Engineering Titanium Dioxide-Poly(Vinylidene Fluoride) and Titanium Dioxide-Silicon Dioxide Capacitors for Improved Energy Storage

ENGINEERING TITANIUM DIOXIDE-POLY(VINYLIDENE FLUORIDE) AND TITANIUM DIOXIDE-SILICON DIOXIDE CAPACITORS FOR IMPROVED ENERGY STORAGE

By Michael Bryant

A Thesis Submitted in Partial Fulﬁllment of the Requirements for the Degree of Master of Science in Applied Physics

Northern Arizona University August 2019

Approved: Dr. Randy Dillingham, PhD, Chair Dr. John Gibbs, PhD Dr. Mark Loeﬄer, PhD ABSTRACT

ENGINEERING TITANIUM DIOXIDE-POLY(VINYLIDENE FLUORIDE) AND TITANIUM DIOXIDE-SILICON DIOXIDE CAPACITORS FOR IMPROVED ENERGY STORAGE

Michael Bryant

Ceramic-polymer capacitors provide a promising ability to improve energy storage due to their averaging effect of high dielectric constant and high dielectric strength materials. Titanium dioxide and poly(vinylidene fluoride) dielectric films were first fabricated in 2011 using a spin coating technique; however, this technique has limited applications within electronics. Within recent years, the dielectric films were fabricated using a resistive thermal evaporator, but the quantity of titanium dioxide which could be evaporated and incorporated into the films was found to be limited to 17% of the total dielectric film composition. The purposes of this study are to co-deposit the materials using two separate evaporation techniques to show that doing so is a viable method and to study the electrical properties of a titanium dioxide dominant capacitor. The titanium dioxide and poly(vinylidene fluoride) capacitor is fabricated via physical vapor deposition using thermal resistive evaporation and electron beam gun evaporation. This capacitor is compared to titanium dioxide and silicon dioxide capacitors fabricated using the same methods. The dielectric films are fabricated by co-depositing materials using thermal resistive evaporation and electron beam gun evaporation. The metal electrodes are deposited using sputter coating or electron beam gun evaporation. The dielectric thin films are characterized for their breakdown voltage, dielectric strength, capacitance, dielectric constant, thickness, composition, and surface topography using a scanning electron microscope, an energy

ii dispersive X-ray spectrometer, an atomic force microscope, a capacitance measuring RC circuit, and a breakdown voltage tester. Empirical models are created for the titanium dioxide-silicon dioxide capacitors relating the titanium dioxide percentage to the dielectric constant and dielectric strength. The fabricated ceramic-polymer capacitor consisted of 94.10 ± 0.09 % titanium dioxide, and had a breakdown voltage of 19.61 ± 0.01 V, a dielectric strength of 24.15 ± 0.02 MV m−1, a capacitance of 26.123 ± 3.347 nF, a dielectric constant of 33.62 ± 4.45, a thickness of 812.0 ± 0.3 nm, maximum energy storage of 5.02 ± 0.46 µJ, and volume energy density of 0.0868 ± 0.0079 J cm−3. In comparison, the five titanium dioxide and silicon dioxide capacitors had a titanium dioxide composition ranging from 0 % to 100 %, a breakdown voltage ranging from 0.49 ± 0.01 V to 3.25 ± 0.01 V, a dielectric strength ranging from 0.50 ± 0.01 MV m−1 to 18.36 ± 0.06 MV m−1, a capacitance ranging from 54.93 ± 2.43 nF to 150.20 ± 8.19 nF, a dielectric constant ranging from 15.41 ± 0.68 to 87.75 ± 10.79, a thickness ranging from 98.21 ± 0.12 nm to 177.04 ± 0.14 nm, a maximum energy storage ranging from 0.0677 ± 0.00155 µJ to 0.4044 ± 0.0127 µJ, and volume energy density ranging from 0.0103 ± 0.0003 J cm−3 to 0.00970 ± 0.0012 J cm−3. The empirical models suggest that to maximize energy storage through composition, two-fifths of the composition of the dielectric film should be titanium dioxide and three-fifths should be silicon dioxide. When comparing the titanium dioxide and poly(vinylidene fluoride) capacitors to the titanium dioxide and silicon dioxide capacitors, the capacitor with poly(vinylidene fluoride) exhibited superior energy storage and energy density properties.

iii ACKNOWLEDGMENTS

I would like to thank the following people for their help and support: Dr. Randy Dillingham, committee chair Dr. John Gibbs, committee member Dr. Mark Loeﬄer, committee member Dr. William "Buzz" Delinger, electronics advisor Dr. Dylan Nicholls, Nanomaterials Laboratory postdoctoral researcher Joel Johnson, Nanomaterials Laboratory graduate researcher Taylor Thomas, Nanomaterials Laboratory graduate researcher Aubrey Funke, Imaging Histology Core Facility Assistant Director Miles Knight, undergraduate research assistant Cameron Richards, undergraduate research assistant My family and friends.

iv Contents

1 Introduction 1

2 Background 5 2.1 Capacitors ...... 5 2.2 Thin Film Deposition ...... 7 2.2.1 Physical Vapor Deposition ...... 8 2.3 Materials ...... 11 2.3.1 Ceramics ...... 12 2.3.2 Polymers ...... 13 2.3.3 Composites ...... 13

3 Methods 16 3.1 Purpose ...... 16 3.2 Deposition Equipment ...... 17 3.3 Capacitor Fabrication Process Overview ...... 20 3.4 Material Preparation ...... 20 3.5 Film Deposition Procedure ...... 21 3.5.1 Electrodes ...... 21 3.5.2 Dielectric Film ...... 22 3.6 Film Analysis ...... 24 3.6.1 Structure ...... 25

v 3.6.2 Composition ...... 30 3.6.3 Electrical Properties ...... 32

4 Results and Discussion 34 4.1 Overview ...... 34 4.1.1 Titanium Dioxide-Poly(vinylidene Fluoride) Capacitor . . . . 34 4.1.2 Titanium Dioxide-Silicon Dioxide Capacitors ...... 35 4.2 Titanium Dioxide-Poly(vinylidene Fluoride) Films and Capacitor . . 36 4.2.1 Deposition Current, Composition, and Surface Features of the Films ...... 37 4.2.2 Composition, Structure, and Electrical Properties of the Ca- pacitor ...... 45 4.2.3 Prediction of Composition to Maximize Energy Stored using Literature Values ...... 52 4.3 Titanium Dioxide-Silicon Dioxide Film and Capacitors ...... 55 4.3.1 Surface Features of the Film ...... 56 4.3.2 Composition, Structure, and Electrical Properties of the Ca- pacitors ...... 57

5 Conclusions and Future Work 68

A Designing, Building, and Automating a High-Vacuum Physical Va- por Deposition System 70

B LabVIEW: Breakdown Voltage Measuring Circuit 75

C Additional Results Data 80 C.1 Titanium Dioxide-Poly(vinylidene Fluoride) Films ...... 80 C.2 Titanium Dioxide-Poly(vinylidene Fluoride) Capacitor ...... 83 C.3 Titanium Dioxide-Silicon Dioxide Capacitors ...... 84

vi D Statistical Methods 94

E MATLAB: Results Calculations 96

Bibliography 111

vii List of Figures

2.1 A model of a parallel-plate capacitor...... 6 2.2 A diagram of an electron gun bombarding material with electrons, and the resulting vaporization and byproducts of the process...... 10 2.3 A diagram of a glow discharge sputter coater with argon ions bombarding a target material which causing the material to gain momentum and coat a substrate...... 11 2.4 A diagram illustrating the phase transformations and corresponding temperatures for titanium dioxide...... 13

3.1 A model and diagram of the Torr International, Inc. deposition system. 19 3.2 A diagram of the products of the capacitor fabrication process. . . . . 20 3.3 A model of the Zeiss Supra 40VP scanning electron microscope. . . . 27 3.4 The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-poly(vinylidene ﬂuoride) capacitor. 31

4.1 A graph comparing the composition to the dielectric constant for the ﬁve titanium dioxide-silicon dioxide capacitors...... 35 4.2 A graph comparing the composition to the dielectric strength for the ﬁve titanium dioxide-silicon dioxide capacitors...... 36 4.3 The phase image produced by the atomic force microscope of Film 7. 40 4.4 The phase image produced by the atomic force microscope of Film 8. 41

viii 4.5 The phase image produced by the atomic force microscope of Film 9. 41 4.6 The phase image produced by the atomic force microscope of Film 10. 42 4.7 The phase image produced by the atomic force microscope of the poly(vinylidene fluoride) dominant side of the titanium dioxide-poly(vinylidene fluoride) film...... 43 4.8 The phase image produced by the atomic force microscope phase image of the middle of the titanium dioxide-poly(vinylidene fluoride) film. . 43 4.9 The phase image produced by the atomic force microscope phase image of the titanium dioxide dominant side of the titanium dioxide- poly(vinylidene fluoride) film...... 44 4.10 The carbon elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene fluoride) capacitor...... 45 4.11 The fluorine elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene fluoride) capacitor...... 46 4.12 The titanium elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene fluoride) capacitor...... 46 4.13 The oxygen elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene fluoride) capacitor...... 47 4.14 The carbon and fluorine elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide- poly(vinylidene fluoride) capacitor...... 48

ix 4.15 The titanium and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide- poly(vinylidene fluoride) capacitor...... 49 4.16 The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-poly(vinylidene fluoride) capacitor with thickness measurements...... 50 4.17 A graph comparing the composition to the literature values for the dielectric constant for titanium dioxide-poly(vinylidene fluoride) capacitors...... 53 4.18 A graph comparing the composition to the literature values for the dielectric strength for titanium dioxide-poly(vinylidene fluoride) capacitors. 54 4.19 The plot of the product of the dielectric constant and dielectric strength squared as a function of titanium dioxide concentration for titanium dioxide-poly(vinylidene fluoride) capacitors...... 55 4.20 The phase image produced by the atomic force microscope of the titanium dioxide-silicon dioxide film...... 56 4.21 The titanium elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-silicon dioxide Capacitor 1...... 58 4.22 The silicon elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide- silicon dioxide Capacitor 1...... 59 4.23 The oxygen elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-silicon dioxide Capacitor 1...... 59

x 4.24 The titanium and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide- silicon dioxide Capacitor 1...... 60 4.25 The silicon and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide- silicon dioxide Capacitor 1...... 61 4.26 The titanium, silicon, and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide-silicon dioxide Capacitor 1...... 62 4.27 The plot of the product of the dielectric constant and dielectric strength squared as a function of titanium dioxide concentration for titanium dioxide-silicon dioxide capacitors...... 66

A.1 The LabVIEW front panel for automating the pumps...... 72 A.2 The LabVIEW block diagram 1 for automating the pumps...... 73 A.3 The LabVIEW block diagram 2 for automating the pumps...... 74

B.1 The LabVIEW front panel for the breakdown voltage measuring circuit. 75 B.2 The LabVIEW block diagram for the breakdown voltage measuring circuit...... 76 B.3 The LabVIEW sub-VI block diagram 1 for the breakdown voltage measuring circuit...... 77 B.4 The LabVIEW sub-VI block diagram 2 for the breakdown voltage measuring circuit...... 77

xi B.5 The LabVIEW sub-VI block diagram 3 for the breakdown voltage measuring circuit...... 77 B.6 The LabVIEW sub-VI block diagram 4 for the breakdown voltage measuring circuit...... 77 B.7 The LabVIEW sub-VI block diagram 5 for the breakdown voltage measuring circuit...... 78 B.8 The LabVIEW sub-VI block diagram 6 for the breakdown voltage measuring circuit...... 78 B.9 The LabVIEW sub-VI block diagram 7 for the breakdown voltage measuring circuit...... 78 B.10 The LabVIEW sub-VI block diagram 8 for the breakdown voltage measuring circuit...... 79 B.11 The LabVIEW sub-VI block diagram 9 for the breakdown voltage measuring circuit...... 79 B.12 The LabVIEW sub-VI block diagram 10 for the breakdown voltage measuring circuit...... 79 B.13 The LabVIEW sub-VI block diagram 11 for the breakdown voltage measuring circuit...... 79

C.1 The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 1. . . . . 86 C.2 The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 2. . . . . 87 C.3 The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 3. . . . . 88 C.4 The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 4. . . . . 89

xii C.5 The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 5. . . . . 90 C.6 The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 1 with thickness measurements...... 91 C.7 The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 2 with thickness measurements...... 91 C.8 The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 3 with thickness measurements...... 92 C.9 The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 4 with thickness measurements...... 92 C.10 The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 5 with thickness measurements...... 93

xiii Chapter 1

Introduction

Two of the most common energy storage devices are batteries and capacitors. Relative to batteries, capacitors typically have lower energy density, but higher power output. Capacitors are used in such applications as digital memory, pulsed power and weapons, power conditioning, signal coupling and decoupling, high-pass and low- pass filters, noise suppression, motor starters, signal processing, sensing, oscillators, and in producing light. The primary function of a capacitor is to store electrical energy in an electric field. The electric field can be manipulated by a change in medium or geometry of the capacitor. Hence, the ability to store electrical energy is material dependent. The material used in capacitors to alter properties is called a dielectric (which is commonly a ceramic, a polymer, or a combination of the two). Each material has properties which may or may not be more desirable than another material depending on the service conditions. While each material has its own properties, materials can be combined which give rise to new properties. Two properties that are vital to power applications of capacitors are capacitance and breakdown voltage. The maximum energy that can be stored within a capacitor is dependent on these two. Capacitance is the ability to store electric charge for a given voltage. Breakdown voltage is the maximum

1 electric potential difference with which a material can withstand without becoming conductive. The more voltage a capacitor can withstand, the more charge will be able to be stored and the more electric potential energy can be accumulated. The dielectric material is what determines the capacitance and breakdown voltage of a capacitor. One method for fabricating capacitors is through a technique called physical vapor deposition. The technique uses evaporation through momentum transfer to deposit material. This technique was used here to deposit both conducting plates (i.e. electrodes) and dielectric material. The relevant materials for this study are titanium dioxide, silicon dioxide, and poly(vinylidene fluoride). The former two are ceramics and the latter is a polymer. Titanium dioxide has a high dielectric constant, but low dielectric strength. The polymer has opposite properties of a high dielectric strength, but low dielectric constant. When combined, the materials give rise to a composite material which have a combination of the two properties. In addition to these materials, silicon dioxide is a ceramic with a moderately high dielectric strength, but low dielectric constant. When combined with titanium dioxide, the maximum energy storage is able to be increased (relative to just using one of the two materials), but should not have the potential for an increase as much as the combination of titanium dioxide and poly(vinylidene fluoride) does. Thus far, studies on the combination of titanium dioxide and poly(vinylidene fluoride) composite films for their electrical properties have been limited. In 2011, Ningli An et al. produced a capacitor using a spin-coating method [1]. The dielectric constant and dielectric loss of the capacitor was characterized using various frequencies. The method for fabrication is not ideal for integrated circuits, so the research presented here was conducted using other deposition techniques. In 2013, Joel Iwagoshi, at Northern Arizona University, fabricated two capacitors with dielectric films containing 17% titanium dioxide and 83% poly(vinylidene fluoride) using resistive ther-

2 mal deposition [2]. The thinner of the two had a capacitance of 6 nF and a breakdown voltage of 2.4 V. The second capacitor had a capacitance of 40 nF and a dielectric strength of 0.6 ± 0.3 MV m−1. In 2014, Crystal Ewen, at the same institution, fabricated capacitors of identical composition which had an average capacitance of 30 ± 2 nF and dielectric strength of 103 MV m−1 [3]. Ewen attempted to introduce a higher concentration of titanium dioxide into the films using a thermal evaporator, but was unsuccessful due to the differences in melting points of poly(vinylidene fluoride) and titanium dioxide. To continue the ceramic-polymer capacitor research, an investigation into a higher ratio of titanium dioxide to poly(vinylidene fluoride) was conducted by co-depositing poly(vinylidene fluoride) and titanium dioxide rather than depositing a mixture of the two from the same source. The poly(vinylidene fluoride) was deposited using a resistive thermal evaporator while the titanium dioxide was deposited using an electron beam gun. The question that this study will answer is how a titanium dioxide dominant titanium dioxide-poly(vinylidene fluoride) capacitor compares to capacitors that are poly(vinylidene fluoride) dominant in terms of the dielectric constant and dielectric strength. Since capacitance is dependent on the thickness of the capacitor, the dielectric constant of the capacitors was examined and compared to the previously fabricated capacitors. The dielectric constant being a factor by which the electric field is effected by a material relative to a vacuum. In addition, an effective medium theory was used to calculate a dielectric constant approximation and compared to the experimental dielectric constant. The volume energy density was calculated to compare to capacitors in power applications. For the titanium dioxide-silicon dioxide capacitors, multiple were fabricated, empirical models were produced relating the composition to the dielectric constant and dielectric strength, and a prediction were developed on what composition will produce a dielectric film which can store the most energy. Energy storage can be manipulated via changes to the geometry or dielectric

3 composition of the capacitor. The purpose of this study is to provide insight into alterations to composition which can be made to produce capacitors useful for future energy storage applications.

4 Chapter 2

Background

2.1 Capacitors

Capacitors are energy storage devices made up of two conductors separated by a non-conductive region [4]. An energy source is attached to the conductors which creates an electric potential diﬀerence, or voltage, between them due to charge buildup. The ability of a capacitor to store charge per voltage applied is called the capacitance. The capacitance is deﬁned by Q C = , (2.1) V

where C is the capacitance (F), Q is the magnitude of charge on each plate (C) and V is the magnitude of voltage across the conductors (V). One type of capacitor is the parallel-plate capacitor, as shown in Figure 2.1 which uses two parallel conductive plates of area, A, and separated by a distance, d. Between the plates, a non-conductive dielectric (i.e. insulator) is used to alter the capacitance of the capacitor by changing the absolute permittivity, . Absolute permittivity is the measurement of capacitance per distance when forming an electric ﬁeld in a medium.

5 Figure 2.1: A model of a parallel-plate capacitor.

Capacitance can also be expressed in terms of its absolute permittivity and the geometry of the capacitor (i.e. electrode size and distance between electrodes). This is given by A C = , (2.2) d

where is the absolute permittivity (F m−1), A is the area of the parallel plates (m2), and d is the distance between the plates (m). The absolute permittivity can also be expressed as

= r0, (2.3)

where r is the relative permittivity, or dielectric constant, and 0 is the permittivity of free space (F m−1). When the medium between the plates is a vacuum, the absolute permittivity is equal to the permittivity of free space. The absolute permittivity can be altered by manipulation of the relative permittivity by the choice of materials for the dielectric [5]. The dielectric constant can be expressed as

Cd r = . (2.4) 0A

6 The dielectric strength is a quality of a dielectric that describes its maximum voltage for a given length of the material that can be applied without it becoming conducting. The voltage that, when applied, causes the material to lose its insulating qualities and become conducting is called the breakdown voltage [6]. The dielectric strength is the magnitude of the critical electric ﬁeld which corresponds to the breakdown voltage over the thickness of the material and is expressed by the following

V |E~ | = B , (2.5) cr d

~ −1 where |Ecr| is the magnitude of the critical electric ﬁeld (V m ) and VB is the breakdown voltage (V). The maximum energy stored within a capacitor is given by

1 U = CV 2. (2.6) max 2 B

The energy stored is limited by the capacitance and maximum voltage which can be applied (i.e. the breakdown voltage). In order to study these electrical properties, the electrodes and dielectric ﬁlm are created using a thin ﬁlm deposition technique called physical vapor deposition.

2.2 Thin Film Deposition

Thin films are those which are on the order of 0.1 microns in thickness [7]. Thin film processing is accomplished in several steps which include emission of the source material, transport, deposition, annealing, and analysis. The source is where the material of the film begins and is initially a solid. The source material is evaporated or sputtered by means of physical vapor deposition. The material is transported through vacuum. The deposition is the process of the film developing onto a substrate. The

7 three factors which govern this step, aside from transport, are substrate condition, reactivity of source material with the substrate, and energy input to the surface of the substrate [8]. These factors determine such characteristics as contamination of the film by the substrate, quality of film growth, and penetration depth into the substrate. Annealing is an optional step which is the heating of the film for the removal internal stresses and to strengthen it. The final step is to analyze (or characterize) the film for its structure, composition, and other properties. The structure is necessary to characterize as the capacitance and breakdown voltage properties are related to the thickness of the dielectric film. Composition of the dielectric film is important to ensure that there is a uniform distribution of the material and that the elements of the material are present in the expected quantities. During the transport phase of the thin film processing, the mean free path of a particle is inversely related to the pressure within the container [9]. It is therefore necessary to reducing the pressure to allow for the material to travel from the source to the substrate. Reducing pressure also has the added benefit of decreasing contamination during the deposition phase. Reduction of pressure is done using vacuum technology. Once an adequate vacuum is achieved, the material can be evaporated, transported, and deposited. This is done by means of physical vapor deposition.

2.2.1 Physical Vapor Deposition

Physical vapor deposition includes a variety of techniques, but the relevant techniques in this thesis are electron beam deposition, resistive thermal evaporation, and sputter deposition.

Electron Beam Deposition

Electron beam deposition uses an electron gun, which bombards the source material with electrons. The electrons experience a Lorentz force from the electric and

8 magnetic ﬁelds which is given by

~ ~ ~ ~ ~ F = FE + FB = qeE + qe~v × B, (2.7)

~ ~ ~ where F is the force on the electron (N), FE is the force from the electric field (N), FB ~ is the force from the magnetic field (N), qe is the charge of an electron (C), E is the electric field (N C−1), ~v is the velocity of the electron (m s−1), and B~ is the magnetic field (T). The source material is held by a crucible or hearth. Upon vaporization, the material travels to the substrate along with positive ions and X-rays. The positive ions are generated from the incoming beam of electrons interacting with the vaporized material and the X-rays from exciting electrons within the material. The X-rays pose undesirable effects to dielectric films for electronic applications by trapping charges within the film [10]. A diagram of physical vapor deposition via the electron gun is shown in Figure 2.2. A filament is attached to a 10 kV energy source. The filament is heated and the electrons are accelerated from the filament and guided into the hearth containing the material by a magnet. In the figure, an example copper hearth is used and is cooled using water (indicated by the tube entering the hearth). The electrons provide enough energy for the solid material to be vaporized. The material, along with X-rays, travel toward the substrate and impinge upon it.

9 Figure 2.2: A diagram of an electron gun bombarding material with electrons, and the resulting vaporization and byproducts of the process.

Resistive Thermal Evaporation

The method of evaporation through electrically heating a source is called resistive thermal evaporation. A tungsten boat is used in this study. A power source is connected to the boat and a current is sent through. Due to the resistance in the boat, some of the electrical energy is transformed into thermal energy which heats the material contained within the boat until vaporization occurs.

Sputter Deposition

Sputter deposition, or sputter coating, is a method which utilizes ion bombard- ment to deposit material onto a substrate. The ion transfers momentum to the target material which causes the material to travel towards the substrate with such high energy that it is driven into the substrate and forms a very strong atomic bond. The

10 sputter coater with a glow discharge setup, as shown in Figure 2.3, uses a method by which the chamber containing the substrate and target is ﬁlled with argon gas. A bias is created between the target and the stage, containing the substrate, so that the argon gas between them becomes ionized [11]. The ions are propelled with high momentum into the target material perpendicularly [12]. The stage is biased negatively causing some ions to fall out of the plasma into the substrate to enhance resputtering.

Figure 2.3: A diagram of a glow discharge sputter coater with argon ions bombarding a target material which causing the material to gain momentum and coat a substrate.

2.3 Materials

Materials are typically classified into four categories: metals, ceramics, polymers, and composites [13]. A fifth type, which depending on its chemical composition can be classified as a composite, is a semiconductor. The characteristics of materials arise from their structure and composition. The properties of materials are mainly due to their formation in bulk material rather than from each individual atom. The properties of bulk material are related to the types of atoms, bonds between atoms, coordination of atoms, microstructure of phases, and bulk arrangement. The relevant materials for the capacitors in this study are the ceramics silicon dioxide and titanium dioxide along with the polymer poly(vinylidene fluoride).

11 2.3.1 Ceramics

Ceramics are materials which are comprised of one or more metals with a non- metal. They are considered inorganic nonmetallic materials. They are inorganic because they lack a carbon-hydrogen bond and nonmetallic because they contain nonmetallic elements of either oxygen, nitrogen, carbon, or hydrogen.

Silicon Dioxide

Silicon dioxide (SiO2) is a ceramic occurring oxide most commonly appears in the crystalline and amorphous forms. It has a 1:2 ratio of silicon to oxygen. As a bulk material, silicon dioxide has a dielectric constant of 3.6 to 4.2 and a dielectric strength of 25 to 40 MV m−1.

Titanium Dioxide

Titanium dioxide (TiO2) is a ceramic occurring oxide sourced from ilmenite, rutile, and anatase. It has a 1:2 ratio of titanium to oxygen. As a bulk material, titanium dioxide has a dielectric constant of 30 to 100 and a dielectric strength of 2 to 12 MV m−1 [14].

Titanium (Ti) can oxidize (becoming TiO2) and go through phase transformations

◦ via annealing. Annealing between 400 to 800 C will produce the anatase form of TiO2 which is the form used in this study. The phase transformations and corresponding annealing temperatures are shown in Figure 2.4.

12 Figure 2.4: A diagram illustrating the phase transformations and corresponding temperatures for titanium dioxide.

2.3.2 Polymers

Polymers are classiﬁed as either thermoplasts, thermosets, or elastomers [15]. Thermoplasts are long-chain linear molecules that are formed at temperatures above critical temperature. A characteristic of a thermoplast is that it is brittle at room temperature.

Poly(vinylidene Fluoride)

Poly(vinylidene ﬂuoride) (PVDF) is a thermoplast ﬂuoropolymer. The chemical

formula is -(C2H2F2)n-. It has a 2:2:2 ratio of hydrogen to carbon to ﬂuorine. As a bulk material, PVDF has a dielectric constant of 6 to 12 and a dielectric strength of 200 MV m−1 [16].

2.3.3 Composites

Composite materials are materials with a combination of two or more materials that are distinct in structure and composition, and which are each present in significant quantities. Composite materials are deﬁned on the macroscale rather than the

13 microscale (i.e. not as being comprised of diﬀerent atoms, but of diﬀerent materials). In this work, the two composites formed by co-depositions for the capacitors are

TiO2-PVDF and TiO2-SiO2. The properties of composite materials are related to the materials with which they consist. Experimentally this can be determined through characterization techniques. However, an mathematical approximation exists for the eﬀective dielectric constant of composites.

Eﬀective Dielectric Constant Approximation

For composite materials, the dielectric constant of the host material is related to the molecular polarizability of the inclusion material by the Clausius-Mossotti relation [17] as expressed by

r,1 − 1 4π X = Nαp, (2.8) r,1 + 2 3

where r,1 is the dielectric constant of the host material, N is the number of molecules,

3 and αp is the polarizability (m ). The polarizability is expressed as

r,2 − 1 3 αp = a , (2.9) r,2 + 2

3 where r,2 is the dielectric constant of the inclusion material and a is the radius (m ). The Maxwell-Garnett approximation is used to calculate the eﬀective dielectric constant of a two-material composite [18]. This is expressed as

− − eff r,1 = δ( r,2 r,1 ), (2.10) eff − 2r,1 r,2 − 2r,1

where eff is the eﬀective dielectric constant and δ is the volume ratio of inclusion material to total material.

14 The approximation for the eﬀective dielectric constant of a two-material composite is expressed as

2(1 − δ)r,1 + (1 + 2δ)r,2 eff = r,1 . (2.11) (2 + δ)r,1 + (1 − δ)r,2

In this study, the experimental dielectric constants determined with analytical methods were compared to the eﬀective dielectric constant approximations calculated using this.

15 Chapter 3

Methods

3.1 Purpose

The purpose of this work was to create capacitors from composite ﬁlms of TiO2-

PVDF (with a higher concentration of TiO2) and TiO2-SiO2 to study the effective dielectric constant and effective dielectric strength as they relate to the composition of each capacitor by measuring breakdown voltage, capacitance, and the geometry of the capacitors. To accomplish this, a series of TiO2-PVDF films were grown with various currents (and therefore evaporation temperatures) in order to determine the current that produced a high evaporation rate and no decomposition of the polymer. The experimental effective dielectric constants for the composite films were compared to the effective dielectric constant approximation. A TiO2-PVDF capacitor were made to help fill in the gap for a TiO2 dominant capacitor in the existing literature. A series of TiO2-SiO2 capacitors with varying compositions were fabricated, characterized, and empirical models developed to predict the composition which yields that maximum energy stored. These capacitors were fabricated using physical vapor deposition (i.e. sputter coating, electron beam gun evaporation, and resistive thermal evaporation) and char-

16 acterization techniques (i.e. atomic force microscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy, breakdown voltage measuring instrumentation, and capacitance measuring instrumentation). The methods for fabrication and characterization are discussed in this chapter.

3.2 Deposition Equipment

A Denton Desk II Sputter Coater, which uses a glow discharge setup, and a Torr International, Inc. deposition system were used to deposit the films. Originally, a high-vacuum physical vapor deposition system was built for this study, but was set aside for the Torr International, Inc. deposition system. The process of designing, building, and automating it is detailed in Appendix A. A diagram depicting the layout of the Torr International, Inc. deposition system is shown in Figure 3.1. The top diagram is a front/side view with the electron gun on the lower right hand side of the chamber and the resistive thermal evaporator on the lower left hand side. The platform is hanging from the top of the chamber. All three shields are moved out of the line of sight from the sources and the platform. The bottom diagram is an aerial view of electron gun (right) and resistive thermal evaporator (left). The shields are the tear shaped objects and are moved out of the line of sight. The quartz crystal microbalances are protruding from a flange in the upper right hand corner of this image. In the experimental setup, the quartz crystal microbalances were moved to be next to the platform in order to get a better measurement of the film thickness. The system uses a Pfeiffer Compact Full Range Gauge to measure pressure and quartz crystal microbalances to measure deposition rate. The deposition rate interfaces are an Inficon SQC-310C and an Inficon SQM-160 for the electron gun and thermal evaporator, respectively. The electron gun is also controlled using the Inficon SQC-310C. The electron gun has the ability change the source material while

17 the system is under vacuum using an Inﬁcon CI-100 Indexer. The Torr International, Inc. deposition system is capable of achieving a high-vacuum (i.e. a pressure in the 10−3 to 10−9 Torr range). For all depositions with the electron gun, an accelerating voltage of 10 kV was used and the ﬁlament current was adjusted to alter the emission current.

18 Figure 3.1: A model and diagram of the Torr International, Inc. deposition system where a.) is a model of a front/side view and b.) is a diagram of an aerial view from inside. The labeled components are 1.) substrate platform, 2.) substrate platform shield, 3.) electron gun, 4.) resistive thermal evaporator, 5.) quartz crystal microbalances, 6.) electron gun, 7.) electron gun shield, 8.) resistive thermal evaporator, and 9.) resistive thermal evaporator shield.

19 3.3 Capacitor Fabrication Process Overview

The dielectric films were created via physical vapor deposition using an electron gun and a resistive thermal evaporator in the Torr International, Inc. deposition system. Contacts were made with the film using gold palladium (AuPd) which were deposited using the sputter coater or with copper (Cu) using the Torr International, Inc. deposition system. An aluminium (Al) mask was used to expose the bottom electrode when depositing the dielectric film and a paper mask was used to expose a circular region when depositing the top electrode. A diagram depicting product of each step of the capacitor fabrication process is shown in Figure 3.2. Wires were attached to the electrodes using CircuitWorks Conductive Epoxy.

Figure 3.2: A diagram of the products of the capacitor fabrication process: a.) a rectangular silicon substrate, b.) substrate with bottom electrode deposited, c.) composite ﬁlm deposited after bottom portion was masked, and d.) top electrode is deposited after substrate is masked leaving a circular region on top of the composite ﬁlm exposed.

3.4 Material Preparation

Prior to depositing the TiO2-PVDF ﬁlm, the PVDF was prepared using the solvent dimethylformamide (DMF) to reduce the polymer chain length to allow for easier evaporation. The mixture consisted of 0.330 g of PVDF in powder form and 4 mL of DMF. The PVDF was measured using a Sartorius analytical balance with a 0.001 g resolution. A Daigger hot plate and magnetic stirrer was used to warm and stir the

20 mixture. The mixture was stirred at 30 rpm at 60 ◦C for one hour. The mixture was then transferred to a boat and placed in a Lab-Line Squaroid Duo-Vac Oven at 60 ◦C at a low-vacuum pressure for one hour to remove the solvent.

3.5 Film Deposition Procedure

The film deposition procedure includes the deposition of bottom and top electrodes with the sputter coater and Torr International, Inc. deposition system, and the deposition of the dielectric film with the Torr International, Inc. deposition system. The substrate material is left ambiguous in the descriptions as the procedures are written in a general sense as the fabrication process is similar for all films and capacitors. Any differences in the fabrication process are noted.

3.5.1 Electrodes

The electrodes were deposited using either a sputter coater or electron gun. The sputter coater was used to deposit AuPd while the electron gun was used to deposit Cu. The electron gun was useful for depositing on larger pieces of silicon and Cu is less expensive than AuPd. However, pumping the Torr International, Inc. deposition system down to a pressure in the 10−6 Torr range took several hours, so sputter coating was the preferred method for the deposition of electrodes. The bottom electrode for the TiO2-SiO2 capacitors were thicker (at 200 nm) to prevent the detection of the Si wafer by the spectrometer.

Sputter Deposition

The substrate (which was a Si wafer, or a masked Si wafer with the bottom electrode and dielectric ﬁlm already deposited) was placed in the sputter coater on the stage. The chamber was pumped down to a pressure of 100 mTorr and argon was

21 introduced into the chamber. The chamber was brought up to 500 mTorr using the argon and then reduced to 100 mTorr to ﬂush the system. This was done three times to ensure an adequate amount of argon was present within the chamber. The sputter coater was then run for 300 or 600 seconds at 45 mA and a pressure of 200 mTorr to produce electrodes with approximately 100 or 200 nm of thickness. These thickness values are based on the guidelines set by the sputter coater manufacturer [19].

Electron Gun Deposition

The Si wafer substrate was secured to the platform in the Torr International, Inc. deposition system. A shield was moved to block the line of sight from the electron gun to the substrate. The chamber was pumped down to a pressure in the 10−6 Torr range. The electron gun was powered on and turned up until the desired evaporation rate was observed on the quartz crystal microbalance. The shield was moved out of the line of sight between the electron gun and substrate, allowing the source material to deposit onto the substrate. Once the desired thickness of 30 nm was reached, the shield was moved into the line of sight between the electron gun and substrate, the electron gun was powered down, and the system was then brought up to atmospheric pressure.

3.5.2 Dielectric Film

The deposition method for each material used in the dielectric ﬁlms are shown in Table 3.1.

22 Material Deposition Method

TiO2 Electron gun PVDF Resistive thermal evaporator Ti Resistive thermal evaporator

SiO2 Electron gun

Table 3.1: The deposition method used for each material used in the dielectric ﬁlms.

The substrate (which was a Si wafer, or AuPd or Cu coated Si wafer) was secured to either the electron gun shield or platform in the Torr International, Inc. deposition system. The former was for the deposition of the TiO2-PVDF ﬁlm and the latter for the Ti-SiO2 ﬁlm. If the sample was meant to be a capacitor then the mask was placed over half of the substrate in order to shadow mask and prevent the deposition over the entire bottom electrode. The electron gun shield and substrate was moved out of the line of sight from the material sources when the substrate was attached to the shield, or a shield was moved to block the line of sight from the material sources to the substrate when depositing onto the platform. The chamber was pumped down

−6 to a pressure in the 10 Torr range. Prior to depositing the Ti-SiO2 film, a 10 nm adhesion layer of Ti was deposited to help the SiO2 adhere to the AuPd. The indexer was used to select Ti and the electron gun was brought up to the desired evaporation rate. The platform shield was moved out of the line of sight between the electron gun and substrate. Once the desired thickness was reached, the electron gun was powered down. The indexer was used to change the material to SiO2 for the electron gun. At this point, the thermal evaporator had a boat containing PVDF and the electron gun had TiO2 in its crucible prior to the deposition of the TiO2-PVDF film, or the thermal evaporator had a boat containing Ti and the electron gun had SiO2 in its crucible prior to the deposition of the Ti-SiO2 film. The electron gun and resistive thermal evaporator were powered on and turned up until the desired evaporation

23 rates were reached. The electron gun shield was moved into the line of sight of the material sources when depositing onto the substrate attached to the shield, or the shield was moved out of the line of sight between the material sources and substrate when depositing onto the platform. The material was deposited until the desired thickness was reached. Once the desired thickness was reached, the electron gun shield was moved out of the line of sight when depositing onto the substrate attached to it or the shield was moved into the line of sight between the material sources and substrate when depositing onto the platform. The electron gun and resistive thermal evaporator were powered down, and the system was then brought up to atmospheric pressure. After deposition, the Ti-SiO2 ﬁlms were annealed using a Thermolyne 21100 tube furnace at 500 ◦C for two hours to transform the Ti into the anatase form of

TiO2 in order to produce TiO2-SiO2 ﬁlms.

3.6 Film Analysis

The techniques used for analyzing the films and capacitors were atomic force microscopy, energy dispersive X-ray spectroscopy, scanning electron microscopy, and equipment was used to analyze properties involving capacitance instrumentation and breakdown voltage instrumentation. The structure was measured using an atomic force microscope (AFM) and a scanning electron microscope (SEM). The composition was measured using an energy dispersive X-ray spectrometer (EDS). The electrical properties of the film was measured using capacitance instrumentation and breakdown voltage instrumentation. The film surface topography and composition were measured prior to the deposition of the top electrode. The capacitance was measured next after the electrodes were deposited. After that, the breakdown strength was measured. The capacitor was then split into two, using a pair of forceps, down the middle of the top electrode. The film thickness was measured last by imaging the cross section

24 of the ﬁlm using the SEM. Speciﬁc details of the analysis are given in the following sections.

3.6.1 Structure

The surface topography of the ﬁlms were characterized using an AFM while the ﬁlm thicknesses were characterized using an SEM. The distribution of elements were determined using a combination of the SEM and spectrometer, but that is covered in the next section on composition.

Atomic Force Microscope

The use of force to determine surface topography was done using an Oxford In- struments Asylum Research MFP-3D Origin+ AFM. The samples were clipped to a sample holder on the scanning stage and the head was placed into position over the sample. To detect at the atomic scale, the AFM used a cantilever which was attached to the head. It was dragged across the surface in close proximity to determine surface properties in the lateral (xy) and vertical (z) directions. The z-range resolution of this model is 15 µm. The cantilever consists of a tip that is mounted onto a cantilever spring. This spring must have a spring constant smaller than the effective spring constant between the atoms of the material being analyzed. Therefore, the equation for a simple harmonic oscillator is used to determine the maximum spring constant for the cantilever spring. The cantilever used is an Oxford Instruments AC240TS-R3. This cantilever has a spring constant of 2 N m−1 which is ideal for measuring the surface topography of soft materials such as PVDF. A laser was shone onto and deflected off of the cantilever and onto a photo detector. Changes in the position of the cantilever are detected by the position of the reflected laser on the photo detector. The AFM had several modes of operation available, but of particular interest to this study was the tapping mode. For the application of characterizing films made of

25 soft materials such as polymers, the tapping mode provides the ability to characterize the surface structure while minimizing damage. This mode causes the cantilever to oscillate vertically with a particular amplitude and frequency. When the cantilever came into contact with the sample surface, the oscillation amplitude was reduced and the frequency of oscillation was offset. From these changes, height, amplitude, and phase images were produced. The height image helped to determine the range of distance from the lowest to highest point of the sample. Amplitude was useful for determining how the tip was deflected for the improvement of image quality. The amplitude images were used for critiquing whether the best images had been created by minimizing the deflection. Producing phase images was the purpose of using the AFM as they showed the composition, adhesion, friction, and viscoelasticity of the sample [20]. The shortcoming of phase imaging was that it incorporated the height variation of the sample so the interpretation of these images may not have been reliable for determining specific characteristics of the surface if the sample had varying height.

In this study, phase imaging was used to study the surface structure of both TiO2-

PVDF and TiO2-SiO2 composite ﬁlms. The images were taken of varying ratios of

TiO2:PVDF and a single image was taken of one of the TiO2-SiO2 films. One characteristic of the films, imperative to know for the purpose of this study, is whether the materials making up the film have an equal distribution. Although another technique is more useful for this (i.e. elemental mapping), phase imaging was used to see if the other technique’s results could be supported. In addition, the materials have different adhesion, friction, and viscoelasticity so a sample was created which had a visible gradient due to varying composition. This was done by using a long strip of Si that extended over both material sources. The gradient was only present on this sample and not on the other films and capacitor dielectric films. Phase imaging was used to determine if the composition at three locations across the sample would

26 show variation in these different properties. Shading was used in these three images to make the change in composition apparent. The varying coloration (in the shaded and non-shaded images) represent different changes in phase. All other images in this study were left in grey scale. AFM is one method which was used to characterize the physical structure of the films, the other method used was the scanning electron microscopy.

Scanning Electron Microscope

The SEM was a Zeiss Supra 40VP model. A model of the SEM is shown in Figure 3.3. It consists of an electron gun, accelerating anode, focusing magnet, scanning magnet, backscattering electron detector, secondary electron detector, X-ray detector, and sample stage.

Figure 3.3: A model of the Zeiss Supra 40VP scanning electron microscope: 1.) sample, 2.) scanning coils, 3.) objective lens, 4.) in-lens detector, 5.) multihole aperture (aperture changer), 6.) anode, and 7.) electron gun. [21]

Electrons were generated by an electron gun and accelerated by a high voltage

27 between the cathode (i.e. filament) in the electron gun and the accelerating anode. The electrons passed through a Wehnelt cylinder to columnize the beam. The SEM used a Schottky field emission electron gun. Schottky-emission uses a combination of thermal energy and high voltage to generate an electron beam. The Schottky-emission gun used a tungsten crystal coated with zirconium (II) oxide (ZrO). Once the electrons passed through the anode, they passed a series of magnetic lenses to focus the beam. The magnetic lenses utilized the Lorentz force to manipulate the beam according to the parameters set by the user. The microscope was kept at a high-vacuum pressure. This is done to prevent the electron gun filament from oxidizing, to increase the free mean path, and to reduce contamination. When the electron beam interacted with the sample, it produced Auger electrons, secondary electrons, backscattered electrons, characteristic electrons, continuum X- rays, and fluorescent X-rays. All of these products from the interaction of an electron beam with a sample came from a particular region called the interaction volume. The processes for the emission of secondary electrons, backscattered electrons, and characteristic X-rays are as follows. Secondary electrons are referred to as such, because they are stimulated by either a photon or primary electron. The secondary electrons occur when the primary electron gives energy to an electron, within the atom, to be ejected. Backscattered electrons are primary electrons which enter an atom, but get scattered back out of the atom. Characteristic X-rays are produced when a primary electron ejects a secondary electron causing a higher energy electron to de-excite and take its place [22]. The process emits energy as a photon (i.e. characteristic X-ray) in order to conserve energy. The Auger effect occurs when an inner-shell vacancy in an atom is filled by an outer-shell electron and the emitted radiation from the de-excited electron is ab- sorbed causing another electron to be emitted. These emitted electrons are called Auger electrons. Continuum X-rays, or Bremsstrahlung, are X-rays produced from

28 the deceleration of a charged particle by the atomic nucleus or another charged particle. The kinetic energy is converted and emitted as radiation (i.e. continuum X-rays). The SEM had secondary electron detectors and backscattered electron detectors. The secondary electron detectors were Everhart and Thornley and In Lens, and the backscattered electron detectors were Robinson and Solid State detectors. It had a resolution of 2 nm, and has apertures of 10 µm, 20 µm, 30 µm, 60 µm, 120 µm, and 200 µm. For this study, a working distance of 12.9 to 13.0 mm, accelerating voltage of 10 kV, and a magnification of 15,740 to 21,720 was used. The SEM was used to determine the thickness of the dielectric films and to image the top of the capacitor to obtain elemental maps. The elemental mapping technique is detailed in the next section (3.6.2). To obtain an image of the dielectric film, the capacitor was split in half using a pair of forceps. One half of the capacitor was oriented vertically using a Ted Pella, Inc. Set Screw Vise. A piece of Cu tape was placed on the backside of the capacitor to mark the location of the film. The vise with capacitor was secured to the specimen stage with carbon tape. Using the SmartSEM software, the system was pumped down to a high-vacuum. With the same program, the electron gun was turned on and the capacitor was set in position for an image using the stage controller. Once the appropriate parameters were set (i.e. working distance and magnification) and the image was in focus, an image was taken. The image was opened in the SmartTiff software and thickness measurements were made using the point-point feature. The SEM was useful for imaging a sample and characterizing the structure using secondary electrons, but there was another technique which also utilizes an electron beam to help characterize samples. This technique is called energy dispersive X-ray spectrometry and was used to characterize the composition of the samples.

29 3.6.2 Composition

The composition of the ﬁlms are characterized using an EDS.

Energy Dispersive X-ray Spectrometer

The EDS was a Thermo Scientific UltraDry model and was attached to the same vacuum chamber used for the SEM. The EDS consisted of an energy source, a sample holder, a detector, and analyzer equipment. The energy source emitted X-rays which bombarded the material of the sample being held onto a sample holder. The atoms in the sample produced characteristic X-rays which provided a unique signature which was used to identify present elements. The model was capable of detecting continuum and characteristic X-rays. The radiation was picked up by a detector and then processed by a computer system where they were compared to standards for known elements. For the composition analyses, a working distance of 13 mm, accelerating voltage of 10 kV, and magnification of 1000 to 2000 was used. The EDS was limited to what elements could be detected as lighter elements with electrons with lower energy emit radiation in the ultraviolet range. These elements included hydrogen, helium, and lithium. The samples were secured to a Ted Pella, Inc. pin stub specimen mount using carbon tape. When analyzing any films containing PVDF, the films were hung off the specimen holder to avoid picking up the carbon present in the carbon tape (since carbon is present in PVDF it is important to avoid picking up extraneous carbon). The pin stub was secured to the specimen stage. Using the SmartSEM software, the system was pumped down to a high-vacuum. With the same program, the electron gun was turned on and the capacitor was set in position for an image using the stage controller. Once the appropriate parameters were set (i.e. working distance and magnification) and the image was in focus, the Thermo Scientific Pathfinder X-ray Microanalysis software was used to obtain spectrums and elemental maps.

30 A spectrum generated by the EDS, for the TiO2-PVDF capacitor’s dielectric ﬁlm, is shown in Figure 3.4. The y-axis was the number of counts that the detector detected and the x-axis was the energy in electron volts (keV). The peaks were the characteristic X-rays used to identify the elements present in the sample, while the peak intensity could be used to quantify the abundance of each element after the removal of a continuum. From the net counts, the weight percentages and atom percentages were calculated by the microanalysis software.

Figure 3.4: The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

In addition, a qualitative analysis was produced in the form of elemental maps. These maps gave the spatial locations of each detected element in the sample, which was useful for determining the distribution of heterogeneous samples.

31 Once structure and composition was characterized, the electrical properties, which arise from structure and composition, were characterized using capacitance and breakdown voltage instrumentation.

3.6.3 Electrical Properties

The breakdown voltage and capacitance of the samples were measured using two diﬀerent circuits described below.

Breakdown Voltage Measuring Circuit

Breakdown voltage is the minimum voltage that, when applied, the insulator becomes conducting, so a DC voltage was applied across the capacitor, in small increments, until this occurred. The breakdown voltage was defined here as the greatest increase of change in current per change in time. The I-V plot for the capacitor maintained a steady average until the current exponentially increased followed by a spike. This spike in current was the greatest increase of change in current per change in time and corresponded to the breakdown voltage. The breakdown voltage was tested using instrumentation consisting of a KORAD KA3005P programmable power supply and LabVIEW. The capacitor was put in series with the programmable power supply. The voltage and current across the capacitor was measured directly from the programmable power supply. The LabVIEW program (see Appendix B) controlled the power supply to output voltages in increments of 10 mV s−1. This occurred until a preset maximum voltage was reached or the user stopped the program upon visual inspection of the I-V plot. The differences in each recorded current was calculated. The largest current difference was where the capacitor was considered to be conductive and when the materials breakdown voltage was reached. The corresponding voltage was considered the breakdown voltage.

32 Capacitance Measuring Circuit

The capacitance instrumentation used the electrical reactance of circuit elements to determine the capacitance. A sinusoidal voltage was applied across a resistor and capacitor in series (i.e. an RC circuit). The measured phase angle between the signal measured across the voltage source and across the capacitor, and known resistance and frequency was used to calculate the capacitance. The capacitance in terms of frequency, resistance, and the phase angle is given by

1 C = , (3.1) 2πfRtan(φ)

where φ is the phase angle, f is the frequency (s−1), and R is the resistance of the resistor in series with the capacitor (Ω). The phase angle is given by

∆T φ = , (3.2) T

where ∆T is the diﬀerence in period between the voltage source and capacitor (s) and T is the period (s). The capacitor was placed in series with the resistor and the AC voltage was generated using a BK PRECISION 4011A 5MHz Function Generator. The waveforms from the function generator and across the capacitor were measured using a RIGOL DS1102E Digital Oscilloscope. A potentiometer was used as a resistor to allow for adjustment of the measured phase angle as displayed on the screen of the oscilloscope. The frequency of the function generator was changed to produce the desired phase angle. Once this angle was achieved, the resistance of the potentiometer was measured using a Fluke 117 True RMS Multimeter. The measured phase angle, frequency, and resistance was put into a MATLAB code as inputs and the output was the capacitance.

33 Chapter 4

Results and Discussion

4.1 Overview

This section contains an abbreviated version of the results of this study, and the details and other results are provided in Sections 4.2 and 4.3.

4.1.1 Titanium Dioxide-Poly(vinylidene Fluoride) Capacitor

The composition, dielectric constant, and dielectric strength of the TiO2-PVDF capacitor are displayed in Table 4.1.

Property Capacitor Value

Composition (%) TiO2: 94.10 ± 0.09, PVDF: 5.90 ± 0.09 Dielectric Constant 33.62 ± 4.45 Dielectric Strength (MV m−1) 24.15 ± 0.02

Table 4.1: The composition, dielectric constant, and dielectric strength of the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

34 4.1.2 Titanium Dioxide-Silicon Dioxide Capacitors

The equations relating TiO2 concentration percentage to the dielectric constant and dielectric strength are as follows

r = 0.7084c + 5.8740, (4.1)

and ~ |Ecr| = −0.1284c + 17.7088, (4.2)

where c is the concentration of TiO2 as a percentage of the total TiO2 and SiO2. The composition is compared to the dielectric constant and dielectric strength of

2 the ﬁve TiO2-SiO2 capacitors in Figures 4.1 and 4.2, respectively. The R value for the dielectric constant and TiO2 percentage data set is 0.8770 and for the dielectric

strength and TiO2 data set is 0.7070.

Figure 4.1: A graph comparing the composition to the dielectric constant for the ﬁve titanium dioxide-silicon dioxide capacitors.

35 Figure 4.2: A graph comparing the composition to the dielectric strength for the ﬁve titanium dioxide-silicon dioxide capacitors.

The composition to maximize energy storage is two-ﬁfths TiO2 and three-ﬁfths

SiO2.

4.2 Titanium Dioxide-Poly(vinylidene Fluoride) Films

and Capacitor

This section is divided into dielectric ﬁlm deposition current and the corresponding ﬁlm composition and topography (in Section 4.2.1), and the electrical properties of the

TiO2-PVDF capacitor (in 4.2.2). The ﬁrst step was to determine at what rate allows for the evaporation of PVDF without decomposing the material. A quantitative analysis using EDS was performed to determine atom percentages of the elements present within the ﬁlm and in what ratio to each other. In addition, a qualitative analysis with the EDS was done to determine the spatial locations of each element to ensure an even distribution and to determine whether the elements that make up

36 each material were in the expected locations. The AFM was used to examine surface

features of the TiO2-PVDF ﬁlms to determine phase and morphological diﬀerences for

ﬁlms with varying TiO2 and PVDF composition. The EDS data used for calculations can be found in Appendix C labeled Additional Results Data. The statistical methods and MATLAB code used for calculations are accessible in Appendices D and E labeled Statistical Methods and MATLAB: Results Calculations, respectively.

4.2.1 Deposition Current, Composition, and Surface Features

of the Films

The TiO2-PVDF ﬁlms were deposited onto Si substrates which were coated with

Cu while the PVDF films were deposited directly onto Si. The TiO2-PVDF films are labeled Films 1 through 10 where Films 1 through 5 were deposited using an AC deposition current of 80 A and Films 6 through 10 were deposited using an AC deposition current of 100 A. The PVDF films were deposited directly onto a Si substrate are labeled Films 10 though 15. They were deposited using an AC deposition

current of 120 A. The TiO2-PVDF capacitor was created using a deposition current of 80 A for the dielectric ﬁlm. As demonstrated in this section, decomposition of PVDF occurred above this current.

The element ratios (from the EDS analysis) of the TiO2-PVDF and PVDF films are presented in Table 4.2. When the PVDF was deposited at 80 A and 100 A, the material demonstrated a varying degree of decomposition with a higher current causing more decomposition on average. The decomposition was worst for the PVDF deposited at 120 A. A deposition at 50 A was attempted, but no material deposited. The 80 A and 100 A depositions were meant to create capacitors (hence why a layer of Cu was deposited). The PVDF films were deposited onto a Si substrate only which did not have the same adhesion properties as the capacitor, so it is unknown whether this had a significant effect on the EDS results.

37 Film Carbon:Fluorine Titanium:Oxygen

1 0.95 ± 0.20 0.56 ± 0.02 2 1.30 ± 0.16 0.50 ± 0.05 3 1.35 ± 0.13 0.34 ± 0.02 4 1.34 ± 0.12 0.23 ± 0.05 5 1.36 ± 0.23 0.00 ± 0.00 6 1.04 ± 0.12 0.61 ± 0.02 7 0.35 ± 0.04 0.66 ± 0.03 8 1.76 ± 0.06 0.55 ± 0.03 9 2.19 ± 0.07 0.48 ± 0.07 10 1.70 ± 0.06 0.28 ± 0.06 11 4.60 ± 0.45 0.00 ± 0.00 12 1.85 ± 0.05 0.00 ± 0.00 13 1.02 ± 0.02 0.00 ± 0.00 14 4.06 ± 0.32 0.00 ± 0.00 15 1.24 ± 0.03 0.00 ± 0.00

Table 4.2: The element ratios of elements in the titanium dioxide-poly(vinylidene fluoride) and poly(vinylidene fluoride) films.

The results for the carbon to ﬂuorine ratio when the deposition current is var- ied indicates that the PVDF is decomposing. Decomposition of PVDF via resistive thermal evaporation was found to occur by Iwogoshi et al. when the temperature during the evaporation process became too high [23]. This is likely due to too high of a vapor pressure and molecular weight. When the molecular weight is too high, the kinetic energy of the molecules must be higher (from a higher velocity) to compensate for a higher mass. A threshold velocity must be met in order for the molecules to evaporate. When the kinetic energy necessary to evaporate is higher than the energy

38 necessary to keep the bonds together then the molecule will decompose. In addition, the low vapor pressure indicates that there might be high intermolecular forces which is causing the material to resist evaporation even further. When the carbon to fluorine ratio was closest to a 1:1 ratio, the film had a burnt appearance. In order for more carbon to be incorporated into the film, a higher deposition current was necessary. This indicates two things. First, that the bonds between the carbon and fluorine are breaking at lower deposition currents. The second is that the carbon requires more energy to evaporate and that it is reacting with the trace amounts of oxygen present within the vacuum. In Joel Iwagoshi’s thesis, he maintained that a carbon to fluorine ratio of 1.29 to 1.97 was achieved by using the EDS. However, when the penetration depth was decreased, the carbon to fluorine ratio decreased to 0.289. The samples are secured within the EDS system using carbon tape. When a higher penetration depth is achieved, the EDS picks up the carbon present in the carbon tape. To avoid this, the composition analysis was done on a portion of the sample that was hung off the stub containing the tape. Although it is possible to evaporate PVDF without decomposition, albeit at an excessively slow rate, it is likely much more time efficient and practical to do so using a technique other than resistive thermal evaporation (such as sputtering). Lastly, the output from the EDS came into question during the last few months of this project. For a period, the system was unable to detect carbon when aimed at carbon tape. An engineer came out to fix the system, but the problem persisted.

Furthermore, the EDS data for the TiO2-PVDF films, PVDF films, and TiO2-PVDF capacitor were slightly altered during a software update. It is believed that the problem was specific to carbon as the titanium:oxygen ratio always remained consistent to what was expected (close to a 1:2 ratio). The same EDS was used for the TiO2-SiO2 capacitors, because the problem is assumed to be only with carbon.

39 The AFM phase images of Films 7 through 10 are presented next in Figures 4.3 through 4.6. Film 7 has the highest concentration of TiO2 relative to PVDF and

Film 10 has the highest concentration of PVDF relative to TiO2. As the film number increases for these films, the amount of PVDF relative to TiO2 increases. The films with a higher ratio exhibit a more rapid phase change across the film than does the films with a lower ratio. These images demonstrate a composition dependent difference in film formation.

Figure 4.3: The phase image produced by the atomic force microscope of Film 7.

40 Figure 4.4: The phase image produced by the atomic force microscope of Film 8.

Figure 4.5: The phase image produced by the atomic force microscope of Film 9.

41 Figure 4.6: The phase image produced by the atomic force microscope of Film 10.

Lastly, a long rectangular piece of silicon was placed within the deposition chamber at close proximity to the material sources. This caused a gradient eﬀect for the deposited material. The phase images for a location close to the PVDF source, a location between the two sources, a location close to the TiO2 source are presented next in Figures 4.7 through 4.9. The images are colorzied to better demonstrate the phase diﬀerences within and between the images.

42 Figure 4.7: The phase image produced by the atomic force microscope of the poly(vinylidene fluoride) dominant side of the titanium dioxide-poly(vinylidene fluoride) film.

Figure 4.8: The phase image produced by the atomic force microscope phase image of the middle of the titanium dioxide-poly(vinylidene ﬂuoride) ﬁlm.

43 Figure 4.9: The phase image produced by the atomic force microscope phase image of the titanium dioxide dominant side of the titanium dioxide-poly(vinylidene ﬂuoride) ﬁlm.

The phase images exhibit a change in phase across the sample. An ability of the AFM is to detect changes in properties on surfaces such as hardness. These images demonstrate that the properties across the sample change due to the change in composition. However, the phase images also take into account topometric differences (i.e. the slope of the surface) [24], so it also a possibility that one side of the sample had a greater height than the other due to differences in the rate of deposition and the material source distance to the substrate. In any case, the film formation, according these images, demonstrates that the co-deposition technique using an electron gun and resistive thermal evaporator is a viable method for fabrication of dielectric films due to the homogeneous formation across the sample.

44 4.2.2 Composition, Structure, and Electrical Properties of the

Capacitor

Composition

From the EDS analysis, the carbon:ﬂuorine ratio is 1.05 ± 0.92, and the titanium:oxygen ratio is 0.46 ± 0.02. The capacitor is 5.90 ± 0.09 % PVDF and 94.10

± 0.09 % TiO2. The spatial locations of each element are presented in Figures 4.10 through 4.13 in elemental maps for carbon, ﬂuorine, titanium, and oxygen, respectively. The maps for carbon and ﬂuorine, and titanium and oxygen have been overlaid onto two SEM images in Figures 4.14 and 4.15 to help determine if the locations correspond properly.

Figure 4.10: The carbon elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

45 Figure 4.11: The ﬂuorine elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

Figure 4.12: The titanium elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

46 Figure 4.13: The oxygen elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

47 Figure 4.14: The carbon and ﬂuorine elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

48 Figure 4.15: The titanium and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

The TiO2-PVDF capacitor was deposited using an AC deposition current of 80 A. A dielectric film deposition was performed at 50 A, but no film was deposited. It is possible that there is a deposition current which would allow for the deposition of the PVDF without decomposition, but rather than spend time trying to locate this current–time was spent creating TiO2-SiO2 capacitors. A deposition current of 80 A was chosen because the Films 1 through 5 demonstrated element ratios close to 1. The ratio of carbon:fluorine was 1.05 ± 0.92. The elemental maps for carbon and fluorine show that the locations of the elements do not coincide which may indicate that the material did decompose. These maps do give definitive evidence that the elements are evenly distributed across the analyzed area.

49 Structure and Electrical Properties

The capacitance, dielectric constant, and dielectric strength of the capacitor are presented in this section. When the capacitor was attached to the RC circuit, the measured frequency was 1000.0 ± 0.1 Hz, the measured resistance was 9.75 ± 0.01 kΩ, and the measured phase angle was 32 ± 1 ◦. Equation 3.1 was used to calculate capacitance. The calculated capacitance of the capacitor is 26.123 ± 3.347 nF. The thickness measurements from the SEM are used to calculate the dielectric constant and dielectric strength, so are shown in Figure 4.16. The measured thickness is 812.0 ± 0.3 nm.

Figure 4.16: The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-poly(vinylidene ﬂuoride) capacitor with thickness measurements.

The diameter of the electrode is 9.525 ± 0.001 mm. The area of the electrode is 7.126 × 10−5 ± 0.000 × 10−5 m2. The experimental dielectric constant was calculated using Equation 2.4 yielding a value of 33.62 ± 4.45. Equation 2.11 was used to calculate the dielectric constant approximation. To produce the lower end of the

50 range for the dielectric constant approximation, δ is taken to be the largest possible fraction of the inclusion material to the host material and the dielectric constants for the materials (i.e. 30 to 100 for TiO2 and 6 to 12 for PVDF) are taken to be the smallest possible. For the upper end of the range for the dielectric constant approximation, δ is taken to be the smallest possible fraction of the inclusion material to the host material and the dielectric constants for the material are taken to be the largest possible values. The dielectric constant approximation is 64.06 ± 35.95. The measured breakdown voltage of the capacitor is 19.61 ± 0.01 V. The dielectric strength of the capacitor (i.e. the measured breakdown voltage divided by the film thickness) is 24.15 ± 0.02 MV m−1. Using the capacitance and breakdown voltage, the maximum stored energy was calculated using Equation 2.6 yielding a value of 5.02 ± 0.46 µJ. The volume energy density is 0.0868 ± 0.0079 J cm−3 where the volume was calculated using the the area of the electrode multiplied by the film thickness. The capacitance of the capacitor was measured to be 26.123 ± 3.347 nF which is similar to that found by Crystal Ewen in her thesis (i.e. 30 ± 2 nF) and in range with Joel Iwagoshi’s results from his thesis (i.e. 6 to 40 nF). Although their capacitors are with a composition that is PVDF dominant, the capacitor from this thesis does have a dielectric constant which falls within the range of the dielectric constant approximation from the effective medium theory. The experimental dielectric constant is 33.62 ± 4.45 whereas the approximation is 64.06 ± 35.95. The range for the approximation is so large, because the dielectric constant for TiO2 has been found to be in the range of 30 to 100. A different TiO2 source, causing a variation in the dielectric constant, and different deposition method, causing different amounts of decomposition of TiO2, than what was used in the theses of Ewen and Iwagoshi could explain the disparity in the lower than expected capacitance. Deposition by electron gun is also not ideal for dielectric film deposition due to being known to trap charges within the film which may have contributed to this. The dielectric strength was determined to be 24.15 ±

51 −1 −1 0.02 MV m . The dielectric strength of TiO2 is 6 MV m and PVDF is 200 MV m−1. The dielectric strength for the composite seems reasonable as it fits between the range of these two values and is closer to that of TiO2 (which makes up 94.10 ± 0.09 % of the film). Ewen found a dielectric strength of 103 MV m−1 and Iwagoshi found a dielectric strength of 0.6 ± 0.3 MV m−1. The volume density of the capacitor in this thesis is 0.0868 ± 0.0079 J cm−3 which is significantly lower than those used in power applications (at least 1 to 2 J cm−3). Ewen determined her capacitor had an

−3 energy density of 0.49 J cm which indicates that a TiO2 dominant capacitor is not ideal. This is expected since the maximum energy stored within a capacitor is proportional to the breakdown voltage squared and is proportional to the capacitance.

The TiO2 contributes most to the capacitance whereas the PVDF contributes most to the breakdown voltage. Therefore, a PVDF dominant capacitor would be expected to be ideal.

4.2.3 Prediction of Composition to Maximize Energy Stored

using Literature Values

The dielectric constant for TiO2 has been found to be in the range of 30 to 100 and for PVDF has found to be in the range of 6 to 12. The dielectric strength for TiO2 has been found to be in the range of 2 to 12 MV m−1 and for PVDF has been found to be 200 MV m−1. Using the median value of the ranges, models can be created to predict the concentration which would yield the greatest amount of energy stored.

Assuming a linear relationship, the equations relating TiO2 concentration percentage to the dielectric constant and dielectric strength are as follows (and their plots are given in Figures 4.17 and 4.18, respectively)

r = 0.5600c + 9, (4.3)

52 and

~ |Ecr| = −1.9300c + 200, (4.4)

where c is the concentration of TiO2 as a percentage of the total TiO2 and PVDF.

Figure 4.17: A graph comparing the composition to the literature values for the dielectric constant for titanium dioxide-poly(vinylidene ﬂuoride) capacitors.

53 Figure 4.18: A graph comparing the composition to the literature values for the dielectric strength for titanium dioxide-poly(vinylidene ﬂuoride) capacitors.

The maximum energy stored within a capacitor can be represented as the following

1 1 U = (Ad)( |E~ |2) = X Y , (4.5) max 2 0 r cr 2 0 geometry concentration

where

Xgeometry = Ad, (4.6)

and ~ 2 Yconcentration = r|Ecr| . (4.7)

Equation 4.6 is a function which can alter the energy stored by changes to the geometry of the capacitor and Equation 4.7 is a function which can alter the energy stored by changes to the composition of the capacitor. Both of these function can be manipulated to maximize the energy stored, but of particular interest to this study is the function for concentration. Equations 4.3 and 4.4 can be plugged into Equation 4.7 to make it a function of

54 the concentration of TiO2 as a percentage of TiO2 and PVDF. This is given by

3 2 Yconcentration = 2.0860c − 398.7960c + 15452.0000c + 360000.0000. (4.8)

The plot for this function is presented in Figure 4.19. The maximum of this function occurs at one-fourth TiO2 (and three-fourths PVDF).

Figure 4.19: The plot of the product of the dielectric constant and dielectric strength squared as a function of titanium dioxide concentration for titanium dioxide-poly(vinylidene ﬂuoride) capacitors.

4.3 Titanium Dioxide-Silicon Dioxide Film and Ca-

pacitors

This section is divided into ﬁlm topography (in Section 4.3.1), and capacitor composition, structure and electrical properties of the TiO2-SiO2 capacitors (in Section 4.3.2). The same analysis process with the EDS, AFM, and SEM was done to the

ﬁlms and capacitors that were performed for the previous section. A TiO2-SiO2 ﬁlm

55 was grown to determine the surface features. The ﬁlm is primarily SiO2 with TiO2

dispersed throughout. Following this film, five TiO2-SiO2 capacitors were made, referred to as Capacitors 1 through 5, using various deposition rates to create films with various compositions. The EDS data used for calculations and SEM images used for thickness measurements can be found in Appendix C labeled Additional Results Data. The statistical methods and MATLAB code used for calculations are viewable in Appendices D and E labeled Statistical Methods and MATLAB: Results Calculations, respectively. Less detail is given for the methods than in the previous section since they are identical.

4.3.1 Surface Features of the Film

The ﬁlm was deposited onto a piece of Si coated with AuPd. A phase image was

generated by the AFM for the TiO2-SiO2 ﬁlm and is displayed in Figure 4.20.

Figure 4.20: The phase image produced by the atomic force microscope of the titanium dioxide-silicon dioxide ﬁlm.

The TiO2-SiO2 ﬁlm was originally created as a capacitor, but the AuPd bottom electrode covering the Si was not deposited thick enough to prevent the EDS from

56 detecting it. Instead, the film was used to analyze the surface features. The generated phase image shows circular objects embedded in another material. It is hypothesized that the small circular objects are TiO2, because the Ti deposition rate was about a tenth of the SiO2 deposition rate. The highest deposition rate of the Ti, according to the quartz crystal monitor, was 0.3 Angstroms per second. This was due to the deposition technique being used to evaporate the Ti for these films (i.e. resistive thermal evaporation) limits the ability to heat the material to a high enough temperature for efficient evaporation. The image demonstrates an equal distribution of the TiO2 within the SiO2.

4.3.2 Composition, Structure, and Electrical Properties of the

Capacitors

Composition

The element ratios and material percentages for the TiO2-SiO2 capacitors are presented in Tables 4.3 and 4.4, respectively.

Capacitor Titanium:Oxygen Silicon:Oxygen (Titanium + Silicon):Oxygen

1 0.0889 ± 0.0106 0.1661 ± 0.0112 0.2550 ± 0.2292 2 0.0000 ± 0.0000 0.1999 ± 0.0109 0.1999 ± 0.1201 3 0.0590 ± 0.0063 0.2345 ± 0.0083 0.2935 ± 0.1956 4 0.2271 ± 0.0211 0.1233 ± 0.0103 0.3505 ± 0.4626 5 0.1856 ± 0.0193 0.0000 ± 0.0000 0.1856 ± 0.1690

Table 4.3: The element ratios of elements in the titanium dioxide-silicon dioxide capacitors.

57 Capacitor Titanium Dioxide (%) Silicon Dioxide (%)

1 34.86 ± 6.75 65.14 ± 10.89 2 0.00 ± 0.00 100.00 ± 0.00 3 20.10 ± 3.87 79.90 ± 13.13 4 64.81 ± 9.11 35.19 ± 4.73 5 100.00 ± 0.00 0.00 ± 0.00

Table 4.4: The material ratios of compounds in the titanium dioxide-silicon dioxide capacitors.

The spatial locations of each element in Capacitor 1 are presented in elemental maps in Figures 4.21 through 4.23 for titanium, silicon, and oxygen, respectively. The maps for titanium and oxygen, silicon and oxygen, and titanium, silicon, and oxygen have been overlaid onto three SEM images in Figures 4.24 through 4.26 to help determine if the locations correspond properly.

Figure 4.21: The titanium elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-silicon dioxide Capacitor 1.

58 Figure 4.22: The silicon elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-silicon dioxide Capacitor 1.

Figure 4.23: The oxygen elemental map produced by the scanning electron microscope and energy dispersive X-ray spectrometer for the titanium dioxide-silicon dioxide Capacitor 1.

59 Figure 4.24: The titanium and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide-silicon dioxide Capacitor 1.

60 Figure 4.25: The silicon and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide-silicon dioxide Capacitor 1.

61 Figure 4.26: The titanium, silicon, and oxygen elemental maps produced by the scanning electron microscope and energy dispersive X-ray spectrometer overlaid on top of scanning electron microscope image for the titanium dioxide-silicon dioxide Capacitor 1.

The ﬁve capacitors ranged from being 0.00 % to 100.00 % TiO2. The titanium plus silicon to oxygen ratio ranges from 0.1999 ± 0.1201 to 0.3505 ± 0.4626. Although it is expected that TiO, TiO3, SiO, and SiO3 were created, a ratio of 0.5 would have been ideal. The elemental maps reveal that the Ti and Si are approximately in the same location as the O (possibly indicating no decomposition) and that there is an even distribution of the materials across the analyzed area.

Structure and Electrical Properties

The capacitance, dielectric constant, and dielectric strength of the capacitors are presented in this section. The measurements used to calculate the capacitance and the calculated capacitance of Capacitors 1 through 5 are displayed in Table 4.5.

62 Capacitor Frequency (kHz) Resistance (Ω) Phase Angle (◦) Capacitance (nF)

1 2370 ± 1 2.3 ± 0.1 17 ± 1 95.50 ± 4.22 2 2583 ± 1 2.3 ± 0.1 26 ± 1 54.93 ± 2.43 3 2287 ± 1 2.3 ± 0.1 19 ± 1 93.12 ± 4.11 4 1338 ± 1 2.3 ± 0.1 18 ± 1 150.20 ± 6.63 5 4260 ± 1 64 ± 0.1 46 ± 1 563.70 ± 8.18

Table 4.5: The frequency, resistance, and phase angle produced by the capacitance measuring instrumentation used to determine capacitance, and the calculated capacitance of titanium dioxide-silicon dioxide capacitors.

The thickness measurements from the SEM are used to calculate the dielectric constant and dielectric strength. Table 4.6 contains the average and standard deviation for each set of measurements.

Capacitor Thickness (nm)

1 161.63 ± 0.13 2 177.04 ± 0.14 3 129.33 ± 0.19 4 160.84 ± 0.12 5 98.21 ± 0.12

Table 4.6: The average thicknesses of the titanium dioxide-silicon dioxide capacitors.

The experimental dielectric constant and dielectric approximations were calculated in the same manner as the previous section. The dielectric constant ranges used here are 30 to 100 for TiO2 and 3.6 to 4.2 for SiO2. The experimental dielectric constants and dielectric approximations are presented in Table 4.7.

63 Capacitor Experimental Dielectric Constant Dielectric Constant Approximation

1 24.47 ± 2.18 36.60 ± 19.92 2 15.41 ± 1.42 3.90 ± 0.30 * 3 19.09 ± 2.94 47.68 ± 23.90 4 38.29 ± 3.42 8.74 ± 2.00 5 87.79 ± 10.79 65.00 ± 35.00 *

Table 4.7: The experimental dielectric constants and dielectric constant approximations of the titanium dioxide-silicon dioxide capacitors. *The ranges for Capacitors 2 and 5 are not approximations, but are the established dielectric constant ranges for pure silicon dioxide and pure titanium dioxide, respectively.

The breakdown voltage and dielectric strength, for the four capacitors, are presented in Table 4.8.

Capacitor Breakdown Voltage (V) Dielectric Strength (MV m−1)

1 2.91 ± 0.01 18.00 ± 1.39 2 3.25 ± 0.01 18.36 ± 1.48 3 1.43 ± 0.01 11.06 ± 1.63 4 1.27 ± 0.01 7.90 ± 0.62 5 0.49 ± 0.01 4.99 ± 0.62

Table 4.8: The breakdown voltage produced by the breakdown voltage measuring instrumentation and dielectric strength of the titanium dioxide-silicon dioxide capacitors.

Using the capacitance and breakdown voltage, the maximum energy stored and volume energy density were calculated and are displayed in Table 4.9.

64 Capacitor Energy Storage (µJ) Energy Density (J cm−3)

1 0.4044 ± 0.0127 0.03510 ± 0.0029 2 0.290 ± 0.009 0.0230 ± 0.0002 3 0.0952 ± 0.0030 0.0103 ± 0.0016 4 0.121 ± 0.004 0.0106 ± 0.0009 5 0.0677 ± 0.002 0.0097 ± 0.0012

Table 4.9: The maximum energy storage and volume energy density of the titanium dioxide-silicon dioxide capacitors.

The equations and plots relating the dielectric constant and dielectric strength were presented at the beginning of this chapter in Section 4.1. They are Equations 4.1 and 4.2, and Figures 4.1 and 4.2. Equations 4.1 and 4.2 can be plugged into Equation 4.7 to make it a function of

the concentration of TiO2 as a percentage of TiO2 and SiO2. This is given by

3 2 Yconcentration = 0.01168c − 3.1247c + 195.4430c + 1842.1000. (4.9)

The plot for this function is presented in Figure 4.27. The maximum of this function occurs at two-ﬁfths TiO2 (and three-ﬁfths SiO2).

65 Figure 4.27: The plot of the product of the dielectric constant and dielectric strength squared as a function of titanium dioxide concentration for titanium dioxide-silicon dioxide capacitors.

The capacitance of the TiO2-SiO2 capacitors ranges from 54.93 ± 2.43 nF to

563.70 ± 8.18 nF. This is 2.10 to 21.58 times greater than the TiO2-PVDF capacitor.

This can be explained by the thickness of the TiO2-PVDF capacitor being at least

4.58 times greater than the thickest TiO2-SiO2 capacitor and the capacitance being inversely related to the ﬁlm thickness. The smallest capacitance corresponds to the capacitor that has no TiO2 whereas the the highest capacitance is entirely TiO2.

The capacitance demonstrates that as the TiO2:SiO2 ratio increases, the capacitance increases (and likewise for the experimental dielectric constant). The experimental dielectric constant ranges from 15.41 ± 1.42 to 87.79 ± 10.79. This is consistent with the dielectric constant of SiO2 being 3.6 to 4.2 and TiO2 being 30 to 100. The

66 experimental dielectric constants fail to be consistent with the dielectric constant approximations (using the Maxwell-Garnett approximation) for Capacitors 2, 3, and 4. A possible explanation for this is that the EDS data is incorrect. The EDS data

states that there is no TiO2 in Capacitor 2; however, an adhesion layer of Ti was used so there is at least a 10 nm thick layer. In addition, the material should have ideally

deposited as TiO2 and SiO2, but the less than favorable ratios indicate the presence

of TiO and SiO (and probably small amounts of TiO3 and SiO3) which have diﬀerent electrical properties. The dielectric strength of the capacitors range from 4.99 ± 0.62 MV m−1 to 18.36 ± 1.48 MV m−1. This is not consistent with the literature values

−1 for the dielectric strength of TiO2 as being 6 MV m and of SiO2 as being 25 to 40

−1 MV m . Even though the TiO2-PVDF capacitor was only 5.90 ± 0.09 % PVDF, the dielectric strength is 24.15 ± 0.02 MV m−1 which demonstrates the potential for polymer-ceramic capacitors for their ability to have high dielectric strength. The

−3 energy density of the TiO2-SiO2 capacitors ranged from 0.0097 ± 0.0012 J cm to

−3 0.03510 ± 0.0029 J cm whereas the TiO2-PVDF capacitor had an energy density

−3 of 0.0868 ± 0.0079 J cm . Therefore, TiO2-PVDF capacitor had an energy density that was 2.18 to 8.95 times higher than the set of TiO2-SiO2 capacitors.

67 Chapter 5

Conclusions and Future Work

The results demonstrate that it is possible to fabricate ceramic-polymer dielectric materials using independent evaporation techniques via co-deposition with a resistive thermal evaporator and electron gun which allows for the control of the ratio of materials. This was an issue with the previous studies which attempted to control

TiO2 composition using only a resistive thermal evaporator. This approach allows for the control of the dielectric constant and dielectric strength of composite ﬁlms. The fabricated ceramic-polymer capacitor consisted of 94.10 ± 0.09 % titanium dioxide, and had a breakdown voltage of 19.61 ± 0.01 V, a dielectric strength of 24.15 ± 0.02 MV m−1, a capacitance of 26.123 ± 3.347 nF, a dielectric constant of 33.62 ± 4.45, a thickness of 812.0 ± 0.3 nm, maximum energy storage of 5.02 ± 0.46 µJ, and volume energy density of 0.0868 ± 0.0079 J cm−3. In comparison, the ﬁve titanium dioxide and silicon dioxide capacitors had a titanium dioxide composition ranging from 0.00 % to 100.00 %, and had a breakdown voltage ranging from 0.49 ± 0.01 V to 3.25 ± 0.01 V, a dielectric strength ranging from 4.99 ± 0.62 MV m−1 to 18.36 ± 1.48 MV m−1, a capacitance ranging from 54.93 ± 2.43 nF to 563.70 ± 8.18 nF, a dielectric constant ranging from 15.41 ± 1.42 to 87.79 ± 10.79, a thickness ranging from 98.21 ± 0.12 nm to 177.04 ± 0.14 nm, a maximum energy storage ranging from 0.0677 ±

68 0.002 µJ to 0.4044 ± 0.0127 µJ, and volume energy density ranging from 0.0097 ± 0.0012 J cm−3 to 0.03510 ± 0.0029 J cm−3. The results indicate that better energy

storage is achieved with lower amounts of TiO2 composition when compared to other studies involving the fabrication of TiO2-PVDF capacitors. When comparing the the TiO2-PVDF capacitors to the TiO2-SiO2 capacitors, the capacitors with PVDF exhibited superior energy storage and energy density properties. Two avenues of future research would be to study the eﬀects of annealing on the electrical properties of dielectric ﬁlms and to systematically vary the ratios within the

ceramic-polymer dielectric ﬁlms to optimize energy density. The TiO2-SiO2 capacitors in this study were annealed at 500 ◦C. There are studies which exist that suggest annealing temperature impacts the capacitance due to structural changes, but this was not explored using the materials in this study. For optimizing the energy density, the same method utilized for predicting the concentration which creates the maximum energy stored for the TiO2-SiO2 capacitors could be used.

69 Appendix A

Designing, Building, and Automating a High-Vacuum Physical Vapor Deposition System

The construction of the deposition system included selecting an appropriate pressure gauge and vacuum pumps, designing the physical layout, implementing the resistive thermal evaporator and electron gun, designing and building the water cooling system, designing and building a substrate platform, creating a high-vacuum, and automating the system with LabVIEW. The design of the system was a two-part chamber (top and bottom) where the top portion was meant to be used for the Varian e-Gun 980-0001 model electron gun and the bottom for the resistive thermal evaporator. The greatest distance that the material needed to be transported was two-thirds of a meter. Therefore, a Pfeiﬀer Vackuumtechnik Wetzlar GMBH model turbomolecular pump was chosen to create a high-vacuum to provide the appropriate free mean path and an Edwards Two Stage 8 model oil-rotary vacuum pump was chosen as its backing pump. The substrate was attached to the top of the chamber. The sample platform was designed

70 in SolidWorks and the design was given to a machinist to fabricate out of aluminium. A turbomolecular pump was attached horizontally to the bottom chamber of the system which was attached to the roughing pump. The pressure gauge was attached to the bottom portion too. A Televac CC-10 Wide Range Gauge was initially used to measure the pressure; however, it was determined to be contaminated when compared to a working pressure gauge on the Torr International, Inc. deposition system. The gauge was then replaced by a KJLC 354 Series Ion Gauge. The top and bottom chambers had doors and windows (one of each for each top and bottom parts). A ﬂange was attached to the back of the top portion of the chamber for electrical feed throughs and plumbing for water cooling of the electron gun. A ﬂange was also used for a quartz crystal monitor placed next to the electron gun. A second quartz crystal monitor was placed on the ceiling of the top part of the chamber. Both quartz crystal monitors required plumbing for water cooling. The chamber was grounded in three locations for safety when using the high voltage electron gun. The electron gun was interlocked with the pressure gauge to ensure an adequate pressure before the gun could be turned on. When the system was initially tested, it was determined that the resistive thermal evaporator was too far away from the substrate. The quartz crystal monitor meant for the polymer was unusable since the z-factor for the material was unknown and the quartz crystal monitor on the ceiling of the system had water cooling pipes that were clogged. The quartz crystal monitors were removed from the system and the resistive thermal evaporator was moved to the top part of the chamber. The quartz crystal monitor on the ceiling of the chamber was replaced with a shield to cover the substrate until the material sources were evaporating at the desired rate. The second design moved the resistive thermal evaporator to the top chamber, next to the electron gun so that they were the same distance away from the substrate. The pumps were automated using LabVIEW and are displayed in Figures A.1 to A.3.

71 The electron gun worked initially. However, during one of the depositions, the emission current meter on the front panel of the Varian e-Gun Control Unit 922- 0020 model power supply dropped to 0 mA indicating that no electrons were being accelerated from the filament. The filament was being heated, as it was glowing, so it was receiving power. After the circuit was checked outside of the power supply, it was hypothesized that the problem must be occurring inside the power supply. The electron gun uses two voltages, one to heat the filament and the other to accelerate electrons, due to safety concerns with handling the 10 kV capacity capacitor, a second power supply was ordered. This power supply came with the 10 kV capacitor removed (and not included). It was at this point that this deposition system was set aside for the Torr International, Inc. deposition system.

Figure A.1: The LabVIEW front panel for automating the pumps.

72 Figure A.2: The LabVIEW block diagram 1 for automating the pumps.

73 Figure A.3: The LabVIEW block diagram 2 for automating the pumps.

74 Appendix B

LabVIEW: Breakdown Voltage Measuring Circuit

The LabVIEW program for controlling the programmable power supply is presented in this appendix. The front panel, shown in Figure B.1, contains a VISA resource selector, current and voltage indicators, and a display for an I-V plot. The block diagrams for the main VI and sub-VIs are shown in Figures B.2 to B.13.

Figure B.1: The LabVIEW front panel for the breakdown voltage measuring circuit.

75 Figure B.2: The LabVIEW block diagram for the breakdown voltage measuring circuit.

76 Figure B.3: The LabVIEW sub-VI block diagram 1 for the breakdown voltage measuring circuit.

Figure B.4: The LabVIEW sub-VI diagram 2 for the breakdown voltage measuring circuit.

Figure B.5: The LabVIEW sub-VI block diagram 3 for the breakdown voltage measuring circuit.

Figure B.6: The LabVIEW sub-VI block diagram 4 for the breakdown voltage measuring circuit.

77 Figure B.7: The LabVIEW sub-VI block diagram 5 for the breakdown voltage measuring circuit.

Figure B.8: The LabVIEW sub-VI block diagram 6 for the breakdown voltage measuring circuit.

Figure B.9: The LabVIEW sub-VI block diagram 7 for the breakdown voltage measuring circuit.

78 Figure B.10: The LabVIEW sub-VI block diagram 8 for the breakdown voltage measuring circuit.

Figure B.11: The LabVIEW sub-VI block diagram 9 for the breakdown voltage measuring circuit.

Figure B.12: The LabVIEW sub-VI block diagram 10 for the breakdown voltage measuring circuit.

Figure B.13: The LabVIEW sub-VI block diagram 11 for the breakdown voltage measuring circuit.

79 Appendix C

Additional Results Data

C.1 Titanium Dioxide-Poly(vinylidene Fluoride) Films

The net counts (from the EDS analysis), weight percentages, and atom percentages of the TiO2-PVDF and PVDF ﬁlms are presented in Tables C.1 through C.3.

80 Film Carbon Fluorine Titanium Oxygen

1 160 ± 26 651 ± 86 4694 ± 193 5674 ± 138 2 498 ± 49 2242 ± 159 1342 ± 152 2205 ± 138 3 464 ± 30 1806 ± 135 1966 ± 175 4270 ± 93 4 494 ± 37 2586 ± 136 166 ± 98 774 ± 70 5 140 ± 16 802 ± 101 0 ± 0 473 ± 50 6 536 ± 47 711 ± 50 6770 ± 224 6996 ± 102 7 564 ± 57 982 ± 147 4084 ± 211 4513 ± 149 8 3188 ± 73 6548 ± 152 897 ± 65 1951 ± 89 9 3082 ± 67 6351 ± 150 263 ± 47 678 ± 79 10 2082 ± 58 6265 ± 147 139 ± 44 627 ± 75 11 232 ± 17 573 ± 37 0 ± 0 0 ± 0 12 1417 ± 33 4161 ± 59 0 ± 0 0 ± 0 13 1700 ± 35 6096 ± 67 0 ± 0 0 ± 0 14 308 ± 19 792 ± 39 0 ± 0 0 ± 0 15 1610 ± 33 5692 ± 66 0 ± 0 0 ± 0

Table C.1: The net counts produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-poly(vinylidene fluoride) and poly(vinylidene fluoride) films.

81 Film Carbon (%) Fluorine (%) Titanium (%) Oxygen (%)

1 1.05 ± 0.17 1.74 ± 0.23 22.91 ± 0.69 13.61 ± 0.33 2 4.13 ± 0.41 5.03 ± 0.36 7.37 ± 0.51 4.90 ± 0.31 3 3.35 ± 0.22 3.91 ± 0.29 8.91 ± 0.52 8.77 ± 0.19 4 4.45 ± 0.33 5.23 ± 0.28 1.10 ± 0.22 1.62 ± 0.15 5 1.44 ± 0.16 1.68 ± 0.21 0.00 ± 0.00 1.04 ± 0.11 6 2.44 ± 0.21 3.71 ± 0.26 52.84 ± 1.10 28.74 ± 0.42 7 4.29 ± 0.43 4.00 ± 0.60 31.70 ± 0.91 16.16 ± 0.53 8 22.06 ± 0.51 19.82 ± 0.46 9.56 ± 0.39 5.79 ± 0.26 9 23.81 ± 0.52 17.17 ± 0.41 2.72 ± 0.27 1.90 ± 0.22 10 18.11 ± 0.50 16.82 ± 0.39 1.47 ± 0.24 1.73 ± 0.21 11 26.91 ± 1.97 9.26 ± 0.60 0.00± 0.00 0.00 ± 0.00 12 43.35 ± 1.01 36.98 ± 0.52 0.00± 0.00 0.00 ± 0.00 13 38.74 ± 0.80 60.11 ± 0.66 0.00± 0.00 0.00 ± 0.00 14 30.31 ± 1.87 11.79 ± 0.58 0.00± 0.00 0.00 ± 0.00 15 40.40 ± 0.83 51.66 ± 0.60 0.00± 0.00 0.00 ± 0.00

Table C.2: The weight percentages produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-poly(vinylidene fluoride) and poly(vinylidene fluoride) films.

82 Film Carbon (%) Fluorine (%) Titanium (%) Oxygen (%)

1 2.60 ± 0.42 2.73 ± 0.36 14.24 ± 0.43 25.32 ± 0.62 2 9.63 ± 0.95 7.40 ± 0.53 4.30 ± 0.30 8.58 ± 0.54 3 7.72 ± 0.50 5.70 ± 0.43 5.15 ± 0.30 15.18 ± 0.33 4 10.24 ± 0.77 7.62 ± 0.40 0.64 ± 0.13 2.80 ± 0.25 5 3.50 ± 0.40 2.57 ± 0.32 0.00 ± 0.00 2.57 ± 0.32 6 5.33 ± 0.47 5.13 ± 0.36 28.95 ± 0.60 47.14 ± 0.69 7 9.84 ± 0.99 27.82 ± 0.92 18.23 ± 0.52 27.82 ± 0.92 8 38.54 ± 0.88 21.89 ± 0.51 4.19 ± 0.17 7.60 ± 0.35 9 41.84 ± 0.91 19.07 ± 0.45 1.20 ± 0.12 2.51 ± 0.29 10 33.96 ± 0.95 19.93 ± 0.47 0.69 ± 0.11 2.44 ± 0.29 11 44.81 ± 3.28 9.75 ± 0.63 0.00± 0.00 0.00 ± 0.00 12 57.69 ± 1.34 31.12 ± 0.44 0.00± 0.00 0.00 ± 0.00 13 50.16 ± 1.03 49.20 ± 0.54 0.00± 0.00 0.00 ± 0.00 14 48.48 ± 2.99 11.93 ± 0.59 0.00± 0.00 0.00 ± 0.00 15 52.84 ± 1.08 42.72 ± 0.50 0.00± 0.00 0.00 ± 0.00

Table C.3: The atom percentages produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-poly(vinylidene fluoride) and poly(vinylidene fluoride) films.

C.2 Titanium Dioxide-Poly(vinylidene Fluoride) Ca-

pacitor

The net counts, weight percentages, and atom percentages for the TiO2-PVDF capacitor are presented in Table C.4.

83 Element Net Counts Weight Percentage (%) Atom Percentage (%)

Carbon 33 ± 22 0.87 ± 0.58 1.81 ± 1.21 Fluorine 37 ± 21 1.31 ± 0.74 1.73 ± 0.98 Titanium 12445 ± 230 53.88 ± 0.52 28.22 ± 0.27 Oxygen 1545 ± 50 38.88 ± 1.26 60.97 ± 1.97

Table C.4: The net counts, weight percentages, and atom percentages produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-poly(vinylidene ﬂuoride) capacitor.

C.3 Titanium Dioxide-Silicon Dioxide Capacitors

The net counts, weight percentages, and atom percentages for the TiO2-SiO2 capacitors are presented in Tables C.5 through C.7.

Capacitor Titanium Silicon Oxygen

1 404 ± 73 1159 ± 70 1613 ± 49 2 0 ± 0 1534 ± 73 1827 ± 48 3 365 ± 70 2442 ± 74 2879 ± 53 4 890 ± 98 811 ± 62 1435 ± 47 5 595 ± 194 0 ± 0 1449 ± 40

Table C.5: The net counts produced by the energy dispersive X-ray spectrometer of elements in titanium dioxide-silicon dioxide capacitors.

84 Capacitor Titanium (%) Silicon (%) Oxygen (%)

1 5.57 ± 0.64 6.11 ± 0.37 20.94 ± 0.64 2 0.00 ± 0.00 8.19 ± 0.39 23.36 ± 0.61 3 6.46 ± 0.67 15.06 ± 0.46 36.58 ± 0.67 4 14.31 ± 1.24 4.56 ± 0.35 21.04 ± 0.69 5 12.81 ± 1.28 0.00 ± 0.00 23.05 ± 0.64

Table C.6: The weight percentages produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide capacitors.

Capacitor Titanium (%) Silicon (%) Oxygen (%)

1 5.57 ± 0.64 10.41 ± 0.63 62.66 ± 1.90 2 0.00 ± 0.00 12.52 ± 0.60 62.63 ± 1.65 3 4.18 ± 0.44 16.62 ± 0.50 70.87 ± 1.30 4 13.70 ± 1.19 7.44 ± 0.57 60.32 ± 1.98 5 9.06 ± 0.91 0.00 ± 0.00 48.81 ± 1.35

Table C.7: The atom percentages produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide capacitors.

The spectrums generated by the EDS for the TiO2-SiO2 capacitors are displayed in Figures C.1 through C.4.

85 Figure C.1: The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 1.

86 Figure C.2: The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 2.

87 Figure C.3: The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 3.

88 Figure C.4: The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 4.

89 Figure C.5: The spectrum produced by the energy dispersive X-ray spectrometer of elements in the titanium dioxide-silicon dioxide Capacitor 5.

The thickness measurements using the SEM images are shown in Figures C.6 through C.9.

90 Figure C.6: The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 1 with thickness measurements.

Figure C.7: The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 2 with thickness measurements.

91 Figure C.8: The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 4 with thickness measurements.

Figure C.9: The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 4 with thickness measurements.

92 Figure C.10: The cross-sectional image produced by the scanning electron microscope of the titanium dioxide-silicon dioxide Capacitor 5 with thickness measurements.

93 Appendix D

Statistical Methods

To propagate the error for element ratios, material percentages, dielectric strength, experimental dielectric constants, maximum energy storage, and volume energy density, the uncertainties were added in quadrature [25]. The general form is given by Equations D.1 and D.2. (x)...(z) q = (D.1) (u)...(w)

r δq δx δz δu δw = ( )2 + ... + ( )2 + ( )2 + ... + ( )2 (D.2) q x z u w

The thickness error was calculated using the standard deviation given by

v u N u 1 X σ = t |A − µ|2 (D.3) N − 1 i i=1

where µ is given by

N 1 X µ = A (D.4) N i i=1 The error in the capacitance calculation was calculated using the error propagation for general functions where the general form is given by Equations D.5 and D.6.

94 f = f(x, ..., z) (D.5)

r ∂f ∂f δf = (δx )2 + ... + (δz )2 (D.6) ∂x ∂z

For the trigonometric function used in the capacitance equation, the error is expressed by

∂ δtan(φ) = δφ tan(φ) (D.7) ∂φ

95 Appendix E

MATLAB: Results Calculations

The following function was used to calculate the capacitances.

1 %%%Function to calculate capacitance

2 %f= frequency(Hz)

3 %phi= phase angle(degrees)

4 %R= resistance(Ohms)

6 function C = cap(f,phi,R)

8 C = (tan(phi.*(pi/180))*(2*pi.*f.*R)).^(−1)

10 end

The following function was used to calculate the dielectric constant approximations.

1 %%%Function to calculate the dielectric constant approximation

2 %del= fraction of inclusion material to total material

3 %ep1= host material dielectric constant

4 %ep2= inclusion material dielectric constant

96 5

6 function dielectricTH = epEFF(del,ep1,ep2)

8 epEFFnum = (2*(1−del)*ep1) + ((1+2*del)*ep2);

9 epEFFden = ((2 + del)*ep1) + ((1−del)*ep2);

11 epEFF = (ep1*epEFFnum)/epEFFden;

13 end

The following script was used to calculate the element ratios to determine the proper deposition current for the PVDF.

1 %%PVDF/TiO2 composite film element ratios uncertainties

3 %atom percentages for individual films(CF TiO)

4 f1 = [2.60 2.73 14.24 25.32];

5 f2 = [9.63 7.40 4.30 8.58];

6 f3 = [7.72 5.70 5.15 15.18];

7 f4 = [10.24 7.62 0.64 2.80];

8 f5 = [3.50 2.57 0 2.57];

9 f6 = [5.33 5.13 28.95 47.14];

10 f7 = [9.84 27.82 18.23 27.82];

11 f8 = [38.54 21.89 4.19 7.60];

12 f9 = [41.84 19.07 1.20 2.51];

13 f10 = [33.96 19.93 0.69 2.44];

15 %atom percentages error for individual films(CF TiO)

16 df1 = [0.42 0.36 0.43 0.62];

17 df2 = [0.95 0.53 0.30 0.54];

18 df3 = [0.50 0.43 0.30 0.33];

19 df4 = [0.77 0.40 0.13 0.25];

97 20 df5 = [0.40 0.32 0.00 0.32];

21 df6 = [0.47 0.36 0.60 0.69];

22 df7 = [0.99 0.92 0.52 0.92];

23 df8 = [0.88 0.51 0.17 0.35];

24 df9 = [0.91 0.45 0.12 0.29];

25 df10 = [0.95 0.47 0.11 0.29];

28 %atom percentages array containing all films

29 f = [f1; f2; f3; f4; f5; f6; f7; f8; f9; f10];

31 %atom percentages error array containing all films

32 df = [df1; df2; df3; df4; df5; df6; df7; df8; df9; df10];

34 %atom ratios array containing all films(C:F Ti:O)

35 for a = 1:10

37 b = 1;

38 c = 2;

40 for d = 1:2

42 rf(a,d) = f(a,b)/f(a,c);

44 b = 3;

45 c = 4;

47 end

49 end

51 %atom ratios error array containing all films(C:F Ti:O)

52 for e = 1:10

98 53

54 j = 1;

55 g = 2;

57 for h = 1:2

59 drf(e,h) = rf(e,h)*sqrt(((df(e,j)/f(e,j))^2) + ... ((df(e,g)/f(e,g))^2));

61 j = 3;

62 g = 4;

64 end

66 end

69 %%PVDF film element ratios and uncertainties

71 %atom percentages for individual films(CF)

72 f11 = [44.81 9.75];

73 f12 = [57.69 31.12];

74 f13 = [50.16 49.20];

75 f14 = [48.48 11.93];

76 f15 = [52.84 42.72];

79 %atom percentages error for individual films(CF TiO)

80 df11 = [3.28 0.63];

81 df12 = [1.34 0.44];

82 df13 = [1.03 0.54];

83 df14 = [2.99 0.59];

84 df15 = [1.08 0.50];

99 85

86 %atom percentages array containing all films

87 f = [f11; f12; f13; f14; f15];

89 %atom percentages error array containing all films

90 df = [df11; df12; df13; df14; df15];

92 %atom ratios array containing all films(C:F)

93 for a = 1:5

95 rf(a,1) = f(a,1)/f(a,2);

97 end

100 %atom ratios error array containing all films(C:F)

101 for e = 1:5

102

103

104 drf(e,1) = rf(e,1)*sqrt(((df(e,1)/f(e,1))^2) + ... ((df(e,2)/f(e,2))^2));

105

106

107 end

The following script was used to calculate all values (except capacitance) for the

TiO2-PVDF capacitor.

1 %%%Element ratio and error

3 sigmaC = 1.21;

4 C = 1.81;

100 5 sigmaF = 0.98;

6 F = 1.73;

8 CF = C/F;

10 sigmaCF = CF*sqrt((((sigmaC)/(C))^(2)) + (((sigmaF)/(F))^(2)));

12 TO = 28.22/60.97;

13 sigmaT = 0.27;

14 T = 28.22;

15 sigmaO = 1.97;

16 O = 60.97;

18 sigmaTO = TO*sqrt((((sigmaT)/(T))^(2)) + (((sigmaO)/(O))^(2)));

20 %%%Material percentage and error

22 sigmaC = 1.21;

23 C = 1.81;

24 sigmaF = 0.98;

25 F = 1.73;

27 sigmaT = 0.27;

28 T = 28.22;

29 sigmaO = 1.97;

30 O = 60.97;

32 CFmed = (abs(C−F)/2) + F;

33 sigmaCFmed = sqrt(.5*((sigmaC^2)+(sigmaF^2)) + (sigmaF^2));

35 PVDFmatpercentage = (CFmed*100)/(CFmed + T);

36 sigmaPVDFmatpercentage = ...

sqrt(100*((((CFmed/((CFmed+T)^2))*sigmaCFmed)^2)) + ...

101 (((CFmed/((CFmed+T)^2))*sigmaT)^2))

37 TiO2matpercentage = (T*100)/(CFmed + T);

38 sigmaTiO2matpercentage = ...

sqrt(100*((((T/((CFmed+T)^2))*sigmaT)^2)) + ... (((T/((CFmed+T)^2))*sigmaT)^2));

40 %%%Average thickness and standard deviation

42 th = [809.4 873.2 816.2 808.7 801.7 808.7 766.1].*10^(−9);

44 thAVG = mean(th);

46 thS = std(th);

49 %%%Dielectric strength and error

51 Vb = 19.61;

52 sigmaVb = 0.01;

54 thAVG = 8.12e−7;

55 sigmathAVG = 0.3e−9;

57 DS = Vb/thAVG;

58 sigmaDS = DS*sqrt((((sigmaVb)/(Vb))^2) + (((sigmathAVG)/(thAVG))^2));

61 %%%Capacitance error

63 C = 78.334e−9;

64 f = 1710;

65 sigmaf = 0.1;

66 R = 529;

102 67 sigmaR = 0.1;

68 PHI = (24/180)*pi;

69 sigmaPHI = pi/180;

71 sigmaC = C*sqrt(((2*pi)^−1)*((sigmaPHI/(cos(PHI)^2))^2) + ... (((sigmaR)/2.3)^2) + ((sigmaf/f)^2));

73 %%%Dielectric constant and error

75 dia = 9.525e−3;

76 r = dia/2;

77 A = pi*(r^2);

78 sigmaA = [1.87518793416258e−11];

79 d = 8.12e−7;

80 sigmad = 0.3e−9;

81 C = 26.123e−9;

82 sigmaC = 3.458e−9;

83 epsilonNAUGHT = 8.854187812813e−12;

85 dc = (C*d)/(epsilonNAUGHT*A);

88 sigmadc = dc*sqrt(((sigmad/d)^2) + ((sigmaC/C)^2) + ((sigmaA/A)^2));

91 %%%Energy stored, volume energy density, and error

93 C = 26.123e−9;

94 sigmaC = 3.347e−9;

96 BV = 19.61;

97 sigmaBV = 0.01;

103 99

100 Emax = .5*C*((BV)^2);

101 sigmaEmax = Emax*sqrt(.5*(((sigmaC/C)^2) + 2*((sigmaBV/BV^2))));

102

103

104 A = [7.12557392480856e−05];

105 sigmaA = [1.87518793416258e−11];

106

107 d = 812e−9;

108 sigmad = 0.3e−9;

109

110 V = A*d;

111 sigmaV = V*sqrt(((sigmaA/A)^2) + ((sigmad/d)^2));

112

113 Eden = Emax/V;

114 sigmaEden = Eden*sqrt(((sigmaEmax/Emax)^2) + ((sigmaV/V)^2));

115

116 Eden = Eden*(100^−3);

117 sigmaEden = sigmaEden*(100^−3);

The following script was used to calculate all values (except capacitance) and

generate all plots for the TiO2-SiO2 capacitors.

1 %%%Atom Percentages and errors

3 atomperTi = [5.57 0 4.18 13.70 9.06];

4 sigatomperTi = [0.64 0 0.44 1.19 0.91];

5 atomperSi = [10.41 12.52 16.62 7.44 0];

6 sigatomperSi = [0.63 0.60 0.50 0.57 0];

7 atomperO = [62.66 62.63 70.87 60.32 48.81];

8 sigatomperO = [1.90 1.65 1.30 1.98 1.35];

104 10 %%%Average thickness and standard deviation

12 th1 = [164.5 164.5 149.1 149.4 164.6 154.2 185.1].*10^−9;

13 th2 = [174.8 185.1 185.1 200.7 164.5 169.7 159.4].*10^−9;

14 th3 = [118.3 118.3 113.2 123.5 128.6 133.7 169.7].*10^−9;

15 th4 = [154.2 159.4 159.4 174.8 174.8 138.8 164.5].*10^−9;

16 th5 = [100.9 107.2 88.47 113.5 107.2 88.25 81.94].*10^−9;

18 thAVG1 = mean(th1);

19 S1 = std(th1);

21 thAVG2 = mean(th2);

22 S2 = std(th2);

24 thAVG3 = mean(th3);

25 S3 = std(th3);

27 thAVG4 = mean(th4);

28 S4 = std(th4);

30 thAVG5 = mean(th5);

31 S5 = std(th5);

33 d = [thAVG1 thAVG2 thAVG3 thAVG4 thAVG5];

34 sigmad = [S1 S2 S3 S4 S5];

36 %%%Breakdown voltages and errors

38 BV = [2.91 3.25 1.43 1.27 .49];

39 sigBV = [0.01 0.01 0.01 0.01 0.01];

41 %%%Phase angles, resistances, and frequencies from capacitance ... measuring

105 42 %%%instrumentation and errors

44 sigPHI = 1*pi/180;

45 PHI = [17 26 19 18 46]*pi/180;

47 sigR = 0.1;

48 R = [2.3 2.3 2.3 2.3 64];

50 sigf = 1e3;

51 f = [2370 2583 2287 1338 4260]*10^3;

53 %%%Calculated capacitance

55 C = [95.50 54.93 93.12 150.20 564]*10^−9;

57 %%%Electrode area and error

59 A = pi*(((9.525e−3)/2)^2);

60 sigA = A*sqrt(pi*2*(0.001/9525)^2);

63 for x = 1:5

65 %%%Element ratio and error

67 elratTiO(x) = atomperTi(x)/atomperO(x);

68 elratSiO(x) = atomperSi(x)/atomperO(x);

70 sigelratTiO(x) = ...

elratTiO(x)*sqrt(((sigatomperTi(x)/atomperTi(x))^2) + ... ((sigatomperO(x)/atomperO(x))^2));

71 sigelratSiO(x) = ...

elratSiO(x)*sqrt(((sigatomperSi(x)/atomperSi(x))^2) + ...

106 ((sigatomperO(x)/atomperO(x))^2));

73 atomperTiSi(x) = atomperTi(x) + atomperSi(x);

74 sigatomperTiSi(x) = atomperTiSi(x)*sqrt(((sigatomperTi(x))^2) ... + ((sigatomperSi(x))^2));

76 elratTiSiO(x) = atomperTiSi(x)/atomperO(x);

77 sigmaelratTiSiO(x) = ...

elratTiSiO(x)*sqrt(((sigatomperTiSi(x)/atomperTiSi(x))^2) ... + ((sigatomperO(x)/atomperO(x))^2));

79 %%%Material percentage and error

81 totTiSi(x) = atomperTi(x) + atomperSi(x);

82 sigtotTiSi(x) = ...

totTiSi(x)*sqrt(((sigatomperTi(x))/(atomperTi(x))^2) + ... (((sigatomperSi(x))/(atomperSi(x)))^2));

84 perTi(x) = atomperTi(x)/totTiSi(x);

85 sigperTi(x) = ...

perTi(x)*sqrt(((sigatomperTi(x)/atomperTi(x))^2) + ... ((sigtotTiSi(x)/totTiSi(x))^2));

87 perSi(x) = atomperSi(x)/totTiSi(x);

88 sigmaperSi(x) = ...

perSi(x)*sqrt(((sigatomperSi(x)/atomperSi(x))^2) + ... ((sigtotTiSi(x)/totTiSi(x))^2));

90 %%%Dielectric strength and error

92 Ecr(x) = BV(x)/d(x);

93 sigEcr(x) = Ecr(x)*sqrt(((sigBV(x)/BV(x))^2) + ... ((sigmad(x)/d(x))^2));

107 94

95 %%%Capacitance error

97 sigC(x) = ...

C(x)*sqrt(((2*pi)^−1)*((sigPHI/((cos(PHI(x)))^2))^2) + ... (((sigR)/R(x))^2) + ((sigf/f(x))^2));

99 %%%Dielectric constant and error

100

101 dc(x) = (d(x)*C(x))/((8.85418782e−12)*A);

102 sigdc(x) = dc(x)*sqrt(((sigmad(x)/d(x))^2) + ... ((sigC(x)/C(x))^2) + ((sigA/A)^2));

103

104 %%%Energy stored, volume, and volume energy density, and error

105

106 Emax(x) = .5*C(x)*((BV(x))^2);

107 sigEmax(x) = Emax(x)*sqrt(.5*(((sigC(x)/C(x))^2) + ... 2*((sigBV(x)/BV(x))^2)));

108

109 V(x) = A*d(x);

110 sigV(x) = V(x)*sqrt(((sigA/A)^2) + ((sigmad(x)/d(x))^2));

111

112 Eden(x) = Emax(x)/V(x);

113 sigEden(x) = Eden(x)*sqrt(((sigEmax(x)/Emax(x))^2) + ... ((sigV(x)/V(x))^2));

114

115 end

116

117 %%%Energy density unit conversion

118 Eden = Eden*(100^−3);

119 sigEden = sigEden*(100^−3);

120

121

108 122 %%%Variables for plotting andR −squared calculations

123

124 perTi = perTi.*100;

125 yneg = [6.75 0.00 3.87 4.73 0.00];

126 ypos = yneg;

127

128 xneg = sigdc;

129 xpos = sigdc;

130 R = corrcoef(dc, perTi);

131 Rsq = R(1,2).^2;

132

133 Ecr = Ecr./1e6;

134 xneg2 = sigEcr./1e6;

135 xpos2 = sigEcr./1e6;

136 R2 = corrcoef(Ecr, perTi);

137 Rsq2 = R2(1,2).^2;

138

139 %%%Composition vs. dielectric strength and dielectric constant plots

140

141 figure(1)

142 coefficients = polyfit(dc, perTi, 1);

143 xFit = linspace(1.52, 82, 1000);

144 yFit = polyval(coefficients , xFit);

145 hold on;

146 plot(xFit, yFit,'k −');

147 grid on;

148 errorbar(dc, perTi,yneg,ypos,xneg,xpos,'.')

149 xlabel('Dielectric Constant');

150 ylabel('Titanium Dioxide (%)')

151 ylim([−5 105])

152 title('Composition and Dielectric Constant of Capacitors')

153 hold off

154

109 155 figure(2)

156 coefficients2 = polyfit(Ecr, perTi, 1);

157 xFit2 = linspace(1.9, 20, 1000);

158 yFit2 = polyval(coefficients2 , xFit2);

159 hold on;

160 plot(xFit2, yFit2,'k −');

161 grid on;

162 errorbar(Ecr, perTi,yneg,ypos,xneg2,xpos2,'.')

163 xlabel('Dielectric Strength(MVm^{ −1})');

164 ylabel('Titanium Dioxide (%)')

165 ylim([−5 105])

166 title('Composition and Dielectric Strength of Capacitors')

167 hold off

168

169 %%%Titanium dioxide composition to produce maximum energy storage

170 x = 0:.01:100;

171 Uplot = (0.0265717.*x.^3)−(5.81881.*x.^2)+(313.019.*x)+609.218;

172

173 [i,j] = max(Uplot);

174 xMAX = (j−1)/100;

175

176 %%%Yconcentration vs. titanium dioxide plot

177 figure(3)

178 plot(x,Uplot)

179 xlabel('c (%)')

180 ylabel('Y_{concentration}')

181 title('Y_{concentration} asa function of titanium dioxide ... concentration')

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113