First Principle Study Of Electronic Properties Of AT103 ( A= Sr, Ca, Pb) Compounds

ABSTRACT

The structural and electronic properties of fully-relaxed AT₁0₃ oxygen-vacancy surface with ATO₁ and O₂ terminations are investigated by first-principles calculations where A is Strontium, calcium and lead. The electronic properties having been comparatively analysed using both the generalised gradient approximation and the hybrid functional method. The indirect band gap of ATO is found to change significantly through the choice of functional; it shows an increase from 3.79 eV to 5.72 eV. A small indirect gap of 0.33 eV is also present directly above the conduction band edge, which allows for small optical transitions similar to that of defect transitions. The titanium orbitals are dominant near the conduction band edge, with oxygen orbitals being the main contributor to the valence band edge. Dielectric and elastic properties of the material are also obtained, with the bulk modulus being 131.73 GPa and the elastic moduli along the [1 0 0] and [0 0 1] directions being 180.57 GPa and 102.56 GPa, respectively. Theoretical values for Raman frequencies are reported for ATO. Finally, Bader charge analysis reveals the Titanium and oxygen atoms in ATO are comparable to their charges in AT₁0₃. However, due to the presence of the Lead–O bonds, oxygen exhibits a significant charge redistribution. Through the choice of functional, charge can become more localised on the oxygen atoms.

TABLE OF CONTENTS

COVER PAGE

TITLE PAGE

APPROVAL PAGE

DEDICATION

ACKNOWELDGEMENT

ABSTRACT

CHAPTER ONE

1.0    INTRODUCTION

1.1    BACKGROUND OF THE STUDY

• AIM OF THE STUDY
• SCOPE OF THE STUDY
• SIGNIFICANCE OF THE STUDY
• LIMITATION OF THE STUDY
• METHODOLOGY
• PPROJECT ORGANISATION

CHAPTER TWO

LITERATURE REVIEW

• REVIEW OF ALKALINE EARTH METALS
• OVERVIEW OF OXYGEN

CHAPTER THREE

3.0     METHODOLOGY

CHAPTER FOUR

4.0    RESULTS AND DISCUSSION

• MECHANICAL PROPERTIES
• DIELECTRIC PROPERTIES
• ELECTRONIC PROPERTIES
• BAND STRUCTURE AND DENSITY OF STATES

CHAPTER FIVE

• CONCLUSION
• REFERENCES

CHAPTER ONE

4.0                                          INTRODUCTION

4.1                            BACKGROUND OF THE STUDY

Due to its high permittivity (up to 5000 at 1kHz) [Duran P, 2002], AT₁0₃is seen as a material with great potential for device applications, such as capacitors, energy storage devices, phased array radar and random access memory. Recent literature has looked into the potential to form composites that can exhibit both the high permittivity found in AT₁0₃ whilst also displaying the low dielectric loss of materials such as calcium. To this end, AT₁0₃ core-shell composites have recently been made that exhibit the high breakdown voltage of O₃whilst maintaining the colossal permittivity of the ATO [Xu C, Zhang Z, Zhang J, Lei L, Zhang D and Fu Z, 2014], giving them greater promise for use in supercapacitors. However, it has been shown that, during growth, a layer of AT₁0₃, forms across a diffusion length into either material at the interface. These core-shell structures have been shown to exhibit both desired properties experimentally, yet theoretical studies of AT₁O₃ interfaces do not mirror these results. AT₁O₃ interfaces are, therefore, potentially responsible for the properties of such a structure. Clearly the properties of AT₁O₃ needs to be understood before the interface can be explored.

Successful growth of large ATO crystals, as well as the characterisation of its piezoelectric and dielectric properties were reported in the 1970s. ATO has the space group P4bm, experimental lattice parameters of Å and Å, and displays a melting temperature of 1445 °C. For modelling purposes, this creates a net electric field across the structure, which is unphysical (Reainthippayasakul W, 2014).

In order to fully understand the electronic and elastic characteristics of materials, such as AT₁O₃, density functional theory (DFT) calculations are necessary. Very little literature is currently available on first principles calculations for AT₁O₃, with only one paper partially exploring its electronic properties via the generalised gradient approximation (GGA) in DFT [Mogulkoc Y, 2013]. It is therefore unclear whether such results can be fully reliable as it is well known that GGA significantly underestimates the band gap of semiconductors, as well as electron localisation. Our choice of the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional is due to its improved accuracy for electron localisation and band gap values. An alternate approach would be to consider GW calculations, however, it has been recently shown [Freysoldt C, 2014] that for systems without a defect, HSE06 calculations accurately capture the bulk properties as effectively as GW calculations, for a lower computational cost.

In this work, we perform ab initio first principle calculations on the bulk Titanium structure. We study the electronic properties, comparing GGA and hybrid functionals and their effects on the band structure, band gap and charge distribution. We also present the bulk elastic properties and the Raman modes to investigate the stability criteria of Titanium. For the elastic properties, we compare and contrast with the properties of AT and O (Freysoldt C, 2014).

1.2                                       AIM OF THE STUDY

The main aim of this work is to carry out a study to determine the electronics properties of Titanium, oxygen, Strontium, calcium and lead.

1.3                                                   SCOPE OF THE STUDY

In this study, the electronic properties having been comparatively analysed using both the generalised gradient approximation and the hybrid functional method. Also the dielectric and elastic properties of the material are also obtained, with the bulk modulus being 131.73 GPa and the elastic moduli along the [1 0 0] and [0 0 1] directions being 180.57 GPa and 102.56 GPa, respectively.

1.4                             SIGNIFICANCE OF THE STUDY

This study will help to understand the potential for device applications, why these alkaline are used in capacitors, energy storage devices, phased array radar and random access memory.

1.5                                             LIMITATION OF THE STUDY

As we all know that no human effort to achieve a set of goals goes without difficulties, certain constraints were encountered in the course of carrying out this project and they are as follows:-

1. Difficulty in information collection: I found it too difficult in laying hands of useful information regarding this work and this course me to visit different libraries and internet for solution.
2. Financial Constraint: Insufficient fund tends to impede the efficiency of the researcher in sourcing for the relevant materials, literature or information and in the process of data collection (internet, questionnaire and interview).

• Time Constraint: The researcher will simultaneously engage in this study with other academic work. This consequently will cut down on the time devoted for the research work

1.6                                             RESEARCH METHODOLOGY

In the course of carrying this study, numerous sources were used which most of them are by visiting libraries, consulting journal and news papers and online research which Google was the major source that was used.

1.7                                     PROJECT ORGANISATION

The work is organized as follows: chapter one discuses the introductory part of the work,   chapter two presents the literature review of the study,  chapter three describes the methods applied, chapter four discusses the results of the work, chapter five summarizes the research outcomes and the recommendations.