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LIBRARY
Michigan State
University

 

 

 

This is to certify that the

dissertation entitled

Photoemission Studies Of Classic
And Novel Thermoelectric Materials

presented by

VIKTORIA AUGUSTA GREANYA

has been accepted towards fulfillment
of the requirements for

Ph. D , degree in PQYS iCS

Mam

 

 

Major professor
Rong Llu

Date 06/04/01

MSU i: an Affirmative Action/Equal Opportunity Institution 0-12771

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

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6’01 c:/CiRC/DatoDuo.pG5-p.15

 

PHOTOEMISSION STUDIES OF CLASSIC AND NOVEL
THERMOELECTRIC MATERIALS

By

Viktoria Augusta Greanya

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2001

ABSTRACT

PHOTOEMISSION STUDIES OF CLASSIC AND NOVEL
THERMOELECTRIC MATERIALS

By

Viktoria Augusta Greanya

Thermoelectric materials have been studied vigorously since the 19505. Recent
advances in materials synthesis and theory have rejuvinated the field in the last decade.
The thermoelectric properties of materials are related to their electronic structure. In
addition, many of these materials behave quasi—low-dimensionally, making them ideal
candidates for study using angle resolved and angle integrated photoelectron
spectroscopy (ARPES and AIPES). We report the first detailed study of the valence band
electronic structure of BizTe3, BiZSe3 and CsBifle6 using ARPES and AIPES.
Experimental results are compared with local density approximation (LDA) band
structure calculations and (when available) with de Haas-van Alphen and Shubnikov-de
Haas experiments.

BizTe3 is currently the best room temperature thermoelectric material known.
Dispersions of the valence bands were determined using ARPES. A six-fold k-space
degeneracy in the valence band maximum is found. The quasi—two-dimensional nature of
the electronic structure was demonstrated by the weakly dispersive bands along the F—Z
direction. The density of states (DOS) for this material was also studied using AIPES.
Spectra were taken at multiple photon energies. Six valence band peaks were found.

Good correspondence with the calculated DOS was found.

BiZSe3 is isostructural to BizTe3 but its thermoelectric performance is significantly
worse. The valence band dispersions for this material have been determined, as well as
the DOS. We find the valence band maximum to be located at I‘. Ten easily identifiable
bands are seen within 4 eV of the Fermi level. The energy bands in the F-2 direction are
found to be flatter than those predicted by theory. The AIPES measurements revealed a
total of nine bands, which correspond well to the calculated DOS.

CsBi4Te6 is a novel thermoelectric material, recently discovered in the chemistry
department of Michigan State University. This material exhibits quasi-one-dimensional
behavior, which is related to its unique crystal structure. The highly anisotropic band
dispersions might explain the large value of the figure of merit, ZT, observed in the hole-
doped systems. The AIPES spectra show several large features, which are in qualitative

agreement with the calculated DOS.

lCopydghtby
VIKTORIA AUGUSTA GREAN YA

2001

DEDICATION

To my husband, Jason.

I would like to thank my family and friends who’ve given me their love and support.

I would also like to thank Rong Liu and Cliff Olson for their insight and encouragement.

ACKNOWLEDGEMENTS

I would like to thank Dr. S. D. Mahanti and P. Larson for many helpful
discussions and for the permission to use their band structure calculation results. I would
also like to thank D.-Y. Chung and M. G. Kanatzidis for their beautiful samples. This
work was partially supported by the NSF under award No. DMR9801776, and by the
Center for Fundamental Materials Research (CFMR) at Michigan State University. This
work is based upon research conducted at the Synchrotron Radiation Center, University
of Wisconsin, Madison, which is supported by the NSF under Award No. DMR9531009.
Ames Laboratory is operated for the U. S. DOE by Iowa State University under Contract

No. W-7405-ENG-82.

vi

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LIST OF TABLES ix
LIST OF FIGURES x
Chapter 1 Introduction 1
Chapter 2 Thermoelectrics 4
2.1 Fundamentals of Thermoelectrics 4
2.2 Devices and Applications 10
2.3 Recent Developments 11
2.3.1 Complex Materials 13
2.3.2 Low Dimensional Materials 14
Chapter 3 Photoelectron Spectroscopy 16
3.1 Photoemission Process 16
3.2 Photoemission Formalism 22
3.3 Angle Integrated Photoemission 23
3.4 Angle Resolved Photoemission 23
Chapter 4 Experimental Details 28
4.1 Light Source 23
4.2 Experimental Chambers and Electron Energy Analyzers 30
4.3 Sample Preparation 32
4.4 Energy Reference and Resolution 33
4.5 Spectral Modeling 35
4.6 Comparison to Band Structure Calculations 35
Chapter5 BizTe3and BiZSe, 38
5.1 BizTe3 Results and Discussion 41
5.1.1 Band Dispersions 41
5.1.2 Density of States 51
5.1.3 Summary 55
5.2 BiZSe3 Results and Discussion 56
5.2.1 Band Dispersions 56
5.2.2 Density of States 6;
5.2.3 Summary 7
Chapter 6 CsBiJeF 7’
6.1 Results and Discussion :2
6.1.1 Band Dispersions 82
6.1.2 Density of States 84

 

6.1.3 Summary

 

vii

Chapter 7 Summary

 

 

References

viii

87
89

LIST OF TABLES

Table 5.1 Comparison of photoemission and calculated DOS peaks for BizTe3. For the
purpose of comparison, the energy reference (zero of energy) was set such that the
highest valence band DOS peak, and the lowest observed binding energy peak are
coincident. The peak positions from the LDA calculation are labeled DOS, and the
observed peak positions are labeled AIPES.“ 54

Table 5.2 Comparison of photoemission and calculated DOS peaks for BiZSe3. For the
purpose of comparison, the energy reference (zero of energy) was set such that the
highest valence band DOS peak, and the lowest observed binding energy peak are
coincident. The peak positions from the LDA calculation are labeled DOS, and the
observed peak positions are labeled AIPES.‘l 69

ix

LIST OF FIGURES

Figure 2.1 (a) The Fermi distribution function f(E) at T: 0 (dashed line) and T:
300K(solid line). (b) the density of states , g(E), for a free electron gas. (c) f(E)g(E) at
T=0 (dashed line) and T=300K (solid lines). kBT is small compared to BF. 7

Figure 2.2 Transport properties calculated for an idealized semiconductor at room
temperature, plotted as a function of carrier concentration. At carrier concentrations
close to that of a metal, high electrical conductivity is accompanied by low thermopower
and high thermal conductivity. At carrier concentrations of an insulator, the thermal
conductivity is low, and the thermopower is high, but the electrical conductivity is low.‘8

Figure 2.3 (a) diagram of a basic thermoelectric device. The n- and p-type pellets are
connected electrically in series. The electrons (and holes) move in the direction of
current flow, driving the heat with them. See text. (b) An illustration of a cooling module.
The module consists of arrays of n- and p-type pellets. The modules are then connected
mechanically to a heat sink on the hot side, and a cooling plate on the cold side.”__ 12

Figure 3.1 A graphical representation of the requirement that the photon energy be
greater than the materials surface potential barrier in order for the excited electron to
escape to the vacuum. Here 4) is the magnitude of the materials work function, hv is the
incident photon energy, Ekin is the electrons measured kinetic energy, EV is the vacuum
level, e¢ + ¢, and EF is the Fermi level.” 17

Figure 3.2 A graphical representation of the three step photoemission process. The
three steps are labeled above. In step 1: absorption. In step 2: migration, and step 3:
escape. 18

Figure 3.3 In step 1 the electron, in its unexcited initial state, E,, is excited to the final
state Ef by a photon typically of energy ~20 eV. From conservation of energy, we relate
the electrons measured kinetic energy Ekin to the photon energy hv and the vacuum
energy E,, which is a sum of the surface potential and the electron’s binding energy EB.19

Figure 3.4 The universal curve showing the photoelectrons mean free path as a
function of kinetic energy. This represents the depth from which an electron can escape
without scattering. The open circles correspond to the scattering lengths of different

materials. At the kinetic energies in which we’re interested, the mean free path is less
than 20 A. 20

Figure 3.5 A graphical representation of the three step model highlighting the
secondary electron contribution. The shaded region is the inelastic scattering
background, which can be subtracted from the spectra.” 21

Figure 3.6 A graphical representation of the conservation of momentum. Here 4) is
the work function of the material, EV is the vacuum level, EF is the Fermi level, k is the
wave vector inside the crystal, and K is the wave vector outside the crystal.15 25

Figure 3.7 A 2-dimensional k-space map relating the photon energy and analyzer
angle to the experimentally determined V0. In this figure, V0 is 10 eV. The y-axis in
this map is the kz direction as well as photon energy. The x-axis is k,l (in this case ky ).
Data points are at 10° intervals in 0 and 5 eV intervals in Em. 26

Figure 3.8 (a)EDCs measured from GaAs in normal emission. (b) comparison of
LDA calculations and observed dispersions for the valence band of GaAs. Symbols are
the observed bands and the dashed lines are the calculations.” 27

Figure 4.1 Schematic of the Aladdin ring at the Synchrotron Radiation Center in
Stoughton, WI. The Microtron injects 1 GeV electrons into the storage ring. Experiment
beamlines are situated to take advantage of the photons radiating from the nearly
relativistic orbiting electrons. Our experiments were performed on the ERG-SEYA
beamline in the upper right corner of the figure. 29

Figure 4.2 A schematic layout of the beamline (side view). As the beam approaches
the monochrometer the metal flat 7° grazing mirror can be moved into or out of the beam
to select either the ERG or Seya gratings.34 30

Figure 4.3 The double-pass cylindrical mirror analyzer. The electrons enter through
a large aperture. The electrons then pass between two cylinders at a potential difference.
They are filtered and focused through two passes, ending at a channeltron detector. _ 31

Figure 4.4 The hemispherical analyzer. Electrons pass through a series of lenses to a
pair of hemispheres set at different voltages. The potential difference effectively selects
the kinetic energies of the electrons which reach the channeltron. 32

Figure 4.5 An illustration of the sample mount. The sample is attached to the
aluminum mount by a vacuum-compatible epoxy. An aluminum pin is attached to the
sample and the epoxy is cured. Aqueous graphite is then used to coat the sample, to
ensure good electrical contact. 33

Figure 4.6 (a) An EDC of the Fermi edge of a clean platinum foil. The Fermi energy
is determined by the midpoint of the leading edge. (b) The width of the leading edge is
determined to be its measured width minus the top and bottom 10%. 34

Figure 4.7 An example of the spectral modeling results (see text). The spectrum was

taken at I‘ of BizTe3. The solid line is the measured data; the dotted line is the modeling
result; the dot-dashed lines are the individual Lorentzian peaks used in the modeling. 36

xi

Figure 5.1 The crystal structure of BizTe3. The large circles are the Te atoms; the
small circles are the Bi atoms. The hexagonal unit cell is indicated. Atoms occur in the
order Te(l)-Bi-Te(2)-Bi-Te(1) where Te(l) and Te(2) are inequivalent Te sites. 39

 

Figure 5.2 (a) The Brillouin zone for BizTe3 of the rhombohedral unit cell. The
shaded region is the bisectrix plane. (b) The bisectrix plane with the major symmetry
lines indicated. 40

Figure 5.3 Energy distribution curves (EDCs) for an n-type BizTe3 sample taken
along F—Z (normal emission). The corresponding k-points are shown in the insets. The
energy is referenced to the valence band maximum (see text). 43

Figure 5.4 (a) Band dispersions for n-type BizTe3 along F—Z from LDA band structure
calculation by Larson et al.10 (b) The intensity plot of the second derivatives of the EDCs
(821/3152) as a function of energy and k in a linear gray scale with dark corresponding to
high intensity. (c) Band dispersions extracted from spectral modeling (see text). __ 44

Figure 5.5 Energy distribution curves (EDCs) for an n-type BizTe3 sample taken
along F—a—U (off-normal emission). The corresponding k-points are shown in the insets.
The energy is referenced to the valence band maximum (see text). 46

Figure 5.6 (a) Band dispersions for n-type BizTe3 along F—a—U from LDA band

structure calculation by Larson et al.10 (b) The intensity plot of the second derivatives of
the EDCs (821/8132) as a function of energy and k. (c) Band dispersions extracted from
spectral modeling. 47

Figure 5.7 EDCs for an n-type BizTe3 sample taken along (a) Z—F, (b) F—F, and (c)
F—L. The corresponding k-points are shown in the insets. The energy is referenced to
the valence band maximum. 49

Figure 5.8 EDCs for a p-type BizTe3 sample (solid lines) taken along (a) F-Z (normal
emission) and (b) F—a—U (off-norrnal emission). The corresponding k-points are shown in
the insets. The energy is referenced to the experimental Fermi level reference derived

from a clean platinum foil in electrical contact with the sample. The EDCs for an n-type
sample are also shown (dashed lines) for comparison. 50

Figure 5.9 Angle Integrated photoemission spectra for BizTe3. Arrows indicate peaks
1—6. For the purpose of comparison, the energy reference (zero of energy) was set such
that the lowest binding energy peak in the spectra coincides with the position of the
corresponding peak in the LDA calculations. 52
Figure 5.10 Total density of states of BizTe3. The arrows indicate the positions of the
photoemission peaks seen in the observed spectra. The energy reference (zero of energy)
was set such that the highest valence band DOS peak, and the lowest observed binding
energy peak coincide." 54

xii

Figure 5.11 Energy distribution curves (EDCs) for an n-type BizSe3 sample taken
along F-Z (normal emission). The corresponding k‘points are shown in the inset. The
energy is referenced to the valence band maximum (see text). Energy resolution is 0.1
eV. 57

Figure 5.12 (a) Band dispersions along I‘-Z in BiZSe3 from band structure calculation

by Larson et a1.12 (b) The intensity plot of the second derivatives of the EDCs (821/ 8E2)
as a function of energy and k in a linear gray scale with dark corresponding to high
intensity. (c) Band dispersions extracted from observed spectra (see text). 59

Figure 5.13 Energy distribution curves (EDCs) for an n-type BiZSe3 sample taken
along Z-F (off-normal emission). The corresponding k-points are shown in the inset.

The energy is referenced to the valence band maximum (see text). Energy resolution was
100 meV. 61

Figure 5.14 (a) Band dispersions along Z-F from band structure calculation by Larson
et al‘0 (b) The intensity plot of the second derivatives of the EDCs (821/8E2) as a
function of energy and k. (c) Band dispersions extracted from observed spectra. __ 63

Figure 5.15 EDCs for a Bi28e3 sample taken along (a) F-a-U, (b) F—F, and (c) l"-L.
The corresponding k-points are shown in the insets. The energy is referenced to the
valence band maximum. Energy resolution was 0.1 eV. 64

Figure 5.16 Higher resolution EDCs for a BiZSe3 sample taken along G-Z (normal
emission) The corresponding k-points are shown in the inset. The energy is referenced to
the experimental Fermi level reference derived from a clean platinum foil in electrical
contact with the sample. Energy resolution was 37.6 meV. 66

Figure 5.17 Angle Integrated photoemission spectra for Bi28e3. Arrows indicate peaks
1-9. For the purpose of comparison, the energy reference (zero of energy) was set such
that the lowest binding energy peak in the spectra coincides with the position of the
corresponding peak in the LDA calculations. 68

Figure 5.18 Total density of states of Bi28e3. The arrows indicate the positions of the
photoemission peaks seen in the observed spectra. For the purpose of comparison, the

energy reference (zero of energy) was set such that the highest valence band DOS peak,
and the lowest observed binding energy peak coincide.“ 69

Figure 6.1 The crystal structure of CsBi4Te6. The small white circles are the Te
atoms; the small black circles are the Bi atoms; the larger gray circles are the Cs atoms.72
Figure 6.2 The Brillouin zone for CsBi4Te6 of the monoclinic unit cell. The three
important symmetry directions are indicated. 72

Figure 6.3 Energy distribution curves (EDCs) for an n-type CsBi,,Te6 sample taken
along l"-X. The energy is referenced to the experimental Fermi level derived from a

xiii

clean platinum foil in electrical contact with the sample. Varying the analyzer angle at 2°
intervals varied momentum k. 75

Figure 6.4 A comparison of EDCs for n- and p-type CsBi,,Te6 samples taken at select
k-points near F along F—X. The n-type spectra are referenced to the experimental Fermi
level. The p-type spectra were rigidly shifted by 0.05 eV toward higher binding energies
(see text). 76

Figure 6.5 (a) Band dispersions (small symbols) along F—X from band structure
calculation by Larson et a]. The dispersions of select features seen in the spectra are
overlaid (cross symbols). (b) Band dispersions (small symbols) along RV and F—Z from
band structure calculation. 78

Figure 6.6 EDCs for an n-type CsBi,,Te6 sample taken along (a) F-V and (b) I‘-Z.
The energy is referenced to the experimental Fermi level derived from a clean platinum
foil in electrical contact with the sample. Energy resolution in these spectra is 45 meV.80

Figure 6.7 Higher resolution EDCs for a p-type CsBi4Te6 sample taken along F—V.
The energy is referenced to the experimental Fermi level derived from a clean platinum
foil in electrical contact with the sample. The spectra are taken every 0.5°. Our k-
resolution is 2°, and the energy resolution is 35 meV. 81

Figure 6.8 Angle Integrated photoemission spectra for n-type CsBi4Te6. For the
purpose of comparison, the energy reference (zero of energy) was set such that the lowest
binding energy peak in the spectra coincides with the position of the corresponding peak
in the LDA calculations. 83

Figure 6.9 The calculated density of states of CsBi4Te6. 85

xiv

Chapter 1 Introduction

The thermoelectric (TE) properties of materials have been studied since the mid-
19‘h century. The usefulness of the TB effect was not, however, fully appreciated until
the 19505 when the larger TE efficiencies of doped semiconductors were discovered.
From the 1950s to the 19708, there was a significant amount of activity in TE research
with the hope of (among other things) replacing compressor based refrigeration
technology. Several good thermoelectric materials were found. However, their TE
efficiency was still not high enough for TB devices to replace already existing technology
in home and commercial refrigeration. For more than 30 years, BizTe3 and its alloys
have been the best room temperature TE materials. The field gradually lost its
momentum and funding due to the lack of significant progress. "2‘3"

Recently, there has been a revival in this field of study, which can be attributed to
several things. First, the increased sophistication of materials synthesis techniques have
taken the search for novel TE materials in new directions. 5° For example, in their papers
published in 1993, Hicks and Dre‘sselhaus discussed the possible increase in TE
efficiency in quantum well and quantum wire structures.7 The surprising discovery of
the high temperature superconductivity in the complex copper oxides in the late 19803
inspired the search for better TE materials in complex bulk materials where physical
properties, such as electrical conductivity, can be tuned by varying the doping. Second,

TEs have found applications in new areas, such as cooling for microelectronics, and

power generation on satellites. 8

At Michigan State University (MSU) there exists an active interdisciplinary effort
on TE research. Dr. Kanatzidis’ group in the Chemistry department is one of the leaders
in the country on exploratory synthesis of novel bulk TE materials.’ They are focusing
on creating multinary Bi chalcogenides based on the BizTe3 parent compound; Since
BizTe3 is the best room temperature TE materials known, it is hoped that the TB
properties can be further optimized in complex compounds that use BizTe3 as a building
block. Several promising new materials have been found. In particular, CsBi,,Te6 has
generated a significant amount of interest in both scientific and technological
communities. Although its room temperature TE efficiency is still inferior to that of
BizTe3, it is the best low temperature (~250K) TE material known to date.9

A material’s TE properties depend sensitively on the details of its electronic
structure. Therefore, a thorough understanding of the electronic structures of these
materials is important. Professor Mahanti’s group in the Physics department of MSU is
performing band structure calculations using modern computation methods within the
local density approximation (LDA). Their results on BizTe3'0'“, Bi28e3‘2'“, and
CsBi.,Te,,13 have provided important insights about their TE properties.

However, LDA calculation has its limitations. It is important to verify these
calculation results experimentally. Angle resolved photoemission (ARPES) is one of the
most direct and powerful probes of the electronic structures of solids. Using this
technique, band dispersions can be determined, which can be directly compared with
band structure calculation results. ”"5”“ We have carried out the first detailed ARPES
studies of BizTe3‘8'”, Bi28e3'9'“, and CsBi4Te620. The dispersions of the valence bands

were determined. The densities of states were also studied using angle integrated

photoemission. Some general agreements with the calculation results, as well as some
discrepancies, were found. The implications of our results on the TE properties of these

materials are discussed.

Chapter 2 Thermoelectrics

2.1 Fundamentals of Therrnoelectrics

The TE properties of materials have been studied for well over a century.
Thomas Seebeck first discovered the TB phenomenon in 1823, when he noticed that a
temperature gradient placed across a sample resulted in a voltage drop across the sample.
If heat is applied to one end of a conductor and cold is applied to the opposite end, the
charge carriers in the conductor move in the direction from hot to cold. The electric field
which results is pr0portional to the temperature gradient by a constant S

E = SV T ,
where S is the thermopower (alternately defined as the average entropy per charge carrier
divided by the electron charge.) It is this effect that is the foundation of the
thermocouple.

Shortly thereafter, in 1834, Jean Peltier discovered that when a current passed
through a circuit of two different conductors, a thermal effect was found at the junctions.
The temperature at the junction would rise or fall depending on the direction of the
current flow. The Peltier coefficient, H, is the rate of heat flow divided by the magnitude

of the current,

In 1838, Heinrich Lenz showed that a water droplet placed on a junction of Bi and Sb
metal wires was frozen when an electric current was passed through the junction. The ice
drop melted when the current was reversed.

In 1854 William Thomson Lord Kelvin determined the thermodynamic
relationships behind these effects, describing the coupling between thermal and electrical
currents:

J = 0'[E — SVT]
and
Q = (o’I‘S)E — W T
where J is the electrical current density, 0' is the electrical conductivity, E is the electric
field, S is the thermopower, T is temperature, Q is the heat current density, and K is the
thermal conductivity. Lord Kelvin hypothesized that the Peltier coefficient and the
thermopower were related as:
II = ST.
This is the Kelvin relation of irreversible thermodynamics.3 Lars Onsager proved this to
be true in 1931. Thermoelectric materials are often discussed in terms of their
thermopower rather than their Peltier coefficient, because S is more easily measured."2'3

The net thermopower in a material depends on the transport of both the electrons

and holes in the material. The total thermopower will be

_ Gas: + abs}:
’0' o; + 0,,
Where S, and 0', are the thermopower and electrical conductivity of the electrons and Sh

and 6,, are the thermopower and electrical conductivity of the holes. The thermopower

for electrons and holes have opposite signs. Thus the thermoelectric effect of electrons

and holes tend to cancel each other if both electrons and holes are present. In a metal, the
fermi function,
1

f(E)=W—,

"'T +1

e

describes the distribution of electrons as a function of energy. At T=0, electrons fill the
bands to the Fermi energy. At a finite temperature, some electrons are thermally excited
to above the Fermi energy, leaving behind holes below the Fermi energy (see Figure 2.1
(a)). The density of states for a free electron gas is shown in Figure 2.1 (b). As seen in
Figure 2.1(c) from the product of the density of states and the Fermi distribution, the
number of electrons and holes are almost equal, which explains the very small
thermopower observed for metals. The thermopower for a free electron gas is estimated
to be
S = Lilia
6 E F
where kB is Boltzmanns constant, and EF is the Fermi level.3 Typical values of S for
metals lie it the range of —20uV/K S S .<_ 20ttV/K.21

In contrast, the thermopower for semiconductors can be quite large. In extrinsic

semiconductors, doping can affect the carrier concentration, n, creating an excess of

electrons (or holes). The thermopower in this case is a linear function of —ln(n)

k n
81 11(5)]

where e is the electron charge and E is the quantum concentration

kaT)%
27m2

 

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0.4 -—
0.2 -

 

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I.0— /
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holes
(C) 9(E)f(E)

  

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Figure 2.1 (a) The Fermi distribution function f(E) at T: 0 (dashed line) and
T: 300K(solid line). (b) the density of states , g(E), for a free electron gas. (c) f(E)g(E)
at T=0 (dashed line) and T=300K (solid lines). kBT is small compared to EF.

and m is the mass.22 Seen in Figure 2.2 (b) is a calculation of the thermopower for an
idealized semiconductor. In the metal limit on the right, the thermopower is very low.

The thermopower increases with decreasing carrier concentration until the carrier

1000

100

u.
"‘ 0

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Figure 2.2

room temperature, plotted as a function of carrier concentration.
concentrations close to that of a metal, high electrical conductivity is accompanied by
low thermopower and high thermal conductivity. At carrier concentrations of an
insulator, the thermal conductivity is low, and the thermopower is high, but the electrical

conductivity is low.1

1
Metal

1 L I J

 

LL...—

0 .
1015 101? 1018 1019 1020 1021 1022

C ARRER C 01113 INTRA‘HDH n(c:ln'1]

Transport properties calculated for an idealized semiconductor at
At carrier

 

concentration reaches 0 in a true insulator.

The efficiency of TE materials for converting heat to current and vice versa is

[(T;. - T.)(7—1)]
2“. + m

 

for power generation, and

yr. —T.
[(T. -T.)(7+1)l

 

for cooling, where T, and T, are the temperatures of the cold and hot sides, respectively,
and y = m , where ZT is the dimensionless figure of merit. The figure of merit is
defined as

ZT = USzT/(K‘L + Kc)
where KL is the lattice thermal conductivity and K, is the electron thermal conductivity.
For a material to have a high ZT, and therefore be an efficient TE material, it must have a
high thermopower and a high electrical conductivity while simultaneously having a low
thermal conductivity."2 This is difficult to achieve as the electrical and thermal
conductivities are interdependant and vary with temperature. Metals follow the
Wiedemann-Franz Law, which states that the ratio of thermal to electrical conductivity,
K/O', is proportional to temperature.’ Therefore, the ZT of metals is also low because the
high electrical conductivity is accompanied by high thermal conductivity. This can be
seen in Figure 2.2 (a), (c), and ((1). Figures 2.2(a), (c), and ((1) show the resistivity (1/0'),
thermal conductivity K, and ZT of an idealized semiconductor from the metal limit (right)
to the insulator limit (left). Insulators have low Z T due to their low electrical
conductivities. It was not until the 19505 that the increased TE efficiencies of d0pcd

semiconductors were discovered. In order for the hole and electron thermopower not to

 

cancel each other due to thermal excitation and still maintain a large enough electrical
conductivity, it has been determined that semiconductors with energy gaps on the order

of 10k,,To where k,3 is the Boltzman constant, and T is the maximum operating

0

temperature, are good candidates as TE materials.”3

2.2 Devices and Applications

A TE device, often called a Peltier device, typically consists of alternate n- and p-
type pellets connected electrically in series. In this configuration these pellets are said to
be connected thermally in parallel, i.e. the pellets will all drive the heat in the same
direction. In a cooling device (shown in Figure 2.3 (a)), a current flowing through the
material drives the hot carriers (electrons in the n-type and holes in the p-type materials)
from one surface of the material to the other, effectively pumping heat from one side of
the device to the other. This effect is fully reversible. By reversing the direction of the
current flow, the cooling side becomes the hot side and vice versa. A heat sink or fan
attached to the hot side of the device provides heat dissipation (Figure 2.3(b)), which is
necessary as the efficiency of the TB device depends on an Optimum operating

temperature.23

With the increase in ZT resulting from the discovery the doped semiconductors, it
was realized that TE devices had the potential to revolutionize the cooling, heat-
reclamation and power industries, if materials with sufficiently high ZT values could be

found. It was this high potential that fueled the large effort on TE research in the 1950s,

10

‘605 and ‘70s. Although there is no theoretical limit to the value of ZT, thus far very few
bulk materials have been found with a ZT greater than 1 which corresponds roughly to an
efficiency of ~10% (e.g., PbTe has a ZT ~ 1.2 at 700 K', while optimized BizTe3 has a
ZT=0.95 at room temperature’).

Currently TE devices are being used in many specialized areas. They are best
suited for situations where the efficiency is a lesser concern than the size, lifetime, and
reliability of the device. As a TB device has no moving parts, it has a significantly
greater lifetime. These devices also benefit from a smaller size (compared to other
devices), and are highly controllable. One example of the current applications of TE
devices is a personal refrigerator, which is manufactured by IglooTM. TE devices are also
used to supply power to satellites and interplanetary probes such as the Voyager
spacecraft, as well as submarines. To be economically viable, household refrigerators
and air conditioners must have an efficiency of ~30%; industrial air conditioning for
office buildings and such requires an efficiency of ~85-90%. To begin approaching these

efficiencies we need to find materials with ZT values of 3 or 43"”

2.3 Recent Developments

In recent years there has been a renewed interest in finding better TE materials, in
part due to the advanced synthesis capabilities now available, as well as new innovative
uses of TE devices. The recent efforts to develop new materials have focused on three

main directions: quantum well structures, correlated metals and

11

 

FdCI.‘

Released Released Released Relaxed Released Released
Heat Heat Heat Heat Heat Heat

0 ‘0 fr 0 i}

 

 

— i} i} i} i} i} ’L} +
Absorbed Ab scab ed Ab sorted Absorbed Ab sorbed Absorbed
Heat Heat Heat Heat Heat Heat

(a)

  
 
 
 
 
 
 
   
  

cold plate
pre-tapped hole

module
thermal interface
material

metal flatwasher
steel lockwasher
stainless steel
screw

Figure 2.3 (a) diagram of a basic thermoelectric device. The n- and p-type
pellets are connected electrically in series. The electrons (and holes) move in the
direction of current flow, driving the heat with them. See text. (b) An illustration of a
cooling module. The module consists of arrays of n- and p-type pellets. The modules are
then connected mechanically to a heat sink on the hot side, and a cooling plate on the
cold side.23

semiconductors, and complex small band-gap semiconductors. It has been shown that

the ZT for a single quantum well increases as the well width decreases. A value of ZT= 2
has been estimated for a single well. However, modeling suggests that devices made of
multiple quantum well systems may not achieve the same increase in efficiency. Highly
correlated semiconductors, also called Kondo insulators, are also thought to be likely
candidates as high ZT materials, although progress has been disappointing as yet. To
date, the best Z T achieved with these materials is 0.25. Complex small band-gap
semiconductors have been the most promising from a device standpoint.’ The

developments in complex materials and low dimensional materials are discussed below.

2.3.1 Complex Materials

The approach to the search for good TEs in complex materials is guided by an
idea pr0posed by Glen Slack in 1995. He proposed that a good TE material would
conduct electricity like a crystal, and conduct heat like a glass.° The lowest thermal
conductivity of a material is mostly limited by its lattice vibrations (phonons). The
pr0position is that materials with complex crystal structures, such as materials with a
large number of atoms per unit cell, or with a high average coordination number per
atom, might possess a low lattice thermal conductivity. One group of materials under
investigation is the filled skutterudites, such as LaFe3CoSb,2. These materials have a
cage-like unit in the crystal structure. A weakly bound rare-earth atom inside the cage
“rattles”, disrupting the phonons and therefore giving rise to low lattice thermal

conductivity."”

13

Professor Mercouri Kanatzidis’ group in the Chemistry department of MSU
focuses on finding new multinary Bi chalcogenides, which use BizTe3 as a building block
in the crystal structure. Since BizTe3 is the best room temperature TE material to date,
and Bi is a heavy element, it is hoped that the TB properties can be further optimized in
the complex Bi chalcogenides. Several of these materials, such as CsBi4Te69, BaBiTe325,
and B-KzBiSSeBZ", have shown promising TE characteristics, and are currently under

study for use in devices at Tellurex, a TB device company.23

2.3.2 Low Dimensional Materials

In 1993, Hicks and Dresselhaus discussed how, in a highly anisotropic material, a
high carrier mobility along a certain direction coupled to high effective masses in the
other two orthogonal directions, can also lead to a high ZT value. They determined ZT in

a three-dimensional material to be

 

 

F3
1 7 25 5
- _FS____
B 2 5 6Fl
5
where F is the Fermi-Dirac integral
2kT-3- 1 x'dx
F. *=4n' B 2mmm 2 —'T—"',
.(C) (,2 H . , 9 less.“

and (k is the reduced chemical potential 5* = C k T' The parameter B is defined as
B

14

 

3
l 2
37: h ’ eKL

where m,, my, and mz are the effective masses of the band extrema in the respective
directions, [1, is the carrier mobility along the direction of the current flow (chosen here
as the x direction), yis the k-space degeneracy of the band extrema,27 and KL is the lattice
thermal conductivity. A high value of B and therefore ZT can be achieved if the material
possesses simultaneously a high degree of k-space degeneracy, a low lattice thermal
conductivity, a high carrier mobility in one direction, and high effective masses in the
other two orthogonal directions. This idea was originally applied to quantum well
structures and quantum wires, with the value of ZT being slightly altered with each
lowered dimension.7 This is now applied to bulk materials, which are, so far, better suited
to technological manufacturing and application.‘ The parameter B illustrates explicitly the
dependence of the materials TE properties on the details of the electronic structure.
Photoelectron spectroscopy is the idea tool with which to study this aspect of these

materials, as it is the most direct experimental probe of a material’s occupied bands.

15

Chapter 3 Photoelectron Spectroscopy

Einstein first introduced the theoretical principles of photoemission in 1905 with
his work on the photoelectric effect.28 Previous to Einstein’s theoretical work on the
subject, it was known from experiment that light incident on a clean metal surface would
induce charges to be released from that sample. The maximum kinetic energy with
which these particles were released did not depend on the intensity of the incoming light,
but was related to the frequency of the incident light. Valence electrons in metals, though
present, are unable to escape into the vacuum due to a surface potential e¢, where o is the
work function of the material. Einstein proposed the photon model of light and realized
that for electrons to be able to escape from the crystal the minimum photon energy
required was equal to the work function of the material, hvmin = co, as shown in Figure

3.1.'4

3.1 Photoemission Process

Photoelectron spectroscopy (PES) measures the kinetic energy of electrons
emitted from a material as a result of photon bombardment. The most intuitive
description of the photoemission process is the three-step model developed by Berglund

and Spicer.29 In this model, the process is separated into three distinct steps, each With Its

own implications on the resulting photoemission spectrum.

16

 

Energy

E=Ef IIIIIIIIII-IIIIlla-IIIIIII

 

 

 

 

_>
I; (1) wave vector in vacuum

 

 

 

 

wave vector in crystal

Figure 3.1 A graphical representation of the requirement that the photon
energy be greater than the materials surface potential barrier in order for the excited
electron to escape to the vacuum. Here (1) is the magnitude of the materials work
function, hv is the incident photon energy, Ekin is the electrons measured kinetic energy,
EV is the vacuum level, e¢ + (l), and EF is the Fermi level.'4

The three steps are:
1. photoexcitation of the electron
2. migration to the surface
3. escape to the vacuum
as shown in Figure 3.2. In the first step the electron in its initial state is excited to a

higher final state by the absorption of an incident photon. The final state will be at an

energy hv higher than the initial state. This excited photoelectron is then transported

l7

Analyzer:
Ekin

 

 

 

 

Figure 3.2 A graphical representation of the three step photoemission process.
The three steps are labeled above. In step 1: absorption. In step 2: migration, and step 3:
escape.
through the solid to the surface of the crystal in the second step. If the additional energy
imparted to the electron was greater than the work function, then the photoelectron can
escape from the solid into the vacuum in step three.

Figure 3.3 shows the energetics of the photoexcitation process that occurs in step
one. From conservation of energy we can relate the observed kinetic energy to the photon
energy and the binding energy of the electron as

Eun=hv-EB-e¢.
Momentum is also conserved in this process. The momentum of the incident photons is

negligible for photons with energy in the ultraviolet range (in our case ~20 eV), only

vertical transitions are possible.

18

 

 

 

0-<¥ 4
m

m 6-
ca

 

 

 

 

 

Figure 3.3 In step 1 the electron, in its unexcited initial state, E, is excited to
the final state Ef by a photon typically of energy ~20 eV. From conservation of energy,
we relate the electrons measured kinetic energy Ekill to the photon energy hv and the
vacuum energy E,, which is a sum of the surface potential and the electron’s binding

energy EB.

Step 2 involves the transport of the excited electron to the surface of the sample.
During this step the electrons may scatter inelastically from other electrons or phonons,
which results in kinetic energy losses. For most materials the kinetic energy dependence
of the mean free path of electrons falls within a universal curve (Figure 3.4). At the
kinetic energies we are concerned with, the electron escape depth is only 5-20 A.
Electrons that escape from the sample without scattering, called primary electrons, lose

no energy. Their contribution to the spectrum has a structure

19

I,
I I

l
1 000

I I [I lull
a!"
I
l Laluul

SmtlanngLe-ngm ')
8
O
l l I$i1nl
4f
’0
O
lJlllul

   

 

 

 

10. =- __
i- I
1 I l . l , I
1 10 1 00 1 000
Electron Kinetic Energy (eV)

Figure 3.4 The universal curve showing the photoelectrons mean free path as
a function of kinetic energy. This represents the depth from which an electron can escape
without scattering. The open circles correspond to the scattering lengths of different
materials. At the kinetic energies in which we’re interested, the mean free path is less
than 20 A.”
representative of the material’s electronic structure. Electrons that scatter at least once
before escaping the sample, called secondary electrons, contribute a smooth background
to the spectrum (Figure 3.5).”"5 The secondary background can be approximated as
pr0portional to the total primary intensity at higher kinetic energies and subtracted from
the spectra." Because the escape depth of the photoelectrons is typically only a few

atomic layers, PES is especially surface sensitive. It is for this reason that PES

CXperiments are done in ultra-high vacuum, to minimize the amount of

20

Step 1

 

 

 

 
  

AEva

   

\\\\l\‘ \\\\\.\\\\\\\x t -
‘

 

 

 

  

surface potential

 

 

 

 

l
crlistal <——> vacuum

 

surface

Figure 3.5 A graphical representation of the three step model highlighting the
secondary electron contribution. The shaded region is the inelastic scattering
background, which can be subtracted from the spectra.”
surface adsorption and degradation.

In the final step the electrons whose energies are large enough to overcome the
surface potential barrier escape the sample to the vacuum. These electrons are collected
and energy analyzed.” '5'”

While the three-step model is effective as a tool for the visualization of the

photoemission process it is not, strictly speaking, entirely correct. A more correct

formulation, called the one-step model, was presented by Pendry et al.” In this

21

formulation the total photocurrent is the sum of the bulk and surface photocurrents. The
surface is approximated by a step function with a real surface potential, which is allowed
to differ from that of the bulk. Calculations using this model have produced good results
in copper. However, they are not significantly different from the results found with the

three-step model, which has the advantage of being conceptually simple.”

3.2 Photoemission Formalism

The interaction between an incident photon and an electron is governed by the

matrix element:
j<f,Z|E-Z+K-Eli,ié>l
where Z is the vector potential of the photon field, E is the momentum operator of the

electron, and 'ijc.) and I f 75> are the initial and final states, respectively. Within the

Coulomb gauge 371 = 0, and we can write the excitation probability as
_. _. 2
w, ~ '(f,klA - plz,k)| 6(E, — E, -hv)
from Ferrni’s Golden Rule, where E,- and Ef are the initial and final state energies. The 8

function ensures the conservation of energy. The photocurrent as a function of final state

energy, also called the energy distribution curve (EDC), can be written as

I<E.1~Zl<f.kIZ-Eli,k>|26(E..-E.)6(E.—E.--hv)
11f

Where the function 6(Ekm — E f)describes the restriction that only electrons wrth energ1es

14
greater than the minimum energy escape the sample to be measured.

22

3.3 Angle Integrated Photoemission

AIPES is the measurement of the photoelectrons over a large solid angle,

typically over the entire Brillouin zone. The EDC is then

[(Ek) z I XKijlZ. 5':,'12>'26(E, — 13,.— hv)6(E,,, — 19,)

El 1;;
This represents the joint density of states (DOS), modified by matrix elements. The
effects of the matrix element can be observed by varying the incident photon energy,
which is possible if a synchrotron light source is used. The matrix element effects will

cause modulations in the intensity of the features as the photon energy is varied.

3.4 Angle Resolved Photoemission

In ARPES the photoelectrons in a much smaller solid angle, typically < 2°, are
collected by the analyzer. As a result, both the momentum and the energy of the
photoelectrons are determined. This allows for a detailed mapping of the energy bands of

a material.

We can relate the electron’s kinetic energy to its momentum as electrons in
vacuum,
EM,l = h2K2/2m.
As the electron escapes the sample its momentum component parallel to the sample

surface is conserved, and can thus be written as

23

It." =21 =1/i—22Em Sine,

where If is the photoelectron’s momentum outside the crystal, I; is the electron
momentum inside the crystal, and 0 is the polar angle at which the electrons were
detected. The momentum component perpendicular to the sample surface is not

conserved, however, due to the presence of the surface potential. k i therefore remains

indeterminate (see Figure 3.6). The energy distribution curve is then defined as
.. .. .. _. .. 2 _. _. _. _.
I(E,,k) z jzl(f,k'/1. ply.» 5(E, — E, —ha))6(k, —k,.)6(K,, -k,,)6(Ek,n — 12,)
an i.f
where (XE-Z) identifies momentum conservation during the photoexcitation process,

and 6(KII - 12:) is the momentum conservation parallel to the surface as the photoelectron
escapes the material.

The indeterminacy of ki implies that we cannot fully ascertain the band
dispersions in three-dimensions. However, for quasi-two dimensional materials properly
orienting the crystal results in the band dispersion being negligible in the k i direction and
its electronic structure is only dependent on k". For a three-dimensional material, band
dispersions along ki can be probed by measuring EDCs at normal emission. In the
normal emission geometry

’91 = K11 = O:

k i can be varied by varying the photon energy."

24

 

 

 

 

I I: 0,0... H
Energy a
i i Kl.
K" R
EV. ' l ‘ vacuum I
(I) surface
E;-
crystal

Figure 3.6 A graphical representation of the conservation of momentum.
Here 4) is the work function of the material, EV is the vacuum level, EF is the Fermi level,

k is the wave vector inside the crystal, and If is the wave vector outside the crystal.”

It is also possible to determine three dimensional band dispersions by making the
following approximation. If we assume that the final state bands are free-electron like,
then the final state energy can be written as

71sz
E . =
km 2m

 

_V0

Where V0 is the inner potential. This assumption is valid for photon energies greater than

100 eV. However, it has been shown that it is also a good approximation for much

25

 

ZVo=10ev

 

0 H.,...,...,...,...,...,...,...,...
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 i!
Ky.theta

 

 

Figure 3.7 A 2-dimensional k-space map relating the photon energy and analyzer
angle to the experimentally determined V0. In this figure, V0 is 10 eV. The y-axis in
this map is the kz direction as well as photon energy. The x-axis is kll (in this case ky ).
Data points are at 10° intervals in 0 and 5 eV intervals in Em.

lower energies. We can then solve for k i

 

2m
kl =\/F(Ekm + Vo)"k112-

The result is that each photon energy describes a parabolic arc in k-space, as
shown in Figure 3.7. Different k-pointss along an arc are reached by varying the angle at
which the photoelectrons are measured. V0 is determined empirically by fitting to the
normal emission spectra. This is done by identifying critical points in the normal
emission spectra, which correspond to symmetry points in the Brillouin zone. Once V0 is
determined, then we also know the photon energy and angle required to reach every k-
points in the Brillouin zone.“"'5""'32

ARPES has been successfully used to map out the three-dimensional energy
bands in many materials. This includes elemental metals, such as Cu, Au, Ni16 and wide
gap semiconductors, such as Si33 and GaAs”. Some ARPES results on GaAs by Chiang

et al.32 are shown in Figure 3.8(a) as an example. As can be seen in Figure 3.8(b), there is

26

an excellent agreement between the observed band dispersions and those from LDA

calculations. There have been fewer ARPES studies of complex narrow gap

semiconductors.

GOA: (110) MIN. EfllSSlON SPECTRA

 

 

 

 

 

 

 

 

 

 

 

 

 

A “-5 I
\/ h'
A 1 “VI
\, f 25.0
g 1-
15 I'
Ev- no I '
6 530090339 ~,‘fg°to§b‘ Ava.“ «’1’.
g g .2 - ‘3 a, “‘3“! 0‘0” G O ’ "'
a- r ’2 ‘ °" ' ‘9"4 ’ ‘
r- .3- .4- ,’ rgxlh'wlfirs 3' 051 -
)- ~ I
g g s 1| ," 2“." x 2" d
3 a ’0 0‘9 conga ‘
:2 .
. < 4' 7
5 ommssrou
g 401'. I 1 q
i ' A. I", 04 Q X: no A
.'2_0°°' ['0' . ’I “al in.
- 0090009“ °oo7
l
"‘L 1 r r x I A F
CRYSTAL “NM Ill
aaalaaaalaaaa m

 

 

 

 

.15 4o , .5 E.
um. sun: am E. («1

(a) (b)
Figure 3.8 (a)EDCs measured from GaAs in normal emission. (b) comparison

of LDA calculations and observed dispersions for the valence band of GaAs. Symbols are
the observed bands and the dashed lines are the calculations.”

27

Chapter 4 Experimental Details

4.1 Light Source

All experiments were carried out at the Synchrotron Radiation Center in
Stoughton, Wisconsin, which is operated by the University of Wisconsin, Madison. The
1 GeV storage ring, named Aladdin (Figure 4.1), provides a continuous spectrum of
photon energies from infrared to soft x-rays. A monochrometer built after the port allows
the selection of any energy. The ability to vary photon energy is the prime advantage of
using a synchrotron light source compared to a lab source such as a helium lamp. Most
measurements were taken on the Ames-Montana Extended Range Grasshopper (ERG)-
Seya beamline. The ERG-Seya beamline has the advantage of combining a Seya
monochrometer, which was designed for the energy range 14-40 eV, with an ERG
monochrometer, which was designed for higher energies from 40 to 1500 eV (Figure
4.2).“ The beam spot size at the sample was 0.6 mm in diameter for the Seya and 1mm x
3 mm for the ERG. The Seya beam is nearly completely linearly polarized in the

horizontal plane.

28

 

 

 

 
  
 

   

1W4 111111//4m

 

 

 
 
 
 
 

 

 
  

 

 

 
 

 

 
 

NIM “
. BmTGM —
, Marti!
Grasshopper
TsGTll , Multi-
— Layer
—' EFlG- ——
6108 MeV
Microtron

 

 

Fluorescence

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 I [Set Optiml
0 10 upl Setup l I

Figure 4.1 Schematic of the Aladdin ring at the Synchrotron Radiation Center in
Stoughton, WI. The Microtron injects 1 GeV electrons into the storage ring. Expenment
beamlines are situated to take advantage of the photons radiating from the nearly
relativistic orbiting electrons. Our experiments were performed on the ERG-SEYA
beamline in the upper right comer of the figure.

 

29

Focus

 
 
 
  

 

  

 

 

1.3 an beyond Iange
124.6 an above floor Seya Grating
MZEllipsoidal Wror Seya Cylinditzl Glass
2' Grazing 3' Grazing
Exit Entrance
Experiment Slit Slit
Chamber }
f T Aladdin
Flat nempt Mm I‘m; Mew Flat Some
13' Gazhg 25 7' Grazing
'W'D' M0 C natal Mirror
39W 9mm ( rizontal)

Figure 4.2 A schematic layout of the beamline (side view). As the beam approaches
the monochrometer the metal flat 7° grazing mirror can be moved into or out of the beam
to select either the ERG or Seya gratings.”

4.2 Experimental Chambers and Electron Energy Analyzers

Two separate ultra-high vacuum (UHV) chambers and analyzers were used in
these experiments. For the AIPES experiments, a double-pass cylindrical mirror analyzer
(CMA) was used. The CMA, seen in Figure 4.3, consists of an inner cylinder kept at
ground and an outer cylinder, which is at a negative voltage. Electrons emitted from the
sample, also kept at ground, are filtered through two stages”17 (Figure 4.3). This

chamber was at 1x10‘lo Torr pressure during the experiments. The spectra were taken at

1' com temperature.

30

 

 

 

 

 

 

 

 

Figure 4.3 The double-pass cylindrical mirror analyzer. The electrons enter through
a large aperture. The electrons then pass between two cylinders at a potential difference.
They are filtered and focused through two passes, ending at a channeltron detector.

In the ARPES experiments, a movable 50-mm radius hemispherical analyzer with
an angular acceptance of i1° was used. The hemispherical analyzer consists of several
focusing lenses at the entrance aperture and two concentric hemispheres, seen in Figure
4.4, set at different voltages. The voltage difference selects electrons with specific
kinetic energies to reach the channeltron detector at the exit slit.'5"7 The analyzer is

mounted on a goniometer with two degrees of rotational freedom (the polar angle 9, and
the azimuthal angle 11)). The chamber pressure was 3x10'” Torr during experiments. A
closed cycle helium refrigerator was used to keep the sample at 20K, to reduce thermal

broadening in the spectra.

31

 

Figure 4.4 The hemispherical analyzer. Electrons pass through a series of lenses to a
pair of hemispheres set at different voltages. The potential difference effectively selects
the kinetic energies of the electrons which reach the channeltron.

4.3 Sample Preparation

n- and p-type BizTe3, CsBi4Te6, and n-type BiZSe3 were studied for the work
described in this dissertation. BizTe3 and BiZSe3 both have layered structures and their
crystals have a flake—like morphology. They were attached to sample holders using a
low-vapor pressure epoxy. X-ray Laue pictures were taken to help orient the samples in
the chamber.35 They were oriented with the bisectrix plane in the horizontal plane of the
chamber. Samples were cleaved in situ just before measurements by knocking off the

POStS glued to the top of the samples (Figure 4.5). The CsBi,,Te6 crystals have a

32

 

1 . .
A1 pin sample A1 post

Figure 4.5 An illustration of the sample mount. The sample is attached to the
aluminum mount by a vacuum-compatible epoxy. An aluminum pin is attached to the
sample and the epoxy is cured. Aqueous graphite is then used to coat the sample, to
ensure good electrical contact.

needle-like morphology. These samples were mounted with the needle direction in the

horizontal plane of the chamber. The samples were examined using thermopower

measurements, the sign of which indicate the type of doping.

4.4 Energy Reference and Resolution

In an EDC measurement, the photon energy is fixed and the photoelectron yield is
measured as a function of the electron’s kinetic energy. It is often desirable to convert
the energy scale from kinetic energy to binding energy. For metallic samples, the
conversion is usually done using a good metal, such as a Pt foil, as a reference. Figure
4.6(a) shows the spectrum measured from a clean platinum foil. The sharp leading edge

marks the highest occupied energy level, namely the Fermi energy. If the

33

 

 

  

 

 

 

 

 

 

 

l l l l l l
Pt Pt
A High Resolution High Resolution
3 hv=22eV a hv=22eV
'E 'E
2 =3 , 90%
.D
it”. 3
3‘ 29
§ ii
E E
10%
I I l 4 l A L I l l 44 A.
18.01 7.91 7.817.717.61 7.5 18.017.917.817.717.6l7.5
Binding Energy (eV) Binding Energy (eV)

(a) (b)
Figure 4.6 (a) An EDC of the Fermi edge of a clean platinum foil. The Fermi energy
is determined by the midpoint of the leading edge. (b) The width of the leading edge is
determined to be its measured width minus the top and bottom 10%.
foil is in electrical contact with the other samples to be measured, the Fermi levels of all
samples and the platinum foil are aligned. Therefore the kinetic energy at the midpoint of
the Pt leading edge corresponds to zero binding energy.

Additional information can be learned from the platinum spectrum as well. In a
metal, measured by ideal equipment, the Fermi function’s leading edge will only be
broadened by kBT. A real spectrometer has a finite energy resolution. Therefore the
Fermi edge is further broadened by the instrument function. If the temperature is low
enough (~20 K in our experiments), the temperature broadening is very small (~2 meV)
and the instrument broadening dominates. The width of the leading edge, measured from
10% to 90% of the edge height, is considered as the instrument resolution, as shown in

Figure 4.6(b) and is typically on the order of $100 meV for modern experiments. For

34

semiconductors, the binding energy is typically reference to the valence band maximum

(VBM).3°

4.5 Spectral Modeling

When several peaks appear in a spectrum and are close in energy, the binding
energies of the peaks are often obscured. To find the binding energies accurately, the
EDCs can be modeled with each peak represented by a Lorentzian function. The total
spectrum is a sum of Lorentzians multiplied by the Fermi-Dirac function”"" This sum is
then convolved with a Gaussian representing the instrument resolution. The instrument
resolution is determined from spectra taken of a platinum foil in electrical contact with
the sample (see above). The peak positions and widths are parameters, which are
adjusted until a good fit with the measured spectrum is obtained. An example of the

results achieved by modeling is shown in Figure 4.7

4.6 Comparison to Band Structure Calculations

Our experimental results are compared to the band structure calculations by P.
Larson and S. D. Mahanti. The calculations were performed using the full-potential
linearized augmented plane wave (FLAPW) method within the local density-functional

approximation (LDA). Scalar relativistic corrections were included in the calculation

35

 

 

 

 

 

 

 

l | l ! l
5
a
"5"
- 5 s '
.a '11
<3! "
V H
3‘ 4 3!: i
__ 1!. i
In .- i l
r: .1 1 s
8 g .3", 1 t.
is "' (E. I "t l t
.1 '1 . ; '1... l ‘
.5 -~'l.' ;. .J' 3' 3. _1 g
D , - _..__.-a ---D‘ " .2“. -;._ ‘.-"' fir-'91..“ J,;"("}:§, ’1'...
3 2 l 0

Binding Energy (eV)

Figure 4.7 An example of the spectral modeling results (see text). The spectrum was
taken at I‘ of B12T63. The solid line is the measured data; the dotted line is the modeling
result; the dot-dashed lines are the individual Lorentzian peaks used in the modeling.

and the spin-orbit interactions were included in a second variational procedure.""“"2'l3
Before comparing LDA band structure calculations to PBS measurements, there
are limitations in both which need to be addressed. We have already discussed the
complexities of interpreting the photoemission spectra due to matrix element effects,
atomic cross-section effects, surface effects, etc. In addition, in an LDA calculation the
ground state electronic structure is calculated. However, PES measures the excitation
spectrum of electrons from the material. Starting with a system of N electrons, the
incident photon effectively removes an electron from the system, leaving behind a

photohole. In comparing these spectra with calculations we make the assumption that the

36

N electron system before photoexcitation is the same as the N-l electron system after
excitation. Screening, relaxation, and other many-body effects are ignored.”

In an LDA calculation, the electron-electron interactions are accomodated in the
exchange potential. For simple metals, such as gold and silver, this treatment is adequate.
However, for highly correlated electron systems, such as the transition metals and rare
earths, LDA calculations often fail to describe the electronic structure properly. For
example, LDA often fails to predict or underestimates the gap in some transition metal
oxides. Also, LDA tends to predict bands that are more dispersive than those seen
experimentally.

Another problem that arises when comparing the spectra of the doped
semiconductors to the LDA calculations is the presence of disorder in the samples. In the
n-type BizTe3, for example, the crystal has a small amount of excess tellurium, which
substitutes for bismuth in the crystal structure. This disorder might have a significant
effect on the band structure of the material. Band structure calculations assume a
perfectly periodic crystal lattice and cannot, therefore, accommodate disorder in the

lattice. 38

37

Chapter 5 BizTe3 and BiZSe3

BizTe3 and its alloys are the best room temperature bulk thermoelectric materials
found to date (ZT~ 0.95).9 BizTe3 is a narrow gap semiconductor with an indirect gap of
~ 0.15 eV.39 BiZSe3, which is isostructural to BizTe3, has a small thermopower, S~10
uVK'l compared to that of BizTe3 S~260 uVK"."° BiZSe3 is also a narrow gap
semiconductor with an indirect gap of approximately 0.3 eV.“

The crystal structure of both of these materials is rhombohedral with the space

group D;d(R3m) with five atoms in the unit cell (Figure 5.1). The structure can be

visualized as quintuple-layer leaves stacked along the c-axis in the unit cell with Van der
Waals bonding between the leaves. The five individual atomic layers occur in the
sequence Te/Se(l)-Bi-Te/Se(2)—Bi-Te/Se(1) where the Te/Se(1) and Te/Se(2) are
nonequivalent tellurium/selenium sites.4143 The Brillouin zone is shown in Figure 5.2(a).
Figure 5.2(b) shows the bisectrix plane (the ZY plane) with the major symmetry lines
indicated. Because of the weak Van der Waals bonding between the leaves, both
materials behave quasi-two-dimensionally.
n-type BizTe3 and Bi28e3 crystals were grown by slow cooling of a molten

Bi/Te(Se) mixture. These samples are naturally doped n-type. In BizTe3 the mixture

38

        
 
       
        

  

.s
s
’c

Q
,ca
1'

at

I
‘1’.

  

’9‘
33!.‘3‘.
'1:

5??
O

1
a

Figure 5.1 The crystal structure of BizTe3. The large circles are the Te atoms; the
small circles are the Bi atoms. The hexagonal unit cell is indicated. Atoms occur in the
order Te(1)-Bi-Te(2)-Bi-Te(1) where Te(l) and Te(2) are inequivalent Te sites.

contained ~1.7% excess tellurium as a dopant, which substitutes for bismuth atoms in the
crystal."4 It is believed that the doping in BiZSe3 is substitutional, as it is in BizTeJ. We
also studied p-type BizTe3. These samples were purposely doped with additional
bismuth, which substitute for tellurium atoms in the crystal. As yet p-type BizSe3 samples

have proven unobtainable."5

39

 

 

 

‘ v
re-..n.n.
-

r a u e
t‘\90'b
e r . .

1 .. , . . v . . r . .. a 5 »
pp‘CJ‘IJQO‘a-'-n¢4-vovOtp~ “1.1.4.”
. , i a . . . t . . ~ .

a y . e 1 o
.,....-......u. .q ..oe-r
..r~..r.».--o-
\ .a..«.~«24-2
.un-e
‘.r.rl
\.~.~t

. . . .
.xx..\~v~..

. r .
4:2.‘Iab-v""‘

a n . .
Crab-baAt‘
, n .a -

|1lvvvuotb.\\

 

Figure 5.2 (a) The Brillouin zone for BizTe3 of the rhombohedral unit cell. The
shaded region is the bisectrix plane. (b) The bisectrix plane with the major symmetry
lines indicated.

5.1 BizTe3 Results and Discussion

While the transport and thermoelectric properties of BizTe3 have been extensively
studied,"""47 it is only recently that the details of its electronic structure have been
examined using modern LDA band structure calculation methods.'°'3”'48 The calculations
by Larson et al.‘° and Mishra et at."8 find that the spin-orbit interaction is important in
predicting the gap structure of BizTe3. They find a six-fold k-space degeneracy in the
valence band maximum (VBM) and a two-fold k-space degeneracy in the conduction
band minimum (CBM). This calculation result is only partially consistent with
Shubnikov-de Haas (SdH) and de Haas—van Alphen (deA) experiments, where a six-
fold degeneracy was found for both the VBM and CBM.49 Resistivity measurements have
also been completed on Bi2Te3."° A high degree of anisotropy was found, with the
conduction in the z direction lower than in the x-y plane.

Previous PES studies have been performed on BizTe3. Ueda et al.performed the
most recent study, using angle integrated PES and inverse PES50 to examine the effective
density of states of this material." Prior to that, Benbow er al.performed several PES
studies, both angle integrated and angle resolved, in the early 19805.52 The energy

resolutions in these studies are lower than those that can be achieved today.

5.1.1 Band Dispersions

Figure 5.3 shows the EDCs for an n-typc BizTe3 sample taken at normal emission

(Corresponding to k—points along F-Z shown in the inset). The initial state energies were

41

referenced to the VBM (EVBM), denoted by the arrows, whose determination is explained
below. As can be seen, ten bands, indicated by arrows and labeled 0 through 9, are easily
identifiable in these EDCs. The features show changes in relative strength because of
matrix element and cross section effects, but significant dispersion along F-Z is not
apparent. To examine the F-Z dispersions more closely, the second derivatives of the
EDCs with respect to energy were obtained. Shown in Figure 5.4(b) is an intensity plot
of the second derivatives as a function of energy and k in a linear gray scale with dark
corresponding to high intensity. The dark areas correspond to the energy bands.“"’3 The
intensity plot gives a direct qualitative view of the band dispersions. To get more
quantitative information, the EDCs were modeled as described in section 4.4. The band
dispersions extracted from the modeling are shown as filled circles in Figure 5.4(c),
whose size is approximately the size of the energy resolution (100 meV).

As can be seen in Figure 5.4(c), band 0 is extremely flat. Its energy was pinned at
the experimental Fermi level, as discussed in section 4.4. This band is the donor impurity
band, which resides in the narrow band gap (Egz0.15 eV) of the intrinsic material. Band
1 is the highest valence band. Along this symmetry line it reaches a maximum energy at
approximately 1/2 F2 and disperses toward higher binding energies to either side of the

local maximum. Bands 2 through 6 are quite flat showing very little dispersion. The lack

42

 

Intensity (Arb. units)

 

T I 1 U I r I I—

 

 

lrL :5 )

 

Figure 5.3

98
1+

7
t

2

_. l

3

Tfi

 

lr1 FTj

(a. F—Z
n-type BizTe3

ghv (eV)

   

25

24

23

 

Binding Energy (eV)

Energy distribution curves (EDCs) for an n-type BizTe3 sample taken
along F—Z (normal emission). The corresponding k-points are shown in the insets. The

energy is referenced to the valence band maximum (see text).

43

 

Flrl C .1! In

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1/
14“ .1 -—l
1
0.511 _ —
1
EVBM chIN/ 9|)
1
'0.5-1
1 2
1 3
as E 4
l
j 5
-1.5-1
1/\ 5
1\ 7
-21
1
l
-2.5-j 8
.1
: 9
-3__
i
-35’

°I‘ Z I‘ Z I‘ Z
(a) (b) (C)

Figure 5.4 (a) Band dispersions for n-type BizTe3 along T-Z from LDA band structure
calculation by Larson et at.10 (b) The intensity plot of the second derivatives of the EDCs
(821/ BE) as a function of energy and k in a linear gray scale with dark corresponding to
high intensity. (c) Band dispersions extracted from spectral modeling (see text).
of dispersion in the bands in the kz direction indicates that the material behaves quasi-two
dimensionally.

Shown in Figure 5.4(a) are the band dispersions for intrinsic Bi 2Te3 along F-Z as
calculated by Larson et at.” using the self-consistent full-potential linearized augmented

plane wave (FLAPW) method with spin-orbit interactions included. The calculation

results of Mishra et al.48 are similar. Within 3.5 eV below EVBM Larson et al.find nine

44

valence bands. The calculation shows the top valence band well separated from the
lowest conduction band, with a local maximum around 1/2 I7. Although this band has
the same dispersive trend as that of the observed one, it has a significantly higher binding
energy. The calculated bands along this direction have dispersions of 0.3-0.5 eV,
compared to the small dispersions (less than 0.1 eV) in the observed bands (bands 2
through 6).

Figure 5.5 shows the off-normal emission EDCs taken from an n-type sample for
k-points along the F—a-U line. The photon energy (hv) and the polar angle (0) are varied
simultaneously to reach the desired k-points, which are shown in the inset. Again, the
energy is referenced to the valence band maximum, EVBM. Figure 5.6(a), (b), and (c)
show the band dispersions along F—a—U as calculated by Larson et al., the intensity plot of
the second derivative of the measured spectra, and the band dispersions extracted from
spectral modeling (filled circles), respectively. The calculation shows nine very
dispersive valence bands. In contrast to the bands along F-Z, which have dispersions of
0.3-0.5 eV, bands along this direction have dispersions as large as 1.5 eV. The top
valence band reaches a maximum near the point, “a” which is also the absolute maximum
of the valence bands. A VBM along F-a-U implies that it is six-fold degenerate in k-
space. This result is consistent with the result of the deA and SdH experiments.”

In our experiment, we observed ten bands in the n-type sample (labeled as 0
through 9 in Figure 5.6(c)). Band 0 is the donor impurity band, which is non-dispersive,

and its energy was pinned at the Fermi level reference. It is localized around the F point;

disappearing within 12% of FaU from I‘. The remaining nine bands are highly

dispersive. Band 1, which is the highest valence band, reaches a maximum at

45

 

 

’ Fri—I.FT Tfilrlrfi1rrr1rr
° (b) F—a-U
r.’ l n-type BiQTe3
1 §9,hv(eV0

 

I = 19° 27
III33I223:5:flb::=2213122::::::i:: ’

- 17°,27 U
“15°, 26
M130, 26
W13 25
W0, 25

f 8°,24 a

7°,23

 

Intensity (Arb. units)

 

 

 

lllllllllllllllll Lllr

I3 22 1 () -1
Binding Energy (eV)

 

Figure 5.5 Energy distribution curves (EDCs) for an n-type BizTe3 sample taken
along F—a—U (off-normal emission). The corresponding k-points are shown in the insets.
The energy is referenced to the valence band maximum (see text).

46

 

1.2 J a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.6 (a) Band dispersions for n-type BizTe3 along F-a-U from LDA band
structure calculation by Larson et a1.” (b) The intensity plot of the second derivatives of

the EDCs (821/31?) as a function of energy and k. (c) Band dispersions extracted from
spectral modeling.

approximately 20% of FaU from F. It then disperses toward higher binding energy and
converges with lower bands, becoming barely visible after the point “a”. This dispersion
is quite different from that of the calculation, which shows the top valence band to have

two local maxima, one near the F point (approximately 10% of FaU from I‘), the other

near the “a” point (approximately 40% of FaU from F), the latter being the absolute

47

maximum. The theoretical calculations of the effective mass tensor associated with the
VBM agree very well with deA results. Note that deA measurements do not give the
position of the maximum in k-space. Furthermore, band 2, the second highest valence
band, is separated by ~600 meV from band 1 at the I‘ point. It disperses toward lower
binding energy and reaches a maximum near the point “a”, after which its intensity
diminishes. This dispersion behavior is also very different from that of the calculation.
The remaining valence bands appear to have qualitative correspondence with theory
although it is difficult to trace the dispersion of each band given the high density of bands
in this material and their complicated structure.

Spectra from the n-type sample were also taken along the three other symmetry
lines Z-F, F—F, and F—L. They are shown in Figure 5.7(a), (b), and (c) respectively. The
impurity band can be seen near the Z and F points. The valence bands are quite
dispersive along these directions. The top valence band disperses toward higher binding
energies away from the Z and F points, thus the VBM is not located along these
directions.

The local valence band maxima observed along F-a-U and F—Z are very close in
energy. The maximum along F—a-U is slightly higher than the one along F-Z Therefore
the maximum along F-a-U is the absolute VBM. However, the difference is small, being
only ~30 meV, which is smaller than our experimental resolution. Higher resolution
measurements should make a better distinction. A VBM along F-a-U is consistent with
both band structure calculations and deA experiments. Shown in Figure 5.8(a) and (b)
are the EDCs from a p-type sample (solid lines) for k-points along F-Z and F-a-U

respectively. The initial energy is referenced to the experimental Fermi level reference

48

Intensity (Arb. units)

Figure 5.7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the valence band maximum.

derived from a clean platinum foil in electrical contact with the sample. EDCs from the
n-type sample are superimposed (dashed lines, also referenced to the experimental Fermi
level) for comparison. As can be seen, the spectra from the p- and n-type samples have
rather similar spectral features. The main differences between the two are: (1) the

impurity band in the p-type sample (labeled as band 0) is seen only as a tail, which is

' 1 ' T(a)'z-i«‘ W F j 1 WSW-F f1 1(ctr-1'.

n-type Bare, E 1: n-zype Bare. n-type BbTee
W
F L
l.
1 1

l A J Z J 1 l L l g l L [F

1 0 3 2 1 0 1 0

Binding Energy (eV) Binding Energy (eV) Binding Energy (eV)

EDCs for an n-type BizTe3 sample taken along (a) Z-F, (b) F—F, and (c)
I‘—L. The corresponding k-points are shown in the insets. The energy is referenced to

expected because the chemical potential for a p-type semiconductor lies just below the

49

 

 

 

-Tfiijhsq... .(beFS-Bj.

 

 

| P; l —- p-type BirTe

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A A
33 3

ea .8

:s :3

- 2'

33 v

.é‘ r?!

(I) m

c: c:

d) d)

H H

.5 E ,,

I]: 0:,
:' ."4 -
i6 '
9 7 o’ 2
8 1 ’0
L l l l I J 1 l l l l 1‘ ' l ‘ r
3 2 1 0
Binding Energy (eV) Binding Energy (eV)

Figure 5.8 EDCs for a p-type BizTe3 sample (solid lines) taken along (a) I‘-Z (normal
emission) and (b) F—a—U (off-normal emission). The corresponding k-points are shown in
the insets. The energy is referenced to the experimental Fermi level reference derived
from a clean platinum foil in electrical contact with the sample. The EDCs for an n-type
sample are also shown (dashed lines) for comparison.

impurity level; (2) the top few valence bands (band 1 through 4) are shifted toward lower
binding energy (by approximately 0.095 eV for band 1, and 0.2 eV for bands 24) in the

p-type sample relative to those in the n-type sample. The amount of shift is on the order

of the band gap and the direction of the shift is consistent with the p—type doping.

50

The remaining bands, 5 through 9, appear not to be shifted. This may be due to
the fact that the p-type sample is substitutionally doped with excess bismuth, which
occupies the tellurium sites. The calculation by Larson et al.'° shows that, along the F—a—
U line, the top valence bands have predominantly tellurium character and so would be
more affected by the loss or addition of tellurium in the crystal. Along the F—Z line, the
calculation finds the t0p valence band is a Bi-Te hybridized band. The hybridization is
caused by the inclusion of the spin-orbit interaction, which also pulls the top valence

band towards higher binding energies.

5.1.2 Density of States

Angle-integrated photoemission spectra of single crystal p-type BizTe3 were taken
at three photon energies, hv=l9, 22, 25 eV (Figure 5.9). Varying the photon energy does
not change the binding energies of the spectral features, but the features do display
intensity modulations due to matrix element effects as discussed in section 3.3. These
intensity modulations in the spectra allow us to identify many bands which might have
been difficult to distinguish had the spectra been taken at a single photon energy. Our

experimental setup did not allow for a measurement of a Fermi level reference. For the

51

 

 

Intensity (Arb. units)

 

 

 

 

-8 -6 -4 -2
Energy (eV)

Figure 5.9 Angle Integrated photoemission spectra for BizTe3. Arrows indicate peaks
1-6. For the purpose of comparison, the energy reference (zero of energy) was set such
that the lowest binding energy peak in the spectra coincides with the position of the
corresponding peak in the LDA calculations.
purpose of comparison, the energy reference was set such that the lowest energy valence
band peak in the BizTe3 spectra coincides with the corresponding peak in the band
structure calculation.

The spectra of BizTe3 (Figure 5.9) contain six easily indentifiable peaks, labeled 1
through 6, with energies of -l.l, -1.37, -2.07, -2.66, -3.77, and -4.51 eV, respectively.

These features come to prominence at different photon energies. At hv = 19 eV peak 1 is

most intense but loses intensity, becoming approximately equal in intensity to peak 2 at

52

hv = 22 eV, further losing intensity at hv = 25eV. Peak 3 is rather narrow in the hv = 19
eV spectrum, broadening as the photon energy is increased. Peak 4, which is difficult to
identify at hv = 19 eV and 25 eV, gains intensity with increased photon energy. Peak 5
can easily be identified at all photon energies. Peak 6 loses intensity with the increase of
photon energy, becoming indistinguishable from the background at hv = 25 eV.

The calculated LDA DOS for BizTe3by Larson et al. is shown in Figure 5.10 with
arrows indicating the positions of the experimentally observed peaks.ll Seven features
were identified in the theoretical DOS. Table 5.1 shows the values for the features in the
theoretical DOS, labeled as DOS, and the observed energies, labeled AIPES. As the
theoretical DOS does not include the matrix element effects, we will not be able to
compare it directly with the experimental spectral shape. We will instead focus on the
positions of the dominant peaks.

In both the experimental spectra and the theoretical calculation a double peak
structure was seen at higher energies. The calculated separation of these peaks is 0.3 eV,
which agrees very well with the observed separation of 0.27 eV. The positions of the
next
three peaks in our experiment (peaks 3, 4, and 5) agree very well with the calculated
positions at -2.1, -2.6, and -3.9 eV, respectively. Experimental peak 6 is slightly below a
DOS peak, while the DOS peak at -5.3 eV was not observed. The overall agreement
between theoretical and experimental valence band peak positions is remarkably good

and well within the experimental resolution (0.08 eV).

53

 

IUhCO

81211133

 

 

 

 

7 T T j 3 1T
8 L e 5 4 r
l l l
s — 3 _
l

4 .. -1
3 - _

2 - J
1 ‘ a

o I J_ g _l I l l V
-a -7 -e .4 .2 .1 0

Energy[eV|

Figure 5.10 Total density of states of BizTe3. The arrows indicate the positions of the
photoemission peaks seen in the observed spectra. The energy reference (zero of energy)
was set such that the highest valence band DOS peak, and the lowest observed binding
energy peak coincide.”

 

 

 

 

 

 

 

 

 

 

 

 

 

AIPES -1.1 -l.37 -2.07 -2.66 -3.77 -4.51
(eV)
DOS (eV) -1.1 -1.4 -2.0 -2.5 -3.8 -4.2 -5.2
Table 5.1 Comparison of photoemission and calculated DOS peaks for BizTe3. For

the purpose of comparison, the energy reference (zero of energy) was set such that the
highest valence band DOS peak, and the lowest observed binding energy peak are
coincident. The peak positions from the LDA calculation are labeled DOS, and the
observed peak positions are labeled AIPES.ll

54

5.1.3 Summary

ARPES studies of BizTe3 show that the VBM is located along the F—a-U line and
therefore is six-fold degenerate in k-space. This is consistent with the result of the LDA
band structure calculation.‘°'"8 However, we also find some discrepancies between our
data and the calculation results. The position of the VBM along F-a-U is different. Also,
we find that the bands along F—Z have minimal dispersions (<O.l eV), compared to the
larger dispersions (0.3-0.5 eV) predicted by the calculation. Possible reasons for this
discrepancy are the disorder caused by the dopants, the electron-phonon interaction, and
the electron-electron interaction. These three effects could cause band narrowing. The
flat bands along F—Z could generate carriers with large effective masses along this
direction which, coupled with the high degeneracy of the bands along the ab-plane of the
crystal, can explain the remarkable thermoelectric properties of BizTe3. Also, we did
observed the top valence band along F-Z at a lower binding energy. The higher binding
energy of that band in the claculation is due to spin-orbit interaction. Finally, these
observations indicate that the subtle details of the electronic structure of BizTe3 are not
fully understood and illustrate the need for further investigation.‘8

From the angle integrated PES study, the agreement between the ab initio
FLAPW calculated peak positions and the experimental valence band peak positions in
BizTe3 is very good. We observed 6 peaks which compare well within the experimental
resolution of 0.08 eV to the calculated peaks. The exceptions to this are the final

calculated peak, which we did not see, and the observed peak at —4.5 eV. With improved

55

energy resolution of the experiment and by incorporating matrix element effects into the

calculated DOS, a better agreement should be obtained.”

5.2 31281:, Results and Discussion

In an effort to understand why BiZSe3 has such lackluster TE properties“, when
compared to BizTe3, several band structure calculations have been performed?” The
LDA calculations by Larson et a1.find qualitatively similar results to a comparable study
by Mishra et a1.48 They find that the spin orbit interaction has very little effect for BiZSe3.
They find a gap size that is in agreement with previous experiments (~0.32 in the
calculation'7"” and ~0.35 eV previously measured“) They also find the conduction band
minimum and the valence band maximum to occur at I‘, which are non-degenerate in k-
space. We also study BiZSe3 in an attempt to understand why a material which is

isostructural to BizTe3 has such a poor TE performance.

5.2.1 Band Dispersions

EDCs for n-type BizSe3 taken at normal emission with varied photon energies
(along the F—Z symmetry line) are shown in Figure 5.11. The corresponding k-points are

shown in the inset. The observed kinetic energies are referenced to the experimentally

56

 

 

 

 

 

 

 

 

 

T z I I 1
F—Z
l l' n-type BiZSe3
l ‘\ hV(CV)=
MW”
MW 29
\—281
G .
.E ~ 27J
5f 261
E . 25
E: 241
'53
a
8
E
H
2 '
5 4 i 231
7 6 A ‘ ‘ a
8 r . 1
3 .
9 ‘ A
g 0
1 a 1 ./'\ 22
3 2 . . 1 0
Bindrng Energy (eV)

Figure 5.11 Energy distribution curves (EDCs) for an n-type BiZSe3 sample taken
along F-Z (normal emission). The corresponding k-points are shown in the inset. The

energy is referenced to the valence band maximum (see text). Energy resolution is 0.1
eV.

57

determined valence band maximum (EVBM), which will be described later in greater detail.
The spectra were taken at 1 eV intervals and are stacked vertically for clarity. The spectra
have been normalized to the photon flux. They show a remarkably low secondary
background.

In these spectra, a total of ten bands can be identified, labeled 0 through 9, and are
indicated by arrows. The experimental Fermi level lies just above band 0. The feature
intensities are highly photon energy dependent which is most likely due to matrix
element and cross-section effects. There is also some dispersion in the features. The
dispersion in the bands in this direction is generally on the order of 100—200 meV, and
can be seen more clearly in Figure 5.12(b) and (c). Shown in Figure 5.12(b) is an
intensity plot of the second derivatives of the EDCs with respect to energy as a function
of energy and k in linear gray scale with dark corresponding to high intensity. The dark
areas correspond to the energy bands.'°'53 The energy reference will be discussed below.
The intensity plot gives a direct qualitative and objective view of the band dispersions.
Figure 5.12(c) is a plot of the dispersions of the features identified in the spectra. The
bands are labeled 0 through 9, and are indicated by filled circles whose size is
approximately the size of the energy resolution. Figure 5.12(c) compliments the intensity
plot in Figure 5.12(b), giving us a quantitative view of the band dispersions. From these
two figures, we see that bands 1 through 9 are not entirely flat along this direction.

As can be seen in Figure 5.12(b) and (c), we identified band 0 as an impurity band
lying above the valence band maximum, and bands 1 through 9 as the valence bands.

There are several reasons for this assignment. First, band 0 is very flat along F-Z

58

—L

 

 

 

1
:
1
0.5-
J 1 . .
VBM 1 _ i 1531;“
d_ ._ ‘1 _.
l 1
1 r. ' Czl‘ufci‘.‘ .
:1 t “i ”a; r~
‘0 '5 ‘4
4N , ,gff'
>~ - f
9 I .. 2
a) '1 1: "11:32:. $3.21.:
LE 1 :3 ' fee 3
U) : "it.5..i.’~".§‘.';'.-,:;.l,1~
.E '1 "" «‘3‘??- 4
U -1'5-l/\ 1.15:...
m 4 ' .~ .- "i 5
q 'T ‘1.- 6
1 iii-7 1.2‘..::;,::;;‘,,;;
2.54 8
l
3 9
-3 _1
s
i
-3.5

 

 

 

 

(a) (b) (C)

Figure 5.12 (a) Band dispersions along F-Z in BiZSe3 from band structure calculation
by Larson et al.12 (b) The intensity plot of the second derivatives of the EDCs ( 821/ BE)

as a function of energy and k in a linear gray scale with dark corresponding to high
intensity. (c) Band dispersions extracted from observed Spectra (see text).

(dispersion is less than 0.03 eV) and is pinned at the experimental Fermi level. This
suggests that it is an impurity band. Second, this material is n-doped, therefore the
impurity band should lie above the valence band maximum. Third, the separation

between bands 0 and 1 is approximately 0.38 eV, which is comparable to the band gap of

this material measured by other experimental methods. Last, with this band assignment, a

59

good correspondence between the observed and calculated bands can be found, as will be
discussed below.

In Figure 5.12(b) and (c), we see that band 1 is more dispersive than band 0, with
a local maximum at the I‘ point. This band disperses ~0.2 eV to a minimum at the Z
critical point. Band 1 is also well separated from the remaining valence bands; at the I‘
point band 2 lies at more than 0.6 eV higher binding energy. The remaining valence
bands 3-9 each disperse less than 0.2 eV along F-Z, and are relatively flat compared to
the lower binding energy peaks.

Shown in Figure 5.12(a) are the LDA band calculations for intrinsic Bizse3 along
F—Z by Larson et (11.”12 Within 3.5 eV below EVBM Larson er al.find nine valence bands.
The top valence band has a maximum at the I‘ point, dispersing ~0.4 eV to a minimum at
Z. This band has a slightly higher binding energy than its observed counterpart, but the
dispersion has roughly the same shape. The second valence band is separated from the
top valence band by ~ 0.5 eV and is much less dispersive than the top valence band. The
remaining valence bands predicted by theory are approximately twice as dispersive as the
fairly flat bands observed experimentally, indicating that the material is more anisotropic
than predicted.

Off-normal emission spectra of n-type BiZSe3, taken along the Z-F symmetry line
(at k-points shown in the inset), are shown in Figure 5.13. The initial state energies are
once more referenced to EVBM. The energy resolution in these spectra is 0.1 eV. Ten

bands, labeled 0 through 9, are identified in the spectra at the 2 point. In these spectra we

60

 

 

Z-F
2 F n-type Bi,ZSe3

hv, 0:
F 20,26

W 20,2

19,22
19,21}
18,18

18,16
Mk 17,1
L 17,12
c 17,10

 

 

 

 

 

 

 

Intensity (Arb. units)

17,8
16,6
16,4

 

 

 

\e
‘00
‘q
‘6‘
‘0:
b
but
I»

 

 

 

l Zj

3 2 . . 1 0
Binding Energy (eV)

 

Figure 5.13 Energy distribution curves (EDCs) for an n-type BiZSe3 sample taken
along Z-F (off—normal emission). The corresponding k-points are shown in the inset.

The energy is referenced to the valence band maximum (see text). Energy resolution was
100 meV.

can clearly see that band 0 exists only at the F point. A small remnant shoulder appears
at the k—point just adjacent to I‘, possibly indicating the presence of a band just above the

Fermi level. The valence bands are highly dispersive in this direction.

61

Figure 5.14(a), (b), and (c) show the theoretical band structure, the second
derivative intensity map, and the experimentally observed dispersions seen along the Z-F
symmetry line. The energy reference is the same as in Figure 5.13. Band 0, labeled in
Figure 5.14(c), exists only at the Z point, separated from the valence bands by
approximately 0.4 eV. The top valence band (band 1) has a local maximum along this
symmetry line, at ~10%7F, with a secondary maximum at ~45%2F. Overall, the
valence bands in this direction are fairly dispersive, on the order of 0.5-1 eV. However,
due to the complex nature of the band structure, it is impossible to trace the dispersion of
each individual band.

In Figure 5.14(a), the LDA calculations also show a highly dispersive and
complex electronic structure. Nine total bands are seen along the Z-F symmetry line
within 3 eV of EVBM. The top valence band disperses a total of ~1 eV, moving to a local
maximum at ~35 % 277. Many of the higher binding energy bands disperse more than 2
eV along the Z-F line. Much like the dispersion along the I‘-Z line, there is less
dispersion seen in the experimentally observed bands than in the theoretical predictions,
most especially in the low binding energy bands near EVBM.

Shown in Figure 5.15 (a), (b), and (c) are the spectra taken along the remaining
three major symmetry lines of interest, F-a-U, F-F, and F-L, respectively. Similar to the
dispersions seen in along the Z-F direction, the spectra Show many dispersive bands, with

the bands along the F—L line (Figure 5.15(c)) especially well defined. Band 0 shows

62

 

Band 0

0.5 . I
., ..- ,. <—shoulder

 

 

 

 

 

15,,,,.,,._L
e...
0.5 ..~. O..+
d".
-1 ’0. ”.OJ
one ‘.
-15 x L\' O .CO .3
" o o 0 4
o “a
'2‘; .:. “a .4
1 0%.
as; . .
J . ”O. .
I , s O 0
3‘: I d. . .5
1 -
3.5-4 1
-4 : a

 

 

 

 

 

N
‘11
N
TI
N
‘11

(a) (b) (C)

Figure 5.14 (a) Band dispersions along Z—F from band structure calculation by Larson
et al'° (b) The intensity plot of the second derivatives of the EDCs (821/8152) as a
function of energy and k (c) Band dispersions extracted from observed spectra.

63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'(a) 125-0 1 7 Tow—F - I ‘(c) r-l
U n-typc 1.355% n-type 8128c3 ‘ l' L n-type BiISe3
l" 5

L
A
.3
E
5
.o'
:3

rs: -_
w
t:
3

:1 L
t—t

L-
L J _I I r L I r I 1 LP

 

 

 

 

 

 

 

 

3 _ .2 1 0 3. .2 1 0 3 2 1 0
Binding Energy (eV) Binding Energy (eV) Binding Energy (eV)

Figure 5.15 EDCs for a BiZSe3 sample taken along (a) F-a-U, (b) F-F, and (c) F-L.
The corresponding k-points are shown in the insets. The energy is referenced to the
valence band maximum. Energy resolution was 0.1 eV.
intensity only at the F point. The remaining valence bands disperse towards higher
binding energies as we move away from the 1" point, where a local maximum exists in the
top valence band.

Figure 5.16 shows spectra taken at higher resolution along the 1"-Z line, looking at
a small range of binding energies around the Fermi level to which the spectra are
referenced. In this energy range we should see bands 0 and 1 clearly. We see instead

two double peak structures, which we label as bands 0,, 02, 1,, and 12. Arrows indicate

the peak positions, determined by Spectral modeling. The combined width of bands 11
and 12 are less than 0.2 eV, which is consistent with the width of the band as seen in the
second derivative intensity map along the F-Z line (Figure 5.12(b)). It is possible that
these bands are almost degenerate and so were not resolved in the band structure
calculations (Figure 5.12(a)) or the lower energy resolution spectra (Figure 5.11).

The double-peak structure of band 0 is more difficult to understand. As p-type
BiZSe3 can so far not be synthesized, we cannot compare n- and p-type spectra in an
attempt to clarify the origin of the bands. According to both the theoretical

‘8 and the SdH measurements’4 the lowest conduction band should disperse

calculations'z'
more than 0.5 eV from the F point, to either side of F. While the presence of the 0
bands does not extend past the F point along the F—a—U, F -L, and F -F symmetry lines,
both 01 and 02 exist along the entire length of F-Z. Band 01 is flat for the length of the
symmetry line, and is closest to the Fermi level. This band is most likely the impurity
band.

Band 02 disperses towards higher binding energies by 0.06 eV from F to Z at low
photon energies (at higher photon energies the peaks 01 and 02 are difficult to
distinguish). This has the opposite dispersion we would expect according to the
calculation. However, the fact that this band does not exist along the other symmetry
lines, and the large degree of separation of this band from the other identified valence
bands, argues that it is a conduction band remnant. Its dispersion is perhaps severely
altered by the significant amount of doping and the impurity band above it. This would

alter the conduction band k-space degeneracy of this material from y=1 at the F point, to y

= 2 along F-Z.

65

 

l T I F l
F-Z
n-type Bi28e3
hv(eV)=

 

WM 27

 

L---'------—---24l

 

 

¥—-—22

21

Intensity (Arb. units)

20

19
18

17

1

I I A — 1A

0.8 0.6 0.4 0.2 0.0 -0.2
Binding Energy (eV)

 

 

 

Figure 5.16 Higher resolution EDCs for a Bizse3 sample taken along G-Z (normal
emission) The corresponding k-points are shown in the inset. The energy is referenced to
the experimental Fermi level reference derived from a clean platinum foil in electrical
contact with the sample. Energy resolution was 37.6 meV.

66

5.2.2 Density of States

Angle integrated PES spectra of n-type BiZSe, were taken at 7 photon energies, hv
= l7, 19, 20, 21, 22, 23, and 25 eV (Figure 5.17). No Fermi level reference was
measured, and the energy reference was set such that the first peak in the BizSe3 valence
band spectra coincides with the corresponding peak in the LDA calculations.

A large number of peaks can be identified in the spectra in Figure 5.17, having
energies of —l.1, -1.46, -2.03, -2.64, -3.08, -3.52, —4.26, -4.66, ~5.62 eV, respectively.
These peaks are labeled 1 through 9. Peak 1 is most prominent and identifiable at all
photon energies, with its highest intensity at hv = 17 eV. Peak 2 is most easily
distinguishable at hv = 19 eV, but not individually discemable at hv = 17 eV or 25 eV.
Peak 3 loses intensity with decreasing photon energy, with a relative maximum at hv =
25 eV. At hv = 23 eV peak 4 is easily identified from the background but loses intensity
by hv = 21 eV to become a minimum at that energy. Peak 5 is easily visible at hv =17,
19, 20, and 21 eV while peak 6 is most obvious at hv = 20 eV. Peaks 7 and 8 are
identified at hv = 19 eV and 17 eV, respectively, while peak 9 is best seen at hv = 19, 20
and 21 eV. The LDA calculation finds a total of 8 peaks, shown in Figure 5.18, with
arrows indicating the positions of the observed peaks. Despite seeing 9 peaks in the
observed spectra, we find good agreement between the calculated peak positions and
those seen in our experiment (Table 5.2). The double peak structure has a separation of

0.36 eV between peaks 1 and 2 in the observed spectra compared to the calculated value

67

 

hv=
25 eV_

23 qu

 

 

Intensity (Arb. units)

20 eV‘

 

 

19 eV_

 

 

1 17eVJ

I
-6 -4 -2 0
Energy (eV)

 

Figure 5.17 Angle Integrated photoemission spectra for BiZSe3. Arrows indicate peaks
1-9. For the purpose of comparison, the energy reference (zero of energy) was set such
that the lowest binding energy peak in the spectra coincides with the posrt1on of the
corresponding peak in the LDA calculations.

of 0.4 eV. This double-peak structure was also found in BizTe3. The calculated peak at -
2.1 eV corresponds well to peak 3. This peak was not seen in previous angle integrated
photoemission studies, most likely due to the lower resolution. Another factor may be
that the matrix element effects were obscuring this peak which could not be resolved as
the previous studies have used a helium lamp source, which emits photons at only

hv =21.2 eV. The experimentally observed peaks 4 and 5, seen at -2.64 and -3.08 eV,

respectively, lie symmetrically on either side of the calculated peak at -2.9 eV. Peak 6 (-

68

3.52 eV) lies about 0.3 eV above the calculated peak at -3.8 eV. Peaks 7, 8, and 9 clearly

correspond to the calculated peaks at -4.4,- 4.6, and -5.4 eV, respectively.“

 

(~03

 

 

 

 

_
p—
h

0 l 1 l l
.4
Energy [eV]

 

Figure 5.18 Total density of states of BiZSe3. The arrows indicate the positions of the
photoemission peaks seen in the observed spectra. For the purpose of comparison, the
energy reference (zero of energy) was set such that the highest valence band DOS peak,
and the lowest observed binding energy peak coincide.ll

 

AIPES (eV) -1.10 -l.46 -2.03 —2.64 -3.08 -3.52 —4.26 -4.66 -5.62

 

 

 

 

 

 

 

 

 

 

 

 

 

DOS (eV) -l.l -l.5 -2.1 2.9 -3.8 -4.4 -4.6 -5.4

 

Table 5.2 Comparison of photoemission and calculated DOS peaks for BiZSe3. For
the purpose of comparison, the energy reference (zero of energy) was set such that the
highest valence band DOS peak, and the lowest observed binding energy peak are
coincident. The peak positions from the LDA calculation are labeled DOS, and the
observed peak positions are labeled AIPES.‘l

69

5.2.3 Summary

In summary, ARPES and AIPES experiments have been carried out on n-type
BiZSe3. There is very good agreement between the theoretical calculations and the
valence bands seen in the ARPES spectra. It was found that the valence band maximum
is located at the F point and therefore is non-degenerate. Although the bands along the
F—Z line are relatively flat, there is a measurable dispersion in those bands. The low k-
space degeneracy of the VBM and the lesser degree of anisotropy may account for this
materials poor TE properties as compared to that of BizTe3. There are some discrepancies
between the LDA calculations and our observed Spectra. Those are probably due to the
doping in the material or the electron-electron interaction.19

There is also good agreement between the observed DOS and that seen by the
calculation. Nine peaks were observed in the experimental DOS, compared to eight in the
calculation. In most cases, the agreement between observed and calculated peak positions
is well within the experimental resolution of 0.08 eV. We observed a peak at —3.08

which was not seen in the theoretical DOS.”

70

Chapter 6 CsBi4Te6

CsBi4Te6 is one of the exciting new TE materials discovered in Professor
Kanatzidis’ lab. It has a modest room temperature ZT of 0.65 (compared to optimized
BizTe3 with a ZT of 0.95). However, at 225 K the CsBi.,Te6 ZT increases to 0.82, which
is a significant improvement over BizTe3 (ZT~0.58) at the same temperature. The two
materials have a roughly equivalent thermal conductivity, suggesting that the cause of the
increased ZT is electronic in nature. CsBi4Te6 is a narrow-gap semiconductor, with a gap
size estimated at between 0.05 and 0.11 eV.9'l3

The crystal structure of CsBi4Te6 is monoclinic, space group C2/m, with 88 atoms
in the unit cell (see Figure 6.1). The structure consists of Bi,,Te,5 laths connected via Bi-
Bi bonds, forming two-dimensional slabs. Of the bismuth chalcogenide compounds, the
Bi-Bi bonds are unique to this material. These slabs are each separated by a layer of Cs
atoms. The crystals of this material have a needle-like morphology. The b-axis of the
Bi,,Te6 laths, which is normal to the plane of the paper in Figure 6.1, is the needle growth
axis and is the direction of highest charge mobility.9 The Brillouin zone of the monoclinic
unit cell is shown in Figure 6.2. The three major symmetry lines of interest are indicated.

The F—X symmetry line corresponds to the direction of needle growth, perpendicular to

the page in Figure 6.1.

71

 

 

 

 

 

 

 

O O O Q 0 0 g . C O O
Bi-Bi bond
0 Cs
0 Te
0 Bi

Figure 6.1 The crystal structure of CsBi4Te6. The small white circles are the Te
atoms; the small black circles are the Bi atoms; the larger gray circles are the Cs atoms.

 

 

"3
in

‘V

Figure 6.2 The Brillouin zone for CsBi,,Te6 of the monoclinic unit cell. The three
important symmetry directions are indicated.

72

The F—Z line is in the direction perpendicular to the Cs atoms layers, and F -V is in the
direction of the Bi-Bi bonds.

N- and p-type CsBi,,Te6 samples were synthesized by vapor transport reaction of
Cs and BizTe3. For the n-type CsBi4Te6, Bi,_9Te3., was used for Te-doping. For p-type
BizTe3, stoichiometric amounts of Bi/Te were used without additional intentional doping.
It is currently unknown how the doping occurs in this material, although it is believed to

be substitutional, as is the case with BizTe3 and BiZSe3.”

6.1 Results and Discussion

The LDA calculation by Larson etal.13 predicts more than seventy valence bands
within 5 eV below EVBM. This large number of bands is a consequence of the large
number of atoms per unit cell in this material. These bands do not become degenerate due
to the low symmetry of the crystal structure. The calculation shows that the valence
bands are most dispersive along the direction of needle growth (F-X). The dispersion in
the other two orthogonal directions (F-V and F-Z) is minor. The VBM occurs at the F
point, which is non-degenerate in k-space. The effective mass tensor of the valence band
maximum is found to be highly anisotropic. The effective mass in the F-V direction (the
direction of the Bi-Bi bonds) is nearly a factor of 50 larger than that along the F-X
direction, whereas the effective mass along the F-Z direction (through the Cs layers) is ~5
times larger than that along the F-X direction. This indicates that the hole transport

through the Bi-Bi bonds is prohibited and is confined to the planes perpendicular to the

Bi/Te slabs.

73

6.1.1 Band Dispersions

Shown in Figure 6.3 are the EDCs taken from an n—type sample for k-points along
the F -X symmetry line. The spectra were taken with an energy resolution of 46 meV.
The initial state energies were referenced to the Fermi level (BF). The spectra were
normalized to photon flux and have been smoothed using a binomial function. The
inelastically scattered secondary electron background has been subtracted. We can
identify two features, labeled A and B, just below B... These two features can be
discerned more clearly in the higher resolution spectra (solid curves) shown in Figure 6.4.
Both features are intense only near the F point. Peak A appears to be non-dispersive and
might be an impurity state due to the n-type dopants, which reside within the narrow band
gap. Peak B is then the top valence band. It has the lowest binding energy at the F point,
away from which it apparently converges with the other valence bands at higher binding
energies.

The assignment of peak A as an impurity state is further supported by the
comparison between the n- and p—type spectra (solid and dashed curves respectively)
shown in Figure 6.4. In this figure, the initial energies for the n-type and p-type spectra
were referenced to E; the p-type spectra were then rigidly shifted toward higher binding
energies by 0.05 eV. As can be seen, after this shift the p- and n~type spectra match
reasonably well except that peak A is missing in the p-type spectra immediately below
EF. This is consistent with the notion that peak B is an n-type impurity state. This also

indicates that the energy gap is minimally EG = 0.05 eV, which is comparable to the

74

 

TIfijWIlI

hv= 21 év

   
    
   

(BYE-type fiCfisIBLTe; . T .
F-X-F'

Intensity (Arb. units)

 

 

llLllLlllllllLlllJ

4 3 2 1 0
Binding Energy (eV)

 

Figure 6.3 Energy distribution curves (EDCs) for an n-type CsBi,,Te6 sample taken
along F-X. The energy is referenced to the eXperimental Fermi level derived from a

clean platinum foil in electrical contact with the sample. Varying the analer angle at 2°
intervals varied momentum k.

75

 

Intensity (Arb. units)

 

      
  

  

    
   

 

 

 

‘ , , ,"s't‘ :;
C ' 4‘1. :
. 1 1 AB
0.6 0.4 0.2 0.0
Binding Energy (eV)

Figure 6.4 A comparison of EDCs for n- and p-type CsBi4Te6 samples taken at select
k-points near F along F—X. The n—type spectra are referenced to the experimental Fermi

level. The p-type spectra were rigidly shifted by 0.05 eV toward higher binding energies
(see text).

76

band gap determined by other experimental methods (0.05-0.1 eV)’ and that predicted by
the band structure calculation (0.04 eV).’3

The majority of the valence bands lie between 0.3 eV and 5 eV below EF (Figure
6.3). As mentioned earlier, the band structure calculation performed by Larson et a1.”
predicts more than seventy valence bands in this energy range. Obviously, it is
impossible to identify each individual band from the spectra because of lifetime and
instrument broadening. However, a few prominent spectral features can be identified
(labeled as features A-F) and their approximate dispersions can be traced, as marked by
tick marks in Figure 6.3. At the F point, approximately 0.4 eV separates peak B and the
next identifiable feature, C. Feature C disperses toward higher binding energies as It was
scanned from F to X. So do most of the other features. As k was further scanned from X
to F’ in the next zone, the dispersions are reversed as expected from symmetry. In
particular, features D, E and F are degenerate at the X point and disperse apart in both
directions.

The dispersions of the selected spectral features in Figure 6.3 are plotted as
crosses in Figure 6.5 where the results of the band structure calculation by Larson et al.13
are also shown (small symbols). The observed dispersions are qualitatively consistent
with the general dispersion trend in the calculated bands. In particular, both the

experiment and calculation find that the top valence band along F—X has a maximum

77

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

é3;:IEIIIJEIIISIIHIIIEP‘P1:11.: .3!
:ESEE:"‘: : a... e ee cc.
—‘."‘I "I
0.0 L's 1*
:91! ...,
4 ~ -...::: .
:0-‘0 3 ' I! "I '01..
21;: HI ‘* rut 5111 max
-1.0:I.I I II; III; 3‘31 1:":
31:1 1.1:; . 11» 3:11 llrllil
A i111 ialsu s 1:831: rim-r
>113 -2.0 55!; giggii' ::::i¥.é§ii§ Emil
v ills. 211:3: ”l” 51131552355111
“'1- ;_,g It ::::...~a§‘;
E5 55;: east} , 3.1:; ::;;§-§j
‘1’ '3” $53? 1311;; iii? iii: :iilitisi
LE 3115+ 5‘45: it ti!’ PIE "Inn-l
:ii;;'==u:‘I o If.“ II“ :IHEII‘I
41-0 a..-.IIIOI2!! iii :;;: ;?§; :!!*l;l
a:::::::::::: 53,33; _:3.: 11115111
_......--a--""'::::-.a:i 3:15: ::::-.ae
E ............. ‘ '-1:Eii'i;i:1=1:'=;:
-s.o—: .......... ~ mm 1m:
51
:1
-6.0 ,
I X

 

 

 

(a)

Figure 6.5 (a) Band dispersions (small symbols) along 11X from band structure
calculation by Larson et al. The dispersions of select features seen in the spectra are
overlaid (cross symbols). (b) Band dispersions (small symbols) along F-V and F-Z from
band structure calculation.

at the F point. Some differences can be observed. For instance, in the observed spectra,
the second highest valence band, C, is separated from the top valence band, B, by
approximately 0.4 eV at the F point, whereas the theory predicts a separation of only 0.2
eV. Also, peak B is seen to disperse by as much as 0.8 eV from F to X while theory
predicts a dispersion of only 0.6 eV.

Figure 6.6 (a) shows EDCs taken from an n-type sample for k-points along the I"-

V symmetry line. The Brillouin zone is very short in this direction. The F-to-V distance

78

corresponds to approximately l.7° angular difference at hv=2l eV, which is roughly the
size of our angular resolution (A0 = 2°). The energy resolution of these EDCs is 45 meV.
The spectra shown were taken at 1° intervals, spanning approximately two Brillouin
zones. The spectral features show changes in relative intensity because of matrix element
effects, but significant dispersion is not apparent. Peaks A and B can be seen near EF and
they do not disperse in this direction. This was confirmed in the higher resolution spectra
(35 meV) taken at 05° intervals (Figure 6.7). However, due to the fact that our
resolution is larger than the length of the symmetry line in this direction, the spectra in
Figure 6.6(a) and Figure 6.7 are averaging over k—points along the entire F-V symmetry
line, making identifiable dispersion unlikely. From the measured width of the feature we
can assign a maximum possible dispersion for these peaks. The combined peak widths
are < 0.2 eV. The calculated dispersion of the top valence band along this direction is
approximately 0.05 eV. Studies using analyzers with much higher angular resolution will
have to be made in order to quantify the dispersions along this direction.

Figure 6.6(b) shows EDCs taken from an n-type sample for k—points along the F-Z
symmetry line. Varying the photon energy in the normal emission geometry varied the k
vector. The Brillouin zone is also short in this direction. The F-to-Z distance
corresponds to approximately 4 eV difference in photon energy. The spectra shown were
taken at 1 eV intervals spanning approximately one and half zones. Peaks A and B can

be seen and they do not disperse in this direction (we are not limited by our k-space

79

 

..,m..,fi.filfi.q.fifi T.e..e.e...4fi rwpvqn
CsBi4Te6 (a) CsBr4Te6 (b)
F-V E F-Z E

h =21 v normal emissio
V e g /V hv (CY):
i 525

       

Intensity (Arb. units)

 

 

 

 

 

H4 HABHHZHHI M0 4 31” 21 ‘1 M0
Binding Energy (eV) Binding Energy (eV)

Figure 6.6 EDCS for an n-type CsBi,,Te6 sample taken along(a) F-V and (b) F-Z.
The energy is referenced to the experimental Fermi level derived from a clean platinum
foil in electrical contact with the sample. Energy resolution in these spectra is 45 meV.

resolution in this direction). The lack of dispersion in the t0p valence band along F-V
and F-Z indicates heavy carrier effective masses in these two directions. Some small
dispersions can be seen in the higher binding energy bands along F-Z (e.g., roughly 0.5

eV in feature F), though, overall, not as much as seen along F-X.

80

 

 

 

 

 

 

F r H
CsBi4Te6
F-V
P'tYPe
a
:3
.ci
5’.
29
E
(D
E
l"
J I l g A
0.3 0.2 0.1 0.0 01
Binding Energy (eV)

Figure 6.7 Higher resolution EDCS for a p-type CsBi,,Te,5 sample taken along F ~V.
The energy is referenced to the experimental Fermi level derived from a clean platinum
foil in electrical contact with the sample. The spectra are taken every 0.5°. Our k-
resolution is 2°, and the energy resolution is 35 meV.

81

Compared to the calculated band dispersions (Figure 6.5(b) and (c)), the observed
bands along F-Z are flatter than predicted. In particular, the calculation shows the top
valence band to disperse about 0.3 eV from F to Z. The measured spectra show no
discemable dispersions within the experimental resolution (0.046 eV). In the F-V
direction, due to the limited k-resolution, a detailed comparison of dispersions with

theory is impossible.

6.1.2 Density of States

Angle integrated photoemission spectra of CsBi4Te6 were taken at 4 photon
energies, hv = 19, 22, 23, and 25 eV G’igure 6.8). The spectra were taken with an energy
resolution of 0.08 eV. As with BizTea, and BizSe3 no Fermi level reference was
measured, and the energy reference was set such that the lowest binding energy peak
in the CsBi4Te6 valence band spectra coincides with the corresponding peak in the LDA
calculations.

Due to the large number of bands in the valence band of this material, we will not
be able to resolve individual peaks. As we did in the ARPES study, we will focus on the
main identifiable features. Three major features can be identified in the spectra, labeled 1
through 3, shown in Figure 6.8. Overall, the intensity of the entire spectrum decreases as
the photon energy increases from 19 to 25 eV. Of the three major features, peak 1

shows the most variation with photon energy, becoming almost unidentifiable at

82

 

23 eV

Intensity (Arb. units)

22 eV

 

 

 

1 19 eV
-3 -6 -4 -2 0
Energy (eV)

 

Figure 6.8 Angle Integrated photoemission spectra for n-type CsBi4Te6. For the
purpose of comparison, the energy reference (zero of energy) was set such that the lowest
binding energy peak in the spectra coincides with the position of the corresponding peak

in the LDA calculations.
25 eV. Peak 2, the most intense peak, is approximately 2 eV wide, centered around -
1.25 eV energy, and does not vary much from 19 to 25 eV, beyond the overall decrease in
intensity. Peak 3 has energy -4.78 eV and is roughly 4 eV wide. A minor feature with
energy -3.4 appears at 22 eV and maintains its intensity at 23 and 25 eV.

The shape of the observed spectra agree qualitatively with the LDA DOS
calculations by Larson et al.”, shown in Figure 6.9 As is to be expected in the band

structure of a material with such a complex crystal structure, the calculated DOS shows a

83

large amount of structure. The experimental resolution in this study, 0.08 eV, is much
larger than the widths of the individual peaks in the DOS. As such, we will be
concentrating on the general shape of the DOS spectrum and comparing it to the largest
features in the calculated DOS shape as such. In addition, due to the difficulty of the
calculation only 36 k-points were used, resulting in a significant amount of structure in
the DOS. As more k-points are used in the calculation, it is expected that the DOS will
smooth out as the peaks are averaged.

The calculated DOS also sees three major features. The observed peak 1 shows
good correspondence to the small, low intensity calculated feature at ~O.5 eV., although
the energies are not the same. Peak 2, which is ~2 eV wide, is consistent with the
roughly 1.5 eV wide feature centered around ~1.25 eV in the DOS. Peak 3 corresponds
to the 4 eV wide DOS feature centered around ~3.5 eV. The separation between peaks 2

and 3 is 2.53 eV, which agrees well with the roughly 2.5 eV separation seen in the DOS.

6.1.3 Summary

In CsBi4Te,5 we find that the valence band maximum is located at the F point
consistent with the band structure calculation result. We also find that the electronic
structure is quasi-one-dimensional in that band dispersions are much stronger in the F-X

direction than in the other two orthogonal directions. In particular, the t0p valence

84

 

 

10

 

 

O l l
4 -2 0

Ens-w [8V]

 

Figure 6.9 The calculated density of states of CsBi4Te6.

band is very flat along F-V and 1"-Z, indicating heavy carrier effective masses in these
two directions. By comparing the spectra measured from n- and p-type samples, we
estimate a band gap of approximately 0.05 eV, which is comparable to the value observed
by other experiments9 and that predicted by band structure calculation”. Our results
provide support for the postulation that the large anisotropy in the carrier effective

masses is the reason for large value of ZT observed in the hole-doped systems?“'3

85

The observed DOS for this material shows several large features which do not
very significantly at multiple photon energies. This is most likely due to the fact that
there are a large number of peaks in the DOS, and with this resolution, they are not
resolvable individually. There may be variations due to matrix element effects in the
individual peaks, but in the spectrum as a whole, these are not significant enough to
change the overall shape of the DOS. The theoretical calculation agreed qualitatively

with the observed DOS.55

86

Chapter 7 Summary

In summary, we have carried out the first detailed ARPES studies of BizTe3,
Bi28e3, and CsBi4Te6. The valence bands of the three materials show several similar
characteristics. They have highly complex electronic structures, with multiple dispersive
bands within 5 eV of the Fermi energy. The single, nondispersive peak, positioned just
below the Fermi energy, localized near the I“ point and along F-Z is common in all three
materials. This feature is clearly identified as an impurity band in BizTe3 and CsBi4Te6
by the comparison of the spectra from n- and p-type samples. All three materials display
anisotropy in the band dispersions, most significantly in CsBi4Te6 and BizTe3. This
degree of anisotropy was underestimated in the LDA calculations.

The high value of ZT in BizTe3 seems to be driven in part by the large k—space
degeneracy of its valence band maximum. The observed six-fold k-space degeneracy of
the VBM confirms both previous experiments and the LDA band calculations. This
material also benefits from a highly quasi-two-dimensional electronic structure. In
CsBi4Te6, however, the valence band maximum is non-degenerate in k-space (in
agreement with theory). Perhaps the high degree of anisotropy in the valence bands is
responsible for the high ZT value in the hole doped systems. BiZSe3 has neither a high k-
space degeneracy (non-degenerate in the valence band), nor a significant low-
dimensionality. This may partially explain why its TE properties are poor, especially in
comparison to BizTe3 and CsBi4Te6.

The agreement between the band structure calculations and our observed

dispersions was good in all materials, especially considering their complex electronic and

87

crystal structures. In conclusion, we have demonstrated that ARPES is a useful tool for
studying the electronic structure of TE materials. Our results provide a critical
verification of the band structure calculation results, and help to guide the search for

novel TE materials.

88

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23 Tellurex is a Michigan-based TE device company has an excellent website with both
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5° In an inverse photoemission (IPES) experiment, a material is bombarded with electrons

and the resulting Bremsstrahlung radiation emitted from the sample is analyzed.
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structure of the conduction bands. This method is starting to become more useful

91

 

as the analyzer performance and sophistication increases. For more information
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55 V. A. Greanya, W. C. Tonjes, Rong Liu, C. G. Olson, D.-Y. Chung, and M. G.
Kanatzidis, unpublished.

92

 

 

  

    

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