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Nanoantennas for Solar Energy Harvesting Nanoantennas for Solar Energy Harvesting Ahmed M A Sabaawi Newcastle University Newcastle upon Tyne, UK. A thesis submitted for the degree of Doctor of Philosophy June 2015 TO my beloved wife, Nadia AND my loving sons, Omar , Mohammed, Yousif and Ibrahim. Acknowledgements After the end of my four-year journey in PhD study, I must begin my ac- knowledgement with thanking the almighty Allah for giving me the strength and the courage to be what I am now. I am using this opportunity to express my sincere gratitude to many kind people around me who supported me throughout my PhD study. It would not have been possible to write this thesis without their help and support, to whom I would like to give particular mention here. First and foremost I wish to thank my first supervisor, Dr Charalampos Tsi- menidis, for his aspiring guidance and constructive criticism which paved my way during my study. From him, I received unlimited help and support and from him I learnt how to think positively and how to be a successful researcher. I would also like to show my greatest appreciation to my second supervisor, Prof Bayan Sharif, for his invaluable friendly advices on both aca- demic and personal level, for which I am extremely grateful. I am sincerely grateful to both of my supervisors for being supportive and helpful since the days I began working on my project. I express my warm thanks to my fellow postgraduate students at the school of Electrical and Electronics Engineering: Ibrahim, Sabah, Abdulrahman, Mohamad, Emad, Muayad, Salah, Sedki, Sangar and Oras for their endless support and for sharing their truthful and illuminating views on a number of issues related to the project. They provided me with a great academic and social atmosphere, which motivated me to do my best and to be as successful as they are. I would like to acknowledge the financial, academic and technical support of the Higher Committee of Education Development (HCED) in Iraq, particu- larly in the award of a fully-sponsored scholarship that provided the necessary financial support for this research. I would like to show my deepest apprecia- tion to the Ministry of Higher Education in Iraq and the University of Mosul for providing me with a study leave to get the degree of PhD from Newcastle University. I also thank the School of Electrical and Electronic Engineering for their assistance and support since my first day in the school, especially the kind Postgraduate Research Coordinator, Gillian Webber and the lovely Receptionist, Deborah Alexander. I owe a very important debt to my parents, brothers and sisters who have given me their endless love and support throughout. Without their encouragement, this thesis would not have been written. Last but not least, my heartfelt appreciation goes to my wife, Nadia, and my sons, Omar, Mohammed, Yousif and Ibrahim for their personal support and great patience at all times. From them I stole great moments and special days for the sake of study. They offered me all these sacrifices without showing any grievance. My lovely family has been a constant source of love, motivation and energy ever since, for which my mere expression of thanks likewise does not suffice. Abstract Recent years have witnessed an enormous interest in developing solar cells by utilising different materials to increase their efficiency. This interest was motivated by the rapid world demand on cheap and clean energy sources, where the main source of world’s power is the fossil fuels. The current pho- tovoltaics technology can not meet the solar power market due to the very low efficiency provided. The philosophy of this thesis is to find an efficient alternative by designing an efficient nanoantenna for receiving the solar radi- ation and coupling it to an integrated rectifier for AC to DC conversion. This thesis presents the design and optimisation of different types of nanoantennas with a performance comparison to find the optimum solution for this applica- tion. The figure of merit in choosing the best design was the captured electric field in the feed gap of the nanoantenna and the area under curve, which is essential in calculating the harvested energy. In addition, this thesis investi- gates the use of nanoarray instead of single elements. The aims is to increase the captured electric field at the gap of the array where all the elements will contribute in increasing the field in one common gap. Feeding lines will be employed to drive the captured fields from the centre of each single element towards the common gap. Another reason behind using nanoarrays is to re- duce the number of rectifiers by using one rectifier per array instead of one rectifier per single element, and hence increase the total efficiency. Futher- more, a simple analysis on dipole nanoantenna using method of moments (MoM) is presented in this thesis. The results obtained from this method is compared with those found from finite element method (FEM) simulations and an acceptable agreement is achieved. To calculate the total conversion efficiency of solar rectennas, it is important to compute the rectification ef- ficiency of the metal/insulator/metal (MIM) diode along with the coupling efficiency between the antenna and the diode. To this end, quantum mechan- ics was used to calculate the characteristics of the MIM diode. The results show that bowtie nanoantennas are the best candidate for this application in either the single and array form since they have wider bandwidth and larger area under curve. Additionally, the analysis using MoM gives the designer better understanding on how the system works and exhibits lower complexity and reduced computational requirements. Contents Nomenclature xviii Nomenclature xix 1 Introduction 1 1.1 Introduction................................. 2 1.2 HistoricalOverview............................. 3 1.3 WhySolarRectennas? ........................... 5 1.4 SolarRectennaStructureandTheoryofOperation . ...... 5 1.5 Contribution................................. 6 1.6 PublicationsArisingFromThisResearch . .... 7 1.7 ThesisOutline................................ 8 2 Background 10 2.1 ElectromagneticTheory. 11 2.1.1 Maxwell’sequations . 11 2.1.2 Boundaryconditions . 12 2.1.3 Waveequations........................... 14 2.2 ClassicalAntennaTheory. 15 2.2.1 Antennaradiation. 16 2.2.2 Reciprocitytheorem . 18 2.2.3 Near-andfar-fields. 19 2.3 Nanoantennas: FromRFtoOpticalFrequencies . ..... 21 2.3.1 Physicalpropertiesofnanonatennas . .. 23 2.3.2 Skindepthanddimensionscaling . 24 2.3.3 Surfaceplasmonresonance. 25 2.3.4 Input impedance, matching and loading of nanoantennas..... 25 vi CONTENTS 2.4 ChapterSummary.............................. 27 3 Numerical Electromagnetics 29 3.1 Introduction to Numerical Methods in Electromagnetics .......... 30 3.2 KeyElementsofNumericalAnalysis. .. 32 3.3 BasisFunctions ............................... 34 3.3.1 Pulsefunction ........................... 34 3.3.2 Triangularfunction. 35 3.3.3 Sinusoidalfunction. 36 3.4 Convergence, Stability and Accuracy of Numerical Solutions....... 37 3.5 MethodofMoments ............................ 40 3.6 FiniteElementMethod ........................... 44 3.7 FiniteDifferenceTimeDomainMethod . .. 48 3.7.1 Yee’scell .............................. 50 3.7.2 FDTDsolutionstability . 53 3.8 PerfectlyMatchedLayer . .. .. .. .. .. .. .. 54 3.9 HybridComputationalMethods . 55 3.10 ChapterSummary.............................. 55 4 Design and Optimisation of Nanoantennas for Solar Energy Harvesting 56 4.1 DesignConsiderations ........................... 57 4.1.1 Materialchoice........................... 58 4.1.2 Configuration............................ 59 4.1.3 Frequencyrangeandsourceexcitation. .. 60 4.1.4 Simulationmethodandboundaryconditions . .. 61 4.2 SimulationResults ............................. 64 4.2.1 Dipolenanoantenna . 67 4.2.2 Squarespiralnanoantenna . 70 4.2.3 Logarithmicspiralnanoantennas . 70 4.2.4 Bowtienanoantenna . 71 4.3 PolarisationResponse. 76 4.4 Increasing The Near-field Enhancement By Coupling More Antenna Ele- ments .................................... 77 4.4.1 Bowtienano-array . .. .. .. .. .. .. .. 80 vii CONTENTS 4.4.2 Squarespiralnano-array . 80 4.4.3 LogarithmicspiralNano-array . 82 4.5 Using Auxiliary Ring Resonator for Local Field Enhancement at The FeedGap .................................. 85 4.5.1 The effect of the distance between the ring and the dipole..... 88 4.5.2 Theeffectofthegeometricalshapeofthering . ... 90 4.6 ChapterSummary.............................. 92 5 Parametric Study of Nanogap-based Planar Bowtie Nanoarrays 95 5.1 BowtieNanoantennas............................ 96 5.2 BowtieNanoarray.............................. 99 5.2.1 Effectoffeedinglinesconfiguration . 100 5.2.2 Effectofelementsspacing . 104 5.2.3 Feedinglinewidtheffect . 105 5.2.4 Effectofgapsizeatthefeedingpoint . 106 5.3 OptimisedBowtieNanoarray . 107 5.4 Angle of Incidence Effect onThe Nanoarray Response . ...... 108 5.5 EffectofSharpEdgesofBowtiesandFeedingLines . .. .. 109 5.6 Integrating the Rectifier into theBowtieNanoarray . ........ 110 5.7 CharacteristicsoftheMIMDiode . 115 5.8 ChapterSummary.............................. 118 6 Analysis of Nanoantennas and the Efficiency of Solar Rectennas 121 6.1 IntegralEquationApproach. 122 6.2 CouplingTheIRWireAntennatotheMIMDiode. 131 6.3 SolarRectennaConversionEfficiency . 138 6.3.1 Antenna-dependentefficiency . 140 6.3.2 Diode-dependentefficiency . 141 6.3.3 Optimisationofthe diode-dependent efficiency . .. .. 146 6.4 The effect of using different metals on the left side of thediode
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