Functionalization of transparent conducting oxides. Zinc ferrite spinel in ZnO

Functionalization of transparent conducting oxides Zinc ferrite spinel in ZnO

Kristian Haug

Master’s Thesis, Spring 2019

Functionalization of transparent conducting oxides

Zinc ferrite spinel in ZnO

Kristian Haug

Thesis submitted for the degree of

Master in Material Science and Nanotechology 60 credits

Department of Physics

Faculty of mathematics and natural sciences

UNIVERSITY OF OSLO

c 2019 Kristian Haug

Functionalization of transparent conducting oxides http://www.duo.uio.no/

Acknowledgements

This thesis is submitted as a part of the masters degree in Material Science and Nanotechnology by the Department of Physics at the University of Oslo. The work has been performed in association with the Structure Physics and the Light and Electricity from Novel Semiconductors (LENS) group.

Firstly i would like to thank my four supervisors, Øystein Prytz, Ole Bjørn Karlsen, Lasse Vines and Calliope Bazioti for invaluable help and guidance throughout these two years. I had never a question unanswered or not discussed in a serious way.

Furthermore i would like to give a big thanks to Phuong D. Nguyen for the help with the electron microscope, the eager for excellent results and the interesting discussions following.

In addition I would like to thank Thomas Aarholt for the programming and simulation help and Tarjei Bondevik for the help with DFT calculations. You have both been helpful in multiple ways with discussions and motivation which i am very grateful for. Thanks to Augustinas Galeckas for the help with diffuse reflectance spectroscopy.

I would also like to thank the Structure Physics group for a very good scientific and social environment, the Electrochemistry group for the help in the lab and the Light and Electricity from Novel Semiconductors group for optical measurements.

A special thanks to two of my best friends, Sindre R. Bilden and Monika Løberg for the never ending support and understanding. You always kept my spirit up and a smile on my face.

In addition I would like to thank my family for giving me the ability to ask scientific questions and the possibility to pursue my interest for science. You built the foundation for me to follow my dreams and I am not able to express my gratitude or how much this means to me. Thank you!

I have to admit that I probably got spoiled by all the people willing to help me pursue my interests for this research and I would like to thank you all for making this my two best years as a student. It has been hard work, but also very rewarding.

Abstract

With ever increasing energy consumption world wide, accompanied with an increase in temperature, more and cleaner energy is needed. Solar cells have been the topic of research for decades and have steadily improved. The silicon solar cell is close to reaching its maximal theoretical potential, at least in the lab, and hence the need for new technology to improve it further.

In the present master project, a suggestion for absorbing parts of the solar spectrum other- wise not fully exploited in the conventional silicon solar cell is presented. We propose that this can be achieved by introducing nanoparticles with a larger band-gap than Si into a transparent conductive oxide on top of the conventional silicon solar cell.

In this thesis, our hypothesis was that nanoparticles of zinc ferrite spinel (ZnFe₂O₄) with a band-gap of ≈ 2 eV, could be grown in ZnO through a process of solid state precipitation.

This could be achieved by saturating the ZnO matrix with Fe at high temperatures, and then subsequently cooling the samples below the solubility limit, thereby nucleating and growing the spinel phase. If this is successful, we would expect these samples to absorb in a broader range of the spectrum, thereby enhancing the harvesting of sunlight.

We found that for rather high cooling rates (quenching), on the order of 10 minutes, Fe induces and/or decorates inversion domain boundaries (IDBs) in the ZnO, similar to what has been reported in literature earlier. The minimum distance between the basal plane IDBs is approximately 6 nm, probably limited by the strain induced in the ZnO lattice. More surprising, these structures are identified also in samples with much lower cooling rates, on the order of 30 hours, also with no indication of formation of the spinel phase. This indicates either that the IDB structures form quickly at high temperatures, thereby locking the Fe into meta-stable structures that block the formation of the spinel, and/or that the temperature window of the spinel growth is rather narrow, so that even the low cooling rate leaves insufficient time for any perceptible nucleation and growth.

When the samples are annealed a second time at temperatures below the solubility limit, the spinel phase forms at 1000 ^◦C, but not at 800 ^◦C. This may indicate that the growth is kinetically blocked, and that a certain activation energy is needed for the spinel to form. This should be further studied to form smaller particles then what was done in this thesis.

Measurements of the optical properties were performed, revealing strong similarities in the optical absorption between samples with IDBs and with the spinel phase, with an onset at

around 2 eV. These similarities suggest that the origin of this 2 eV optical gap is the octahedrally coordinated Fe-O structural unit, which is present in both the IDBs and in the spinel. This interpretation is further supported by previous work using density functional theory, which found that the Fe and O states are the main contributors to the top of the valence band and bottom of the conduction band in the zinc ferrite spinel.

Contents

1 Introduction and motivation 1

2 Materials and methods 5

2.1 The Fe₂O₃ - ZnO system . . . 5

2.1.1 Zink oxide (ZnO) . . . 6

2.1.2 Zink ferrite spinel (ZnFe₂O₄) . . . 7

2.1.3 Inversion domain boundaries (IDBs) . . . 8

2.2 Synthesis . . . 9

2.2.1 Ball-milling . . . 9

2.2.2 Solid-state sintering . . . 9

2.3 Experimental . . . 10

2.3.1 Scanning electron microscopy (SEM) . . . 10

2.3.2 Transmission electron microscopy (TEM) and Scanning transmission elec- tron microscopy (STEM) . . . 10

2.3.3 Energy-dispersive X-ray spectroscopy (EDS) . . . 13

2.3.4 Electron energy loss spectroscopy (EELS) . . . 13

2.3.5 Diffuse reflectance spectroscopy . . . 13

3 Results and discussion 15 3.1 Sample overview and characteristics . . . 15

3.1.1 Surface conditions and zinc evaporation. . . 18

3.2 Inversion domain boundaries (IDBs) . . . 21

3.2.1 Distribution of basal-IDB layers. . . 23

3.3 Zinc ferrite spinel . . . 26

3.4 Structural similarities between IDBs and zinc ferrite spinel . . . 34

3.5 Optical properties . . . 37

3.5.1 Diffuse reflectance . . . 37 3.5.2 Low-Loss Electron Energy Loss Spectroscopy (EELS) . . . 39

4 Conclusion and suggestions for future work 41

4.1 Conclusion . . . 41 4.2 Suggestions for future work . . . 42

5 Appendix 43

Chapter 1

Introduction and motivation

Since the first silicon solar cell was made in 1941 [1] the dedication to increase its efficiency has been immense due to high presence of silicon on earth and the easy way of making this into a solar cell. Improvements has been made in design to increase the absorption and decrease the reflection as well as better instruments and research on doping concentrations has made the solar cell to increase its efficiency from 1%in 1941 to 24.7% in 2014 [2].

When light hits a solar cell the photon excites an electron generating an electron-hole pair.

After a short amount of time this electron-hole pair can recombine creating unwanted heat in the material and a loss of electric current. This leads to the need to remove the charge carriers as quickly as possible. Today the normal way of doing this is by having a metal contact, most commonly used is silver, to remove the charge carriers from the top of the solar cell. The prob- lem with using silver is that this material is not transparent leading to it blocking out light that was meant to create the current in the solar cell and thus lowering the efficiency.

Ideally the metal contact should be placed all over the solar cell for charge carriers to have the lowest travelling distance possible, but due to silver not being transparent this is not pos- sible due to no light reaching the solar cell. One way of solving this problem is by implementing a transparent conductive layer that removes the charge carriers as well as letting light through.

One such material is zinc oxide (ZnO).

Zinc oxide is a transparent conductive oxide (TCO) with a band gap of 3.2 eV and is already used in photovoltaic (PV) devices such as Panasonic HT (Heterojunction with Intrinsic Thin layer). Zinc oxide has also a low cost compared to other TCOs such as indium-tin-oxide (ITO),

Figure 1.1: Schematic of a multi junction solar cell but is at the moment not efficient enough to compete with ITO.

Due to silicon solar cells having an indirect band-gap of 1.1 eV it absorbs mostly red light leav- ing higher energy photons to generate heat in the material which reduces the overall efficiency of the solar cell. By implementing something with a higher band-gap that absorbs higher energy photons, more of the energy absorbed will be converted to electrical energy rather then thermal energy. One possible way of implementing something like this is by adding nano particles to the ZnO layer as shown in Figure 1.1 that can absorb high energy photons and increase the efficiency.

An important aspect of quantum dot solar cells is defect control and interface properties surrounding the nano particles. A good suggestion for a place to start looking for nano particles that is possible to create and has a good structure match with ZnO is to look at different ternary zinc oxides.

A literature review, shown in Table 1.1, was done to find some promising ternary zinc oxides with a band-gap higher than that of silicon and out of all of these, two spinels showed to be promising. This is ZnFe₂O₄ and ZnSb₂O₄. Due to size difference and amount of articles written where iron oxide has been mixed with zinc oxide to create inversion domain boundaries in zinc oxide the idea is to try to create nano particles of the ZnFe2O4 spinel in ZnO matrix.

Table 1.1: Literature review of band-gaps for different ternary zinc oxides.

Ternary oxide Band gap [eV] Reference Zn₂M o₃O₈ 0.0944 (DFT) [3]

ZnM o₈O₁₀ 0.181 (DFT) [4]

Zn₂P tO₄ 0.631 (DFT) [5]

Zn₃In₂O₆ 0.683 (DFT) [6]

Zn₂SnO₄ 0.825(DFT) [7]

ZnV₂O₄ 1.1 [8]

ZnM n₂O₄ 1.24 [9]

Zn₂V O₄ 1.601 (DFT) [10]

Zn₄As₂O₉ 1.620 (DFT) [11]

Zn₂As₂O₇ 1.763 (DFT) [12]

Zn3As2O8 1.897 (DFT) [13]

ZnF e₂O₄ 1.9 [14]

ZnSb₂O₄ 1.92 [15]

ZnW O₄ 2.14(DFT) [16]

Zn2V2O7 2.505 (DFT) [17]

ZnBa₂O₃ 2.672 (DFT) [18]

Zn₃B₂O₆ 2.697(DFT) [19]

ZnT iO₃ 2.88 [20]

Zn₂In₂O₅ 2.8/3.4 [21]

ZnSb₂O₆ 3.0-3.1 [22]

Zn₂T iO₄ 3.1 [23]

ZnSiO₃ ≈ 3.4 [24]

Zn₄B₆O₁₃ 3.41 (DFT) [25]

ZnSnO₃ 3.5/3.9 [21]/ [9]

ZnM oO₄ 3.55 (DFT) [26]

ZnCO3 3.56(DFT) [27]

ZnCo₂O₄ 3.72 [28]

ZnSO₄ 3.82 (DFT) [29]

ZnB₄O₇ 4.66 (DFT) [30]

ZnP2O6 4.664 (DFT) [31]

ZnGa₂O₄ ≈5 [32]

Zn₂SiO₄ 5.5 [24]

Chapter 2

Materials and methods

This chapter gives an overview of the different materials used and produced in this work, their characteristics and the methods used to create and characterize them.

2.1 The Fe

O

- ZnO system

The idea is to use Fe₂O₃ and ZnO powders to get a mixture of iron, zinc and oxygen and from this mixture nucleate out small particles of the ZnFe₂O₄ spinel inside the ZnO matrix. From the phase diagram in Figure 2.1, the solubility of Fe in ZnO is relatively low for temperatures below 1200 ^◦C, but then increases rapidly from 7 at% to 35 at% at 1600^◦C. This can be used to make a series of samples with the same heat-treatment temperature only varying composition. One possible way to nucleate out the spinel phase in ZnO is by dissolving all of the iron inside the ZnO matrix and when cooled down the spinel phase should start growing. Different composition and cooling rate will be an important factor here.

One starting composition would for instance be a Fe/(Fe + Zn) ratio of 10%. Where this would then create 15% of the spinel phase and the rest ZnO. With this composition, the phase diagram in Figure 2.1 shows that it would be sufficient enough to heat treat it at 1400^◦C to homogenize the sample and when cooled, particles of zinc ferrite spinel (ZnFe2O4 ) should form.

To obtain a uniform distribution of iron and small grains throughout the sample the powders were ball-milled. Then the powders were pressed to a pellet and sintered at high temperature to be sure of a completely uniformly distribution of iron in the ZnO matrix. Temperatures and

Figure 2.1: Phase diagram of Fe and Zn in air [33]. In ZnO matrix (Zincite) the solubility of iron is low below 800 ^◦C and relatively high at 1400 ^◦C. This can be used to solid state precipitate spinel with the same heat-treatment, but with different composition.

durations may vary depending on the characterization results.

2.1.1 Zink oxide (ZnO)

Zink oxide has wurzite type structure with the hexagonal Bravais lattice with space group P6₃mc in Hermann-Mauguin notation. This structure is non-centrosymmetric, which leads to there being a difference in which direction to look down the c-axis hence looking down the [001]

direction is different from looking down the [001] direction. This gives a polar direction in ZnO and gives rise to properties that will be discussed later.

ZnO is a natural n-type semiconductor due to its tendencies to make zinc vacancies in the structure. The direct band gap is approximately 3.2 eV, which is outside the range for visible light and hence it is transparent. This leads to the material to be a good transparent conductive oxide.

2.1.2 Zink ferrite spinel (ZnFe

O

)

The oxide spinel has cubic face-centered Bravais lattice and can be described by the AB2O4

formula where A are divalent atoms and B are trivalent atoms. In a normal spinel, A is tetra- hedrally and B is octahedrally coordinated, while in an inverse spinel B takes both tetrahedrally and octahedrally coordination, while A only takes octahedrally coordination. Most spinels are either normal or inverse spinel, but they can also be both normal and inverse spinel at the same time. The cite occupation can then be described as (A1−cB_c)(A_cB2−c)O₄ where c is 0≤ c≤1 and is called the inversion parameter [34].

In bulk, zinc ferrite is a normal spinel where Zn occupies A position and Fe occupies B position and the inversion parameter (c) is 0. However, nano-sized particles has been reported to always have a mixed structure of both normal and inverse spinel [35].

According to the phase diagram in Figure 2.1, in the case of the spinel, this phase goes gradu- ally from a normal spinel with ZnFe₂O₄ to the inverse spinel hematite (Fe₃O₄). The reason for some materials to chose a normal or an inverse spinel is explained in literature to be due to the crystal field splitting (CFSE) [36]. Why zinc ferrite spinel turns to a partially normal and inverted spinel with decreasing particle size is not fully understood, but it is known to have an impact on both optical and magnetic properties of the system [37], making this material challenging to work with.

Nanoparticles of zinc ferrite spinel has been researched for a while due to its optical, elec- trical and magnetic properties and has a lot of different applications from electrode material for supercapacitors to water splitting [38] [39].

Even though bulk ZnFe₂O₄ is paramagnetic, nanoparticles of the spinel has shown to be stronger than many of the conventional bulk ferrites, but the magnetization is strongly de- pendent on the size of the particles [40]. The most prominent change reported when reducing the particle size is the transition from a normal to inverse spinel. From crystal field splitting theory the change from a normal to an inverse spinel in this structure is whether the Fe³⁺ is octahedrally or tetrahedrally coordinated. In a normal spinel both the Fe³⁺ atoms is octahed- rally coordinated and the d⁵, high spin configuration terminates the magnetic properties of one another leaving the net magnetization to be zero at room temperature. In an inverse spinel, one of the Fe³⁺ is tetrahedrally coordinated and the other octahedrally coordinated. Since ∆_O

Figure 2.2: An illustration of both the basal and pyramidal plane in inversion domain bound- aries.

is different from ∆_t, these orbitals have different energies, leading to be a net magnetization and thus the observed increase in magnetization with decreasing size.

2.1.3 Inversion domain boundaries (IDBs)

Since ZnO lacks inversion symmetry, the +c and -c directions are different. The characteristic structure and properties of this direction has been thoroughly studied and through this work inversion in the structure has been observed. Why this inversion is observed in pure ZnO is due to defects in the system. In pure ZnO, these IDBs are very attractive to electrically point defects and can thus destroy the desired semiconducting properties [41].

ZnO samples doped with trivalent atoms, the most prominent examples being Fe and In, have shown to create IDBs in ZnO where octahedrally coordinated single layers of atoms are formed. These layers flip the c-axis of ZnO and thus are called inversion domain boundaries.

These IDBs are divided into a basal plane which is parallel with the [001] planes in ZnO, and a pyramidal plane which goes from one basal plane to the next and is in the [210] direction as illustrated in Figure 2.2. In both cases the iron is octahedrally coordinated and inverts the c-axis of ZnO [42].

2.2 Synthesis

2.2.1 Ball-milling

High energy ball-milling, that was used in this work, was used to ensure small particle sizes and thus lower diffusion distances as well as generating a uniform distribution of powders through- out the sample. This was needed to easier and faster achieve a homogeneous sample at high temperatures due to evaporation of ZnO creating an undesirable iron to zinc ratio. This will be further explained in Chapter 3.

The ball-milling process that was used in this work used a 125 mL Agate (SiO₂) jar with 30

× 10mm Agate balls. Approximately 15.8 gram of ZnO and 3.6 gram of Fe₂O₃ powders were mixed together with isopropanol for the 10% Fe/(Fe + Zn) ratio sample. Then ball-milled for 2 hours at 300 rpm.

2.2.2 Solid-state sintering

Solid-state sintering is a process where solid particles is compacting to make a solid without being in liquid phase. The driving force here is solid-state diffusion between the particles and is commonly used for materials that has a high melting point or where it is unfavorable to reach liquid phase. Due to high surface energy between powders, the sintering process is mostly driven by thermodynamics, creating lower energy for the system [43]. Since small particles have a higher surface energy, the sintering process happens faster and thus can be used in cases where a long sintering time is unfavorable.

Figure 2.3: Illustration of the electron-specimen interaction and some possible signals generated.

2.3 Experimental

This section will give a brief introduction to electron microscopy, electron energy loss spectro- scopy and diffuse reflectance. This section is based on the electron microscopy theory presented by Fultz and Howe [44] and Williams and Carter [45] and the diffuse reflectance by Mirabella [46].

2.3.1 Scanning electron microscopy (SEM)

A scanning electron microscope generates images by shooting electrons with a converged beam while scanning over the sample generating different signals as shown in Figure 2.3. The volume probed by the incoming electron beam is increasing with acceleration voltage and decreasing with atomic number and density of the sample. The SEM column with the main components are illustrated in Figure 2.4a.

2.3.2 Transmission electron microscopy (TEM) and Scanning trans- mission electron microscopy (STEM)

In a transmission electron microscope (TEM), the electrons transmits the sample and are pro- jected onto a detector below. Multiple detectors, biprisms and apertures can be inserted for doing different spectroscopy measurements or to manipulate contrast in the image. While elec- trons are typically accelerated at 15 kV for the SEM, the TEM uses 100 - 400 kV and can thus have higher resolution. Since the electron beam is transmitted through the sample, the need

(a) (b)

Figure 2.4: Illustrations of the beam path in SEM (a) and TEM (b) with the main components drawn.

(a) (b)

Figure 2.5: A ray diagram for TEM (a) with a parallel incoming beam and for STEM (b) with a convergent beam.

Figure 2.6: Image from three different STEM-detectors taken simultaneously, showing different contrast for each detector. Please note the dark areas from the HAADF detector, due to lower mass, are the same areas appearing bright at the ADF detector, due to diffraction contrast.

for very thin samples is necessary and hence extensively sample preparation.

The TEM can be operated in two main modes. TEM mode, illustrated in Figure 2.5a, uses a parallel incoming electron beam. Contrast in images taken in this mode contains mass- thickness, diffraction, surface and more. In STEM mode, illustrated in Figure 2.5b, a converged beam is used while scanning over the sample. With different detectors, features of the sample contributing to different types of contrast can be distinguished. Electrons hitting the high- angle annular dark field (HAADF) detector is usually electrons that has been scattered at more than 50 mrad and the main contributor to this scattering effect is mass. This means that the contrast seen in HAADF images is mainly mass contrast. The annular dark field (ADF) detector absorbs electrons scattered at 10 - 50 mrad, where diffraction and strain are the big contributors to contrast. Electrons scattered less than 10 mrad gives contrast in the bright field (BF) detector and this can be used to map the effect of lighter elements like oxygen. The different contrast arising from different detectors can be seen in Figure 2.6.

2.3.3 Energy-dispersive X-ray spectroscopy (EDS)

In Energy-dispersive X-ray spectroscopy (EDS), the x-rays from the sample are collected. These x-rays consist of characteristic photons and can be used to calculate the chemical composition of different areas in the sample. The energy resolution is an important limiting factor for EDS characterization due to overlapping areas and hence wrong chemical composition.

2.3.4 Electron energy loss spectroscopy (EELS)

Electrons transmitted through the sample, may cause inelastic interactions with the electrons of the sample. The electron loss resulting from this, contain information about the chemistry and can be used to measure the electronic behavior of the sample. In this work, the low loss region has been used to extract the onset for the electron energy loss spectrum. This can be used to calculate the band-gap with a small probe volume compared to the diffuse reflectance spectroscopy. More about this is explained in Chapter 3.

2.3.5 Diffuse reflectance spectroscopy

The diffuse reflectance measurements was done in collaboration with the Light and Electricity from Novel Semiconductors (LENS) group and the method used is described by Mirabella [46]

for the interested reader.

F(R) = (1−R)²

2R (2.1)

While execution of diffuse reflectance spectroscopy is relatively simple, interpretation of the data is more challenging. In comparison with absorption measurements, surface effects and multiple scattering leave a larger impact. To simulate the adsorption spectra, an inversion of the diffuse reflectance data is done with the help of the Kubelka-Munk function as shown in Equation 2.1. The raw diffuse reflectance data is shown in Figure 2.7a and the data after the Kubelka-Munk function shown in Figure 2.7b.

(a) Raw diffuse reflectance data.

(b) The data after the Kubelka-Munk function was used on the raw diffuse reflectance data from Figure 2.7a.

Figure 2.7: Diffuse reflectance data before (a) and after (b) the inversion from the Kubelka- Munk function.

Chapter 3

Results and discussion

In this section, the results is discussed consecutively for each main feature observed starting with inversion domain boundaries (IDBs), followed by the formation and structure of the zinc ferrite spinel. Then we continue with the structural similarities between the IDBs and the spinel and end with optical properties.

As mentioned in the introduction, the motivation for this work was to form nanoparticles of the zinc ferrite spinel embedded in zinc oxide for optical applications. From the phase diagram in Figure 2.1, at room temperature, the solid-solubility of iron in ZnO is quite low compared with the solubility at high temperatures, giving reasons to believe that the cooling rate can have a big impact on the formation of spinel particles. Quazi-periodic structures in ZnO referred to as IDBs were observed even after heat-treatment at 800 ^◦C for 34 hours, showing cooling rate to be important for the formation of zinc ferrite spinel.

3.1 Sample overview and characteristics

After the synthesis steps described in section 2.2, every sample that were prepared had cracks as shown in Figure 3.2. Due to evaporation of Zn at high temperatures, described in section 3.1.1, absence of Zn close to these cracks were highly likely. This would lead to a wrong Fe/(Fe + Zn) ratio around these cracks and thus were an undesired feature. Multiple samples were made with a fixed heat-treatment step, only varying pellet mass and the force used pressing them to avoid this feature. Varying from 1.0, 1.5, 2.0 and 2.5 tons of force and changing the pellet thickness from 1.5 g, 2.0 g and 2.5 g, had seemingly no change to the size or amount of cracks and thus

pellets of 1.5 grams and a force of 1.0 tons were used for samples shown in Table 3.1.

Table 3.1: Heat-treatment (HT) temperature and duration for different composition.

Sample Nominal

number composition HT step 1 HT step 2 Characteristics

1 10% Fe 24h @ 1400^◦C - IDBs

2 10% Fe 24h @ 1000^◦C - Iron-rich precipitations

3 10% Fe 4h @ 1400^◦C - IDBs

4 5% Fe 4h @ 1400^◦C - IDBs

5 10% Fe 4h @ 1400^◦C 34h @ 800^◦C IDBs

6 5% Fe 4h @ 1400^◦C 34h @ 800^◦C IDBs*

7 10% Fe 12h @ 1400^◦C 36h @ 1000^◦C Spinel 8 10% Fe 12h @ 1400^◦C 112h @ 1000^◦C Spinel 9 10% Fe 12h @ 1400^◦C 160h @ 1000^◦C Spinel*

10 5% Fe 12h @ 1400^◦C 19h @ 1000^◦C -

11 5% Fe 12h @ 1400^◦C 36h @ 1000^◦C Spinel*

12 0% Fe 12h @ 1400^◦C - -

* Not proven characteristic but believed to be of similar characteristics as other samples.

Sample 1, shown in Figure 3.2a, had clearly IDBs observed all over the sample where it was possible to tilt to the [100] zone-axis for ZnO and no indication of any zinc ferrite spinel.

Since the formation of spinel particles was the motivation, heat-treatment at a lower tem- perature was tried for sample 2 compared to sample 1. Sample 2 was heat treated at 1000^◦C for 24 hours and after investigating sample 2 with EDS in the SEM, shown in Figure 3.1a, precipitations of Fe-rich areas were observed. This is an indication that the sample was not ho- mogenized, probably due to unwanted remains of Fe₂O₃, or there was zinc ferrite spinel particles that were in the micrometer size region which are bigger than the particles we want to form.

Thus the heat treatment at 1400^◦C was used for the remaining samples.

Sample 3 was the most investigated out of the samples shown to have IDBs. Even though this sample had clearly formed IDBs all over the TEM sample, there was a colour change at the cross section, shown in Figure 3.2b, giving reasons to believe that Fe was not uniformly distributed, even though this was not observable with SEM and EDS. Due to this, the heat treatment step at 1400^◦C for the remaining samples were increased to 12 hours to exclude the colour change to have an impact.

(a) EDS map of the Fe-Kα peak for sample 2. (b) EDS map of the Fe-Kα peak for sample 3.

Figure 3.1: EDS map of the Fe-Kα peak in a SEM, showing a precipitation of iron rich phases in sample 2 compared with sample 3.

In sample 4, which had 5% Fe and was heat-treated at 1400^◦C for 4 hours (same as sample 3), IDBs were observed. While the spacing between basal IDBs in sample 3 was more or less the same, in sample 4 there was a wide variation of spacing. This will be shown further in section 3.2.1.

Sample 5 and 6 were additionally heat treated for 34 hours at 800^◦C to try to from spinel particles. We observed IDBs in sample 5 showing that this duration and temperature was not sufficient to form zinc ferrite spinel nanoparticles and proving that these IDBs are relatively stable. Sample 6 was not investigated further due to sample 5 showed to have IDBs.

Sample 7, 8 and 9 were all homogenized at 1400^◦C for 12 hours to achieve a homogeneous sample before cooled down to room temperature. These samples were never investigated to have IDBs, but since sample 4, which was only heat-treated for 4 hours and sample 1 which was heat-treated for 24 hours both had IDBs, it is safe to assume these samples also had IDBs after the first heat-treatment step.

Since creating nanoparticles of spinel was the goal and this had failed for the sample that was heat-treated at 800^◦C for 34 hours, a series of samples were additionally heat-treated at 1000^◦C.

Sample 7 and 8 were heat-treated at 1000^◦C for 36 and 112 hours respectively and shown to have zinc ferrite spinel particles and hence sample 9, that was heat-treated for 160 hours, was

never investigated due to a trend in increasing particle size with increasing heat-treatment time.

Sample 10 and 11 were never investigated in the TEM due to the time consuming process of investigating them, but were in SEM and EDS of similar structure as sample 7 and 8 that were shown to have spinel.

Sample 12 was made as a reference sample for the diffuse reflectance measurement to exclude variables arising from the technique used.

To summarize, all of the samples that were homogenized at 1400^◦C exhibited IDBs after the first heat-treatment step. After the second heat-treatment step at 1000^◦C, the IDBs were gone and the zinc ferrite spinel was observed for the 10% Fe case. The samples with the same second heat-treatment step for 5% Fe were never thoroughly studied in the TEM and thus not proven to have spinel particles, but SEM images showed no big precipitation of iron rich phases giving reasons to believe that the same features were formed as in the corresponding 10% Fe samples.

3.1.1 Surface conditions and zinc evaporation.

In all of the samples that were homogenized at 1400^◦C, evaporation of Zn was detected at the surface, leaving a characteristic surface texture as seen in Figure 3.3. Evaporation of Zn at high temperatures is a known phenomenon in ZnO and has been reported in multiple articles [47] [48].

In this work the evaporation of Zn changed the desired composition and was needed to be taken into account during TEM sample preparation where only a small section of the samples are being studied.

A cross section image was taken in a scanning electron microscope (SEM) as shown in Figure 3.4 showing how far the morphology different features at the surface went into the pellet due to Zn evaporation. From quantification in EDS, the Fe/(Fe + Zn) ratio went from above 20 % inside the crystals at the surface down to 10%, which is the bulk composition for this sample, where the crystals end. This gives an indication of how far into the pellets the evaporation of Zn needs to be taken into account and was used as a rough guideline when making TEM samples of bulk that is supposedly unaffected by the surface conditions.

(a) 10% Fe, heat-treated at 1400^◦C for 24 hours, referred to as sample 1.

(b) 10% Fe, heat-treated at 1400^◦C for 4 hours, re- ferred to as sample 3.

(c) 10% Fe, heat-treated at 1400^◦C for 4 hours be- fore heat-treated at 800^◦C for 34 hours referred to as sample 5.

(d) 10% Fe, heat-treated at 1400^◦C for 12 hours before heat-treated at 1000^◦C for 112 hours referred to as sample 8.

Figure 3.2: Cross-section images, taken with reflected light in a stereo microscope, of samples heat-treated at 1400^◦C for a minimum of 4 hours.

Figure 3.3: A SEM image showing different environment between the middle and the edge at the surface of the pellet after heat-treatment

Figure 3.4: EDS quantification in SEM showing compositional changes as we move from the surface to the centre of the sample, due to Zn evaporation. The Fe/(Fe + Zn) ratio was 10.7, 19.2 and 24.5 for area 1,2 and 3 respectively.

3.2 Inversion domain boundaries (IDBs)

Samples of ZnO doped with iron, ball-milled and heat-treated at high temperatures has been shown to have quazi-periodic structures that flip the c-axis of ZnO referred to as inversion do- main boundaries (IDBs). H. Schmid et al. showed that there are two main types of these IDBs.

One completely full octahedral monolayer of iron, which lays in the (001) plane of ZnO called basal IDBs and complementary pairs in the (215) plane, called pyramidal IDBs [49].

In all of the samples that were homogenized at 1400^◦C and investigated in the TEM after this step, atomic layers containing iron were observed with EDS shown in Figure 3.5. Due to the strong similarities between these iron layers and the IDBs reported by H. Schmid et al. [49] [50], T Yamashita et al. [51], T. Walther et al. [52], O.K. Scherger et al. [53] and F. Wolf et al. [42], these iron containing layers are believed to be IDBs.

The HAADF images in Figure 3.5c and 3.5i shows darker atomic planes compared to the surroundings. These are the iron planes described as the IDBs and are darker due to difference in atomic number between Zn and Fe or the density difference.

In the ADF-STEM images shown in Figure 3.5b and 3.5h, the IDBs exhibit high intensities which can be interpreted as mainly diffraction contrast since mass contrast would have given opposite intensities due to iron being lighter then zinc. The high diffraction contrast in the ADF images is believed to be due to high strain induced by the iron layers.

Areas with high strain in a sample usually have high energy locally around the strained areas and if this energy gets too high, the system often tries a new configuration to relax. To see if this could lead to the formation of zinc ferrite spinel the samples were cooled at different rates going from quenched in air to a gradually cooling over a 5 hours period and heated-treated again at 800^◦C for 34 hours without having recognizable change showing that these IDB layers are relatively stable. Everywhere in the samples where it was possible to tilt to the [100] zone axis for ZnO, it was possible to see the IDBs and thus leaves the impression of an uniform distribution throughout the bulk of the samples.

(a) ABF-STEM image. (b) ADF-STEM image.

(c) HAADF-STEM im- age.

(d) EDS map of Fe-Kα. (e) EDS map of Zn-Kα. (f) EDS map of O-Kα.

(g) ABF-STEM image. (h) ADF-STEM image.

(i) HAADF-STEM im- age.

(j) EDS map of Fe-Kα. (k) EDS map of Zn-Kα. (l) EDS map of O-Kα.

Figure 3.5: STEM images and EDS maps taken at the [100] projection, showing both the basal and pyramidal IDBs containing iron as reported in literature.

3.2.1 Distribution of basal-IDB layers.

Due to the increased intensity in the ADF images at the IDBs, by acquiring intensity profiles it was possible to make a program that could calculate the distances between each basal IDB.

Due to strain in the system and the fact that the intensity peak is measured from the middle of the iron layers the distances are a bit inaccurate, but this is the same for both samples and thus the comparison between these should be the same.

By changing the Fe/(Fe + Zn) ratio from 10% to 5% without varying the heat-treatment time and temperature, as was done with sample 3 and 4, the distances between the basal planes in the IDBs started to vary. Figure 3.6 shows the distribution of basal planes and it is possible to see in the 10 % sample, basal IDBs are formed periodically, exhibiting a mean of ≈ 7.0 with a standard deviation of ≈ 1.0. On the contrary, in the case of the 5% sample, the basal IDBs showed a mean of≈13.4 with a standard deviation of≈4.8, showing a less periodically ordering of the IDBs.

This distribution of distances could mean that for less Fe %, IDBs have more freedom to be formed, while as Fe % increases, the system is restricted to form a more organized structure.

In Figure 3.6 there seems to be a minimum distance between the IDBs that the structure can form. This could be attributed to the high strain localized at the IDBs, putting a limitation on how close the IDBs can form.

The consensus in literature is that for each time crossing the IDBs, either it being the pyr- amidal or the basal plane, the direction of the c-axis in ZnO flips. This results in some rules for how the pyramidal and basal planes form. In Figure 3.7, the ADF image shows the IDBs where the distances between the basal planes varies and thus leaves a variation in the sizes of the pyramids due to possible variations in Fe concentrations. Arrows has been drawn in these images illustrating the c-axis of ZnO and as seen in the image, there are no arrows going the same direction crossing only one IDB.

To summarize, samples homogenized at 1400^◦ C have been shown to have inversion domain boundaries (IDBs) with distribution dependent on the composition. For heat-treatment at 1400^◦ C for 4 hours the samples were seemingly successfully homogenized in the TEM, but showed some optical variation in Figure 3.2b and??, hence the main strategy to homogenize the samples was to heat-treat them at 1400^◦ C for 12 hours which is successfully shown in Figure 3.2d.

Figure 3.6: The distance between basal IDBs for the 10% (sample 3) and the 5% (sample 4 ) sample with a gamma distribution used as curve fitting. The mean(µ), median (µ_1/2), standard deviation (σ) and number of counts (n) were calculated and the results showed more distributed distances and an average distance of approximately half between basal IDBs for the 5% sample compared to the 10% sample.

Figure 3.7: ADF-STEM image of the inversion domain boundaries with arrows illustrating a direction of the c-axis of ZnO.

3.3 Zinc ferrite spinel

After additional heat-treating at 1000^◦C of the homogenized samples that were shown to have IDBs, particle like features were observed. These were identified with Selected area diffraction (SAD) and EDS quantification as zinc ferrite spinel, shown in Figure 3.9.

The STEM images shown in Figure 3.8, give an overview of a typical area of the samples containing spinel, including grains containing round spinel particles and elongated lamellas of spinel separated by ZnO. The thickness of these lamellas is approximately 100 nm for sample 7, heat-treated at 1000^◦C for 36 hours and 180 nm for sample 8, heat-treated at 1000^◦C for 112 hours. Thicker lamellas were not observed, giving reasons to believe that these lamellas are not platelets similar to the iron layers in the IDBs, rather implying these lamellas to be rod shaped.

Table 3.2: EDS quantification results

Average Fe/(Fe + Zn) ratio Standard Deviation σ # measurements

65.9 1.0 10

Quantification of the spinel particles showed a small variation in the Fe/(Fe + Zn) ratio, with the average composition being approximately 2/3. From the phase diagram in Figure 2.1, the spinel composition should not have a Fe/(Fe + Zn) ratio of less than 2/3 and where the ratio is less, we probably have zinc substituting iron. In defect chemistry this substitution is written as Zn^/_Fe which means that we have zinc on iron position and since the charge of iron is 3+ and zinc is 2+ we get one effectively negative charge. This effectively negative charge needs to be compensated for and the system can do this either by creating interstitial zinc or by oxygen vacancies.

As discussed in section 3.1, all of the samples cracked at high temperatures, generating a high surface area and thus a probability for increased oxygen vacancies and zinc evaporation.

Both of these defects are common in ZnO [54]. Even though this was accounted for when mak- ing TEM samples by polishing off areas close to these cracks, the possibility for defects is still present.

Assuming that there are no structural changes where the iron is randomly distributed before achieving the spinel phase, the diffusion length for iron is much shorter going from one basal

(a) BF image. (b) ADF image.

(c) HAADF image.

Figure 3.8: STEM images showing the distribution of spinel, shown as bright in the ADF and dark in the HAADF images.

(a) HAADF-STEM image, showing

where spectrum 5 originates from. (b) EDS map of O-Kα.

(c) EDS map of Fe-Kα. (d) EDS map of Zn-Kα.

(e) Spectrum taken from the drawn area in Figure 3.9a showing Fe-Kα, O-Kα, Zn-Kα and a calculated composition related to the spinel.

Figure 3.9: HAADF-STEM image and the corresponding EDS chemical maps and a spectrum

that are elongated in the same direction as the IDBs. Alternately the formation of spherical particles would have been expected due to smaller surface area, but this leads to the iron at the end of the IDBs to have a longer diffusion length perpendicular with the c-axis in ZnO before reaching the correct amount of iron to form the spinel phase. Due to diffusion along the c-axis in ZnO to be faster then the a-axis [55] this effect with rod shaped particles would have probably happened without there being any correlation between the structure in ZnO and the zinc ferrite spinel, but rather just due to diffusion distances and the time period used of 112 hours to be too short to achieve total equilibrium.

Contradictory to what was just stated, Figure 3.10 shows converged beam diffraction (CBED) patterns revealing a preferred orientation relationship between the two phases described by:

[100] ZnO || [101] spinel. These Kikuchi patterns were taken without tilting the sample after reaching the zone axis for ZnO, showing the spinel rods not to be randomly oriented.

The HR-HAADF image in Figure 3.11 shows the interface between ZnO and the spinel rods and the corresponding fast fourier transforms. Arrows show the [001] direction for ZnO and the [111] for spinel together with the parallel lines drawn in red, showing the corresponding planes.

In the spinel, these atomic planes are completely occupied with octahedral coordinated iron and no zinc, as shown in Figure 3.12b. One question that might rise from what was just stated is, why there is a variation in contrast in these layers if they contain only the same atoms?

The reason for this is due to the density of each layer where the bright ones consist of more atoms than the darker ones and this leads to higher intensity in the HAADF image. This will be further discussed in section 3.4. It is also worth mention that the interface between the ZnO and the spinel is however not a perfect interface. This will be further discussed in section 3.4.

The Fe/(Fe + Zn) ratio in ZnO between each layer of spinel was shown to be < 1% with EDS, implying that almost all of the iron in the system is typical inside the spinel particle.

Schmid and Mader [56] calculated the solid-solubility of Fe in ZnO between the IDBs to be less then 0.4%, giving reasons to believe similar Fe solid-solubility in ZnO for samples containing spinel. It is important that this iron content is low, due to the need for low diffusion of iron if this material is used together with a silicon solar cell since iron reduces the efficiency and lifetime of the silicon solar cell greatly [57].

In summary. Samples containing IDBs were heat-treated at 1000 ^◦C for a minimum of 36 hours and were shown to have spinel particles embedded in ZnO matrix. Several of these spinel

particles were shown to have a preferred orientation relationship to the ZnO and were also shown to have iron layers orientated the same way as the basal planes in the IDBs relative to ZnO, but with an interface between the ZnO and the spinel that appears diffuse. This relationship between the orientation of the spinel and the IDBs will be further discussed in the coming section.

The (111) planes in the spinel phase, notated by red lines in Figure 3.12b consist of only octahedrally coordinated iron and matches the coordination and distances between atoms in the basal plane in the inversion domain boundaries (IDBs). This indicates there being a correlation between the IDBs and the preferred growth direction in the spinel phase and why the two zone axis are correlated.

Figure 3.10: Overview image of zinc ferrite spinel rods with corresponding kikuchi pattern when tilted to the [100] zone axis for ZnO.

Figure 3.11: A HAADF image of the interface between ZnO (top left) in the [100] projection and spinel (bottom right) in the [101] projection.

(a) ZnO in the [100] projection.

(b) Zinc ferrite spinel in the [110] projection.

Figure 3.12: An illustration of the ZnO and zinc ferrite spinel with the same projection as in Figure 3.11 and with corresponding red lines drawn. In both the illustrations, Zn is drawn in gray and Fe in light brown.

(a) The [111] projection of the octahedral iron layer in the zinc ferrite spinel.

(b) The [001] projection of the octahedral iron layer in the basal-IDBs.

Figure 3.13: The octahedrally coordinated layer of iron for the spinel and the basal-IDBs, showing a fully occupied layer for the IDBs, but with some voids in the spinel case.

3.4 Structural similarities between IDBs and zinc ferrite spinel

The similarities in orientation between the IDBs and the ZnO matrix on the one hand, and the zinc ferrite spinel and the ZnO on the other, are striking. This may indicate that these struc- tures are related. For instance, we may consider the possibility of the IDBs to be a precursor to a later growth of the zinc ferrite spinel lamellas described in section 3.3. It is therefore inter- esting to consider the structural similarities between the spinel phase as described in literature and the proposed structure of the IDBs.

To understand the orientation relationship between the ZnO and the zinc ferrite spinel de- scribed at the end of the previous section, it is necessary to look at the planes in the spinel structure only occupied with iron and compare them with the iron planes in the IDBs. Briefly explained previously, these (111) planes in the spinel are not completely occupied with iron as seen in Figure 3.13a compared with the basal plane (001) in the IDBs, shown in Figure 3.13b.

This is due to the tetrahedrally coordinated zinc atoms shown with arrows in Figure 3.14a, that are placed right above and below these holes in the spinel structure.

(a) An illustration of the octahedral layer of iron in the zinc ferrite spinel with its nearest surroundings, drawn with arrows showing the zinc atoms placed on top and below the holes in Figure 3.13a.

(b) An illustration of the octahedral layer of iron in the zinc ferrite spinel, without the zinc atoms drawn with arrows in Figure 3.14a and the iron atoms not contributing to the iron monolayer.

Figure 3.14: The octahedrally coordinated layer of iron for the spinel and the basal-IDBs, showing a fully occupied layer for the IDBs, but with some holes in the spinel case.

Figure 3.15: An illustration of the basal-IDBs, showing similarities with the iron layer from the spinel, illustrated in Figure 3.14b.

Figure 3.16: A propose of the degree of Fe ordering as a function of Gibbs free energy at room temperature, illustrating IDBs to be an intermediate stage with a high activation energy in the solid state precipitation of zinc ferrite spinel.

and the adjacent iron that is not a part of the iron monolayer, gives Figure 3.14b. This figure, that is a part of the spinel, resembles the basal plane of the IDBs, shown in Figure 3.15, with an inversion in the ZnO c-axis across the iron layer and gives an indication of why inversion naturally occurs when crossing one iron layer in the IDBs.

Given these structural similarities and the similar orientation relationships relative to the ZnO matrix, it is tempting to propose that the IDBs represent an intermediate stage in the solid state precipitation and growth of spinel particles. A proposed degree of Fe ordering as a function of Gibbs free energy at room temperature is shown in Figure 3.16. Here we propose that the IDBs have a lower energy compared to iron randomly distributed in the ZnO matrix. This is proposed due to the low solid solubility of iron in ZnO at room temperature, and the samples quenched from 1400 ^◦C seemingly have no areas without IDBs. Furthermore, we propose that once the IDBs have formed, an energetic barrier exists prematurely the spontaneous formation of the spinel phase. This is supported by the observations from heat-treatment above 800 ^◦C is needed for the spinel to form. This can be thought of as an activation energy for the growth of the phase.

In summary, the structural similarities between the basal-IDBs and the zinc ferrite spinel and their direction in the ZnO matrix are striking. All of the samples where spinel were observed, e.g. sample 5 and 6, were first homogenized at 1400 ^◦C for 12 hours. After this heat-treatment step there is believed to be IDBs in every grain in the bulk of the samples containing octahed- rally coordinated monolayers of iron perpendicular to the [001] direction of ZnO. After further

heat-treating of these samples at 1000 ^◦C for 36 and 112 hours, rods of zinc ferrite spinel were formed and observed to lie in the same direction related to ZnO as the basal IDBs. The proposed explanation for this is that the IDBs are a precursor to the spinel and hence similar relation to ZnO.

3.5 Optical properties

Optical active zinc ferrite spinel particles embedded in ZnO matrix was the motivation for this work and thus natural to look at the optical properties. In this section, diffuse reflectance and low-loss electron energy loss spectroscopy (EELS) was used to measure the band-gap of the system.

3.5.1 Diffuse reflectance

Diffuse reflectance was measured for samples proven to have IDBs and spinel, referred to as sample 3 and sample 7 respectively and a reference sample of ZnO referred to as sample 12 in Table 3.1. The reasons for not doing absorption measurements are due to low transmission of optical light through the sample and very porous samples, making it challenging to get them thin enough for transmission to occur.

While execution of the experiment is relatively simple, interpretation of them are more chal- lenging. As explained in section 2.3.5, the Kubelka-Munk function was used on the data to simulate the absorption spectra, followed by a scaling for a more accurate onset.

What the correct scaling is depends if the sample has an indirect or direct band gap, by taking the square root for indirect or squared for direct. ZnO is known to have a direct band- gap of 3.2 eV and as seen in Figure 3.17b the straight lines matches the expected value of 3.2 best with the squared graph rather than the square rooted in Figure 3.17a for ZnO. For the spinel and IDBs, the onset is approximately the same, but the slope of the linear fitting is differ- ent. This shows that the spinel and the IDBs have an indirect band-gap of approximately 1.9 eV.

From density functional theory (DFT) calculations shown in Chapter 5 and confirmed by Soliman et al. [58], the band-gap in the spinel arises from the d-orbitals in the octahedrally coordinated iron, as the valence band, and to the p-orbitals in the surrounding oxygen which

(a) A scaling of Figure 2.7b used for indirect band-gaps, showing that ZnO is below the ex- pected value and the spinel and IDBs are close.

(b) A scaling of Figure 2.7b used for direct band-gaps, showing a close match to expected values for ZnO. The slope of the linear fit for the spinel and IDBs is too high for this to be a direct band-gap.

Figure 3.17: Diffuse reflectance data and calculations showing an indirect band gap for the spinel at 1.8 eV and a direct band-gap for ZnO of 3.1 eV, from sample 3(IDB), sample 7 (spinel) and sample 12(ZnO). Black dotted lines are background subtraction and linear fitting. Green arrows shows which eV the dotted lines cross, showing the onset for the band-gap.

contributes to most of the conduction band. Due to this, the distance between the oxygen and the iron atoms are important for the band gap.

F. Wolf et al. reported the Fe-O distance for the IDBs to be 0.208 nm and the Fe-O distance in the spinel to be 0.204 nm [42] showing big similarities of the nearest environment for the iron atoms.

3.5.2 Low-Loss Electron Energy Loss Spectroscopy (EELS)

Where diffuse reflectance measurements have a large probe volume, a more localized approach can be useful to exclude factors like surface effects or multiple scattering. For this we can use electron energy loss spectroscopy (EELS) in the TEM. In Figure 3.18a, the raw EELS data is shown for electron loss from 2 to 55 eV which is in the low loss region.

The band-gap region from Figure 3.18a is shown in Figure 3.18b. Here both the onset from the spinel and the ZnO is included with linear fit, showing the band-gap. Explained by Rafferty and Brown [59] the curvature of the onset can show if there is a direct or indirect band gap, where the onset for the direct band-gap is sharper compared to the indirect. In Figure 3.18b the ZnO has a direct band-gap of 3.2 eV and the spinel has an indirect band-gap of 2.0 eV and a direct band-gap of 2.5 eV. This is in compliance with Granone et al. [37].

(a) Raw EELS data from sample 7 (spinel), showing where the low-loss region is extracted from.

(b) The low-loss region of the EELS data for the spinel and the ZnO, showing the onset.

Figure 3.18: EELS data, showing the onset for the ZnO and spinel with a linear curve fit from where the band-gap can be extracted. Figure 3.18b shows the indirect band-gap of the spinel

Chapter 4

Conclusion and suggestions for future work

4.1 Conclusion

In this thesis we have studied the ZnO-Fe₂O₃ system to explore the possibility to create com- posite structures of ZnO and ZnFe₂O₄ for photovoltaic applications. Our hypothesis was that the ZnFe2O4 spinel could be precipitated in the ZnO matrix if samples of high Fe content were cooled from the high solubility region, into the low solubility region. The samples would then in effect be super-saturated by Fe and a process of solid state precipitation and growth of ZnFe₂O₄ would be initiated.

In the case of rather high cooling rates (quenching), the Fe induces and/or decorates in- version domain boundaries in the ZnO, similar to what has been reported in literature earlier.

There seems to be a minimum distance between the basal IDB planes probably limited by the strain induced in the ZnO lattice. More surprising, these structures are identified also in samples with much lower cooling rates with no indication of formation of the spinel phase. This indicates either that the IDB structures form quickly at high temperatures, thereby locking the Fe into meta-stable structures that block the formation of the spinel, and/or that the temper- ature window of the spinel growth is rather narrow, so that even the low cooling rate leaves insufficient time for any perceptible nucleation and growth.

When the samples are annealed a second time at temperatures below the solubility limit, the spinel phase forms at 1000 ^◦C, but not at 800 ^◦C. This may indicate that the growth is kin-

etically blocked, and that a certain activation energy is needed for the spinel to form. Once the spinel phase is allowed to form, the growth seems rather rapid, with 100 nm rod-like particles forming even after 36 hours.

Turning to the optical properties. The diffuse reflectance measurements shows a big simil- arity in optical absorption for the spinel and the IDBs. This is understood originates from the distance between the octahedrally coordinated iron and the surrounding oxygen atoms and thus should be similar for the IDBs and the spinel. The indirect band-gap is a positive property for solar cells due to the lower probability for recombination.

4.2 Suggestions for future work

The formation of IDBs has been studied in several previous work, but there is still no clear evid- ence of at which temperatures these IDBs form. This is an open question which can possibly be investigated in-situ with TEM using a heating holder, or with a series of samples heat-treated at different temperatures.

A series of samples should be made to investigate if the size and morphology of the spinels can be controlled by either temperature, cooling rate or composition.

Measurements of electric properties are important, to ensure that the ZnO matrix has not changed in a way that makes the material unsuitable as a transparent conductive oxide.

Due to the very structural arrangement of the IDBs relative to ZnO, the ZnO matrix and the IDBs are suggested to be a precursor for spinel growth. With implantation of Fe in thin transparent ZnO wafers or films, the sample can possibly be incorporated into a PV Cell.

However, while our samples have many grain boundaries that could facilitate diffusion, such features are not in single crystal samples. The dynamics of IDBs and spinel formation could therefore be significantly different and a dedicated study of the samples would be needed.

Chapter 5 Appendix

The included report is from a course called quantum mechanical modelling of nano-materials where the zinc ferrite spinel structure was investigated with density functional theory (DFT).

This report calculates the density of states (DOS) for the structure which is in compliance with other DFT articles [58] and can be used to describe which orbitals contributing to the band-gap in the spinel.

FYS-MENA4111

Kvantemekanisk modellering av nanomaterialer

Examining the ZnFe 2 O 4 spinel structure

Kristian Haug

Abstract

This project is about the ZnFe2O4spinel structure which is a quite complex structure with a need of relatively high cutoff energy and k-point density. Nanoparticles of this structure will in theory have a good structural match with ZnO and a band gap which absorbs the blue light which makes this possible to have on top of regular solar cells. The density of states graphs show a high density of d-orbitals for iron around the band gap which can be interesting.

1. Introduction

Today there is a lot of research going on about usingZnO as a conductive layer on top of conventional solar cells instead of using silver wires as is used today becauseZnO is transparent. By implementing nano particles ofFe2O3

into bulkZnOand heat treat this it should be possible to create someZnFe2O4nano particles which has a band gap of xxx. This layer of ZnO with ZnFe2O4 nano particles will be able to absorb the blue light in the sunlight while letting other wavelengths go true into the conventional silicon solar cell.

The motivation for this project is to look at theZnFe2O4

structure and get to know it better.

Figure 1:ZnFe₂O₄structure.

2. Method

The calculations used in this report is based on the Kohn- Sham equation in Vienna Ab Initio Simulation Package (VASP). The exchange correlation that is used is the gen-

2.1. Cutoff energy

To calculate the sufficient cutoff energy, the relative energy between the structure and the same structure with one oxygen vacancy was calculated and shown in Figure 2.

The convergence criteria for this structure is:

∆E_{Di f f}

∆Ecuto f f < ^3meV 50eV

and this is achieved at cutoff energy 500eV.

Figure 2:Cutoff energy difference between ZnFe₂O₄ and the same structure with one oxygen less gives relative energy.

2.2. K-point density

For sufficient kpoint density the energy difference was calculated the same way as in section 2.1 by calculating the relative energy between the structure and with one

The convergence criteria that was used for the k-point density is:

∆EDi f f

∆Nk < ^3meV 1

This is quite high but is still only achieved at k-point density 6. As seen in Figure 3 the derivative varies a lot and a k-point density at 9 is needed for a convergence criteria of 1meV/∆N_k

Figure 3:Energy difference between ZnFe2O4and the same structure with one oxygen less as a function of k-point density.

2.3. Relaxation

For it to be possible to calculate the correct density of states or band gap the the structure needs to be relaxed.

This is done in the INCAR file that is needed as an input file in VASP. The cell parameters is shown in Table 1 and 2 and shows a decrease in cell length after the relaxation.

Table 1:Before relaxation

a 8.442099999999 0.00000000000 0.0000000000000

Table 2:After relaxation

a 8.191919493752 0.000000000000 0.000000000000 b 0.000000000000 8.191919493752 0.000000000000 c 0.000000000000 0.000000000000 8.191919493752

2.4. Plotting the band structure

To plot the most detailed band structure it is needed to be plotted as a function of the wave vector k. The Brillouin zone for the space group Fd-3m is shown in Figure 4.

Figure 4:The k-vector types of space group Fd-3m. Reciprocal-space group ( Im -3 m )

To make sure that the charge density is not changed the INCAR file is changed by adding ICHARG = 11 and ISMEAR = 0. This is important to have a good sampling of k-points.

3. Results

A good way of visualising the electronic structure is by plotting the density of states and the band diagram.

3.1. Density of states

From Figure 5 it is possible to see a small band gap

from and what bonds that are binding. e.g. as shown in Figure 8 the s orbital to the oxygen atoms is not binding.

In all of these plots the density of states is plotted as a function of the energy minus the fermi energy.

Figure 5:Density of states for the structure.

Figure 6:Local density of states for zinc

Because of the high density for iron close to the band

Figure 7:Local density of states for iron

Figure 8:Local density of states for oxygen

3.2. Band diagram