Temperature and Frequency Dependence of Complex Permittivity in Metal Oxide Dielectrics: Theory, Modelling and Measurement (eBook)

My principal research interests lie in room-temperature maser, the measurement and modelling of the dielectric properties of microwave dielectric materials, the design of high Q-factor and Purcell-factor resonators and density functional calculations of materials. Other research areas are microwave filter design, photonic bandgap structures, metamaterials and the measurement of the electrical and magnetic properties of thin films at microwave frequencies. 

Supervisor’s Foreword 6
Abstract 8
Acknowledgements 9
Contents 10
List of Figures 13
List of Tables 17
1 Introduction 19
1.1 The Radio Revolution 19
1.2 Metal Oxide Microwave Dielectric Ceramics 21
1.3 Review of Dielectric Loss 22
1.4 Structure of Thesis 27
1.5 Publications by the Author 28
References 28
2 Modelling Dielectric Resonators 31
2.1 Introduction to Microwave Dielectrics 31
2.2 Measuring Microwave Dielectric Properties 33
2.3 Modelling Shielded Dielectric Resonators 34
2.4 Maxwell Equations in Cylindrical Coordinates 37
2.5 Multilayer Waveguide Eigenvalues 43
2.6 The Radial Mode Matching Method 49
2.7 Calculating Resonator Losses 54
2.8 Example Resonator 57
2.9 Summary and Conclusions 58
References 59
3 Measurement of Dielectric Properties 60
3.1 Dielectric Resonator Measurements 60
3.2 Calculating Dielectric Properties 63
3.3 Cryogenic Measurements 65
3.4 Characterisation of Ag-Plated Cavity 68
3.5 Characterisation of Single-Crystal Quartz Support 70
3.6 Magnesium Oxide --- MgO 71
3.7 Lanthanum Aluminate --- LaAlO3 73
3.8 Titanium Dioxide (Rutile) --- TiO2 76
3.9 Aluminium Oxide (Sapphire) --- Al2O3 79
3.10 Summary and Conclusions 82
References 82
4 Lattice Dynamics and Density Functional Perturbation Theory 85
4.1 Lattice Dynamics 86
4.2 Hamiltonian of a System of Ions and Electrons 87
4.3 The Born--Oppenheimer Approximation 87
4.4 Hellmann--Feynman Theorem 88
4.5 Hohenberg--Kohn Theorem 90
4.6 Kohn--Sham Orbitals 90
4.7 The Local Density Approximation 91
4.8 Linear Response DFT 92
4.9 Phonon Modes in Crystals 94
4.10 Long-Wavelength Phonons and Electric Fields 96
4.11 Implementation 99
4.12 The Lydanne-Sachs-Teller Relation 100
4.13 Summary and Conclusions 101
References 102
5 Harmonic Properties of Metal Oxide Dielectrics 103
5.1 Magnesium Oxide --- MgO 103
5.2 Lanthanum Aluminate --- LaAlO3 111
5.3 Titanium Dioxide (Rutile) --- TiO2 113
5.4 Aluminium Oxide (Sapphire) --- ?-Al2O3 120
5.5 Summary and Conclusions 123
References 124
6 Theory of Anharmonic Phonons 126
6.1 Beyond the Harmonic Approximation 127
6.2 Anharmonic Hamiltonian 128
6.3 Quantum Field Theory of Anharmonic Phonons 132
6.4 The Evolution Operator 135
6.5 Graphical Representation of Green Functions 137
6.6 Evaluating Matsubara Sums 137
6.7 The Self Energy, ? 138
6.7.1 Loop Interaction 139
6.7.2 Bubble Interaction 140
6.7.3 Higher Order Interactions 143
6.8 Dyson's Equation and Dressed Phonons 145
6.9 Summary and Conclusions 147
References 147
7 Anharmonic Properties of MgO 149
7.1 Introduction 149
7.2 Self-energy of Phonons 149
7.3 The Effect of Isotopes on Self-energy 152
7.4 Linear Coefficient of Thermal Expansion 153
7.5 Thermal Strain Contribution to Phonon Self-energy 157
7.6 Temperature Coefficient of Permittivity 158
7.7 Dielectric Loss 159
7.8 Phonon--Phonon Contribution to the Self-energy 160
7.9 Two-Phonon Density of States 162
7.10 Energy Conservation Surfaces 163
7.11 Weighted Two-Phonon Density of States 166
7.12 Anharmonic Phonon Coupling Tensors 167
7.13 The Relaxation Frequency, ? 169
7.13.1 Frequency Dependence 170
7.13.2 Temperature Dependence 173
7.14 Summary and Conclusions 176
References 176
8 Discussion and Conclusions 178