Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations

1-1-2003

Cu-based transparent conducting oxides based on the delafossite structure

Robert Bruce Gall Iowa State University

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Recommended Citation Gall, Robert Bruce, "Cu-based transparent conducting oxides based on the delafossite structure" (2003). Retrospective Theses and Dissertations. 19966. https://lib.dr.iastate.edu/rtd/19966

This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Cu-based transparent conducting oxides based on the Delafossite structure

by

Robert Bruce Gall

A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

Major: Materials Science and Engineering

Program of Study Committee: David P. Cann, Major Professor Steve Martin Gordon Miller

Iowa State University

Ames, Iowa

2003 11

Graduate College

Iowa State University

This is to certify that the master's thesis of

Robert Bruce Gall has met the thesis requirements for Iowa State University

Signatures have been redacted for privacy TABLE OF CONTENTS

CHAPTER 1. INTRODUCTION i 1.1 Background 1 1.1.1 Transparent Conducting Oxides and Coatings: Historical 1 Perspective 1.1.2 Transparent Conducting Oxides and Coatings: Material 3 Evaluation 1.1.3 Transparent Conducting Oxides: Device Possibilities 7 1.1.4 Transparent Conducting Oxides: Requirements 10 1.1.5 Transparent Conducting Oxides: Relationship between 17 Electrical and Optical Properties 1.2 Delafossites Structure 21 1.2.1 AB02 Overview 21 1.2.2 Overview of the Delafossite Structure 23 1.2.3 Crystal Chemistry in Delafossites 31 1.2.4 Electronic Transport Properties 35 1.2.5 Potential Bipolar Conductivities 36 1.3 Synthesis of Cu Based Delafossites 39 1.3.1 Overview of Delafossite Synthesis 39 1.3.2 Solid State Synthesis 41 1.4 Research Plan 42

CHAPTER 2. HIGH TEMPERATURE PHASE EQUILIBRIA 44 2.1 Introduction 44 2.2 Experimental 45 2.2.1 Synthesis 45 2.2.2 Crystal Structure Analysis 47 2.3 Results and Discussion 48 2.4 Conclusions 62

CHAPTER 3. DOPING METHODS 63 3.1 Experimental 63 3.1.1 Synthesis 63 3.1.2 Crystal Structure Analysis 65 3.2 Results and Discussion 68

CHAPTER 4. DEFECT CHEMISTRY 72 4.1 Introduction 72 4.2 Delafossite Doping 74 4.2.1 Undoped 74 4.2.2 Donor Doped 84 4.2.3 Acceptor Doped 88 1V

CHAPTER 5. ELECTRICAL AND OPTICAL PROPERTIES 91 5.1 Introduction 91 5.2 Experimental 92 5.2.1 Synthesis 92 5.2.2 Crystal Structure Analysis 94 5.2.3 Density 94 5.2.4 Electrical Characterization 94 5.2.5 Optical Characterization 96 5.3 Results and Discussion 97 5.3.1 Synthesis 97 5.3.2 Density 102 5.3.3 Undoped CuGa02 Electrical Properties 102 5.3.4 Donor Doped CuGa02 Electrical Properties 107 5.3.5 Acceptor Doped CuGa02 Electrical Properties 108 5.3.6 CuGa~l_X~InX0 2 Electrical Properties 110 5.3.7 CuGa02 Optical Properties 111 5.4 Conclusions 113

CHAPTER 6. CONCLUSIONS AND FUTURE WORK 114 6.1 Synthesis and Phase Equilibria 114 6.1. l Synthesis and Phase Equilibria: Conclusions 114 6.1.2 Synthesis and Phase Equilibria: Future Work 116 6.2 Electrical and Optical Properties 117 6.2.1 Electrical and Optical Properties: Conclusions 117 6.2.2 Electrical and Optical Properties: Future Work 118

APPENDICES 120 Appendix I: Unit Cell Regression Diagnostics 120 Appendix II: Rietveld Refinement 121 Appendix III: Seebeck Measurements 122

REFERENCES 139

ACKNOWLEDGEMENTS 1a5 1

CHAPTER 1. INTRODUCTION

1.1 Background

l.l.l Transparent Conducting Coatings: Historical Perspective

Transparent conducting materials, both oxides and coatings, have been known for a long time. Transparent conducting oxides (TCO) were first reported by K. Badeker in 1907 when he published that thin films of cadmium metal deposited in a glow discharge chamber could become transparent through oxidation and still remain electrically conducting [1 ] .

Since then, TCO's use in technological applications has dramatically increased. Currently,

TCO's are used in solar cells, heat reflecting "smart" windows, flat-panel and liquid crystal displays, and gas sensors.

Architectural applications and flat-panel displays (FPD's) are the two dominant markets for TCO's. The architectural applications for TCO's are for energy efficient windows. These windows, with tin oxide coatings, are efficient in preventing radiative heat loss because tin oxide has a low emissivity, ~ 0.16 [2]. Thus, these "low e" windows are ideal for cold to moderate climates [2]. In 1996, the annual consumption of TCO-coated glass in the U.S. was 7.3 x 10~ m2, but this number continues to grow as the demand for displays and photovoltaics increases dramatically.

With the flat-panel display technology industry alone undergoing a rapid growth,

28% of the display market with $17 billion in 2000 and a prof ected $27 billion by 2005 [2], it 2

is apparent that the development of new and improvement of old TCO materials becomes increasingly important.

Similar to TCO's, transparent conducting coatings (TCC) have been utilized since the last century. They first appeared in the form of thin film electrodes of silver and platinum on selenium photoelectric coatings [2]. TCC's entered the commercial market in the 1930's with the first solid-state photodetectors, which were Schottky barrier cells with transparent metal front electrodes. When wide-band-gap semiconductors were discovered, practical applications of TCC's increased significantly [3] . During WWII, for example, tin oxide

_coatings were introduced into commercial Nesa glass, a transparent electrically conductive coating with de-icing and de-fogging capabilities on commercial and military aircraft.

Thin films, approximately 100-200 ~ in thickness, of some metals have been found to have similar properties to TCC's. Their advantages lie in their chemical compatibility with substrates, their small work function, and their ease in deposition; however, these films are not very stable and their properties are time dependent [4]. Thin metal films also lack the superior stability and mechanical hardness that the transparent coatings possess [4].

The intensity of the transmitted light through a material is governed by the following equation:

Equation 1.1 I = I o exp~— ax~,

where Io is the initial light intensity hitting the surface, I is the final intensity of light emitted

through the material, a is the absorption coefficient (cm-1), and x is the distance the

transmitted light travels in the material. With absorption coefficients on the order of 109, thin 3

metal films must have an approximate thickness of 10 ~ to have a high transparency in the visible region of the light spectrum [5]. However, if a metal film approaches this thickness, its mean free path, or average distance between collisions, is reduced due to scattering of the charge carriers at the surface, and thus a dramatic decrease in conductivity is observed [5].

1.1.2 Transparent Conducting Coatings: Materials Evaluation

For non-metallic materials, the optical properties are dictated by both the electronic band gap and the charge carrier density [3]. Figure 1.1 illustrates a schematic of the transmission spectrum for a given material.

The electronic band gap determines the lower wavelength limit (~,g), for optical transmission, ~300nm, below which absorption takes place from the excitation of electrons in the valence band to the conduction band. Equation 1.2 illustrates the relationship between

~,g and a materials band gap:

_ he Equation 1.2 ~bg — ~ Eg

where h is Planck's constant (4.136 x 1015 eV s), c is the speed of light (2.99 x 108 m/s), and

Eg is the materials band gap. Typically a band gap greater than approximately 3.0 eV is required in order for transparency over the visible spectrum to occur [3]. 1 material TCO hypothetical a for spectra transmission Typical 1.1: Figure S

The upper wavelength limit, ~Ip, for transparency is determined by free carrier absorption according to the charge carrier density, Equation 1.3.

1 2 mc2 Equation 1.3 ~p = 2 ~z i 4~ y e2

where m is the mass of an electron (9.11 x 10-31 kg), (N/V) is the charge carrier density, and e is the charge of an electron (1.602 x 10-19 C). This upper limit is usually in the infrared for semiconductors and ultraviolet for metals [3]. Typical materials that are both transparent and conducting include In20 3, Sn02, CdZSn04, and ZnO; however indium tin oxide (ITO, In20 3 doped with 9 mole % Sn) remains as the current standard [4]. Table 1.1 illustrates some properties of these materials.

Table 1.1: Properties of TCO's at room temperature f 4 Crystal Conductivity Band-Gap Dielectric Refractive Compound Structure (S/cm) (eV) Constant Index Sn02 Rutile 10-1000 3.7-4.6 9.4-12 1.8-2.2 In20 3 C-rare earth 10-1000 3.5-3.75 8.9 2.0-2.1 ITO C-rare earth 100-1000 3.5-4.6 — 1.8-2.1 Cd2SnOa Sr2Pb04 100-1000 2.7-3.0 — 2.05-2.1 Zn0 Wurtzite 1-1000 3.1-3.6 8.5 1.85-1.90

With its high mobility ( 160 cm2/Vsec), high conductivity ( 104 SZ -1 cm-1), ease of processing, and its high transparency above 480 nm, ITO has many advantages [6].

However, ITO, a bixbyite derivative of fluorite, has a limited transparency in the blue-green 6

region of the visible spectrum due to its band gap of approximately 3.5 eV, thus creating problems in certain photovoltaic applications [6]. Furthermore, as the demand for TCO applications continues to increase, the cost and availability of indium oxide begins to play a factor [3]. Other factors that must be examined when considering TCO materials include: substrate compatibility, abrasion resistance, and ease and economics of deposition [3].

Sn02, which forms a rutile structure, is another transparent conductor that has had successful commercialization. This is primarily due to its acceptable electrical and optical properties [3]. It also displays excellent chemical stability and mechanical hardness.

Additionally, Sn02 can be fabricated in simple and inexpensive methods based on low materials cost [3].

In the 1970's, In2O3 coatings began to overtake Sn02 in commercial applications [3].

Much of its success came from the need for transparent electrodes in LCD's, for indium oxide can easily be fabricated with the required tolerances of flatness in mind. Another key advantage is that it can be etched more easily than tin oxide, and thus it facilitates a more economical photoetching procedure during the fabrication of digital displays. It should be noted that although Sn02 is more chemically inert, the stability of In2O3 is sufficient enough for many applications [3 ] .

It wasn't until 1972 that knowledge of the spinel Cd2SnO4 as a coating possibility began to arise [3] . With the chemical stability, abrasion resistance, hardness, and etching behavior similar to In2O3, it was not very long until Cd2SnO4 began to flourish as a TCC. If large-scale applications are considered, Cd2SnO4 has the added advantage of low raw material cost [3]. Recently, GaIn03 has also been identified as a transparent conducting material [7].

Its structure is distinctly different from ITO, which retains the bixbyite-type cubic crystal structure of In20 3, for the Ga site is tetrahedrally coordinated and the In site is octahedrally coordinated. While its resistivity is comparable to other conventional wide-band-gap transparent conducting materials, GaIn03 possesses superior light transmission and index matching with typical glass substrates [7].

This new discovery, as well as the growth of the TCO industry, has sparked the search for new compounds and structures including spinels [8], pyrochlores [9], delafossites

[10-34], and others. Limitations on the existing materials also becomes more apparent with the increasing need for larger-area display devices with greater writing speeds [2]. It has become increasingly important to reduce the resistivity while maintaining the transparent nature in TCO layers, for the screen size of FDTV's and the graphics of portable computers have both increased dramatically [2].

1.1.3 Transparent Conducting Oxides: Device Possibilities

In the past, TCO materials have been predominantly n-type. This has limited their applications since functional semiconducting devices require a p-n junction. It wasn't until recently that p-type TCO materials have become well-known [35], and with their discovery, the possibility of device applications. However, since their conductivities are several orders of magnitude lower than their n-type counterparts, many groups have sought new materials in hopes of reaching reasonable values.

The problem with past p-type materials has been the strong localization of the holes that occurs within the valence band. This is due to the large electronegativity of the oxygen 8

anion, and therefore the valence band in most oxides is localized by the oxygen anion. When holes are introduced at the valence band edge, they are localized on the oxygen anion and in essence form a deep trap [36]. In order to solve this localization problem, a cation species with a closed electronic configuration with a comparable energy to the oxygen's 2p electrons is required in order to shift the valence band edge up from the 2p levels of the oxygen to the newly configured anti-bonding levels. Therefore, the localizing effect in the valence band is reduced considerably, and holes can be effectively doped into the valence band, thus improving conductivity. This doping can be achieved either through the substitution of a divalent cation for the trivalent cation or through intercalation of oxygen.

Some new p-type conducting TCO's include CuAl02 [10, 36-50], CuGa02 [1 1, 36-

41, 51], CuIn02 [47, 52-56] and CuSc02+X [12]. Figure 1.2 illustrates the optical characteristics and Seebeck measurements for a thin CuAl02 film [2].

CuAlO~ Optical Transmission

200 Seebeck C©eff. r , ~ Transmission ,~ :' . *' .~~~ ,Percent..

d T tK) Vs~i i I I 0Zso, goo ~oa0 ~Sao Zaao Photon wavelength (nm)

Figure 1.2: Optical and Seebeck measurements for a thin CuAl02 film 9

Generally, the Seebeck coefficient is written in the following form:

Equation 1.4 S = k In Nv + C

e (n

where k is Boltzmann's constant, Nv is the density of states, n is the carrier density, and C is the transport constant. As the equation indicates, in order to attain a high Seebeck coefficient, high density of states must be attained. A positive value of the Seebeck coefficients indicates that the majority carriers are holes, while a negative value indicates that the majority carriers are electrons. See Appendix III for a more detailed discussion of thermoelectric properties and measurements.

With CuAl02 being a very stable material and Sr-based materials having low processing temperatures, these new materials offer a great deal of promise which can lead to the future development of such devices as transparent thin film transistors [35], UV emitting diodes, and UV photovoltaic devices [57]. Exploiting the transparency in the infrared spectra, p-type conductors have also been considered as RF shields for IR sensors [57].

Current electromagnetic-interference (EMI) shielding solutions involve coatings made from soft metals such as gold or copper that is directly deposited onto the sensor window.

Performance would improve if this grid structure was replaced with a continuous coating of an IR-transparent-electrical conductor [58].

Even though transparency and conductivity can coexist in applicational use, there generally exists a trade off. For example, for IR sensors, good conductivity is essential, while optical transparency becomes less important [57]. In contrast, for photovoltaic 10

applications, transparency is of tremendous importance, and conductivity is of less significance [57].

1.1.4 Transparent Conducting Oxides: Requirements

Although other properties are important, the primary requirements for a transparent conducting oxide are high conductivity and transparency. As stated before, the conductivity of a TCO must be approximately 104 S~ "1 cm"1, with a high transparency in the ultraviolet and visible spectrum (>85%). The other important properties include: substrate compatibility, abrasion resistance, ease and economics of deposition, as well as cost and availability of raw matenals.

In order to compare the performance of transparent conducting materials, a figure of merit, ~~, was established by G. Haacke in 1976 [59]. He found that the electrical and optical properties of a TCC are best characterized by the electrical sheet resistance, RS, and the optical transmission, T [59]. The sheet resistance can be calculated through Equation 1.5.

1 Equation 1.5 RS = , 6t

where Q is the electrical conductivity (Sl-1 cm"') and t is the thickness of the coating (cm). It should be noted that the units of RS are given in ~ /a, i.e. the resistance of any given square surface area.

The ratio of initial radiation entering the coating, Io, and the final radiation leaving the other side of the coating, I, is known as the optical transmission, T (see Equation l.l) [59]. 11

Utilizing the above two equations, and the added stipulation that the maximum arc occurs at

90% optical transmission, the new figure of merit described by Haacke can be seen in

Equation 1.6,

T.io Equation 1.6 ~PTc = = 6 t exp(— l Oa t) RS

If we assume a given sheet resistance, Equation 1.6 can be written as follows:

Equation 1.7 ~PTc ~ exp-- A~ 6 I I , l~

where A is a constant. From Equation 1.7, it can be seen that the basic materials parameter that determines the figure of merit for a transparent conducting material is a/~. However, for convenience the relationship of Q/a will be discussed instead.

For a semiconductor, Equation 1.8 illustrates the relationship between 6 and tx.

*2 6 ~zcnv2,u 2m Equation 1.8 = , a e

where c is the velocity of light, n is the index of refraction, v is the light frequency, µ is the carrier mobility, m* is the effective mass of an electron, and e is the electron charge [59].

Table 1.2 offers a comparison of figure of merit values for several different materials. 12

Table 1.2: Comparison of figure of merit values for various materials f 59 (PTC ~iQ~3 ~-Il Material T10 RS (S2/square) 1 Sn02 0.20 10 20 In20 3/Sn02 0.16 3.1 52 Cd2Sn04 0.17 2.4 71

Based on Equation 1.6, it is apparent that in order for a semiconductor to be considered a good transparent conductor it must have a high mobility and a high effective mass. For most transparent conductors, the effective mass is relatively constant, 0.3m for

ZnO, Sn02, and Cd2Sn04 [60]. Therefore, a material's electron mobility becomes the key parameter for a high figure of merit.

The limitations in mobility are a consequence of two things: the electron-scattering mechanisms that operate within a material, and the weak overlap of cation orbitals [60].

Some scattering mechanisms, such as scattering due to phonons, are present even in pure crystals. Typical mobilities based on these mechanisms axe about 250 cm2/Vs for low doping levels. For higher doping levels, which are needed for TCC's, scattering from ionized dopant atoms becomes an important absorption mechanism that limits the mobilities to values less than 90 cm2/Vs [60]. If both mechanisms are considered, the mobility values further decrease to approximately 66 cm2 V-1 s-1. Although it doesn't take place in all films, another scattering mechanism that lowers a materials mobility even more is grain-boundary scattering [60].

As stated above, a material's mobility is also related to the overlap of the molecular orbitals. A weak overlap of cation orbitals results in narrow bands that contain the conduction electrons. Figure 1.3 illustrates that as the atoms are brought together from 13

infinity, the atomic orbitals begin to overlap and form bands. As the conduction band becomes increasingly narrow, polaron conduction mechanisms can begin to dominate [61].

This introduces a thermally activated mobility that is significantly smaller than the band mobility [61].

cnerg}~ electron = CJ (~faeu~~m level) E Eiectrcan ~S E~~~ E

iter~it~mie ~epr~rat.i~n (R) R = ~r P Tbc solid Isc~l.tt~d atoms

Figure 1.3: Formation of band due to atomic orbital overlap [62]

The amount of cation overlap is primarily a function of crystal structure [63]. For example, TiO, with the rocksalt structure, has significant cation overlap, which results in a wide conduction band and high conductivities [61]. Figure 1.4 illustrates the 6-type 3t2g overlap present in Ti0 along the <110> direction, which results from the close-packed structure [61 ] .

Hosono, et al., proposed that metal oxides composed of heavy metal cations with an electronic configuration of (n-1)d' °ns° also achieved large orbital overlap between s orbitals, and thus wide conduction bands [63]. As shown in Figure 1.5, the overlap between the 14

spherically symmetric ns orbitals is larger for the heavy metal cations than for light metal cations. The ns orbitals are only of interest for they are insensitive to any angular variation in the M-O-M bonds, while pp or dp orbitals show a high spatial anisotropy [63].

Figure 1.4: 3t2g cation-cation orbital overlap in Ti0 [61]

Since a transparent conductor must have aband-gap greater than 3 eV in order to have optical transparency in a visible region, it cannot consist of oxides that contain transition-metal cations and rare-earth cations as a major constituent [64]. This is because these elements have open d or f shell electronic configurations, and thus have optical absorption bands that are caused by intrashell transitions in the visible spectrum [64].

Instead, the large band gap requires an oxide that is an intrinsic insulator. This is due to the low energy of O 2p orbitals, for they represent the top of the valence band [63]. 15

/~\ M M

Figure 1.5: Overlap of ns orbitals for heavy and light metal cations [63)

The fundamental absorption edge for these transparent conductors usually lies in the

UV spectra, and shifts to shorter wavelengths as the charge carrier density increases [65].

This shift, known as the Moss-Burnstein shift, is due to the filling of the states near the bottom of the conduction band. If we assume parabolic bands, then this shift, DE, can be described for afree-electron Fermi gas, see Equation 1.9 [65].

hz ~3N3 Equation 1.9 OE ~-1 8m,,~ ~ Tzn J

where m*~~ is the effective mass of the conduction band.

The free carrier absorption, which determines the upper wavelength limit, is primarily dependent upon the charge carrier density, see Equation 1.10 [61], 16

Equation 1.10 wP = ~eZn2 /som ,

where WP is the plasma frequency, n is the charge carrier density, and Eo is the permittivity of free space. The plasma frequency for the conduction of electrons in a transparent conductor divides the optical properties [60]. At high frequencies, above W P, the electrons cannot respond, and thus the material responds as a transparent dielectric. However, at frequencies below c~P, the material reflects and absorbs the incident radiation [60]. Equation 1.10 governs the relationship between the plasma frequency and other material properties. It should be noted that the plasma frequency is proportional to the square root of the conduction-electron concentration. The maximum plasma frequency and electron concentration of transparent conductors is generally a function of the materials resistivity, see

Table 1.3 [60].

Table 1.3: Approximate resistivities and plasma wavelengths for some transparent conductors f 60 Material Resistivity (µS2 cm) Plasma Wavelength (µm) Ag 1.6 0.4 TiN 20 0.7 In20 3:Sn 100 >1.0 CdZSn04 130 >1.3 ZnO:AI 150 >1.3 SnO2:F 200 >1.6 ZnO:F 400 >2.0

With charge carrier densities close to 1018 cm3 , semiconducting materials typically have an upper wavelength limit larger than 10 µm [61]. For example, with an electron concentration of approximately 1021 cm 3, ITO's plasma edge occurs just above 1µm [61]. 17

Thus, semiconducting materials that are transparent throughout the visible spectrum should have aband-gap greater than 3 eV and a charge carrier density less than 1021 cm 3 [61].

1.1.5 Transparent Conducting Oxides: Relationship between Electronic and Optical Properties

The optical properties of TCO's in the upper wavelength region can be calculated based on Maxwell's equations as well as the Drude theory of free electrons [66]. If we assume nearly free electrons, Maxwell's equations allow for a complex permittivity, which is a function of frequency and conductivity, to be defined [66]. By applying the Lorentz oscillator model, the motion of the ensemble of free electrons can be described by a second order differential equation. Finally, solving this equation leads to a complex conductivity which is a function of the carrier concentration, the effective mass of the free carriers, the relaxation time, and the frequency of the electric field [66].

From the complex permittivity and conductivity, the Equations 1.1 l and 1.12 can be derived for the real and imaginary parts of the permittivity [66]

Equation 1.1 l £ 1 - £ oo and

Equation 1.12 E 2 — 18

where z is the relaxation time and w is the frequency of the electric field. It should be noted that the above equations assume that the electrons are completely free and that 1/z « W [66].

Based on the above equations, the real and imaginary parts of the refractive index maybe determined as follows:

1 2 2 2 El Equation 1.13 N=~ - E1 + E2 + ~ 2 2 and

1 Equation 1.14 k' _ -1 El 2 + ~22 2 _ £ 1 2 2

where N is the refractive index and k' is the extinction coefficient. As described earlier, at high frequencies, the TCO material behaves like a dielectric, while at low frequencies, where both N and k' are large, the material possesses anear-unity reflectance [66].

Once a TCO material's electrical properties are established, it is possible to successfully model its optical properties. Figures 1.6 and 1.7 illustrate how the optical properties are affected by the material's conductivity. Figure 1.6 shows the variation in reflectance as a function of wavelength for various levels of carrier concentration [66]. It should be noted that the film had afree-carrier mobility of 100 (cm2/Vs), a thickness of 0.5

µm, an assumed high-frequency permittivity of 4, and an assumed effective mass of 0.3 me

[66]. As the figure shows, once the plasma wavelength is surpassed for the films with high carrier concentrations, ahigh reflectance (~90%) is attained. The films with lower carrier 19

concentrations would also achieve similar reflectance levels, but only at wavelengths beyond the modeled range.

The variation in absorbance with wavelength for various levels of carrier concentrations is shown in Figure 1.7 [66]. It should be noted that the parameters for the above samples remained unchanged. As the figure illustrates, due to the increased carriers to absorb photons, as the carrier concentration is increased, the height of the free-carrier absorption band increased. Also, in the visible spectrum (i.e. w > Wp), the films are mainly free of absorption. This is due to the fact that the electrons are out of phase with the electric field at the high frequencies, and thus are unable to absorb energy [66]. 20

0.9 1.4 1.9 2.4 Wavelength (Nm)

Figure 1.6: Variation in reflectance as a function of wavelength for various carrier concentrations [66]

45 40

R • „ 35 i S

• i t 30 i i a~ i • • • • ~ 25 • • 4 a 20 ~~

i ,°n 15 • a • Q 10 5 ,. ~' 0 0.4 0.9 1.4 2.4 Wavelength {~~)

Figure 1.7: Variation in absorbance as a function of wavelength for various carrier concentrations [66] 21

1.2 Delafossite Structure

1.2.1 A~ 0 2 Overview A+iB+30.22 The structure and coordination of the ions in compounds vary according to the stability map shown in Figure 1.8 [13 ] . Table 1.4 illustrates the coordination classes for the AB02 compounds. The variability in these compounds is thought to be dependent on both the ionic radii and electrostatic forces [13].

From Figure 1.5, it is apparent that for the A-site, the smaller noble metal cations correspond to the structure with the lowest coordination. Even though it has a relatively small ionic radii, Li does form either the a-LiFe02 or the ~3-NaFe02 structure, with 6-fold and

4-fold coordination respectively. Continuing down the first period in the periodic table, Na forms the 6-fold coordinated a-NaFe02 structure, while K, Rb, Cs all form the eight-fold coordinated KFe02 structure.

In the case of the smaller atomic radii B-site cations, the preferred tetrahedral coordination can be achieved if the A-site cation also adapts to the 4-fold coordination.

When this occurs, the wurzite related orthorhombic ~-NaFe02 structure is formed. Another important AB02 structure not shown on the stability map is the ordered NaCI with 6:6:6 coordination. In this structure, separate sublattices form, with each sublattice containing either the A or B-cation alone [14] . By ordering itself into these separate sublattices, the structure is able to reduce its electrostatic potential energy. It is also important to note that the A and B-cations can order themselves into separate layers along the <111> direction in the cubic NaCI-type pseudo-cell. This results in either a hexagonal or rhombohedral structure [14] . 22

~.

~~ ~ ~ ~~~~~as~~ ~ ~~~~

r +~ ~~ ry } ~~ '# 3 3 L 1

4 t 1 t i ~► t t t I

.,~

u ~~

F~Q~

Figure 1.8: Stability plot for AB02 compounds [13] 23

Table 1.4: Coordination classes for AB02 Compounds [13] Coordination Class AB02 Compound AIIBVIOZN CuFe02 Delafossite Rhombohedral or Hexagonal A~'B~'02n' (3-NaFe02 Orthorhombic A VIB VIOZVI a-LiFe02 Tetragonal a-NaFe02 Rhombohedral NaCI Cubic A VIIIB IVO2VI ~e0 2 Orthorhombic

1.2.2 Overview of the Delafossite structure

The first delafossite compound, CuFe02, was discovered by Soller and Thompson in

1935 [13 ] . Their discovery was later confirmed by Pabst several years later [67]. Although its discovery took place close to seventy years ago, only small amounts of literature can be found regarding the delafossite structure or its properties. However, recent developments have shown that the delafossite structure is capable of strong orbital overlap due to the heavy metal elements, and thus lead to increased conductivities [41] . AiiBvl The chemical formula for the delafossite structure is O~'2, with the A and B sites containing monovalent and trivalent cations respectively. Figure 1.9 shows the linearly coordinated metal A1+ cations that are stacked alternately between layers of edge-sharing

B3+0 6 octahedra, perpendicular to the c-axis. Depending on the stacking, see Figure 1.10, the B3+0 6 octahedral layers can lead to either rhombohedral or hexagonal structures, with space groups 3R (3 m) and P63/mmc respectively [15]. 24

Figure 1.9: Delafossite crystal structure, Al+B3+02 25

b)

Figure 1.10: Schematic representation of the arrangement of the B3+06 layers in the a) hexagonal and b) rhombohedral structures

While the valence state of the Cu ion is typically 2+, in the delafossite structure, as stated above, the Cu ion assumes a valence state of 1+. Galakhov, et al. [68], found that the

Cu 2p spectrum of CuFeO2 was similar to that of Cu2O, where the Cu ions have a valence state of l+. Their experiments found that the Cu 2p spectrum of CuFeO2 showed no multiplet splitting, indicative of a full Cu 3d shell. Therefore, the ground state configuration of the Cu ions in CuFeO2 is predominantly 3d10. This results in a single core level peak with a 2p-13d10 configuration [68].

Even though there are no oxygen atoms within each A cation layer, two oxygen atoms are linearly coordinated to each A cation in axial positions; further indication of the monovalent state of the Cu cation [41] . The BO2 layers consist of edge sharing B3+06 octahedra, with each oxygen atom in pseudo-tetrahedral coordination as B3A0 [41] . It should be noted that although most delafossites form the rhombohedral structure, only the rare earth containing delafossites form the hexagonal structure [16] . 26

Due to its highly anisotropic crystal structure, the lattice parameters of the delafossite system are strongly influenced by the ionic radii of the B-site cation. As Figures 1.11 and

1.12 illustrate, the a-axis is highly dependent upon the ionic radii of the B-site cation, while the c-axis remains somewhat constant. Based on the delafossite structure, one might expect both the a- and c-axis lattice parameters to vary in a similar fashion based on changing the B- site cation. However, due to the fact that the B-site cation in only incorporated into the

B3+06 octahedra, which are located in the ab plane of the structure, any changes that occur on the B-site primarily impacts the a cell edge length. Also, due to the repulsive nature of the

B3+ cations along the shared edges, a distortion occurs within the octahedra resulting in a shortened bonding distance between the O anions. As the B-site cation radii is increased, the

B-O distance increases while the O-O contact distance remains relatively unchanged. Thus, there is little impact on the c-axis lattice parameter.

As Figure 1.12 illustrates, while it is relatively independent of the B-site atomic radii, the c-axis is highly dependent upon the A-site atomic radii. This is an apparent connection since the c-axis is primarily dependent on the O-A-O bonding distance, and thus on the A- site atomic radii.

It has been shown that solid-solutions on both the A- and B-site can highly influence the delafossite cell dimensions. In a work by Tanaka, et al. [69], they investigated the variation of the A-site atomic radii on the unit cell dimensions through a solid solution of

Pdl _XPtXCo02. As Figure 1.13 illustrates, while varying the A-site atomic radii has little impact on the a-axis, it has a dramatic effect on the c- axis dimension. 27

3.8 I ~ ~ I ~-. 0 °Q... v ~ ~ Q a. PdRh Q z ~ 3.6 w ~ ~ O • ~ ' ` PdCr

V

a ti AgRh, ♦~ 3.4 w ca O Q V ♦

v ++w AgCr, AA W

a ~- CuRh, .~ w 3.2 • ov CuCr, v J ~a

v AgSc ._ a C~ • ~ 3.0 Q ~ Q w M w

t~1~ CuSc, V •~

V I I 2.8 V I 0.60 0.70 0.80 0.90 1.0 1.1 1.2 Ionic Radii of B-site (A)

Figure 1.11: Variation in the a-azis as a function of B-site radii

19.5 I I ca c C~ 1= a~ (A) 19.0 as Q ~ Q w Q

V ~ }~}~~ ~ ~ VI 18.5 aQ ~ a Q •• Parameter 18.0 o V r L a• v ~ w 17.5 O w, Lattice V LL • a ~ • V • 17.0 • • -axis

c Q~'~ V ~ ~ ~ ~ ~ ~ ~ V~ v V V V v I V 16.5 0.60 0.70 0.80 0.90 1.0 1.1 1.2 Ionic Radii of B-site (d)

Figure 1.12: Variation in the c-azis as a function of B-site radii 28

17.82

2.86 (A) (A) 17.8

2.84

~~ 17.78 Parameter Parameter 2.82 -

Lattice 17.76 Lattice

2.8 - -axis -axis c a 17.74

2.78 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fraction of Pt, x Fraction of Pt, x

Figure 1.13: Variation in a- and c-azis as a function of Pt content

A similar solid solution study, but involving the B-site was performed by Tate, et al.

[57]. They examined the CuGal_XFeXO2 solid solution, in hopes of achieving the excellent transparency of CuGaO2 while maintaining the high conductivity of CuFeO2, and found the expected trends in unit cell dimensions with variation of the B-site atomic radii. Figure 1.14 illustrates the variation in both the a- and c-axis as well as the unit cell volume as a function of Fe content.

In the delafossite compounds, an interesting structural phenomenon is observed in the coordination environment of the trivalent B3+ ions. Rather than having ideal octahedral symmetry, these octahedra are slightly flattened in their c-axis dimension [15]. Their degree of distortion, as illustrated in Figure 1.15, can be determined based on the ratio between the

O-O bond distance found in the hexagonal O layers (do) and the distance between consecutive layers (dl). This distortion can be influenced by the B-site ionic radii, see Figure

1.16, and thus it has been suggested that the distortion is caused by the electrostatic repulsion of neighboring B-site cations [15] . 29

a. 0. Fraction of Fe,x

Figure 1.14: Variation in cell dimensions as a function of Fe content [57] 30

do

Figure 1.15: O-O bond distance in the hexagonal O layers (do) and between the consecutive layers (dl)

+ + M M M~ M ~ U C~ ~ 1.28 r '

1.24

1.16

1.12

0.6 0.7 0.8 0.9 1 1.1 B-site Ionic Radii (A)

Figure 1.16: Octahedra distortion as a function of B-site ionic radii 31

1.2.3 Crystal Chemistry in Delafossites

In 1971, Shannon and Rogers developed a model for the electronic transport properties in delafossites [14] . They found that the delafossite structure can exhibit both metallic, in the cases of Pd and Pt, and semiconducting, in the cases of Ag and Cu, behavior

[14]. Their model, which was later modified by Jacob [17] and Tanaka [18], hypothesized that the behavior of the molecular orbitals was the source for the differing nature of the structure [14] .

A1+ The key feature of the delafossite structure is the close packed planes of the cations, which has been shown to be strongly correlated to both the electronic and optical properties. Since the interatomic distance between the A cations is so small, actually approaching the distance in metals, the crystal field at the A-site splits the d-orbitals into two doubly degenerate bands, a 4dXy, 4dX2-y2 band with low energy and a 4dXZ, 4dyZ band with high energy. Figure 1.17 illustrates the schematics of the d-orbitals, while Figure 1.18 illustrates the band structure of both metallic PdCoO2 and semiconducting AgCoO2.

In the delafossite structure, the 4dZ2 orbitals are directed toward the oxygen ions.

Therefore, the crystal field effects increase the energy of the 4dZ2 orbitals close to the Ss level, which results in the hybridization of the A-cation 4dZ2 orbitals. In Orgel's work, it was suggested that the linear bonding for d10 ions produced hybridized wave functions derived from the 4dZ2 and 5s orbitals [ 70]. Orgel went on to add that if the 4dZ2 and S s orbitals are initially degenerate, then the stable configuration must be a distortion of the purely cubic symmetry. This reasoning results from the fact that initial degeneracy requires no energy expenditure in the formation of the 1/ ~(d 2 + s) hybrid orbitals 70 . Z [ J 32

In Figure 1.19, the energy levels for the cation are perturbed by the linear crystal field effects and by the d-s hybridization [14] . Oxygen, which is tetrahedrally coordinated to three

B-cations and one A-cation, has orbitals that are assumed to be in the spa hybridization state.

Three of the hybrid orbitals are used in the bonding with the B-sublattice cations, while the fourth orbital, having proper symmetry, is used in the formation of a Q bond with the pZ and

1/~(dZ2 +s) orbitals of the A-cation [14].

d.= (or, do) orbital d„: orbital e~x~ Orbll ~. dss ~ t~~(4)~'0(~) d„t ®:~~(B)~i sin (rp) dam. ~C8)4~i cos (+p)

d~:-,,• orbita dry orbital d~t~ Mt h 91::(4)

Figure 1.17: Schematics of d orbitals [71] 33

SpX Spy L4] 4dZ2+5 s [2]

E1 EF AgCo02

4dZ2-5 s [2] EF PdCo02 4~z 4dyZ [4] E3 4dXy 4dXz_y2 [4]

N

[16] 2xOsp3

A~+ O

Figure 1.18: Band structures for both metallic and semiconducting delafossites [61]

Figure 1.19: Schematic of the 4dZ2 f Ss hybridized orbitals [61] 34

The interaction between the oxygen wavefunction and the pZ and 1/~(d ZZ +s) wavefunctions of the A-cation produce a bonding valence band and an antibonding conduction band [14]. Each of these bands contains four states per formula unit. Even though the four cation wavefunctions are nonbonding with respect to the anion sublattice, they are strongly oriented in the direction of the A-cation nearest neighbors that exist in the basal plane of the structure [14]. As stated above, due to the small distance between A- cations, their wavefunctions undergo a considerable mixing and metallic bands in the basal plane typically form. Table 1.5 illustrates the bond lengths in certain delafossites compared to their respective metal [13].

When a d10s1 ion is used as the A-cation, any metallic bands that were formed by the direct interaction between the cations become filled [14]. In this case, EF, occurs in the energy gap between the filled metallic bands and the empty conduction band. This results in either semiconducting or insulating behavior, depending on the size of the energy gap. In the case when the A-cation is a d10s° ion, the metallic bands are only partially filled, and thus metallic behavior is observed [14].

Due to the metallic interactions, an additional stabilization to the overall bonding occurs. This essentially renders any assignment of an oxidation state for the A-cation as a formality [14]. Thus, the first coordination sphere for the A-cation actually contains not only the two anions, but the six cations as well. Keeping this in mind, the structure can be viewed as containing layers of cations that are metallic in nature, and that are stacked in between and covalently bonded to two layers of octahedrally coordinated B-cations [14]. 35

Table 1.5: Bond length in some delafossites compared to their resuective metal f 13 Electron A - A Bond Length in A - A Bond Length in Metal Configuration Respective Metal (A) Delafossite Respective Delafossite (A) Pt Sd106s° 2.77 PtCo02 2.83 Pd 4d10Ss° 2.75 PdCo02 2.83 PdCr02 2.923 PdRh02 3.021 Cu 3d104s1 2.56 CuCo02 2.849 CuAl02 2.857 CuCr02 2.975 CuGa02 2.975 Ag 4d10Ssl 2.89 AgCo02 2.873 AgAl02 2.89 AgCr02 2.984 AgGa02 2.989

1.2.4 Electrical Transport Properties

The large anisotropy in the delafossite structure transcends into its properties, for large anisotropies are observed in both the conductivities and activation energies within the respective compounds, see Table 1.6. With a short A-A bond length it is no surprise that the electrical conductivity in the basal plane is quite high. This indicates that the metal-metal interactions in the basal plane are significant and give rise to a relatively broad conduction band [19]. Since the metallic bands are primarily confined to the A sublattice, the observed conductivity in the c-direction is considerably lower [14].

The primary reason for these anisotropies in both resistivity and activation energy is due to the anisotropy in the material's mobility. If one assumes that the energy required for the generation electron-hole carriers should be independent of direction, than anon-activated mobility perpendicular to the c-axis and an activated mobility in the c-direction is required 36

[14]. This result is consistent with the higher conductivity in the basal plane and the lower conductivity in the c-axis direction, which is most likely due to the polaron hopping mechanism [14].

Table 1.6: Anisotropies in resistivity and activation energy in delafossites [14 Compound p c-axis (~2-cm) Ea c-axis (eV) p l c-axis (~2-cm) Ea 1 c-a~cis (eV) PtCo02 1.0 x 10-3 - 3 x 10-6 - PdCo02 2.1 x 10-3 - 2 x 10-6 - CuCo02 5.0 x 10~ 0.70 2 x 105 0.20 CuFe02 3.0 x 103 0.23 5 x 10"1 0.05 AgFe02 2.0 x 1010 0.80 3 x 10~ 0.70

1.2.S Potential Bipolar Conductivities

In the past, TCO materials have been predominantly n-type. This has limited their applications since functional semiconducting devices require a p-n junction. It wasn't until recently that p-type TCO materials have become known [10], and with their arrival, the possibility of transparent devices has become a reality. However, since their conductivities are several orders of magnitude lower than their n-type counterparts, many researchers have sought new materials in hopes of reaching reasonable values.

The problem with past p-type materials has been the strong localization of the holes that occurs within the valence band. This is due to the large electronegativity of the oxygen anion, and therefore the valence band in most oxides is localized by the oxygen anion. When holes are introduced at the valence band edge, they are localized and in essence form a deep trap [36]. In order to prevent localization, a cation species with a closed electronic configuration with an energy comparable to the oxygen 2p level is required in order to shift 37

the valence band edge up to the newly configured anti-bonding levels, see Figure 1.20.

Therefore, the localizing effect in the valence band is reduced considerably and holes can be effectively doped into the valence band, thus improving conductivity.

Energy ~ Bottom of Conduction

Eg ~ Top of ~' ~, Valence Band , , , , , Closed Shelr • ~ ~ •' Oxygen Cation `, ,' Ion (e.g. Cu+ d10)

Figure 1.20: Chemical bond schematic between a closed shell cation and an ozygen ion

The delafossite structure is one such material that has the potential to achieve high p- and n-type conductivity. The presence of the B02 layers in which the B-site cations occupy the octahedral sites is desirable for n-type conductivity. These B06 octahedra axe edge shared, and thus the distance between neighboring B cations is very short with no intervening oxygen atoms. Therefore, if heavy metal cations are employed, as stated above, significant overlap can occur and high conductivities being obtained.

The linear coordination of the A-site cations within the delafossite structure indicates that oxygen ligands experience a strong repulsion between their 2p electrons and the d10 electrons of the A-site cations. Therefore it is reasonable to expect that the d10 electrons are lying on almost the same energy level as the oxygen's 2p electrons [41]. The tetrahedral 38

coordination environment of the oxygen ion also promotes the delocalization of the valence band edge. This is due to the distribution of the 8 electrons (including 2s2) in the spa hybridization to the four v bonds with the coordinating cations which reduces the nonbonding nature of the oxide ions.

The bipolar dopability of certain delafossite compounds can also be understood through the equilibrium doping theory. Utilizing the "doping limit rule" established recently

[72, 73], the band-edge positions within a material dictate the degree of self-compensation of that material [37]. That is to say a compound with a higher valence band maximum (VBM) is easier to dope p-type, while a compound with a lower conduction band minimum (CBM) facilitates in n-type doping. In the Cu-based delafossites, the Cu 3d and O 2p states push up the VBM, thus leading to betterp-type conductivity [37].

From Wei's work [37], the calculated band alignments for CuAl02, CuGa02, and

CuIn02 are shown in Figure 1.21. The calculations were based on the local density approximation (LDA) using the general potential linearized augmented plane wave method

(LAPW) [37]. The slightly higher VBM's for CuGa02 and CuIn02 result from the coupling between the group-III d orbitals and the O p orbital. Therefore, this is a good indication that

CuGa02 and CuIn02 are more conducive top-type conductivity. Also, with the low CBM in both CuGa02 and CuIn02, n-type conductivity may also be obtained [37]. 39

i.~7 o.~s o.~i

CL~A1C)~ ~ilGaQ 2 ~t1111'~2

Figure 1.21: Calculated band alignments in CuAl02, CuGaOZ, and CuInOZ delafossites [37]

1.3 Synthesis of Cu Based Delafossites

1.3.1 Overview of Delafossite Synthesis

The synthesis of the delafossite structure can be quite difficult due to the low free energies of formation of some of the constituent binary oxides. Typical values for PdO,

PtO2, and Ag2O are —5.6, -79.5, and —1.1 kJ/mol respectively [13]. These low values cause these oxides to have very low decomposition temperatures: 800, 650, and 300 °C respectively

[13]. As a result, ternary oxides that contain both a noble metal and a transition metal are difficult to prepare, for the noble metal oxides typically decompose in open systems before the reaction can be completed [13]. However, work performed by Shannon, et al., has found that synthesis in some cases of ternary oxides can be successful if closed systems are utilized. 40

Figure 1.21 illustrates a Richardson diagram for the noble metal oxides that are of interest in the synthesis of the Delafossite structure. Although the thermodynamic instability of the noble metal oxides is apparent from the diagram, Shannon, et al., have found success in synthesizing the delafossite structure through metathesis, oxidizing-flux, hydrothermal, and solid state reactions [13 ] . For solid state reactions, they found that Cu based delafossites can be formed at ambient pressures. Other oxide reagents have been unsuccessful due to the high temperatures needed for solid-state diffusion as well as their inherent instability.

However, if pressure is applied, synthesis of almost all delafossite phases by this method becomes possible [13].

Pay '100

50 - ~~ _ ...~••~ ~~ 0 ~o' -~~ ~- -~ ~Agz, X02 4A~ ~ ~~ .~ ~4

~~

x~ ~~~ ~

r'''' te ..•~''~ ~~ ~r -250 - r 2~~.. ~~~k~~ r~ -300 - ~~ +.-""' -350 ~~ 0 200 400 600 800 1000 Temperature, K

Figure 1.21: Richardsen diagram for several noble metal ozides 41

Metathetical reactions involving an exchange of anions between two reagent phases have been successful in synthesizing Pt, Pd, and Cu based delafossites [13]. This synthesis typically involves low pressures and low temperatures, and often reacts a halide of the noble metal with a transition metal oxide. These reactions are often carried out in a sealed silica tube at temperatures ranging from 500 to 700 °C [13 ] .

In the case of hydrothermal reactions, they are typically carried out in sealed, thin- walled platinum or gold tubes. These reactions are usually run with an externally applied pressure of 3000 atm, temperatures ranging from 500 to 700 °C, and a dwelling period of approximately 24 hours [13 ] .

Although highly unusual due to the low processing temperatures, oxidizing flux reactions have had success in the synthesis of Ag based delafossites [13]. This reaction uses oxidizing conditions and involves the use of aloes-melting, oxidizing flux. Typically, reacting compounds are sealed in an evacuated silica tube and heated at 350 °C for approximately 4 days [13 ] .

1.3.2 Solid State Synthesis

The principal method of fabricating polycrystalline bulk materials via solid state means is through sintering. Sintering is a reacting process in which fine particles are heated at elevated temperatures to form a dense body. There are three stages that occur during the sintering process. In the first stage, spongelike structures are formed when the fine grains become smooth and begin to fuse along their common boundaries. During the second stage, the grains begin to grow while the pores shrink. This continues to occur until the isolated pores exist at the grain intersections. In the final stage, the remaining pores are eliminated 42

and the average particle size increases. This is a result of the smaller grains being consumed in order for the larger grains to continue to grow [74].

1.4 Research Plan

The primary objective for this work is to develop a bipolar Cu-based delafossite compound that can be doped to achieve high conductivities. The key to attaining the above goal is three-fold: first, attain a reproducible solid state synthesis route that will produce single phased structures. This includes optimizing conditions for synthesis, and gaining an understanding of the important thermochemical parameters that effect the reaction. Second, the inter-relationship between the crystal structure dimensions and the conductivity must be established. In anisotropic systems such as the delafossite, the band structure is strongly influenced by the overlap of the cation orbitals; therefore, in order to achieve the maximum mobility, B-site substitutions will be explored in an attempt to minimize the A-A interatomic distance. The effect of the ionic radii of B-site cations on the a-axis lattice parameter can be seen in Figure l.11. Finally, it must be verified that the lattice can accommodate high conductivities through donor and acceptor doping without the formation of conducting ionic defects.

In order to obtain compounds that can be doped both p- and n-type, the defect equilibrium between the delafossite compounds and the dopant ions must be established.

This can be achieved through a solid state synthesis that employs controlled atmospheres and quenching capabilities. Reactions 1.1 and 1.2 illustrate an electronic compensation reaction for donor and acceptor doping: 43

Reaction 1.1: Cue 0 + 2SnO2 Z cucao2 ~ 2Cu~u + 2SnGa + 400 + 2e'

Reaction• 1.2: Cue 0 + 2NiO + —1 0 2 T 2 CuGa02 > 2Cucux + 2NiGa + 400x + 2h • 2

It should be noted that similar reactions are only stable over a certain range of pO2, refer to

Figure 1.14. It is also important to note that the enthalpies of these electronic and ionic defect reactions are highly dependent upon the crystal structure. Therefore, as stated above, the key to achieving high p- and n-type conductivities is through modification of the structures lattice parameter through varying the B-site atomic radii. 44

CHAPTER 2. HIGH TEMPERATURE PHASE EQUILIBRIA

2.1 Introduction

while signl~ Cant work has been achieved in the investigations of Cu-based delafossites [10, 12-14, 16, 20, 42-50, 68, 75-79], only minimal results have been reported for delafossites containing B-site cations of Ga [13-15, 39, 40, 57] and In [39, 52, 53, 80]. A previous study involving a CuGal_XFeX0 2 solid solution was published by Tate, et al. [57].

The current work investigates the phase equilibria through x-ray diffraction studies of the

CuGal_XInX0 2 with the aim of establishing the stability regions the of delafossite phase.

In a work by Shimode, et al.[53], the synthesis techniques for the CuIn02 phase were established. They showed that CuIn02 could not be synthesized through solid state means, and instead a low temperature cation exchange had to be employed. For their reactions,

LiIn02, which was prepared by solid state means, was used as a reactant for an exchange reaction with CuCI. Similar conclusions were obtained in the analog Ag-based delafossite compositions [80].

In their attempts to synthesize CuIn02 via solid state reactions, Shimode utilized two separate reaction systems. The first involved reactions of copper and indium oxides, while the second involved a reaction between copper oxide and indium hydroxide. As stated above, both attempts failed to produce the CuIn02 delafossite phase.

while solid state synthesis has shown little success in the formation of the CuInCJ2 delafossite phase, it has been successfully employed in synthesizing other Cu-based 45

delafossites including the CuGa02 phase. Typical solid state reactions involve temperatures between 1000 °C and 1200 °C, with dwelling times ranging from several hours to several days.

In this work, the high temperature stability regions for the CuGa02 delafossite phase were investigated. Once these regions were established, a B-site solid solution of In and Ga was investigated. The possibility of achieving a CuGal _XInX0 2 solid solution would offer the excellent transparency of CuGa02 while maintaining the n- and p-type conductivity of

CuIn02. Finally, the variations in the unit cell dimensions were investigated as a function of the mole fraction In present in the batch composition.

2.2 Experimental

2.2.1 Synthesis

CuGatl_X~InX0 2 powders were prepared from stoichiometric mixtures of Cu20 (Alfa

Aesar, 99%), Ga20 3 (All-Chemie LTD., 99.999%), and In20 3 (Indium Corp., 99.99%) powders. To enhance mixing of the binary oxides of the B-site cations, (1-x)Ga20 3-xIn20 3 powders were vibratory-milled in ethanol using a Sweco mill for a period of 6 hours. Once the powders were dried over night, they were then pre-reacted, see Reaction 2.1, at 1100°C in a Carbolite high temperature tube furnace in flowing air.

Reaction 2.1 (1-X) Ga203 + X In203 -~ Ga2(1-x)~2x03 46

The pre-reacted powders from the above reaction were then mixed with Cu2O powder according to the desired ratio, and then re-milled for a period of 6 hours. The powders were then calcined from 1000 °C to 1200 °C for 4 hours in various atmospheres according to the following reaction:

Reaction 2.2 Cu2O + Ga2~l-X~In2xO3 ~ 2 Cu Ga{1_X~InXO2

A high temperature quenching apparatus was used to "freeze" in the desired phases of the calcined powders in order to examine the high temperature phase equilibria [81] . The quenching system employed was magnetically operated and allowed for sample transfer from the hot zone of the furnace to room temperature while maintaining controlled atmospheres.

It should also be noted that premixed N2-02 cylinders were utilized in order to vary the oxygen partial pressure during calcinations. Finally, 0 2 sensors (Australian Oxytrol

Systems) were also employed to establish the precise pO2.

Figure 2.1 illustrates the quenching system that was utilized. The mechanism that allowed for the sample to be quenched consisted of a rod composed of a high temperature metal alloy that was attached to an alumina crucible with the other end welded to two

Neodymium-Iron-Boron magnets. This rod was then enclosed in a sealed stainless steal tube that is mounted to the furnace's end-cap. An exterior magnet was then employed to allow movement of the interior rod, and consequently the alumina crucible. It should be noted that an inner alumina U-tube was placed inside the larger tube in order to facilitate a more efficient sliding path. 47

End Cap

Magnets

Crucible

Alumina Tube

Figure 2.1: Schematic of quenching system

2.2.2 Crystal Structure Analysis

Once the final powder had been reacted, it was then characterized through x-ray diffraction at the Materials Analysis and Research Laboratory. This analysis allowed for the determination of phases and the approximate amount of those phases. The scans were run with Cu-Ka radiation from 15° to 70°, at a step size of 0.03 degrees, and a count time of 2 seconds/degree.

The lattice parameters of the delafossite phase were then calculated using the

UnitCell software [82], see Appendix I, which utilized the Cohen least squares method [83].

In order to simplify calculations, the hexagonal system was utilized. The plane-line spacing equation, see Equation 2.1, combined with the Bragg's law gives Equation 2.2 48

4h2 +hk+k2 l2 Equation 2.1 2 -- 2 + 2 d 3 a c

4hz+hk+kZ+l2 Equation 2.2 sinZB—~'2 4 3 a2 cZ

The lattice parameters and structural data were then refined by Le Bail full-pattern decomposition and Rietveld analysis, using the Rietica software [84], see Appendix II. It should be noted that the Pearson IV function was utilized for the diffraction profile and all atom occupations were fixed to 1. Finally, the percent formation of the delafossite phase was determined through the use of a Si internal standard, see Appendix III.

2.3 Results and Discussion

The XRD data on the CuGa02 powders showed that the delafossite phase was stable over the temperature range 1000 to 1075 °C at a p02 of Sx 10-5 atm, while at 1100 °C a secondary phase of Cu metal began to form. At a p02 of 0.001 atm, the delafossite phase coexisted with other secondary phases. This could be due to a limitation in the calcination kinetics based on the short calcination times. At a p02 of 0.21 atm, the cubic spinel phase

CuGa20 4 with cuprite was predominant at 1100 °C, while at 1050 °C the spinel phase with both cuprite and tenorite was predominant.

In a work by Jacob and Alcock [85], they established the thermodynamic stability regions for the Cu-AI-O system. Figure 2.2 shows the Richardson diagram illustrating the 49

boundary lines between the stable phases. While their work in the Cu-AI-O system established all stability regions, in a later work with the Cu-Ga-O sytem [86], they were only able to establish the boundary between the CuGa20 4 + Cu0 region and the CuGa02 delafossite region (Figure 2.3).

Using free energies of formation for the respective compounds provided by Jacob and

Alcock [86], a temperature versus log pOz phase diagram for the Cu-Ga-O system was established and compared against experimental data (Figure 2.4). It should be noted that theoretical thermodynamic data could only be attained for the boundary between region 2 and 3 of the graph (indicated with a solid line), see Reaction 2.4 below, and thus all other boundaries are extrapolated based on experimental data. As Figure 2.4 illustrates, there are four separate phase regions, with the following reactions governing their boundaries:

Reaction 2.3 2Cu + Gaz0 3 (~3) + %2 OZ --~ 2CuGa02

Reaction 2.4 8CuGa02 +OZ ~ 4CuGa20 4 +2Cu20

Reaction 2.5 CuGa 2 0 4 + Cu 2 0+ %2 O 2 --~ CuGa 2 0 4 + 2Cu0 50

Temperature (°C) 0 500 1000 1500 100

~ -100 5

~ -200 a

-300

-aoo 0 500 1000 1500 2000 Temperature (K)

Figure 2.2: Richardson diagram for the Cu-A1-O system 51

Temperature (°C) 0 500 1000 1500 100

-100

s 0 L -2~~ a

-300

-aoo 0 500 1000 1500 2000 Temperature (K)

Figure 2.3: Initial Richardson diagram for the Cu-Ga-O system based on Jacob and ~lcocks work 52

1150

1100

1050 (°C)

1000

950

900 Temperature

550 /CuGa O +CuO CuGa2 O 4 +Cu 2 O 2 4 800 -. -6 -5 -4 3 -2 -1 0

Log p02

Figure 2.4: Temperature vs. logp02 phase diagram for the Cu-Ga-O system at 1 atm of total pressure 53

Based on the experimentally established boundary between the Cu + Ga20 3 region and the CuGa02 delafossite region, a similar boundary line was established for the Cu-Ga-O

Richardson (Figure 2.5). .4 While Jacob and Alcock found that CuGa02 was stable in p021evels of both 10 and .6 10 atm until approximately 1025 °C, it was established in this work that CuGa02 was stable at 1100 °C in a p02 level of Sx10 5 atm.

In attempts to create a solid solution with the CuGa02 delafossite phase, In was introduced into the system. The products that resulted from solid solution reactions that took place at a p02 of Sx10 -5 atm under a N2 flow rate of approximately 100 mL/min are listed in

Table 2.1. It should be noted that when the flow rate was increased to approximately 260 mL/min., the .solid solution compounds exhibited an increased formation of both Cu metal and Ga20 3. The table also illustrates that as the fraction of In was increased, the formation of the CuGa02 delafossite phase decreased with increased formations of Cu metal, cuprite, and

Ga20 3. The 0.1 mole fraction compound shows a deviation from this trend; however, since phase calculations were based on the (012) peak, a preferred grain orientation could have been observed. 54

Temperature (°C) 0 500 1000 1500 100

1 0 _; ' 10-2~, _ ~, -100 ~ - - _ ~. .. '-'--- a -~.~ h . _ ,,~ ,~ ,~ w ~_o~__ ~,.r ~ ~ ~ , .. ~, .s ~ -200 ~'"'~ ' ri ~ , 4 1 ~C~ ~~ ~ + ~ ~~ ~ + , ZGa .Q 2 ~ ~4

1 ~-8~ -300 1 ~u + Ga 2 O~~

10- - -aoo ~ ~ ~ ~ i I i ' i ~ ~ ~ 0 500 1000 1500 2000 Temperature (K)

Figure 2.5: Final Richardson diagram for Cu-Ga-O system 55

Table 2.1: Resulting products from solid state reactions with various amounts of In Mole Temp. Time Percent Fraction In (°C) (hrs.) Products Delafossite 0.00 1050 12 CuGa02 100 0.00 950 16 CuGa02, Cu20, Ga20 3 81.3 0.05 1050 12 Cu(Ga,In)02, Cu20, Ga20 3 83.3 0.05 950 16 Cu(Ga,In)02, Cu20, Ga203 62.7 0.10 950 16 Cu(Ga,In)02, Cu, Cu20, Ga20 3 9.2 0.25 950 16 Cu(Ga,In)02, Cu, Cu20, Ga20 3 32.1

The table also shows that for an In mole fraction of 0.05, the delafossite phase with the highest purity was synthesized at 1050 °C in a p02 of Sx10 -5 atm for 12 hours. However, in order to attain high density samples, a significant difference between the calcination and sintering temperatures is required. Therefore, since the upper phase boundary for the

CuGa02 delafossite in pure N2 is approximately 1100 °C, the compound synthesized at 950

°C is more desirable. While this compound showed a lower delafossite purity level, the remaining products were simply un-reacted precursors.

The 0.05 In mole fraction powders that were calcined at 950 °C were then pelletized

-5 and sintered at 1050 °C in a p02 of Sx10 atm for 16 hours. The resulting powder diffraction patterns obtained for the above compound as well as a pure delafossite phase that was pelletized and sintered under the same conditions are shown in Figure 2.6 (a) and (b) respectively. As the figure illustrates, the un-reacted precursors that were present in the calcined sample were eliminated at the higher sintering temperatures, thus forming the single phase CuGao.95~0.0502 compound. This pattern is also shifted slightly to the left with respect to the pure CuGa02 compound due to its increase in lattice parameter. X-ray fluorescence 56

(XRF) was performed on the CuGao.9s~o.os02 compound in order to establish the stoichiometry. This resulted in an approximate stoichiometry of CuGao.93s~o.o6s~2•

CuGa02 i , t 20 30 ao so 60 70 2A (Degrees)

Figure 2.6: Diffraction patterns for (a) CuGao.93sIno.o6s02 and (b) CuGa02 samples

In examining the a-axis lattice parameter and unit cell volume for the delafossite solid solution compounds, both exhibited an increasing trend up to an In mole fraction of 0.1, as shown in Figures 2.7 and 2.8. However, as the mole fraction of In was further increased to

0.25 mole fraction, the a-axis lattice parameter and unit cell volume both remained relatively unchanged. Based on this trend, and the fact that single phase CuGa02 was obtained in a

0.05 In mole fraction sintered pellet, the maximum solubility of In in the CuGal _XInX0 2 solid solution was approximated to be between 0.05 and 0.1 mole fraction In. As Figure 2.9 illustrates, the trend seen in the c-axis lattice parameter becomes less clear. It should also be noted that the increased value in the error bars at the higher In compositions is due to the presence of more impurity phases with increased concentrations. 57

950 °C N 2 2.992

2.989 (A)

2.985

Parameter 2.981

2.977 Lattice

2.974 -axis a

2.970 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 Fraction of In, x

Figure 2.7: Variation in the a-azis lattice parameter as a function of In content

950 °C N 2 (~►3) Volume Cell Unit

0 0.05 0.1 0.15 0.2 0.25 0.3 Fraction of In, x

Figure 2.8: Variation in the unit cell volume as a function of In content 58

950 °C N

z

17.220 (A) 17.200

17.180 Parameter

17.160 Lattice -axis

c 17.140

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 Fraction of in, x

Figure 2.9: Variation in the c-axis lattice parameter as a function of In content

Unlike the study performed by Tate, et al., no delafossite phase within the

CuGal _XInX0 2 solid solution could be synthesized for an In mole fraction greater than 0.25. It should be noted that although the delafossite structure did form up to the above limit, the actual In content incorporated into the structure remains uncertain due to the presence of impurity phases in the respective XRD scans. In the case of the single phase 0.05 mole fraction In compound, x-ray fluorescence was performed in order to establish the amount of

In present. This resulted in a calculated In mole fraction of 0.06. Future work is set out to establish these values in the other compounds in an attempt to gain a better understanding of alternative techniques that could improve phase pure solid solutions. 59

This limit in the formation of a delafossite solid solution could be due to the difficulty in synthesizing CuIn02 via solid state means, which in turn could be a result of the high stability of the In20 3 bixbyite structure. In our study, all solid state approaches to synthesizing pure CuIn02 resulted in the formation of Cu, CuO, and In20 3. Even prolonged calcination times and increased temperatures and pressures proved to have little success.

Based on the results of the x-ray diffraction, see Figure 2.10, the high-purity CuGa02 compound that was calcined at 1050°C in a p02 of Sx 10-5 atm was selected for both Le Bail full pattern decomposition and Rietveld analysis in order to refine its lattice parameters. The selected powder was then palletized and sintered in the above conditions for 24 hours and then quenched. Table 2.2 illustrates the resulting diffraction data for the CuGa02 delafossite phase. 60

s000 7000 0 6000 (CPS) 5000

4000 0 0 3 000 0 0

Intensity 2000 0 0 0 0 0 0 1000 0 ~~ 0 CuGa02 i ~ i 20 30 40 50 60 70 28 (Degrees)

Figure 2.10: Diffraction pattern for CuGa02

Table 2.2: Diffraction data for CuGaO h k l dial. dabs. I/lo 0 0 3 15.448 15.481 14 0 0 6 31.216 31.249 70 1 0 1 35.162 35.178 3 0 1 2 36.334 36.373 100 1 0 4 40.782 40.816 30 0 1 5 43.876 43.893 4 0 1 8 55.682 55.713 25 1 1 0 62.338 62.356 25 1 1 3 64.657 64.666 2 1 0 10 65.23 7 65.272 10 61

In Rietveld analysis, the quantities used to estimate the agreement between the

observed and theoretical model during the course of the refinement are as follows: the profile

quantity, Rp, the weighted profile quantity, Rte,, the expected quantity ReXp, and finally the

goodness of fit quantity, ~, which is defined as (R~,/ReXp)2. If the ~ value is lower than 1.69,

refinement is suitable. The resulting quantities after refinement was performed are shown in

Table 2.3.

Table 2.3: Rietveld refinement results for CuGaO a (~) c (~) V (~3) Rv R„~, XZ 2.976 17.160 131.622 6.590 8.517 1.600

In comparing the refined lattice parameters with those of previous works with

CuGa02 as well as other Cu-based delafossites, see Table 2.4, we notice a good agreement.

Also, with a ~ value of 1.6, the theoretical fit to the observed pattern is indeed reasonable.

Table 2.4: Lattice parameters for Cu-based delafossite compounds Composition a (t~) c (t~) Ref. CuIn02 3.292 17.388 [53] CuGa02 2.976 17.160 This work CuGa02 2.975 17.154 [13] CuAl02 2.857 16.943 [44] CuCo02 2.830 17.743 [13] CuCr02 2.975 17.096 [13] CuFeOz 3.035 17.166 [13] 62

2.4 Conclusions

Based on experimental results from the high temperature phase equilibria study and the theoretical data from thermodynamic calculations, the stability regimes (T, p02) for the

CuGa02 delafossite phase were established. Based on the XRD data, the isovalent substitution of In for Ga in the batch composition resulted in both the a-axis lattice parameter and the unit cell volume to increase as the In content increased up until an approximate In mole fraction of 0.1. with a single phase CuGa02 compound being attained for an In mole fraction of 0.05, a solubility between 0.05 and 0.1 mole fraction In in the CuGal _XInX0 2 solid solution was assumed. Rietveld refinement was utilized on the CuGa02 phase to determine the a- and c-axis lattice parameters of 2.976 ~ and 17.160 ~ respectively. 63

CHAPTER 3. DOPING METHODS

3.1 Experimental

3.1.1 Synthesis

In order to promote better doping incorporation into the B-site position, various

processing methods were employed. In order to gain an accurate comparison, each method

involved doping of 5% Sn in the CuGa02 compound in hopes of attaining an

n-type delafossite. Once the processing was complete, the samples where characterized

through ~;RD to verify phase purity.

The first method involved Sn02 as the dopant. In this case, the dopant was added in

the stoichiometric batch composition as follows:

Reaction 3.1 Cu20 + xGa20 3 + 2(1— x)SnOZ —~ 2CuGaxSn,_XOZ

The powders were then vibratory milled in ethanol for 6 hours to reduce any agglomerations, and then calcined at 1050 °C for 12 hours in flowing N2 (0.001% 0 2) and then quenched.

The second method also involved Sn02 as the dopant, but in this case the dopant oxide was pre-reacted with the Ga20 3 according to the following reaction:

Reaction 3.2 xGa20 3 + 2(1— x)Sn02 -~ Ga2xSn2~1-x)~3 64

The powders were vibratory milled according to the method above and then pre-reacted at

1100 °C for 12 hours in air. The pre-reacted powders were then mixed with Cu20 according to the following equation:

Reaction 3.3 Cu2G + Ga2xSn2~~-x>03 ~ 2CuGaxSn1-x0 2

The powders were then vibratory milled again for 6 hours in ethanol and calcined at 1050 °C in flowing N2 for 12 hours and then quenched.

The third method involved SnC20 4 (tin oxalate), in which a wet synthesis was employed. While literature has extensively shown synthesis routes involving oxalates, they do not mention the use of oxalates and oxides in a solution. Instead, acetates and chlorides, which can easily be put into solution, are typically used as sources for the host sites. The decomposition and then the precipitation of the starting materials was not sought, instead, the formation of Sn layers on the Ga20 3 oxide powders was desired. Therefore, stoichiometric amounts of SnC20 4 were placed into 60 mL of H2O2. After several minutes of stirring,

Ga20 3 powders were then added to the solution. The solution was then heated on a hot plate and stirred overnight. The resulting powders were then vibratory milled and pre-reacted according to the methods described above. Cu20 was then added to the pre-reacted powders according to the reaction above, and the powders were milled and calcined according to methods described above.

The final method involved tin (IV) isopropoxide (Sn[OCH(CH3h]4), which was in the form of 10% weight/volume in isopropanol and toluene. Similar to the oxalate dopant, issues were encountered with respect to doping solution based materials into an oxide host 65

compound. In this case, no pre-reaction of the B-site was performed. Instead, stoichiometric

amounts of Cu20 and Ga20 3 were added to the tin isopropoxide solution. The solution was

then stirred and allowed to evaporate until powders remained. These powders where then vibratory milled in ethanol and calcined at 1050 °C in flowing N2 for 12 hours and then quenched.

3.1.2 Crystal Structure Analysis

With phase purity being a critical issue, quantitative analysis was performed in order to establish the relative amounts of phases present. For powder samples, the internal standard method was employed. This method had to be abandoned for pellet specimens since the added standard could only be added prior to the pelletizing and sintering process, thus creating phase impurities. Instead, the external standard method was utilized for pellet specimens.

For the internal standard method [87], a known amount of a compound is added to the pure sample. This added compound acts as an internal standard. It should be noted that the compound chosen for an internal standard must not be already present in the sample and must have a similar mass absorption coefficient. The ratio of intensities can then be written as follows:

w j Ki j

I~ P j l~'~m Equation 3.1 j Kljpz wj Ky IyZ w2 KyZ Z Pj ~'Z PZ l~'~m 66 where I1~ is the intensity of the ith line of a compound j, IyZ is the intensity of the yth line of a compound z, K represents a constant for a given line of a given compound, µm is the mass absorption coefficient for the sample, p is the sample density, and wj and wZ are the weight fractions of the respective phases. In the reduced equation, µm has cancelled out, leaving a simple linear relationship between the observed intensities and concentration. Equation 3.1 can be simplified as follows:

I l j Ki j PZ Equation 3.2 = ci w , where cl = I yZ j KyZ pj

For the final answer, the addition of the internal standard must be corrected for as follows:

Equation 3.3 w j measured w j (actual) — 1—wZ

In the above case, Ili corresponds to the intensity of the (111) peak for Si, and I~ corresponds to the intensity of the (012) peak for CuGa02. Table 3.1 illustrates the respective parameter values for the CuGa02 compound and the Si (silicon) standard.

Table 3.1: Parameter values for CuGaO, with Si standard Compound weight % K p (g/cm3) µm (cm2/g) CuGa02 70.3 1.4 6.262 46.3 Si 29.7 4.7 2.32 63.7 67

The external standard method [87] compares the intensity of pure "A" to that of a mixture. The following is a brief derivation of the relationships:

~'V j K l j

P j lu Equation 3.4 I i j m, s w j ~m~j I i pure j 1 K y Z ~m, s

~"j~m,j

where µm,s is mass absorption coefficients of the given sample and µmy is the mass absorption coefficient of the desired phase. Table 3.2 illustrates the mass absorption coefficients that were for several impurity phases. These values are weighted sums on the individual elements mass absorption coefficients.

Table 3.2: Mass absorption coefficients for several impurity phases Compound µI„ (cm2/g) Cu 51.79 Cu20 46.08 Ga203 46.41 CuGa20a 44.99 Sn02 194.76 NiGa20 4 44.16 MgGa20 4 42.51

Given these values, µm,s can be found utilizing the following two equations: 68

N ~m,z w z _ z 2 Equation 3.5 lu m, R 1—wj

~Llm, -~-' Equation 3.6 lu m, s w l lu m, j R ~m, R

where µm,R is the summation of the mass absorption coef~ cients for the remaining phases.

As Equation 3.5 illustrates, the weight fraction of each additional phase must be present in order to establish the relative amount of the desired phase. While this can be overlooked in the case of one additional phase, it becomes an issue when several additional phases are present. In this case, separate pure standards for each additional phase would need to be synthesized, and multiple equations solved simultaneously. Since most of the final samples in this work only deal with small amounts of a single impurity phase, these additional steps will be ignored. Therefore, the values given in a multiphase sample are significantly reduced from their actual values and will only be given to establish trends.

3.2 Results and Discussion

Figures 3.1-4 illustrate the respective XRD patterns for the CuGa02 + 5% Sn doped samples according to the doping methods described above. Utilizing the external standard method, the relative percent formation of the delafossite phase for each sample was approximated, see Table 3.3. 69

Table 3.3: Percent formation of the delafossite chased based on the donin~ methods Dopant % Delafossite Un-reacted Oxide 39.6 Pre-reacted Oxide 62.3 Oxalate 0.00 Isopropoxide 40.7

4000 3500 .--~N ~ o 3000 0

(CPS) 0 2500 2000

1500 o.-~ d-o o~ o ~ ~ o ~ 0 Intensity 1000 o

500 (~ ~ ~ o 0 CuGa02 ~ i r Cu

f Ga203

I li l II ~ u ~ i ~~I ~ ~ ~~ I i I ~I. ~ Ii~ .0 Sn02 I ~ ( r ~ ~ ~ 20 30 40 50 60 70 28 (Degrees)

Figure 3.1:5% Sn doped CuGa02 with un-reacted Sn02 ~o

6000 ~-►.

~ 5000 0

~ 4000 0 0 r..i 0 •~ 3000

.~ 2000 o ~ ~ 0o O H o ~ `^ o 1000 ~ ~ ~ o

0 CuGa02 ~ ~ l ~ I ~ ~ C u20 r Sn02 r ~ ~ , ~ 20 30 40 50 60 70 28 (Degrees)

Figure 3.2:5% Sn doped CuGa02 with pre-reacted Sn02

s000 7000

6000 (CPS) 5000 4000 3000

Intensity 2000 1000 0

Ga203

I I II ~ n ~ I .d ~ ~ ~~ ~u 20 30 40 50 60 70 28 (Degrees)

Figure 3.3:5% Sn doped CuGa02 with tin oxalate precursor 71

4000 3500 0 3000 0 (CPS)

2500 N .-r O 2000 ...O N ~ 1500 _ O _O ~ O ~ ~ O h ....+ O ~ ~ ~ Intensity 1000 o ~' 500 0 CuGa02 ~ I ~ ~ ~ ! ~ i Cu

Ga203

Sn02 - ( t ~ ~ ~ 20 30 40 50 60 70 28 (Degrees)

Figure 3.4:5% Sn doped CuGaU2 with tin (I~ isopropoxide precursor

Based on the above data, it is apparent that the doping method that resulted in the highest formation of the delafossite phase involved the pre-reaction of the B-site oxides.

Also, while doping with the tin isopropoxide resulted in a higher formation of the delafossite phase than the tin oxide doping method, larger amounts of tin oxide were observed in the isopropoxide sample. It can therefore be concluded that the tin oxide sample showed a better incorporation of the dopant.

As Figures 3.2 and 3.4 also illustrate, broadening of the (012) peak occurred for the pre-reacted and isopropoxide samples. In the case of the isopropoxide sample, this can be attributed to texturing, especially since the (006) peak showed higher intensities than the expected 100% (012) peak. This trend was not observed in the pre-reacted sample; therefore, the influence of texturing on the broadening of the (012) peak is unclear. ~2

CHAPTER 4. DEFECT CHEMISTRY

4.1 Introduction

The addition of dopants to metal oxides has a profound effect on their properties, either by enhancing or reducing certain behaviors depending on applications. The current discussion will be limited to the effects of substitution by aliovalent cation impurities on metal oxides since isovalent dopants have no significant effect on the defect chemistry [88].

In dealing with defect chemistry, the Kroger-Vink notation is often used; see the following for the proper notion:

where the primary term denotes either a metallic dopant (M) or a vacancy (V), the subscript term denotes the host lattice site (o for oxygen, m for metal, i for interstitial, and s for surface), and the superscript term denotes the relative substituted charge (slash for negative, dot for positive, and x for neutral). Therefore the above term is read as an oxygen vacancy that leaves a positive two charge within the host lattice.

In a defect reaction the following three conditions must be met: electroneutrality, which states that the sum of the positive species in the reaction must equal the sum of the negative species. The second condition is the mass action law, which is written as follows: 73

K = IY]r Izl~ [Wlw[xY'

for which the reaction is wW + xX -~ yY + zZ and K is the equilibrium constant for the given reaction. The final condition is that the defect reaction is balanced, both chemically and with respect to the lattice sites.

It is important to note that in terms of atomic defects, there are two types which may occur in an ionic crystal (MO): Schottky and Frankel defects. A Schottky defect consists of a cation (M) and an anion (0) vacancy, while a Frankel defect consists of a vacancy of one of the sublattices plus an interstitial. There is also an anti-Frankel defect which consists of a vacancy plus an anion interstitial [89]. If we combine the equilibrium expression for the defect concentrations from above with the condition of charge compensation for all defects, the defect concentrations at a particular temperature can be calculated as a function of their interaction with the given atmosphere, or more specifically with the oxygen partial pressure

(p02), and the materials composition [89].

A useful method used to present defect equilibria was proposed by Brouwer, in which the defect concentrations as a function of oxygen partial pressure are graphed on a log-log plot [90]. There are three regions to a Brouwer plot: reducing, intermediate, and oxidizing.

When low oxygen partial pressures are achieved the atmosphere is said to be reducing. In this case, oxygen is released from the oxide leaving behind oxygen vacancies which are electrically compensated by electrons, thus the material is classified as n-type. At high oxygen partial pressures oxidation occurs. In this situation, oxygen is incorporated from the surrounding atmosphere into the oxide, thus the material is classified as p-type since the 74

charged defects are now compensated by holes. Finally, at intermediate pO2's, either electronic or ionic defects will become prevalent.

4.2 Delafossite Doping

4.2.1 Undoped

Now that an overview of defect chemistry has been given, the defect reactions and relevant Brouwer diagrams will now be established for the bipolar doping of the CuGa02 delafossite compounds. It should be noted that ionic radii, valence stability, and coordination number play a crucial role in the selection of possible dopant candidates. Therefore with the

B-site host cation Ga3+ having an ionic radii of 0.76 A and a C.N. 6, the n-type dopant selected was Sn4+ (0.83 A) and the p-type dopants selected were Nit+ (0.83 ~) and Mgt+

(0.86 A).

For the following analysis, Schottky defects will be assumed to be the dominant ionic intrinsic defect, with concentrations significantly lower than the intrinsic electronic defects at the stoichiometric composition. The defect chemistry and Brouwer diagram will now be constructed for the donor doped CuGa02 compound. The following are the equilibrium reactions and mass-action expressions for CuGa02:

Equation 4.1 200 ~ 0 2 + 2Vo' + Cu~u + Gaya + 4e~

Equation 4.2 K„ _ ~Vo' ~ n 4 p02 7s

Equation 4.3 02 ~ 200 + V~u + GaGa + 4h'

4 Equation 4.4 K P _ VCu p0 2

Equation 4.5 nil ~ Vcu + VGa + 2Vo'

Equation 4.6 Ks — LVcu JLVca JLVo~ JZ

Equation 4.7 nil ~ e + h'

Equation 4.8 KI = np

Equations 4.1 and 4.2 are valid under oxidizing conditions, Equations 4.3 and 4.4 under reducing conditions, and Equations 4.5-8 under intermediate conditions. For simplicity, the current analysis will begin with the stoichiometric compound under oxidizing and reducing conditions; however, the following assumptions should be stated. First, as

Equation 4.5 illustrates, the intrinsic ionic defects are given as copper, gallium, and oxygen vacancies. While an oxygen interstitial is another possible ionic defect, based on the

CuGa02 delafossite crystal structure, it is highly unlikely. Figure 4.1 illustrates the variation of the interstitial radius as a function of the B-site ionic radii previously established by

Mason and Ingram [91] . The figure depicts the interstitial site, see inset for site schematic, 76

required in order for an oxygen interstitial to fit within the structure. For the CuGa02 compound, the interstitial site that is present cannot accompany an oxygen interstitial, therefore its presence as a defect is highly unlikely.

This conclusion verified by examining the variation in lattice parameters as a function of Sn doping, see Figure 4.2. As the figure illustrates, as the Sn doping level is increased the a-axis lattice parameter remains constant while the c-axis lattice parameter shows a large decreasing trend. Since the c-axis is primarily dependent upon the O-A-O bond length, this observed trend indicates a reduction in this bond length that can be attributed to copper vacancies. An ~;RD study, see Figure 4.3, showed Cu20 impurities in a Sn doped CuGa02 pellet, indicating that the excess Cu could be a result of the copper vacancies. ~~

1.5 Y Intersticial Site

1.4

In 1.3 Sc r 2- < 0

1.2

Ga

1.1 y AI Cr

1.0 ~ i ~ ~ ~ ~ i 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05

63+ Radius (A►)

Figure 4.1: Variation in interstitial radius with B-site ionic radii. Interstitial site schematic is shown in the inset 78

2.990 1'7.195

i

(~) 2.988 17.190 A~ ~.+. G/~ 2.985 r 17.185 1..~

2.983 17.180 .,. n

Parameter 2.980 17.175 ~

2.978 17.170

Lattice 2.975 17.165 ~

2.973 17.160 -axis a

2.970 ' ' ' ' ' 1,7.15 5 0 1 2 3 4 5 6 Sri

Figure 4.2: Variation in the a- and c-axis lattice parameters as a function of Sn dopant 79

6000 N 5000 O

(CPS) 4000 0 0 0 3000 ~t 2000 o ~ 0 0 M O

Intensity O O 1000 0

0 CuGa02

Cu20 r i l 20 30 40 50 60 70 28 (Degrees)

Figure 4.3: 2.5% Sn doped CuGa02 indicating the presence of a Cu20 impurity phase

The other assumption is that while gallium vacancies are possible within the structure, their overall concentrations are minimal. Therefore, while they will remain present in the respective equilibrium reactions, their role will be essentially ignored.

Reduction:

The equilibrium reaction and mass-action law for the reduction region are given by

Equations 4.1 and 4.2. The electroneutrality condition for this region is given as follows:

Equation 4.9 2LVo' ~ = n

Substituting this result into Equation 4.2, the following results are observed: 80

1 K = n n 2 02 Equation 4.10 n 2 p 2

1 _1 Equation 4.11 n = ~4Kn ~6 pO2 6

Combining Equation 4.9 and Equation 4.1 gives,

1 1 Equation 4.12 ~Vo' ~ _ ~ ~4Kn ~6 p02 6

Combining this result with Equation 4.5 gives,

/ 1 1 _~~ 6p 2 6 Equation 4.13 Ks =Vcu Vca — 4Kn O ~z /

_ 1 ,~~ 1 6 Equation 4.14 Vcu = 2~4Kn ~ 6 Ks Vca 02

Oxidation:

Equations 4.3 and 4.4 give the equilibrium reaction and mass-action law for the oxidation region. In this region, the electroneutrality condition is the following:

Equation 4.15 81

Substituting this result into Equation 4.3 gives,

41pa Equation 4.16 K = P C p0 2

This reduces to the following relationship:

~ 1 Equation 4.17 p = ~4Kp ~s p02

Combining Equations 4.15 and 4.3 gives,

~ ~ Equation 4.18 ~Vcu ~ - ~4Kp~5 p~z

Finally, inserting this equation into Equation 4.5 gives the following results:

1 1~

Equation 4.19 KS = ~4K p ~s p0z [V Ga ] [ V ~ • ] Z i

1 1 _ 1 l 1 io ,~~ - 2 Equation 4.20 Vo' = KS 4Kp - io pQ2 VGa i 82

Intermediate:

Due to the small indirect band gap that is present in the delafossite compounds, electronic compensation will be assumed within the intermediate region with the following electroneutrality condition:

Equation 4.21 n = p

Combining this result with Equations 4.4 and 4.8, the following is obtained:

Equation 4.22 V~u = KPKI p02

Combining this equation with Equation 4.6, the following result is obtained:

1 _1 1 _1 Equation 4.23 ~Vo' ~ = Ks KP 2 K, ~V~Q r 2 pOZ 2

Within this region, the electron and hole concentrations remain unchanged.

By utilizing the above results, Figure 4.4 illustrates the Brouwer diagram established for the undoped CuGa02 compound. 83 compound

2 CuGa0 undoped the for diagram Brouwer 4.4: Figure 84

4.2.2 Donor Doped

While the reduction and oxidation regions remain unchanged, when dopants are introduced into a system the intermediate region is subdivided into two additional regions, the ionic and the electronic, see Equations 4.S and 4.6 and 4.7 and 4.8 for the equilibrium reactions and mass-action laws respectively. In the ionic region, the ionic defects are the primary charge carriers, with the following electroneutrality condition:

Equation 4.24 lSn~a ~ _ ~Vcu

By combining this equation with Equation 4.4, the following results are obtained:

K p _ Equation 4.25 ~Snca 1[~ 4 p0 2

1 ~ 1 1 ~

Equation 4.26 p= SnGa 4 Kp 4 p02 ~ ~

Then if we substitute Equation 4.26 into Equation 4.8 we attain the following results:

1/ 1 1 a Equation 4.27 Kj =nSnGa Kp4p02 85

1 1 _ 1 Equation 4.28 4 a n= KI SnGa 4 K P X02

It should be noted that within this region, the oxygen and copper vacancy concentrations remain unchanged.

In the electronic region, the electronic defects are the primary charge carrier with the following electroneutrality condition:

Equation 4.29 ~Sn~Q ~ = n

Substituting this result into Equation 4.4, the following results are observed:

t .. 2 Equation 4.30 K n = VO `~n Ga p~2

..l f 2 Equation 4.31 VO J Kn LSn Ga pO2 Z

Substituting the above equation into Equation 4.6 the following is observed:

Equation 4.32 86

KS ~~~ 1 ~ 4 Equation 4.33 Vcu — Vca SnGa p O 2 K n

combining the above results for the 4 separate regions, a Brouwer diagram can be established, see Figure 4.5. 87 compound

2 CuGa0 doped donor the for diagram Brouwer 4.5: Figure 88

4.2.3 Acceptor Doped

Similar to the donor doped compounds, the intermediate region is again subdivided into electronic and ionic regions. In the ionic region, the electroneutrality condition is as follows:

Equation 4.34 2lVo ~~ = LNica

Substituting this result into equation 4.2 we obtain the following results:

Equation 4.3S Kn = ~~Nico~ n2 p~2 2

1 / Nita ~2 1 Equation 4.36 n - 4 — K n ~ 2 ~ p O 2

Substituting this result into Equation 4.8 the following results are obtained:

1 ' \ Z 1 Equation 4.37 K _ K Nl~~ p~Z a ' —p 2 i

_~ ~K Ni~ l 2 -' Equation 4.38 I Ga p~2 p = ~ Kn 2 i 89

Again the oxygen and copper vacancy concentrations remain unchanged.

For the electronic region, the electroneutrality condition is as follows:

Equation 4.3 9 Nita = p

Combining this equation with Equation 4.4 the following results are obtained:

4 V ' Ni' _ Cu Ga Equation 4.40 K P p0 2

Equation 4.41 LV~u~ = KP LNI~a ~p~2

Then by substituting this result into Equation 4.6 the following is obtained:

Equation 4.42 KS = Kp ~Nica ~4 ~Vca ~~Vo~

2 V "' 1 1 Equation 4.43 V..~ = KS Ni' O 2 ~0 Ga Ga 2 p 2 K PH

Again, in the electronic region, the electron and hole concentrations remain constant.

Combining the above results for the respective regions, a Brouwer diagram for the acceptor doped CuGa02 compound can be established, see Figure 4.6. 90

n c~ 91

CHAPTER 5. ELECTRICAL AND OPTICAL PROPERTIES

5.1 Introduction

The TCO properties of bulk and thin ~ lm CuGa02 specimens have been established in previous works [11, 51, 57]. However, none of these works has discussed the properties of donor and acceptor doped CuGa02. This work, utilizing the previous chapter on the defect chemistry for both donor and acceptor doped CuGa02, will discuss electrical properties of the doped specimens in attempts to achieve a bipolar doped TCO material.

With the low and activated mobility values observed in the Cu-based delafossites it e+ has been suggested that the conductivity is by small polarons hopping between Cu'+ and Cu ions [16, 42, 51, 76, 79]. A polaron is comprised of a charge carrier, in this case holes, and the distortion of the ionic lattice caused the carrier [92]. In the case of small polarons, the lattice distortion extends only over distances smaller than the lattice constant. Energetically, half of the bandwidth is smaller than the minimum polaron binding energy, which is the increase in energy from an infinitely slow carrier (zero bandwidth) due to polarization and distortion of the lattice by the charge carrier [92].

The activated character of the mobility can be understood by examining the polarization that accompanies the lattice distortion caused by the motion of the hole.

Because a hole stays on a given lattice site for a longer than the vibrational lattice period, a hole would be trapped in its own polarization. The thermal energy is therefore needed to activate the hole for motion to occur [92]. 92

5.2 Experimental

5.2.1 Synthesis

Based on the investigation discussed in Chapter 3, all doped compounds involved a

pre-reaction of the dopant and the Ga20 3 powders. For the donor doped compounds Sn02

was utilized, while for the acceptor doped compounds Ni0 and Mg0 were used. In each case, stoichiometric amounts of the dopant and the Ga20 3 powders were

vibratory-milled in ethanol for 6 hours and then reacted at 1100 °C in air for 12 hours

according to the following reactions:

Reaction 5.1 (1 - x)Ga 2 0 3 + 2x Sn0 2 -~ Ga 2 1-x Sn 2x O 3

Reaction 5.2 ~1-x~Ga20 3 +2x Ni0 ~ Ga2~,_x~Ni2X0 3

Reaction 5.3 ~l - x~Ga20 3 + 2xMg0 -~ Gaza-x)Mg2X03

The pre-reacted powders from the above reactions were then mixed with Cu2U powder according to the desired ratio, and then re-milled for a period of 6 hours. The powders were then calcined at 950 °C for 16 hours in various atmospheres according to the following reactions:

Reaction 5.4 C'u20 +Ga2(~-x)Sn2x0 3 -~ 2CuGa~1_x~Snx02 93

Reaction 5.5 Cu2O+Ga2(~-x)Ni2xO3 ~ 2CuGa~,_x~NixO2

Reaction 5.6 Cue 0 + Ga2(~-x)Mg2X 0 3 —~ 2 CuGa~l-x)MgX 0 2

It should be noted that each compound was quenched in an attempt to "freeze in" the delafossite phase.

Given to the defect reactions established in Chapter 4, in order to attain bipolar conductivities, the donor and acceptor doped samples must be synthesized at the lowest and highest possible stable pO2's for the CuGaO2 compound respectively. According to Figure

2.5, this corresponded to approximately 0.1% 0 2 for p-doped samples and 0.001% 0 2 for n- doped samples.

Once the powders had been calcined, S wt.% acetone based binder (Ferro, lot #

1052007) was added. The powders were then ground and sent through a number 50 mesh sieve. These powders were then pelletized using a Carver Press and a %2" diameter steel die under two-staged pressures of 4000 and 7000 lbs. The pellets then underwent a binder burnout at 600 °C for 6 hours and then sintered at 1OS 0 °C for 16 hours all under the desired atmosphere.

After the pellets had been sintered, they were reground and 5 wt.% binder was again added. The powders were ground once more and again placed through a number 50 mesh sieve. The finely ground powders were then pelletized, then underwent binder burnout, and finally sintered all according to the methods described above. 94

5.2.2 Crystal Structure Analysis The reacted compounds were then characterized through x-ray diffraction at the

Materials Analysis and Research Laboratory. This analysis allowed for the determination of phases and the approximate amount of those phases. The scans were run with Cu-Ka radiation from 15° to 70°, at a step size of 0.03 degrees, and a count time of 2 seconds/degree.

The lattice parameters of the delafossite phase were then calculated using the UnitCell software [82] as discussed in Section 2.1.3.

5.2.3 Density

The densities of the pellets were determined by Archimedes principle with water as the fluid [93]. It should be noted that all cited densities are apparent values, meaning that internal pores within the samples were not accounted for.

5.2.4 Electrical Characterization

For conductivity measurements, the top and bottom surfaces of the pellet were sputter coated with gold using an Edwards Scancoat Six sputter coater. Additional silver electrodes

(SPI Flash-Dry Silver Paint) were painted on both sides of the pellet to ensure proper contact during the respective runs.

A sample's resistance was measured by impedance spectroscopy using a Solartron

1260 impedance analyzer from approximately 0 to 150 °C. Given the sample's geometry, the conductivity values were obtained. Figures 5.1 and 5.2 illustrate schematics of the sample holder and the experimental set-up respectively that were designed by Jeremy Schrooten. 95

„„ ~, „ ,,

1:..::.::::.

):: I

~~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~ ♦~~~~~~♦~~i~i~i~i~i~i~i~i ~

~~ ll ~~ ~~ ~~ ~~

Figure 5.1: Schematic of the sample holder for conductivity measurements

Figure 5.2: Schematic of the experimental set-up for conductivity measurements 96

Since Cu-based delafossites exhibit low mobility values, a Hall mobility set-up could not be utilized. Instead, the sample properties were verified using thermoelectric measurements. In this case, a temperature gradient was placed across the diameter of the sample and the voltage generated from the sample was recorded, see Appendix III for a more detailed discussion of thermoelectrics. For small polarons, the Seebeck coefficient is given by•

k nFF k No Equation 5.5 S =— =—ln e kT e NA

where NA/No is the ratio of the density of the polarons taking part in the conduction process and the density of the Cul+ ions and all other parameters being defined earlier. The parameter No can be calculated form the cell dimensions, and from this value and utilizing the above equation the charge carrier density, NA can be determined. Finally the mobility value can be established by rearranging the conductivity equation as follows:

Equation 5.6 ,u = ~p NA e~-'

5.2.5 Optical Characterization

The ultra violet-visual (UV-Vis) spectrum of the CuGa02 powders were investigated using a Perkin Elmer Lambda 19 spectrometer. For this measurement, a small amount of

CuGa02 powder was smeared onto transparent tape, forming aquasi-thin film. The sample was then placed in the UV-Vis spectrometer and scanned from 180 to 3200 nm. 97

The infrared (IR) spectrum of the CuGa02 powders were examined using a Broker

IFS66V/S fourier transform infrared (FTIlZ) spectrometer. In this case 100mg of KBr was added to approximately 1 mg of CuGa02 powder and ground together. The combined powders are then pressed in a die to obtain a transparent disk. The sample was then loaded into the instrument and run from 12,000 to 25,000 nm. The percent transmission was obtained by dividing the single channel result from the sample by a reference. In order to obtain accurate results, 34 scans were performed all at wavenumber 4 cm1 resolution.

5.3 Results and Discussion

5.3.1 Synthesis

Figures S .3-5 and Table 5.3 illustrate the increase in phase purity fora 2.5

Sn doped CuGa02 compound with each consecutive grinding.

Table 5.3: Percent delafossite formation as a function of the number of regrinds Regrinds % Delafossite None 56.2 One 66.3 Two 96.7 98

2000 N O 1500 (CPS) ~o 0 0 1000

0 500 O pp O O Intensity ~ '_', C O r-+ ...~. O r, O 0 CuG a02 ~ I ~ ~ I ~ ~ Cu20 r ~ I Ga203

Sn02 I ~ ( r ~ ~ ~ ~ 20 30 40 50 60 70 28 (Degrees)

Figure 5.3: 2.5% Sn doped CuGa02 powder after calcine at 950 °C

6000

5000 0

(CPS) 4000 0 0 0 3000

2000 0 00 0 M 0 Intensity O O O 1000 O

0 C uG a02

C u20 r i I 20 30 40 50 60 70 28 (Degrees)

Figure 5.4: 2.5% 5n doped CuGa02 pellet after sinter at 1050 °C 99

10000

0 8000 (CPS)

6000 0 0

4000 0 0 0

Intensity M 0 0 O 2000 O O

CuGa02

Sn02

I t a ~ I I 20 30 ~ ~ ~ 40 50 60 70 28 (Degrees)

Figure 5.5: 2.5% Sn doped CuGa02 pellet after regrind and sinter at 1050 °C

Based on the above figures and table, it is apparent that a second grinding step is necessary in attaining high purity and highly crystalline CuGaO2 ceramics. After the initial calcination, a significant amount of the delafossite phase forms; however, there are still remnants of all three precursor phases. Once these powders were reground, pelletized, and sintered at elevated temperatures, almost all of the precursor phases were eliminated.

Finally, after an additional regrind, an additional increase in phase purity, peak intensity, and sharpness were observed.

As mentioned previously, in order to attain high n- and p-type conductivities, the donor and acceptor doped CuGaO2 compounds were synthesized at the respective spectrums on the phase stability regions. This corresponded to approximate pO2's of 0.001% and 0.1

0 2 for the donor and acceptor doped samples. While the phase purity of the donor doped 100

samples at their respective pO2 was not an issue, acceptor doped samples could not be obtained at their desired pO2. Figure 5.6 illustrates a temperature versus log pO2 phase

diagram for 1% Mg doped CuGaO2 samples. While the addition of small dopants should not

significantly affect the thermodynamic stability of the CuGaO2 compound, Figure 5.6 clearly

illustrates that the 1% Mg doped CuGaO2 sample was only stable at a pO2 of approximately

0.002% 0 2. It should be noted that while the figure shows the presence of impurity phases at

the 0.002% 0 2 level, these phases were simply unreacted precursors and were eliminated at the higher sintering temperatures. This phase stability at only the lower pO2 levels was also observed for the Ni doped compounds. 101

1150

Cu+Ga O 1100 2 3 /

1050 (°C)

~-0.005% 02 -v0. l % 02 1000

■~ ~ t 950 Q ~ ;

900 —0.002% 02 0.01% 02 Temperature

CuGaO~ 850 Cu20 CuGa O +Cu O /CuGa O +CuO <:1~.20:~ 2 4 2 2 4 I I 800 -6 -5 -4 -3 -2 -1 0 Log p02

Figure 5.6: Temperature vs. log p02 phase diagram for 1% Mg doped CuGa02 102

5.3.2 Density

All specimens had an apparent density of approximately 90%theoretical, and therefore no composite correction was necessary [94].

5.3.3 Undoped CuGa02 Electrical Properties

Based on the defect chemistry established in Chapter 4, Figure 5.7 illustrates the approximate working p02 range, black circle, for the undoped CuGa02 in the Brouwer diagram. As the diagram suggests, p-type conductivity should be observed. The yellow line illustrates the expected conductivity levels as a function of oxygen partial pressure.

~L~'O ]_ fl ~~ = p

u bJJ

1o~pOa

Figure 5.7: Brouwer diagram for undoped CuGa02 illustrating the conductivity level (yellow line) as a function ofp02

The log conductivity versus inverse temperature data. that was obtained for the undoped CuGa02 pellet sample is shown in Figure 5.8. The room temperature conductivity was 3.3 x 10-3 S/cm and compared favorably with literature values. 103

-1.80

-z.00

~ -z.2o v b -2.40

WD -2.60

-z.so

-3.00 2.4 2.6 2.8 3.0 3.2 3.4 3.6 1000/T (K-1)

Figure 5.8: Log conductivity vs. inverse temperature for undoped CuGaOZ 104

As Figure 5.8 illustrates, the undoped CuGa02 exhibited intrinsic behavior, meaning the conductivity was temperature dependent and follows the Arrhenius relationship shown in

Equation 5.7,

Equation 5.7 6 = 6 o exp — EA ~ kT ~

where EA is the activation energy for hopping and k is Boltzmann's constant (8.6174 x 10-5 eV/K). In order to determine this value, the natural log is taken resulting in the following:

Equation 5.8 In 6 =1n 60 — EA —1~ T~

where In Qo is the y-intercept and -EA/k is the slope of the graph. Based on the linear curve fit shown in Figure 5.8, the activation energy for hopping was determined to be approximately

0.144 eV which agreed well with the literature value.

The thermoelectric measurements resulted in a positive Seebeck coefficient which indicated p-type conductivity, thus confirming the Brouwer diagram in Figure 5.6. Figure

5.9 illustrates the Seebeck coefficient as a function of inverse temperature. Based on the sample dimensions and the fact there are three formula units per unit cell, the No value was calculated as 4.76 x 1021 cm-3. Combining this value and the room temperature Seebeck coefficient of 782.6 µV/K, the charge carrier density, NA, and mobility, µ, were determined to be 5.4 x 1017 cm3 and 0.039 cm2/Vs respectively. Figure 5.9 also illustrates the Fermi level, 105

EF, as a function of inverse temperature, with the room temperature value of approximately 0.24 eV agreeing very well with the literature values Table 5.4 compares the TCO properties of CuGaO2 from this work with other literature values. 106

T(K) 300 350 400 450 500 550 750 l T 034 goo 032 .. • t~7 x 6so 0.30 ~;., C 0.28

600 az6

. 550 I 1 I I I I I I 1 I I I I I I I I I l I t I t I 1 0.24 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 1000/T (K-1)

Figure 5.9: Seebeck coefficient and Fermi level as a function of inverse temperature

Table 5.4: TCO properties of undoped CuGa02 Property Thin Film [ 11 ] Bulk [51] Bulk, This Work 6RT (S/cm) 6.3 x 10-2 5.6 x 10"3 3.3 x 10"3 µ (cm2/Vs) 0.23 0.015 0.039 N (cm"3) 1.7 x 10'~ 2.4 x 10'~ 5.4 x 10" S (µV/K) 560 790 782.6 lay

5.3.4 Donor Doped CuGa02 Electrical Properties

Figure 5.10 illustrates the Brouwer diagram for the Sn doped CuGa02 compounds, with the yellow line again indicating the conductivity levels as a function of oxygen partial pressure. If the approximate p02 working range is examined, it is apparent that a decrease in conductivity should be observed.

= ~==11 ►~f~l~ ~ = fl ~~'~~ll~ ~i .~

arw~.-..~r.Nas.~.

F ~~ 1 ''~ f ~~~

Figure 5.10: Brouwer diagram for Sn doped CuGa02 indicating the conductivity level (yellow line) as a function of p02

The log conductivity versus inverse temperature data for the 2.5% Sn doped CuGa02 sample is shown in Figure 5.11. The room temperature conductivity value for the sample was 1.5 x 10~ S/cm, which was approximately 3 orders of magnitude less than the undoped.

This decrease in conductivity confirmed the hypothesis established by the defect model. It is also important to note the relative temperature independence of the conductivity, indicating the expected extrinsic behavior. 108

-s.00

-s.so

b -6.00 wo 0

-6.s0

-7.00 3.0 3.1 3.2 3.3 3.4 3.s

1000/T (K-1)

Figure 5.11: Log conductivity vs. inverse temperature for 2.5% Sn doped CuGa02

5.3.5 Acceptor Doped CuGa02 Electrical Properties

Figure S .12 illustrates the Brouwer diagram for the Ni doped CuGa02 compounds, with the yellow line again indicating the conductivity levels as a function of oxygen partial pressure. If the approximate p02 working range is examined, it is apparent that with the doping of acceptors into the material, the p-type nature of the material should be enhanced, and thus an increased conductivity should be observed. 109

`3~ r ~~~ J

o' 1;2, -12 ~~~

1,~G , 1,~..,.

1c~~ p~}a

Figure 5.12: Brouwer diagram for Ni doped CuGa02 indicating the conductivity level (yellow line) as a function of p02

The log conductivity versus inverse temperature data for the 2.5% Ni doped CuGa02 sample is shown in Figure 5.13. The room temperature conductivity value for the sample was 6.5 x 10-3 S/cm, which was approximately double the value of the undoped. Mg was also attempted as an acceptor dopant, but conductivity measurements could not be obtained.

It is currently unclear as to why Mg did not increase the conductivity values, especially with single phase samples being obtained. Therefore future work will set out to establish the explanation for this phenomenon. 110

-1.80

-2.00

~ -2.20 V ~ i ~ ~ b -2.40 wo 0 -2.60

-2.80

-3.00 2.4 2.5 2.5 2.6 2.6

Figure 5.13: Log conductivity vs. inverse temperature for 2.5% Ni doped CuGa02

Another critical issue with the acceptor doped samples was the small increase in conductivities. By introducing such a large number of charge carriers, a significant increase in conductivity should have been observed. It can therefore be concluded that not all the charge carriers are being effectively doped into the system; however, what occurs with the remaining carriers is currently not understood. It is most likely that the acceptor dopants are forming defect complexes without electronic compensation.

5.3.6 CuGa~l x~Inx0 2 Electrical Properties

Conductivity measurements obtained for the single phased CuGaa.93s~o.o6sG2 compound indicated an order of magnitude reduction in the room temperature conductivity, -4 approximately 3.7 x 10 S/cm, compared with the undoped CuGa02 compound. 111

5.3.7 CuGaO2 Optical Measurements

Utilizing the LTV-Vis transmission spectra, the direct band gap, Eg, was determined by plotting (cxh v)2 vs. h v [95], where h is Planck's constant, a is the absorption coefficient, and v is the frequency. Figure 5.14 illustrates the transmission spectrum for the UV-Vis with the inset illustrating the (cxh v)2 vs. h v plot, which resulted in an experimental optical band gap of approximately 3.48 eV. With the transmission measurements performed on powders, in order to obtain c,~ an approximate thickness of 600 µm was utilized. Based on the minimum particle size of 297 µm established by the sieve, the approximate thickness was based on an assumed two particle layer thick powder film.

Figure 5.15 illustrates the transmission spectra for CuGaO2 powders in the mid-IR region. The inset figure has shows the horizontal axis as wavenumber for comparison purposes, while the main ~ gure is labeled as wavelength to estimate the total transmission window for the CuGaO2 compound. The observed plasma wavelength in the mid-IR for the

CuGaO2 powder was approximately 15,000 nm. This resulted in an approximate transmission window from 300 to 15,000 nm.

Previous work has investigated the bonding modes in thin film CuAlO2, which resulted in weakly intense absorption bands at 1470 and 1395 cm 1. The frequencies of these bands were about twice that of the major phonons in Cu2O and Al2O3, indicating that the pair of bands may involve Cu-O-AI-O-Cu bonds along the c-axis [58]. These weakly intense bands could not be observed in the CuGaO2 powders due to the scattering that occurred from the particles. 112

100

80

60

40 Transmission

20

0 0 500 1000 1500 2000 2500 3000 3500 Wavelength (nm)

Figure 5.14: UV-Vis transmission spectra for CuGa02 powders, (ahv)2 vs. by plot is shown in the inset

Wavenumber (cm"I) 1040 960 880 800 720 640 100

80

60

40 Transmission

20

0 9000 10000 11000 12000 13000 14000 15000 16000 Wavelength (nm)

Figure 5.15: % Transmission as a function of wavelength and wavenumber for CuGa02 powders 113

5.4 Conclusions

The electrical and optical properties of doped and undoped CuGa02 were established.

In the undoped CuGa02, the positive Seebeck coefficient of 782.6 µV/K confirmed the p- type nature of the material. Utilizing this value and a room temperature conductivity of 3.3 x

10 3 S/cm, calculated values of 0.144 eV, 0.039 cm2/Vs, and 5.4 x 101~cm3 for the hopping activation energy, mobility, and charge carrier density were established respectively. Based on the stability regimes (T, p02) that were previously established for the CuGa02 delafossite phase, single phase donor and acceptor doped CuGa~2 compounds were synthesized within the limit of XRD. Conductivity measurements confirmed the expected trends based on the defect chemistries. Room temperature conductivities for 2.5% Sn and Ni doped CuGa02 compounds were 1.5 x 10-6 and 6.5 x 10"3 S/cm respectively. While the p-type nature of the

CuGa02 compound was enhanced by acceptor doping, the limited increase in conductivity confirmed the difficulties in doping delafossite compounds. Finally based on the optical data an approximate transmission window of 14,700 nm with an optical band gap of 3.48 eV was established for CuGa02 powders. 114

CHAPTER 6. CONCLUSIONS AND FUTURE WORK

Delafossite type transparent conducting oxides continue to show tremendous potential for the use as a bipolar transparent conducting oxide. Once this potential is reached, numerous device possibilities can become a reality. From active circuits such as switches and amplifiers [96] to windows that can power entire sky scrappers, it is an exciting field that could mimic what is now science fiction. While these applications seem farfetched, this work has shown promise, both in the processing and conductivities of CuGa02 compounds, leaving the door open to new and improved strategies that could make these and other discoveries a reality.

6.1 Synthesis and Phase Equilibria

6.1.1 Synthesis and Phase Equilibria: Conclusions

The high temperature phase stability of the CuGa02 delafossite phase was established via solid state synthesis. This stability region was from approximately 0.1% to 0.001% 0 2 in a temperature range of 950 to 1075 °C.

From the results of the phase stability study, a B-site solid solution between Ga and In was examined in an attempt to exploit the high transparencies of Ga and high bipolar conductivities of In based compounds. While previous works had established a solid solution between Ga20 3 and In20 3 [97], the difficulty in synthesizing CuIn02 compounds via solid state synthesis limited the extent of solid solution in Cu(Ga,In)02. In this work, the 115

maximum solid solution of In into CuGa02 was obtained with the approximate composition of CuGao,93s~o.o6s~2•

The variation in the cell dimensions as a function of In content were investigated through a diffraction study. It was observed that the a-axis lattice parameter and unit cell volume increased up to an approximate In mole fraction of 0.1, above which the values remained relatively constant. This increasing trend became less clear with the c-axis lattice parameter. It was therefore concluded that the solubility of In in the CuGa02 structure was limited to between 0.05 and 0.1 mole fraction. The observed trends confirmed the expected impact on the cell dimensions of increasing the B-site ionic radii within the delafossite structure.

Utilizing a phase pure CuGa02 sample, the lattice parameters were refined by Le Bail full pattern decomposition and Rietveld refinement. This resulted in a- and c-axis lattice parameters of 2.976 A and 17.160 A respectively.

The high temperature phase equilibria was also investigated in the bipolar doping of the CuGa02 compounds. While the thermodynamic stability of the CuGa02 phase should not have been dramatically influenced by these aliovalent substitutions, acceptor doped compounds were not stable at the higher p02 values. Instead, they had to be synthesized at the lower p02 stability limit for the CuGa02 phase. 116

6.1.2 Synthesis and Phase Equilibria: Future Work

With the approximate phase stability regions established in this work based on a sample matrix, new work should set out to confirm these boundaries. While thermal gravimetric and differential thermal analyses were both performed on CuGa02 specimens, no apparent phase transformations were observed. Therefore, theoretical thermodynamic calculations and/or modeling should be explored. These calculations could also encompass the thermodynamic issues regarding the phase stability of the acceptor doped CuGa02 compounds.

Another important issue deals with chemical and phase composition of the samples.

Especially with the doped compounds, the amount of dopant incorporation within the crystal structure is vital to the understanding and thus improvement of sample performance. A quantitative XRD analysis was performed in this work. While this gave some pertinent information regarding phase purity, it can only be viewed as a beginning. Impurity standards should be synthesized to facilitate more accurate determinations of relative phase amounts.

Also, ~;RF, microscopy, and TEM should be performed to confirm batch stoichiometries and phase purities.

Finally, while this work focused on bulk synthesis, it is imperative that thin films be produced in order to attain more applicable results. This includes accurate optical measurements and conductivity values that can used as a better gauge for device applications.

The current work maybe applied to the synthesis of thin film targets; however, an important processing difference exists. The bulk pellets that were synthesized in this study were 1/a" in diameter, while the target specimens for thin film depositions would require a diameter of 2".

Therefore, while solid state synthesis could still be employed, a different forming technique 117

would have to be established in order to fabricate dense targets. Possible solutions could involve cold or hot isostatic presses (CIP and HIP) which attain significantly larger pressures than a manual press. However, if a HIP is employed, the established phase stability regions that were established in this work might not be applicable at high pressures. Therefore, a new phase stability study would have to be performed. Once phase pure target specimens were established, the effects of key variables within the deposition process should also be investigated.

6.2 Electrical and Optical Properties

6.2.1 Electrical and Optical Properties: Conclusions

The electrical and optical properties of doped and undoped CuGa02 compounds were examined in this work. The electrical properties of undoped CuGa02 compounds agreed very well with literature values. Due to the small polaron mechanism that describes the conductivity in most Cu-based delafossites, Hall effect measurements could not be performed. Instead, based on a room temperature conductivity of 3.3 x 10-3 S/cm and a

Seebeck coefficient of 782.6 µV/K, calculated values for the hopping activation energy, mobility, and charge carrier density were estimated as 0.144 eV, 0.039 cm2/Vs, and 5.4 x

1017cm3 respectively. It should also be noted that the positive Seebeck coefficient confirmed the p-type nature of the CuGa02 compound.

Based on the established defect chemistry, donor and acceptor doped CuGa02 compounds were expected to exhibit reduced and increased conductivities respectively. 118

These calculations were indeed confirmed with room temperature conductivities of 1.5 x 10-6 and 6.5 x 10-3 S/cm for 2.5% Sn and Ni doping respectively. While single phase Mg doped

CuGa02 compounds were established, their observed conductivities were significantly lower than their Ni counterpart. Thermoelectric measurements were not performed on these samples, and thus their bipolar conductivities were not established.

Utilizing the UV-Vis and IR data, a transmission window from approximately from

300 to 15,000 nm was established for CuGa02 powders. Also, an optical band gap of 3.48 eV was estimated through an (cxh v)2 vs. h v plot. While low percent transmissions were observed throughout the spectrum, this was attributed to scattering due to the relative size of the particles.

6.2.2 Electrical and Optical Properties: Future Work

With the undoped CuGa02 compounds demonstrating satisfactory levels of p-type conductivity, a more thorough investigation into bipolar doping should be performed. This would include examining the conductivities and thermoelectric properties as a function of doping levels for both donor and acceptor doped compounds as a means of establishing a doping limit. This survey might also reveal some informative trends regarding dopant incorporation within the delafossite structure as well as establishing bipolar conductivities.

It has been suggested that in the layered structure of the delafossites, the B-site position can be occupied by a wide spectrum of divalent/tetravalent or even monovalent/pentavalent coupled cations [81]. It is thought that the Bo.s Bo.s 02 slabs are stabilizing structural elements that govern the course of reduction and oxidation processes.

Therefore, it is possible that Cu-based mixed-valence compounds could exhibit increased 119

phase stability regions, thus expanding the working regions within a compounds respective

Brouwer diagrams. Consequently, increased conductivities could be achieved.

Improved measurement techniques should also be examined. Currently, conductivity measurements can only be performed at low temperatures and in constant atmospheres. The ability of attaining high-temperature conductivity measurements in a broad p02 range could offer tremendous insight into the defect chemistry of the compounds, thus revealing possible conductivity mechanisms. More specifically, the p02 dependence on the conductivities and consequently on the charge carrier densities could establish the equilibrium constants for a respective defect reaction. These values could then be utilized in determining the energies of formation of the various defects within the delafossite structure.

Finally, once thin ~ lm strategies have been investigated, two important issues become enhancing the basal plane conductivity and establishing satisfactory optical properties.

Currently, some conductivity is lost in the c-axis due to small transitions between the hybridized states. It has been suggested that the strong covalency in the Cu-O bond reduces this band gap, thus increasing the number of transitions [25]. It is therefore essential to reduce this covalency if maximum basal plane conductivities are to be achieved. This could be achieved through doping on the A-site or through the introduction of Cu vacancies.

In examining the optical properties, it is imperative that the IR characteristics be fully examined. This could lead to tremendous insight to bonding characteristics within the delafossite structure. Also, by maximizing their IR properties, new doors that lead to additional applications could be revealed and opened. 120

APPENDICES

Appendix I.• Unitcell Regression Diagnostics

The Unitcell software utilizes regression diagnostics to the least squares method in order to identify influential data and sources of collinearity. It should be noted that these are single-observation diagnostics and therefore cannot detect detrimental effects caused by masking effects. The following are brief descriptions of the main diagnostics that are used

[98]:

• Hat. Hat values give information regarding the amount of influence each observation

has on the least squares result. Any hat values that are greater than the cutoff value of

2p/n are flagged as potential leverage points, where n is the number of observations

and p is the number of parameters.

• Rstudent. Since ordinary residuals are not always useful because influential data

often have very small residuals, Rstudent is designed to take influence into account

by dividing the residual by the sgrt(1-h). Any Rstudent value above the 95% cutoff

value is flagged as a potentially detrimental observation.

• Dfits. This is a deletion diagnostic that involves the change in the predicted value

upon the deletion of an observation. The value given in the diagnostics is the change

in the calculated value upon the deletion of an observation as a multiple of the

standard deviation of the calculated value. Any Dfits values greater than the cutoff

value of 2sgrt(p/n) are flagged as potential deleterious points. 121

• sig(i). This is the value that sigmafit (the standard error of the fit) would assume if

the observation of i was deleted. If a value is significantly below the sig(i) value,

then the deletion of that observation would improve the overall fit.

• DFbetai. This diagnostic flagges the change in each fitted parameter upon the

deletion of an observation i. Its value is given in terms of a percentage of the

standard error. If an observation would cause any parameter to change by more that

30% of its standard error it is flagged as being potentially suspicious.

Appendix II: Rietveld Refinement

Reitveld refinement involves a generation of an entire powder pattern in discrete steps and fit by minimizing the differences between the calculated and observed diffraction patterns using the least-square refinement methods. It also provides quantitative phase analysis. The program utilized in this work incorporates a previous program written by

Wiles and Young back in 1981, but involves the addition of many new features which will not be discussed here [84].

The principal fit parameters are grouped into two categories: structural and instrumental. The structural parameters involve the atomic coordinates, equipoint occupation members, and Debye-Waller temperature factors. These parameters will not be discussed in length, but essentially characterize the atoms and crystal structure of a given sample. The instrumental parameters include peak shape factors, background, intensity scale factor, counter zero, and the halfwidths of peaks [87]. 122

Appendix III: Seebeck Measurements

Historical Overview:

In 1822-23 Seebeck described in the "Reports of the Prussian Academy of Sciences", experimental results in which he found that a compass needle was deflected when placed near a closed loop formed between two dissimilar conductors which where placed in a thermal gradient [99]. In this report, Seebeck falsely concluded that the observed interaction was a magnetic phenomenon, and consequently attempted to relate the Earth's magnetic field based on the temperature difference between the equator and the poles [100] . Although he was incorrect in the observed phenomenon, Seebeck did arrange materials in order of the product SQ, where S is the Seebeck coefficient and Q is the electrical conductivity. This product has the units of volts per degree, or now commonly expressed as µV/K [100] .

This extensive series compiled by Seebeck is even today quite accurate. Had Seebeck utilized the first and last terms in his series (PbS and Fe respectively) as thermocouples to generate electrical energy, he could have obtained an efficiency of nearly 3%, which on the order of the most efficient steam engine at the time [101 ] . Looking back at his work, it has since become apparent that the observed phenomenon was actually the discovery of the thermoelectric effect which was caused by an electric current that flowed in the circuit [100].

Twelve years after Seebeck's discovery, a French watchmaker, Peltier, published axi article in a French journal that described his observations of temperature fluctuations that occurred in the boundary between two different conductors when a current was passed through them [102] . This phenomenon, later termed the Peltier effect, consisted of the generation or absorption of heat, at a rate Q, at the junction between two different conductors when a current, I, is passed between them according to the following: 123

Equation A. l Q =III ,

where II is the Peltier coefficient [101 ] .

Even though the Peltier effect is closely linked to the Seebeck effect, it wasn't unti11838, that Lenz explained the true nature of the Peltier effect. In a simple experiment,

Lenz placed a droplet of water in a dent between the junction of bismuth and antimony rods.

Depending on the current direction in the loop, the droplet either froze or melted. It was known at this time that in order to freeze 1 g of water, 80 cal must be removed from the system. Therefore, Lenz concluded that the current direction generated an electric current that either absorbed or generated heat at the junction of the two conductors [1 O1 ].

With other important scientific discoveries happening around the same time, it wasn't until 1885 when the use of thermoelectric phenomena was first applied to generating electricity by Rayleigh [100] . Although his calculations on the efficiency of a thermoelectric generator were incorrect, they gave way to the implementation of a successful theory by

Altenkirch in 1909, in which he showed that "good" thermoelectric materials should incorporate large Seebeck coefficients with low thermal conductivity, ~ [100]. These characteristics were sought in order to retain the heat at the junction while maintaining low electrical resistance to minimize Joule heating [100] .

Theory:

A brief theoretical discussion describing why a voltage is generated in a closed loop under an applied temperature gradient will now be entertained. In order to examine this question, a good starting point is treating the conduction of electrons in the material as an 124

ideal gas. By doing this, the kinetic energy of the gas particles will differ significantly over the temperature gradient, with the particles in the hotter areas having the greater energy

[103]. Thus, the movement of electrons in the hotter regions to the colder regions of the material can be described as a thermally-driven diffusion flux. This transport of electrons will continue until the build up of electrons in the cold region is balanced by the resulting electrostatic potential difference [103]. The resulting electric field is related to the temperature gradient according to the following relationships:

0V 0T Equation A.2 =E=5 , dx dx

where O V is the potential difference, E is the electric field, and dx is the mean free path length.

In this example, the material would be classified as n-type, or that its major carrier type was electrons, and thus the resulting Seebeck coefficient was negative. A positive

Seebeck coefficient is more regularly seen in semiconductors than metals, where by doping, holes can become the dominant charge carrier.

Figure of Merit:

The thermoelectric effect can be described by afigure-of-merit, Z, based on the following relationships:

S 26 Equation A.3 Z= , 125

where Z is in units of K"l. Since Z may vary as a function of T, at a given temperature a useful non-dimensional figure-of--merit is ZT [100] . It is apparent that in order to maximize a materials merit, a large c~o~ product is desired. When this relationship is applied to metals, which have high electrical conductivities but possess low Seebeck coefficients, low figure of merit values result. A similar observation occurs in insulators, for they posses high Seebeck coefficients but have a significantly lower conductivity.

At first glance, it appears that a high figure of merit of a material can be achieved if the material possesses a low thermal conductivity. However, this is not the case in all materials. The proportionality coefficient between the heat flux and the temperature gradient is represented by the thermal conductivity, which can also be explained by the sum of two components, a lattice and an electronic [103 ] . The former is due to phonons while the latter is due to carriers. In the case of metals, the Wiedemann-Franz law describes the coupling that occurs between the electrical conductivity and the electronic component of the thermal conductivity according to the following equation:

Equation A.4 ~~T~ ~Zk 3e6(T) LoT6~T~,

Based on this relationship, the bulk of the heat in the material is transported by charge carriers; therefore, a low A results in a low Q as well. However, if the heat transport is dominated by phonon propagation, then reducing A in order to achieve maximum ZT values is a viable approach [103 ] . Figure A. l illustrates the dependence of ZT on the three primary parameters (cx, Q, and ~). 126

~~~

Figure A.1: Relationship between electrical conductivity, Seebeck coefficient, and thermal conductivity on the figure-of--merit term ZT [103] 127

It should be noted that the abscissa, which identifies the carrier concentration, is only utilized as a guide and not as a representation for optimizing the carrier concentration.

Thermoelectric Semiconductors:

In discussing thermoelectric materials, three general categories exist: metals, semiconductors, and insulators. For our purposes, our discussion will be limited to semiconductors, which have properties that are well suited for thermoelectric applications[103]. With their characteristic band gaps in which the Fermi level lies, semiconductors tend to have larger Seebeck coefficients with respect to their metal counterparts. Within the semiconductor classification, those materials that possess relatively flat energy bands tend to have the highest Seebeck coefficients (~100's µV/K). This results from the Seebeck coefficient being dependent on the effective mass, which is given by the inverse curvature of the energy bands in reciprocal space [103].

While the electrical and thermal conductivities can be tailored in semiconductors through doping, this tailoring can have adverse effects on the figure-of--merit values. Since the Seebeck coefficient is approximately proportional ton "2~3 in the parabolic band approximation, where n is the carrier concentration, excessive doping of the semiconductor can reduce the Seebeck coefficient by moving the Fermi level closer to the conduction or valence band in the case of n- andp-type materials [103]. By thinking of the Seebeck coefficient as a measure of the energy transported per charge carrier, which is proportional to the difference in energy between the conduction band edge and the Fermi level, the above relationship becomes clearer. Through doping, the presence of donor states lowers the Fermi level closer to the conduction band, thus decreasing this energy difference [103]. 128

Another important consideration involves the presence of minority or intrinsic carriers, for they decrease the Seebeck coefficient since electron/hole pairs caJrry energy but possess no net charge. Therefore, semiconductors with a relatively large band gap, Eg >_ 10 kBT, should be used in order to avoid intrinsic conductivity within the anticipated operating temperature range for the material [103 ] .

The general category of semiconductors can be characterized by two subcategories: those in which charge carriers move by itinerant motion through relatively broad bands and those that move by a thermally activated hopping mechanism. In the case of broad band . I. semiconductors, the Seebeck coefficient and electrical conductivity are functions of the materials charge carrier density. If we assume that most of the heat is transported by the lattice, i.e. ~ « ~,, then:

Equation A.5 S ~ 2 k B =172 ~V / K e

In the case of simple band-type conductors, the electrical conductivity can be written as follows:

Equation A.6 ~ = ne,u ,

where µ is the electron mobility. V'Vhile the above expression shows no explicit temperature dependence, since the electrical conductivity shows a strong dependence on temperature, either and or both the carrier concentration and the mobility must be temperature dependent. 129

In the case of carrier concentration in semiconductors, it in fact increases exponentially with temperature according to the following equation:

E Equation A.7 n = no exp — 2k sg T, ,

where no is the initial carrier content [103 ] .

Narrow-band materials such as oxides based on transition metals exhibit a hopping mechanism. The carriers in this case are no longer electrons or holes, but can rather be described as localized particles that move in response to athermally-activated diffusion process. This diffusive motion is coined "hopping", and the hopping distance, or mean free path is comparable to the respective lattice spacing. If the interaction between the carrier and lattice is large enough, the carrier polarizes the lattice and forms a quasiparticle called a polaron [104]. While lattice vibrations reduce the electron mobility in all other electronic conduction mechanisms, in small polaron conductions, the lattice vibrations actually enable it to take place much like for ionic conductivity. The resulting low but activated mobilities (<_

1 cm2/Vs) and large carrier concentrations (~10 22 cm-3) give rise to intermediate conductivity values (106 — 102'5 S/cm), as well as small to negligible activation energies [104] .

The hopping motion described above can be treated as a simple diffusion process where given the total density of conducting sites N, a fraction of which c are occupied by charge carriers, the Nernst-Einstein equation can be used to calculate the conductivity as follows: 130

Equation A.8 6=~Nc~eu=~k~TD , B

where D is the small polaron "diffusivity":

Equation A.9 D = g(1— c)ea zv exp — EH kBT

where g is a geometric factor, a is the jump distance between equivalent sites, v is the lattice vibrational frequency, EH is the activated hopping energy, and (1-c) is the probability that the adjacent site is of appropriate valence for an exchange to occur. Combining the above to equations, we arrive at the following equation for conductivity:

gNc~l—c~e2a Zv —EH Equation A.10 6= k a T eXp k B T '

or a simplified version can be written as:

Equation A.11 6 = ~ exp kET , s

where vo is simply the remaining terms in the numerator and denominator [104].

In the case of small polarons, the Seebeck coefficient can be written as follows: 131

2~1—c~ Equation A.12 S=±kB In , e [ c ]

where all terms have been defined above and the entropy of transport term has been neglected. The t sign is determined by whether the polaron forms around the trapped hole or electron and the factor of 2 accounts for spin degeneracy [105]. The characteristics of small polaron conduction, i.e. activated mobility, becomes evident in the above equations, i.e. the conductivity is thermally activated while the Seebeck coefficient is temperature independent

[43].

Jonker-Type Analysis:

An effective way of examining experimental data is by constructing a Jonker plot

[104]. The analysis involves a plot of the Seebeck coefficient vs. the logarithm of electrical conductivity, which results in a "pear-shaped" figure, see Figure A.2. Information regarding the intrinsic band gap and density of states-mobility product can be obtained from the size and position of a given plot. In the case of small polaron systems, completely distinct curves are obtained for n- and p-type conductors [104]. The approach is outlined below. 132

~oa.€~a

Figure A.2: Small polaron systems compared to Jonker behavior

In order to describe the n-to p transition in the intrinsic region, Jonker's approach assumes atwo-band model for both the conductivity and Seebeck coefficient. Since we are only interested in the behavior of the large carrier concentrations, only the extrinsic "legs" of the Jonker plot will be considered. The n-type leg of the plot results from combining the following equations for conductivity and Seebeck coefficient:

Equation A.13 6_ = neu_ ,

and

kB N_ Equation A.14 e n

resulting in the following: 133

kB A_ kB Equation A.15 S_ _ — In N_ eu_ e + In 6_ , e e

where N_ is the density of states, n is the density of carriers, and A_ is the transport constant.

Similar equations are obtained for the p-type leg, noting the different terminology and opposite signs [104].

If we consider the density of states and transport constants to be equal for both mechanisms, we obtain the dashed lines in Figure 4 with slopes equal to ~ kB/e. It should be noted that in order to make an accurate comparison with the small polaron curves, the lines have been normalized to unit conductivity at S = ~ S 9 µV/K [104] .

The following procedure outlines the derivation of the small polaron curves in Figure

4, i.e. the dashed lines. If we define the valence ratio as q = c/(1-c), by using the above equation for the Seebeck coefficient of small polarons, we arrive at the following relationship

+ Se Equation A.16 q = ~ — 2 exp (1— c~ kB

with a similar equation being established in the case of a p-type system. In either case, by utilizing the above equation, the valence ratio can be re-written as follows:

Equation A.17 c~l — c~ = q~l + q~z 134

This same product can be isolated in the above equation for conductivity, giving the following equation:

Equation A.l 8 c~l — c~ _ (S2Nv) eXp k a T '

where the product ~ (ge2a2/kBT) is constant at a fixed temperature. If we further assume that the conduction site density, N, jump frequency, v, and the hopping activation energy are independent of stoichiometry, it follows from the equation for the temperature dependent conductivity that the maximum conductivity will occur at c = 0.5. Therefore, the c/(1-c) product can be normalized as follows:

c~l — c~ _ 6 Equation A.19 0.5 2 6,,,a,~

Thus if we combine this equation with equation for the valence ratio the small polaron curves are obtained [104].

From Figure A.2, it is apparent that small polaron behavior dominates in the vicinity of the ma~cimum conductivity, which requires sufficient carrier concentrations. If this requirement is not met, linear behavior will be observed and thus band-type or -small polaron conduction mechanisms will not be able to be differentiated [104]. 135

Seebeck Coefficient Measurements:

The traditional approach to measuring the Seebeck coefficient in electroceramic materials is to place a sample across the hot zone of a furnace so that a measurable temperature gradient can be measured. If measurements are taking as the furnace is heated, then a plot of D V vs. OT can be produced, the slope of which is the negative of the measured

Seebeck coefficient, see Figure A.3 (a). Each DT therefore represents a different average defect population. It has been shown that as long as OT is remarkably small, the Seebeck coefficient will be independent of the experimental conditions [106] .

There are two ways to deal with the changing of the average point defect population during measurements, either through data corrections or changes in experimental techniques.

In terms of experimental methods, if the furnace temperature can be reduced while an auxillary heater can increase the temperature of the hot zone, the average temperature can be maintained, see Figure A.3 (b) [107] . An alternative is to pulse the hot end temperatures by a rapid, short duration influx of heat. Since thermal equilibrium occurs at a quicker rate than point defect equilibrium, the measurements can be taken during the reduction of the transient thermal gradient, thus maintaining the bulk defect population over the unaffected region of the sample [107] . 136

(a) (b)

z~ "— ~ 7'~,„,~

Figure A.3: Temperature vs. thermal gradient in (a) conventional and (b) straddle methods, with the filled circles representing the steady-state straddle method [107J

While the above experimental techniques are indeed effective, they are require sophisticated equipment. An alternative approach is called the "steady state straddle" approach. This method utilizes afour-point set-up and in which the sample is placed in the natural thermal gradient near the hot zone of the furnace. These four-points lead to six combinations of electrodes/thermocouples and thus to six corresponding DT `s and D V `s.

There will be one maximum, two large, one medium, and two small OT readings. Therefore, for each OT above the average sample temperature, there is a OT below it, thus canceling any inhomogeneities [107] .

Experimental ~ V vs. OT data tend to follow a straight line similar to Figure A.4. This slope of this line is the negative of the Seebeck coefficient while the x-intercept is the ~T°ffset.

If the correlation factor, r2, is less than 0.99 or the OT°ffset is greater than 1 °C, then there is a good possibility that the thermocouples are contaminated [107] . 137

Figure A.4: Sample thermoelectric plot utilizing steady-state straddle method [107]

When examining the error in thermoelectric measurements, the major source of error comes from OT, in which both geometric and thermal components must be taken into account. Experiments have suggested that individual temperatures can be recorded to ~ 0.5

°C such that OTcan be measured to ~ 1.0 °C. This corresponds to an 10% uncertainty with a maximum gradient of 10 °C and a S% uncertainty with a maximum gradient of 20 °C. An excellent estimate of the overall experimental uncertainty can be determined by dividing the

0 T°ffset by the ~ TmaX [107 ] .

Another correction that must be taken into account involves the reference wire. Since the measured Seebeck coefficient is a combination of both the sample and the reference wire, the value from the reference wire must be subtracted. If the reference wire is platinum, that corresponds to the following:

Equation A.20 Sm = SS — SPt , 138

where the subscripts denote the measured, sample, and platinum (~ -20µV/K at 1000 °C) values [107]. 139

REFERENCES

1. Lewis, B.G. and D.C. Paine, Applications and processing of transparent conducting oxides. MRS Bulletin, 2000: p. 22-27. 2. Ginley, D.S. and C. Bright, Transparent conducting oxides. MRS Bulletin, 2000: p. 15-18. 3. Haacke, G., Transparent conducting coatings. Annual Review of Material Science, 1977.7: p. 73-93. 4. Hartnage, H.L., Semiconducting Transparent Thin Films. 1995, London: Institute of Physics Publishing. 5. Hummel, R.E., Electronic Properties of Materials. 3rd ed. 2001, New York: Springer. 6. Tahar, R., et al., Tin doped indium oxide thin films: Electrical properties. Journal of Applied Physics, 1997. 83(5): p. 2631-2645. 7. Phillips, J.M., et al., Transparent conducting thin films of GaInO3. Applied Physics Letters, 1994. 65(1): p. 115-117. 8. Omata, T., New ultraviolet-transparent electroconductive oxide, ZnGa2O4 spinel. Applied Physics Letters, 1994.64(9): p. 1077-1078. 9. Mohanavelu, R., A.P. Constant, and D.P. Cann. Synthesis of new pyrochlore compounds for transparent conductor applications. in Proceedings of the 9th US- Japan Seminar on Dielectric and Piezoelectric Ceramics. 1999. Okinawa, Japan. 10. Kawazoe, H., et al., p-Type electrical conduction in transparent thin films of CuAlO2. Nature, 1997.389: p. 939-942. 11. Ueda, K., et al., Epitaxial growth of transparent p-type conducting CuGaO2 thin films on sapphire (001) substrates by pulsed laser deposition. Journal of Applied Physics, 2001. 89(3): p. 1790-1793. 12. Duan, N., et al., Transparent p-type conducting CuScO2+x films. Applied Physics Letters, 2000. 77(9): p. 1325-1326. 13. Shannon, R.D., D.B. Rogers, and C.T. Prewitt, Chemistry of noble metal oxides. I. Synthesis and properties of ABO2 delafossite compounds. Inorganic Chemistry, 1971. 10(4): p. 713-718. 14. Rogers, D.B., et al., Chemistry of noble metal oxides. III. Electrical transport properties and crystal chemistry of ABOZ compounds with the delafossite structure. Inorganic Chemistry, 1971. 10(4): p. 723-727. 15. Buljan, A., P. Alemany, and E. Ruiz, Electronic structure and bonding in CuMO2 (M = Al, Ga, Y) delafossite-type oxides: An Ab initio study. Journal of Physics Chemistry B, 1999. 103: p. 8060-8066. 16. Benko, F.A. and F.P. Koffyberg, Opto-electronic properties of p- and n-type delafossite CuFeO2. Journal of Physics and Chemistry of Solids, 1987.48(5): p. 431- 434. 17. Jacob, A., et al., Luminescent properties of delafossite-type oxides LaCuO2 and YCuO2. Solid State Communications, 1997. 103(9): p. 529-532. 140

18. Tanaka, K., et al., Origin of the metallic conductivity in PdCoO2 with delafossite structure. Physica B, 1998. 245: p. 157-163. 19. Seshadri, R., et al., Metal-Metal bonding and metallic behavior in some ABO2 delafossties. Chemistry of Materials, 1998. 10: p. 2189-2196. 20. Dordor, P., et al., Crystal growth and electrical properties of CuFeO2 single crystals. Journal of Solid State Chemistry, 1988. 75: p. 105 -112. 21. Doumerc, J.P., et al., Luminescence of the Cu+ ion in CuLaO2. Journal of the Less- Common Metals, 1989. 148: p. 333-337. 22. Doumerc, J.P., et al., Sur l'existence d'oxydes et de solutions solides de structure delafossite. Materials Research Bulletin, 1992.27: p. 39-43. 23. Effenberger, H., Structure of hexagonal copper(I) ferrite. Acta Crystallographica, 1991. C47: p. 2644-2646. 24. Elazhari, M., et al., Oxidation at low temperature of some delafossite-type oxides CuMO2 (M = Sc, Ga, Y, La, Nd, Lao.sYo.$)• European Journal of Solid State Inorganic Chemistry, 1997.34: p. 503-509. 25. Boutinaud, P., et al., Energy levels of Cu+ in the oxide insulators CuLaO2 and CuZr2(PO4)3. Journal of Physics and Chemistry of Solids, 1995.56(9): p. 1147-1154. 26. Gong, H., Y. Wang, and Y. Luo, Nanocrystalline p-type transparent Cu Al-O semiconductor prepared by chemical-vapor deposition with Cu(acac)2 and Al(acac)3 precursors. Applied Physics Letters, 2000.76(26): p. 3959-3961. 27. Isawa, K., et al., Thermoelectric power ofdelafossite-derived compounds, RCuO2+S (R = Y, La, Pr, Nd, Sm, and Eu). Phsical Review B, 1998.57(13): p. 7950-7954. 28. Kandpal, H. and R. Seshadri, First principles electronic structure of the delafossites dlo_dlo ABO2 (A=Cu, Ag, Au; B=AI, Ga, Sc, In, Y): evolution of interactions. Solid State Sciences, 2002.4: p. 1045-1052. 29. Kuhn, P., A. Reller, and H.R. Oswald, Synthesis, structure and thermal reduction behavior of delafosstte-type CuRhxAll x0 2. Journal of the Less-Common Metals, 1988. 137: p. 231-239. 30. Lalic, M.V., et al., Changes induced by the presence of Zn or Ni impurity at Cu sites in CuAlO2 delafossite. Solid State Communications, 2003. 125: p. 175-178. 31. Nagarajan, R., et al., New CuM2~3Sb1~3O2 and AgM2~3Sb1~3O2 compounds with the delafossite structure. Solid State Sciences, 2002.4: p. 787-792. 32. Prewitt, C.T., R.D. Shannon, and D.B. Rogers, Chemistry of noble metal oxides. Il. Crystal structures of PtCoO2, PdCoO2, CuFeO2, and AgFeO2. Inorganic Chemistry, 1971. 10(4): p. 719-723. 33. Trari, M., et al., Oxidation of delafossite-type compounds by chimie douce. Annales de Chimie, 1994. 19(7-8): p. 521-524. 34. Trari, M., et al., Room temperature chemical oxidation of delafossite-type oxides. Journal of Solid State Chemistry, 1994. 111: p. 104-110. 35. Kudo, A., et al., Fabrication of transparent p-n heterojunction thin film diodes based entirely on oxide semiconductors. Applied Physics Letters, 1999. 75(18): p. 2851- 2853. 36. Yanagi, H., et al., Chemical design and thin film preparation of p-type conductive transparent oxides. Journal of Electroceramics, 2000.4(2/3): p. 407-414. 141

37. Nie, X., S. Wei, and S.B. Zhang, Bipolar doping and band-gap anomalies in delafossite transparent conductive oxides. Physical Review Letters, 2002. 88(6): p. 066405-1 - 066405-4. 38. Yanagi, H., et al. Transparent p- and n-type conductive oxides with delafossite structure. in Materials Research Society Symposium Proceedings. 2000. 39. Robertson, J., et al., Electronic structure of p-type conducting transparent oxides. Thin Solid Films, 2002.411: p. 96-100. 40. Yanagi, H., K. Ueda, and H. Hosono, Electrical transport properties and electronic structure of transparent conductive oxides with delafossite structure. Transactions of the Materials Research Society of Japan, 2001.26(3): p. 997-1000. 41. Kawazoe, H., et al., Transparent p-type conducting oxides: Design andfabrication of p-n heterojunctions. MRS Bulletin, 2000: p. 28-36. 42. Benko, F.A. and F.P. Koffyberg, Opto-electronic properties of CuAlO2. Journal of Physics and Chemistry of Solids, 1984.45(1): p. 57-59. 43. Ingram, B.J., et al., Electronic structure and small polaron hole transport of copper aluminate. Phsical Review B, 2001. 64(155114): p. 1-7. 44. Ishiguro, T., et al., High temperature structural investigation of the delafossite type compound CuAlO2. Journal of Solid State Chemistry, 1982.41: p. 132-137. 45. Ishiguro, T., et al., Single-crystal growth and crystal structure refinement of CuAlO2. Journal of Solid State Chemistry, 1981.40: p. 170-174. 46. Ishiguro, T., et al., Charge-density distribution in crystals of CuAlO2 with d-s hybridization. Acta Crystallographica, 1983. B39: p. 564-569. 47. Attili, R.N., et al., Delafossite oxides ABO2 (A = Ag, Cu; B = Al, Cr, Fe, In, Nd, Y) studied byperturbed-angular-correlation spectroscopy using a I11Ag(~-)II1Cd probe. Phsical Review B, 1998. 58(5): p. 2563-2569. 48. Yanagi, H., et al., Electronic structure and optoelectronic properties of transparent p- type conducting CuAlO2. Journal of Applied Physics, 2000. 88(7): p. 4159-4163. 49. Stauber, R.E., et al. Growth and chemical substitution of transparent p-type CuAlO2. in Materials Research Society Symposium Proceedings. 2000. 50. Lalic, M.V., et al., Influence of Cd impurity on the electronic properties of CuAlO2 delafossite:first principles calculations. Journal of Physics: Condensed Matter, 2002. 14: p. 5517-5528. 51. Benko, F.A. and F.P. Koffyberg, The optical interband transitions of the semiconductor CuGaO2. Physica Status Solidi, A, Applied Research, 1986. 94: p. 231-234. 52. Shimode, M., et al., Ion exchange synthesis and structure of new delafosstite-type Culn D2. Materials Transactions, JIM, 2000.41(9): p. 1111-1113. 53. Shimode, M., M. Sasaki, and K. Mukaida, Synthesis of the delafossite-type CuInD2. Journal of Solid State Chemistry, 2000. 151: p. 16-20. 54. Hosono, H., et al., Frontier of transparent conductive oxide thin films. Vacuum, 2002. 66: p. 419-425. 55. Yanagi, H., et al., Bipolarity in electrical conduction of transparent oxide semiconductor CuInO2 with delafosste structure. Applied Physics Letters, 2001. 78(11): p. 1583-1585. 142

56. Yanagi, H., et al., Fabrication of all oxide transparent p-n homojunction using bipolar CuInO2 semiconducting oxide with delafossite structure. Solid State Communications, 2002. 121: p. 15-18. 57. Tate, J., et al., P-type oxides for use in transparent diodes. Thin Solid Films, 2002. 411: p. 119-124. 58. Johnson, L.F. and M.B. Moran. Infrared transparent conductive oxides. in Window and Dome Technologies and Materials VII. 2001. 59. Haacke, G., New figure of merit for transparent conductors. Journal of Applied Physics, 1976.47(9): p. 4086-4089. 60. Gordon, R.G., Criteria for choosing transparent conductors. MRS Bulletin, 2000: p. 52-57. 61. Cann, D.P., Unpublished. 2001, Iowa State University. 62. Kasap, S.O., Principles of Electronic Materials and Devices. Second ed. 2000, Dubuque: McGraw-Hill. 63. Hosono, H., et al., Workt'ng hypothesis to explore novel wide band gap electrically conducting amorphous oxides and samples. Journal ofNon-Crystalline Solids, 1996. 198-200: p. 165-169. 64. Kawazoe, H. and K. Ueda, Transparent conducting oxides based on the spinel structure. Journal of the American Ceramic Society, 1999.82(12): p. 3330-3336. 65. Chopra, K.L., S. Major, and D.K. Pandya, Transparent conductors - A status review. Thin Solid Films, 1983. 102: p. 1-46. 66. Coutts, T.J., D.L. Young, and X. Li, Characterization of transparent conducting oxides. MRS Bulletin, 2000: p. 58-65. 67. Pabst, A., Notes on the structure of delafossite. American Mineralogist, 1946.31: p. 539-546. 68. Galakhov, V.R., et al., Valence-band spectra and electronic structure of CuFeO2. Physical Review B, 1997.56(8): p. 4584-4591. 69. Tanaka, K., M. Hasegawa, and H. Takei, Crystal growth of PdCoO2, PtCoO2 and their solid solution with delafossite structure. Journal of Crystal Growth, 1997. 173: p. 440-445. 70. Orgel, L.E., An Introduction to Transition Metal Chemistry Ligand--Field Theory. 1960, New York: John Wiley &Sons Inc. 71. Dunn, T.M., D.S. McClure, and R.G. Pearson, Some Aspects of Crystal Field Theory. 1965, New York: Harper &Row Publishers. 72. Zhang, S.B., S. Wei, and A. Zunger, A phenomenological modelfor systematization and prediction of doping limits in II- VI and I-III- VI2 compounds. Journal of Applied Physics, 1998. 83(6): p. 3192-3196. 73. Zhang, S.B., S. Wei, and A. Zunger, Microscopic origin of the phenomenological equilibrium "doping limit rule" in n-type III-V semiconductors. Physical Review Letters, 2000. 84(6): p. 1232-1235. 74. Blumenthal, R.N. and M.A. Seitz, Experimental Techniques, in Electrical Conductivity in Ceramics and Glass, Part A, N.M. Tallan, Editor. 1974, Marcel Dekker, Inc.: New York. 75. Ishiguro, T., et al., A new delafossite-type compound CYO2. Journal of Solid State Chemistry, 1983.49: p. 232-236. 143

76. Berko, F.A. and F.P. Koffyberg, The optical bandgap and band-edge positions of semiconducting p-type CuY02. Canadian Journal of Physics, 1985. 63: p. 1306-1308. 77. Isawa, K., et al., Synthesis ofdelafossite-derived phases, RCu02+with R = Y, La, Pr, Nd, Sm and Eu, and observations of spin-gap-like behavior. Physical Review B, 1997.56(6): p. 3457-3466. 78. Nagarajan, R., et al., P-type conductivity in CuCrl xMgx0 2 films and powders. Journal of Applied Physics, 2001. 89(12): p. 8022-8025. 79. Berko, F.A. and F.P. Koffyberg, Preparation and opto-electronic properties of semiconducting CuCr02. Materials Research Bulletin, 1986. 21: p. 753-757. 80. Ashmore, N.A., J.E. Clayton, and D.P. Cann, Synthesis and processing ofAgln02 delafossite by cation exchance reactions. Thin Solid Films, 2002.411: p. 140-146. 81. Sturzenegger, M. and H.R. Oswald, Thermochemical resistivity of delafossite-type AgNio.STio.s02 and CuNio.STio.s02. Solid State Ionics, 1993. 63-65: p. 274-280. 82. Holland, T. and S. Redfern, UnitCell. 1998. 83. Cullity, B.D., Elements of X-ray Diffraction. 1978, Don Mills, Ontario: Addison- Wesley Publishing Company, Inc. 84. Hunter, B., Rietica. 1997. 85. Jacob, K.T. and C.B. Alcock, Thermodynamics of CuAl02 and CuA120 4 and phase equilibria in the system Cu20-Cu0A1 20 3. Journal of the American Ceramic Society, 1975.58(5-6): p. 192-195. 86. Jacob, K.T. and C.B. Alcock, Thermodynamics and phase equilibria in the system Cu20-Cu0-(~3)GaZ0 3. Revue Internationale des Hautes Temperatures et det Refractaires, 1976. 13(1): p. 37-42. 87. Krawitz, A.D., Introduction to diffraction in materials science and engineering. 2001, New York: John Wiley &Sons, Inc. 88. Smyth, D.M., The effects of dopants on the properties of metal oxides. Solid State Ionics, 2000. 129: p. 5-12. 89. Weller, M., Defects in oxide ceramics and their characterization Part I. General properties of oxides. Journal of Materials Education, 1995. 17: p. 1-32. 90. Brouwer, G., A general asymptotic solution of research equations common in solid- state chemistry. Philips Research Report, 1954. 9: p. 366-376. 91. Mason, T.O. and B.J. Ingram, Interstitial radius in Cu-based delafossites, R.B. Gall, Editor. 2003: Evanston, IL. 92. Bosman, A.J. and H.J. van Daal, Smallpolaron versus band conduction in some transition-metal oxides. Advances in Physics, 1970. 19(77): p. 1-116. 93. Reed, J.S., Principles of Ceramic Processing. Second ed. 1995, New York: John Wiley &Sons, Inc. 94. McLachlan, D.S., M. Blaskiewicz, and R.E. Newnham, Electrical resistivity of composites. Journal of the American Ceramic Society, 1990. 73(8): p. 2187-2203. 95. Pankove, J.I., Optical Processes in Semiconductors. 1971, Englewood Cliffs, N.J.: Prentice-Hall. 96. Thomas, G.A., Invisible circuits. Nature, 1997. 389: p. 907-908. 97. Edwards, D.D., P.E. Folkins, and T.O. Mason, Phase equilibria in the Ga20 3-In20 3 system. Journal of the American Ceramic Society, 1997.80(1): p. 253-257. 98. Holland, T. and S. Redfern, A brief guide to using the regression diagnostics. 1998. 144

99. Seebeck, T.J., Magnetic polarization of metals and minerals. Abhandlungen der Deutschen Akademie der Wissenschaften zu Berlin, 1822-1823: p. 265. 100. Rowe, D.M., Introduction, in CRC Handbook of Thermoelectrics, D.M. Rowe, Editor. 1995, CRC Press: New York. p. 1-5. 101. Ioffe, A.F., Semiconductor Thermoelements and Thermoelectric Cooling. 1956, London: Infosearch Limited. 102. Peltier, J.C., Nouvelles experiences sur la caloricite des courans electrique. Annales de Chimie, 1834. LV1: p. 371. 103. Cook, B.A., A comparison of thermoelectric phenomena in diverse alloy systems, in Materials Science and Engineering. 1999, Iowa State University: Ames. 104. Nell, J., et al., Jonker-type analysis of small polaron conductors. Journal of Solid State Chemistry, 1989. 82: p. 247-254. 105. Tuller, H.L. and A.S. Nowick, Small polaron electron transport in reduced CeO2 single crystals. Journal of the American Ceramic Society, 1977.38: p. 859-867. 106. Wagner, C., Thermoelectric power of cells with ionic compounds involving ionic and electronic conduction. Progress in Solid State Chemistry, 1972. 7: p. 1-37. 107. Hong, B.S., S.J. Ford, and T.O. Mason, Equilibrium electrical property measurements in electroceramics. Key Engineering Materials, 1997. 125-126: p. 163- 186. 145

ACI~~TOWLEDGEMENTS

Throughout the course of this work, there have been numerous people that have assisted me, supported me, and motivated me to achieve my goals. I would first like to thank my major professor Dr. David Cann, for without whom I would probably have been able to

leave Iowa sooner. While this is most certainly the case, I have enjoyed the opportunities

and appreciated the support he has given me throughout this work. Finally, the friendship

that has developed here and will soon be moving on is something that I'll never forget. I

would also like to thank my committee members, Dr. Gordon Miller and Dr. Steve Martin.

Their insightful comments and honest answers have been an asset to this work and the work

to follow.

I would like to thank Lanny Lincoln for his technical assistance and tips on fishing,

Scott Schlorholz for his insight on ~:RD, and Joel Harringa for his assistance with the

thermoelectric measurements. I would also like to thank Jason Saienga and Chad Martindale

for their help with the electrical and optical measurements throughout this work.

I must also thank the members of my group from over the years: Jane Clayton,

Charles Chao, Tiffany Byrne, Nathan Ashmore, Meagen Marquardt, Seymen Aygun, and

Naratip. Their lighthearted discussions abilities to put things in perspective have made my

time and work here more enjoyable. In addition, I must thank Carmen Neri, Krista Briley,

and Lynne Weldon for their tremendous patience with my many questions and needs.

My friendships to Joe Schramm and Melbs LeMieux must also be thanked. Their

company for many lunches, late nights, and long Sunday afternoons kept me sane over the

years. To my many other friends over the years, I must also pay tribute, for they have made

me laugh, encouraged my decisions, and taught me lessons. I must also thank my brother 146

and grandparents for their golf matches over the years, their continued support, and their tremendous insight into my past and future decisions.

Finally I must thank my parents. Not only for their financial contributions for rent

and education, but for their love and support that have made me the man I am today. You

have been my role models and my friends over the years and for that I axn truly thankful.