication of

32

two-band conduction where the conduction and valence bands affect the transport properties
simultaneously.
In this conduction model, the conduction band overlaps the valence band to some extent and
the negative overlapping energy is defined as ΔE. Since both electrons and holes participate in
the transport, the Hall coefficient must be expressed as follows rather than Equation (21) [64]:

RH =

p − nb 2

(24)

e( p + nb) 2

where p is the hole concentration, n is the electron concentration and b is the ratio of electron
mobility to hole mobility. The concentrations of holes and electrons can be expressed with the
reduced Fermi level relative to the top of the valence band and the bottom of the conduction
band. The value is positive for the Fermi level within the band and negative for outside the band.
The expressions for the carrier concentrations are:
*
4 ⎛ 2π mp kT
⎜
p=
π⎜
h2
⎝

⎞
⎟
⎟
⎠

4 ⎛ 2π mn*kT
n=
⎜
π⎜
h2
⎝

⎞
⎟
⎟
⎠

3/ 2

F1/ 2 (ηp )

(25)

F1/ 2 (ηn )

(26)

3/ 2

*

where the subscripts p and n represent holes and electrons and m and η are the effective mass
and the reduced Fermi level, respectively. Then ΔE is obtained as:

ΔE = −(ηn + ηp )kT

(27)

Provided that acoustic phonons dominate the carrier scattering, the Seebeck coefficient for two
types of carriers can be deduced from Equation (10) as follows [58]:

33

S=

S pσ p + S nσ n

σp +σn

=

⎧
⎫
⎤
⎤⎪
k ⎪ p ⎡ 2 F1 (η p )
nb ⎡ 2 F1 (η n )
− ηp ⎥ −
− ηn ⎥ ⎬
⎢
⎨
⎢
e ⎪ p + nb ⎣ F0 (η p )
⎢
⎥
⎦⎪
⎦ p + nb ⎣ F0 (η n )
⎩
⎭

(28)

where σp and σn are the electrical conductivity for holes and electrons, respectively. Under a
rigid band scenario, p-type doping only shifts the Fermi level downward and does not affect the
overlap [46]. Using the parameters given in Ref. [65] and assuming that all the parameters are
composition independent, the Seebeck coefficient and the Hall coefficient can be calculated as a
function of the hole concentration. The parameters used for room-temperature calculations are
listed in Table 2 and the results are shown in Figure 17.
Table 2 Parameters used in the two-parabolic-band calculations for the Seebeck coefficient and
the Hall coefficient at room temperature. (me is the electron rest mass)
*

Parameter

-ΔE

b

mn

Value

0.0156 eV

6.4

2me

mp

*

6me

Ga-doping can move the Fermi level downward to the valence band and thus increase the
hole concentration and meanwhile reduce the electron concentration. With the introduction of
extra holes, the Seebeck coefficient begins to increase and finally change the sign from negative
to positive as can be seen in Figure 17. However, the Hall coefficient is maintained negative even
though the Seebeck coefficient has become positive. The reason for the disagreement in sign is
the large mobility difference between electrons and holes. As the Hall coefficient is related to
the square of b while the Seebeck coefficient is only related to the first power of b, this behavior

34

0.025

0

0.000

3

50

RH (cm /C)

0.050

S (μV/K)

100

-50

-100

-0.025

0

2×10

20

4×10

20

6×10

20

8×10

20

-0.050
21

10

-3

Hole concentration (cm )
Figure 17 Calculated room-temperature Seebeck coefficients (blue squares) and Hall coefficients
(pink circles) as a function of the hole concentration for a p-type doped CoSi using the
two-parabolic-band model.
can be observed when the value of b is much greater than unity. Besides explaining the
interesting contradiction, the two-band model can be used to elucidate the change of the
resistivity as well. The electrical conductivity of a material with two types of carriers can be
expressed as:

σ = σp +σn

(29)

Since the mobility of holes is much smaller than electrons, the rising hole concentration
cannot compensate the loss of the mobility initially. However, the further increase of the hole
concentration outweighs the mobility loss and finally reduce the electrical resistivity. However,

35

this cannot explain the fact that the samples with extremely high hole concentrations (i.e. the
20% Ga-doped sample) still show higher resistivity than CoSi. This interesting fact has also
been found for Fe and Al doped CoSi alloys. McNeill et al. and Li et al. both proposed a
hypothesis that the higher resistivity for Al-doped CoSi samples was ascribed to the additional
scattering between electrons and holes [60,66]. The model fitting in the study of Asanabe et al.
for Fe-doped CoSi showed enlarged hole effective mass when the dopant level is above 8
mol%, implying that the hole mobility became smaller with the rising hole concentration [58].
Both explanations attributed the enormous increase in the resistivity to the reduction of carrier
mobility, which does happen to our Ga-doped samples. As shown in Table 1 and Figure 15(b),
the Hall mobility decreases drastically with the rising Ga concentration. Since the electrical
resistivity of Ga-doped alloys is escalated while the absolute value of the Seebeck coefficient
is smaller than pure CoSi, the thermoelectric power factor is decreased by Ga-doping.
The thermal conductivity continues to decrease with increasing Ga concentration as shown in
Figure 18(a). The lattice thermal conductivity can be calculated using Equation (6) with a Lorenz
number for free carriers and the results are shown in Figure 18(b). The thermal conductivity
reduction totally originates from the reduction of the lattice contribution. The reduction of the
lattice thermal conductivity can be understood by the alloying mechanism as we mentioned in
section 1.3. Because there are large atomic weight and size differences between Ga and Si,
phonons can be scattered quite intensively by the point defects associated with the Ga
substitution. The enhanced scattering is more pronounced at low temperature as can be seen in

36

(a)

0.5
x=0.00
x=0.01
x=0.05
x=0.10
x=0.15
x=0.20

κ (W/cm K)

0.4
0.3
0.2
0.1
0.0
50

100

150

200

250

300

350

T (K)
(b)

κl (W/cm K)

0.5

κl (W/cm K)

0.4

0.3

0.5
0.4
0.3
0.2
0.1
0.0

80 K
300 K

0
0.2

0.05 0.1 0.15 0.2
Ga concentration, x

0.1

0.0
50

100

150

200

250

300

350

T (K)
Figure 18 Temperature dependence of (a) the thermal conductivity and (b) the lattice thermal
conductivity for Ga-doped CoSi alloys with various Ga concentrations. The inset in (b) is the
lattice thermal conductivity as a function of Ga concentration.

37

Figure 18(b). The reduction is less near room temperature because the phonon-phonon Umklapp
scattering instead of point-defect scattering becomes dominant at higher temperature. The effect
of point-defect scattering is roughly proportional to x(1-x), where x is the dopant concentration
[62]. Therefore, lower lattice thermal conductivity is expected for higher dopant concentrations
up to 50 mol%.

0.07
x=0.00

0.06

x=0.01
0.05

x=0.05
x=0.10

0.04
ZT

x=0.15
x=0.20

0.03
0.02
0.01
0.00
50

100

150

200

250

300

350

T (K)
Figure 19 Dimensionless figure of merit as a function of temperature for Ga-doped CoSi alloys
with various x.

The dimensionless figure of merit is shown in Figure 19. Even though the thermal
conductivity is decreased by Ga doping, the reduction cannot compensate the decreasing power
factor. As a result, the 1% Ga-doped sample shows the same room-temperature ZT as the
non-doped CoSi while the ZT values for the other samples are much lower.
38

3.3 CoSi1-xBx Alloys
In addition to Ga, the other p-type dopants like Fe and Al also led to a severe increase in the
resistivity even if only small amounts of dopants were used. The increasing resistivity is
definitely detrimental to the power factor. However, in a study on B-doped CoSi, previous
researchers found the resistivity was decreased while the Seebeck coefficient was enhanced by
0.5 mol% B doping [63]. They also attributed the enhancement of power factor to the p-type
doping effect. Since B is in the same column as Al and Ga in the Periodic Table, it is expected as
a p-type dopant when substituting for Si. Based on our previous results and those for Al and Fe
doped samples, p-type doping will cause the inverse effect rather than enhance the power factor.
Therefore, it is of great interest to investigate the effect of B doping. In this section, we extended
the study on CoSi1-xBx alloys to higher B concentrations (x= 0.00-0.10) and the effect of B
substitution is elucidated [67].
All the CoSi1-xBx alloys in this study were also prepared by arc melting. The B element is
from Plasmaterials, Inc. with a purity of 99.9%. In contrast to the pure CoSi, the B-substituted
samples were seldom shattered during the preparation. As we shall see, this behavior is due to the
unique morphology of these samples.
The XRD patterns show that the CoSi phase is observed in all samples as can be seen in
Figure 20(a). However, a secondary phase is detected in the CoSi0.90B0.10 sample as shown in
Figure 20(b), while this impurity phase is not found in the other B-substituted samples. A
successful B substitution effect would be reflected in the change of the lattice parameter due to
the large size difference between B and Si atoms (atomic radii of 87 and 111 pm, respectively).
39

Intensity (arb. unit)

(a)

x=0.10
x=0.05
x=0.02
x=0.01
x=0.005
x=0.00
20

30

40

50
60
2θ (degree)

70

80

90

34

CoB (111)

CoB (011)

CoB (200)

Intensity (arb. unit)

(b)

36

38
2θ (degree)

40

42

Figure 20 (a) XRD patterns of B-substituted CoSi alloys with various x and (b) magnified region
for the x = 0.10 sample with 2θ ranging from 33 to 42 degrees, as indicated by the red dashed
box in (a). CoB peaks are indicated based on PDF #03-065-2596.

40

4.450
MSU
ORNL

Lattice Constant (Å)

4.448

4.446

4.444

4.442

4.440
0

0.02

0.04

0.06

0.08

0.1

B concentration, x

Figure 21 Lattice constant of CoSi1-xBx alloys as a function of B concentration.
Consequently, the lattice constant was determined with both the XRD results from MSU and
ORNL, as shown in Figure 21. The two independent results agree with each other, showing no
pronounced shift in the lattice constant with increasing B concentration. Any difference between
the lattice constants is likely due to the experimental effects instead of the compositional
differences. The impurity peaks shown in Figure 20(b) were identified as a CoB phase.
According to the trend of the lattice constant, we speculate that this impurity phase is likely
present in the other samples with lower B concentrations even though the XRD cannot detect it.
Larere et al. found that B segregated at the grain boundaries in their investigation on
B-substituted CoSi alloys [68]. Their results imply that the same effect can occur in our samples.
41

(a)

(b)

50μm

50μm

(c)

(d)

50μm

50μm

Figure 22 SEM and Auger B map images: (a) and (c) are SEM images of x = 0.02 and 0.10
samples; (b) and (d) are B maps of x = 0.02 and 0.10 samples, respectively. The B distribution is
marked by the green color.
In order to verify the above hypothesis, Auger microscopy was used to determine the chemical
composition and B distribution for CoSi1-xBx alloys. As can be seen in Figure 22, B is only
present along the grain boundaries as the green phase for both x = 0.02 and 0.10 samples. The
chemical compositions within the grains and grain boundaries are listed in Table 3. Both the
samples have B only present at the grain boundaries while the B content within the grains cannot
be detected. The ratio of Co to B atoms is close to 1, indicating the CoB phase as we observed in
XRD patterns. The Auger microscopy provides a strong corroboration of the XRD results and
proves our assertion that CoB phase is also present in samples with lower B concentrations. The

42

Table 3 Surface chemical composition (at. %) analyzed by Scanning Auger Nanoprobe.
Grains

Grain Boundaries

x

B

C

Si

Co

B

C

Si

Co

0.00

0.0

3.0

36.0

61.0

0.0

3.2

37.1

59.7

0.02

0.0

3.1

35.6

61.3

45.5

2.7

1.9

49.9

0.10

0.0

4.9

35.9

59.2

41.9

4.2

2.1

51.8

above two investigations show that the solubility limit for B in CoSi is extremely low, in stark
contrast to the reported solubility of 0.5 mol%.
Our collaborators at Northwestern University (NU) carried out atom-probe tomography
analysis on the x = 0.02 sample to determine the chemical composition as a function of the
distance away from the grain boundaries (the B-rich phase). Their results show that the
composition of the B-rich phase at the grain boundaries is also close to CoB (see Table 4). The
matrix composition is almost stoichiometric CoSi despite a very low B concentration. The B
concentration seems to increase when approaching the grain boundaries. Based on this study, we
estimate the solubility limit for B in CoSi is lower than 0.06 mol%. The composition near the
center of the tested grain even shows B solubility as low as 0.03 mol%. The existence of Mn is
likely due to the impurity of starting Co materials. For CoSi, 1 mol% substitution leads to a
20

replacement of approximately 4.5×10
19

means no more than 2.7×10

-3

cm

-3

cm

host atoms. As a result, this kind of B solubility

Si atoms are replaced. Provided that one B atom introduces

one hole after doping and based on the semi-quantitative analysis in section 3.2, the increasing

43

hole concentration can only result in a small downward shift of the Fermi level and thus the
p-type doping effect of B is supposed to be negligible.
Table 4 Chemical composition (at. %) determined by atom-probe tomography.
Element

B-rich phase

< 1 μm from interface

~ 10 μm from interface

Co

56.21

50.21

50.29

B

43.59

0.03

0.015

C

0.020

0.0022

Not Detected

Mn

0.184

0.0055

0.0024

Si

Not Detected

49.76

49.69

The temperature dependence of the electrical resistivity of all the CoSi1-xBx samples is
shown in Figure 23. The resistivity first decreases with increasing B concentration all the way to
2 mol%, then monotonically increases with the further increase of x. The Hall measurements
show almost unchanged carrier concentration as shown in Figure 24. The Hall coefficients for all
the B-substituted samples are always negative over the entire temperature range, indicating
electrons are dominant in transport. These results are consistent with the low B solubility limit in
CoSi. The holes introduced by B doping are too few to affect the Hall coefficients as well as the
Hall carrier concentration. On the other hand, the mobility is indeed affected by B substitution.
Both the x = 0.01 and 0.02 samples show higher carrier mobility than the pure CoSi around room
temperature. The mobility for the above two samples is almost proportional to T

44

-3/2

, indicating

0.00025

ρ (Ω cm)

0.00020

0.00015

x=0.00
x=0.005

0.00010

x=0.01
x=0.02

0.00005

x=0.05
x=0.10

0.00000
50

100

150

200

250

300

350

T (K)

Figure 23 Temperature dependence of the electrical resistivity of CoSi1-xBx samples.
acoustic phonons dominate the carrier scattering. When the B concentration further increases, the
-3/2

carrier mobility decreases and deviates from the T

relation. Thus, the trend of the resistivity is

determined by the compositional dependence of the carrier mobility. The decrease of the
mobility with higher B concentrations is understandable because the rising quantities of the
B-rich phase at the grain boundaries can intensively enhance the interface scattering. However, it
is interesting to elucidate the increasing mobility as found in the x = 0.01 and 0.02 samples.
Since the samples used in our study are arc-melted polycrystals, the most influential defect, i.e.
cracks, can easily form during the rapid heating and cooling preparation process. The measured
resistivity is affected by these defects critically. Figure 25 shows some reported resistivity data
45

(a)

5.0E+20

n (cm-3)

4.0E+20

3.0E+20
x=0.00
x=0.005
x=0.01
x=0.02
x=0.05
x=0.10

2.0E+20

1.0E+20

0.0E+00
50

100

150

200

250

300

350

T (K)
(b)

900

-3/2

T

800

x=0.00
x=0.005

600
μ (cm2/Vs)

700

x=0.01
x=0.02

500

x=0.05

400

x=0.10

300
200
100
0
50

100

150

200

250

300

350

T (K)
Figure 24 Hall results for CoSi1-xBx samples as a function of temperature: (a) Hall carrier
concentration; and (b) Hall mobility.

46

100

ρ (μΩ m)

10

1
Asanabe 1964 P
Nikitin 1970 S
Lue 2004 P
Petrova 2010 S

Asanabe 1965 P
Fedorov 1995 S
Skoug 2009 P

0.1
0

50

100

150

200

250

300

350

T (K)
Figure 25 Reported electrical resistivity of CoSi (solid lines) and the resistivity of our
CoSi0.98B0.02 sample (grey dashed line). Data is from [58], [57], [69], [54], [62], [70], and [71]
in chronological order. P represents polycrystalline samples and S single crystals.
for pure CoSi samples. We can clearly see huge differences among these studies. The unusually
high resistivity of some CoSi specimens can be attributed to the cracks within specimens or the
off-stoichiometric compositions. The resistivity of our CoSi0.98B0.02 sample is close to those
lowest values that have ever been reported, indicating the sample quality is improved by 2 mol%
B substitution. The polycrystalline CoSi is a brittle material and tends to crack due to the
intergranular failure along the grain boundaries [68]. It has been pointed out that B segregation
can enhance the mechanical properties by improving the cohesive strength at grain boundaries

47

for another intermetallic Ni3Al system [72]. Our qualitative observation of an increased
mechanical integrity of B-substituted samples is consistent with this picture. Thus we
hypothesize the same benefit of B to the CoSi intermetallics: modest quantities of B substitution
can minimize the possibility of intergranular fracture and hence reduce the microcracks to
maintain the low electrical resistivity. The exact effect of B on the fracture performance of CoSi
is being investigated by our collaborators at ORNL.
The temperature dependence of the Seebeck coefficients is shown in Figure 26. The Seebeck
coefficients for all the samples are negative over the investigated temperature range, consistent
with the Hall results. The values are between -90 and -100 μV/K at room temperature with no
clear dependence of B concentrations. Based on the calculated density of states shown in Figure
8, slight p-type doping can probably enhance the Seebeck coefficient because the variation
around the Fermi level becomes larger. This is likely the reason for the trivial increase in the
Seebeck coefficients for some of the B-substituted samples near room temperature. The power
-2

-1

factor is enhanced to 60 μWK cm

at room temperature for the x = 0.02 sample, a 70%

increase relative to our CoSi sample and 50% larger than the typical value of Bi2Te3 material [73]
(see Figure 27). Some of the other B-substituted samples also show enhanced power factors.
These power factors are amongst the highest reported for any materials at room temperature.
The critical problem for CoSi is the quite high thermal conductivity compared to
state-of-the-art thermoelectric materials. B substitution cannot efficiently reduce the lattice
thermal conductivity as shown in Figure 28. In the meantime, the electronic contribution to the
total thermal conductivity is increased due to the lower resistivity. This disadvantage leads to a
48

0
-10

x=0.00
x=0.005
x=0.01
x=0.02
x=0.05
x=0.10

-20
-30
S (μV/K)

-40
-50
-60
-70
-80
-90
-100
-110
50

100

150

200

250

300

350

T (K)
Figure 26 Temperature dependence of the Seebeck coefficient of CoSi1-xBx samples.

Power Factor (μW K-2 cm-1)

70

x=0.00
x=0.005
x=0.01
x=0.02
x=0.05
x=0.10
Bismuth Telluride

60
50
40
30
20
10
0
50

100

150

200

250

300

350

T (K)
Figure 27 Temperature dependence of the power factor of CoSi1-xBx samples. The dashed line
represents the power factor of the state-of-the-art Bi2Te3 material [73].
49

(a)

0.50
x=0.00
x=0.005
x=0.01
x=0.02
x=0.05
x=0.10

κ (W/cm K)

0.40

0.30

0.20

0.10

0.00
50

100

150

200

250

300

350

T (K)
(b)

0.45
0.40

x=0.00
x=0.005

0.30
κl (W/cm K)

0.35

x=0.01
x=0.02

0.25

x=0.05
x=0.10

0.20
0.15
0.10
0.05
0.00
50

100

150

200
T (K)

250

300

350

Figure 28 Temperature dependence of (a) the thermal conductivity and (b) the lattice thermal
conductivity of CoSi1-xBx samples.
50

room-temperature ZT of only 0.12 for the x = 0.02 sample. A ZT improvement is expected by
lowering the lattice thermal conductivity while maintaining the electrical properties. It may be
achieved by either isoelectronic substitution or grain size reduction. The results of these two
approaches are shown and discussed in the following chapters.

3.4 Summary
According to the calculated density of states, it is promising to obtain a larger Seebeck
coefficient by p-type doping because of the sharper features near the top of the valence band. In
this chapter, we showed and discussed the thermoelectric properties of Ga- and B-substituted
CoSi samples. The solubility limit for Ga in CoSi is more than 20 mol%, while B shows
extremely limited solubility below 0.06 mol%. As a result, Ga-doped samples exhibit
pronounced p-type doping effects for the semimetallic CoSi. The Seebeck coefficient changes
sign from negative to positive with increasing doping level. The Hall coefficient shows opposite
signs to the Seebeck coefficients over wide temperature and Ga concentration ranges due to a
large electron to hole mobility ratio. With the rising Ga concentration, the hole mobility
decreases drastically and thus the increasing hole concentration cannot outweigh the loss of the
mobility, resulting in higher resistivity compared to non-doped CoSi. The lattice thermal
conductivity is reduced by Ga-doping due to enhanced phonon scattering by point defects. In
sum, Ga-doping, like the other p-type dopants such as Fe and Al, is detrimental to the total
thermoelectric performance.
On the other hand, B shows trivial p-type doping effect because of the limited solubility. The
51

extra amounts of B segregate at the grain boundaries in a form of CoB phase. The Seebeck
coefficient is almost unchanged and the Hall carrier concentration is maintained the same,
showing no dependence of the B concentration. However, B is beneficial to the reduction of the
electrical resistivity. This advantage is supposed to originate from the healing effect of B on the
internal cracks. The thermoelectric power factor is enhanced due to the improved electrical
conductivity for samples with modest B concentrations. It is promising to obtain high-quality
polycrystalline intermetallics like CoSi using intentional grain boundary segregations. The
important role of B in CoSi alloys will also be seen in the next chapter, where we try to further
improve the thermoelectric performance by isoelectronic elemental substitutions.

52

Chapter 4 Isoelectronic Substitution Effects on the Thermoelectric Properties of CoSi

4.1 Background and Motivation
As we mentioned in section 3.3, some researchers underestimated the thermoelectric power
factor of CoSi because the electrical resistivity of their samples was unreasonably high due to
extrinsic factors. Modest B substitution is able to improve the quality of the polycrystalline
samples and thus maintain the electrical resistivity as low as the handbook value [54]. The
decisive drawback for the CoSi0.98B0.02 sample is the high thermal conductivity, in spite of the
quite high power factor. The large power factor suggests that the electrical properties have been
tuned properly. In order to further enhance its thermoelectric performance, we proposed to take
advantage of Rh and Ge substitution on Co and Si sites respectively to reduce the lattice thermal
conductivity through phonon - point-defect scattering.
Since Rh and Ge are in the same columns as the corresponding host atoms in the Periodic
Table, they are supposed to be isoelectronic with Co and Si atoms. So the electronic properties
are expected to be unaffected. Ge shows quite large solubility in CoSi as we illustrated in section
3.1 because CoGe and CoSi are isostructural. Even though RhSi is stable with a B31 structure
below 1353 K, it has a B20 cubic structure at higher temperature [74]. Since our preparation
method is based on arc melting, Rh should possess a large solubility in CoSi because these two
monosilicides are also isostructural. In this chapter, the thermoelectric properties of
Co1-xRhxSi0.98B0.02 [75] and CoSi0.98-xGexB0.02 alloys are presented and discussed. A
quantitative analysis of the reduction of the lattice thermal conductivity is highlighted.
53

4.2 Co1-xRhxSi0.98B0.02 Alloys
The Rh wire used in this study was from Sigma-Aldrich with a purity of 99.9%. We initially
attempted to prepare Co1-xRhxSi alloys without B substitution by the same arc melting
procedure. However, those samples easily shattered presumably due to intensive internal stress.
Thus we could not obtain an appropriate sample to measure the transport properties. We did not
meet such issues when preparing Co1-xRhxSi0.98B0.02 samples, implying that 2 mol% B
addition again plays an important role in preserving the sample quality. Although we did not
carry out element mapping for these Rh-substituted samples, we assume that B still segregates at
the grain boundaries in a form of B-rich phase. The XRD patterns of Co1-xRhxSi0.98B0.02
samples only show a CoSi B20 structure as can be seen in Figure 29(a). Figure 29(b) displays the
lattice constants for these samples. It can be seen that B substitution has trivial influence on the
lattice constant of CoSi. The lattice constant varies linearly with the Rh concentration, indicating
a solid solution is successfully formed. The solubility limit for Rh in CoSi has not been reached
and should be above 20 mol%.
Figure 30 shows the electrical resistivity of the CoSi and Co1-xRhxSi0.98B0.02 samples as a
function of temperature. It can be clearly seen that all B-added samples exhibit similar low
resistivity above 200 K due to fewer or no cracks within the samples. The presence of
microcracks cannot be excluded for the CoSi sample because its resistivity is much higher than
the other samples. At low temperature (around 80 K), the resistivity increases monotonically
with the increasing Rh concentration, suggesting enlarged residual resistivity with Rh
substitution. The presence of the gap around 300 K is attributed to two independent measurement
54

(a)

(b)

4.52

Lattice Constant (Å)

4.50
4.48
4.46
4.44
4.42
0.00

0.05

0.10

0.15

0.20

Rh concentration, x
Figure 29 (a) XRD patterns of the CoSi and Co1-xRhxSi0.98B0.02 samples with various Rh
concentrations. (b) Lattice constant as a function of the Rh concentration. Closed circles
represent Co1-xRhxSi0.98B0.02 samples and the open square represents CoSi.
55

0.30
CoSi
x=0.00

0.25

x=0.05
x=0.10

ρ (mΩ cm)

0.20

x=0.20
0.15

0.10

0.05

0.00
0

100

200

300

400

500

600

T (K)
Figure 30 Electrical resistivity of CoSi and Co1-xRhxSi0.98B0.02 samples vs. temperature.
systems, and is within the sum of the estimated uncertainties of the two measurement schemes.
The temperature dependence of the Seebeck coefficient of CoSi and Co1-xRhxSi0.98B0.02
samples is shown in Figure 31. The absolute Seebeck coefficient increases drastically from 15 to
29 μV/K with increasing Rh concentration at 80 K, which can be understood by Equation (16).
The Seebeck coefficient shows a pronounced compositional dependence above room temperature:
the value first increases with the Rh concentration and the x = 0.10 sample possesses the largest
Seebeck coefficient; whereas the x = 0.20 sample definitely exhibits lower Seebeck coefficients

56

0
-10

CoSi

-20

x=0.00
x=0.05

-40
S (μV/K)

-30

x=0.10

-50

x=0.20

-60
-70
-80
-90
-100
-110
0

100

200

300

400

500

600

T (K)
Figure 31 Seebeck coefficient of CoSi and Co1-xRhxSi0.98B0.02 as a function of temperature.
than the other two samples from room temperature to 560 K. Compared to CoSi and
CoSi0.98B0.02, the Seebeck coefficients of the x = 0.10 sample are still lower at temperatures
above 400 K. This fact is not consistent with the supposition that Rh does not affect the band
structure. Based on our Hall measurements (see Figure 32), we find that the Hall electron
concentration increases slightly with the increasing x. In the meantime, the mobility decreases
drastically at 80 K with the rising Rh concentration and deviates from the acoustic phonon
scattering mechanism. The acoustic phonon scattering is still dominant for all the Rh-substituted
samples around room temperature. Thus, the Seebeck coefficient increment at low temperature

57

(a)

5.00E+20

n (cm-3)

4.00E+20

3.00E+20
CoSi
2.00E+20

x=0.00
x=0.05
x=0.10

1.00E+20

x=0.20
0.00E+00
50

100

150

200

250

300

350

300

350

T (K)
(b)

900

-3/2

T

800

x=0.00

μ (cm2 /Vs)

700

x=0.05

600

x=0.10

500

x=0.20

400
300
200
100
0
50

100

150

200

250

T (K)
Figure 32 Hall results for CoSi and Co1-xRhxSi0.98B0.02 samples as a function of temperature:
(a) Hall carrier concentration; and (b) Hall mobility.
58

stems from the enhanced carrier scattering, while the decrease at high temperature is attributed to
the increasing electron concentration. Based on the above results, Rh substitution still influences
the electronic structure even though it is isoelectronic with Co. It likely causes a closing of the
pseudo gap or an upward shift of the Fermi level. A better understanding of the change of the
-2

-1

electronic structure requires further investigations. As a result, a power factor of 60 μWK cm

at room temperature is obtained for the x = 0.10 sample as shown in Figure 33, while the other
two Rh-substituted samples show lower power factors at temperatures above 200 K. We did not
prepare samples with Rh concentrations over 20 mol% due to the decreasing trend of the power
factor.
70
CoSi

Power Factor (μW K-2 cm-1)

60

x=0.00
x=0.05

50

x=0.10
x=0.20

40
30
20
10
0
0

100

200

300

400

500

600

T (K)
Figure 33 Power factor of CoSi and Co1-xRhxSi0.98B0.02 samples vs. temperature.

59

Figure 34 shows the temperature dependence of the thermal conductivity. Over the entire
temperature range, the thermal conductivity drops monotonically with the increasing Rh
concentration. The thermal conductivity for the x = 0.20 sample is only 31% of that of the pure
CoSi at 80 K and 66% at room temperature. The lattice thermal conductivity can be obtained
using the aforementioned method in section 1.3 and the results are shown in Figure 35. It can be
clearly seen that the suppression of the thermal conductivity is ascribed to the considerable
reduction of the lattice component.
0.5
CoSi
x=0.00
x=0.05
x=0.10
x=0.20

κ (W/cm K)

0.4

0.3

0.2

0.1

0.0
50

100

150

200

250

300

350

T (K)
Figure 34 Temperature dependence of thermal conductivity of CoSi and Co1-xRhxSi0.98B0.02
samples.
In order to illustrate the effect of Rh substitution on the reduction of the lattice thermal
conductivity, we use the Debye approximation to evaluate the experimental data. The lattice

60

CoSi
x=0.00
x=0.05
x=0.10
x=0.20

κl (W/cm K)

0.4

0.30
κl (W/cm K)

0.5

0.3

80 K
300 K

0.20
0.10
0.00
0

0.2

0.05 0.1 0.15 0.2
Rh concentration, x

0.1

0.0
50

100

150

200

250

300

350

T (K)
Figure 35 Lattice thermal conductivity of CoSi and Co1-xRhxSi0.98B0.02 samples as a function
of temperature. Solid curves are the calculated results using the Debye approximation. The inset
is the lattice thermal conductivity as a function of Rh concentration.
thermal conductivity under this approximation can be expressed as [76,77]:

κl =

k 4T 3

θ /T

∫
2π 2 h 3v 0

x 4e x

τ −1 ( x )(e x − 1) 2

dx

(30)

where x = ħω/kT, ω is the phonon frequency, v is the mean sound velocity, θ is the Debye
temperature and τ is the phonon relaxation time. The Debye temperature is taken as 625 K as
reported in literature [71]. This Debye temperature implies the highest phonon energy of 54 meV
in our approximation. According to the inelastic neutron scattering results, the experimental
phonon density of states of CoSi almost vanishes when the phonon energy is above 56 meV [78],

61

indicating the Debye temperature used here is quite accurate. The longitudinal sound velocity
can be calculated as [79]:

vl =

4
B+ G
3

(31)

ρ

and the transverse sound velocity can be expresses as [79]:

vt =

G

(32)

ρ

in both cases, B is the bulk modulus, G is the shear modulus and ρ is the sample mass density.
For a cubic crystal structure, only three elastic constants, i.e. c11, c12 and c44, exist and the
relations between the elastic constants and the moduli are as follows [80]:

c + 2c12
B = 11
3

(33)

c − c + 3c44
G = 11 12
5

(34)

With the experimental elastic constants [71], the longitudinal sound velocity is determined as
7313 m/s and the transverse velocity is 4129 m/s at room temperature. The mean sound velocity
is calculated as [25]:
1/ 3

⎛
⎞
3
v=⎜
⎟
⎜ v −3 + 2 v −3 ⎟
t ⎠
⎝ l

(35)

and it gives rise to a mean velocity of 4600 m/s. The total phonon scattering rate is supposed to
be the sum of various scattering processes. In this approximation, we only take into account three
types of phonon scattering mechanisms: grain-boundary, point-defect and phonon-phonon

62

Umklapp scatterings. The expression for the scattering rate is [77,81]:
−1
−1
−1
τ −1 = τ gb + τ pd + τ Umklapp
4

2

θ

−
v
⎛k ⎞
⎛k ⎞
= + A ⎜ B ⎟ x 4T 4 + BU ⎜ B ⎟ x 2T 3e 3T
L
⎝ h ⎠
⎝ h ⎠

(36)

where L represents the grain size, A and BU are two pre-factors for point-defect and Umklapp
scatterings, respectively. Figure 36 shows the grain size distribution evaluated with the SEM
images in Figure 22. An average size of 30 μm is determined by the reported method [82]. Since
the preparation procedures for our samples are the same, it is reasonable to fix L at this value for
all samples. Returning to the point-defect scattering, A can be expressed as [81]:

A=

VΓ

(37)

4π v3

32
28
24

Counts

20
16
12
8
4
0

0

10

20

30

40

50

60

Grain Size (μm)
Figure 36 Grain size distribution of polycrystalline CoSi1-xBx samples in Figure 22.
63

where V is the average volume per atom and Γ is the point-defect scattering parameter. The
expression of BU is as follows [81]:

BU =

hγ 2

(38)

Mv 2θ

where γ is the Grüneisen parameter and M is the average atomic mass. The scattering parameter
Γ for point defects is the sum of two effects, i.e. the mass fluctuation (ΓM) and the strain field
effect (ΓS) caused by the atomic size differences. For our Rh-substituted samples, we ignore the
B substitution effect and only take into account the effect of Rh substitution for Co sites. The two
fluctuations contribute to Γ as [83]:
2
1
⎛ M i ⎞ 1 2 ⎛ M i − M i2 ⎞
∑ ci ⎜ M ⎟ fi fi ⎜ M ⎟
⎜
⎟
⎠
i
i =1 ⎝
⎝
⎠
n

ΓM =

2

(39)

n

∑ ci

i =1

2
⎛ M i ⎞ 1 2 ⎛ ri1 − ri2 ⎞
∑ ci ⎜ M ⎟ fi fi ε ⎜ r ⎟
⎜
⎟
⎠
i
i =1 ⎝
⎝
⎠
n

ΓS =

n

∑ ci

2

(40)

i =1

In both cases, the subscript i represents i

th

sublattice (i.e. Co and Si sublattices) and the

superscripts 1 and 2 represent two different atoms in the sublattice (i.e. Co and Rh). The symbol
c is the occupancy for the sublattice (ci = 1 for each Co and Si sublattice), M is atomic mass, f is
1

2

fractional concentration (fi + fi =1), r is atomic radius and ε is an adjustable parameter. The
average sublattice mass and radius are defined as [83]:
1
M i = fi1M i + fi2 M i2

64

(41)

ri = fi1ri1 + fi2 ri2

(42)

and the average mass of the alloy is [83]:
n

∑ ci M i

M = i =1
n

(43)

∑ ci

i =1

The adjustable parameter ε is supposed to be related to the Grüneisen parameter [84]. With an
experimental Poisson’s ratio of 0.27 for CoSi [71], we can estimate the adjustable parameter
using the analysis proposed by Abeles as [84]:

ε =10.76+34.45γ +27.56γ 2

(44)

A Grüneisen parameter of 1.73 for CoSi was obtained by Delaire et al. using first-principles
calculations [78]. We attempted to use this value to calculate the lattice thermal conductivity for
our samples. However, the obtained lattice thermal conductivity values are much higher than the
experimental data, implying the calculated Grüneisen parameter is too small for our
approximation. Then we tried another calculation results also based on density functional theory
[80] to determine the Grüneisen parameter using the following expression [27]:

γ=

3β BVm
CV

(45)

where β is the volumetric thermal expansion coefficient, B is the bulk modulus, Vm is the volume
per mole, and CV is the molar heat capacity at constant volume. Based on the room temperature
literature results [80], β is 2.11×10

-5

-1

K , B is 2.11×10

11

Pa, Vm is 1.34×10

-5

3

m /mol and CV is

40 J/mol K. This gives rise to a Grüneisen parameter of 4.5. Since β and CV have the same

65

temperature dependence while B and Vm are weakly temperature dependent, we can assume that

γ is a constant over our experimental temperature range.
Using the above method and parameter values (θ = 625 K, v = 4600 m/s, γ = 4.5, L = 30 μm),
the lattice thermal conductivity is calculated for the x = 0.05 sample as a solid curve shown in
Figure 35. It is clearly seen that the calculated curve agrees with the experimental data quite well
especially at temperatures ranging from 200 K to 300 K. The pure CoSi is supposed to exhibit no
point-defect scattering. However, the calculated values are about 6 times larger at 80 K and 2
-42 3

times larger at 300 K than the experimental data if we set A as zero. A value of 0.58×10

s for

A gives the best match between the calculation and the experimental data, as shown in Figure 35.
The non-zero value of A is more reasonable because lattice imperfections always exist in
crystalline samples. A little larger A value of 0.94×10

-42 3

s is used for the x = 0.00 sample

because B substitution probably introduces more lattice imperfections. For the x = 0.10 and 0.20
samples, the large Grüneisen parameter makes the calculated values lower than the experimental
data. Smaller Grüneisen parameters like 4.15 for the x = 0.10 sample and 3.7 for the x = 0.20
sample provide better coincidences. The parameters used in the Debye approximation for various
samples are listed in Table 5.
It is surprising that the Grüneisen parameters used in our calculations are two to three times
the typical values for intermetallic compounds [78]. This discrepancy was also found in FeSi,
which is an isostructural material with CoSi. The first-principles calculations give rise to a
Grüneisen parameter of 1.6 for FeSi, while several times larger values (γ > 4 for various phonon
frequencies at temperatures below 300 K) were obtained based on experimental results [78].
66

Table 5 Values used in the Debye approximation for CoSi and Co1-xRhxSi0.98B0.02 samples.
Parameter

CoSi

x = 0.00

x = 0.05

x = 0.10

x = 0.20

γ

4.5

4.5

4.5

4.15

3.7

ε

N/A

N/A

724

628

516

L (μm)

30

30

30

30

30

-42 3

s )

0.58

0.94

1.92

3.11

4.82

-18

s/K)

2.23

2.23

2.18

1.81

1.37

A (10

BU (10

Delaire et al. attributed the enlarged values to the electron-phonon coupling and drew a
conclusion that the electron-phonon interaction was due to the sharp features around the Fermi
level in the electronic density of states [78]. Since the density of states of CoSi also shows such
sharp features as illustrated in section 1.4, this material likely exhibits a larger Grüneisen
parameter than expected. Even though Delaire et al. pointed out that the coupling in CoSi is
weaker than in FeSi, considering the FeSi system shows much larger Grüneisen parameters for
the acoustic phonons (9±1 for 26 meV acoustic peak at room temperature) [78], it may be
reasonable to use an average Grüneisen parameter of 4.5 for CoSi. The reason for the decreasing

γ in the x = 0.10 and 0.20 samples can also be understood by the change of the electronic
structure. It was found that the Grüneisen parameter of FeSi became smaller with increasing
temperature due to the closing of its narrow band gap. Returning to Figure 32, the rising carrier
concentration with the increasing Rh concentration is also likely due to the closing of the pseudo
gap as we mentioned before. Moreover, we notice that the Seebeck coefficients of Rh-substituted
67

samples bend upward at lower temperature compared to the pure CoSi. This fact may also
indicate that the pseudo gap is narrowed to some extent by Rh substitution. Thus, Rh substitution
probably plays the same role in the electronic structure of CoSi as the thermal disorder effect in
FeSi, causing a smaller γ for samples with higher Rh concentrations. A complete understanding
of the effect of Rh substitution on the electronic structure of CoSi still requires more
investigations like first-principles calculations.
The large Grüneisen parameters directly cause intensive strain field effect on the lattice
thermal conductivity reduction based on Equations (40) and (44). The ε values listed in Table 5
are larger than 500 for all Rh-substituted samples. It has been reported that substituted
ZrNiSn-based half-Heusler alloys also show a ε value above 500 [83]. It is true for CoSi that the
atomic size fluctuation plays a more important role than the mass fluctuation in the lattice
thermal conductivity reduction. For instance, Al substitution for Si sites can induce a drastic
reduction of the lattice thermal conductivity. Since the mass difference between Al and Si atoms
is negligible (< 4%), the reduction is supposed to stem from the atomic radius difference (Al is
125 pm while Si is 111 pm). The peak broadening at high angles in Figure 29(a) also implies a
large strain effect within the Rh-substituted samples. In the next section, we will show another
example to confirm the large strain field effect in CoSi alloys as well.
The temperature dependence of ZT is shown in Figure 37. Compared to CoSi, ZT is increased
by a factor of 2.5 for the x = 0.10 sample. This sample also shows a 25% increase relative to the
x = 0.00 sample, due to the reduction of the lattice thermal conductivity. Unfortunately, the 20%
Rh-substituted sample shows a lower ZT than the 10% sample at room temperature because of
68

the reduced Seebeck coefficient as well as the power factor. As a result, ZT cannot be further
improved by more isoelectronic substitutions.
0.16
CoSi
x=0.00

0.12

x=0.05

ZT

x=0.10
x=0.20

0.08

0.04

0.00
50

100

150

200

250

300

350

T (K)
Figure 37 Temperature dependence of ZT of CoSi and Co1-xRhxSi0.98B0.02 samples.

4.3 CoSi0.98-xGexB0.02 Alloys
Ge and Sn are also candidates for isoelectronic substitutions for Si sites in CoSi. As we
mentioned in section 3.1, Ge doubtlessly shows a quite large solubility in CoSi. We attempted to
prepare CoSi1-xSnx alloys with x ranging from 0.05 to 0.20 by arc melting. However, Sn only
agglomerated as a separate phase and thus did not form a solid solution with CoSi. The addition
of B again facilitated the preparation while the CoSi1-xGex alloys without B addition easily
shattered during the processing. As shown in Figure 38(a), the XRD patterns for Ge-substituted

69

Intensity (arb. units)

(a)

x=0.20
x=0.10
x=0.05
x=0.00
CoSi
20

30

40

50

60

70

80

90

2θ (deg)
(b)

Lattice Constant (Å)

4.50

4.48

4.46

4.44

4.42
0.00

0.05

0.10

0.15

0.20

Ge concentration, x
Figure 38 (a) XRD patterns and (b) Lattice constant as a function of the Ge concentration for
CoSi0.98-xGexB0.02 alloys.
70

CoSi0.98B0.02 alloys only display a B20 single phase and the peaks continue to shift to lower
angles with the increase of Ge concentration. The lattice parameter varies linearly with the
substitution concentration, as can be seen in Figure 38 (b).
The thermoelectric properties, i.e. the electrical resistivity, Seebeck coefficient, power factor
and thermal conductivity, are shown in Figures 39-42. Unlike the behavior of Rh-substituted
samples, Ge substitutions, except for x = 0.05, cause a pronounced increase in the resistivity over
a wide temperature range from 80 to 600 K. The Hall results show that the carrier concentration
20

is not affected by Ge substitution (at room temperature, n = 4.25×10
4.11×10

20

-3

cm

20

for x = 0.05 and n = 4.16×10
20

sample (n = 6.16×10

-3

cm

-3

cm

for x = 0.00, n =

for x = 0.10), except for the 20% Ge

-3

cm at room temperature). Therefore, the rising resistivity is attributed to

the decrease of the carrier mobility. The Seebeck coefficients are almost the same for the x =
0.00, 0.05 and 0.10 samples from 200 to 300 K, consistent with the constant carrier concentration.
The former two samples even show the same values at higher temperature, while the Seebeck
coefficients for the x = 0.10 sample are enhanced compared to the other two at temperatures
2

above 300 K. The enhancement is likely due to the enhanced carrier scattering (μ = 84 cm /Vs
2

for x = 0.10 compared to μ = 95 cm /Vs for x = 0.00 at room temperature), provided that the
Fermi level of the x = 0.10 sample is the same as that of the parent. The Seebeck coefficients for
the x = 0.20 sample are much lower than the other samples over a wide temperature range from
200 to 600 K. According to Equation (10), the Seebeck coefficient is directly related to the Fermi
level. Since the rising resistivity indicates additional carrier scattering processes in this
sample, the decrease of the Seebeck coefficient is presumably due to its higher Fermi level. This
71

0.30

ρ (mΩ cm)

0.20

x=0.00
0.10

x=0.05
x=0.10
x=0.20

0.00
0

100

200

300

400

500

600

700

T (K)
Figure 39 Electrical resistivity as a function of temperature for CoSi0.98-xGexB0.02 samples.

0
-20

x=0.00
x=0.05

S (μV/K)

-40

x=0.10

-60

x=0.20

-80
-100
-120
-140
0

100

200

300

400

500

600

700

T (K)
Figure 40 Seebeck coefficient as a function of temperature for CoSi0.98-xGexB0.02 samples.
72

80
x=0.00

Power Factor (μW K-2 cm-1)

70

x=0.05

60

x=0.10
x=0.20

50
40
30
20
10
0
0

100

200

300

400

500

600

700

T (K)
Figure 41 Temperature dependence of the power factor of CoSi0.98-xGexB0.02 samples.
0.4
x=0.00
x=0.05

0.3
κ (W/cm K)

x=0.10
x=0.20
0.2

0.1

0.0
50

100

150

200

250

300

350

T (K)
Figure 42 Temperature dependence of the thermal conductivity of CoSi0.98-xGexB0.02 samples.
73

is also consistent with the higher carrier concentration observed in this sample. The
compositional dependence of the Seebeck coefficient due to Ge substitution is similar to that of
Rh substitution as we discussed in section 4.2. Both the isoelectronic substitutions influence the
electrical properties to some extent. The power factor is not increased by Ge substitution because
the enhancement of the Seebeck coefficient is compensated by the lower carrier mobility for the
x = 0.10 sample, as shown in Figure 41. The Ge substitution effect on the thermal conductivity
reduction is similar to that of Rh substitution, as can be seen in Figure 42. Based on the electrical
properties of the x = 0.05 sample, this substitution level shows a subtle effect on the electronic
structure. Thus, we can use the Debye approximation in section 4.2 to calculate the lattice
thermal conductivity of this sample with the same Grüneisen parameter.

0.30
5%Ge Experiment

0.25

κl (W/cm K)

30 μm Calculation
7 μm Calculation

0.20
0.15
0.10
0.05
0.00
50

100

150

200

250

300

350

T (K)
Figure 43 Lattice thermal conductivity and Debye approximation results with different grain
sizes as a function of temperature for the CoSi0.93Ge0.05B0.02 sample.
74

The atomic mass and size of Ge give rise to a smaller pre-factor for point-defect scattering
-42 3

than Rh with a value of 1.55×10

s while the almost same pre-factor for Umklapp scattering.

The calculated lattice thermal conductivity curve is shown in Figure 43. The calculation with an
L value of 30 μm is quite consistent with the experimental data around room temperature even
though it is much higher at low temperature. The discrepancy probably originates from the
unknown grain size of this sample. If a smaller L value of 7 μm instead of 30 μm is used while
maintaining the other parameters the same, the calculation coincides with the experimental data,
as can be seen in Figure 43.
0.30
5% Ga Experiment
5% Ga Calculation
5% Ge Experiment
5% Ge Calculation

κl (W/cm K)

0.25
0.20
0.15
0.10
0.05
0.00
50

100

150

200

250

300

350

T (K)
Figure 44 Experimental lattice thermal conductivity and calculated curves for 5 mol% Ga and 5
mol% Ge substituted CoSi samples.
In section 3.2, the lattice thermal conductivity of Ga-doped CoSi samples has been discussed.
We also attributed the reduction to the point-defect scattering. It is noticeable that the lattice
75

thermal conductivity reduction due to Ga doping is more than Ge substitution, as shown in
Figure 44. Since the mass difference between Ga and Si is even less than that between Ge and Si,
the point-defect scattering parameter ΓM for Ga-doping is smaller than that for Ge substitution.
Therefore, the further reduction of the lattice thermal conductivity is presumably due to the large
strain field effect in Ga-doped samples. The calculated pre-factor A value for 5 mol% Ga doping
is 2.42×10

-42 3

s , about 1.6 times the value for 5 mol% Ge substitution. With BU of 2.18×10

-18

s/K and L of 30 μm, we can calculate the lattice thermal conductivity for the 5 mol% Ga-doped
sample (see Figure 44). The obtained curves in Figure 44 quantitatively demonstrate the
importance of the strain field effect on the lattice thermal conductivity reduction of CoSi. On the
other hand, the coincidence between the experimental and calculation results suggests that the
large Grüneisen parameter and adjustable parameter ε are reasonable for the CoSi system.
0.16
x=0.00
x=0.05

0.12

ZT

x=0.10
x=0.20

0.08

0.04

0.00
50

100

150

200

250

300

350

T (K)
Figure 45 Temperature dependence of ZT of CoSi0.98-xGexB0.02 samples.
76

Enhanced ZT values are obtained for the x = 0.05 and 0.10 samples due to the lattice thermal
conductivity reduction, as shown in Figure 45. Even for the isoelectronic substitution, it is not
trivial to identify an optimized substitution level to achieve the highest ZT, because this kind of
substitution still affects the electrical properties. The 20% Ge substituted sample exhibits lower
ZT around room temperature than the parent sample, despite the fact that this sample exhibits the
largest lattice thermal conductivity reduction.

4.4 Summary
In this chapter, we studied and discussed the thermoelectric properties of isoelectronic
elements, such as Rh and Ge, substituted CoSi0.98B0.02 samples. The electrical resistivity is not
affected by Rh substitution whereas large Ge substitutions lead to rising resistivity. Both the
substitutions show a pronounced effect on the Seebeck coefficients, suggesting the electronic
structure are still influenced to some extent. The lattice thermal conductivity is reduced
drastically by isoelectronic substitutions due to the point-defect scattering. Both the mass and
strain filed fluctuations contribute to the reduction. The Debye approximation can provide a
quantitative analysis of the reduction. According to the analysis, the latter plays a more important
role in the lattice thermal conductivity reduction because of a large Grüneisen parameter. Two
examples, i.e. Al and Ga doping results, are taken to illustrate the presence of the large strain
field effect in CoSi samples. All these results prove that the large Grüneisen parameter and
adjustable parameter used in our Debye approximation are practical and reasonable. The 10% Rh
sample shows an enhanced room temperature ZT of 0.15 while a value of 0.14 is obtained for the
77

5% Ge sample. A further improvement is not possible for each individual substitution because
the carrier concentration increases and the power factor starts to decrease rapidly with the
increasing substitution level. However, higher ZT values are likely obtained when Rh and Ge
substitutions are used together.

78

Chapter 5 N-type and Double Doping Effects on the Thermoelectric Properties of CoSi

5.1 Background and Motivation
As we discussed in section 3.2, p-type dopants like Ga, Al and Fe lead to a drastic increase in
the electrical resistivity and hence a decrease in the power factor. Therefore, it is not feasible to
use p-type doping to improve the thermoelectric properties of CoSi. On the contrary, n-type
doping is likely to reduce the resistivity because of the rising carrier concentration. According to
Sakai et al.’s study, the room-temperature Seebeck coefficient is not lowered severely for CoSi
samples doped with small amounts of Ni [46]. This probably gives rise to an enhanced power
factor in n-type doped CoSi alloys. In the past, the n-type doping effect has been only reported
for Ni-doped CoSi samples [57,66]. We intend to explore other possible n-type dopants for CoSi
as well as the effects of n-type doping on the thermoelectric properties. The elements such as Pd
and Pt in the same column as Ni in the Periodic Table are candidates for n-type doping.
Therefore, we investigated the influences of small amounts of these elemental substitutions and
the results are discussed in section 5.2 [85].
On the other hand, according to Equation (10) and (16), the Seebeck coefficient can be
increased by enhancing the carrier scattering (or increasing the scattering constant λ) for a fixed
value of the Fermi level. It is possible to achieve this by appropriate p- and n-type co-doping.
Thus, we intend to use the same amounts of Fe and Ni to dope CoSi simultaneously. The
co-doping effects on the thermoelectric properties will be discussed in section 5.3.

79

5.2 Ni-, Pd- and Pt-substituted CoSi Alloys
Co1-xMxSi alloys (x = 0.002 and 0.01 for M = Ni; x = 0.01 for M = Pd; and x = 0.01, 0.02,
and 0.05 for M = Pt) were also prepared by arc melting. Since NiSi, PdSi, and PtSi all show a
MnP-type B31 structure [74], the solubility for these elements is likely not more than that of Ni.
The XRD patterns of Ni- and Pd-substituted samples only show a CoSi single phase, as shown in
o

Figure 46(a). However, a tiny impurity peak is observed at 2θ = 29.95 for the 1 mol% Pt sample.
Samples with higher Pt concentrations, i.e. 2 mol% and 5 mol%, were prepared in order to verify
the presence of the secondary phase. It is clearly seen in Figure 46(b) that the impurity peaks also
appear in these two samples. The peaks are at the same positions and the intensity becomes
stronger with the increasing Pt concentration, suggesting the same composition and the
increasing quantities of the secondary phase. We attempted to indentify the phase with the
JCPDS database in Jade 9.0; however, no powder diffraction file matches these peaks.
In order to indentify the chemical compositions of the secondary phase, microstructure
observations were carried out using SEM with the BSE mode. Figure 47 displays the BSE
images of the Pt-substituted samples. A phase separation can be clearly seen in these images.
Since the Pt-rich phase has a larger atomic weight, its color is brighter than the matrix CoSi
phase. With the increase of Pt concentration, the quantity of the Pt-rich phases increases
obviously. It is also noticeable that the impurity phase seems to segregate along the grain
boundaries. This can be seen more clearly in Figure 47(c) and (d). These results are similar to
those of the B-substituted samples in section 3.3. The average chemical compositions of the dark

80

Intensity (arb. units)

(a)

Co0.99Pt0.01Si
Co0.99Pd0.01Si
Co0.99Ni0.01Si
Co0.998Ni0.002Si
CoSi

20

30

40

50

60

70

80

90

2θ (degree)

(b)

Intensity (arb. units)

impurity peaks

Co0.95Pt0.05Si
Co0.98Pt0.02Si
Co0.99Pt0.01Si
CoSi

20

30

40

50
60
2θ (degree)

70

80

90

Figure 46 XRD patterns of (a) Ni-, Pd-, and Pt-substituted CoSi samples and (b) 1 mol%, 2
mol%, and 5 mol% Pt-substituted CoSi samples.

81

(a)

(b)

100 μm

100 μm

(c)

(d)

100 μm

100 μm

Figure 47 BSE images of (a) CoSi, (b) 1 mol% Pt, (c) 2 mol% Pt, and (d) 5 mol% Pt samples.
and bright phases for each sample were determined by EDS, and are listed in Table 6. We can see
clearly that the dark phase in all samples is stoichiometric CoSi, whereas Pt is only detected in
the bright regions. The possible chemical formula for this impurity phase is PtCoSi2
(Pt1.15Co1.13Si2.00 for Pt0.01, Pt1.10Co1.09Si2.00 for Pt0.02 and Pt1.15Co1.13Si2.00 for Pt0.05).
The solubility of Pt cannot be detected by EDS, indicating that the solubility limit of Pt in CoSi
is extremely low or Pt is completely immiscible with CoSi.
The temperature dependence of the electrical resistivity of Ni- and Pd-doped CoSi samples
and that of Pt-substituted samples are shown in Figure 48(a) and (b), respectively. In this chapter,
the resistivity of our pure CoSi sample is as low as a single crystal reported in Petrova et al.’s
82

Table 6 Chemical compositions (at. %) of bright and dark regions of CoSi and Pt-substituted
samples in Figure 47.
Bright
Sample

Co

Dark

Si

Pt

Si

Pt

50.4

CoSi

Co

49.6

0.0

Pt0.01

26.4

46.8

26.8

50.6

49.4

0.0

Pt0.02

26.0

47.7

26.3

47.9

52.1

0.0

Pt0.05

26.4

46.8

26.8

49.5

50.5

0.0

study [71], indicating this is a high-quality sample with a stoichiometric composition. The
samples doped with small amounts of Ni show lower resistivity than that of CoSi around room
temperature. The reduction is attributed to an increase of the carrier concentration, as shown in
Figure 49(a). As we discussed in section 3.2, the Hall results of CoSi samples are influenced by
holes and electrons simultaneously. However, the large negative Seebeck coefficient as well as
the large electron to hole mobility ratio of CoSi indicates the effect of holes is negligible at room
temperature. Since n-type doping further increases the electron concentration, it is reasonable to
assume a single conduction band for the transport of n-type doped CoSi samples. Thus, the
electron concentrations are calculated based on this one-band model. We will also use this
assumption to evaluate the Fermi level and the electron effective mass for Ni-doped CoSi
samples in the following text. The Hall mobility decreases with the increasing Ni concentration,
as shown in Figure 49(b). In general, one expects that the mobility will be proportional to T

83

-3/2

(a)

0.15

ρ (mΩ cm)

0.10

CoSi
Ni0.002
Ni0.01
Pd0.01

0.05

0.00
50

100

150

200

250

300

350

T (K)
(b)

0.15

ρ (mΩ cm)

0.10

CoSi
Pt0.01

0.05

Pt0.02
Pt0.05

0.00
50

100

150

200

250

300

350

T (K)
Figure 48 Temperature dependence of the electrical resistivity of (a) Ni- and Pd-doped CoSi
samples and (b) Pt-substituted CoSi samples.

84

(a)

6

n (1020 cm-3)

5
4
3
CoSi

2

Ni0.002
Ni0.01

1

Pd0.01

0
50

100

150

200

250

300

350

T (K)
(b)

1000
CoSi
Ni0.002
Ni0.01
Pd0.01
N+A
N+A
N+A

μ (cm2/Vs)

800
600
400
200
0
50

100

150

200

250

300

350

T (K)
Figure 49 Hall results of n-type doped samples: (a) electron concentration and (b) mobility. The
solid lines designated “N+A” are fits using a combination of neutral impurity and acoustic
phonon scattering.

85

0.0025

1/μN (Vs/cm2)

0.0020
0.0015
0.0010
0.0005
0.0000
0.000

0.002

0.004

0.006

0.008

0.010

0.012

Ni concentration, x
Figure 50 Reciprocal neutral impurity scattering mobility as a function of Ni concentration.
for acoustic phonon scattering and independent of temperature for neutral impurity scattering.
The combination of the two scattering mechanisms leads to an expression of the mobility as:

1

μ

=

1

μN

+

1

μA

= C N + C AT 3 / 2

(46)

where C stands for constant and the subscripts N and A represent neutral impurity and acoustic
phonon, respectively. By fitting the reciprocal Hall mobility, we can obtain the two best constants
for different scattering processes. The results are drawn as solid curves in Figure 49(b). Around
room temperature, the mobility is dominated by acoustic phonon scattering and it is not affected
severely by Ni doping. The constant 1/CA changes as 614319, 611127 and 582438 for CoSi,
Ni0.002 and Ni0.01 samples, respectively. The differences between the acoustic constants are
within 5%. In contrast, the constant CN varies dramatically as 0.000284, 0.000563 and 0.00214

86

for CoSi, Ni0.002 and Ni0.01 samples, respectively. Since the neutral impurity scattering rate is
roughly proportional to the neutral impurity concentration [86], CN increases linearly with the Ni
concentration as shown in Figure 50. The enhanced neutral impurity scattering of electrons due
to Ni doping leads to the rising resistivity at low temperature as shown in Figure 48(a). The 1
mol% Pd-doped sample shows almost the same electron concentration and mobility as the 1% Ni
sample and hence a comparable behavior of the resistivity.
All the Pt-substituted samples show lower resistivity around room temperature than the pure
CoSi as shown in Figure 48(b). The carrier concentration also increases with the rising Pt
concentration as can be seen in Figure 51(a). This increase can be hardly attributed to the n-type
doping effect based on our XRD and BSE studies. One possibility is that the higher carrier
concentration stems from the Pt-rich phase. We speculate that this phase is very metallic and it
can improve the grain boundary connectivity and hence the electrical conductivity. It can be seen
in Figure 51(b) that the mobility remains high for these Pt-substituted samples around room
temperature. Furthermore, the decrease of the mobility at low temperature is much less than that
of Ni doping. This phenomenon is analogous to skutterudite-silver composites, in which the
segregation of conducting silver phase at grain boundaries can also benefit the resistivity
reduction [87].
Figure 52 displays the temperature dependence of the Seebeck coefficient. For Ni-doped
samples, the room-temperature Seebeck coefficient drops off monotonically with the rising Ni
concentration. Using Equations (7) and (10), we can quantitatively evaluate the Fermi level and
the electron effective mass of the Ni-doped samples with the Seebeck coefficient and the carrier
87

6

(a)

n (1020 cm-3)

5
4
3
CoSi
2

Pt0.01
Pt0.02

1

Pt0.05

0
50

100

150

200

250

300

350

T (K)
(b)

1000
CoSi
800

Pt0.01

μ (cm2/Vs)

Pt0.02
600

Pt0.05

400

200

0
50

100

150

200

250

300

350

T (K)
Figure 51 Hall results of Pt-substituted samples: (a) carrier concentration and (b) mobility.

88

Table 7 Room-temperature carrier concentration, mobility, Seebeck coefficient, reduced Fermi
level and effective mass of Ni-doped CoSi samples.
Sample

n (10

20

-3

cm )

2

*

μ (cm /VS)

S (μV/K)

η (kT, 0.026 eV)

m (me)

CoSi

3.94

119

-92.2

2.73

2.49

Ni0.002

4.45

111

-86.7

2.97

2.54

Ni0.01

5.32

92

-83.3

3.13

2.73

concentration data. As we discussed above, the electron scattering is dominated by acoustic
phonons at room temperature for all Ni-doped samples. Thus, the scattering constant can be
chosen as λ = -1/2 at room temperature. The calculated results are summarized in Table 7. It can
be seen that the Fermi level is increased by Ni-doping and in the meantime the electron effective
mass increases with the doping level. The increasing effective mass can also explain the decrease
* -5/2

of 1/CA, which is supposed to be proportional to (m )

[86]. When only taking into account

the influence of the effective mass on the carrier mobility, we can obtain the mobility of doped
samples using the data of pure CoSi. The calculated room-temperature mobility for Ni0.002 and
2

Ni0.01 are 113 and 94 cm /Vs respectively, in good agreement with the experimental data as
listed in Table 7. The change of the effective mass implies that the rigid band assumption is not
accurate enough for the CoSi system: n-type doping likely broadens the conduction band as the
effective mass increases. On the other hand, both the 1 mol% Ni- and Pd-doped samples show
quite large Seebeck coefficients at 80 K (-50 μV/K for Ni0.01). In our aforementioned discussion,
the electrons are scattered predominantly by neutral impurities for Ni-doped samples at this

89

temperature. This scattering mechanism gives rise to a scattering constant of λ = 0 instead of λ =
-1/2. Assuming that the effective mass is temperature independent, we can determine the Fermi
level of the 1% Ni sample using the known effective mass in Table 7 and its carrier concentration
in Figure 49(a). With the calculated Fermi level and the given scattering constant, a Seebeck
coefficient of -46 μV/K at 80 K is obtained for this sample, in good agreement with the
experimental value of -50 μV/K.

0
CoSi
Ni0.002

-20

S (μV/K)

Ni0.01
Pd0.01

-40

Pt0.01
Pt0.02

-60

Pt0.05

-80

-100
50

100

150

200

250

300

350

T (K)
Figure 52 Temperature dependence of the Seebeck coefficient of Ni-, Pd-, and Pt-substituted
CoSi samples. Solid lines are a guide to the eye.
The Seebeck coefficient of the Pt-substituted samples drops off with the rising Pt level
around room temperature, due to the increasing carrier concentration as shown in Figure 51(a).
90

The 1 mol% Pt sample shows the same Seebeck coefficient as CoSi around room temperature. In
combination with the lower electrical resistivity, this sample exhibits a higher power factor than
CoSi, as shown in Figure 53. It is noticeable that the pure CoSi sample shows a
-2

-1

room-temperature power factor of 63 μWK cm , which is already 50 % larger than that of the
-2

-1

state-of-the-art Bi2Te3 material. The Pt0.01 sample exhibits a power factor of 73 μWK cm

at

room temperature, a 16% increase relative to the CoSi sample. This increase was also confirmed
by the ZEM measurements. However, Ni-doped samples show decreased power factors because
the reduction of the Seebeck coefficient and the mobility simultaneously outweighs the increase
of the carrier concentration.
80
CoSi
Ni0.01

Power Factor (μW/cm K2)

60

Pd0.01

Pt0.01

70

Ni0.002
Pt0.02

Pt0.05
50
40
30
20
10
0
50

100

150

200

250

300

350

T (K)
Figure 53 Power factor as a function of temperature for Ni-, Pd-, and Pt-substituted CoSi
samples. Solid lines are a guide to the eye.

91

The temperature dependence of the thermal conductivity is displayed in Figure 54. The
thermal conductivity of Ni-doped samples is almost the same as that of CoSi around room
temperature because the mass and size differences between Co and Ni atoms are negligible. It is
understandable that the 1% Pd sample shows lower thermal conductivity than the 1% Ni sample
due to the larger mass and size differences between Co and Pd atoms. Pt substitutions lead to a
significant reduction of the thermal conductivity at low temperature, while the values around
room temperature are not decreased too much. As a result, the pure CoSi sample shows a
room-temperature ZT of 0.11. All the n-type doped samples exhibit lower ZT values than CoSi.
An enhanced ZT of 0.13 is obtained for the 1% Pt sample, while the other two samples with
higher Pt concentrations possess lower ZT at room temperature.
0.6
CoSi
Ni0.002

0.5

κ (W/cmK)

Ni0.01
Pd0.01

0.4

Pt0.01
Pt0.02
0.3

Pt0.05

0.2

0.1
50

100

150

200

250

300

350

T (K)
Figure 54 Temperature dependence of the thermal conductivity of Ni-, Pd-, and Pt-substituted
CoSi samples. Solid lines are a guide to the eye.

92

5.3 Co1-x-yFexNiySi Alloys
CoSi samples doped by equal amounts of Fe and Ni were prepared as Co1-x-yFexNiySi alloys,
where x = y = 0.025, 0.05 and 0.10 respectively. The XRD patterns only show a single CoSi
phase for all the samples. The peaks shift to lower angles for samples with larger x and y,
indicating an enlarged lattice constant with the introduction of co-doping atoms.
0.9
x=y=0.00

0.8

x=y=0.025

0.7

x=y=0.05
x=y=0.10

ρ (mΩ cm)

0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

100

200

300

400

500

600

700

T (K)

Figure 55 Temperature dependence of the electrical resistivity of Co1-x-yFexNiySi alloys.
The electrical resistivity as a function of temperature is shown in Figure 55. With the rising
co-doping concentration, the electrical resistivity increases monotonically and severely. The
electrical resistivity shows a metallic behavior for CoSi with a positive temperature coefficient,
whereas the temperature coefficients change to small negative values for the three co-doped

93

(a)

1.0E+22

n (cm-3)

x=y=0.00
x=y=0.025
x=y=0.05
x=y=0.10

1.0E+21

1.0E+20
50

100

150

200

250

300

350

T (K)
(b)

1000

x=y=0.00
x=y=0.025
x=y=0.05
x=y=0.10

μ (cm2/Vs)

100

10

1
50

100

150

200

250

300

350

T (K)
Figure 56 Hall results for Co1-x-yFexNiySi alloys: (a) carrier concentration and (b) mobility.

94

0
x=y=0.00

-20

x=y=0.025

-30

x=y=0.05

-40
S (μV/K)

-10

x=y=0.10

-50
-60
-70
-80
-90
-100
-110
50

150

250

350

450

550

650

750

T (K)
Figure 57 Temperature dependence of the Seebeck coefficient of Co1-x-yFexNiySi samples.
samples. The Hall measurements show that the carrier concentration increases with the
increasing co-doping level, as can be seen in Figure 56(a). Thus, the rising resistivity originates
from the severe reduction of the carrier mobility, as shown in Figure 56(b). Since Fe introduces
holes while Ni brings about electrons, the carrier concentrations of both types are increased.
According to Equation (24), the rising p and n can induce smaller Hall coefficients and hence
larger Hall carrier concentrations for a two-band conduction material. It is also noticeable that
the mobility for co-doped samples is weakly dependent of temperature. As we discussed in
section 5.2, the significant reduction of the mobility is likely caused by the enhanced neutral
impurity scattering or even ionized impurity scattering. We do not claim the ionized impurity
95

scattering in section 5.2 because the use of this mechanism cannot agree with the experimental
data for samples doped by small amounts of Ni. In contrast, we consider the ionized impurity
scattering for the co-doped samples only because this mechanism fits the experimental data
better.
Figure 57 displays the temperature dependence of the Seebeck coefficient. The absolute
Seebeck coefficient decreases with the increasing co-doping concentration. There are two
possibilities responsible for the reduction: first, provided that the doping efficiency of Fe and Ni
is the same, both dopants will introduce the same quantities of holes and electrons. However, the
electrons possess smaller effective mass than the holes and thus the Fermi level may be still
moved upward, analogous to the n-type doping effect but less than Ni doping alone. This may be
proven by the fact that the Seebeck coefficient for the x = y = 0.025 sample is similar to that of
the 1% Ni sample in section 5.2. Moreover, the Seebeck coefficient bends upward at higher
temperature with the increasing co-doping concentration, implying higher Fermi levels for these
samples as well. On the other hand, with the rising hole concentration, the Seebeck coefficient is
now influenced by both carriers as indicated by Equation (28). The hole contribution to the
Seebeck coefficient is weighted against that of electrons and hence reduce the Seebeck
coefficient. This can be confirmed by measuring the Seebeck coefficient of a sample with more
21

Fe than Ni like one of x = 0.06 and y =0.04 (n300K = 1.0×10
20

y = 0.05 sample (n300K = 9.5×10

-3

cm ) in comparison with the x =

-3

cm ). Based on the former possibility, this sample should

have a lower Fermi level and hence a larger Seebeck coefficient because the Ni content is
reduced. However, a lower Seebeck coefficient of -45 μV/K for the x = 0.06, y = 0.04 sample is
96

obtained at room temperature compared to -69 μV/K for the x = y = 0.05 sample, indicating a
detrimental effect of p-type dopants to the Seebeck coefficient.
As we demonstrated above, the change of the mobility shows the presence of the additional
scattering processes in the co-doped samples. Thus, the electrical conductivity deteriorates due to
the reduction of mobility. The Seebeck coefficient, however, cannot be improved by co-doping
because the introduction of excess holes annihilates the advantage of intensive carrier scattering.
As a result, the power factor is decreased by a factor of 3 for the x = y = 0.025 sample and
continues to drop off for higher co-doping concentrations compared to CoSi at room temperature,
as shown in Figure 58. Even though the maximum power factor shifts to higher temperature with
the increasing co-doping level, the values are still much lower than CoSi over the entire
temperature range.
80
x=y=0.00
x=y=0.025
x=y=0.05
x=y=0.10

Power Factor (μW/cm K2)

70
60
50
40
30
20
10
0
50

150

250

350

450

550

650

750

T (K)
Figure 58 Temperature dependence of the power factor of Co1-x-yFexNiySi samples.

97

The electrical properties cannot be improved by the co-doping approach due to the
semimetallic nature of CoSi. The electron-dominated Seebeck coefficient is sensitive to the hole
concentration. Fedorov and Zaitsev proposed two possible ways to enhance the Seebeck
coefficient [54]: either reduce the overlapping between the conduction and valence bands or
create a potential barrier to scatter the holes rather than electrons. They proved that the
overlapping might be separated to some extent by distorting the lattice. It is likely but not
practical to achieve this by applying pressure on samples [54]. They speculated that it is more
realistic to deform the lattice using atoms with considerably different size to dope CoSi.
However, as we discussed in chapter 4, the isoelectronic substitutions cannot improve the
Seebeck coefficient even though the atomic size difference between the impurity and host atoms
is already quite large (at least, the improvement is trivial as shown in the 10% Ge sample). On
the other hand, it is possible to produce scattering or filtering potential barriers by grain
boundary modifications [41,82]. We have shown that both B and Pt substitutions are able to form
a secondary phase at grain boundaries. In fact, our collaborators at ORNL suggested the presence
of an energy barrier at the grain boundaries for B-substituted samples. Furthermore, considering
the higher carrier concentration of the 1% Pt sample, the unchanged large Seebeck coefficient
probably implies an energy filtering effect. But we cannot draw a solid conclusion that the
filtering effect does exist in these materials because the enhancement is too small. All in all, we
indeed obtained enhanced thermoelectric properties by either isoelectronic substitutions or
impurity phase formations.
The thermal conductivity is reduced by Fe and Ni co-doping. Since the atomic size and mass
98

differences between impurity and host atoms are quite small, the lattice thermal conductivity
reduction is limited. As a result, ZT continues to decrease with the increasing co-doping level due
to the drastic reduction of the power factor as shown in Figure 59. Even though the
high-temperature thermal conductivity of co-doped samples was not measured, the peak ZT
values for these samples cannot exceed that of CoSi due to the low power factor.

0.12
x=y=0.00

0.1

x=y=0.025
x=y=0.05

ZT

0.08

x=y=0.10

0.06
0.04
0.02
0
50

100

150

200

250

300

350

T (K)
Figure 59 Temperature dependence of ZT of Co1-x-yFexNiySi samples.

5.4 Summary
In this chapter, we studied the thermoelectric properties of CoSi samples doped by small
amounts of Group 10 elements such as Ni, Pd and Pt and samples co-doped by Fe and Ni. Ni and

99

Pd are effective n-type dopants, while Pt is hardly miscible with CoSi and it segregates along
grain boundaries as a possible phase of PtCoSi2. In contrast to our expectation, the reduction of
the Seebeck coefficient outweighs the decrease of the resistivity and thus the power factor is
decreased by n-type doping. By analyzing the Hall and Seebeck coefficient results, we find that
the Fermi level is indeed raised by n-type doping while the electron effective mass seems to
increase with the increasing doping level. These results indicate that the band structure of the
doped samples still change (e.g. conduction band broadening) and thus the rigid band assumption
is not perfectly applicable to the CoSi system. An interesting observation is that both 1% Ni and
1% Pd samples show quite large Seebeck coefficients at low temperature. The enhancement can
be attributed to the enhanced carrier scattering at that temperature based on the analysis of carrier
mobility. It suggests a possibility to enlarge the Seebeck coefficient by enhancing the carrier
scattering. The Pt-substituted samples exhibit lower electrical resistivity than CoSi around room
temperature due to the increase of the carrier concentration. The Seebeck coefficient is
maintained for the 1% Pt sample and thus the power factor is improved by 16% for this sample
compared to the high-quality CoSi. The reduction in resistivity due to conducting phases at grain
boundaries is a promising method for improving the power factor of these materials and might be
effectively applied to other thermoelectric materials.
By co-doping CoSi with the same amounts of Fe and Ni, we attempted to enhance the carrier
scattering while maintaining the Fermi level. The drastic mobility reduction indicates additional
scattering processes in the co-doped samples. However, the absolute Seebeck coefficient
continues to decrease with the increasing co-doping concentration. The reduction can be
100

attributed to either the rising Fermi level or the detrimental effect of holes. As a result, an
improvement can be hardly achieved by the co-doping method.
It is difficult to improve the thermoelectric performance of CoSi due to its nature of band
overlapping. We expect that its performance might be enhanced by either band separation or
selective carrier filtering. The above two ideas likely correspond to isoelectronic substitutions
and grain boundary modifications, respectively. As we discussed in the preceding sections, the
enhancement of the Seebeck coefficient is too trivial to be attributed to the two concepts, and
thus the performance is mainly improved by the lattice thermal conductivity reduction. Up to
now, the improvement of the electrical properties is only observed in the 1% Pt sample,
considering that other enhancements, including those reported in literature, are due to the
comparison with low-quality (off-stoichiometric or microcracks-filled) parent samples.
The effects of elemental substitutions on the thermoelectric properties of arc-melted CoSi
have been systematically and comprehensively investigated so far. The dimensionless figure of
merit is still one magnitude lower than state-of-the-art thermoelectrics due to the high lattice
thermal conductivity. Grain size reduction or nanostructuring have been proven successful to
produce thermoelectric materials with lower lattice thermal conductivity [33]. Thus, the
influence of another preparation method, namely powder processing, will be our focus in the
subsequent chapter.

101

Chapter 6 CoSi Samples Prepared by Powder Processing

6.1 Background and Motivation
To the best of our knowledge, CoSi is one of the thermoelectric materials with the highest
power factor. However, the advantage of the electrical properties is offset by the high thermal
conductivity and thus its ZT is quite less than unity. Since the high power factor induces a large
electronic contribution to the thermal conductivity, the lattice thermal conductivity is the only
adjustable property. Provided that the lattice contribution can be neglected, the room-temperature
ZT is only determined by the Seebeck coefficient and the Lorenz number. It can be enhanced to
0.35 using the values presented in the previous chapters. Even though the value is still below
unity, it is worth finding an approach to obtain such a huge improvement.
In past decades, powder processing has boosted the research interest of preparing
nanostructured bulk thermoelectric materials [33,88]. The grain size can be reduced down to
nano-scale by high-energy ball milling and hence the number of interfaces is escalated after
appropriate consolidation. Given that the mean free path of carriers is much shorter than phonons,
it is believed that the nanogranular structure is helpful to stimulate intensive phonon scattering at
interfaces while maintaining or hardly affecting the electrical properties. The effect of grain size
reduction on the lattice thermal conductivity can be evaluated using the aforementioned Debye
approximation. Using the same pre-factors A and BU, we can determine the lattice thermal
conductivity of CoSi with various grain sizes, as shown in Figure 60. The lattice thermal
conductivity can also be evaluated as [27]:
102

0.50
30 μm

κl (W/cm K)

0.40

0.30
1 μm

0.20

500 nm
100 nm

0.10

20 nm

κmin

0.00
50

100

150

200

250

300

350

T (K)
Figure 60 Lattice thermal conductivity of CoSi samples with various grain sizes. From top to
bottom: 30 μm, 1 μm, 500 nm, 100 nm, 20 nm and κmin, respectively.

1
3

κ l = CV vl

(47)

where l is the phonon mean free path. The minimum value is determined using the
aforementioned room-temperature CV, sound velocity, and interatomic spacing of 0.2286 nm as
the mean free path. It is clearly seen that the lattice thermal conductivity continues to approach
the minimum value with the decreasing grain size.
On the other hand, the carrier mobility is supposed to decrease with the increasing interfaces
and thus the electrical resistivity is raised by nanostructuring [35]. However, it has been reported
that the Seebeck coefficient is likely enhanced by energy filtering effect for nanostructured

103

materials (superlattices [89] or nanogranular bulks [41]). Thus, an enhanced Seebeck coefficient
is expected to compensate the carrier mobility reduction for powder processed CoSi. It is worth
mentioning that the improvement of the Seebeck coefficient is not widely observed. It is more
realistic to expect that the reduction of the carrier mobility is less than that of the lattice thermal
conductivity and hence an overall improvement can be achieved.

6.2 Ball Milling, Consolidation and Thermoelectric Properties
In this chapter, we intend to prepare CoSi samples with reduced grain sizes by powder
processing. The starting CoSi materials were prepared with the same arc melting and annealing
procedure as mentioned previously. Subsequently, the ingots were pulverized and milled using
the SPEX 8000M high-energy ball mill and the milling time was maintained as 100 minutes. To
minimize oxidation, samples were loaded and taken out in an argon-filled glove box and vials
were also sealed under argon atmosphere before milling (see section 2.1). We found that the
selection of vial set influenced the thermoelectric properties severely. Samples milled in an 8007
stainless steel vial set were contaminated by Fe because their thermoelectric properties are
similar to those of p-type doped samples. In contrast, the tungsten carbide vial set shows little
impact on the thermoelectric properties.
Powders were compacted under argon atmosphere using either PECS or hot pressing (HP).
The sintering temperature, pressure, and ramp rates of the temperature and the pressure were
varied for PECS to investigate the influence of densification conditions. Hot pressing is a
comparable consolidation method to PECS, except that the high temperature is achieved by
104

heating elements instead of Joule heating for PECS. The samples prepared in various conditions
are listed in Table 8, where RR is ramp rate, P is pressure, soak is the holding time at the highest
3

temperature and pressure, and density is relative to the theoretical value of 6.59 g/cm . It is
clearly seen that the density decreases with the decreasing PECS temperature and thus a
o

temperature of 1100 C is required to achieve a relative density above 95%. The decrease of the
pressure also leads to a lower density, but not as much as the temperature. The change of the
ramp rates shows little effect on the sample quality.
Table 8 CoSi samples with various preparation conditions.
Sample

T ( C)

o

RR of T
o
( C/min)

P (MPa)

RR of P
(MPa/min)

Soak (min)

Density

PECS-1

1100

50

60

5.5

20

97.9%

PECS-2

1000

50

60

5.5

20

93.3%

PECS-3

900

50

60

5.5

20

91.4%

PECS-4

1100

50

30

5.5

20

94.5%

PECS-5

1100

30

60

3.7

20

96.8%

HP

1100

20

60

4.0

60

98.2%

The XRD pattern of the 100-minute ball-milled powders shows pronounced peak broadening,
as shown in Figure 61. The crystallite size estimated by the Scherrer equation is 17 nm.
Considering that partial broadening is caused by the strain effect, the actual size should be larger
than this value. Peak broadening is not observed for the densest PECS sample (PECS-1)

105

compared to the arc-melted CoSi, implying that their grain sizes are comparable. In fact, the
XRD patterns of samples consolidated at lower temperature (PECS-2 and PECS-3) are still the
same as the arc-melted one. All these results indicate a substantial grain growth during
consolidation.

Intensity (abr. units)

PECS-1

BM powder

Arc-melted

20

30

40

50

60

70

80

90

2θ (degree)
Figure 61 XRD patterns of the arc-melted CoSi, 100-minute ball-milled CoSi powders, and
PECS-1 CoSi sample.
Figure 62 presents the SEM fracture surface images of PECS-1 and HP CoSi samples. These
two samples possess the highest densities of 98%. A great number of pores and voids are
observed within the grains and grain boundaries of both samples. The theoretical density is
hardly achieved due to the presence of the isolated pores. Both samples consist of smaller grains
with a size around 2 μm, compared to the size of tens μm for the arc-melted CoSi. Submicron
106

grains can also be found in the PECS-1 sample, while the grains are almost larger than 1 μm for
the HP sample. The average grain composition determined by EDS is close to CoSi for both
samples (44.5 at. % Co and 55.5 at. % Si for the PECS-1 sample; 44.7 at. % Co and 55.3 at. % Si
for the HP sample).

2 μm

2 μm

Figure 62 SEM fracture surface images of the PECS-1 (left) and HP (right) CoSi samples.
The temperature dependence of the electrical resistivity is shown in Figure 63. All the
powder processed samples show drastic increase in the resistivity relative to the arc-melted CoSi.
It has been reported that the strain and defects produced during ball milling can degrade the
electrical conductivity [41,90]. Among them, the PECS samples even show higher resistivity
than the HP sample. Considering that the PECS-1 sample possesses the similar density and grain
size as the HP one, the huge resistivity discrepancy between them is interesting. The difference
probably stems from the sintering method itself. For example, PECS may cause more carriers
trapping at grain boundaries [91]. On the other hand, the resistivity is directly related to the
porosity, as can be seen in Figure 64. The increasing porosity leads to an increase in the electrical

107

0.0005
Arc-melted
PECS-2
PECS-4
HP

ρ (Ω cm)

0.0004

PECS-1
PECS-3
PECS-5

0.0003

0.0002

0.0001

0.0000
50

100

150

200

250

300

350

T (K)
Figure 63 Temperature dependence of the electrical resistivity of PECS and HP samples.
0.0004

ρ (Ω cm)

0.0003

0.0002

0.0001
0

2

4

6

8

10

Porosity (%)
Figure 64 Room-temperature electrical resistivity as a function of porosity for PECS and HP
CoSi samples. The dashed line is a guide to the eye.

108

resistivity [92]. The drastically rising resistivity is not desired for the improvement of the
thermoelectric performance.

0
Arc-melted
PECS-1
PECS-2
PECS-3
PECS-4
PECS-5
HP

-10
-20

S (μV/K)

-30
-40
-50
-60
-70
-80
-90
-100
50

100

150

200

250

300

350

T (K)
Figure 65 Temperature dependence of the Seebeck coefficient of PECS and HP samples.
Figure 65 displays the temperature dependence of the Seebeck coefficient. The Seebeck
coefficients of samples prepared by powder processing are all lower than that of arc-melted CoSi
around room temperature. The Seebeck coefficient was measured for some of the ingots before
powder processing and the reduction was only observed after consolidation. It is also noticeable
that all the PECS samples exhibit lower Seebeck coefficients than the HP sample. The origin of
the difference has not been elucidated. The PECS samples, except for PECS-1, show similar

109

Seebeck coefficients around room temperature regardless of the density. The decreasing Seebeck
coefficient may be attributed to two reasons. First, the increase of the interfaces and the
associated imperfections and defects are possible to produce more carriers in the PECS or HP
samples and hence a lower Seebeck coefficient [93]. Second, the potential barrier at grain
boundaries is so high that electrons with intermediate energy are also filtered [36]. These
electrons, unlike the low energy ones, contribute positively to the Seebeck coefficient. Therefore,
the Seebeck coefficient and the electrical conductivity both decrease after powder processing.
Table 9 Hall results of PECS and Arc-melted samples at 80 and 300 K.
80 K
Sample

n (10

20

-3

cm )

300 K
2

μ (cm /Vs)

n (10

20

-3

cm )

2

μ (cm /Vs)

Arc-melted

2.15

916

3.94

119

PECS-2

2.28

109

4.47

38

PECS-3

2.25

129

3.83

49

PECS-4

2.23

158

4.47

52

HP-0.5 mol% Ni

2.44

168

4.22

68

The Hall measurements were carried out for some samples to verify the former hypothesis.
We did not obtain the Hall results for all samples because cutting of the PECS and HP samples
was extremely time-consuming and they tended to chip during sectioning. The 80 K and
room-temperature Hall results are listed in Table 9. The carrier concentration of the PECS

110

samples at both 80 and 300 K seems higher than that of the arc-melted one (except for PECS-3,
which shows a comparable carrier concentration with the arc-melted one at room temperature).
In fact, the PECS samples show a carrier concentration similar to the 0.2 mol% Ni-doped CoSi.
Therefore, the slight increase of the carrier concentration cannot result in such a huge decrease in
the Seebeck coefficient as we discussed in section 5.2.

0
-10
Arc-melted

-20

HP

S (μV/K)

-30

HP-0.5 mol% Ni

-40
-50
-60
-70
-80
-90
-100
50

100

150

200

250

300

350

T (K)
Figure 66 Temperature dependence of the Seebeck coefficient of Arc-melted, HP, and HP-0.5
mol% Ni samples.
On the other hand, if the reduction is caused by the latter mechanism, the Seebeck coefficient
of a sample with electron distribution moving to higher energy is supposed to be larger. This may
be interpreted as that a sample with higher Fermi level contradictorily shows a larger Seebeck
111

coefficient. Thus, another HP sample doped by 0.5 mol% Ni (HP-0.5 mol% Ni, density 97.1%)
was prepared the same as the HP one. The Seebeck coefficient of this sample is shown in Figure
66. It can be clearly seen that the Seebeck coefficient of the HP Co0.995Ni0.005Si sample is
larger than the HP CoSi sample over the entire temperature range and almost the same as the
arc-melted CoSi at room temperature. The Seebeck coefficient is enhanced by n-type doping for
powder processed samples, in stark contrast to the conventional concept as we mentioned in
section 5.2.
It has been suggested that the prevention of oxidation is of great importance for good
electrical properties [93]. Even though we had prepared the samples carefully, the interfaces
were inevitably oxidized probably during ball milling, transferring or sintering. The formation of
even a thin layer of oxides can substantially produce a high potential barrier at grain boundaries
and hence an excessive energy filtering effect. Based on this assumption, it is better to remove
the oxides by H2 reduction after pressing. Besides the above reason, the grain boundary potential
barrier also likely stems from the misfit angles of grains or other defects [82], inevitably
associated with powder processing. We cannot draw any solid conclusion about the reason for
the decreasing Seebeck coefficient unless more investigations are made to identify the oxidation
or understand the influence of high-energy ball milling and consolidation.
The thermal conductivity is indeed reduced by powder processing, as shown in Figure 67(a).
The reduction of the thermal conductivity is mostly due to the suppression of the lattice part, as
shown in Figure 67(b). The behavior of the lattice thermal conductivity is analogous to those
with reduced grain sizes (see Figure 60). In fact, the lattice thermal conductivity of the HP
112

sample is similar to the calculation results with a grain size of 1 μm, which is in agreement with
the SEM results. The differences between the PECS and HP samples are still related to the
porosity[94], as can be seen in Figure 68. The lattice thermal conductivity systematically
decreases with the increasing porosity. The reduction is always less than the decrease of the
carrier mobility and the electrical conductivity of the corresponding sample. This fact violates
the purpose of the nanostructuring of bulk materials, which involves a larger decrease in the
lattice thermal conductivity relative to the carrier mobility reduction.
Since we have exerted ourselves to prepare the samples carefully, the undesired large
reduction of mobility likely originates from the material system itself. The mean free path of
electrons can be roughly estimated as [95]:

lelectron =

1.5π h
2
e 2 kF ρ

(48)

where ρ is the electrical resistivity and kF is the Fermi wave vector. Using the room-temperature
carrier concentration and resistivity of the high-quality CoSi in section 5.2, lelectron is estimated
as 17.7 nm. In the meantime, the mean free path of phonons can be evaluated with Equation (47)
and this gives rise to lphonon of 2.8 nm. It is clearly seen that the phonon mean free path, on the
contrary, is shorter than that of electrons. Even though Sales et al. pointed out that the mean free
path of phonons was supposed to be longer considering that only acoustic phonons contribute to
the specific heat [95], we may still conclude that the two mean free paths lie in the same range.
In a calculation study of bulk nano-grained Mg2Si materials, Satyala and Vashaee found that the
decrease of the mobility was always comparable to the lattice thermal conductivity reduction

113

(a)

0.6
Arc-melted
PECS-1
PECS-2
PECS-3
PECS-4
PECS-5
HP

0.5

κ (W/cm K)

0.4
0.3
0.2
0.1
0.0
50

100

150

200

250

300

350

T (K)
(b)

0.5
Arc-melted
PECS-1
PECS-2
PECS-3
PECS-4
PECS-5
HP

κl (W/cm K)

0.4

0.3

0.2

0.1

0.0
50

100

150

200

250

300

350

T (K)
Figure 67 Temperature dependence of (a) the thermal conductivity and (b) the lattice thermal
conductivity of PECS and HP CoSi samples.

114

0.12

κl (W/cm K)

0.10

0.08

0.06

0.04
0

2

4

6

8

10

Porosity (%)
Figure 68 Room-temperature lattice thermal conductivity as a function of porosity for PECS and
HP CoSi samples. The dashed line is a guide to the eye.
regardless of the chosen grain sizes [96]. Their simulations suggested that the electron and
phonon mean free paths of Mg2Si were in the same range and thus nanostructuring was not
expected to enhance ZT efficiently. To the best of our knowledge, no experimental ZT
enhancement has been reported for nanogranular Mg2Si-based materials thus far [97-99].
Nanostructuring presumably influences the electrical properties so negatively that the advantage
of the lattice thermal conductivity reduction is annihilated.
As a result, the total thermoelectric performance of the PECS and HP samples is not
improved, as can be seen in Figure 69. The electrical properties are significantly degraded and
thus powder processing is not beneficial compared to arc melting. It is worth mentioning that our
HP samples show higher ZT than those low-quality CoSi alloys reported in literature. An
115

incorrect conclusion thus can be drawn with a choice of a low-quality control sample.

0.12
Arc-melted
PECS-1

0.10

PECS-2
PECS-3

0.08
ZT

PECS-4
0.06

PECS-5
HP

0.04

HP-0.5 mol% Ni

0.02
0.00
50

100

150

200

250

300

350

T (K)
Figure 69 Temperature dependence of ZT of PECS and HP samples.

6.3 Summary
In this chapter, we investigated the possibility to enhance ZT by reducing the grain size of
CoSi. The arc-melted ingots can be pulverized down to submicron powders with high-energy
ball milling. These powders can be consolidated to dense pellets by either PECS or HP at a
o

temperature of 1100 C and a pressure of 60 MPa. The obtained PECS and HP samples exhibit
an average grain size of 2 μm as indicated by SEM images.
The electrical resistivity is drastically increased while the Seebeck is decreased for the
powder processed samples. The increase of the resistivity can be attributed to the strain and

116

defects produced during ball milling as well as the intensive carrier scattering at interfaces. It is
quite surprising to observe the decrease in the Seebeck coefficient. We proposed two possible
reasons for this: firstly, the carrier concentration rises due to the introduction of defects; secondly,
the excessive energy filtering effect is detrimental to the Seebeck coefficient. According to the
Hall measurements, we notice that the increase of the carrier concentration is too slight to cause
such a huge decrease in the Seebeck coefficient. On the other hand, a HP sample doped by 0.5
mol% Ni was prepared additionally to demonstrate the presence of excessive filtering. More
investigations are required to know the grain boundary constituents to clarify the origin of the
potential barrier (oxidation or defects associated with high-energy ball milling or PECS).
The lattice thermal conductivity is reduced as expected. However, the reduction is always
less than that of the mobility. By estimating the mean free paths of electrons and phonons, we
notice that the electron mean free path is likely in the same range as that of phonons. Since the
nanostructuring concept is established on an assumption that phonon mean free path is larger
than that of electrons, it may not be feasible for the CoSi system to take advantage of grain size
reduction to improve ZT.
Nevertheless, it is still worth studying the thermoelectric properties of various bulk
nanostructured materials to understand the fundamental transport principles and find out
appropriate processing conditions. It is also more promising to mass-produce thermoelectric
elements using the combination of ball milling and pressing. Finally and hopefully, we can
improve the thermoelectric properties of any given material under a theoretical direction and
bring the products to market.
117

Chapter 7 High-temperature Thermoelectric Materials based on β-FeSi2

7.1 Background and Motivation
Nowadays, most high-efficiency thermoelectric materials are based on expensive elemental
constituents. The high manufacturing cost may restrict their large-scale applications despite the
higher conversion efficiencies. Considering the compromise between the materials abundance
and their efficiency, β-FeSi2 is one of the promising inexpensive materials for high-temperature
power generation [100]. This material was first reported by Abrikosov in 1956 [101]. Afterwards
in 1964, its thermoelectric properties were studied by Ware and McNeill [102] and its potential
for power generation has been explored since then.
Semiconducting β-FeSi2 shows an orthorhombic crystal structure (space group Cmca). Its
3

theoretical density is 4.93 g/cm [103] and the relatively low density is another advantage of this
material. The nature of the band gap has not been elucidated yet. Experimental results showed a
direct band gap of 0.87 - 0.90 eV [104,105], whereas theoretical calculations presented a smaller
indirect gap of 0.44 - 0.78 eV [106-109]. The electrical properties can be tuned by p-type (e.g. Al
on Si sites [110]) and n-type (e.g. Co, Ni or Pt on Fe sites [111-113]) doping. In the past, the
reported highest ZT around 900 K ranged from 0.19 to 0.42 for 6 mol% Co-doped samples [114].
The large range in values stems almost completely from the difference in the high-temperature
thermal conductivity measurements.
In this chapter, we tried to more fully explore the electrical and thermal transport properties

118

and verify the thermoelectric performance of Co-doped β-FeSi2 materials. Since the solubility
limit of Co in β-FeSi2 was reported as high as 12 mol% [115], the dopant concentration up to 11
mol% was intentionally used to replace Fe in our study. Furthermore, the lattice thermal
conductivity of Co-doped β-FeSi2 is about two times that of state-of-the-art materials [116].
Therefore, ZT is expected to be further enhanced by reducing the lattice thermal conductivity. In
combination with the Co alloying effect, more intensive phonon scattering can be achieved by
nanostructuring. Ball milling and PECS thus were employed to prepare nanogranular samples.
Alternatively, it is believed that intentionally added nanoparticles can act as phonon scattering
centers and thus also reduce the thermal conductivity [33]. A thermal conductivity reduction has
been previously demonstrated for Y2O3 particles dispersed into the β-FeSi2 matrix [117].
Therefore, a composite made up of a nano-grained matrix and nano inclusions should exhibit
very low thermal conductivity. Based on this idea, composites consisting of β-FeSi2 and SiC
nanoparticles were investigated.

7.2 Co-doped β-FeSi2 Materials
The preparation procedure of β-FeSi2 has been illustrated in section 2.1. To prepare the
doped samples, Co was melted together with Fe and Si to form Fe1-xCoxSi2 (x = 0.05 – 0.11)
ingots before milling. All the pellets in this study possessed densities of more than 96% relative
to the theoretical value. The XRD patterns only show a β-FeSi2 single phase for all samples (see
Figure 70). The existence of FeSi phase is a well-known issue which affects the purity of β-FeSi2
[118-121]. This problem was avoided using our preparation method. The chemical composition
119

(a)

Intensity (arb. units)

β-FeSi2 (x = 0.00)

β-FeSi2 (PDF #01-071-0642)

20

30

40

50

60

50

60

2θ (degree)

(b)
x = 0.11

Intensity (arb. units)

x = 0.10
x = 0.09
x = 0.08
x = 0.07
x = 0.06
x = 0.05
x = 0.00

20

30

40
2θ (degree)

Figure 70 XRD patterns of (a) β-FeSi2 and PDF #01-071-0642; and (b) Co-doped β-FeSi2
materials.

120

1
x=0.00
x=0.05
x=0.06
x=0.07

0.1
ρ (Ω cm)

x=0.08
x=0.09
x=0.10
x=0.11

0.01

0.001
0.5

1

1.5

2

2.5

3

3.5

103/T (K-1)
Figure 71 Electrical resistivity of Co-doped β-FeSi2 samples vs. reciprocal temperature. The
solid curves are only a guide to the eye.
of the x = 0.08 sample determined by EDS also proves a single phase solid solution (determined
formula Fe0.920Co0.081Si2.320).
Figure 71 displays the temperature dependence of the electrical resistivity. The pure β-FeSi2
exhibits much higher resistivity than the doped samples. It has been reported that the resistivity
of n-type doped β-FeSi2 at low temperature (below 120 K) was consistent with the
variable-range hopping mechanisms [122]. The resistivity of Co-doped β-FeSi2 between 150 K
and 900 K were also analyzed with the small polaron hopping mechanism based on the
resistivity and Hall results [111,112,123]. We attempted to measure the carrier concentration and
the mobility of our samples. However, no convincible results were obtained because of the

121

non-linear behavior of the Hall resistance versus the magnetic field. The deviation from the
linear relation has been explained by two views: Arushanov et al. believed that the co-existence
of light and heavy electrons resulted in the anomalous behavior [124], while Lengsfeld et al.
ascribed it to the extrinsic magnetic clusters [125]. Due to the severe deviation, the accurate
carrier concentration and mobility cannot be directly obtained through our Hall measurements. In
fact, the conclusion of small polaron hopping was drawn based on the direct Hall mobility results
[112]. In stark contrast, the room-temperature mobility was an order of magnitude higher when
the two-band model was considered [124]. And the results of Arushanov et al. also indicated that
the electron scattering was simply dominated by acoustic phonons [124]. In a word, the
underlying conduction mechanism is still open to question. Returning to our results, the pure
β-FeSi2 still behaves like a slightly doped sample as its resistivity decreases obviously with the
increasing temperature at temperatures below 400 K. This is presumably caused by the
impurities in our starting materials (Fe, 99.95% purity) or the Co contamination from the
tungsten carbide vial set. The resistivity drops off quickly at temperatures above 700 K,
indicating that the intrinsic region has been reached. The resistivity monotonically decreases with
the rising Co content, presumably due to the increase of the electron concentration.
The temperature dependence of the Seebeck coefficient is presented in Figure 72. The
absolute Seebeck coefficient decreases with the increasing doping level. This agrees with the
change of the resistivity and can be also attributed to the increasing carrier concentration. The
Seebeck coefficient of β-FeSi2 shows a negative sign over the entire temperature range. The

122

0
-100

S (μV/K)

-200
-300
-400

x=0.00
x=0.06

x=0.07

x=0.08

x=0.09

x=0.10

-500

x=0.05

x=0.11

-600
300

400

500

600

700

800

900

1000

T (K)
Figure 72 Temperature dependence of the Seebeck coefficient of Co-doped β-FeSi2 samples.
Solid lines are a guide to the eye.
un-doped β-FeSi2 is supposed to have positive and smaller Seebeck coefficients in this
temperature range according to previous studies [102]. Therefore, our β-FeSi2 sample is slightly
n-type doped, which agrees with the resistivity behavior. The Seebeck coefficient approaches
zero quickly when the temperature is above 700 K, because of the opposite effect of the
thermally excited holes on the Seebeck coefficient. Compared to β-FeSi2, the Co-doped samples
exhibit linearly increasing absolute Seebeck coefficient from 300 to 700 K. This
behavior was also understood by the small polaron conduction mechanism [114,126]. This trend
cannot be understood using the band conduction model for degenerate semiconductors as the
Seebeck coefficient is much larger than that determined by band conduction [126].

123

18

x=0.00
x=0.06
x=0.08
x=0.10

Power Factor (μW K-2 cm-1)

16
14
12

x=0.05
x=0.07
x=0.09
x=0.11

400

500

10
8
6
4
2
0
300

600

700

800

900

1000

T (K)
Figure 73 Temperature dependence of the power factor of Co-doped β-FeSi2 samples. Solid lines
are a guide to the eye.
The power factor of Co-doped β-FeSi2 samples shows pronounced compositional
dependence, as shown in Figure 73. The samples with x ranging from 0.05 to 0.07 all exhibit a
-2

-1

peak power factor of 14 μWK cm at 850 K, while the highest power factor of the x = 0.08 and
-2

-1

0.09 samples occurs at 950 K and is increased to 15 μWK cm . A further increase of the Co
concentration leads to a decrease in the power factor.
The high-temperature thermal conductivity is determined using Equation (20). The thermal
diffusivity and specific heat capacity results are shown in Figure 74(a) and 74(b), respectively. It
is clearly seen that the thermal diffusivity of the x = 0.00 and 0.05 samples continues to decrease
with the increasing temperature. On the contrary, the thermal diffusivity is much flatter for the
samples with higher Co concentrations and it increases a little at temperatures above 900 K. All

124

(a)

4.50

x=0.00
x=0.05
x=0.06
x=0.07
x=0.08
x=0.09
x=0.10
x=0.11

4.00
3.50

D (mm2/s)

3.00
2.50
2.00
1.50
1.00
0.50
0.00
300

400

500

600

700

800

900

1000

T (K)
(b)

0.80

Cp (J g-1 K-1)

0.75
0.70
0.65

x=0.00
x=0.06

x=0.09

x=0.10

0.55

x=0.07

x=0.08

0.60

x=0.05

x=0.11

0.50
300

400

500

600

700

800

900

1000

T (K)
Figure 74 High-temperature thermal conductivity measurements for Co-doped β-FeSi2: (a)
thermal diffusivity and (b) specific heat capacity. Dashed line in (b) is the Dulong-Petit value.
125

0.14
x=0.00
x=0.06
x=0.08
x=0.10

0.12

κ (W/cm K)

0.10

x=0.05
x=0.07
x=0.09
x=0.11

0.08
0.06
0.04
0.02
0.00
300

400

500

600

700

800

900

1000

T (K)
Figure 75 Temperature dependence of the thermal conductivity of Co-doped β-FeSi2 samples.
the samples show less difference in the specific heat capacity. Since the upper temperature limit
o

for our DSC measurement is 600 C, the data was extrapolated assuming that the specific heat
capacity is constant above 850 K. This assumption is quite reasonable because the reported
Debye temperature for β-FeSi2 is 630 K [116], which is more than 200 K below the extrapolated
onset. The Cp data for all samples is larger than the Dulong-Petit value at temperatures above
600 K and even slightly higher than the literature data [116]. Based on the thermal diffusivity
and specific heat capacity data, the thermal conductivity was calculated using the
room-temperature density of each sample. The results are shown in Figure 75. The thermal
conductivity is slightly increased for the x = 0.08-0.11 samples around the highest temperature,

126

presumably due to the increasing electronic thermal conductivity. It is noticeable that the thermal
conductivity is reduced by Co-doping drastically. In fact, the room-temperature thermal
conductivity is composed of 98% lattice part and only 2% electronic contribution for the x = 0.05
sample (calculated as a degenerate semiconductor). Thus, the reduction stems completely from
the lattice thermal conductivity. As we discussed in section 4.2, the point-defect scattering of Co
should be very small due to its similar atomic weight and size to Fe. The drastic decrease in the
lattice thermal conductivity is an interesting phenomenon because it may be ascribed to a strong
electron-phonon interaction. This hypothesis was proposed based on the low carrier mobility and
the possible small polaron conduction for n-type doped β-FeSi2 samples [113,114,127].
0.40
x=0.00
x=0.05
x=0.06
x=0.07
x=0.08
x=0.09
x=0.10
x=0.11

0.35
0.30

ZT

0.25
0.20
0.15
0.10
0.05
0.00
300

400

500

600

700

800

900

T (K)
Figure 76 Temperature dependence of ZT of Co-doped β-FeSi2 samples.

127

1000

Figure 76 displays the temperature dependence of ZT. The x = 0.05-0.10 samples show
comparable ZT values over the entire temperature range. Based on our results, a highest ZT of
0.35 at 950 K is estimated carefully for Co-doped β-FeSi2. The best ZT occurs within a large
range of doping level, implying that an accurate doping concentration and high purity starting
materials are not required to achieve the best performance. In addition, the high doping
concentration can also resist the deterioration which is induced by impurity diffusion during the
high-temperature operation [102]. All the above advantages are very meaningful for practical
applications of thermoelectric power generators.

7.3 β-FeSi2 with Reduced Grain Size and Composites with SiC Inclusions
Since the electronic properties have been tuned properly by Co doping, the further
improvement of ZT can be achieved by reducing the lattice thermal conductivity. The decrease is
expected to be implemented by reducing the grain size or dispersing nanoparticles into the bulk
matrix. We chose the x = 0.08 sample in section 7.2 as the control one (denoted by control).
Compared to the control sample, the preparation procedure for samples with reduced grain size
was changed as follows: (1) the arc-melted ingots were ball milled for 1.5 hours instead of 30
o

o

minutes; (2) the PECS condition was set as 880 C and 40 MPa instead of 1150 C and 30 MPa;
(3) the annealing time was shortened from 100 hours to 24 hours. The holding time for PECS
was still maintained as 8 minutes. Figure 77 displays the XRD patterns of the ball-milled
powders and the annealed pellet (denoted by reduced grain size). The powders obtained from the

128

ingot are a mixture of ε-FeSi and α-FeSi2 phases. The peak is broadened obviously after ball
milling, showing an estimated crystallite size of 34 nm. The peak broadening disappears after
PECS for the reduced grain size sample.

Intensity (abr. units)

ε-FeSi
α-FeSi2

reduced grain size

1.5 h BM powder

control
20

30

40

50

60

2θ (degree)
Figure 77 XRD patterns of the control, the powders ball-milled for 1.5 hours and the reduced
grain size samples.
Figure 78 shows the SEM images of the control and the reduced grain size samples as well as
the ball-milled powders. Most of the powder particles are smaller than 500 nm except for some
large agglomerates. The control sample (96% of the theoretical density) shows a very dense
texture and its grain size is on the order of 10 μm. In contrast, the reduced grain size sample
possesses numerous internal pores and the grains do not connect as well as those in the control
sample. This is consistent with the lower density of this sample (90% of the theoretical value).
129

(a)

(b)

10 μm
(c)

500 nm

2 μm

Figure 78 SEM images of (a) 1.5-hour ball-milled Fe0.92Co0.08Si2 powders; (b) fracture surface
of the control sample; and (c) fracture surface of the reduced grain size sample.
Besides the lower density, this sample also shows a smaller grain size around 1 to 2 μm. This
magnitude of the grain size cannot cause a pronounced peak broadening, in agreement with our
XRD results. The XRD and SEM results both indicate a substantial grain growth associated with
our preparation method.
The thermoelectric properties of the reduced grain size and the control samples are shown in
Figure 79. The electrical resistivity is increased by 52% while the thermal conductivity is
decreased by 30% for the reduced grain size sample. This behavior is likely due to a combined
effect of the rising porosity and the smaller grain size. Meng et al. reported a drastic decrease in
the thermal conductivity of nanostructured β-FeSi2. However, the samples measured in their

130

0

0.008

-50
-100

0.006

S (μV/K)

ρ (Ω cm)

0.010

0.004
0.002

control
reduced grain size

-150
-200
-250

0.000

-300
200

400

600
T (K)

800

1000

200

600
T (K)

800

1000

200

400

600
T (K)

800

1000

0.4

0.06
0.05

0.3

0.04
ZT

κ (W/cm K)

400

0.03
0.02

0.2
0.1

0.01

0.0

0.00
200

400

600
T (K)

800

1000

Figure 79 Thermoelectric properties of the control and the reduced grain size samples.
study showed very low density and the reduction could not be merely attributed to the
minimization of the grain size [118]. On the other hand, the Seebeck coefficient is unchanged, in
stark contrast to the powder processed CoSi samples. Since the thermal conductivity reduction is
offset by the rising resistivity, ZT is not improved for the reduced grain size sample. A higher
density is the key to better electrical conductivity [38]. In order to increase the density while
preventing the grain size growth, a higher PECS pressure rather than temperature is required. It
131

may be also worth trying PECS under vacuum instead of argon atmosphere.
Based on the above results, the nanostructuring of the matrix material was not quite
successful. Thus, we decided to prepare the composites using the same preparation procedure as
the control sample (β-Fe0.92Co0.08Si2). The commercial SiC nanoparticles (beta phase, 95%
purity, 50-60 nm average particle size) are from NanoAmor. Since SiC is a chemically stable
inclusion even at high temperature, it is supposed to only scatter phonons and not affect the
carrier concentration. In this study, three composite samples with SiC concentrations of 1, 3 and
5 wt. % (corresponding to 1.5, 4.4 and 7.1 vol. %, respectively) were prepared. All the composite

Intensity (abr. units)

samples possess relative densities above 95%. The XRD patterns of the composites are shown in

5 wt. % SiC

3 wt. % SiC

1 wt. % SiC

control

20

30

40

50

60

2θ (degree)
Figure 80 XRD patterns of β-Fe0.92Co0.08Si2 - SiC composites.

132

Figure 80. It is seen that the β-FeSi2 phase is formed in each sample. The XRD for the SiC
o

powders was carried out and the pattern shows the most intensive peak at 2θ = 35.7 . Some
small peaks indicate the presence of SiO2, Si and C impurities in the powders, consistent with
o

the relatively low purity of these nanoparticles. A tiny peak found at 2θ = 35.7 for the 5%
sample is likely an index to the existence of SiC, but this peak is not observed for the other two
composites. It is hard to observe the SiC phase because of its low intensity caused by the small
particle size and the low concentration.
(a)

(b)

5 μm
(c)

5 μm
(d)

5 μm

5 μm

Figure 81 BSE images of (a) the control sample; (b) 1 wt. % SiC; (c) 3 wt. % SiC and (d) 5 wt. %
SiC composites.
Figure 81 presents the BSE images of the control sample and the composites. A secondary
black phase is observed in all the composites and its content increases with the increasing SiC

133

Table 10 Chemical compositions (at. %) of the grey region and the black region phases for
samples in Figure 81.
Grey Region

Black Region

Sample

Fe

Co

Si

Fe

Si

C

control

28.83

2.34

68.83

1 wt. % SiC

28.78

2.55

68.67

7.50

43.61

48.89

3 wt. % SiC

29.70

2.67

67.63

6.28

42.26

51.46

5 wt. % SiC

28.56

2.62

68.82

6.52

38.13

55.35

concentration. The chemical compositions of the grey and dark phases in each sample are
determined by EDS and the results are listed in Table 10. The grey region only shows a
composition of the matrix material, while the black region is a C-rich phase. The chemical
composition suggests it is a SiC phase, although we cannot observe it by the XRD. For the 5%
sample, most of the SiC phases show a size around 100-200 nm and only a few large
agglomerates are observed. Since the initial SiC nanoparticles possess an average size of 50-60
nm, the comparable SiC size observed in our samples indicates that we can disperse the
nanoparticles into the matrix homogeneously without significant agglomeration by the current
preparation procedure. On the other hand, all the SiC particles are isolated by the matrix material.
This characteristic is helpful to suppress the diffusion among nanoparticles and thus the
nanoinclusions will hardly coarsen during high-temperature operation [128].
Figure 82 shows the thermoelectric properties of the composites and the control sample. The

134

0.006

0
control
1%
3%
5%

-50
-100

S (μV/K)

ρ (Ω cm)

0.005

-150

0.004

-200

0.003

-250
-300

0.002
200

400

600
T (K)

800

200

1000

0.05

400

600
T (K)

800

1000

200

400

600
T (K)

800

1000

0.4

ZT

κ (W/cm K)

0.3
0.04

0.2
0.1

0.03

0.0
200

400

600
T (K)

800

1000

Figure 82 Thermoelectric properties of the control sample and the SiC composites.
resistivity of all the SiC composites is a little higher than that of the control sample due to the
high resistivity of the inclusions. It is interesting that the increase of the resistivity shows no
clear dependence of the SiC concentration and the increment is relatively small. This
phenomenon probably indicates that the matrix material acts as the main electrical conduction
paths [129]. The Seebeck coefficient is not affected by 1 and 3 wt. % SiC addition; however, the
5% composite exhibits a lower Seebeck coefficient compared to the control one. As we
135

mentioned above, SiC itself is an inert inclusion and hence should not affect the carrier
concentration. The decrease of the Seebeck coefficient is likely caused by other reasons. In a
study of Bi2Te3-SiC composites, Zhao et al. also found the similar change of the Seebeck
coefficient [130]. They proposed that the contamination from the oxidized surfaces of SiC
nanoparticles could decrease the Seebeck coefficient when the SiC concentration reached a
certain amount [130]. In fact, the SiC nanoparticles used in our study also contain oxides and Si
impurities as illustrated in the XRD results. According to our results of β-FeSi2-Si composites
(not shown in this dissertation), the addition of Si can decrease the Seebeck coefficient
drastically. In a word, the decreasing Seebeck coefficient is not purely related to the SiC
inclusions but to some extrinsic impurities. The SiC addition only induces a slight decrease in the
thermal conductivity. As the resistivity is increased, partial decrease even stems from the
reduction of the electronic contribution. This is consistent with Zhao et al.’s observation, where
they found that 1 vol. % SiC addition to Bi2Te3 matrix even increased the thermal conductivity
[130]. They attributed this behavior to the high thermal conductivity of SiC [130,131]. Since the
reduction of the thermal conductivity is less than the decrease of the power factor, no
improvement is obtained for the composites.

7.4 Summary
Co doping is an effective approach to improve the thermoelectric properties of the
semiconducting β-FeSi2 material. Single phase Co-doped β-FeSi2 materials can be prepared
using the sequent arc melting, ball milling, PECS and annealing procedure. The best ZT can be
136

obtained within a quite large doping range (8-10 mol%) around 950 K. The high lattice thermal
conductivity limits the total performance and thus nanogranular samples are expected to show
better ZT. However, a substantial grain growth during the preparation is observed even though
the sample density is as low as 90% of the theoretical value. The reduced grain size sample
shows no gain in the ZT due to its low density. An optimized PECS condition is desired to obtain
enhanced performance. In order to improve the density while restraining the grain growth, a
much higher pressing pressure should be employed.
In fact, nanogranular samples are not favorable for power generation applications due to their
doubtful thermal stability. The nanostructure very likely disappears due to the grain coarsening
after long-term utilization at high temperatures [132,133]. Even though nanostructured
Si0.8Ge0.2 materials have been proven stable after long-time testing [88], the reliable stability
may not be the case for other materials. However, a composite structure consisting of large grain
matrix and nanoinclusions may not encounter such a problem as long as the inclusions are
well-isolated. As a result, it is of great interest to study the nanocomposites rather than the
nano-grained materials for high-temperature power generation.
In this chapter, the inert SiC nanoparticles are selected as the inclusions. Using our current
method, we can disperse the nanoparticles very well into the matrix material without significant
agglomerations. The thermal conductivity is not significantly reduced while the electrical
properties are affected to some extent, resulting in no gain in the ZT. Since SiC is a high thermal
conductivity material, the effect of inclusion scattering may be offset by this nature. It is worth

137

trying other chemically stable inclusions with lower thermal conductivity. For instance, Y2O3
was reported as effective inclusions to reduce the thermal conductivity of β-FeSi2 composites
[117]. Considering that it possesses a lower thermal conductivity than SiC, the improvement is
relatively pronounced. Some inert particles including Si3N4, TiN, TiO2 and ZrO2 and so on are
possible candidates. Furthermore, the reduction of the thermal conductivity may also be
influenced by the inclusions size. It was pointed out that a critical size around 5 nm was required
for inclusions in Si0.8Ge0.2 materials to scatter heat-carrying phonons [128,134]. The SiC size
approximates to a few hundred nm in our study and they are supposed to scatter the long
wavelength phonons. If most of the heat is carried by shorter wavelength phonons, these large
inclusions then cannot effectively reduce the thermal conductivity. The aforementioned various
nanoparticles with a size down to 20 nm can be readily obtained from the commercial company
like NanoAmor. Thus, a more comprehensive understanding of the thermoelectric properties of
nanocomposites can be established after investigating a number of inclusions with various
average sizes.

138

Chapter 8 Conclusions and Future Work

Silicon-based materials are composed of relatively abundant elements in nature and much
more stable and reliable than tellurium-based state-of-the-art thermoelectric materials. The lower
conversion efficiencies however limit their applications despite the above advantages. In this
dissertation, we have comprehensively explored the possible approaches to improve the
thermoelectric properties of semimetallic CoSi and semiconducting β-FeSi2 materials.
The electrical properties of CoSi are quite attractive because this compound shows metal-like
low resistivity but relatively large Seebeck coefficient around room temperature. Its
room-temperature power factor is about 1.5 times that of state-of-the-art Bi2Te3 materials,
making it promising for near-room-temperature applications. Its thermal conductivity, however,
is too high to achieve a good ZT. Using the traditional alloying method, we can use isoelectronic
substitutions like Rh on Co sites and Ge on Si sites to enhance the phonon-point defect scattering
while maintaining the electrical properties. It is not successful to improve the thermoelectric
properties by the ball milling and pressing method because the increase in the resistivity is
always much larger than the thermal conductivity reduction. In fact, this nanostructuring
approach is only applicable to a few systems like Si-Ge alloys, Bi2Te3 and PbTe materials [33].
The electronic and phonon transports are not well understood for these nanostructured materials
and some results even contradict the conventional transport theory [36]. Therefore, more
investigations are definitely required to clarify the principles of the bulk nanostructuring
approach. We expect the answers to some questions like which phonon wavelengths carry most
139

of the heat, what grain size can effectively scatter the dominant phonons, how much the grain
size can affect the carrier mobility, etc.. Even though the thermoelectric properties can be
improved by reducing the thermal conductivity, very few enhancements of the electrical
properties have been obtained so far [36]. It is indeed complicated to improve the electrical
properties of CoSi. The introduction of holes can cause a drastic decrease in the carrier mobility
while the increasing electrons result in a large decrease in the Seebeck coefficient. An enhanced
power factor is only obtained in the Pt-segregated sample. The nature of the band overlapping
lowers the Seebeck coefficient and consequently the power factor. Unfortunately, we have not
found out a way to engineer the inherent band structure or implement a selective scattering of
holes.
The thermoelectric properties of β-FeSi2 can be tuned properly by Co doping. The best
performance does not require an accurate doping level and this feature is quite meaningful for
power generation thermoelectrics. The electronic conduction mechanism and the reason for the
drastic thermal conductivity reduction associated with Co doping are still open to debate.
Compared to nanogranular materials, the nanocomposites with isolated inclusions are more
suitable for high-temperature applications. Even though we did not obtain improved results for
SiC composites, a plethora of inclusions are still on the waiting list. A number of questions are
waiting to be answered, such as what is the critical inclusion size to scatter the dominant
phonons, what is the best particle dispersion (e.g. random or homogeneous dispersion) and which
type of particles is more helpful (e.g. good or poor electric conductors). Given that the thermal
conductivity is dominated by the lattice component and its magnitude is still significantly larger
140

than the minimum thermal conductivity, the prospects of enhancing ZT further by using this
approach are quite good.
The experimental and theoretical studies can cooperate with each other to promote the
development of thermoelectrics. The recent discovery of the thermoelectric potential of mineral
tetrahedrites is a good example for this: the theoretical calculations indicated that this system had
suitable physical properties for thermoelectric applications and the subsequent experimental
results proved the prediction [135]. The experimental results can also lead to a supplement to the
traditional theory. For instance, the intrinsic low thermal conductivity found in AgSbTe2 was
unusual for bulk crystalline materials [27] and a lone-pair electrons theory was subsequently
established to explain the strong anharmonicity [136]. In a word, the development of
thermoelectrics does not only give us a new and deep perspective on solid state physics, but can
also help to ensure us a clean and green energy future.

141

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