Native Defects in CdO and CdCuO Alloys

by

Derrick Tyson Speaks

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Doctor of Philosophy

in

Engineering ‐ Materials Science and Engineering

in the

Graduate Division

of the

University of California, Berkeley

Committee in charge:

Professor Eugene E. Haller, Chair Dr. Wladyslaw Walukiewicz Professor Samuel S. Mao Professor Yuri Suzuki

Spring 2011

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Abstract

Nat i ve Defec t s i n CdO and CdCuO A l loys B y

Der r i ck Tyson Speaks

Do c t o r o f P h i l o s o p h y i n E n g i n e e r i n g ‐ Ma t e r i a l s S c i e n c e a n d E n g i n e e r i n g

Un i v e r s i t y o f C a l i f o r n i a , B e r k e l e y P r o f e s s o r E u g e n e E . H a l l e r , C h a i r

Indium tin oxide (ITO) is the most extensively researched and most commonly used transparent conductive oxide. Despite ITO’s popularity its long term use by industry presents several significant challenges. Indium is an expensive and a non‐abundant metal. The demand for optoelectronic devices is growing far faster than the supply of indium. In the future, this will result in even higher prices for an already expensive material. In addition to cost, ITO has a critical performance flaw. All ITO films and current substitutes for ITO, such as doped zinc oxide and doped tin oxide, achieve low resistivies because they have very high carrier concentrations, not because they have very high mobilities. Significant free carrier absorption exists in the low energy portion of the visible and near infrared solar spectrum. For many devices, this results in a loss of transparency that can negatively affect device performance.

Cadmium oxide (CdO) does not suffer from either the cost or the performance limitation of ITO. CdO displays exceptional mobilities that are approximately five times greater than most ITO. This means free carrier absorption is significantly reduced. Despite CdO’s promise, it has not displaced ITO in the market. The main reason is that this material is not well understood. Before a new transparent conductive oxide is used in a device, a detailed understanding of the optimal deposition parameters, defect behavior, dopant behavior and processing behavior all have to be established. The goal of this work is to provide that understanding. It is shown that the amphoteric defect model can be used to provide a unified explanation for several unresolved questions in CdO, namely, why the carrier concentration in CdO is typically between 2*1019 to 2*1020 cm‐3, why no p‐type films have been fabricated and why there is such a large spread in the reported optical absorption edge, ranging from 2.2 to 2.6 eV. In addition, the optimal deposition and annealing conditions have been determined which yield the lowest carrier concentration and highest mobility undoped CdO ever published. This is an important step for commercialization. Finally, the influence of high doses of irradiation on CdO and CdCuO is considered. Here, it is shown that irradiation provides a method to increase the optical absorption edge and reduce the resistivity by increasing the number of free carriers. However the irradiation dose must be carefully chosen because doses that are too small provide little improvement whiles doses that are too large lead to poor optical performance.

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Table of Contents

1. INTRODUCTION ___________________________________________________ 1

1.1. Energy Has No Substitute_________________________________________ 1

1.2. Energy Only Gets More Expensive__________________________________ 1

1.3. Optoelectronic Devices __________________________________________ 2

1.4. Replacing Indium Tin Oxide _______________________________________ 4

1.5. Early CdO Work ________________________________________________ 4

1.6. Overview______________________________________________________ 5

2. TRANSPARENT CONDUCTIVE MATERIALS_______________________________ 6

2.1. Transparent Conductors and Their Common Applications ______________ 6

2.2. Thin Metal Transparent Conductors ________________________________ 9

2.3. Conjugated Polymer Transparent Conductors _______________________ 10

2.4. Semiconductor Transparent Conductors____________________________ 11

2.5. Transport in Transparent Conductors ______________________________ 12 2.5.1. Conductivity and Scattering in Transparent Conductors ______________ 12 2.5.2. The Total Mobility, a Sum of the Parts ____________________________ 16

2.6. Figure of Merit for Transparent Conductors_________________________ 17 2.6.1. Basic Figure of Merit Definition _________________________________ 17 2.6.2. Alternative Figure of Merit _____________________________________ 18 2.6.3. Optimal Film Thickness ________________________________________ 18 2.6.4. Balancing the Optical and Electrical Properties _____________________ 19 2.6.5. Figure of Merit for Common Transparent Conductors________________ 20 2.6.6. Maximizing the Figure of Merit _________________________________ 22 2.6.6.1. Influence of the Effective Mass _____________________________ 24 2.6.6.2. Influence of the Mobility __________________________________ 25

2.7. Which Dopants to Use in Transparent Conductors?___________________ 26 2.7.1. Metallic Dopants in N‐type Semiconductors _______________________ 26

2.8. Limitations of the Current Technology _____________________________ 27 2.8.1. Transparent Conductive Oxides After Indium Tin Oxide ______________ 27

3. RESULTS ________________________________________________________ 32

3.1. Objective: Optimizing CdO_______________________________________ 32

3.2. Defects in Semiconductors ______________________________________ 33 3.2.1. Defects and Irradiation ________________________________________ 33 3.2.3. Shallow Levels_______________________________________________ 34

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3.2.3. Deep Levels _________________________________________________ 35

3.3. The Influence of Native Defects___________________________________ 36 3.3.1. Defect Induced Free Carrier Stabilization__________________________ 36 3.3.2. Fermi Level Dependent Defect Formation Energy ___________________ 37 3.3.3. The Amphoteric Defect Model __________________________________ 41

3.4. Film Deposition _______________________________________________ 43 3.4.1. Pulsed Laser Deposition of CdO Thin Films ________________________ 43 3.4.2. Deposition Temperature_______________________________________ 44 3.4.3. Annealing __________________________________________________ 50

3.5. Ion Irradiation in CdO___________________________________________ 53 2.5.1. Displacement Damage Dose____________________________________ 53 3.5.2. Fermi Stabilization Energy in CdO________________________________ 55 3.5.3. Light vs Heavy Ion Irradiation ___________________________________ 56 3.5.4. Metastable vs Equilibrium _____________________________________ 57 3.5.5. Defect Formation Rate ________________________________________ 58 3.5.6. Mass of Irradiating Ion ________________________________________ 59 3.5.7. The Metastable State _________________________________________ 60 3.5.8. Role of Anion Vacancies _______________________________________ 63

3.6. Modeling the Optical Properties of CdO____________________________ 65 3.6.1. Variation in the Optical Absorption Edge __________________________ 65 3.6.2. The Burstein‐Moss Effect ______________________________________ 66 3.6.3. Modeling the Optical Absorption Edge____________________________ 69 3.6.4. Free Carrier Absorption _______________________________________ 71

3.7. Carrier Concentrations Beyond the EFS Limit ________________________ 76 3.7.1. Carbon in CdO and Cd0.81Cu0.19O_________________________________ 76 3.7.2. Carrier Concentrations Above Saturation__________________________ 82 3.7.3. Vacancy and Implanted C Concentrations _________________________ 83 3.7.4. Annealing __________________________________________________ 85 3.7.5. Altering the Density of States in CdO and CdCuO ___________________ 88

4. CONCLUSIONS ___________________________________________________ 94

5. REFERENCES _____________________________________________________ 96

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Acknowledgements There are several people I would like to thank that made this research possible and my experience here at Berkeley enjoyable. I was fortunate enough to have three amazing advisors. I have learned a tremendous amount from Dr Wladek Walukiewicz in my time here. Wladek supported me not just in the work presented here, but also on a huge number of other projects. I was always impressed that no matter what I was working on, or how confusing the data might seem at first, Wladek always had thoughtful insights to help guide me towards the next steps in our research. Professor Sam Mao also made significant contributions to this work for which I am grateful. Professor Mao was instrumental in supporting me in the area of film deposition. This was critical not just for me and my projects, but for many other people in the Materials Science Department as well as at the Advanced Light Source. I would also like to thank Professor Eugene Haller. If I had questions about semiconductors, malfunctioning laboratory equipment or European cheeses and chocolates, I was confident that Eugene would know the answer…and he always did.

In addition to my advisors, I would like to thank Dr Kin Man Yu. Kin provided significant support over the years. I am glad I had the opportunity to work with him. Professor Suzuki and Professor Dubon, while technically not my advisors, often played that role for me. I appreciate all of their help. I also want to thank Jeff Beeman. Jeff was incredibly helpful and he performed an amazing number irradiation steps for me. He never once complained about either the crazy number of films I gave him for irradiation or the fact that I never actually paid him…well ok, he never complained too loudly I guess. Thanks Jeff! In addition, David Hom also deserves significant thanks. David always made sure that my paperwork was taken care of at Lawrence Berkeley National Laboratory and that I got paid. That may sound trivial, but it was not. Occasionally, David had to wade through large amounts of red tape here to see that funds got moved correctly from one division to another, and I know that was a lot of work.

I would also like to thank my friends and family. My parents and my two sisters, Natalie and Rachel, provided critical support for me over the years. I have not forgotten that. Finally, there are five students here that made my graduate experience truly amazing: Coleman, Jessica, Joanne, Franklin and Marie. Thanks everyone.

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1. Introduction

1 . 1 . Ene r g y Ha s No Sub s t i t u t e

Research in energy is, in many ways, more critical to society’s well being than other applications. Energy is fundamental to modern industrialized societies; modern economies simply would not exist without an inexpensive energy source. People typically live far from their place of work, and since few people run or bike to work, most require large amounts of energy every working day, before they even start their job. High tech products require energy to make and most come with a battery or an electrical cord; they constantly require some amount of energy. Even non‐high tech products require large amounts of energy. Food, for example, not only takes large amounts of energy to grow and harvest, but it is typically shipped hundreds of miles before the consumer even sees the product on the store shelves. This produces a product that is energy intensive. In the U0S, most manufactured goods such as TV’s, clothes and cell phones are almost always made overseas. They must be shipped thousands of miles from the producer to the consumer, and the producer often ships more than just the final products to the consumer: in many cases they must ship in a portion of the raw materials for the production. This process of separating the consumers from the producers is central to globalization, allowing rich world consumers to take advantage of low labor costs and third world people to be employed outside of agriculture. It allows capital and investments to flow from rich to poor countries and less expensive goods to flow from poor countries to rich countries. However, this process only works if there is a cheap energy source, otherwise transaction costs severely limit the amount of economic value that can be derived.

The connection between cheap energy and the rise of modern, complex economies is well documented. Most scholars accept that the rise of the modern economy with the industrialization of Europe was made possible by the discovery of cheap and abundant energy—fossil fuels such as coal and oil. So it seems reasonable to suggest that a fall in the supply of cheap energy would be a major factor that could cause a decline in the global economic output and, thus, a decline in the societies that are built from it. This is because, while consumer substitution does exist, it is only between different forms of energy (i.e., oil to natural gas, or fossil fuels to nuclear or solar sources), the choice between “energy” and “no energy” often is not a choice, or at least, not a good choice people want to have to make. Since economic output is so dependant on energy, a fall in the availability of energy would necessary lead to a collective loss in the standard of living for everyone.

1 . 2 . Ene r g y On l y Ge t s More E xpen s i v e

The global demand for energy in general, and oil in particular, is expected to continue its dramatic rise as the industrialization of Asia continues and combines with steady (i.e., non‐negative) demand in the West. Given that the supply is not expected to grow at the same rate

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as demand, this imbalance will have to be reflected in a higher future price for all forms of energy. Higher energy prices are expected to shift down the demand curve for products that use large quantities of this more expensive energy and shift up the demand curve for energy efficient products that either reduce energy demand or increase energy supply. Thus, this future shift in the price of energy will have a dramatic influence on the types and quantities of goods people consume in the future as consumers attempt to substitute out of consuming this more expensive good, energy. Optoelectronic devices are an important technology that can help advanced economies transition away from fossil fuels.

1 . 3 . Op toe l e c t r on i c Dev i c e s

Optoelectronic devices are systems where controlling both photonic and electronic properties are critically important and they often play an important role in energy technology. But optoelectronic devices are not just an important technology for the future; they are also used extensively today. Such devices include photovoltaics and flat panel displays, both of which have huge market capitalizations. In 2008, the world market for flat panel displays stood at just over 100 billion dollars [1] with the global PV market at 40 billion dollars [2] (normalized to the value of the US dollar in 2009). To put that in perspective, automobiles typically have one of the largest market capitalizations of any industry for industrialized societies, and in 2008, the world market for automobiles was 1,479.5 billion dollars [3]. This means that the world spends almost one dollar on solar cells and flat panel displays for every ten dollars it spends on automobiles. This is a remarkable sum of capital, as few other industries could even approach this 1/10 ratio. Looking forward, it is expected that the optoelectronic industry will grow in both relative and absolute value, consuming an even larger fraction of the world’s economic output, necessarily at the expense of other industries. This is because it is expected that the global market price for energy will dramatically increase in the next several decades and optoelectronic materials often play and important role in key energy technologies.

As societies shift their consumption from one set of goods to another, production and research dollars flow to support this. Collectively, optoelectronic devices should represent a larger fraction of the global economic output, in terms of market capitalization and research dollars spent, because higher energy prices are either a neutral or net positive to the optoelectronic industry, depending on the product of interest. For example, the growth in flat panel displays is fairly flat as seen by the market capitalization in the Figure 1, the only major shift occurred during the height of the global recession between 2008 and 2009.

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Figure 1: Global market capitalization of flat panel displays.

The higher future price of oil is not expected to have a dramatic effect on the size of the display market because it is not a good for which people can use to substitute oil for. Thus, it is expected that the growth in the display market will mirror rising wages, i.e., growth should be small or negative in the West and high in the East.

It is the photovoltaic market that is expected to increase dramatically over the next few decades. As consumers attempt to substitute out of the consumption of oil, solar cells, as an energy source, can be a direct replacement for fossil fuels in certain applications. Consumers often pick the cheapest option between commodities so, for solar energy to be successful, it does not have to be “cheap” it just has to be “cheaper” than the next best option. It is expected that with the rise in energy prices globally, and the fall in the cost of solar energy due to increase efficiency, this point will soon be reached.

This sharp increase in the photovoltaic market size has already been seen in recent years, as illustrated in Table 1.

Table 1: Photovoltaic shipments in kilowatts for the US and the number companies either importing or producing domestically [4].

Year Number of Companies Imports

Domestically Manufactured Total

2000 21 8,821 79,400 88,221 2001 19 10,204 87,462 97,666 2002 19 7,297 104,793 112,090 2003 20 9,731 99,626 109,357 2004 19 47,703 133,413 181,116 2005 29 90,981 135,935 226,916 2006 41 173,977 163,291 337,268 2007 46 238,018 279,666 517,684 2008 66 586,558 339,947 986,504 2009 101 743,414 539,146 1,282,560

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As stated above, it is this author’s opinion that this growth in the photovolatic industry is not temporary, rather, it is expected to continue as the global market for energy continues to grow rapidly. In order to maintain this growth, costs have to fall, and for this to happen, more intensive research on solar cells needs to be conducted. While there are many different areas that need improvement to reduce the cost of solar energy, one key area is the transparent conductive layer. The following sections will discuss optoelectronic devices in detail the limitations of commercially available transparent conductors.

1 . 4 . Rep l a c i n g I n d i um T i n Ox i de

The dominant transparent conductor in the PV industry is indium tin oxide or ITO. ITO is indium oxide alloyed with several percent tin. ITO is successful because it has low resistivities, typically in the 10‐4 Ωcm range. Previously, higher PV cell cost and smaller market size meant that the properties of ITO were good enough to meet device standards. However, looking forward, for the rapid growth in the PV industry to be maintained, the limitations of ITO must finally be addressed. In particular, there are three critical issues with ITO, two concern cost, and one performance. Indium is an expensive element, using an alloy composed primarily of indium oxide will always result in high device cost. In addition to high material cost, the minimum resistivity in ITO has been reached decades ago. This means that ITO films simply cannot be made any thinner. Ideally, the transparent conductor would have lower resistivities, which would allow thinner, and less expensive, transparent conductor layers to be fabricated. For example, if the next generation transparent conductor could be made with resistivies in the 10‐5 Ωcm range, then all other things being equal, the material cost would fall by a factor of 10 as only 1/10th of the material would be needed. The final deficiency of ITO is that is has significant free carrier absorption, which limits the transmission in the low energy portion of the visible spectrum as well as the in the infrared. The goal of this research is to investigate a new transparent conductive material that will address all of these issues in an effort to design a replacement for ITO. Cadmium oxide (CdO) is one possible candidate to replace indium oxide. The next section will discuss the previous work on CdO, which is very limited. Because CdO is not a well studied material, additional research must be conducted in order to develop a detailed understanding of CdO. This will be necessary if cadmium oxide is to replace indium oxide.

1 . 5 . Ea r l y CdO Work

CdO was first discovered in 1907 when K. Badeker, then a PhD student at the University of Jena, oxidized cadmium metal in a glow discharge chamber [5, 6]. Badeker discovered something quite remarkable for the day; he fabricated a material that was optically transparent and electrically conductive. Badeker had fabricated the first transparent conductive oxide. Up until that point, optical transparency and electrical conductivity were mutually exclusive. Metals were well known to have high conductivities, but were, without exception, opaque. Insulators, such as glasses, were also well known, and while they were clearly transparent, that had never been shown to conduct. While CdO was the first material to display this unusual combination

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of metallic and insulating properties, other systems were later discovered. The most common being doped zinc oxide and doped indium oxide.

Even though ITO is the industry standard today, it was not the obvious frontrunner when considering the timeline for TCOs. ITO was discovered roughly 50 years after Badeker’s work [7]. Despite being discovered long before ITO, little research has been conducted on CdO. Previously, there was little incentive to develop a new TCO system, ITO simply worked too well. This is because two of the majors of limitations of ITO, cost and free carrier absorption, only recently became significant. Given the smaller market for TCO’s in the past, Indium’s limited supply was not a critical issue. Also, free carrier absorption was typical not critical. Today, devices have higher performance requirements, and this requires the materials that compose them, including the TCOs, to have ever greater performance standards. Only when both of these problems became obvious did research seriously consider finding a replace for ITO.

Roughly 80 years went by between CdO’s initial discover and when researchers in any number began looking at the oxide again. Yet even through most of 1990’s and early 2000’s the literature consisted mostly of a handful of growth papers [8, 9, 10, 11, 12]. Researchers had fabricated the film using pulsed laser deposition, chemical vapor deposition, sputtering and spray pyrolysis. Yet a basic understanding of the properties of the films, such as the band gap, were missing. In the mid‐2000’s researchers added to this knowledge with additional studies looking at the optical properties. Theoretical studies on the band structure of the material were also conducted. However, fundamental understand of the material was still lacking. In particular, it was not well understood why CdO was always n‐type with carrier concentrations between 2*1019 and 2*1020 cm‐3. It was not known why a CdO film with carrier concentration below or above this range had never been reported. CdO was always n‐type, even when alloyed with elements that should be acceptors that would make the film p‐type, a result that was very surprising. There was also a large variation in the reported optical absorption edge, ranging from 2.2 to 2.6 eV. Since there is only a single value for the band gap of CdO, it is not obvious why the absorption edge of different CdO films were not the same.

In light of this, the key motivation for this research is addressing these unresolved issues in CdO. A detailed understanding has to be established if CdO is ever going to displace ITO, the most extensively studied TCO. Specifically, in the results section, a single model will be induced that will be used to explain all of these uncertainties.

1 . 6 . Ove r v i ew

The next chapter describes transparent conductors in detail. Here the three main types of transparent conductors will be introduced and their relative advantages and disadvantages will be considered. Next, transport in transparent conductor will be discussed and the factors limiting device performance will be defined. The figure of merit will be introduced and factors that optimize it will be examined. This chapter concludes by comparing ITO with several alternative transparent conductors. It will be shown that ITO’s limitations are fundamental in

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nature and improving performance in transparent conductors really means finding a new material system and not merely improving an existing one.

The following chapter discusses the research results. This chapter begins by considering the types of defects in semiconductors and introduces the amphoteric defect model. This model forms the basis for this research. Following this, optimal deposition conditions for cadmium oxide will be presented. It will be shown that these conditions lead to a significant improvement in properties of CdO. Irradiation studies are also presented which show that native defects play and important role in CdO. The maximum carrier concentration in CdO due to natives defects is determine. In addition, the optical absorption edge is modeled considering the Burstien Moss shift. Computed and experimental data agree very well and this method allows the optical properties to be uniquely determined by knowing just the electrical properties. The results chapter concluded by considering heavily irradiated CdO and CdCuO alloys where is it shown that carrier concentrations beyond that predicted amophteric defect model can be obtained.

2. Transparent Conductive Materials

2 . 1 . T r an spa r en t Conduc t o r s and The i r Common App l i c a t i on s

A transparent conductor is a material that combines two, usually mutually exclusive, properties: it is optically transparent over a certain range and electrically conductive. This means that the material does not absorb photons over a certain range, yet, in the presence of an electric field, charges (either electrons or holes) are mobile. Given that solar cells and flat panel displays are typical applications for these materials, the “range” is commonly defined as the visible window, roughly 400 to 800 nm. This range is highlighted in Figure 2 as the domain between the vertical blue lines.

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Figure 2: Percent transmittance of Zn0.97Al0.03O.

ZnAlO is a commonly used transparent conductor and its percent transmittance curve is characteristic of all transparent conductors currently used by industry. These boundaries in Figure 2 make intuitive sense because this is the region over which the human eye can detector color. Even “transparent” materials are rarely 100% transparent over the entire window, so for a material to be considered transparent it must transmit 80% of the incident light over the visible region. This means that an integration step must be carried out to determine the area under the absorption curve. In practice, researchers often determine the percent of incident light transmitted at 550 nm and use this value as the approximate percent transmission over the entire range. This is represented as the green line in Figure 2. While less accurate, this is often done because it is much easier. By convention, 550 nm is used because it is roughly the center of the visible spectrum and the wavelength at which the human eye is most sensitive.

Assuming the absorption coefficient does not change dramatically between 390 and 750 nm, this simple estimation is often a reasonable approximation. However, there are two things that can occur that invalidate this approximation. If the band gap falls inside this window, or if significant free carrier absorption occurs, then this approximation is usual quite poor.

The point at which a material becomes “conductive” is far more arbitrary because there is an enormous range in the relative conductivity of materials, and, the transition is gradual, not sharp. It is convention to take materials with resistivities 10‐3 Ωcm [13] or less to be “conductive” and materials above this threshold to be “non‐conductive” or “insulators”, though of course, according to this definition, even insulators have some free charge carriers.

Most common materials either have only one of these properties or none of them. For example, metals are typically highly conductive as they have a large number of mobile electrons in the conduction band. However, they absorb light in the visible region because the

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conduction and valence bands overlap (they have zero band gap). Insulators, such as glasses or wide gap semiconductors, such as Magnesium oxide (MgO), have very large band gaps, so they do not absorb light in the visible region. However they usually do not have mobile electrons in the conduction band or mobile holes in the valence band so they do not conduct.

The following figure is a schematic of a flat panel display, showing the position of the transparent conductor (labeled ITO Film) relative to the other layers in the device. A schematic of a solar cell would look very similar. In both cases, charge must be removed while not blocking the light path.

Figure 3: Different layers in flat panel display.

There are many additional applications for transparent conductors other than solar cells and displays. These materials are very useful in advanced window technologies. Here, transparent conductors transmit visible light, but block infrared radiation. This makes them ideal for use as windows in ovens, where heat is better contained in the system while allowing the operator to see inside the closed system. Transparent conductors, in conjunction with electrochromic materials, are currently being developed for use as “smart windows” where a current can be used to control the transparency of the film, allowing the window to change from transparent to opaque by flowing current through the film [14].

There are a variety of different materials that can be used to make a transparent conductor, and they are typically assigned to one of the following three classes: a very thin metal layer, a doped conjugated polymer, or a degenerately doped wide band gap semiconductor (usually an oxide or nitride). Each material class has its own set of characteristic strengths and weakness, so the “best” transparent conductor depends on the particular application. However, as will be discussed, wide gap semiconductors dominate the market today because, for many applications, semiconductor’s cost‐to‐performance cannot be matched by thin metals or polymers.

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2 . 2 . Th i n Meta l T r an spa r en t Conduc t o r s

A thin metal layer is only transparent because appreciable optical processes typically happen over a larger distance (i.e., depth in the film) than conduction processes. In effect, optical absorption is present in thin metal conductors, it just happens to be much less efficient than electron conduction. This is because, while electronic conduction does occur in the bulk as well as surface layer, conduction is often dominated by the surface. Metals are very conductive and their surface layer of a few 10’s of nanometers is often all that is needed to allow a sizable current to flow. The optical absorption coefficient relates the amount of light absorbed as a function of depth. As the material depth increases, the photons have a greater chance to interact with the material and be absorbed. This process usually results in the electrons being promoted from the valence band to the conduction band, though photons can also be absorbed by giving their energy to the free carriers in the material. This second mechanism is significant in metals because of the large electron concentrations. Free carrier absorption also occurs in some semiconductors. Degenerately doped semiconductors often have free carrier absorption in the near infrared and low energy portion of the visible region. Intrinsic semiconductors, having much lower free carrier concentrations, do not display free carrier absorption in this region.

The optical absorption coefficient, assuming the reflection is insignificant, is defined in the following equation:

xeII α−= 0 Equation 1

where I0 is the incident light intensity, I is the transmitted light α is the optical absorption coefficient, and x is the path length of the photons.

The most common transparent metal conductors are silver and gold, because these metals have very high electrical conductivity [15, 16, 17, 18]. Typical film thickness is 5 to 20 nm, any thicker and the metal layer starts to absorb more light than it transmits. This can be demonstrated by solving Equation 1 for α and setting I/I0 equal to 1/2. Silver has an α of about 1.2*106 cm‐1 for visible light [18]. Solving for x yields a film thickness of about 6nm, a very, very thin film.

Using such a thin film does offer some advantages. Metals are typically easy materials to deposit, and a host of different experimental methods exist such as PLD and sputtering. The films, being so thin, exhibit more flexibility than bulk films, a property that is critically important if a flexible substrate, such as polymer, is used. However, the percent transmission often limits the application for which transparent metal films can be used. One reason is electrical conductivity and percent (%) transmission have opposite dependence on the films thickness. The % transmission decreases with film thickness, while electrical conductivity increases. The optimal value for the thickness is typically around 5 to 10 nm, but even here, only about half of the light is transmitted [17]. Also, it is often not practical to try and use a metal layer thinner

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than 5 nm. The minimum film thickness is often limited by surface roughness as a continuous layer is required. For many metal film deposition processes the metal deposits as droplets or aggregates together on plastic and polymer substrates meaning that continuous films less that 5 nm are very difficult to fabricate. Metal transparent conductors are best used when some degree of film flexibility is required and where losses, such as incident light absorption, is not critical.

2 . 3 . Con j u g a t ed Po l yme r T r an spa r en t Conduc t o r s

Conductive polymers are the second major classification of the transparent conductors and, in some ways, they are the most unique of the three types. For reasons that will be discussed, they exhibit the largest spread in mechanical properties, ranging from brittle conductors to very flexible systems, flexibility that is unmatched by oxides or thin metal films. However, conductive polymers do not dominate the market, mainly because their conductivities are too low. Not only do they have very low mobilities, but their optical transparency is often poor as well.

While semiconductor transparent conductors were discovered near the turn of last century, conductive polymers have “only” been around for several decades; they are roughly 70 years younger than transparent conductive oxides. Early work in the field was carried out in the 1970’s, with the seminal discoveries by Ito, Chiang and Shirakawa. Ito in 1973, synthesized polyacetylene thin films [19], Chiang 1977 doped these polymers to make the first “conducting polymers” [20] and Shirakawa and collaborators showed both n‐ and p‐type polymer conductivity in 1978 [21]. However, of the three, only Shirakawa received a Nobel Prize for his research. Shirakawa shared the 2000 Nobel Prize in Chemistry with Heeger and MacDiamid.

The pace of research in the conductive polymers from inception in the 1970’s to today has been furious with numerous advances in the field that improve upon both the electrical and mechanical properties. Yet, despite 40 years of rapid advancement, the electrical properties of conductive polymers still lag their traditional counterparts in the oxides and nitrides, and this will probably always be the case. This is because the very aspect of conductive polymers that gives them their fantastic mechanical properties is a hindrance to their electrical conductivity. In the limit where the electrical properties have been completely optimized (i.e., limiting the intermolecular forces), the system would become a semiconductor where only strong intramolecular forces dominate. However, for applications where mechanical properties are at least as important as electronic properties, conductive polymers face little competition from metals and semiconductors.

Conductive polymers, on a conceptual level, can be imagined to be a one dimensional semiconductor. This is because the bonding along the polymer chain is the same as in a semiconductor, strong covalent bonding. In either direction normal to the polymer chain, the bonds are weak intermolecular forces; this means that typically only the weak Van Der W20s forces holds adjacent chains together. The conduction path for an electronic is now direction

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dependant, motion along the chains is much easier than motion between the chains where the wavefunction of the electrons only weakly, if at all, overlap.

However, polymers are made up a collection of atoms and electrons, whose wavefunctions, at least along the chain, do overlap. This causes of the splitting of energy levels, just as it does in bulk semiconductors, and formation of bands. Bands in polymers tend to be narrow and have smaller gaps than semiconductors, but the physical origin of the band formation is the same. Given defects, variation in chain length and chain orientation as well as fact the electrons have to “hop” from one chain to another at some point in the system, it is not hard to understand why mobilities tend to be very low in conductive polymers. One of the highest polymer mobility is 3cm2/Vs [22], far below what is easily achievable in most semiconductors.

2 . 4 . Sem i condu c t o r T r an spa r en t Conduc t o r s

Where electronic performance is critical and mechanical properties, such as material flexibility, are less important, semiconductor transparent conductors dominate the market. Their exceptionally high conductivity can often be coupled with reasonable mobilities. For example, indium tin oxide (ITO), the most common transparent conductive oxide (TCO), typically has mobilities of about 30 cm2/Vs with carrier concentration between 1020 to 1021 cm‐3, mobilities that are far higher than polymer conductors.

Transparent semiconductors are optically transparent in the visible region because they have a band gap of about 2.8 eV or greater. However, they conduct because they have large numbers of either electrons in the conduction band or holes in the valence band. Typically, this is achieved by adding a dopant to the host matrix, such as Sn in In2O3, or by the presence of native defects, such as oxygen vacancies in ZnO and CdO. In the case of a dopant, such Sn in In2O3 to form ITO, the Sn has one extra electron than the In it replaces. The bonds in the structure will be satisfied with just three of Sn’s four valence electrons, and this extra electron will enter the conduction band where it is free to move in the presence of an electric field. Oxygen vacancies act in a similar way. Each oxygen vacancy is a double donor adding two electrons to the conduction band. In both cases the defect level needs to be very close to either the conduction band (n‐type) or valence band (p‐type) because the defects must be ionized at room temperature to add to the conductivity. For this reason shallow levels are of interest in transparent conductors, not deep states.

A wide variety of transparent semiconductors have been researched and they generally fall into one of three categories. First are the binary systems such as ZnO, SnO2, In2O3 and CdO. The second category are the ternary systems such as MgIn2O4, Cd2SnO4, GaInO3, Cd2SnO4, Zn2SnO4, MgIn2O4, CdSb2O6 [13]. The final category is nitrides, such as Si3N4 and TiN. Yet, despite the wide range of materials groups that have been researched, only binary oxides, often with a n‐type dopant, are technologically useful. Industrial use of ternary oxides has suffered because not only are they more difficult to fabricate and control stoichiometry than binary oxides but there is also no effective dopant that has been found [13, 23, 24, 25, 26, 27, 28]. Nitrides are

12

far less common because, while they have excellent optical transparency, they are often more challenging to fabricate.

2 . 5 . T r an spo r t i n T r an spa r en t Conduc t o r s

2 . 5 . 1 . C o n d u c t i v i t y a n d S c a t t e r i n g i n T r a n s p a r e n t C o n d u c t o r s

Even though oxides have some of the highest conductivity values for any transparent conductor, they are still far less conductive than bulk metals. Figure 4 shows the electron concentration versus the mobility for several different types of materials.

Figure 4: Electron density vs. electron mobility for a variety of materials [29].

As can be seen from Figure 4, most metals have very high electron concentrations, typically between 1022 and 1023 electrons per cubic centimeter, yet their mobilities are in the lower regions of the figure, ranging from about 1 to 100cm2/Vs. Non‐degenerate doped semiconductors, such as Si and GaAs in Figure 4, have electron concentrations below 1019cm‐3, but their mobilities are typically much higher, 100 to 1,000 cm2/Vs. TCOs occupy the region in between metals and non‐degenerate semiconductors on the graph, their electron concentrations of 1020‐1021 cm‐3 are in between the two groups as are their mobilities, which are typically 10‐100 cm2/Vs.

As can be seen from Figure 4, materials can lie on the same constant conductivity contour but still have very different mobilities and conductivities. For example, Bi and ITO have essentially the same conductivity of 104 Ω‐1cm‐1, yet ITO accomplishes this by having a moderately high mobility and carrier concentration while Bi accomplishes this by having a very high carrier concentration and very low mobility. This is because conductivity is related to the total number of carriers and how easily they move. This relationship is shown in Equation 2.

13

μσ ne= Equation 2

where σ is the conductivity, µ is the mobility and e is the charge of the carrier. So the contour lines in Figure 4 represent the condition where the product of n and µ is constant. According to Equation 2, the conductivity can be increased be increasing one or more of the following: the carrier concentration, the charge of the mobile carrier or the mobility. Of course, in practice, the charge of the species is fixed, being either ‐1.602*1019 Coulombs for electrons in an n‐type semiconductor or 1.602*1019 Coulombs for holes in a p‐type semiconductor. Thus, to increase the conductivity, the only options are to increase the carrier concentration or to increase the mobility.

The carrier concentration and mobility in TCOs are coupled; changing one often alters the other. The reason for this behavior is scattering. There are four general types of scattering mechanisms in semiconductors, and they will be briefly discussed next.

The first scattering mechanism is caused by neutral impurities. This tends to be rather weak and is only seen at low temperatures for two reasons. First, at low temperatures other scattering mechanisms (such as phonon scattering) are less important because they are very weak when the system has little thermal energy. Second, low temperatures are required to insure that the donors or acceptors are not ionized. For example, the phosphorus level sits 0.045 eV below the conduction band edge of silicon. For P doped Si at low temperatures, the extra valence electron of P would not be in the conduction band, it would still be bound in the P atom, thus making the P a neutral center. However, P substitutionally replacing Si will still lead to scattering of free charge carriers because it is a deviation from the ideal lattice; disturbances in the periodicity result in scattering. Phosphorus has a different electronegativity and atomic size than the Si atom it replaces. Since neutral impurity scattering is only significant at low temperatures, it is typically not important in TCOs, but it is significant for very pure semiconductors operating far below room temperature.

The second scattering mechanism is scattering due to phonons. In this case, the phonons, being lattice vibrations, necessarily distort the lattice, slightly changing the lattice constant from its ideal equilibrium value. Since the band gap is strongly influenced by the lattice spacing, phonons will cause a fluctuation in the band gap. This modulation of the band gap results in scattering of the electrons. Since phonons are thermal lattice vibrations, the strength of a phonon increases with temperature. Since TCOs typically operate at room temperature, phonon scattering is one mechanism that limits mobilities.

The third, and most important scattering mechanism in TCOs is ionized impurity scattering. In TCOs, increases in carrier concentration is usually the result of doping the materials with an element that has additional (less) valence electrons for an n‐type (p‐type) semiconductor. Or defects, such as anion (cation) vacancies that dope the material n‐type (p‐type). In both cases, either the dopant or the defects donates electrons (holes) to the conduction band (valence band). Since the materials must be charge neutral, the remaining impurity ion or defect has

14

charge equal to the opposite of what it gave up to the conduction or valence band. Thus, a donor leaves behind a positive charge, and an acceptor leaves a negative charge. Electrons and holes, having charge themselves, will feel the charge of these defects through a Coulomb force. This interaction between the charge carriers and the defects is called scattering, and it acts to reduce the mobility of electrons and holes in a semiconductor. Thus, to maximize the conductivity, it is desirable to keep the number scattering centers to a minimum while, at the same time, maximizing the number of ionized impurity centers which acts as dopants; both goals work against the other.

The fourth type of scattering mechanism is grain boundary scattering, though mathematically, surface scattering is very similar. This makes sense because, to an electron moving in the conduction band, disruption to the periodicity of the lattice caused grain boundaries would be similar to the termination of the crystal at the surface. In both cases the electrons can be scattered at the interface, either between two grains or at the interface of the crystal with the environment. However, the two cases are somewhat different because electrons often travel between grains while there is not a high probably that the electrons will exist at distances far from the crystal surface (but, some tunneling of the electron wavefunction does occur). Because of the similarities between grain boundary and surface scattering, the mathematical models for both mechanisms are similar. The early work for describing grain boundary scattering was done in the early 1900’s. This was because researchers were investigating why the resistivity of metal films increased sharply from the bulk values when the films thickness approached a few atomic layers. This work was conducted on alkali metals, and in the early models, it was assumed that the films were prefect crystals, the only disruption of the periodicity of lattice occurring at the metal‐substrate and metal‐environment interface. The original model is attributed to J. J. Thomson in 1901, and it is called the Thomson Formula in his honor [30].

The Figure 5 is a schematic of the original picture that was created by Thomson in 1901.

Figure 5: The original model for electron scattering at surfaces .

It was assumed that all scattering angles were equally probable, and that the probably that an electron would be scattered through a solid angle that would be divided by all possible angles.

15

If the mean value of the path length is taken over all possible θ values than the follow equation is derived [31]:

⎥⎦

⎤⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛=

23log

20

00 tt λλσ

σ Equation 3

where σ0 is the conductivity of the bulk film, σ is the conductivity of the thin film (or polycrystalline film), λ0 is average mean free path length of the electrons and t is the film thickness (or grain size of the polycrystalline film).

Thomson’s Formula shows the basic relationship, as film thickness or grain size becomes much larger than the mean free path length the film’s conductivity begins to approach the bulk film. This makes sense because, in this model, once a film becomes very thick, it is, by definition, the “bulk” material. The equation is less accurate when the film thickness or grain size begins to approach the mean free path length. But, the model does accurately predict that as λ0 become larger relative to t, the conductivity of the thin film and the bulk material diverge more.

This is a very simple model, and, as is often the case, while a simple picture can give a qualitatively useful picture, a more complex model is necessary if quantitative information is needed. These more complex models were developed by Fuchs and others about 35 years after Thomson’s original work [31, 32, 33]. This more recent work addressed the three key deficiencies of Thomson’s Formula namely [31]:

• the mean free path of all electrons must be considered and then averaged for all their free paths, rather than taking the mean of all possible paths for a single electron

• the mean free paths of electrons starting from the surface need to be considered • the statistical distribution of the free paths around the mean value must be considered.

Taking the above into consideration, Equation 4 can be derived. Here the more common resistively form is shown [26].

( )1

153 1

1111231

−

−

−∞

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎠⎞

⎜⎝⎛ −−⎟

⎠⎞

⎜⎝⎛−= ∫ dt

pee

ttp

k kt

kt

iρρ

Equation 4

where t is the film thickness, ρ is the resistivity of the bulk material, ρi is the resistivity of the film, k is the ratio of the film thickness to the intrinsic electron mean free path and p is the probability that electron will be specularly reflected after scattering. Equation 4 is much more complex than Equation 3, however, the basic relationship that rising resistivity with falling thickness is maintained.

In practice most experimentalists do not integrate Equation 4 and solve for ρ/ρi to determine the effect of grain boundary scattering. What is usually done is that the material is envisioned to be a composite, with part of the system having a low resistivity (the crystallites) and part of

16

the system having a high resistivity (the film interface and grain boundaries) [34]. The concept is illustrated in Figure 6.

Figure 6: A polycrystalline film with crystallites represented as the boxes and the grain boundaries as the spaces between boxes [34].

Here each region has its own resistivity. The variables l1 and l2 refer to the length of the grain and grain about boundary respectively. In practice, this means the mobility and carrier concentration is often different between the two regions. Using geometry and summing up the resistivity for all possible paths the following equation is obtained [34]:

( )( )[ ] β

βρβαβ

βρρ+

+++

+=

11211 21 Equation 5

where ρ is the resistive of the polycrystalline film, ρ1 is the resistivity of the crystallites, ρ2 is the resistivity of grain boundaries, β is ratio of l1/l2, or the length of the crystallite parallel to the conduction path divided by the length of the grain boundary parallel to the conduction path and α is ρ1/ρ2, the ratio of the crystallite resistivity to the grain boundary resistivity. In this model, the resistivity of films with very small grain sizes increases because β gets smaller. Typically, ρ is measured in the lab, ρ1 is estimated from measurements on single crystal films of the same material and β is either estimated or can be roughly calculated using techniques such as scanning electron microscopy. In this way the scattering due to grain boundaries can be estimated by solving for ρ2.

2 . 5 . 2 . T h e T o t a l Mob i l i t y , a S um o f t h e P a r t s

The total amount of scattering is simply the sum over all of the contributing scattering mechanisms. This is Matthiessen’s rule and mobilities are treated exactly like adding parallel resistors. Thus, the total film mobility is given by the following equation:

.__.._

11111

boundgrainimpionphononimpneutral μμμμμ+++= Equation 6

17

where µ is the total, or measured mobility, µneutral_imp. is the mobility due to neutral impurity scattering, µphonon is the mobility due to phonon scattering, µion._imp. is the mobility due to ionized impurity scatting and µgrain_bound. is the mobility due to grain boundary scattering. However, as stated above, for TCOs neutral impurity scattering is not significant and it can be ignored. The three scattering mechanisms are significant. This is because TCOs typically operate at room temperature (phonon contribution), are normally polycrystalline with large numbers of grain boundaries (grain boundary contribution) and highly doped, resulting in a large number of ionized impurities (ionized impurity contribution). Thus, the mobility equation for TCO’s can be reduced to:

.__.

1111

boundgrainimpionphonon μμμμ++= Equation 7

It is almost always desirable to have higher mobilities in TCOs. However, since the operating temperature is typically fixed, only µion._imp. and µgrain_bound. can be increased to increase µ. Of these two µgrain_bound. is the easier one to improve. Here, larger grains as well as more closely aligned grains will reduce the grain boundary scattering and thus increase µgrain_bound.. In practice, this is accomplished by optimizing the deposition conditions, such as increasing the adatom mobility during growth and using a lattice matched substrate. This will be discussed in greater detail in the film deposition section. Improvement can also be obtained in the µion._imp by reducing the scattering caused by ionized impurity centers. As mentioned above, the easiest way to do this is to reduce the dopant concentration, but this will also decrease the carrier concentration and, thus, drive down the conductivity.

2 . 6 . F i g u r e o f Mer i t f o r T r an spa r en t Conduc t o r s

2 . 6 . 1 . B a s i c F i g u r e o f Me r i t De f i n i t i o n

The two most important characteristics for any transparent conductor (TC), are its optical transparency and electrical conductivity. As previously discussed above, increasing one often reduces the other. In order to decide if the trade off between these two properties is a good one, the figure of merit is evaluated before and after the change. The figure of merit for TCs, FTC, is defined in the following equation [35].

( )[ ] 1ln1 −+−=== RTRF sTC ραασ

Equation 8

where σ is the electrical conductivity, α is the visible absorption coefficient, ρ is the resistivity, Rs is the sheet resistivity, T is the total visible transmission and R is the total visible reflection. The figure of merit has units of Ω‐1 because length units on σ (or ρ) cancel with those on α. Since it is often assumed that incident light can only be reflected, transmitted, or absorbed, the argument inside the natural log can equivalently be the total visible absorption. However, the

18

figure of merit, by convention, uses transmission and reflection as the argument of the log function because these are the two quantities that are directly measured in the lab.

2 . 6 . 2 . A l t e r n a t i v e F i g u r e o f Me r i t

Equation 8 is the most common figure of merit used, and for that reason, when comparing various TCOs it is the equation that will be used. But it should be noted that is not the only figure of merit for TCOs. An alternative figure of merit for TCOs was developed in the mid 1970’s to address the fundamental weakness in Equation 8, namely that the figure of merit is not an intrinsic material property; it changes with thickness, and this causes the standard figure of merit to weigh the conductivity properties too heavily and under weigh the transmission properties [35]. Because the figure of merit in Equation 8 is a function both of increasing (conductivity) and decreasing (absorption) thickness, it has a critical point, in this case it has an optimal thickness that maximizes the figure of merit. This critical thickness can be found by combining the fundamental equations for sheet resistance and optical transmission. The sheet resistance, Rs, is a measure of the electrical resistivity for a certain film thickness and it is defined as:

tRs ∗

=σ

1 Equation 9

where σ is the electrical conductivity and t is the film thickness. The optical transmission is, T, is the ratio of light leaving the sample to the incident light and that is defined as:

teIIT ∗−== α

0

Equation 10

where I is the light that is transmitted through the sample, I0 is the incident light, α is the absorption coefficient and t is the film thickness.

Using the form of Equation 10 and substituting in Equation 8 the equation can be re‐written as:

tTC etF ∗−∗∗= ασ Equation 11

where σ, t and α have their usual meaning as defined in Equation 9 and 10. Although Equation 11 is more cumbersome, the effect of film thickness is explicitly stated, whereas this relationship is masked in Equation 8. The maximum of the figure of merit comes from the fact that the σ*t term increases with thickness while the exponential term decreases with thickness.

2 . 6 . 3 . Op t im a l F i l m T h i c k n e s s

The critical value of the function in Equation 11 can be found by taking the derivative of Equation 11 and setting it equal to zero. The actual equation is shown as Equation 12.

19

t

ttTC

eete

tF

∗

∗∗ ∗∗−∗=

∂∂

α

αα σσ2 Equation 12

Setting Equation 12 equal to zero and solving yields the following critical thickness value:

α1

max =t Equation 13

When the figure of merit in Equation 11 has been maximized, it represents the ideal thickness, tmax, as shown in Equation 13. Above this thickness, the films will absorb more light, and this decrease in optical transparency will be larger than the decrease in the film resistivity caused by the increased film thickness. Below this thickness the film will be less conductive, and this decrease in conductivity will be larger than the increase in transparency caused by the decreased film thickness.

Thus, for comparisons of different TCOs using Equation 8, all figure of merit values should be recorded using this tmax film thickness. Since α is not constant among TCOs, each TCO will have a different tmax, with more transparent TCO’s (i.e., higher band gap) being thicker and less transparent TCOs (i.e., lower band gap) being thinner. In practice however, this is typically not done. It is rare for researchers to even compute this critical thickness and even rarer for films of this exact thickness to be fabricated and characterized. It is more common to publish results highlighting just the absorption curve with the band gap and electrical conductivity values.

Different ideal thickness values are not the only limitation of using Equation 8. As previously mentioned, the other major problem of the standard figure of merit for TCOs is that it weights resistivity too heavily, meaning that in maximizing the figure of merit the optical properties can sometimes be driven to useless values just to bump up the conductivity. For example, if tmax is substituted into the Equation 11, then the transmission at ideal thickness is found to be 1/e or 37%. This means that to maximize the figure of merit, roughly 2/3rds of the incident light is not transmitted! For most practical applications this represents a case where simply too little light is transmitted, and, as a result, thinner films are used.

2 . 6 . 4 . B a l a n c i n g t h e Op t i c a l a n d E l e c t r i c a l P r o p e r t i e s

While film thickness will always change any figure of merit value, because the fundamental properties of absorption and conductivity are functions of thickness, the unrealistic weighting between the conductivity and transmission can be corrected. Haacke showed that adding a power factor to the transmission term that is larger than 1 can accomplish this [35]. This means the revised figure of merit, F’TC, can be expressed as:

S

x

TC RTF =' Equation 14

20

where x is some number greater than 1, T is the optical transmission and RS is sheet resistance.

This leads to the following expression for the critical thickness, t’max:

α∗=

xt 1'

max Equation 15

where α has its usual meaning and x is the variable used to weight the absorption contribution to the optimal thickness.

At first, this definition might seem rather arbitrary and thus not very practical; however, this is not the case. True, the factor x is a variable that must be set, but, its magnitude determines the percent transmission achieved during ideal conditions, and this can be used as a reference point. This parameter is often determined by the operating conditions in the system, with realistic values being between 90 to 95%. With the ideal % transmission determined, the factor x becomes fixed. For 90% transmission x would be 10 and it would be roughly 20 for 95% transmission.

Even though Equation 14 is a better, more practical method for comparing different TCs, it is not frequently used. One reason is that the value of x has to be determined, and there is no consensus on what % transmission value to use. And while an x of 10 yielding a % transmission of 90 is reasonable for many devices, some applications require higher transparency and, thus, might require 95% or higher. This lack of a single reference % transmission means Equation 8, while less likely to give reasonable % transmission values, is the most commonly used figure of merit.

2 . 6 . 5 . F i g u r e o f Me r i t f o r C ommon T r a n s p a r e n t C o n d u c t o r s

No matter what figure of merit is used, it is generally true that a higher FTC will lead to better device performance, though this is not always the case. Since the figure of merit for TCOs is defined in the visible region (390 to 750 nm), if the device operates outside this window, a new figure of merit, one that contains this news operation window, will need to be computed. Typically, for the best TCs where the growth conditions have been optimized, FTC is between 10 and 1. For lower performing TCs, or for TC where the growth conditions have not been optimized, FTC, is below 1.

21

Table 2: Highest published figure of merit for several common TCO’s [1].

Material Sheet Resistance (Ωcm) Visible Absorption Coeffiecient (α) Figure of Merit (Ω‐1) ZnO:F 5 0.03 7 Cd2SnO4 7.2 0.02 7 ZnO:Al 3.8 0.05 5 In2O3:Sn 6 0.04 4 SnO2:F 8 0.04 3 ZnO:Ga 3 0.12 3 ZnO:B 8 0.06 2 SnO2:Sb 20 0.12 0.4 ZnI:In 20 0.20 0.2

Table 2 shows the highest figure of merits are achieved by ZnO:F and Cd2SnO4, not In2O3:Sn (ITO). This is because the wide band gap of oxides (Eg > 3.4 eV) have essentially the same visible absorption coefficient, since both gaps are much larger than visible light photons. Thus, most of the difference comes from the sheet resistance, which is lower for ZnO doped with fluorine. Materials in the figure with higher α’s usually have lower band gaps and the trends tracks well with the data in Table 2.

It can also be seen that materials with the highest figure of merits tend to use either toxic elements (F in ZnO:F, and Cd in Cd2SnO4) or rare and expensive elements (In in In2O3:Sn). While the market would ideally prefer a stable, high‐performing TCO that uses only non‐toxic and inexpensive elements, such a system does not exist. And thus, the market accepts films with toxic and/or expensive elements that, at first glance, might seem impractical.

Another important trend in Table 2 concerns the dopant used to achieve higher carrier concentrations and, thus, lower sheet resistance. Since most of the data in Table 2 is for films with carrier concentration between 1020 and 1021 cm‐3, the variation in the sheet resistance is often a reflection of the variation of the scattering rate of the free carriers. Even though adding a donor dopant to a cation site and an anion cite has the same effect, donation an electron to the conduction band, its affect on the band structure is very different. For a semiconductor, the valance band can be thought of as the bonding state, and, as such, it is composed of the anion species, because they are more electronegative than the cations. Motion of charge carriers in the valance band has to be through holes, or missing electrons, because most states are filled in the valence band. The conduction band can be thought of as the anti‐bonding state, here most of the states are empty. Motion of charge carriers is through electrons, which are treated as free, or semi‐free. These states are mostly determined by the cation because they are less electronegative than the anion atoms. All of the TCOs in Table 2 are n‐type semiconductors, so it is the motion of electrons in the conduction, not holes in the valance band, that is important. Ideally, all perturbations should be confined to the opposite band of interest. Thus, for an n‐type semiconductor, a dopant that more effectively perturbs the valence band would be more ideal than a dopant that perturbs the conduction band [14]. The opposite would be true for a p‐type TCO such Cu2O and NiO. This means that anion dopants,

22

such as fluorine are generally superior to cation dopants such as B and In, which are generally the metallic dopants. This is illustrated well in the Table 2 with ZnO:F and Sn2O3 being more effective at reducing the sheet resistance than the corresponding metallic dopant. Like all rules, this one has some notable exceptions. Ga in ZnO, despite replacing the cation, is very effective in reducing the sheet resistance, as ZnO:Ga has the lowest sheet resistance in Table 2.

Another important consideration is atomic size. Ideally, the dopant atom would be exactly the same size as the atom it is replacing, which would lead to zero strain in the film. This, of course, is not possible. The best that can be done is to pick an atom close by in the periodic table because the size mismatch typically increases as the separation in the periodic table increases. This is illustrated by considering the last 4 materials in Table 2, where the matrix is ZnO and the dopant sits on the cation site. Here, atoms with size very different from the host cation, either much larger in the case of In and Sn, or much small in the case of B, all have higher sheet resistances, between 8 and 20. Gallium however, is very close in atomic size to Zn, much closer than B, In or Sn. Here, sheet resistance is the lowest of the group V.

2 . 6 . 6 . Ma x im i z i n g t h e F i g u r e o f Me r i t

An interesting question is “what is the highest figure of merit that can be achieved”, or essentially “what is the upper bound limit for the figure of merit in TCs”? Can values far above those in Table 2 be reached? For example, can the figure of merit approach 10 or even 100? The upper limit of the figure of merit can be approximated by using a model of conduction electrons in a metal, as was done by Nudelman and Mitra [36]. The following equation for the maximum FTC was found to be:

( )( )2

2*30

24e

mncFTC λμεπ

ασ

== Equation 16

where σ is the conductivity, α is the absorption coefficient, ε0 is the permittivity of free space, c is the speed of light of vacuum, n is the refractive index of the film (not the carrier concentration) m* is the effective mass µ is the carrier mobility, λ is the wavelength of light, and e is the charge of an electron.

A more detailed examination of Equation 16 shows that only the refractive index n, effective mass, m*, and mobility, µ, vary among TCs. The refractive index varies least of all three parameters, and changes in FTC are rarely caused by this term. The two most important parameters for determining the maximum allowable figure of merit is the m* and µ. So finding the maximum figure of merit reduces to finding the maximum mobility.

The effective mass is related to the curvature of the band. The definition is provided in Equation 17.

23

2

2

2 *11

dkEd

m

h

=∗ Equation 17

where ħ is the reduced Planck constant and d2E/dk2 is the second derivative of the E vs. k curve, and it represents the curvature of the band. Since the second derivative term is in the denominator, higher curvature (i.e., narrower bands) have a higher effective mass. Lower curvature bands, or flatter bands, have a lower effective mass. This relationship of effective mass to band curvature is important because it breaks TCs up into two classifications, those semiconductors with flatter bands which have high effective masses and tend to have lower figure of merits and those semiconductors with narrower bands which have low effective masses and will tend to have higher figure of merits.

A very general rule is that materials with larger differences in electronegativity between the cation and anion will have larger bands gaps and larger effective masses, though this is not always the case because the band structure in semiconductors is quite complex and many factors combine to determine the actual band structure. However, this is a reasonable first approximation. This rough tend in the atomic positions on the periodic table have several implications. First, nitrides tend to have lower effective masses than oxides and materials with cations more to the right on the periodic table tend to lower effective masses than materials with cations situated more to the left side of the periodic table. Also, with the cation fixed, increasing the anion size (i.e., decreasing the electronegativity of the anion) tends to decrease the effective mass. The reverse is also true: with the anion fixed, increasing the cation size (i.e., decreasing the electronegativity of the cations) will decrease the effective mass.

Table 3: Shows effective masses for a variety of semiconductors.

Table 3 Electron effective mass for a variety of semiconductors.

Semiconductor Effective mass CdO 0.21 ZnO 0.3 In2O3 0.35 TiO2 0.6 ZnTe 0.2 GaN 0.19 InN 0.07 InP 0.08 InAs 0.23 InSb 0.014

Table 3 illustrates that there is large spread in the effective masses. For example, InN has one of the lowest m*, just 0.07 and GaN is also very low at 0.19. These value are much lower than comparable oxides, where In2O3 has an m

* of 0.35. Comparing TiO2 with In2O3, ZnO and CdO

24

shows the effect of having a cation that is on the left side of the transitions metals group as opposed to on the right like Zn or Cd. Titanium dioxide has a very low band curvature, the m* is 0.6 in the parallel direction and 1.2 in the perpendicular direction [37], much higher than the m*

of 0.35 for In2O3, 0.3 for ZnO and 0.21 for CdO. Finally, comparing InP, InAs and InSb demonstrates how the effective mass changes as a result of increasing the electronegativity difference between atoms.

2.6.6.1. Influence of the Effective Mass

With an understanding of the tends illustrated in Table 3, one is now in a position to see why some TCs have better properties than other TCs, and one is also in a position to predict what new TC systems should be most promising. Even though nitrides have the best mobilities, they are less common because they are more challenging to fabricate, also, they typically do not have ideal band gaps. Indium nitride, for example, has excellent m*, but its band gap of 0.7 eV is simply too small. Aluminum nitride has a band gap of 6.2 eV, which is far too high; it is an insulator. Only GaN has a reasonable band gap, around 3.4 eV. However, one should not be to quick dismiss nitrides, even though they less popular than oxides, InGaN alloys can be fabricated that have band gaps between 0.7 and 3.4 eV, and this means nitride alloys have the potential to be very useful TCs.

Titanium dioxide is another oxide that has been suggested as a possible replacement for ITO, yet it has not been nearly as successful. Some of the properties of TiO2 make it sound like a prefect substitute. It is fairly inexpensive and easy to fabricate. It is non‐toxic and has a nearly ideal band gap of 3.2 eV. However, as shown above, its m* is extremely large. The electrical properties of TiO2 are simply not good enough. Mobilities are rarely above 10 cm2/Vs, and often much lower; terrible for a semiconductor TC. So, while the optical properties of TiO2 are excellent, the electronic properties of TiO2 do not allow it to be seriously considered for most applications. However, given the otherwise excellent properties of TiO2, various alloys are being researched that may potentially greatly improve the conductivity of the films. If this happens, TiO2 could become a serious competitor to ITO.

The important point here is that before donors or acceptors are added to a transparent conductor, it is important to understand the band structure of the semiconductor. Generally, semiconductors with high band curvature, and thus high effective mass, will always have superior properties. Table 3 suggests, at least in terms of electronic properties, that CdO, InN, InSb and InP and ZnTe are all good choices. By comparison, while some material systems outside these elements (such as Fe2O3 and TiO2 which have higher effective masses) might see considerable improvement in their properties if they are further optimized and new alloys fabricated, it is unclear if the conduction properties could ever be competitive with materials like ITO because the limiting factors are so fundamental in those systems.

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2.6.6.2. Influence of the Mobility

The second critical parameter in the figure of merit of TCs, besides m* which was discussed above, is the mobility, µ. The mobility and effective mass are related, and this relationship is shown in Equation 18.

∗=meτμ Equation 18

where µ is the carrier mobility, m* is the effective mass, e is the charge of the carrier and τ is the relaxation time, or the time between scattering events. Equation 18 is very intuitive, carriers with a lower effective mass are more mobile than higher effective mass carriers. When the time between scattering events is large, τ is large, and this leads to a large µ. The only effective constant for both n and p‐type semiconductors is e, the charge of an electron, which, of course, does not vary between different TCs. However, the charge, e, appears in the numerator because, if the free carrier charge could somehow be doubled, it would result in a higher mobility. Or, equivalently, to maintain constant conductivity one would need to double the τ for a single charge system to match this new double charge carrier system. While e obviously cannot be changed when the carriers are electrons or holes, if the carriers are ions, as is the case for ionic conductors, than e is an integer multiple of the charge of an electron, and it can be greater than 1.

Equation 18 shows that, with all other variables constant, materials with lower m* should have higher µ. However, this does not mean that lower m* semiconductors will always have higher µ’s. The reason is that the spread in τ is typically larger than the spread in m*. The most common TCs have an m* of about 0.3, on the low end the nitrides can have m* of approximately 0.1 and on the high end some of the transition metal oxides have m* of 0.6. Thus, a factor of 10 is the effective maximum that is seen among various semiconductor TCs. However, τ can vary by much more than an order of magnitude, and it is usually the critical parameter in limiting µ. Since τ is a direct measure of the probability of scattering, low µ films typically have large scattering contributions from at least one of the four scattering mechanisms discussed in section 1.4. So, when high mobility TCs are discussed, what is typically meant is TCs where the time between scattering events is large. This is accomplished by reducing ionized impurity and grain boundary scattering.

As an example, consider ZnO. It was determined that single crystals of ZnO, with a carrier concentration of 1016 cm‐3 has a maximum room temperature mobility of about 250 cm2/Vs [29]. Since there are no grain boundaries, and since the carrier concentration, and thus, the ionized impurity concentration is low, this value can be approximated as the scattering due to phonons. In higher carrier concentration films the mobility at low temperature can be used to approximate the mobility due to ionized impurity scattering. For Zn1‐xAlxO with carrier concentration above 1019 cm‐3, low temperature mobilities do not exceed 90 cm2/Vs. The maximum room temperature mobility for heavily doped ZnO is about 66 cm2/Vs. Cadmium

26

oxide, on the other hand, has a similar m* of 0.21 but very different limits on its mobility. The maximum mobility for single crystal CdO is estimated to be approximately 500 cm2/Vs and low temperature Hall effect on films with carrier concentration above 1019 cm2/Vs is typically 200 cm2/Vs for high quality films, far greater than the low temperature mobilities observed for ZnO. In fact, it will be shown in section 2.4.3 and CdO films can be fabricated that have room temperature mobilities of 242 cm2/Vs, which is essential equally to single crystal ZnO. In case the film also has 1,000 more electrons in the conduction band. Compared to ZnO, much higher mobilties are observed in CdO, despite the fact that both oxides have similar m*, showing that reducing the scattering mechanism in TC is critical to increasing the µ and, thus, the figure of merit.

2 . 7 . Wh i ch Dopan t s t o Use i n T r an spa r en t Conduc t o r s ?

2 . 7 . 1 . Me t a l l i c Do p a n t s i n N ‐ t y p e S em i c o n d u c t o r s

When designing a new TCO it is typically best to add a dopant atom to the anion (cation) sites in a n‐type (p‐type) semiconductor and to pick a dopant that has similar size to the atom it is substituting for. This will reduce scattering, by keeping strain to a minimum. As discussed above, what perturbations do remain should be localized to the opposite band from the one charge carriers are moving in (i.e., to the valence band for an n‐type TC and conduction band for a p‐type TC). This reduces scattering, which was shown to be critically important in limiting the mobility in TCs. However, metallic dopants are often used in n‐type TCOs by both industry and academia, which means both criteria are being ignored by each of these groups. The main reason for this seemingly bizarre behavior has to do with the film fabrication. It is sometimes easier to fabricate films using a metallic dopant rather than a group VI dopant. For instances, metallic dopants can easily be added in powder form to PLD targets, allowing for easy fabrication of dense solid targets. There are typically several options for inducing metallic dopants for Chemical Vapor Deposition as well. Adding a Group VII dopant, especially for PLD, can much more challenging. In some cases a fluoride or chloride structure can be added to a solid target, such as SnF2 in ITO deposition, making it is somewhat compatible with PLD. For Group VII dopants a liquid or gaseous source could be used. Chemical vapor deposition and spray pyrolysis are common techniques that are used when gas or liquid sources are required. Both have been successful at incorporating Group VII atoms into TCOs [38, 39, 40], though both suffer from use of a toxic fluorine precursor. The gas and liquid reactants are highly toxic so the process is safer, and sometimes less expensive, if a metallic precursor is used. As can be seen in Table 2, the increase in sheet resistance is only about a factor of 2, so the trade off in lower sheet resistance is typically not worth extra effort required to fabricate the films with Group VII dopants.

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2 . 8 . L im i t a t i on s o f t h e Cu r r en t Te chno l o g y

2 . 8 . 1 . T r a n s p a r e n t C o n d u c t i v e O x i d e s A f t e r I n d i um T i n O x i d e

ITO is currently the standard for TCOs; it is used in most applications where a semiconductor TC is required. However, despite its current success, it is not without its own set of limitations. The three main limitations of ITO are: its lack of high mobility films, saturation of the resistivity in recent years and limited material quantities with high material prices that do now allow a large market expansion. But, before the shortcomings of the world’s most popular TCO are addressed in detail, an alternative material will be suggested, and the specific reasons for ITO popularity will be discussed. This allows all of the previous concepts: figure of merit, carrier concentration, mobility, and transparency to be linked together. Studying these key material properties will highlight both ITOs strengths, as well as its limitations, and this process will immediately suggest an alternative TC material.

Table 4 provides a summary of the typical properties of the established TCOs, ITO and SnO2, as well as two TCOs, ZnO and CdO, that may, one day, replace ITO.

Table 4: Electronic and optical properties of TCOs. O.A.E is the optical absorption edge, % T, the percent transmission, ρ is the resistivity, n is the carrier concentration and μ is the mobilitiy.

Material O.A.E. (eV) % T ρ 10‐4 (Ωcm) n 1020 (cm‐3) μ (cm2/Vs) ITO 3.6‐4.2 90 0.7 to 1 10 to 25 40 to 55SnO2:F 3.7‐4.3 85 8 to 15 2 to 7 10 to 21ZnO:Al,Ga 3.4‐4.0 85 8 to 15 0.5 to 4.5 3 to 16CdO 2.2‐2.6 60 4 to 8 0.4 to 5 53 to 205

ITO is the currently the most ubiquitous TCO, and the reasons are apparent from Table 4. It has a large band gap of approximately 4.0 eV and, thus, its absorption is very small in the visible region. ITO also has the lowest resistivity of all of the TCOs in Table 4. Equation 2 shows the relationship among conductivity, mobility and carrier concentration. Since ITO has the highest carrier concentration and a moderately high mobility, it has the lowest resistivity. In addition, ITO is relatively easy to fabricate, it can be made using all standard film techniques such as PLD, chemical vapor deposition and sputtering. Another excellent quality of ITO is that is it does not require an expensive substrate for film deposition, high performing ITOs can be grown on substrates such as silicon and quartz.

Doped SnO2 is not as good as ITO because it has both a lower carrier concentration and low mobility. ZnO has a similar deficiency with respect to ITO, in that it has slightly lower carrier concentration and mobility. In fact, doped ZnO performs slightly worse than doped SnO2. The most interesting set of materials properties belongs to CdO in the bottom of Table 4. CdO has similar resistivity as the standard substitutes for ITO (SnO2 and ZnO) yet is has exceptionally high mobilities. For even the worst films, CdO has mobilities that are equal to the best

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mobilities found in ITO. Also when comparing high quality CdO to high quality ITO, the mobility gap increases so that CdO is about four times larger. Only a small part of this huge mobility spread is due to the fact CdO has less free carrier than ITO and, thus, less ionized impurity scattering. Even correcting for this extra scattering in ITO, the mobility gap is still extremely impressive. For example, it is extremely difficult to make an ITO with any electron concentration by any method with any post growth treatment that has mobility over 200 cm2/Vs, while achieving even higher mobility in CdO is possible, even on non‐lattice matched substrates. In section 2.4.3, mobility data for CdO thin films will be presented that shows that using PLD even with a non‐lattice matched substrate yields mobility in excess of 240 cm2/Vs, a value that, as of 2010, has never been reach for ITO. The closest one can get with ITO is 225 cm2/Vs with the (001) growth direction and 175 cm2/Vs with the (111) growth direction. In the case where Indium tin oxide is not degenerately doped, it is essentially indium oxide. This data is presented in Figure 7.

Figure 7: Highest published mobility data for In2O3 [41].

In order to achieve mobilities in ITO that are competitive with CdO, two key sacrifices had to be made. First, an expensive substrate that reduces strain, Yttria‐stablized zirconia (YSZ), was used. The CdO values in Table 4 were grown on either sapphire or quartz, much less expensive substrates. Second, the carrier concentration has to be very low, high 1016 to low 1017 cm‐3. This is roughly 100 times less than the carrier concentration for CdO with the same mobility showing that, when high mobilites are required, ITO is simply not competitive with CdO. In fact, the carrier concentration is so low that the system is no longer a degenerate semiconductor. In order to achieve carrier concentration below 1018, tin is not added, it is simply an indium oxide matrix with oxygen vacancies adding free carriers instead of a donor atoms. Together, this means that for ITO to have high mobilities it must have low conductivity and be fabricated on expensive substrates, neither of which is desirable.

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Further, what is extremely impressive about CdO is that these values in Table 4 are for undoped CdO, no n‐type dopant atom is added to provide electrons to the conduction band. By contrast, the other materials systems, doped ZnO, doped SnO2 and doped In2O3 (i.e., ITO), all require large concentrations, typically several percent, of the n‐type dopant. They could, in fact, be called alloys rather than doped semiconductors. CdO relies on oxygen vacancies to add large concentrations of electrons to the conduction band, not donor atoms with one or more extra electrons. This process is extremely efficient in CdO leading to carrier concentrations between 1019 to 1020 cm‐3. By contrast, oxygen vacancies in SnO2 typically do not lead to carrier concentrations much higher than very low 1019 cm‐3, and mobility even for the best films on the best substrates is poor, less than 60 cm2/Vs [41].

In terms of achieving low resistance via high mobility, CdO is clearly superior to ITO. However, there are additional reasons beyond high mobility applications driving the development of a replacement for ITO. As good as the optical and electronic properties of ITO are, they are unlikely to get better in the future. This is because ITO’s properties have essentially saturated, they have remained unchanged for roughly 20 years. This is shown in Figure 8.

Figure 8: Minimum TCO resistivity as a function of year [13].

ITO reached its maximum conductivity value around 1989. 20 years of research has slightly lowered the resistivity, but the gains have been minuscule. If values below this are required, it is likely they will not come from a material’s performance curve that has started to asymptote 2 decades earlier. Doped ZnO shows potential, and even though it has higher resistivity than ITO, the tend is still decreasing resistivity with increasing years for ZnO. There is simply not enough data points to plot a meaningful trend line for CdO, though the starting point of low 10‐3 in the early 2000’s could be added. Moreover, given that the material is not well studied, and the growth conditions have not been optimized yet, it seems reasonable that the slope of the trend line would have more in common with doped ZnO than doped In2O3.

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The third and final limitation of using ITO has to do with its cost and abundance. These two factors are, of course, linked; scarce materials tend to demand a higher market price. The scarceness or rarity of an item should be determined not just relative to other materials (i.e., In to Zn) but also its supply relative to its own demand. This concept of increasing market price as a function of rarity is especially pronounced when the demand for a material starts to surpass its supply. Long term, after subtracting inventory and recycling, societies simply cannot consume more of a good than it produces, so, for a new market equilibrium between supply and demand to be reached, the price has to spike up. This will influence both the aggregate supply as well as aggregate demand. Increasing costs will price some consumers out of the market; shifting the demand curve down, and, where possible, material substitutions will be made. Higher prices will also shift up the supply curve. A high market price will make less efficient material fabrication processes economically feasible; marginal operations that would lose money with a low market price might be profitable with a higher market price. This process is frequently seen in commodity markets like metals and food. The most dramatically illustration was during the 1970’s oil embargo, when a relative small decrease in the production caused a major increase in prices. Though it is not initially obvious, the market dynamics for In shares many similarities with oil; and there is fear in the TC community that, if demand for ITO continues its rapid increase and an no effective TCO alternative is developed, there could be a price spike in In equivalent to that seen in oil.

Indium, like oil, has a very fixed supply. Unlike other goods, it is not a simple process to increase the supply of In. Indium is a rare ore in nature, and it is typically found as a byproduct of mining other ores such as zinc and lead [14]. Given the low In concentrations in ore there are no “indium mines” which are dedicated exclusively to In. That process is not economically efficient even at the current market price. A mine dedicated exclusively to In production could not operate unless there was a huge increase in the price of In, something no one in the TC markets wants to see. So, the problem is that, in order for the price of In to fall, either demand has to decrease (which is not going to happen) or the supply has to increase. And the only way to increase the supply is to increase the price. The other problem with In is that it is already a very expensive ore, so there is little room to increase the price still further to stimulate further production. The price of metals falls roughly in the following order:

Cd<Zn<Ti<Sn<Ag<In [14]

where it can seen that Cd is a very cheap metal and that In is extremely expensive, more expensive even than silver. Given the supply constraints on In, it is simply not possible for In to be widely use in TCs and for it to also be inexpensive at the same time. The only way In can be inexpensive is if no one wants it (ie. if demand collapses) and this might happen if a better TCO is developed.

Looking at the metal price ranking, ideally, a TCO from one of the less expensive metals would be developed. This would allow supply to keep pace with demand and keep a cap on prices. From a cost standpoint, Zn based TCOs look attractive, and they have been extensively studied.

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However, in terms of cost, Cd is the single best choice, yet little research in the material has been done. While it is true that Cd is very toxic, all materials have limitations. The best materials are those for which the strengths can be exploited and the weaknesses minimized. Given Cd’s low material cost, easy of fabrication and exceptional material performance, not considering Cd based TCOs is a huge mistake. From the consumer standpoint, the toxicity of Cd can be controlled, by sealing the products and insuring material recycling and/or decommissioning. This has been true for CdTe based solar cells, which have become very popular because of their exceptional performance to cost ratio.

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3. Results

3 . 1 . Ob j e c t i v e : Op t im i z i n g CdO

The optical absorption edge, free carrier absorption and conduction properties are all related to each other, and they are all important to the performance of TCOs. By noting the interplay between optical and absorption properties in transparent conductors, the parameters limiting CdO’s performance can be defined. Once these variables are known, the deposition and processing can be tailored to maximize the material’s performance for optoelectronic applications.

For TCOs it is always desirable to reduce the absorption and increase the conductivity, but these goals often work against each other. Equation 19 shows the relationship between free carrier absorption, αf, carrier concentration, n, effective mass, m*, and carrier scattering time, τ:

τα *m

nf ∝ Equation 19

Since αf should be minimized for TCOs, it can be seen that the carrier concentration, n, needs to be small, the effective mass, m*, needs to be large and the relaxation time needs to be large. However, optimizing the first two parameters results in undesirable side effects.

Equation 20 shows, again, the relationship between conductivity, carrier concentration and mobility:

μσ ne= Equation 20

where σ is the conductivity, n is the carrier concentration, e is the charge of an electron and µ is the mobility. Equation 21 shows the relationship between mobility, scattering time, and effective mass:

τμ *me

= Equation 21

where µ, e, m* and all τ have their usual meanings.

If the carrier concentration is reduced to minimize the free carrier concentration, then the conductivity of the TCO is reduced. Also, increasing m* is not a good option for either of the following two reasons. First, it is often very challenging to accomplish this as the curvature of the conduction band (or valence band for holes) has to be altered. Second, even when this is accomplished, it results in lower mobility values as seen from Equation 21. This, in turn, would decrease the conductivity, as seen in Equation 20.

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So, the only way to maximize the optical and electronic properties at the same time is if relaxation time is increased. Another way to look at this is to increase the mobility, as relaxation times and mobilities are related. Since all current TCOs, such as ITO and ZnAlO, were maximized considering n, not µ, the only way to reduce free carrier absorption, by increasing the mobility, in these systems is to drive the conductivity down to useless values. CdO, on the other hand, has high mobilities. So the challenge for optimizing CdO is how to increase the mobility (reduce scattering) beyond the current limit of 216 cm2/Vs. Another closely related challenge is how to increase the carrier concentration while not decreasing the mobility. Careful optimization of the deposition conditions and annealing conditions allows this mobility limit to be overcome. This is discussed below in the section 2.4.3, where a new mobility record for CdO has been established.

The final property that needs to be optimized in CdO is the optical absorption edge. Ideally, a TCO would have a combination of both ZnAlO’s and CdO’s properties, having the high optical absorption edge of ZnAlO and the low free carrier concentration of CdO. But, this is very difficult to achieve. It will be discussed how the creation of oxygen vacancies and the Burstein‐Moss effect could increase both the number of free carrier and the optical absorption edge. However, due to compensation, the maximum values that can be achieved are 5*1020 cm‐3 free carrier with an optical absorption edge of 2.8 eV using native defects. Later, the influence of very high doses of C is considered, and it will be seen whether this method can be used to overcome both the carrier concentration limit and the absorption edge limit.

3 . 2 . De f e c t s i n Sem i conduc t o r s

3 . 2 . 1 . De f e c t s a n d I r r a d i a t i o n

Defects play a crucial role in the optical and electronic properties of many semiconductors, and it will be shown that CdO is no different in this regard. Native defects, such as cation and anion vacancies and interstitials, were demonstrated to be the single most important factor controlling the doping limits and surface accumulation layer in InN [42, 43]. Since CdO is the II‐VI analog to III‐V InN, it seems reasonable to assume that many of the important factors controlling the properties of InN will at least play a role in CdO. In the next section the influence of defects on the electronic properties of semiconductors will be briefly discussed. This will provide the basis on which the Amphoteric defect model can be introduced. The Amphoteric defect model, together with ion irradiation, provides a method to determine to what degree native defects influence the electrical and optical properties of CdO. Once this understanding of the factors controlling the key TCO properties are established, improvement to the deposition and processing conditions can be developed to improve the material’s performance.

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3 . 2 . 3 . S h a l l ow L e v e l s

Defects in semiconductors are often considered to belong to one of two groups of impurities: deep level or shallow level. Shallow impurities tend to be delocalized in real space, which means in k‐space they are localized. Thus, they are often considered to be Hydrogenic impurities since their wave functions can be described by the Hydrogenic model. For example, consider a substitutional As atom in Si. Here, As has one extra electron than the Si atom it replaced. Arsenic is a donor here. Because of the Columbic force, there is a force between this electron and the nucleus. Coulomb’s Law describes the force, F, that results when two charges, q1 and q2 are separated by a distance, r.

221

0

*4

1rqqF

πε= Equation 22

Here ε0 is the permittivity of free space. Since force over distance is energy, integrating the above equation yields the Coulomb potential.

reU

041πε

= Equation 23

To represent the charge of an electron, the qs from Equation 22 were replaced by e. One important correction has to be made before this equation can be used to model impurities in semiconductors. Currently, the Coulomb potential is only screened by free space, and this is represented by ε0. However, when the impurity atom is imbedded in the semiconductor, the Coulomb potential is screened by the host matrix. This screening results from the electrons on the Si that further reduce the attractive potential between the extra electron and the impurity nucleus. This interaction can be taken into account by adding the dielectric constant of the host material. The resulting equation is then:

reU

041

πεε= Equation 24

where ε is the dielectric constant of the host material, in this case, Si, and all other variables remain the same.

This equation can be used to model the spherical orbit of an electron around the impurity atom core. The potential represents the binding energy of the electron. If the electron receives energy greater than this attractive force, it will be librated from its orbit.

Since this donor electron orbits inside the host matrix the potential it feels is not just impurity potential but also crystal potential. Thus, the Schrödinger equation must be solved to find the radius at which this electron obits.

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( ) ( ) ( )rErUH ψψ =+0 Equation 25

Plugging into and solving this equation yields the follow equation for the Bohr radius:

*2

204me

hrBohrεπε

= Equation 26

Typical values for the Bohr radius of common dopants in semiconductors are a little less than 10nm. In the context of distances between atoms in a crystal, this is a huge distance. This illustrates the important fact that, in real space, the wavefunctions are diffuse, but are very confined in k‐space. The implication is that these shallow levels are composed of Bloch states very near the conduction band minimum (or valance band maximum for holes). Because of this, there are a few critical implications. First, since these states are composed of Bloch functions very near the band edge, they are highly sensitive to changes in the band edge. For example, any movement in the band, such as that resulting in stress, will induce a change in these defect states. In addition, the effective mass approximation can be used calculate the energy of shallow levels, something that is not true of deep centers.

3 . 2 . 3 . De e p L e v e l s

The second type of defect in semiconductors is deep levels. Here, the physical picture is not that of a hydrogen atom with a potential between by an orbiting electron and a nucleus, but rather a potential caused by broken bonds or electronegativity differences caused by an isovalent impurity (e.g., Se substitutionally replacing O in ZnO). Deep levels are the opposite of shallow levels. Their energy levels are typically deep inside the band gap, close to neither band edge. The potentials are highly localized and the donor electron does not have an orbit that encompasses thousands of atoms. Because the wavefunctions are highly localized in real space, they are very de‐localized in k‐space. Their wavefunctions are constructed from Bloch waves that span multiple bands, sampling a huge region of k‐space. The influence is related to the density of states. For states near the band edge, the density of states is typically low. The density of states increases with distance away from the band edges. For example, for the simple parabolic valance and conduction band case, the density of states is proportionally to the square root of energy. Thus, as the energy increases (i.e., the distance from the band edge increases) the density of states gets larger, resulting in a larger influence on the deep level energy state. This means that their character is primarily not determined by either band edge. The result is that their wavefunctions are insensitive to the movement of the conduction or valence band. Since the wavefunctions are highly localized near the defect center, a tight binding molecular orbital approach seems to be the obvious method to compute their energies. Though it will not be covered here, Green’s function method can be used, rather than the effective mass approach for shallow levels, to compute the defect energies.

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3 . 3 . The I n f l u en ce o f Na t i v e De f e c t s

3 . 3 . 1 . De f e c t I n d u c e d F r e e C a r r i e r S t a b i l i z a t i o n

It should be pointed that out that the simple picture presented above of localized levels always being deep levels is not prefect. Sometimes localized levels are shallow. An example would be VN in InN. Localized defects can have a very large impact on the electronic properties of semiconductors. It is well known that defects can dope a semiconductor either n‐type or p‐type. Anion vacancies add free electrons to the conduction band while cation vacancies add holes to the valence band. Interstitials can be a source of electrons as well. In addition, anti‐site defects can be either n‐ or p‐type dopants, depending on whether the impurity atom has an electron surplus or deficiency with respect to the atom it replaces. These dopant mechanisms in semiconductors were established very early on. However, an understanding of how this defect doping process works at high doping levels did not develop for several more decades. The earliest work that led to a comprehensive understanding was probably that of Brudnyj in 1982 [44]. His original graph is shown in Figure 9.

Figure 9: Electron irradiation of semi‐insulating, n‐ and p‐type GaAs [44].

What was interesting about Brudnyj work was not that he had shown that irradiation can be used to change the carrier concentration, that was established long before, but rather that carrier concentration at large doses seems to converge into a single value. This convergence in the carrier concentration was not, apparently, sensitive to the starting conditions of the films as semi‐insulating, n‐ and p‐type GaAs all reached similar values at electron doses in excess of 1019 cm‐3. Figure 9 suggests that the saturation value is a fundamental material property because its value at high doses is constant and independent of the initial conditions. This result was quite striking at the time. Returning to the original concept of point defects, it seems inconsistent that if irradiation induced vacancies can be either donors or acceptors, that a saturation value should ever be reached for high irradiation doses (i.e., a large concentration of defects). At the time, it seemed more likely that, if donors were typically created (perhaps resulting from the formation of anion vacancies) in the irradiation process, then the films would continue to be more n‐type in character. The number of free electrons should scale with irradiation dose, and

37

a saturate value would not be expected. Similarly, if acceptors were typically created (perhaps resulting from the formation of cation vacancies) in the irradiation process then the films would continue to be more p‐type in character. Clearly the simple model of the formation of donor and acceptor defects scaling directly with irradiation dose was incorrect. The missing concept was that of the variable formation energy of defects. Next, it will be shown how research in early and mid‐1980’s on defect formation energy finally led to the creation of the amphoteric defect model (ADM) in the late 1980’s. The ADM combined all of the pieces, linking the saturation observed in Figure 9 to the Fermi level dependent irradiation induced donor and acceptor defect formation energy.

3 . 3 . 2 . F e rm i L e v e l De p e n d e n t De f e c t F o rm a t i o n E n e r g y

In the mid 1980’s researchers investigated whether the defect formation energy was dependent on the Fermi level, and, if so, what implications this would have [45, 46]. These calculations were typically done using Green’s function method. As described above, since these defects have delocalized wavefunctions in reciprocal space, this method was the obvious choice. While the models themselves were mathematically very detailed, conceptually they were rather simple. These models started with a perfect crystal. Then, it was assumed that the material had some degree of non‐stoichemetry, perhaps induced by growth or processing conditions. There would be an excess of either the cations or anions. This excess, or deficiency of one species, required the incorporation of defects in the film to accommodate this difference. Using the law of conservation of mass, the following general reaction equation was used [45]:

DNCNBNAN DCBA +↔+ Equation 26

where A is the concentration of species A, and NA is number of the A component that is necessary for the reaction, the variables B, C and D have the same meaning except that they represent different species in the reaction. Given the above the reaction equation, the following is the well‐known formulation for the rate law:

( ) [ ] [ ][ ] [ ]

kTG

NN

NN

eBADCTK

BA

DC Δ−

== Equation 27

where K is the temperature dependent rate constant, the brackets denote the concentration of each species, k is the Boltzmann constant, T is the temperature and ΔG is the Gibbs free energy of the reaction. The Gibbs free energy, in turn, is related to temperature, entropy and formation energy by the following equation:

STEG Δ−Δ=Δ Equation 28

where ΔE is the energy required for the reaction to proceed, T is the temperature of the system and ΔS is the entropy associated with the reaction.

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Defining the system in terms of Equation 28 is very useful because it highlights that, for a single formation energy, ΔE, at a set temperature, T, there is a single value for the defect free energy, ΔG. This relationship, together with Equation 27, means that there is a fixed ratio between the product of the reactant concentrations and the product of the product concentrations. Also, Equation 27 shows that the concentrations of defects in the system are not independent of each other; changes in one alter the others. These constraints on defect formation energy and defect species concentrations are immensely important because, if Equation 27 can be solved and the reaction concentrations are known, then the product concentrations can be determined. This also means that the direction that the reaction proceeds (i.e., what defects are created) depends on the starting defect concentrations.

Equations 24 and 25 are the general forms of the equations, so they can be applied to any material system. GaAs was the first material system which was studied in detail using this method, so it will be briefly considered here to demonstrate how the model works. Later, it will be shown how CdO can be modeled in a similar manner.

There are many possible defects that can form in semiconductors such as GaAs. The most obvious would be vacancies, VGa and VAs, anti‐sites, GaAs and AsGa and interstitials, Ga

i and Asi. Early models were constructed based entirely on these defects. This means that four key assumptions were made. First, it was assumed that the system was at equilibrium so that ΔG could be computed. Second, that defect complexes did not form. This means that the formation energy of the defect reaction was often over‐estimated because defect complexes would tend to relax the system. Third, that atoms were not allowed to relax near the defects. This assumption also led to an over‐estimation of the defect formation energy. Fourth, in the initial work, it was suggested that the entropy term was negligible, which resulted in Gibbs free energy being exactly equal to the defect formation energy.

Consider the As vacancy defect, VAs, in GaAs. VAs, since it is a missing anion, is a donor defect, as it adds electrons to the conduction band. The number of electrons it adds to the conduction band depends on the charge of the defect. It is expected that VAs could give up as many as 3 electrons to the conduction band and as few as 0 electrons. If it gave up all 3 electrons the charge of the defect would be 3+, if it gave up 0 electrons the charge of the defect would be 0. This process of moving electrons to and from the defect requires energy. This is because electrons are being exchanged between the defect and a reservoir with potential energy, µ. This potential energy term is related to the Fermi level, and it is often set to be zero at the top of the valence band. It essentially represents the energy of electrons in the system. Since electrons will want to occupy the lowest energy state, if the defect’s energy level is below the Fermi level, then the electron will find it energetically favorable to occupy the defect site. However, if the defect level is above the Fermi level, then the electron will find it energetically more favorable leave the defect and enter the Fermi sea.

The above mechanism represents the Fermi level dependence of the defect formation energy. But there is also a second term that needs to be considered. This is the structural portion of

39

the defect formation energy. Even if no charge is exchanged between the defect and reservoir, energy still has to be expended because bonds are broken and bond lengths change due to the creation of a vacancy. If the two terms are combined, the Fermi level dependent component discussed above and the structural component discussed here, the following equation results:

( ) ( ) NNENENENE electronicstructrual μμμ −Δ=Δ+Δ=Δ )(,),( Equation 29

If Equation 29 is solved for VGa and plotted, Figure 10 is obtained.

Figure 10: Defect formation energy for VGa in GaAs [10].

This equation is actually of the form, y=mx+b where the slope of the line is N (i.e., m), is the charge of the defect. The variable µ (i.e., x) is the Fermi level position with respect to the valance band maximum, or, equivalently the average energy of the electrons in the system. The intercept ΔE (i.e., b) is the structural component of the defect formation energy. The changes in slope are due to changes in the charge of the defect, N. This means as the system moves from left to right in Figure 8, the lowest energy state of VGa changes from 2+ to 1+. Notice that it was predicted that there should be 3+ and 0 charge state. While in theory they could exist, computationally it was found that the 2+ state was lower energy than the 3+ for low values of µ, and that the 1+ state was lower energy than the 0 state for high values of µ [45].

Figure 10, by itself, is not useful for determining which defects will predominantly be formed. This is because VGa represents only 1 term in the reaction equation. It is often the case that one or more defects are consumed to create another defect. For example, if an As anti‐site defect were to jump to an As vacancy, then a Ga vacancy would be left behind. The defect reaction equation would look like the following:

GaGaAs VAsV ↔+ Equation 30

So, when creating a VGa, energy has to be expended. However, energy is gained in the system when VAs and AsGa are consumed. The formation energy, ΔE, necessary to create a VGa is not shown in Figure 8, but rather what is shown is that value minus the corresponding value for VAs and AsGa for each unique position of the Fermi level.

40

The following figure results from that process:

Figure 11: Defect formation energy for VGa in GaAs.

There are a few key features worth noting in Figure 11. First, the slope of the line changes when the charge of one of defects, either on the reactant side or the product side of Equation 30, changes. The number next to the line segments represents the charge removed from the system to create the defect. For example when µ is 1.0 eV (i.e., when the Fermi level is 1.0 eV above the valance band maximum, or equivalently, 0.5 eV below the conduction band minimum) the formation of a VGa consumes 6 electrons. Three electrons are needed for the VGa, two holes are lost from the AsGa and one hole from VAs.

In Figure 10 and 11 the point at which µ becomes zero, crossing from positive to negative values, has no special significance. The curves are qualitative, showing the general tend as Fermi level rises from the top of the valence band to the bottom of the conduction band. For a more quantitative picture to emerge, other interactions, such the attractive and repulsive forces between charged defects, have to be accounted for. If these additional forces are considered, then the zero point becomes very significant. Figure 12 shows the results for these more detailed calculations.

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Figure 12: Defect formation energy for VAs and VGa in GaAs.

The top half of Figure 12 represents the energy necessary to create VAs, or n‐type defects in GaAs. The bottom half of Figure 12 represents the energy necessary to create VGa, p‐type defects in GaAs. Looking at Figure 12, it can be seen that making VAs is energetically favorable (i.e., a negative reaction energy) when the chemical potential, µ, (or equivalently the Fermi level) is above the valence band minimum but below the middle of the band gap. Also, it can be seen that making VGa is energetically favorable when the chemical potential is below the conduction band maximum but above the middle of the band gap. This graph, together with an understanding of the localized nature of point defects, is the final piece necessary to construct the amphoteric defect model. If the top and bottom portions of Figure 12 are combined, it is possible to determine, as a function of the Fermi level, where donor and acceptor defects are energetically more favorable.

3 . 3 . 3 . T h e Amph o t e r i c De f e c t Mode l

The actual defect reactions that were considered for GaAs in the ADM were [47]:

iAsGaAsiGa GaVAsAsGaV ++↔++ Equation 31

GaiAsiGaAs GaAsVAsVGa ++↔++ Equation 32

Of course, these defect reactions are applicable to many other systems, so more generally, one can think of the Ga as representing an arbitrary cation and As representing an arbitrary anion.

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If it is assumed that the concentration of interstitials is much less than the concentration of vacancies then the following defect reactions can be reduced to:

AsGaAsGa VAsAsV +↔+ Equation 33

GaAsGaAs GaVVGa +↔+ Equation 34

Since interstitial atoms can often diffuse rapidly, this is normally a valid assumption. Noting that AsAs and GaGa are simply place holder variables for the perfect lattice, Equations 31 and 32 are identical to those in Figure 12. If the both Equations 31 and 32 are plotted together the following figure is obtained:

Figure 13: Defect formation energy in GaAs [47].

Here, the top curve represents Equations 32 and bottom Equation 33. The right half of the top curve is a consequence of Equation 34 being driven left, and the left half of the curve when the equation is driven right. Now the peaks of the defect formation energy lines, as plotted in Figure 13, are significant. When the Fermi level decreases from the conduction band edge to about 0.7 eV above the valence band maximum, GaAs and VGa are no longer the lowest energy defect configuration; the system spontaneously changes, consuming GaAs and VGa to form VAs. This change in the defect formation energy, which induces a transformation in the stable defect type, is a fundamental property of the material. This means that it is unaffected by growth conditions or doping levels.

The first key result of the amphoteric defect model is that a stabilization energy level exists, a position at which the Fermi level becomes pinned, given a sufficiently high point defect concentration. The second key result is that the position of this level, with respect to vacuum, is constant.

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Figure 14: Band offsets and Fermi stabilization energy in II‐VI semiconductors [48].

As can be seen from Figure 14, the Fermi stabilization energy, EFS, is constant, that is, it is located 4.9 eV below vacuum. What changes between various semiconductors is the position of their valence and conduction band edges with respect to EFS. The reason EFS has a universal position for all semiconductors is because the origin of the defects in all cases are the same. For defect concentrations high enough to reach EFS, the electronic properties of the films are completely controlled by these native defects. These native defects, being point defects, are highly delocalized in k‐space, as discussed above. Thus, their character is primarily determined from all extended states in the Brillouin zone, the largest influence coming from where the density of states is largest. These states are typically far from conduction and valence band edge. Since, far enough way from the band edge, the structure of semiconductors look similar, this means summing over these states leads to a constant value.

3 . 4 . F i lm Depo s i t i o n

3 . 4 . 1 . P u l s e d L a s e r De p o s i t i o n o f C dO T h i n F i l m s

All films were fabricated using pulsed laser deposition. A Lambda Physik excimer laser operating at 248 nm with a peak width of 10ns was used. Films were typically deposited on c‐plane sapphire, though silicon, MgO, GaAs and quartz were also used. All substrates were first cleaned with acetone then followed by methanol. After mounting in the chamber, the substrates were baked at 500°C for 30 minutes in vacuum to remove any residual contamination. The target was either CdO, made by pressing CdO powder into a solid target, or pure Cd metal. In the case of the CdO target, the films were grown with no supplied oxygen, with the background chamber pressure at ~1*10‐6 torr. When the Cd metal target was used,

44

oxygen for the CdO film was supplied by flowing O2 into the chamber during deposition. The background pressure, when adding O2, was 4*10

‐4 torr. Typical depositions were between 300 and 450°C.

3 . 4 . 2 . De p o s i t i o n T emp e r a t u r e

The deposition temperature is one of the most important parameters controlling the structural and, thus, the electronic properties PLD films. Temperature is important because it influences the rate of diffusion of surface atoms. This factor has important implications for grain size and crystal quality. In addition, temperature alters the bulk diffusion in the film during growth. This can change the structure and grain boundaries of the film.

In order to determine the optimal deposition temperature, CdO films were deposited on sapphire from 170 to 530°C. For use as a TCO, the optimal properties are defined as having a large optical absorption edge, low free carrier absorption, and low resistivity. Essentially, this means optimizing carrier concentration and mobility because higher carrier concentrations results in a larger optical absorption edge, higher mobilties in lower free carrier absorption and the product of the two results in lower resisistivies. Because of this, comparing the carrier concentration and mobility, as determined by the Hall effect, at each deposition temperature, will be important.

The structural quality of the film is also an important parameter. Films that display narrow and intense diffraction peaks are higher quality and typically have higher mobilities than films with broad and weak diffraction peaks. Rocking curves, or Xray diffraction scans rotated about the Bragg angle, provide important information concerning the structure of the film. Films with narrow rocking curves have a more perfect lattice, so rocking curves provide a direct method for comparing film quality. A perfect crystal with no defects and a very large number of planes would have a rocking curve with zero thickness. This means all planes have Bragg diffraction at exactly the same angle and any deviation from this angle results in no constructive interference. Of course, perfect crystals do not exist, but single crystal substrates are close and they typically display rocking curves that have a full width at half maximum (FWHM) of about 0.1°.

Figure 15 shows the 2Theta‐Omega scans for CdO film deposition ranging in temperature from 170 to 531°C.

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Figure 15: 2Theta‐Omega scan for CdO as function of deposition temperature.

There are 5 diffraction peaks in Figure 15. The narrowest and most intense peak occurs at 41.6 2θ. This is from the substrate; it is the sapphire (0006) peak. The peak just to right at 44 2θ comes from the sample holder. The remaining 3 peaks are from the CdO films. The lowest peak at 33 2θ is from the CdO (111) planes. The second lowest peak at 38 2θ is from the CdO (002) planes. The peak at very high 2θ is the from the CdO (004) planes, which means it is the second order reflection of the (002). Table 5 provides a summary of the diffraction data displayed in Figure 13, including peak position, peak intensity and position of the reference CdO refraction diffraction peaks. NA means that no diffraction peaks were observed.

Table 5: Xray diffraction peak position and intensity as a function of deposition temperature.

Temperature (°C) (002) Peak Intensity (111) Peak Intensity CdO film 170 37.88 129 32.92 141 CdO film 310 37.96 1231 NA NA CdO film 453 37.92 883 NA NA CdO film 479 38 1493 NA NA CdO film 509 38.02 1590 NA NA CdO film 531 37.99 1537 NA NA CdO reference NA 38.339 NA 33.042 NA

The only CdO film to display the (111) peak is the lowest temperature film deposited below 200oC. This means that CdO deposited at 170°C has 2 growth directions, while CdO deposited above this temperature has a single growth direction. Having more than one growth direction is almost always undesirable, so, from this diffraction scan alone, it seems that higher deposition temperatures yield more optimal films. This point is further reinforced by examining the lattice constant and diffraction peak intensity.

Figure 16 plots the (002) peak position and intensity as a function of deposition temperature.

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Figure 16: CdO (002) peak position (black curve) and intensity (blue curve) as a function of deposition temperature with CdO (002) reference peak position (red line).

Figure 16 makes the trends displayed in Table 5 more obvious. The diffraction peaks, with a single exception, become progressively more intense as the growth temperature is increase from 170 to 509°C. At temperatures above 509°C the diffraction peak intensity begins to decrease. The film deposited at 310°C, is either an outliner, as the intensity of its diffraction peak is much higher than that deposited at 453°C, or it might represent a local maximum. Either way, it does not alter the global maximum diffraction peak intensity which occurs at 509°C.

Figure 16 also demonstrates that the closer the lattice constant becomes to the CdO reference value, the more intense the diffraction peak becomes. This means the closer the black curves (peak position) gets to the red line (the reference CdO) the greater the values of corresponding point on the blue line (peak intensity). This result is expected because the film quality should improve as the lattice constant of the film approaches the lattice constant of the reference CdO. Once the lattice constant of the film and reference CdO are equal, the position of the diffraction peak will be identical.

The fact that the (002) diffraction peak for all CdO films were always less than the CdO reference is significant. This means that the lattice constant of the film is always greater than the reference. Furthermore, it means that all films are under tensile strain. It will be shown later in section 2.7.1 that the lattice constant of CdO increases with irradiation dose [49]. This means that the lattice constant of CdO increases as the concentration of oxygen vacancies increases. This result is consistent with InN, where it was found that N vacancies shift the diffraction peaks to lower 2Theta values [50]. Since oxygen vacancies shift the lattice constant, and add free carriers to conduction band, the Hall data and diffraction data should have a similar dependence on the deposition temperature. Table 6 gives the Hall data and the diffraction peak position as a function of deposition temperature.

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Table 6: Hall data and (002) diffraction peak position as a function of deposition temperature.

Temperature (°C) (eV) (002) Peak n (cm‐3) µ (cm2/Vs) ρ (Ωcm) CdO film 170 37.88 2.61E+20 51.5 4.85E‐04 CdO film 310 37.96 1.17E+20 47.3 1.16E‐03 CdO film 453 37.92 4.29E+19 106.8 1.36E‐03 CdO film 479 38.00 3.93E+19 123.1 1.29E‐03 CdO film 509 38.02 2.70E+19 119.9 1.93E‐03 CdO film 531 37.99 3.92E+19 114.0 1.40E‐03

Table 6 shows the carrier concentration is lowest at 509°C, where the diffraction peak is both the most intense and closest to the reference CdO values. This is a direct result of the concentration of oxygen vacancies decreasing as the deposition temperature increases up to 509°C; oxygen vacancies increase once again as the temperature increases past this point. The mobility has a similar dependence on deposition temperature as the carrier concentration, only it reaches its maximum value at a deposition temperature 30°C lower than the carrier concentration.

Figure 17 shows diffraction peak position and carrier concentration dependence on deposition temperature.

Figure 17 Diffraction peak position (black curve) and carrier concentration (red curve) as a function of deposition temperature.

Figure 17 shows the strong correlation between diffraction peak position and free carrier concentration. The closer the diffraction peaks is to the CdO reference (38.338), the lower the free carrier concentration. However, the minimum resistive occurs at a deposition temperature of 479°C.

The final parameter that was investigated to determine the optimal CdO deposition temperature was the FWHM of the rocking curve. This data is presented in Figure 18.

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Figure 18: Rocking curve for CdO on sapphire as a function of deposition temperature.

Once again the film deposited at 310°C appears to be an outlier as it does not follow the trends of the other 5 films. For all other films, increasing deposition temperature produces two effects. First, the intensity of the peak intensity increases with temperature, and it saturates at about 300 for films deposited at 453°C. This is consistent with the peak heights presented in Table 5, because the center of the rocking curve corresponds to the same condition at the 2Theta peak. Second, as the deposition temperature increases, the FWHM gets smaller. This trends starts from the lowest temperature film and continues all the way up to 509°C. Only at 531°C does the FWHM become larger again. Table 7 shows the FWHM, 2Theta position of the CdO (002) and the carrier concentration.

Table 7: FWHM, carrier concentration and 2Theta position as a function of deposition temperature.

Temperature (°C) FWHM (o) (002) Peak n (cm‐3) CdO film 170 5.35 37.88 2.61E+20CdO film 310 4.85 37.96 1.17E+20CdO film 453 4.66 37.92 4.29E+19CdO film 479 4.7 38 3.93E+19CdO film 509 4.18 38.02 2.70E+19CdO film 531 4.42 37.99 3.92E+19

The FWHM correlates with the carrier concentration at all deposition temperatures, so that the wider the rocking curve the greater the carrier concentration. This is consistent with the claim that free carriers are caused by defects, specifically oxygen vacancies, and films with wider rocking curves have more oxygen vacancies and, thus, more free carriers.

It was shown that structural properties, such as rocking curve width, diffraction peak intensity and diffraction peak position, correlate well with the electrical properties, such as carrier concentration and mobility. Because of this, optimizing the structural factors allows for the optimization of the electronic properties. In theory any of the structural parameters listed above could be used to maximize electronic properties. However, some parameters are more sensitive than others. Diffraction peak intensity, while inversely related to carrier

49

concentration, is not the best structural parameter to optimize. The change in intensity is actually fairly large between most films. But, according to the change in peak intensity, the film deposited at 310°C should have a mobility that is higher than the one that was measured for the 453°C film. This was not the case as the film deposited at 310°C has a mobility less than half of the mobility of the film deposited at 453°C. In addition, if the slit of the diffractometer is changed, then the intensity of the peak will change even if the film’s properties have not. For that reason, diffraction peak intensity is a useful indication of the electrical properties, but it is not the best parameter to optimize.

Diffraction peak position and rocking curve width are the two best structural parameters that indict low carrier concentrations and high mobilities. Diffraction peak position is very sensitive and does not depend on variables such as the detector slit width. The rocking curve width is even more sensitive than the diffraction peak position. As the films approach the minimum carrier concentration, the rocking curve becomes much narrower, decreasing from 4.7° to 4.2°, even though the carrier concentration only fell from 3.9*1019 to 2.7*1019 cm‐3. However, it should be stressed that optimizing the structural properties is no guarantee that the electronic properties will also be optimized. Even though all structural parameters are optimized for the film deposited at 503°C, the film deposited one step lower, at 479°C, had the best electronic properties because it had the lowest resistivity.

Previously, it was shown that the narrowest FWHM is 4.2°. This is actually quite large, much larger than typical FWHM published for ITO or AZO. This significantly larger FWHM implies very poor crystallinity in CdO compared to these ITO and AZO films. However, this lower crystal quality in CdO does not lead to worse mobility. In fact, the mobility in these CdO films far exceeds anything in ITO and AZO in spite of the very broad rocking curves.

Figure 19: Rocking curve FWHM for Zn0.98Al0.02O on (110) sapphire (red line), (001) sapphire (green line) and (012) sapphire (blue line) [51].

Figure 19 illustrates two important facts. First, that the shape of the FWHM peak is similar for ZnAlO (Figure 17) and CdO (Table 7). The there is also a large decrease in the FWHM from room temperature up to about 300°C. The FWHM becomes larger for temperatures above about 500°C. The main difference between ZnAlO and CdO is that CdO does not have the FWHM

50

plateau between 300 to 500°C. Second, the FWHM in Figure 19 at 1 to 2° are far less than the 4 to 5.5° shown in Table 7. In fact, the FWHM for CdO on sapphire has more in common with ZnAlO on glass than it does with ZnAlO on sapphire. The FWHM for ZnAlO was found to be between 4 to 8°. Yet the mobilities of the ZnAlO on sapphire is 5 to 6 times less than that measured for CdO. Initially, it might seem that the gains in mobility of CdO are a direct result of the loss of ionized impurity scattering due to 10 times less free carriers in the film. But mobility gains achieved by reducing the carrier concentration in ZnAlO and ITO are extremely small. Figure 20 demonstrates this important point.

Figure 20: ZnAlO resistivity, carrier concentration and mobility as a function of Al weight percent [52].

Figure 20 shows that carrier concentration changes by 2 orders of magnitude, decreasing from 1*1021 to 1*1019 cm‐3, yet the mobility only increases by about 80% (from 15 to 28 cm2/Vs). This illustrates why every low resistivity ITO and ZnAlO film has carrier concentrations in excess of 1021 cm‐3 because the mobility limit for these materials is low, regardless of the crystal quality. For ITO and ZnAlO the result is that, since the mobility is only weakly affected by adding additional ionized impurity centers, it always makes sense to drive the resistivity down by increasing the free carrier concentration.

Even when CdO has not been doped with donor atoms, the resistivities of CdO compares favorably with the values presented in Figure 20. This means that, even in the absence of intentional donor dopants and very high quality films, as defined by rocking curves with FWHM near 1°, CdO has a clear mobility advantage over ITO and ZnAlO. Thus, for applications where the transparent window lies in the IR region, CdO deposited above 300°C, has properties that no ITO or ZnAlO film can match.

3 . 4 . 3 . An n e a l i n g

Post deposition possessing is an important step that can often greatly improve film quality. So, in addition to optimizing the deposition temperature, the optimal annealing temperature was

51

also investigated. Annealing is often a critical step because heat gives the system enough energy for atomic diffusion to occur, which can then lead to the removal of defects and grain growth, both of which are almost always desirable. However, for TCOs, unlike many other applications, annealing can sometimes result in poorer performances. This is because, while a lower defect concentration in the film reduces scattering and thus increases mobility, it also reduces the free carrier concentration. Maximizing conductivity involves maximizing the product of the carrier concentration with the mobility, not optimizing one variable alone. For this reason, annealing a TCO to improve the conduction properties is more complex and not actually the same thing as simply annealing to remove defects in the film.

Figure 21: Carrier concentration (squares) and mobility (circles) as function of annealing temperature for low (black), moderate (red) and high (blue) quality CdO film.

Figure 21 illustrates that the higher the pre‐anneal mobility is, the higher the post‐anneal mobility will be. This is consistent with the concept that annealing improves film quality by increasing the grain size and reducing defects, so the higher the pre‐anneal film quality, the higher the post‐anneal film quality. Figure 21 also illustrates that better quality films, as defined by high pre‐anneal mobility, can withstand higher temperatures before the film begins to decompose. The lowest quality film sees a sharp reduction in mobility, most likely caused by rapid increase in the oxygen vacancy concentration, at 550°C. The moderate quality CdO film does not see a similar decrease in mobility until 700°C. Even up to the highest temperature, 700°C, the highest quality film does not exhibit a sharp decrease in mobility.

Finally Figure 21 shows that the maximum mobility is obtain for annealing at 500°C. At this temperature the carrier concentration is also a minimum. This temperature is consistent with the mobility as a function of deposition temperature as was presented in Table 6. Here, the optimal mobility was achieved at 479°C. It is expected that these two temperatures should be similar because annealing occurs during film growth as well. So, bulk atoms in the film both during growth and during post‐growth annealing would behave similarly. However the two temperatures do not have to be identical. Surface atom behavior might be very different

52

because, during pulsed laser deposition, the equation describing the adatoms total energy has a kinetic energy terms that comes from ablation and a thermal energy term that comes for the substrate temperature.

It was shown that mobility is an excellent proxy for film quality, but is mobility an effective indicator of resistivity? Figure 22 shows the mobility and resistivity of the same CdO films as a function of annealing temperature.

Figure 22: Resistivity (triangles) and mobility (circles) as a function of annealing temperature for low (black), moderate (red) and high (blue) quality CdO thin films.

Figure 22 show that the lowest resistivity film is actually the lowest quality, lowest mobility, highest carrier concentration CdO film. For all films, the lowest resistivity is achieved by annealing at just 250°C. At 250°C and below, the mobility increases while the carrier concentration is stable. At annealing temperatures above 250°C the carrier concentrations decreases faster than the mobility increase.

The above conclusion is that the lowest quality, lowest mobility CdO film has the lowest resistivity, and, thus, the best conduction properties seems counter‐intuitive. This is because for undoped CdO the free carriers come from oxygen vacancies, or defects in the film. Once free carriers originate from dopant atoms, such at Al, Ga or In, finding the deposition conditions that result in maximum mobility in the undoped CdO becomes a critical step in fabricating the lowest resistivity TCO. This is a consequence of the fact that adding donor atoms to a CdO matrix with higher pre‐doped mobility would be much more effective than adding donor atoms to low mobility CdO film.

Determining the optimal deposition and annealing conditions is important not only for effectively adding donors to CdO, but also for adding acceptors. If p‐type CdO could be fabricated, such as by alloying with Cu, Au or Ag, these acceptors (which make the film p‐type) would have to compete with oxygen vacancies which make the film n‐type. Thus, reducing the concentration of oxygen vacancies is a critical step in the process to make p‐type CdO. The goal

53

here was to see how low the carrier concentration could be driven by careful selection of the deposition and annealing condition. This meant combining the optimal deposition temperature, with a high temperature anneal. Table 8 compares a CdO film deposited at 509°C and annealed for 3 minutes at 750°C with the previously lowest published carrier concentration of undoped CdO deposited on sapphire by any deposition method.

Table 8: Lowest carrier concentration for CdO on sapphire.

Deposition method Carrier concentration (cm‐3) Mobility (cm2/Vs)CVD [52] 2.35*1019 216 PLD 8.26*1018 242

Table 8 shows that the deposition and annealing conditions discussed above lead to the lowest carrier concentration of any CdO deposition on sapphire by any deposition method. This is the first time CdO films have been fabricated with carrier concentrations below 1*1019 cm‐3. Compared to many other semiconductors, this is still a very high carrier concentration; however, most other semiconductors do not have such a low formation energy for anion vacancies. Even though these deposition conditions yield the lowest carrier concentration CdO they are probably not low enough to allow for the easy creation of p‐type CdO. Any acceptors in CdO not only have to compensate for existing oxygen vacancies, but any additional defects that are created by the alloy (because defects will be predominately donors).

3 . 5 . I o n I r r a d i a t i o n i n CdO

2 . 5 . 1 . D i s p l a c eme n t D ama g e Do s e

The previous section discussed the optimization of the deposition conditions for CdO. After fabricating high quality CdO films, the next step was to introduce defects into the films in a controlled manner. This would provide a method of determining how defects affect the electronic and optical properties. In order to introduce high concentrations of point defects, CdO films were irradiated with He+, Ne+, C+ and Ar+ ions. Since each ion has a different mass and radius, the amount of damage produced per ion dose will vary. To account for this, the displacement dose method, developed by the Naval Research Laboratory, was used [53, 54]. Displacement damage dose describes the total damage introduced to the film, it does not depend on the mass of the irradiating species or the rate at which irradiation occurred. The displacement damage dose has units of MeV/g, energy per mass, and is defined in the following equation:

( ) ( )PDNIELD *= Equation 35

where D is the displacement damage dose, NIEL is the non‐ionizing energy loss and PD is the particle dose. NIEL is one of two mechanisms that energetic particles have to dissipate their energy into the lattice. Ionizing energy loss (IEL) occurs when the incident species losses energy by ionizing atoms in the lattice. NIEL is when the incident species transfers energy to the lattice

54

by displacing atoms from their equilibrium position. While bonds are broken, the incident ions do not strip electrons off these atoms in the process. IEL is sometimes referred to electronic stopping and NIEL is sometimes referred to as nuclear stopping. Figure 23 shows both NIEL and IEL for a variety of ions implanted into silicon.

Figure 23: NIEL and IEL for various ions in silicon.

The green line marks the range of the energy scale that is typically used for irradiation experiments to introduce point defects. It can be seen from Figure 23 that, at higher energies, the electronic component becomes stronger while the nuclear component becomes weaker. Higher ion energies results in more energy transfer to the lattice (higher stopping power) because the more energetic ions are, the easier it is for them to strip electrons off the atoms. Initially, it might be assumed that the same is true for the nuclear stopping, that higher energy ions results in more displaced atoms because the irradiating species have more kinetic energy. However, at higher energies, the stopping cross section is smaller. Since these energetic species have more kinetic energy, they spend less time in the vicinity of any given lattice site, so the interaction time between the incident species and the lattice site is far smaller, resulting in less displaced atoms.

In terms of producing defects, the NIEL is the more important term. By displacing atoms, this method induces point defects in the film. A larger NIEL term would result in more point defects so it is important to have an accurate method for determining this quantity. This is shown in Equation 36 [53]:

( ) ( ) ( )[ ] Ω⎟⎠⎞

⎜⎝⎛

Ω= ∫ dETLET

dEd

ANNIEL ,,,

min

θθθσπ

θ

Equation 36

where N is Avogadro’s number, A is the atomic mass and θmin is the scattering angle at which the recoil energy equals the threshold value for atomic displacement, dσ/dΩ is the differential scattering cross section for atomic displacement, T is the recoil energy of the target atom and L

55

is the Lindhard partition factor, which determines what portion of the total energy term is dissipated to ionizing energy loss mechanisms and which to non‐ionizing loss mechanisms. In this study, the Stopping and Range of Ions in Matter (SRIM) was used to compute NIEL for a variety of different ion species.

3 . 5 . 2 . F e rm i S t a b i l i z a t i o n E n e r g y i n C dO

Point defects were introduced into CdO films by ion irradiation. Hall effect was performed after each implantation to determine the effect of irradiation on the carrier concentration and mobility. Figure 24 shows the carrier concentration as a function of displacement damage dose using Ne+. For comparison, irradiation of InN with He+ is also included.

Figure 24: Electron concentration in CdO and InN as a function of displacement damage dose.

Prior to irradiation with Ne+ the CdO film had a carrier concentration of 9*1019 cm‐3, indicating many donor defects are present in the as grown film.

Figure 24 also shows that, for displacement damage doses less than 1.0*1016 MeV/g, there is a linear dependence between carrier concentration and displacement damage dose. Above this value the carrier concentration begins to saturate and reaches and an asymptote at doses above 2.0*1016 MeV/g.

The curves for CdO irradiated with Ne+ and InN irradiated with Ne+ are similar. They both increase linearly with displacement damage doses up to 1.0*1016 MeV/g. They also both saturate with carrier concentration of 4.5‐5*1020 cm‐3. It might be expected that the carrier concentration for CdO and InN reach a similar saturation level. The number of electrons (holes) at saturation is determined by the curvature of the conduction band (valence band) and the distance between the Fermi stabilization level and conduction (valence) band edge. While it will be shown in detail later, essentially an integration is performed, the upper bound being the Fermi level at saturation and the lower bound is the conduction band minimum. Conceptually it is like filling the conduction band with a fluid until the level rises to the Fermi stabilization level, EFS. Only in this case the ‘fluid’ is electrons. Thus, if two films shared a similar conduction band curvature as well as a similar conduction band minimum, the position referenced to

56

vacuum would be expected to be the same and the carrier concentration at EFS should be similar.

The curvature of the conduction band is related to the effective mass of by the following equation:

A1 2

2

2* *11dk

Edm h

= Equation 37

where m* is the effective mass, ħ the reduced Planck constant, d2E/dk2 is the second derivative of the band, so it represents the band curvature. Literature values for the effective mass of InN are close to 0.07, while they are close to 0.2 for CdO. This shows that the curvature is similar for the two semiconductors, much closer than for other oxides like TiO2 with m

* close to 1, though InN does have a higher curvature than CdO.

The second factor that has to be considered is the position of the conduction band edge. Conduction band states are anti‐bonding states, while valence band states are bonding states. Though the bonds are partially covalent, the cation can be thought of as donating electrons while the anion, being more electronegative, can be thought of as accepting electrons. In this way, the anions are considered to comprise the valence band states and the cation the conduction band states. Thus, for a first approximation, the position of the conduction band edge with respect to vacuum should be determined by the electronegativity of the cation and the position of the valence band by the electronegativity of the anion. Cadmium has a Pauling electronegativity of 1.69 while Indium has a Pauling electronegativity of 1.78, very similar. So, given similar band curvatures and conduction band positions, it seems reasonable that CdO and InN have similar carrier concentrations at saturation.

3 . 5 . 3 . L i g h t v s He a v y I o n I r r a d i a t i o n

While irradiation of CdO with Ne+ is consistent with irradiation of InN with He+, irradiation of CdO with He+ is not. This is shown in Figure 25.

Figure 25: Electron concentration in CdO and InN as a function of displacement damage dose using Ne+ and He+.

57

Figure 25 includes data from King et al. which shows that CdO irradiated with He+ is reproducible, and yet still inconsistent with Ne+ irradiation. Figure 25 implies that there are two separate saturation values, one for the heavy Ne+ ion and one for the light He+ ion. This is not predicted by the amphoteric defect model because, since Ne+ and He+ have the same displacement damage dose, they should both produce the same number of defects in the film. Assuming there is no difference in the compensation in the films, the difference in carrier concentration between Ne+ and He+ irradiation implies that there are more than twice as many donor defects in the Ne+ irradiated films.

3 . 5 . 4 . Me t a s t a b l e v s E q u i l i b r i um

One possible limitation of the amphoteric defect model is that it assumes that the system is at equilibrium. When the Fermi level stabilizes, the formation energy of donor and acceptor defects are assumed to be exactly equal, which is the lowest energy state. But, it is possible that the system could be trapped in a metastable state, and, thus, not be at equilibrium. If this were to happen then the system would stabilize at a state different than that predicted by the amphoteric defect model. This would result in a carrier concentration that could be greater or smaller than the equilibrium value.

There are few factors that can drive a system towards a metastable state rather than the equilibrium state. One is time. If the system is not given enough time to reconfigure in order to find the lowest energy configuration, it is often stuck in a local, rather than global, minimum. This process is well document in many areas, such as quenching in metals.

Another factor that can drive a system to a metastable state is if a large activation barrier exists between a local minimum and the global minimum. In this process the system reconfigures to a nearby, lower energy, metastable state and becomes stuck because a large activation barrier exists between the local and the global minimum. This process is also well document in many other systems. A good example is carbon in the diamond configuration. Graphite is actually the equilibrium state for carbon, but carbon will exist as diamond because it can not overcome this activation barrier.

With this in mind, the question is whether the difference in carrier concentration at saturation between Ne+ and He+ irradiation can be explained by one or both of these processes. This would mean that either the Ne+ irradiation overshot the equilibrium carrier concentration and they system was trapped with defects that were donors even though they would, under ideal conditions, be acceptors, or, that some acceptor defects recombined even though they would, under ideal conduction, be stable. Or, if He+ irradiation undershot the equilibrium carrier concentration it would mean that the system was trapped with defects that were acceptors even though they would, under ideal conditions, be donors, or, that some donor defects recombined even though they would, under ideal conditions, be stable. In order to determine why the carrier concentration has two separate saturation values, both the rate at which defects are introduced into the film and the mass of the ion will be considered.

58

3 . 5 . 5 . De f e c t F o rm a t i o n R a t e

Normalizing irradiation with different ions to a common displacement damage dose normalizes the total amount of damage but it does not normalize the rate at which that damage occurs. A single heavy ion will cause considerable more damage to the lattice than a single light ion. As result, irradiation with lighter ions will require a higher dose to cause the same amount of total damage. The implication is that lighter ions often require longer irradiation times because the flux often cannot be scaled at the same rate to compensate the loss in mass.

To determine whether the rate at which CdO is irradiated is important, a “fast” and “slow” Ne+ implant were performed. In this case it is important to keep the irradiating ion constant because the manner in which the ion interacts with and damages the lattice depends on atomic size. In this way, parameters such as the capture cross section were held constant.

Figure 26 shows the irradiation results including “fast” and “slow” Ne+ irradiation.

Figure 26: Electron concentration in CdO as a function of displacement damage dose using “fast” and “slow” Ne+ and He+.

The “slow” implant occurred over 2,500 seconds while the “fast” implant occurred over 25 seconds. This gives a spread in the irradiation time of 2 orders of magnitude. Ideally, a larger window would be studied, but this was largest dynamic range possible. Implant durations above 2,500 seconds require fluxes that are too small while implant durations below 25 seconds require fluxes that are too large.

Figure 26 shows that there is no significant difference between the fast and slow Ne+ irradiation of CdO. Both values are almost identical, 3.7 to 4.0*1020 cm‐3. And while both values are slightly below the previous Ne+ irradiation carrier concentration of 5.0*1020 cm‐3, both fast and slow Ne+ irradiation confirm the higher carrier concentration value. So, at least for Ne+, with the damage rate range of 100 tested, there is no difference in saturation carrier concentration.

59

3 . 5 . 6 . Ma s s o f I r r a d i a t i n g I o n

If the rate of damage is not enough to explain the discrepancy between He+ and Ne+ irradiation then perhaps it is related to the mass. This mechanism is more complex because, as mentioned above, changing the ion mass changes many variables. The damage rate is related to the mass. The more massive the ion the higher the damage rate because larger atoms more easily knock atoms off lattice sites. Also, the density of defects in the crystal around a single incident ion increases with atomic size. Since heavy ions create more vacancies per incident ion than light ions, it is expected that defects will be closer together. If these defects interact with each other, this defect concentration, and its dependence on ion mass, may be important.

In order to determine if the ion mass of the irradiating species is important, irradiation on CdO was conducted with both a very heavy and a very light ion. Argon was chosen as the heavy ion. With an atomic mass of 39.9 amu, it is significantly heavier than Ne and He. It is also one the heaviest elements that could be implanted at LBL through a thickness of approximately 100 nm. Argon is also a good choice as it is also a noble gas. Because it has a filled valence shell, it is unlikely that any Ar will occupy lattice sites and form bonds. Thus, irradiating with Ar+ should not change chemical structure of the film, its only effect being to produce defects. For the “light” ion, ideally, CdO would be irradiated with an element much lighter than He. But this is not possible as the only element lighter than He is H. It is not easy to product irradiation damage with H+, furthermore, it is possible that some H would form bonds with atoms in the lattice. For this reason C was chosen as the “light” element. Carbon is appealing because it far lighter than Ne and Ar. However C does not have a filled valence shell; it is not a noble gas like He, Ne or Ar. In theory, C could act as a donor if it sits on a Cd site or an acceptor if it sits on an O site. However, C on a Cd site seems unlikely. The atom size difference between the two is enormous. The atomic radius of Cd is 161 pm while that of C is 67 pm, so it is questionable whether C, in any quantity, would sit on a Cd site. Carbon could also act as an acceptor if it were to sit on an O site. While this seems far more likely than substitutional C on a Cd site, the solubility is expected to be very low because of the large electronegativity difference between C and O. Small concentrations of C in the lattice are unlikely to change the results much. In order to affect the carrier concentration at saturation, substitutional C would have to be present in very high concentrations. Given that CdO has a density of 8.15 g/cm3 and a molar mass of 128.41 g/mol, there are roughly 3.8*1022 atoms/cm3 in CdO or 1.9*1022 O atoms/cm3. Assuming free carriers are caused exclusively by oxygen vacancies (which each provide two electrons to the conduction band) roughly 1 in 76 oxygen atoms must be vacant. In order to counter all, or even part of the 1 in 76 oxygen atoms, the quantity of C in the lattice would have to be in the several percent range.

Figure 27 shows the results of Ar+ and C+ irradiation, together with the previous irradiation results.

60

Figure 27: Electron concentration in CdO as a function of displacement damage dose for “fast” and “slow” Ne+, He+, C+ and Ar+ [49].

Irradiation with Ar+ and C+ produces carrier concentrations that are clustered very close to the original Ne+ irradiation data, as well as the fast and slow Ne+ irradiation. Thus, whether a heavy ion like Ar+ is used, or light element like C+ is used, the carrier concentration reaches a single value of approximately 5*1020 cm‐3. It is only when a very light ion, such as He+, is used does the carrier concentration saturate to a different value. Thus, it appears that the true carrier concentration at the Fermi stabilization energy level is 5*1020 cm‐3, and that the previously published value of 2*1020 cm‐3 is incorrect.

3 . 5 . 7 . T h e Me t a s t a b l e S t a t e

If the free carrier concentration of 2*1020 cm‐3 is a metastable state, why does it only exist when irradiated with He+, C+, Ne+ and Ar+ all saturate to a different value. Most likely this has to dynamic annealing, which is most efficient when the films are irradiated with very light elements, such as He+. Dynamic annealing has been well documented in elemental semiconductors, such as Si, and III‐V semiconductors, though many of the results can be applied to II‐VI semiconductors.

Early irradiation studies on Si were not concerned with introducing point defects to increase the carrier concentration, but rather to amorphize the semiconductor. Given the carrier concentration in CdO after irradiation, the irradiation dose needs to be high enough that roughly 1 in 100 atoms have been displaced in the lattice. For amphorization the dose has to be high enough to displace every atom, which would lead to a complete disorder of the lattice. So the displacement damage doses for amphorization are about 100 times higher. However, the physical mechanics leading to defect annihilation at low and high displacement damage doses are identical.

For irradiation of semiconductors, the initial displacement of atoms occurs on a time scale of about 10‐11 seconds [55]. For times greater than this, if the atoms are immobile then the cascade is said to quenched, and any defects that result are frozen into the material. However, for time greater than 10‐11 seconds, if the atoms are still mobile then defects, such as vacancies

61

and interstitials, can recombine. This recombination of defects during implantation is called dynamic annealing.

The effectiveness of dynamic annealing depends on many variables. It was shown that implantation at higher temperatures resulted in more significant dynamic annealing. In order to amphorize Si at high temperatures, a larger displacement damage dose is necessary than if the Si is cooled during irradiation. This is because the high temperature irradiation has to create enough damage both to amorphizing the semiconductor and to overcome the annealing that occurs during the implant.

For Si, it was also found that amorphization occurred at lower displacement damage doses than when heavier ions were used. Lighter ions required a higher displacement damage dose to induce the amorphous state. The temperature was constant, so defects are equally mobile in all cases. In fact, it was shown that defects are mobile in Si even at room temperature [56, 57]. For Si, it was found that irradiation with heavy ions resulted in higher defect densities in the cascade. These defects formed clusters that were stabilized so that most of the irradiation induced damage was stable at room temperature. When lighter ions were used, even though the defects are mobile, the defect density in the cascade was too low for a majority of the defects to form stable clusters. This resulted in only part of the irradiation induced damage being stable at room temperature.

In addition to temperature and ion mass, lattice ionicity was also found to be a significant factor that can induce dynamic annealing.

Figure 28: Threshold Si+ dose necessary to induce amphorization in semiconductors [55].

Figure 28 shows the threshold dose of Si+ necessary to amorphize several common semiconductors. A higher threshold dose means dynamic annealing is more efficient. The graph is segmented into three areas. The first region contains semiconductors where dynamic annealing is not present. This is the left portion of Figure 28 and these materials tend be either elemental semiconductors such as Si and Ge, or compound semiconductors that have covalent

62

bonds. This means the electronegative difference between the anion and cation is small, so bonding in these semiconductors is similar to elemental semiconductors. For elemental semiconductors, when a defect is produced, there is no large driving force to recombine. The second region is composed of compound semiconductors that have partially ionic bonds. This is a result of a moderate difference in electronegativity between the cation and the anion. In this region, dynamic annealing starts to become measurable. The third and final region contains semiconductors that tend to have significant ionic bonding character, which is a direct result of the large electronegativity difference between the cations and anions. Defects in these semiconductors have a very large driving force to recombine. Materials in this region also exhibit significant dynamic annealing.

The effect of bond ionicity can clearly be seen by varying the cation and keeping the anion constant. For example comparing the threshold amorphizing doses for InN, GaN, and AlN illustrates the influence of bond ionicity. In each case, as the bonding becomes more ionic, dynamic annealing becomes more significant. While this trend of increasing ionicity leading to increasing dynamic annealing is well documented, it is not well understood [58]. The only things that appear certain are the following: the greater the ionicity of the bonds the greater the electrostatic energy caused by disorder will be [59] and the inability of covalent bonds to rotate may reduce the effectiveness of dynamic annealing in covalent materials [60]. Intuitively, each of the two main mechanisms makes sense. Charged defects in a very ionic material would experience a larger Coulomb force, this would raise the energy of the defect and provides some driving force to reduce the defect concentration. Likewise, forming rigid covalent bonds would make re‐crystallization harder than forming isotropic ionic bond.

Since the mechanism of dynamic annealing is not well understood, most of what exists in the literature is empirical rules. For example, it was found that ionicity, as defined by Phillips is more descriptive than Pauling’s definition.

Equation 38 is the Phillips definition of ionicity:

( ) 2

2

22

2

gh EC

CECI =+

= [59, 61] Equation 38

where I is the ionicity, Eg is the band gap, Eh is the covalent contribution to the band gap, and C is the ionic contribution to the band gap.

Equation 39 is the classic Pauling definition of ionicity:

( )4

2

1BA XX

eI−

−−= Equation 39

where XA and XB are the electronegativity of the cation and the anion.

63

However, since the Pauling’s definition is more common and easier to compute it often used instead of Phillips’ definition.

Using Phillips’ definition, it was found that materials with I values of less than 0.47 tend to displayed little dynamic annealing, and were thus called strongly covalent materials. Materials with I values greater than 0.60 displayed significant dynamic annealing, and were thus called strongly ionic. Materials with 0.47<I<0.60 fell in between, displaying a moderate amount of dynamic annealing, and were considered to have large covalent and ionic contributions to their bonding. Ionicity is computed to be 0.54 for CdO and only 0.33 for InN. Thus, according to the ionicity criteria, it is expected that CdO, which sits very close to the 0.60 cut off, is much more likely to display strong dynamic annealing while InN, being well with in the covalent region, should display no dynamic annealing. This is consistent with He+ irradiation of CdO and InN, as InN, no matter the ion used, reached EFS.

Although not shown in Figure 28, metals are extremely hard to amorphize. In metals, even under intense irradiation, the system is not stable in an amphorous phase because there is almost no barrier to recrystallization. This means, even at cryogenic temperatures, metals experience significant dynamic annealing [58].

3 . 5 . 8 . R o l e o f An i o n V a c a n c i e s

In addition to the mass of the irradiating ion and the ionicity of the bonds, the number of vacancies in the material is a significant factor that determines the stability of defects in the system, and, thus, determines whether EFS can be reached under irradiation. There is no published work investigating the role that oxygen vacancies in CdO play in dynamic annealing, but this phenomenon has been studied in a similar system. Devanathan and Weber modeled 3 oxide systems, Zircon (ZrSiO4), Zirconia (ZrO2) and yttria‐stabilized zirconia (Zr1‐xYxO2, or YSZ) [62]. In terms of irradiation induced defects, the systems are very similar with one key difference: the number of anion vacancies. Here, ZrSiO4 is the system which has a very low concentration of oxygen vacancies, ZrO2 has a moderate concentration of oxygen vacancies and YSZ has a very large concentration of oxygen vacancies prior to irradiation.

64

Figure 29: (a) Number of interstitial atoms in the displacement cascade for Zirconia and YSZ irradiated with Zr+. (b) Total number of interstitials defects in Zircon as a function of time [62].

Figure 29 (a) shows that, in the early stages, for times less 0.3 picoseconds, each oxide has a similar number of cation and anion vacancies. For times less than 0.3 picoseconds, the atoms do not have sufficient time to diffuse and, thus, they cannot recombine or form stable defect centers. At this point, the concentration of interstitials is controlled exclusively by the displacement damage dose, which is similar for both oxides. For times greater than 0.3 picoseconds the blue curves stay close to each other while the yellow curves begin to diverge. The number of anion interstitials in YSZ reaches an asymptote of 0 at 10 picoseconds while the number of anion interstitial in ZrO2 reaches an asymptote of 20 interstitials at 10 picoseconds. It should be noted that interstitial numbers in Figure 27 are only for those introduced by the irradiation, it does not consider interstitials that existed prior to irradiation. So, as seen in Figure 29, at 10 picoseconds when the YSZ has zero anion interstitials, it just means no interstitials caused by irradiation remain. This is the condition for a perfect dynamic annealing of anion interstitials, in that all radiation induced damage is removed.

Figure 29 further reinforces the importance of initial vacancy concentrations. Zircon has very low concentrations of both cation and anion vacancies. Here, irradiation creates a larger numbers of interstitials in the final state. Not only are the stable defect concentrations much higher than in YSZ and ZrO2, but the cations and anions are stable at a similar concentration. Cation and anion interstitials differ by only a factor of two. This result is expected, since ZrSiO4 has a similar number of cation and anion vacancies and, since the total vacancy concentration prior to annealing is small, it is expect both cation and anion values should saturate at a similar, high, level.

Further insight into the effect of anion vacancy concentration can be obtained by studying the distance between nearest neighbor interstitial and vacancy pairs. Devanathan and Weber also investigated this parameter in YSZ [62], and it is also relevant to CdO. This parameter is important because it represents the minimum distance that an interstitial must diffuse to recombine (i.e., repair the damage). Figure 30 (a) shows the distance between interstitial and vacancy pairs in YSZ and ZrO2, while Figure 30 (b) shows this parameter in the final state.

65

Figure 30 (a) Distance between interstitial and nearest vacancy as a fraction of total interstitials at peak damage. (b) final state [62].

Figure 30 (a) shows that, regardless of the initial concentration of vacancies prior to irradiation, all films have similar defect distributions at peak damage. The notable difference being that films with higher initial concentrations have distributions clustered more toward small distances than large. This makes sense because additional vacancies presented before irradiation would tend to decrease the distance between interstitials and vacancies. The main difference shows up after irradiation, in Figure 30 (b), where anion interstitials in YSZ all recombined. According to these calculations, not even a single anion interstitial survives after 30 picoseconds, all recombined with vacancies. This is not the case for anions in ZrO2, or cations in both YSZ and ZrO2. The key point highlighted here that, when the concentration of vacancies is high, the probability of recombination between interstitials and vacancies is also high. This increased probability of recombination leads to dynamic annealing in YSZ, or any other films that has large vacancy concentrations before irradiation. This result can also be applied to CdO. Cadmium oxide has a large anion vacancy concentration because the films have electron concentrations of 9*1019 cm‐3 to 5*1010 cm‐3, and it believed that electrons come from oxygen vacancies. Each oxygen vacancy contributes two electrons to the conduction band. Given the very high vacancy concentration prior to irradiation, each interstitial does not have to diffuse far to recombine with a vacancy, as each interstitial has the opportunity to recombine with pre‐existing vacancies in addition to irradiation induced vacancies. For this reason, in CdO, interstitials do not always reach the critical concentration necessary to form stable clusters, resulting in a saturation of the Fermi level that is lower than EFS.

3 . 6 . Mode l i n g t h e Op t i c a l P rope r t i e s o f CdO

3 . 6 . 1 . V a r i a t i o n i n t h e Op t i c a l Ab s o r p t i o n E d g e

There is not a single optical absorption edge for CdO. Early growth papers for CdO reported values as low as 2.2 eV and as high as 2.6 eV. Of course, there is only one value for the band gap of any material, so this variation increase in the optical absorption edge cannot be accounted for by altering the distance between the valence and conduction bands. CdO films with low free carrier concentrations were typically fabricated by PLD or chemical vapor

66

deposition CVD. These films were observed to have an optical absorption edge between 2.2 and 2.4 eV and had free carrier concentrations in the mid to high 1019 cm‐3. CdO films with high free carrier concentrations were typically fabricated by sputtering or spray pyrolysis. These films were observed to have an optical absorption edge between 2.4 and 2.6 eV and had free carrier concentrations in the low 1020 cm‐3. So, there seemed to be a clear link between carrier concentration and position of the absorption edge. One possible explanation for this is the Burstein‐Moss shift. In the next section the Burstein‐Moss shift will be introduced. Then, irradiated CdO will be modeled to see if, by using the electrical data from Hall effect, it is possible to predict the absorption edge. These modeled absorption edges will be compared to the measured values to see if the observed shift in the absorption edge is a result of the Burstein‐Moss effect.

3 . 6 . 2 . T h e B u r s t e i n ‐Mo s s E f f e c t

In the mid 1950’s Burstein and Moss, independently, were investigating the optical absorption edge in InSb [63, 64, 65]. They found that the energy necessary to excite an electron from the top of the valence band to the bottom of the conduction band was always greater than the band gap, and this value became larger with increased carrier concentrations. They hypothesized that, in heavily doped semiconductors, a large concentration of free electrons occupied all of the states in the bottom of the conduction band. Thus, since new electrons can only be excited to unoccupied states, they would require additional energy. In this way, the “effective band gap” is larger, yet the distance between valence and conduction bands has not changed. According to this original band filling model, the optical absorption edge is given by the following equation:

BMgoptical EEE += Equation 41

where Eoptical is the optical absorption edge, or the minimum photon energy necessary to excite an electron from the highest occupied state in the valence band to the lowest unoccupied state in the conduction band, Eg is the band gap, or separation between valence and conduction band edges, and EBM represents the occupied states in the conduction band. For a parabolic band semiconductor EBM can we written as:

( )32

2*

2

32

nm

EBM πh= Equation 42

where ħ is the reduced Planck constant, n is concentration of electrons in an n‐type semiconductor or concentration of holes in a p‐type semiconductor and m* is the effective mass.

Equation 42 is valid for many wide gap semiconductors. However, in narrow gap semiconductors, the conduction and valence bands are close enough that they can interact. This interaction between the valence and conduction band can lead to the formation of a non‐

67

parabolic band. This means that the energy does not scale with k2. The original study was conducted by Kane, were he modeled the perturbation of the conduction band in InSb [66]. In this case the interaction between the bands distorted the conduction band, squeezing it inward. This reduces the density of states in the conduction band compared to the parabolic case. The non‐parabolic dispersion relation is given by the following equation:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+−= *

0

222

0

22

2222 mkEEE

mkkE ggg

C

hh Equation 43

If k is set to zero then Equation 43 reduces to the parabolic case where E is proportional to k2. So at k=0 there is no perturbation of either band. The strength of the interaction increases with k, so for low values of k the bands tend to be mostly parabolic, while for high values of k they become increasingly non‐parabolic in nature. The implication of this result is that, for low carrier concentrations, when the Fermi level sits close to the conduction band edge, the effects of non‐parabolicity of the bands is not extreme. However, for high carrier concentrations, when the Fermi level sits far from the conduction band edge, the non‐parabolicity of the bands becomes significant. Because of the higher carrier concentrations achieved during irradiation, all calculations use the non‐parabolic dispersion relationship.

Equation 43 relates the band filling due to free carriers in the conduction as a function of k, not carrier concentration, n. Experimentally n is measured in by Hall effect, not k. In order to link the measured carrier concentration to this band filling effect, the following equation is used:

CB

C

TkEcTk

ETk

E

TkE

TkE

dETk

E

e

enB

B

F

B

C

B

F

B

C

⎟⎟⎠

⎞⎜⎜⎝

⎛

+

= ∫∞

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−

/22

13

1π

Equation 44

where n is the carrier concentration as determined by Hall effect, T is the temperature, kB is the Boltzmann constant, EF is the electron energy and EC is the conduction band edge. The carrier concentration as a function of Fermi energy is computed from Equation 44 with k dependence on E being determined by Equation 43.

Equation 43 takes into account the curvature of the conduction band, but there is also curvature in the valence band. In order to model the optical absorption in CdO this second curvature needs to be considered as well. Since electrons are excited from the highest occupied states in the valence band to the lowest unoccupied state in the conduction band, the curvature of the valence band needs to be accounted for. This is done in exactly the same way as for the conduction band, and here it is assumed the valence band is parabolic. This gives the following equation for the valence band:

68

hV m

kE2

22h= Equation 45

where mh is the hole effective mass, and both k and ħ have their previously defined meanings. It should be noted that Equation 45 represents only a very small part of the increase in the optical absorption edge. The hole effective mass is more than 10 times larger than the electron effective mass, owing to the very flat nature of the valence band, so EV is always very small compared to EC.

Starting with Equation 41, setting Equation 43 equal to EBM and adding Equation 45, the following equation is derived:

VCgO EEEE ++= Equation 46

where EO is the optical absorption edge, Eg is the band gap, EC is the band filling or Burstein‐Moss shift and EV is the dispersion relation for the valence band.

Equation 46 provides a good approximation for the change in the optical absorption edge, however, it is incomplete; two additional terms can be added to get a more accurate model. Both of these terms are many‐body effects and they both narrow the band gap. This means they counteract the band filling effect described in Equation 46. In degenerately doped n‐type semiconductors there are very large free carrier concentrations in the conduction band, typically in the 1020 to 1021 cm‐3 range. These electrons, through exchange and Coulomb forces, interact both with other electrons and with the ion cores. This leads to the electron‐electron and electron‐ion terms which modify the band structure by drawing the valence and conduction bands closer together. A detailed explanation concerning the origins of these equations can be found in papers from Hamberg and Granqvist and well as Berggren and Sernelius [67, 68]. Equation 47 shows how the electron‐electron interaction is related to the carrier concentration:

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−−= −

− λπελ

πεF

eekeeE 1

0

2

0

2

tan412

2 Equation 47

where e is the charge of an electron, ε0 is the permittivity of free space, kF is the Fermi wave vector and λ is the Thomas‐Fermi screening parameter. The Fermi wavevector is given by the following equation:

( )31

23 nkF π= Equation 48

where n is the number of electrons in the conduction band, or holes in the valence band. The Thomas‐Fermi screening parameter is given by the following equation:

69

21

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

B

F

ak

πλ Equation 49

where kF is the Fermi wave vector defined in Equation 48 and aB is the Bohr radius.

The electron‐ion term is also related to free carrier concentration, and is given by the following equation:

21

*0

3

300

2

24

⎥⎦

⎤⎢⎣

⎡−=−=− m

neaneE ie ε

πλε

π h Equation 50

where all terms have their same meanings from the above equations.

If Equation 46, 45 and 48 are added, then the complete model for the optical absorption edge is obtained.

ieeeVCgo EEEEEE −− −−++= Equation 51

3 . 6 . 3 . Mode l i n g t h e Op t i c a l Ab s o r p t i o n E d g e

The previous section described the five parameters that control the position of the absorption edge in degenerate semiconductors. Here, it is determined if, from knowing only the electrical properties, the optical properties can be predicted. Hall effect was used to determine the carrier concentration and mobilities of all CdO films. Metal contacts were not deposited, as is typically required for most semiconductors. No matter the growth parameters or dopant, CdO is always highly conductive. In addition, an accumulation layer of electrons exists on the surface [69]. Thus, the surface is even more conductive than the (already very conductive) bulk. This surface accumulation layer is also seen in InN [70, 71]. For this reason the films required no metal contacts. All Hall data was taken using a 0.6 Telsa magnet and 10 mA of applied current. This current is far greater than that typically used for Hall effect. Hall effect run at lower currents does not yield reliable data for CdO. This requirement of very high current is related the magnitude of the Hall voltage, which is given in Equation 52:

dneIBVH −= Equation 52

where VH is the Hall voltage, I is the applied current, B is the magnetic field, d is the thickness, n is the concentration of charge carriers and e is the charge of an electron. Since CdO has very high carrier concentrations, the denominator in Equation 52 is very large, and this causes the measured Hall voltage to be very small. If the Hall voltage becomes too small, significant errors are introduced when the carrier concentration and mobility are computed. The only way to

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counter this is by either using a stronger magnetic field, which for the current setup was limited, or by increasing the current.

Figure 31 shows the absorption curves for each irradiation dose of Ne.

Figure 31: Absorption coefficient squared as a function of photon energy [49].

The absorption edge in CdO shifts from 2.26 eV (as grown) and saturates at high doses at 2.80 eV.

Figure 32 shows the carrier concentration for each irradiation dose of Ne+.

Figure 32: Carrier concentration as a function of displacement damage dose of Ne+.

For each irradiation dose, Equation 51 was solved, using the n value from Figure 32. Figure 33 shows the computed optical absorption edge and compares it with the measured absorption edge for CdO, from Figure 31, as a function of carrier concentration.

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Figure 33: Computed and measured absorption edge of CdO as a function of carrier concentration [49].

Good agreement between the computed and measure values is obtained for large hole effective mass. This is consistent with the valence band having a much lower curvature than the conduction band. Also, the fit is not sensitive to the exact hole effective mass, provided it is at least 3. For values larger than 3 the computed curve asymptotically approaches the measured values.

Figure 33 provides strong evidence that the shift in the optical absorption edge is caused by the Burstein‐Moss effect as, knowing only the electrical properties, the optical properties can be accurately predicted over a wide range of electron concentrations. Figure 33 also shows the significance of including the many‐body effects. If the electron‐electron and electron‐ion effects are not considered, the position of the Fermi stabilization level is exaggerated, thus, reaching saturation at 3.2 eV above of the valence band edge. This value is a full a 0.2 eV above the experimental value and 0.2 eV above the predicted value when these many‐body effects are included. So, it is necessary to include electron‐electron and electron‐ion interactions if an accurate prediction of EFS is required. However, for low carrier concentrations, far from EFS, the influence of these many‐body effects is insignificant. This can be seen by examining Equation 48. Small values of n result in small values of kF which drive Ee‐e (Equation 47) and Ee‐i (Equation 49) to also be small. For CdO before irradiation, and high quality CdO, the free carrier concentration is always low. This means the inclusion of these many‐body effects is not necessary to accurately predict the optical absorption. There are simply not enough free carriers in these films to reduce the band gap by any measurable amount.

3 . 6 . 4 . F r e e C a r r i e r Ab s o r p t i o n

Transparent conductors absorb light via two mechanisms. One mechanism is by promoting an electron from the valence band across the band gap into an empty state. This mechanism was discussed in the previous section when the optical absorption edge was computed including the Burstein‐Moss shift. Another mechanism is promoting an electron to a higher energy state within the conduction band. This process is called free carrier absorption because, unlike the former case, photons are being absorbed by free electrons in the conduction band (or holes in

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valence band). This process usually results in a change in the k value of the electron, and so, to conserve momentum the electron will have to interact with, in addition to the photon, either with a phonon in the lattice or scatter from an ionized impurity center. Since TCOs, by definition, have high concentrations of donors or acceptors, there are always high concentrations of ionized impurity centers making this process very efficient.

In general, both types of absorption discussed above are undesirable in TCOs because they are supposed to be transparent, the onset of either absorption means the amount of light that the TCO transmits to the device is reduced. Figure 34 shows the absorption curve for doped ZnO as well as for CdO. Both have similar conductivities, but they have very different free carrier absorption.

Figure 34: Percent transmittance for ZnAlO and CdO as a function of photon wavelength. ZnAlO has n=7.0*1020 cm‐3, µ=30 cm2/Vs and ρ=3.0*10‐4 Ωcm. CdO has n=4.4*1019 cm‐3, µ=195 cm2/Vs and ρ=7.2*10‐4 Ωcm.

As can be seen in Figure 34, for low wavelengths (high energies) ZnAlO is superior because it transmits more light than CdO. So, ZnAlO is better at reducing the first absorption mechanism. However, for the second absorption mechanism, CdO is clearly much better. At 1100 nm, ZnAlO is strongly absorbing photons, such that less than 70% of the incident light passes through the film. At 1100 nm, CdO is still very transparent, letting about 90% of the incident light pass through the film. For wavelengths longer than 1100 nm the difference in percent transmittance only increases. In fact, CdO does not begin to strongly absorb light until after 3300 nm. Thus, for applications where the device requires higher wavelength photons, CdO has an obvious advantage over ZnAlO and ITO.

Equation 53 shows the relationship between free carrier absorption, αf, effective mass of the electron (or hole) and carrier concentration:

73

τπλα 3*2

2

8 cnmne

r

x

f = [72, 73] Equation 53

where n is the free carrier concentration, e is the charge of an electron, λ is wavelength of the photon, m* is the effective mass, nr is the index of refraction, c is the speed of light and τ is the carrier relaxation time.

The exponent x depends on the scattering mechanism. In metals, x is normally 2. For a semiconductors x is taken to be 1.5 if the scattering is caused by acoustic phonons, 2.5 if the scattering is caused by optical phonons and 3 to 3.5 if the scattering is caused by ionized impurities [72]. However, within the same system, such as semiconductor with strong ionized impurity scattering, a change in x represents a change in these relative ease of scattering. If the exponent is very high it means scattering of free carriers is very efficient at high wavelengths (low energy) but much less efficient at low wavelengths (high energy). If the exponent is very low then the free carrier curve is flatter, which means the efficiency of scattering at low wavelength is similar to that at high wavelengths. Systems with low exponents are typically more defective, meaning large concentrations of ionized impurity center exist and large numbers of defects, such as vacancies, are present. This means the E vs. k dependence becomes smeared out. This is schematically shown in Figure 35.

Figure 35: Band diagram for free carrier absorption for high energy, green arrows, and low energy, red arrows for a crystalline seminconductor.

Figure 35 shows the E versus k diagram for a crystalline system. Here, the E vs. k relationship is well defined. If a free carrier absorbs a high energy photon (green arrow) it must interact with an ionized impurity center in such a way that its final momentum is exactly the value of k given by the curve. It can be seen that red arrow (longer wavelength) requires less change in momentum and is thus more probable than the green arrow (short wavelength). This is represented by x in Equation 53 being greater than one. For an amorphous system, k is not a good quantum number. Here, many defect states exist. This makes the scattering process

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more efficient and less dependent on the wavelength of the photon. The result is that a highly crystalline semiconductor will have a high exponent, close to 3.5, while a highly defective semiconductor will have a low exponent, something less than 3.

Figure 36 shows the absorption coefficient as a function of wavelength for various displacement damage doses using Ne+, from 0 (as grown) to 6.70*1016 cm‐2.

Figure 36: Absorption coefficient, alpha, as a function of photon wavelength, in nanometers for as grown and irradiated CdO.

The spike in the absorption coefficient at long wavelengths is attributed to water vapor, which is known to strongly absorb at 2800 nm and 1900 nm. Close examination of Figure 36 shows that the slope changes uniformly from low to high displacement damage doses, meaning the exponent x in Equation 53 changes uniformly. The only exception to this trend is the 3.35*1016 MeV/g curve. Here, the slope of alpha vs. wavelength does not follow the trend. An even larger problem, however, is the fact that this sample has a negative absorption coefficient from 500 to 1500 nm. This implies that the film is actually emitting light in this region, which is not possible. Another explanation for the negative absorption coefficient as well as the unusual slope of this curve is that something other than air and the sapphire substrate was considered as part of the background for this film. This might imply that some contamination formed a surface layer on the film, which absorbed light and this layer was subsequently removed during the next irradiation. Whatever the cause, it is unlikely that the slope of the 3.35*1016 MeV/g sample will yield useful data.

Table 9 shows the value of the exponent x from Equation 53 computed for each irradiation step, together is the Hall data.

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Table 9: Absorption coefficient exponent, x, as a function of displacement damage dose. R2 for the fit is given along wit the carrier concentration, n.

Displacement damage dose (MeV/g) x R2 n (cm‐3) 9.30*1014 3.51 0.996 1.54*1020

4.65*1015 3.09 0.989 2.68*1020

9.30*1015 2.82 0.997 3.77*1020

1.67*1016 2.05 0.99 4.56*1020

3.35*1016 1.84 0.968 4.98*1020

6.70*1016 2.1 0.979 5.06*1020

Table 9 shows that, with the exception of one sample, the exponent smoothly decreases from 3.5 to 2. This means that the scattering mechanism for lightly irradiated films (9.30*1014 and 4.65*1015 MeV/g) is characteristic of a highly crystalline semiconductor with ionized impurity centers. As the doses increase beyond the mid 1015 MeV/g range, the exponent begins to deviate significantly from the 3 to 3.5 values typical of highly crystalline semiconductors and the scattering becomes more influenced by defects. This means that Figure 35 (b) becomes more accurate. As the dose increase the width of k values enclosed by the arrows becomes even wider.

In addition to altering the exponent, Figure 36 also demonstrates another important changes in the absorption coefficient with irradiation dose. It can be seen that, as the irradiation dose increases, the magnitude of alpha for a given wavelength also increases. Since this absorption is caused by excitation of free carriers, it is expected that an increase in the free carrier concentration from irradiation would result in a larger absorption coefficient. However, this increase in alpha is not equal to the increase in carrier concentration. For example, doubling the displacement damage dose from 4.65*1015 MeV/g to 9.30*1015 MeV/g, increases the free carrier concentration from 2.68*1020 cm‐3 to 3.77*1020 cm‐3. This is a 40% increase in the number of free carriers. But alpha increases by 75%, or roughly double the increase observed in the free carrier concentration. This is because irradiation changes not only the number of free carriers but also the relaxation time. As more irradiation induced defects are formed, recombination times gets shorter. This means, referring to Equation 53, that N in the numerator is increasing and τ in the denominator is decreasing, and both of these lead to a larger absorption coefficient.

The most important conclusion from this data is that CdO, having mobilities that are typically at least 3 times higher than ZnAlO or ITO, offer a significant advantage over other TCOs when free carrier absorption for energies above 0.4 eV is required to be small. However, if the free carrier concentration in CdO is increases to the low 2*1020 cm‐3 range, significant free carrier absorption begins to develop above 0.4 eV. While the magnitude of free carrier absorption becomes large for carrier concentrations approaching 5*1020 cm‐3, it is still far less than the free carrier absorption of ITO films with similar resistivities.

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3 . 7 . Ca r r i e r Concen t r a t i on s Beyond t h e E F S L im i t

3 . 7 . 1 . C a r b o n i n C dO a n d C d 0 . 8 1 C u 0 . 1 9 O

Low to moderate doses of C+ in CdO and CdCuO lead to electrical and optical properties that are consistent with the amphoteric defect model. However, high doses of C+ lead to very unusual behavior that is not predicted by this model. High doses of C+ results in a carrier concentration that greatly exceeds the maximum value predicted when the Fermi level is pinned at the Fermi stabilization level.

Figure 37 shows the carrier concentration as a function of the displacement damage dose using both Ne+ and C+.

Figure 37: Carrier concentration as a function of displacement damage dose including high doses of C+.

The presence of Cu makes no difference in the optical and electric properties, as demonstrated in Figure 37 and the Hall data presented below. Cadmium copper oxide and CdO have the same carrier concentrations and mobilities in both the as grown films and after C+ irradiation. They both also have the same absorption edge before and after irradiation. Xray diffraction shows little Cu incorporated in the lattice. For this reason, it is believe that these results are applicable to pure CdO as well as CdCuO.

There are three distinct regions in Figure 37. The first occurs at the displacement damage doses below 1016 MeV/g. Here, a linear increase in the carrier concentration with displacement damage dose is observed. This represents the region were free carriers are added to the conduction band by the creation of point defects in the film. The second region occurs from 1016 to somewhere below 1018 MeV/g. There is no change in the carrier concentration because, even though additional point defects are created, they compensate each other. In this region, the Fermi level is considered to be pinned at the Fermi stabilization energy. The third region occurs at the displacement damage dose above 1018 MeV/g. Here, carrier concentration rises once more, the carrier concentration becomes “unpinned”, and perhaps the Fermi level becomes “unpinned” as well. This suggests that either the free carriers in this third region are

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not coming from the creation of point defects (because the formation energy of both donor and acceptors should be equal for all displacement damage doses above 1016 MeV/g) or, if these free electrons are still caused by native defects, then the density of states has been dramatically increased.

It should be noted that this third region occurs only at very high irradiation doses. A displacement damage dose of 1018 MeV/g represents a huge amount of damage to the lattice. In many semiconductors, this dose is high enough to displace every atom in the lattice, which results in an amorphous system. Figure 38 shows threshold displacement damage dose necessary to amorphize a variety of semiconductors.

Figure 38: Threshold amorphising displacement damage does for variety of semiconductors.

Cadmium oxide is not listed in Figure 38 because its threshold value is not known. The displacement damage doses necessary to unpin the carrier concentration are high enough that the majority of semiconductors in Figure 38 would be amorphous. As noted in section 2.5.7, CdO is remarkably stable under irradiation, so if GaN does not become amorphous until doses in excess of 1*1020 MeV/g are reached, it is not expected that CdO will become amorphous below this level either. This value of 1*1020 MeV/g is an order of magnitude greater than the highest displacement damage dose of C+.

Xray diffraction provides a direct method to determine whether CdO at high C+ doses results in an amorphous film. Figure 39 shows the Xray diffraction data for CdCuO irradiated with a displacement damage dose of 6.16*1018 MeV/g.

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Figure 39: Xray diffraction scan of heavily irradiated CdO.

As can be seen in Figure 39, the CdO (002) peak still exists, but it is very weak. The height of the peaks is only approximately twice the background level. Figure 39 also indicates that, while the film is highly defective and displays only a weak diffraction peak, it is not amorphous.

Given the exceptionally high free carrier concentrations observed for high displacement damage doses of C+, it is expected that these films will display significant free carrier absorption. Since the magnitude of free carrier absorption is related to the concentration of the free carriers (Equation 53) the free carrier absorption should also be much larger.

Figure 40 shows the optical absorption at low energies.

Figure 40: Optical absorption at low energies as a function of C+ displacement damage dose.

Figure 40 indicates that the film, as grown, has almost no free carrier absorption, which is consistent with its low starting free carrier concentration. As the displacement damage dose increases, the magnitude of the absorption at each wavelength increases and the slope the alpha versus wavelength curve decreases. Table 10 shows the carrier concentration, mobility, magnitude of alpha at a reference wavelength of 2900 nm, and x from Equation 53.

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Table 10: Optical absorption edge, free carrier absorption exponent (x), absorption coefficient (alpha), carrier concentration (n), mobility (µ) and resistivity (ρ) as a function of displacement damage dose.

Displacement damage dose (MeV/g)

Optical absorption edge (eV) x

α (2900nm)

n (cm‐3)

µ (cm2/Vs)

ρ (Ωcm)

9.30*1014 2.49 3.51 4.36*104 1.54*1020 43.7 9.27*10‐4

4.65*1015 2.57 3.09 8.56*104 2.68*1020 24.2 9.64*10‐4

9.30*1015 2.70 2.82 1.50*105 3.77*1020 16.0 1.04*10‐3

1.67*1016 2.76 2.05 1.97*105 4.56*1020 12.4 1.11*10‐3

3.35*1016 2.80 1.84 2.06*105 4.98*1020 11.2 1.12*10‐3

6.70*1016 2.75 2.10 2.37*105 5.06*1020 11.0 1.12*10‐3

1.14*1018 2.68 0.94 2.31*105 5.72*1020 8.5 1.28*10‐3

2.85*1018 2.75 0.69 2.40*105 7.78*1020 6.1 1.31*10‐3

4.17*1018 2.92 0.64 2.75*105 9.03*1020 6.3 1.10*10‐3

6.16*1018 NA 0.53 2.89*105 1.26*1021 4.5 1.11*10‐3

9.24*1018 NA 0.54 2.92*105 1.65*1021 3.2 1.20*10‐3

There are several important trends illustrates in Table 10. The absorption coefficient increases by almost an order of magnitude as the displacement damage dose increases by 4 orders of magnitude. While there is always significant free carrier absorption in all irradiated films, the magnitude of this absorption only becomes significant for displacement damage doses beyond 4.65*1015 MeV/g. Typically the onset of band to band transitions in a direct gap semiconductor is defined as the linear region of the square of the absorption coefficient curve where the magnitude is roughly 1*1010 cm‐2 (or alpha is 1*105 cm‐1). Most irradiated films have alpha’s at 2900 nm that surpass this. And, values of alpha deeper in the infrared are even larger.

In addition, Table 10 shows that, while the concentration of free carriers increases by an order of magnitude during irradiation, the resistivity stays essentially constant at about 1*10‐3 Ωcm. This is because the increase in carrier concentration is almost exactly balanced by the decrease in mobility. Thus, irradiation is not a good method to maximize the conductivity in this transparent conductor. However, low to moderate doses (below 1017 MeV/g) do greatly increase the optical absorption edge (2.2 eV to 2.8 eV) without any deterioration in the conductivity, so irradiation could be a useful processing step to improving performance of this TCO. Doses above 1017 MeV/g should be avoided because they result in significantly greater absorption across the whole spectrum.

This behavior of very high displacement damage doses resulting in poorer optical properties is best displayed when the percent transmittances is plotted next to the solar irradiance, as shown in Figure 41.

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Figure 41: Percent transmittance as a function of wavelength for various displacement damage doses (left) and solar irradiance as a function of wavelength in nanometers (right).

There are two sets of curves in Figure 41. The first set of curves belongs to the as grown and lightly to moderately irradiated films where the displacement damage dose is below 1016 MeV/g. Here, the percent transmittance is above 90% for wavelengths shorter than the free carrier absorption edge and longer than the band edge absorption. In this region, irradiation does provide some advantage to the optical properties because the band to band transition is shifted to higher energies, allowing the capture of a greater percent of the solar irradiance spectrum. But, the results are very different for the second set of curves. These curves belong to the heavily irradiated films where the displacement damage dose exceeds 1016 MeV/g. While increasing displacement damage dose does increase the energy of the band to band absorption, allowing for the capture of photons in the higher energy portion of the solar irradiance spectrum, it also greatly reduces the transmission across the entire energy range. The result is that any advantage obtained by having a higher optical absorption edge, as described in Table 10, are undone by having such a large decrease in the percent transmittance at all wavelengths.

It was shown the magnitude of the absorption coefficient is related to displacement damage dose. However, Table 10 demonstrates that the exponent, x, is the single most sensitive parameter to the displacement damage dose, and, thus, the concentration of vacancies in this material. Carrier concentration, absorption coefficient and the optical absorption edge are all directly related to, and mobility is inversely related to, displacement damage dose but this sensitivity is lost when the Fermi level becomes pinned. For example, when comparing displacement damage doses 6.7*1016 to 1.14*1018 MeV/g almost identical carrier concentrations, optical absorption edges and mobilities are observed. However, since the displacement damage dose has been increased by a factor of 17, the concentration of vacancies is expected to be much greater. Given that the Fermi level is pinned this region, the defects compensate and so only a small change in carrier concentration and mobility is observed. However, the exponent x changes dramatically in this case, falling from 2 to about 1. Thus, understanding the shape of the free carrier absorption curve is very important, even though

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literature on irradiated transparent conductors often neglects this region to focus on the absorption curve at higher energies.

Optical absorption at shorter wavelengths mirrors that at longer wavelengths: higher displacement damage doses shifts the optical absorption edge to higher energies. These shifts are much larger than that observed for CdO pinned at EFS because the carrier concentrations are much larger. This is shown in Table 10 where the optical absorption edge approaches 3 eV. Figure 42 shows the actual absorption data as a function of irradiation dose.

Figure 42: Absorption coefficient squared as a function of photon energy for various C+ displacement damage doses.

The as grown film’s absorption curve differs dramatically from the irradiated films. Here, the film has a carrier concentration of only 7.7*1019 cm‐3 so only a small Burstein‐Moss shift is observed. In addition, it is the only film that has an absorption edge even close to 2.2 eV, the band gap of CdO. The scale is also unusual for most semiconductor absorption curves. As mentioned, typical values near the onset of band to band transitions is 1*1010 cm‐2. While a linear alpha2 vs. photon energy is observed for the as grown film in this 1*1010 cm‐2 region, the heavily irradiated films do not become linear until the low to mid 1011 cm‐2 region. This is the result of a significant absorption at al wavelengths that adds to the band to band absorption.

This large background absorption means determining the band edge of highly damaged films is very difficult. This is because all optical absorption edges were determined by the standard alpha2 vs. energy extrapolation. Equation 54 shows the relationship between absorption coefficient, α, the absorbance, A, the band gap, Eg, and photon energy, hν:

( ) ( ) 21

gEhAh −= υυα Equation 54

It should be noted that Eg is technically the optical absorption edge, as given by Equation 51, but it is often presented in the literature as the band gap. In the extrapolation to find Eg, hν is set to zero, leaving α being equal to A times the square root of Eg. Squaring both sides results in the optical absorption edge being proportional to α2. It should be pointed out that Equation 54 is only an approximation. To fit the edge more accurately, the shape of the absorption curve

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must be fit, as illustrates by Jones et al [74]. However, much of the literature neglects this step and authors often Equation 54 because it gives similar values. This approximate method works well for displacement damage doses below 1017 MeV/g. For higher displacement damage doses the background absorption is comparable to the band to band absorption. This means that Equation 51 is no longer valid, and defining what should be considered as the band to band transitions in the absorption curve becomes much more complex.

3 . 7 . 2 . C a r r i e r C o n c e n t r a t i o n s Ab o v e S a t u r a t i o n

As discussed above, the maximum free carrier concentration that can be achieved in CdO using native defects is 5*1020 cm‐3. If additional defects are introduced they compensate each other because the formation energy for donor and acceptor defects is equal. The amphoteric defect model does not accurately describe the system under these conditions, and the goal here is understand why.

Two fundamental assumptions were made when the amphoteric defect model was originally applied to CdO, and it is possible that either, or maybe both, is no longer valid after high doses of C+. First, it was assumed all free carriers come from the creation of vacancies. Second, it was assumed that the density of states of does not significantly change during irradiation. These imply that Equation 43 is valid before and after irradiation.

High doses of C+ could, in theory, invalidate both assumptions. If C occupies a Cd site it should act as double donor, adding two electrons to the conduction band. To Hall effect, a substitutional C would look much like an oxygen vacancy. Since no vacancies were created in adding these two electrons to the conduction band, the system can continue to form additional substitutional C irrespective of the Fermi level being pinned. However, C could also occupy an O site. In this configuration C is a double acceptor, and large concentrations of C on O sites would trend to make the film p‐type.

Another method would be to form a conductive network within the film. Here, electrons could move both in the matrix CdO phase and impurity phase. The carrier concentration measured by Hall effect would record both electrons in the CdO phase, which is still pinned at the saturation level, and the additional electrons in the impurity phase.

A third method to achieve free carrier concentrations beyond this limit would be to significantly alter the band structure of the material. If the density of states can be increase to at or below EF, then the number of free carriers can be increased even if the Fermi level remains pinned at the same position with respect to vacuum. This is because pinning the Fermi level only fixes the bounds of integration; the function being integrated can still be altered. So, if the density of states is increased, then the number of electrons enclosed between the band edge and EF is also increased. In the next few sections, implantation profiles, Hall effect data and annealing results will be presented in order to determine which of these mechanism is mostly likely responsible for the observed deviation from the amphoteric defect model.

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3 . 7 . 3 . V a c a n c y a n d I m p l a n t e d C C o n c e n t r a t i o n s

In order to determine why high doses C implanted in CdO lead to carrier concentration above the predicted saturation level, the carrier concentration has to be correlated with the concentration of C implanted. Understanding the implantation profile is critical. For C+ irradiation, there are two parameters to model. First is the number of vacancies produced in the film. Ideal, the majority of vacancies produced should be within the film and not the substrate. This is because vacancies in CdO are electrically active and this condition allows the irradiation step to be more efficient. Some vacancies will always be produced in the substrate. However, since these defects in the sapphire substrate are not electrically active, they will not affect the Hall data for the films. Figure 43 shows that this condition has been satisfied.

Figure 43: The number of vacancies produced in CdO and the sapphire substrate by C as a function of depth.

The vacancy profile was computed using SRIM. The defect concentration peak is centered within the film. The number vacancies produced in the middle of the film is more than 3 times greater than the number of vacancies produced in the sapphire substrate near the interface.

The second critical parameter is the number of C atoms that remain in the film after irradiation. These C atoms, in addition to creating vacancies in the film, also have the chance to either occupy lattice sites and form electrically active substitutional defects or possibly to form an extended C network within the film or at the grains boundaries. Figure 44 shows the distributions of C atoms in the film and the substrate after irradiation.

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Figure 44: Concentration of C atoms in CdO and sapphire substrate as a function of depth and implantation dose.

According to Figure 44, the majority of implanted C atoms reside in the film after irradiation. Approximately 72% of the implanted C atoms reside in the film and the remaining 28% reside in the substrate. The total amount of C added to the film depends on the irradiation dose, but the ratio between the C atoms in the film and substrate is maintained.

Figure 43 allows for the estimation of the total number of oxygen vacancies produced during irradiation. Also, Figure 44 provides a means to estimate the total number of C implanted in the film, because the data on the y‐axis is the concentration of atoms per irradiation dose. Table 11 compares the carrier concentration with the total concentration of C implanted in the film and the total concentration of oxygen vacancies formed during irradiation.

Table 11: Total concentration of oxygen vacancies formed, total concentration of C atoms implanted and free carrier concentration as a function of C displacement damage dose.

Displacement damage dose (MeV/g)

O vacancies(cm‐3)

C implanted(cm‐3)

Carrier concentration (cm‐3)

Mobility (cm2/Vs)

Resistivity(Ωcm)

1.14*1018 6.27*1022 2.77*1020 5.72*1020 8.5 1.28*10‐3

2.85*1018 1.56*1023 6.91*1020 7.78*1020 6.1 1.31*10‐3

4.17*1018 2.28*1023 1.01*1021 9.03*1020 6.3 1.10*10‐3

6.16*1018 3.37*1023 1.49*1021 1.26*1021 4.5 1.11*10‐3

9.24*1018 5.05*1023 2.13*1021 1.65*1021 3.2 1.20*10‐3

The total concentration of oxygen atoms in a perfect CdO crystal is 1.91*1022 atoms/cm3. The concentration of oxygen vacancies created during irradiation is at least 3 times the total concentration of oxygen present in the lattice. For the highest displacement damage doses the factor is 26. However, in reality, the maximum number of oxygen vacancies that can be produced and retained in the crystal is simply the total number oxygen atoms in the crystal. This is the condition for amorphisation of the semiconductor. Since Xray diffraction still displays the CdO (002) peak, the net number of oxygen vacancies is clearly less than that

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predicted in Table 11. This demonstrates the strong influence of dynamic annealing in CdO; the vast majority of vacancies created during irradiation are not stable and interstitials and vacancies rapidly recombine. This strong dynamic annealing presents a significant challenge to correlating the exact concentration of vacancies with the displacement damage dose because the exact degree of dynamic annealing cannot be calculated.

However, computing the concentration of C implanted in the film is straightforward. Table 11 shows that large concentrations of C exist in the film after irradiation. The lowest dose of C corresponds to 0.73% of all atoms in the lattice being C while the highest dose corresponds to 5.6%. Interestingly, the with the exception of the lowest dose, the concentration of C is very similar to the free carrier concentration for all irradiation steps.

While the concentration of C implanted in the film and concentration of defects produced during irradiation are useful, they are not, by themselves, conclusive enough to determine the exact origin of the source of the excess free carrier beyond saturation. None of the theories presented above can be ruled out with this information alone. Thus, the annealing data is presented in the next section, will be combined with evidence from this section. It will be shown that both sections 2.7.3 and 2.7.4 work together to provide a convincing explanation for carrier concentrations in excess of saturation achieved in heavily irradiated films.

3 . 7 . 4 . An n e a l i n g

Post irradiation annealing was performed because the manner in which the optical and electrical properties change, with annealing temperature, will be characteristic of the dopant source. For example, if carrier concentrations beyond saturation are the result of C donors, then the carrier concentration and optical absorption edge should be relatively insensitive to annealing temperature. At high temperatures perhaps additional C would become substitutionally incorporated leading to even higher carrier concentrations and absorption edges. If the excess carrier concentrations are caused by an extended carbon network in the films then the electrical and optical properties should be insensitive to annealing temperature. At very high temperatures, the network might decompose, leading to a sudden decrease in the carrier concentration. Finally, if the additional free carriers are the result of an increase in the density of states, then annealing should result in a smooth decrease in both the carrier concentration and optical absorption edge, as these defects are slowly removed during annealing.

Figure 45 shows the absorption data for the as grown, irradiated, and then annealed film.

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Figure 45: Absorption data for as grown, irradiated, and annealed films.

Table 12 shows the optical absorption edge for each film, gives the exponent of the free carrier absorption, as well as the Hall data. It is analogous to Table 12 except in reverse: carrier concentrations are decreasing in Table 12 from annealing rather than increasing in Table 12 from irradiation.

Table 12: Optical absorption edge, free carrier absorption exponent (x), absorption coefficient (alpha), carrier concentration (n), mobility (µ) and resistivity (ρ) as a function of displacement damage dose.

Film

Optical absorptionedge (eV) x

α at 2900nm (cm‐1) n (cm‐3)

µ (cm2/Vs) ρ (Ωcm)

as grown 2.42 1.86 3.24*104 7.42*1019 80.2 1.05*10‐3 irradiated 3.33*1018 (MeV/g) NA 0.55 2.92*105 1.65*1021 3.2 1.20*10‐3 Annealed 150°C 2.55 0.80 3.27*105 1.26*1021 6.0 8.28*10‐4 Annealed 250°C 2.39 0.82 3.27*105 1.01*1021 10.3 6.05*10‐4 Annealed 350°C 2.43 1.81 2.68*105 7.94*1020 15.7 5.03*10‐4 Annealed 400°C 2.43 NA NA 4.92*1020 16.8 7.57*10‐4 Annealed 450°C 2.43 NA NA 1.17*1020 24.6 2.16*10‐3 Annealed 500°C 2.41 NA NA 7.59*1019 38.6 2.13*10‐3 Annealed 550°C 2.41 NA NA 6.41*1019 54.0 1.80*10‐3 Annealed 600°C 2.39 NA NA 5.38*1019 74.4 1.56*10‐3 Annealed 650°C 2.37 NA NA 5.41*1019 77.2 1.49*10‐3 Annealed 700°C 2.36 NA NA 5.55*1019 97.8 1.15*10‐3 Annealed 750°C 2.34 NA NA 6.94*1019 94.2 9.54*10‐4

The NA in Table 12 refers to values that are not available because they could not be computed. For optical absorption edges at high displacement damage doses this was a result of strong background absorption that obscured the band to band absorption. The free carrier absorption exponent x and absorption coefficient at 2900 nm could also not be stated with much confidence for annealing above 350°C. This is because the absorption data for these films is

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very noisy for wavelengths longer than 2500 nm. Also, these films typically had negative absorbance values for certain wavelengths.

Even though x cannot be computed for films annealed above 350°C, the trend is still obvious. The exponent is initially very low for the heavily irradiated film and gradually shifts back towards higher values as the annealing temperature increases, suggesting the removal of defects in the film. The as grown film and the film annealed at 350oC share many similar properties. They have identical carrier concentrations and free carrier absorption exponents. However, the mobility for the irradiated film is much lower, and, as a result, the resistivity is much higher.

Figure 45 shows that irradiation leads to two sets of optical and electrical properties for CdO. One set is composed of irradiated and low temperature annealed films. For these films there is significant free carrier absorption above 0.3 eV and the “transparent” window between the free carrier absorption and the band to band absorption is only semi‐transparent, as significant absorption occurs in this region. This means the absorption coefficient for these films is between 2.1*105 cm‐1 for the irradiated film to 3.6*104 cm‐1 for the 400°C film at 1 eV. Since band edge absorption typically occurs when α reaches 5*105 cm‐1, films annealed at low temperatures absorb an appreciable amount of light at all measured wavelengths. These films can be clearly seen in Figure 45 as having strong low energy absorption, and the cut off occurs at films annealed at 400°C or lower. In addition to having characteristic optical properties, these films also have characteristic electrical properties. All of these films have very high carrier concentrations that are either at or above the saturation value predicted by the amphoteric defect model.

The second set is composed of high temperature annealed film. These films are characterized as having free carrier absorption that occurs below 0.3 eV and band to band absorption that occurs between 2.3 and 2.5 eV. These values are typical of CdO. In addition, the value of the square of the absorption coefficient is near 1010 cm‐2 for the band to band absorption, which is also typical of CdO. This means the optical behavior of these films is similar to un‐irradiated films, and the large perturbation induced by irradiation is removed at temperatures above 400oC. These films display characteristic electrical behavior as well. All high temperature annealed films have carrier concentrations below the saturation value predicted by the ampotheric defect model.

Even though the mobilities are higher for the high temperature annealed films, the lowest resistivities belong to the low temperature annealed films. This is because, while the low temperature annealed films have much lower mobilities, they have even higher carrier concentrations. For high temperature annealed films, carrier concentration continuously falls as the annealing temperature is increased, but mobility increases in such a way that the product of the two is almost completely constant. For carrier concentrations above saturation (i.e., for the low temperature annealed films) annealing lowers the resistivity because large increases in the mobility are observed while only a slight reduction in the carrier concentration

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is seen. The optimal electrical properties are achieved for annealing at 350°C, which represents the last carrier concentration above saturation.

Given the moderate mobilities and very high carrier concentration at all annealing temperatures, the restisitivities of all films are very low. They compare favorably to either ITO or AZO, the dominant TCOs to date. Table 13 is shows the relationship between film thickness and resistivity for AZO deposited on sapphire by PLD.

Table 13: Resistivity, mobility and carrier concentration for pulsed laser deposited 200 nm thick AZO films on sapphire and quartz at 250oC [75].

Substrate Resitivity (Ω cm) Hall mobility (cm2V‐1s‐1) Carrier density (cm‐3) Sapphire 2.2x10‐4 32 8.8x1020

Glass 4.0x10‐4 19 8.2x1020

The film irradiated and annealed at 350°C is very similar to the AZO presented in Table 13. The resistivities are similar because the carrier concentration and the mobilities are similar.

3 . 7 . 5 . A l t e r i n g t h e De n s i t y o f S t a t e s i n C dO a n d C d C uO

Considering the implantation and annealing data, it appears, at first glance, that C acts as a donor. There seems to be a strong correlation between the implant C concentration and the total number of free carriers. However, C as a donor in CdO seems unlikely for several reasons. First, for C to act as donor it would have it sit on Cd site. This would be difficult to achieve given the atomic size and electronegativity difference between Cd and C. While it is always possible that some C would substiutionally replace a small amount of Cd, the huge concentration of free carriers observed would imply a very large solubility of C in CdO. Moreover, even if C could replace Cd, it is expected to be a double donor, so the carrier concentration would, in the absence of other effects, be twice the C concentration, a relationship not observed in Table 15. Oxygen vacancies are still expected to contribute a significant number of electrons to the valence band, in addition to those added to the conduction band via donor atoms. Since there is no way to determine the total number of oxygen vacancies in the lattice, there is no way to decouple the contribution from oxygen vacancies and that from donors. But, if C acts a donor, the concentration of C must be roughly comparable to the concentration of oxygen vacancies; a requirement that seems highly unlikely.

In addition to not describing the implantation results well, C acting as a donor in CdO also does not describe the annealing data well. The carrier concentration decreases gradually with increasing annealing temperature. As a donor, it is expected that the carrier concentration would be relatively stable, especially at low temperatures. Perhaps at higher temperatures interstitial C could be substitutaionlly incorporate, but this would lead to an increase in the carrier concentration, not a decrease. For all these reasons it is not believed that C acts as a donor in CdO.

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Another possible mechanism for carrier concentrations in excess of the maximum predicted by the amphoteric defect model is the formation of a C network within the CdO matrix. This model is consistent with the implantation data, as the formation of a continuous C network would require the concentration of C to be in the range of a few percent of the total atoms in the lattice. Concentrations of C below this level would most likely result in isolated C clusters that would not add to the conduction of the system. However, this model is inconsistent with the annealing data. A gradual decrease in the carrier concentration and increase in the mobility is observed. It is expected that a C network would be stable until very high temperatures, which means conduction from an extended C network should also be stable. Annealing would reduce the carrier concentration and increase the mobility in the CdO matrix, so the trend does model part of CdO:C system. However, a majority of these excess carriers must be coming from outside the CdO matrix in this model, so the large reduction in carrier concentration can not be attributed to reducing defects in the CdO bulk.

The last mechanism that has been suggested was to introduce enough defects that the density of states changes appreciably near EFS. This mechanism is the only one that is consistent with both irradiation and annealing data, for that reason it the most likely origin of the exceptionally high free carrier concentrations. In order to significantly alter the density of states so that the number of free carrier doubles for the same Fermi level and band edge position, a very large concentration of defects must be present. This condition is easily satisfied as the displacement damage doses are high enough to roughly displace every atom in the film between 1 (lowest dose) to 13 times (highest dose). Dynamic annealing reduces this considerably so that the net number of displaced atoms is far less. The films clearly have a large number of defects at high displacement damage doses, as indicated by the low mobilities and weak Xray diffraction peaks.

The annealing data is also consistent with this theory. Defects such as vacancies and interstitials are slowly removed with increasing annealing temperature. This recovery results in a decrease in carrier concentration because an oxygen vacancy recombining with an interstitial removes two electrons from the conduction band. This process also removes an ionized impurity center from the crystal, which reduces ionized impurity scattering and, thus, increases the mobility. This behavior is observed for the post irradiation annealing. This fall in carrier concentration is seen even during the first annealing step, at just 150°C.

Further evidence that the decrease in carrier concentration is a result of removing point defects in the film is provided in Figure 46, where the carrier concentration and mobility for a film that been irradiate and annealed is compared to one that has just been annealed.

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Figure 46: Carrier concentrations (open shapes) and mobilities (closed shapes) for irradiated and annealed film (squares) and only annealed film (circles).

The mechanism is well understood for the annealed films. Here, point defects are removed at annealing temperatures as low as 150°C, driving the carrier concentration from its as grown high of 1*1020 cm‐3 to a low of 2.6*1019 cm‐3, at a temperature of 650°C. Carrier concentrations creep higher for annealing temperatures above 650°C, most likely the result of the creation of oxygen vacancies at these elevated temperatures. The mobility increases in a way that mirrors the decrease in the carrier concentrations, having its greatest rate of change near 400°C and its peak at 750°C. The irradiated and annealed film, while having different values for the carrier concentration and mobility behaves in a similar manner. The carrier concentration begins to decrease at 150°C as well. Once the Fermi level drops below the EFS (about 450°C in Figure 44) the two carrier concentration curves become almost identical, separated only by a factor of two from 450°C to the end of annealing at 800°C. The mobility curves are also similar, when the Fermi level for the irradiated film drops below EFS, the mobility peak for both films are within 50°C of each other.

Figure 46 also provides indirect evidence that the change in the electrical properties is a result of the removal of point defects. A closer look at the absorption data presented in Figure 45 provides a more direct connection between point defects and the unexpectedly high carrier concentrations. Here, Figure 47 is reproduced and the absorption curves are divided into two sections, one section is for films with carrier concentration above saturation, and one for films with carrier concentrations below saturation.

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Figure 47: Absorption data as function of annealing temperature.

This means curves in the left region cannot be modeled using Equation 51 while those on the right can. Curves on the left have three key characteristics. First, they all exhibit strong free carrier absorption. Second, they all appear to have a direct transition between 1 and 1.5 eV. Third, they all absorb strongly between the free carrier and band to band transitions. This third characteristic might be a result of the overlap between first two absorption mechanisms. Curves on the right have three key characteristics as well. First, free absorption is not present, at least above the 0.38 eV, the detector cutoff. Second, they all appear to have band to band absorption between 2.2 to 2.8 eV, similar to CdO with a Burstein‐Moss shift. Third, all films exhibit very little absorption between free carrier absorption and the band edge.

The light green curve, corresponding to the 400°C annealing condition, is the transition region because it has characteristics of films on both the left and right of the figure. It has three strong absorption regions; it has free carrier absorption at low energies and then it appears to have two band to band transitions, one near 1.5 eV and one near 3 eV. It will be shown shortly that it is not a coincidence that the 400°C annealed film, which straddles both regions, has carrier concentration exactly equal to the maximum value predicted by Equation 51.

In order to provide a unified explanation that describes the behavior of both the low temperature annealing absorption curves on the left of Figure 47 and the high temperature curves on the right, the band diagram must be considered in detail.

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Figure 48: Band diagram of CdO computed using self‐interaction‐correct pseudopotentials.

Figure 48 shows the computed band structure of CdO. As with most band structure calculations the values of the spacing between the bands does not agree with experiments, however the position of peaks and valleys are in the correct locations. Figure 48 shows that CdO is an indirect gap semiconductor. The spacing between the top of the valence band at the L point and bottom of the conduction band at the Γ point is 0.9 eV. While some disagreement exists about the exact value of the indirect gap, some sources claim it to be as high as 1.1 eV, this lower value has recently be confirmed with Xray absorption near edge structure by Demchenko and Speaks [76]. The direct gap of CdO is 2.2 eV. This indirect gap is rarely observed in CdO. For CdO with high carrier concentrations, free carrier absorption would mask any indirect transitions. But even in the absence of free carrier absorption, a phonon is required to be emitted or absorb if a photon is to be absorbed to excite and electron across the indirect gap. This process is very inefficient, under typical conditions. However, irradiation might provide a method to increase the efficiency of transitions from the L point to the conduction band.

Figure 49 is a schematic band diagram for heavily irradiated and annealed CdCuO films.

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Figure 49: Schematic band diagram for CdCuO. Direct optical transitions are shown as blue arrows and indirect as red arrows.

Figure 49 represents the classic band diagram picture, and it is applicable, without alteration, only to films annealed above 400°C. Here, indirect transitions are unlikely do to a large change in momentum. This results in only strong absorption between 2.5 to 3.0 eV (the blue transitions) and only weak absorption near the 0.9 eV. Curves with carrier concentrations above that predicted by Equation 51, have large concentrations of defects, which dramatically increase the density of states near the Fermi level and act as a source of additional free electrons. This means the density of states increases sharply near EFS, the green line. When integration between the EFS and band edge is conducted, the number of electrons increases by a factor of two (5*1020 to 1*21 cm‐3). These defects also make indirect transitions more likely because they dilute the selection rules and create scattering centers that allow a change in momentum that is required for the transition. The efficiency of transitions from L to Γ is increased to the point where this indirect absorption is as strong as direct absorption. This can be seen by comparing the values of the absorption coefficients in Figure 47. The film annealed at 400°C is transitioning from a crystalline to an amorphous band structure. The result is that this film strongly absorbs at both direct (blue arrow) and indirect (red arrow) gaps.

In conclusion, high displacement damage doses in CdCuO and CdO has three main effects. First, it greatly increases the maximum number of free carriers. These additional carriers, beyond the level predicted by Equation 51, come not from moving the Fermi level, which still remains pinned, but by increasing the density of states. Second, the resistivity of CdCuO is lowest when the density of states first begins to increases during irradiation (annealing at 350°C), because here the carrier concentration increases faster than the mobility decreases. Third, it makes the indirect absorption, from L to Γ more efficient. The indirect gap absorption under these conditions leads to an absorption coefficient comparable to that of a direct gap absorption.

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4. Conclusions

Many important devices such as flat panel displays and photovoltaics require materials that are both optically transparent and electrically conductive. To date, the dominant transparent conduct has been tin doped indium oxide (ITO). However, long term reliance on ITO presents several problems. Indium is rare and expensive, which means that, as the market for devices such as displays and solar cells expand, indium supply will not be able to keep pace with demand. This will result in indium becoming even more expensive. Beyond the economics, ITO has a critical performance flaw. While low resistivities can be achieved, they are always the result of high carrier concentrations, not high mobilities. This inevitably results in significant free carrier absorption, reducing transmission in the low edge of the visible region or the near infrared. Since this absorption occurs at the edge of the visible region, or just outside, it does not alter ITO’s impressive figure of merit. However, for any device that requires lower energy photons to be transmitted, this presents a significant problem. Future applications will require transparent conductors to be even more conductive so that thinner, and cheaper, layers can be used. ITO cannot meet these future performance standards because its electrical properties have reached an asymptote over a decade ago, despite the fact that is the most expensively studied transparent conductor. A new transparent conductor is needed that addresses all of these issues. Doped zinc oxide has been suggested as a replacement for ITO, however, it only addresses one of the limitations of ITO, that of cost.

It was demonstrated CdO is a potential candidate to replace ITO. CdO and its alloys address all of ITO’s major flaws, something no other transparent conductor has been shown to do. Cadmium is both inexpensive and abundant, meaning cost will be low even in the facing of rising demand. CdO also displays exceptional mobilities that are typically five times greater than those seen in ITO. If carrier concentrations in CdO alloys can be made comparable to ITO then CdO films of the same resistivity could be made five times thinner, leading to significant cost savings.

There are several important advances that were made to the understanding of CdO, and these may eventually help CdO displace ITO. It was demonstrated that the amphoteric defect model can be used to provide a unified explanation for many of the previously poorly understood attributes of CdO. The amphoteric defect model shows that the formation energy for donor defects in CdO is exceptionally low, leading very high as grown carrier concentrations for all CdO films. It is the very low formation energy for oxygen vacancies that explains the lack of p‐type CdO. The importance of dynamic annealing was illustrated by the different carrier concentrations seen at saturation using light versus heavy ion irradiation. Previously published values for the position of the Fermi stabilization level are too low because of a failure to account for dynamic annealing. Before this study, published values for the carrier concentrations for CdO were always between 2*1019 and 2.5*1020 cm‐3. This work has shown that to obtain carrier concentrations above 2.5*1020 cm‐3 irradiation with ions heavier than He+

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must be conducted. This is required because, otherwise, the defect concentration in the damage cascade is not high enough to allow the formation of stable defect clusters. For carrier concentrations below 2*1019 cm‐3, the growth and annealing conditions must be carefully controlled. Deposition at 479°C followed by a high temperature anneal at 750°C results in carrier concentrations of 8*1018 cm‐3. Finally, it was shown that very high displacement damage doses of C+ in CdCuO lead to carrier concentrations of 1*2021 cm‐3, similar to ITO. Irradiation can use be used to both increase the optical absorption edge and reduce the resistivity, provided that the displacement damage dose is not too high.

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