# Continuous flow microwave catalytic chain transfer polymerisation of methyl methacrylate oligomers

код для вставкиСкачатьCharacterization and Applications of Micro- and Nano- Ferrites at Microwave and Millimeter Waves A dissertation submitted by Liu Chao in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering Tufts University February 2016 Advisor: Dr. Mohammed N. Afsar ProQuest Number: 10013462 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest 10013462 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 ABSTRACT Ferrite materials are one of the most widely used magnetic materials in microwave and millimeter wave applications such as radar, wireless communication. They provide unique properties for microwave and millimeter wave devices especially non-reciprocal devices. Some ferrite materials with strong magnetocrystalline anisotropy fields can extend these applications to tens of GHz range while reducing the size, weight and cost. This thesis focuses on characterization of such ferrite materials as micro- and nano-powder and the fabrication of the devices. The ferrite materials with strong magnetocrystalline anisotropy field are metal/non-metal substituted iron oxides oriented in low crystal symmetry. The ferrite materials characterized in this thesis include M-type hexagonal ferrites such as barium ferrite (BaFe12O19), strontium ferrite (SrFe12O19), epsilon phase iron oxide (ε-Fe2O3), substituted epsilon phase iron oxide (ε-GaxFe2-xO3, ε-AlxFe2xO3). These ferrites exhibit great anisotropic magnetic fields. A transmission-reﬂection based in-waveguide technique that employs a vector network analyzer was used to determine the scattering parameters for each sample in the microwave bands (8.2–40 GHz). From the S-parameters, complex dielectric permittivity and complex magnetic permeability are evaluated by an improved algorithm. The millimeter wave measurement is based on a free space quasi-optical spectrometer. Initially precise transmittance spectra over a broad millimeter wave ii frequency range from 40 GHz to 120 GHz are acquired. Later the transmittance spectra are converted into complex permittivity and permeability spectra. These ferrite powder materials are further characterized by x-ray diffraction (XRD) to understand the crystalline structure relating to the strength and the shift of the ferromagnetic resonance affected by the particle size. A Y-junction circulator working in the 60 GHz frequency band is designed based on characterized M-type barium micro- and nano-ferrite. A new fabrication process using ferrite composite is proposed to integrate the Y-junction circulator into the semiconductor substrate. Theoretical design of a high gain Traveling Wave Tube (TWT) amplifier using a metamaterial (MTM) structure and cold-test of the MTM structure are also included in this dissertation. An SWS working around 6 GHz below the X-band waveguide TE10 cutoff frequency is fabricated. iii ACKNOWLEDGMENTS I want to thank my advisor, Professor Mohammed N. Afsar for his continuous guidance, encouragement and support during my graduate career. His ideas and advice have strongly motivated my research work in the electromagnetics and materials field. I am also thankful to my dissertation committee members, Professor Austin Napier, Professor Douglas Preis and Professor Nian Sun for their suggestions and support. I want to thank Dr. Jagadishwar Sirigiri for his guidance on my research of vacuum electronics devices. I am grateful to all my colleagues and friends most especially Dr. Konstantin A. Korolev and Dr. Anjali Sharma for their assistance with the instruments in the laboratory. Finally, I would like to thank my parents for their constant love. iv TABLE OF CONTENTS ABSTRACT ....................................................................................................................... ii ACKNOWLEDGMENTS................................................................................................. iv TABLE OF CONTENTS .................................................................................................. v LIST OF TABLES .......................................................................................................... viii LIST OF FIGURES.......................................................................................................... ix CHAPTER ONE: Introduction......................................................................................... 2 1.1 Crystal Structures of Ferrites ............................................................................... 2 1.1.1 Spinel Ferrites ................................................................................................. 2 1.1.2 Garnet Ferrites ................................................................................................ 4 1.1.3 Hexagonal Ferrites ......................................................................................... 7 1.2 Magnetic Properties ............................................................................................ 10 1.2.1 Demagnetizing Field .................................................................................... 11 1.2.2 Anisotropy Magnetic Field .......................................................................... 14 1.2.3 Remanence Magnetization ......................................................................... 16 1.3 Electromagnetic Properties ................................................................................ 17 1.4 Motivation.............................................................................................................. 22 1.5 Objective ............................................................................................................... 26 1.6 Outline ................................................................................................................... 28 CHAPTER TWO: Characterization Method ............................................................... 29 v 2.1 In-waveguide Method.......................................................................................... 29 2.1.1 Wave Propagation in Waveguide .............................................................. 30 2.1.2 Determination of Scattering Parameters .................................................. 34 2.1.3 Determination of Complex Permittivity and Permeability ....................... 37 2.2 Quasi-optical Method .......................................................................................... 47 CHAPTER THREE: Characterization Results ........................................................... 50 3.1 Barium and Strontium Hexaferrites .................................................................. 50 3.1.1 Quasi-optical Results ................................................................................... 50 3.1.2 Other Characterization Results .................................................................. 60 3.1.3 Characterization of Ferrite/Polymer Composite ...................................... 66 3.2 Epsilon Iron Oxide with Metal/Non-metal Substituted ................................... 77 3.2.1 Synthesis and Structure .............................................................................. 77 3.2.2 In-waveguide Results .................................................................................. 83 3.2.3 Quasi-optical Results ................................................................................... 84 CHAPTER FOUR: Hexaferrites Based In-Plane Y-Junction Circulator ................ 91 4.1 Design of In-plane Y-junction Circulator .......................................................... 92 4.2 Simulation of In-plane Y-junction Circulator .................................................... 98 4.3 Fabrication .......................................................................................................... 100 4.4 Discussion and Conclusion .............................................................................. 106 CHAPTER FIVE: Metamaterial Based Negative Refractive Index Traveling Wave Tube ............................................................................................................................... 107 vi 5.1 Background and Motivation ............................................................................. 107 5.2 Design and Simulation ...................................................................................... 109 5.3 Fabrication .......................................................................................................... 115 5.4 Experimental Results ........................................................................................ 117 5.5 Summary ............................................................................................................. 118 CHAPTER SIX: Conclusion and Future Work ......................................................... 120 APPENDIX I: List of Publications .............................................................................. 123 BIBLIOGRAPHY ........................................................................................................... 125 vii LIST OF TABLES Table 1. Waveguide Modes and Conditions .............................................................. 33 Table 2. Ferromagnetic Resonant Frequency and Anisotropic Field .................... 52 Table 3. Complex Permittivity and Resonant Frequency ........................................ 60 Table 4. Anisotropy Field and Saturation Magnetization ......................................... 60 Table 5. Magnetic Composites Preparation ............................................................... 67 Table 6. Ferromagnetic Resonance and Anisotropic Field ..................................... 71 Table 7. Properties of the Epsilon Gallium Iron Oxide Nano Powders .................. 84 Table 8. Magnetic Parameters of Barium Ferrite Powder ....................................... 98 Table 9. A Fabrication Recipe of The Circulator ..................................................... 105 viii LIST OF FIGURES Figure 1. a) Spinel unit cell structure, b) tetrahedral interstice or ‘A’ sites, and c) octahedral interstice or ‘B’ sites [2]. ...................................................................... 4 Figure 2. Schematic of an ‘‘octant’’ of a garnet crystal structure (lattice constant ‘‘a’’) showing only cation positions. RE represents rare earth [2]..................... 5 Figure 3. An ‘‘octant’’ of a garnet crystal structure (lattice constant ‘‘a’’) showing a trivalent ion of iron on a site surrounded by six oxygen ions in octahedral symmetry, a divalent ion of iron on a site surrounded by four oxygen ions in tetrahedral symmetry, and a rare-earth ion surrounded by 8 oxygen ions which form an 8-cornered 12-sided polyhedron. RE represents rare earth. [2] ..................................................................................................................................... 6 Figure 4. Chemical composition diagram showing how hexaferrite structures are derived from the spinel MeOFe2O3 structure. [2] ................................................ 7 Figure 5. The schematic structure of the hexaferrite BaFe12O19. The arrows on Fe ions represent the direction of spin polarization. 2a, 12k, and 4f2 are octahedral, 4f1 are tetrahedral, and 2b are hexahedral (trigonal bipyramidal) sites. [2]...................................................................................................................... 9 Figure 6. Demagnetizing field of a magnetic plate. .................................................. 12 Figure 7. The rectangular ferromagnetic prisms under investigation. The field H appl is along the z axis......................................................................................... 14 Figure 8. Magnetization with uniaxial crystal symmetry. .......................................... 14 Figure 9. Hysteresis loops of M-type barium hexaferrite powder. .......................... 16 ix Figure 10. Setup of in-waveguide measurement method. ....................................... 30 Figure 11. Electromagnetic waves transmitting through and reflected from a sample in a transmission line ............................................................................... 35 Figure 12. The powder sample is placed in the shim with thin tape on either side ................................................................................................................................... 42 Figure 13. A photograph of X-band waveguide......................................................... 42 Figure 14. Schematic diagram of nanoferrites in waveguide. ................................ 43 Figure 15. Propagating TE10 wave inside waveguide and the loaded material .. 45 Figure 16. Schematic diagram of the free-space quasi-optical millimeter-wave spectrometer in the transmittance mode with BWO as radiation source. ..... 48 Figure 17. The transmittance spectra of the four different size M-type barium ferrite powders. The grain sizes are 3-6 micrometer, 1-3 micrometer, 0.8-1 micrometer and 40-100 nanometer, respectively. ............................................ 53 Figure 18. The transmittance spectra of the two different size M-type strontium ferrite powders. The grain sizes are 3-6 micrometer and 40-100 nanometer, respectively. ............................................................................................................ 54 Figure 19. Real part of relative permeability of 4 BaM powders............................. 55 Figure 20. Imaginary part of relative permeability of 4 BaM powders. .................. 56 Figure 21. Real part of relative permeability of 2 SrM powders. ............................ 57 Figure 22. Imaginary part of relative permeability of 4 SaM powders. .................. 58 x Figure 23. Millimeter wave transmittance spectra of barium and strontium nanoferrites. Ferromagnetic resonance peaks are observed at 42.5 GHz and 48.2 GHz, respectively. ......................................................................................... 59 Figure 24. XRD spectra for SrFe12O19 nanoferrite and micro-ferrite...................... 61 Figure 25. XRD spectra for BaFe12O19 nanoferrite and microferrite. ..................... 62 Figure 26. SEM image of fine barium ferrite at 200 nm scale. The particle size is from 0.8 to 1 micrometer. ...................................................................................... 64 Figure 27. SEM image of fine barium ferrite at 1 um scale. The particle size is from 0.8 to 1 micrometer. ...................................................................................... 64 Figure 28. SEM image of fine barium ferrite with reduced magnification. The particle size is from 0.8 to 1 micrometer............................................................. 65 Figure 29. SEM image of coarse barium ferrite. The particle size is from 3 to 6 micrometer which is much larger than fine barium ferrite. ............................... 65 Figure 30. Ferrite rectangles were patterned from the ferrite photoresist composites by spin casting followed by photolithography. .............................. 68 Figure 31. Transmittance spectra of fine barium ferrite powder (0.8 to 1 micrometer) and its photoresist composite. ....................................................... 69 Figure 32. Transmittance spectra of coarse barium ferrite powder (3 to 6 micrometer) and its photoresist composite. ....................................................... 70 Figure 33. Real magnetic permeability of the coarse barium powder, and coarse barium photoresist composite. ............................................................................. 72 xi Figure 34. Imaginary magnetic permeability of the coarse barium powder, and coarse barium photoresist composite. ................................................................ 73 Figure 35. Real magnetic permeability of the fine barium powder, and fine barium photoresist composite. ............................................................................. 74 Figure 36. Imaginary magnetic permeability of the fine barium powder, and fine barium photoresist composite. ............................................................................. 75 Figure 37. Chemical synthesis procedure of ε-Fe2O3 using a combination of reverse-micelle and sol-gel techniques. ............................................................. 77 Figure 38. Crystal structure of orthorhombic unit cell of ε-Fe2O3. .......................... 79 Figure 39. Schematic illustration of the distribution of metal substitutions of εMxFe2-xO3 (M = Ga (x = 0.61) and degree of metal substitution at each Fe site (FeA-FeD). ......................................................................................................... 80 Figure 40. Magnetic properties of ε-GaxFe2-xO3 for (a) x =0.22, (b) x = 0.40, and (c) x = 0.61. Magnetization versus temperature curves (left) and magnetization versus external magnetic field plots at 300K (right). .............. 82 Figure 41. Complex dielectric permittivity and magnetic permeability of εGa0.22Fe1.78O3 nano-powder. The real part of dielectric permittivity Re(ep) is about 3.4. The density of the powder is 1.30 g/cm3......................................... 83 Figure 42. Complex dielectric permittivity and magnetic permeability of εGa0.29Fe1.71O3 nano-powder. The real part of dielectric permittivity Re(ep) is about 3.7. The density of the powder is 1.31 g/cm 3. ........................................ 84 xii Figure 43. Transmittance spectra of 2 mm thick ε-GaxFe2-xO3 with different gallium concentration. The black curve shows the transmittance of x = 0.22 which has ferromagnetic resonance at 113 GHz. The red curve shows the transmittance of x = 0.29 which has ferromagnetic resonance at 98 GHz. .. 85 Figure 44. Absorption spectra of 2 mm thick ε-GaxFe2-xO3 with different gallium concentration x = 0.29 and 0.22 in the range of 70–120 GHz. ....................... 86 Figure 45. Real part and imaginary part of complex magnetic permeability of εGaxFe2−xO3 for x = 0.29 and 0.22 by using Landau-Lifshitz theory. ............... 88 Figure 46. Real part of complex magnetic permeability μ’ of ε-GaxFe2−xO3 for x = 0.29 (black) and 0.22 (red). .................................................................................. 89 Figure 47. Imaginary part of complex magnetic permeability μ” of ε-GaxFe2−xO3 for x = 0.29 (black) and 0.22 (red). ...................................................................... 90 Figure 48. A circulator together with LNA and PA. The LNA and PA can transmit and receive simultaneously through the circulator which makes it very convenient when operating at millimeter wave frequency. .............................. 91 Figure 49. Top view of the circulator in the CST Microwave Studio. The ferrite disk has a radius of 0.68 mm. .............................................................................. 98 Figure 50. Calculated S-parameter as we want the circulator operating at 60 GHz with consideration of the dielectric loss in ferrite. S31 is the insertion loss. S21 is isolation, the 15 dB isolation bandwidth is 3 GHz, meanwhile, the insertion loss is smaller than 1 dB in the 15 dB isolation frequency range. .. 99 xiii Figure 51. Simulation result from CST Microwave Studio according to above parameters. This simulation of structure follows IBM 90 nm 9RF analog stack CMOS process. Dielectric loss in ferrite, conductor loss, substrate loss are all considered in this simulation. The 15 dB isolation bandwidth is 2.69 GHz and in this frequency range, the insertion loss is smaller than 1.45 dB.............................................................................................................................. 99 Figure 52. Microstrip line on common CMOS structure. Yellow parts show that top layer metal form transmission line with lower layer metal as ground plane and shield from the lossy substrate................................................................... 101 Figure 53. Transverse view of the CMOS structure. Ferrite film will be made between M1 and M2 layer. ................................................................................. 102 Figure 54. (a) SEM image of the surface morphology of a screen-printed BaM film after burnout and sintering procedures. (b) SEM cross section of the same film illustrating elongated grains oriented with their long axis parallel to the film plane. (c)Typical hysteresis loops for screen-printed films illustrating high loop squareness for the easy axis loop perpendicular to the film plane [68]. ......................................................................................................................... 104 Figure 55. A spin casting method for fabrication of circulator on the semiconductor substrate. The process follows a) etching to get the space for ferrite in the central resonator; b) spin casting of ferrite composite to fill the dielectric layer of central resonator; c) lift off or polishing of extra ferrite xiv composite; d) patterning the top layer of photoresist; e) top layer metal deposition; f) lift off or polishing of extra metal. ............................................... 105 Figure 56. The geometry of the electric resonant material. A rectangular hole is made at the center to allow the electron beam traveling through. ............... 110 Figure 57. Effective permittivity and permeability of the beam interaction mode. ................................................................................................................................. 111 Figure 58. The dispersion diagram of the periodic SWS. ..................................... 112 Figure 59. The phase velocity in the operating harmonic. .................................... 113 Figure 60. Simulation results of the S-parameters of the SWS. The peak of S21 at 5.7 GHz is the interaction mode desired. ..................................................... 113 Figure 61. The photograph of the various parts of the SWS................................. 115 Figure 62. Special input board for coupling the signal from a SMA input port. A similar board is also used to couple out the signal at the output port.......... 116 Figure 63. Fully assembled SWS with input and output SMA ports. .................. 116 Figure 64. Simulated S-parameters and experimental measurement results. ... 118 xv 1 Characterization and Applications of Micro- and Nano- Ferrites at Microwave and Millimeter Waves 2 CHAPTER ONE: Introduction A ferrite is a type of compound composed of iron oxide (Fe 2O3) combined chemically with one or more additional metallic elements. They are ferromagnetic as they can be magnetized or attracted to a magnet, and are electrically nonconductive. Since people found out such properties of ferrite materials, people have never stopped exploring the variety of applications in every aspect of human life. This thesis focuses on the microwave and millimeter wave characterization and device of micro- and nano-ferrite materials. 1.1 Crystal Structures of Ferrites Ferrimagnetic materials, or ferrites, are the most popular magnetic materials in microwave applications such as isolators, circulators and phase shifters. There are three practical types of ferrites: spinels, garnets and hexaferrites. 1.1.1 Spinel Ferrites Spinel ferrites are closely-packed cubic possessing the structure of the mineral spinel MgAl2O4, and with the general formula of MFe2O4. M is a divalent metal ion with an ionic radius of ~ 0.6 to 1Å such as Fe, Ni, Mn, Mg, Zn, Co etc, or a combination of ions with an average valence of two. The Fe ions are of the trivalent type Fe3+. The trivalent Fe3+ can be partially or completely replaced by another trivalent ion such as Al3+ or Cr3+, thus producing mixed crystals of aluminates and chromites which are also ferrimagnetic at room temperature if the non-magnetic ions are in small concentrations [1]. 3 The smallest three dimensional unit cell of the spinel lattice is shown in Figure 1a. It has a cubic symmetry with eight molecules of MFe2O4, with the relatively large oxygen ions forming a face-centered cubic structure. Cations occupy the interstices between the oxygen ions layers. Due to two different valence cations available two types of crystallographic sites ‘A’ and ‘B’ are formed. The ‘A’ sites are tetrahedral sites which surrounded by 4 nearest neighboring oxygen ions forming a tetrahedron with their connecting centers as shown in Figure 1b. The ‘B’ sites are octahedral sites surrounded by 6 nearest neighboring oxygen ions forming an octahedron as shown in Figure 1c. A unit cell contains 32 oxygen ions. There are 64 tetrahedral and 32 octahedral sites, of which only 8 and 16 respectively are occupied by cations. Spinel ferrites are the most widely used ferrites due to their high permeability and ease of magnetic property manipulation (e.g. saturation magnetization, magnetic anisotropy etc.). They find practical application in EMI suppression, RF devices (e.g. in antenna miniaturization, inductors). 4 Figure 1. a) Spinel unit cell structure, b) tetrahedral interstice or ‘A’ sites, and c) octahedral interstice or ‘B’ sites [2]. 1.1.2 Garnet Ferrites The general formula for garnet ferrites is 3M2O3·5Fe2O3, where M is a trivalent metal ion, usually rare earth such as nonmagnetic yttrium or magnetic. Yttrium garnet (YIG) is considered the most important magnetic garnet. Although yttrium is not a rare earth metal, as an accompanying element, it is included in the designation “rare earth” garnet [3]. Three different types of sites exist in the garnet structure. They are the (d) sites - tetrahedral, (a) sites - octahedral and (c) sites - 12-sided distorted polyhedral or dodecahedral. In a cubic unit cell containing 4 units of general 5 formula, there are 24 tetrahedral, 16 octahedral and 16 dodecahedral sites. The crystal structure of the garnet is quite complicated and thus difficult to adequately show a three dimensional diagram of all the 160 ions in the unit cell [2]. An octant of the garnet structure that illustrates the cation positions is shown in Figure 2 for simplicity. Figure 2. Schematic of an ‘‘octant’’ of a garnet crystal structure (lattice constant ‘‘a’’) showing only cation positions. RE represents rare earth [2]. The strength of the super exchange interactions between pairs of sublattices is mostly determined by the angles between magnetic ions. The moments of the Fe ions in the tetrahedral (d) sites are antiferromagnetically coupled to those on 6 the octahedral (a) sites by superexchange mechanism as the strongest interaction. The magnetic rare earth ions in the dodecahedral site (c) are antiferromagnetically coupled to the net moment of the Fe ions [1]. The coupling between the ions in the (c) site and the resultant Fe ions is much weaker than that between the Fe ions in the (a) and (d) sites. As a result, the magnetization of the rare earth ions drops very quickly with increasing temperature, approximately as 1/T. A more detailed crystal structure of an octant of the garnet ferrite exhibiting the octahedral, tetrahedral and dodecahedral symmetry is shown in Figure 3 [2]. Garnets, especially YIG, are mostly used for microwave devices. Figure 3. An ‘‘octant’’ of a garnet crystal structure (lattice constant ‘‘a’’) showing a trivalent ion of iron on a site surrounded by six oxygen ions in octahedral symmetry, a divalent ion of iron on a site surrounded by four oxygen ions in 7 tetrahedral symmetry, and a rare-earth ion surrounded by 8 oxygen ions which form an 8-cornered 12-sided polyhedron. RE represents rare earth. [2] 1.1.3 Hexagonal Ferrites Hexagonal ferrites has crystal structure similar to that of the mineral magnetoplumbite (PbFe7.5Mn3.5Al0.5Ti0.5O19), and with chemical composition MeO·xFe2O3, where Me is a divalent ion (e.g. Ba, Pb, Sr etc). Barium hexaferrite is the most common type of hexaferrite. Different types (M, W, Y, Z, U and X) are derived by its combination with the spinal ferrite structure shown in Figure 4 [2]. Figure 4. Chemical composition diagram showing how hexaferrite structures are derived from the spinel MeOFe2O3 structure. [2] The oxygen ions in hexaferrites are closely packed as spinel ferrites. They also contain the Me divalent ion which can replace these oxygen ions in the lattice since they have similar ionic radii. The crystal structure of M-type barium hexaferrite (BaO·6Fe2O3 or BaFe12O19) is shown in Figure 5 [2]. Its structure is 8 constructed from 4 building blocks S, S*, R, R*. S* is 180º rotated of S block along c-axis. S block are spinel with oxygen layers and six Fe3+ ions. R* is 180º rotated R* block which are hexagonal containing three oxygen layers with one oxygen ion replaced by a Ba2+ ion. The unit cell contains ten layers of oxygen atoms along the c axis. In total, the unit cell consists of 38 O2- ions, 2 Ba2+ ions and 24 Fe3+ ions. Fe3+ ions in octahedral (12k, 2a), and hexahedral (2b) sites (16 total per unit cell) have their electron spins up. The Fe3+ ions in octahedral (4f1) and tetrahedral (4f2) sites (8 total per unit cell) have their spins down, which results in a net total of 8 spins up. Therefore a molecular unit has total moment of 4 x 5 μB = 20 μB per Ba2+ ion [2]. Hexaferrites are used in microwave device applications that require low eddy current losses and millimeter wave devices requiring self-bias. 9 Figure 5. The schematic structure of the hexaferrite BaFe12O19. The arrows on Fe ions represent the direction of spin polarization. 2a, 12k, and 4f2 are octahedral, 4f1 are tetrahedral, and 2b are hexahedral (trigonal bipyramidal) sites. [2] 10 1.2 Magnetic Properties Although spinel ferrites exhibit a large static initial permeability, in the range of 10<μr<1000, its permeability at high frequencies drops down to one at around 2 GHz. Spinel ferrites are known as high relaxation loss materials, with typical ferrimagnetic loss (ΔH) in the order of 2-1000 Oe. Therefore, applications of spinel ferrites are usually limited to low frequencies. The garnet ferrites have many applications in RF and microwave devices in past 20 years. G. Menzer first studied the cubic crystal structure of garnet ferrites in 1928. The most famous garnet ferrite, yttrium iron garnet (Y3Fe5O12, or YIG), was first prepared by F. Bertaut and F. Forrat. YIG is a very low loss material at high frequencies. The FMR linewidth, ΔH, of YIG was measured to be ~ 0.2 Oe at 3 GHz. Many commercial magnetic microwave devices are made of YIG substrates. Hexagonal ferrites have a hexagonal crystal structure, which gives this type of ferrite many interesting characteristics. The hexaferrites have a large saturation magnetization (4πMs) and large magnetocrystalline uniaxial anisotropy field (HA). The large HA can help to bias the ferrite at high frequencies therefore the hexaferrites-based devices usually can operate from Ka up to Ku bands. The hexaferrites can be subcategorized into M-type (BaFe12O19), Y-type (Ba2Me2Fe12O22), Z-type (Ba3Me2Fe24O41), etc. M-type ferrites are usually used in junction circulators due to the fact that the easy axis of magnetization is along 11 the c-axis, whereas for Y-type and Z-type ferrites the plane of easy magnetization is perpendicular to the c-axis (within the basal plane). 1.2.1 Demagnetizing Field The demagnetizing field is a magnetic field due to the surface magnetic charges on the interface between the magnetic material and non-magnetic material. It tends to reduce the total magnetic moments inside the magnetic material and the internal magnetic field. As the ferrite applications in microwave and millimeter wave are usually in the film form, a thin magnetic plate is solved to get the demagnetizing field shown in Figure 6. The thickness of this plate, t, is assumed to be infinitely small. No DC magnetic field is applied, so all the magnetic field is generated by the surface magnetic charge. It is assumed that all the magnetic moment was aligned along the z direction. Due to Gauss' theorem, B is continuous on the surface, z=t. B0 Bi , (1) B0 H 0 , (4 Mair 0) , (2) Bi 4 M Hi , (3) therefore, H 0 4 M Hi . (4) On the two sides of the surface magnetic charge, the magnetic field is opposite in direction and equal in magnitude, 2Hi 4 M , (5) H i 2 M . (6) 12 Taking into account the contribution from the plane t=0, we can conclude H i 4 M with the direction along the z-axis. Therefore, the demagnetizing field of an infinite thin magnetic plate is equal to 4 M where M is the magnetization normal to the surface of the plate. In practical situations, the magnetization lies in the film plane in order to minimize the magnetostatic energy. Generation of surface charges on demagnetizing field implies generation of energy with which nature does not comply. Hence, this is an unstable magnetization configuration and, M, in this case would lie in the plane, representing a lower energetic state. Figure 6. Demagnetizing field of a magnetic plate. The formula to calculate the internal field is Hi H a NM , (7) where H a is the applied field, N is the magnetizing factor (in this case, N is equal to 4 ), M is the magnetization along the normal direction. If we are investigating a three dimensional object, as shown in Figure 7, the calculation of demagnetizing factor would be more complicated. A practical formula to calculate 13 the demagnetizing factor of a rectangular ferromagnetic prisms was given by Aharoni [4]. Dz b2, c / 2bc ln( a ,b a a ,b b a b b a ) a,2 c / 2ac ln( ) ln( ) ln( ) a b 2c a ,b a 2c a ,b b b ,c b a,c a c c ab a 3 b3 2c3 a 2 b 2 2c 2 ln( ) ln( ) 2 arctan( ) 2a b,c b 2b a,c a c 3abc 3abc 3a ,b b3,c 3c,a c ( a ,c b ,c ) ab 3abc , (8) Where a 2 b2 c 2 , a ,b a 2 b 2 , b ,c b 2 c 2 , a ,c a 2 c 2 , a , c a 2 c 2 , b , c b 2 c 2 . 14 Figure 7. The rectangular ferromagnetic prisms under investigation. The field H appl is along the z axis. 1.2.2 Anisotropy Magnetic Field The magnetic anisotropy energy implies that the magnetic potential energy depends on the direction of the magnetization. There are mainly three types: magnetocrystalline anisotropy, shape anisotropy (demagnetizing) and stress anisotropy magnetic energies. Magnetocrystalline anisotropy and shape anisotropy will be introduced in this part. Magnetocrystalline anisotropy energy Figure 8. Magnetization with uniaxial crystal symmetry. 15 The uniaxial magnetic anisotropy energy can be expressed as [5] Fu Ku sin 2 sin 2 . (9) If K u >0, Fu is minimum for M perpendicular to c-axis. If K u <0, Fu is minimum for M parallel to c-axis. The magnitude of the magnetic anisotropy field is derived as H k 2 Ku / M s , (10) where M s is the saturation magnetization. The cubic magnetic anisotropy energy can be expressed as FA k1 (12 22 2232 3212 ) , (11) where 1 sin 2 cos2 , 2 sin 2 sin 2 , and 3 cos2 . The maximum magnetic anisotropy field is given as H k 2K1 / M s for K1 >0, (12) and H k 4 K1 / 3M s , for K1 <0. (13) Shape anisotropy energy The demagnetizing field can be expressed in general as H D (N x M x a x N y M y a y N z M z a z ) . (14) The free energy from demagnetizing field can be derived from FD H D dM , (15) so that FD 1/ 2 (N x M2x N y M2y N z M2z ) . (16) 16 The total free energy can be expressed as FD 1 / 2 (N x M 2x N y M 2y N z M 2z ) M H 1 / 2M 2 (N x 1 N y 2 N z 3 ) MHsin cos . (17) Following the procedure in Chapter 5 of [5], the ferromagnetic resonance (FMR) can be derived from F F F2 , (18) M 2 sin 2 0 2 where 0 is obtained from the equilibrium condition F F 0. 1.2.3 Remanence Magnetization Figure 9. Hysteresis loops of M-type barium hexaferrite powder. 17 The remanence magnetization, M r , is the residue magnetization when the applied field is reduced to zero. The position of M r in a hysteresis loop is shown in Figure 9. The remanence magnetization is important to the self-biased junction circulator. 1.3 Electromagnetic Properties Permeability Assume that there is a magnetic dipole immersed in a static magnetic field along the z-axis. The equation of motion of the magnetic dipole moments can be derived as [6] dM 0 M H . (19) dt Assume the total magnetic field and total magnetization can be expressed as H t H 0 zˆ h M t M 0 zˆ m , (20) where H 0 is the applied bias field, M 0 is the DC magnetization, h is the applied AC field, and m is the AC magnetization caused by h . Substituting (1.2) into (1.1) gives the following equations dm 0 ( M 0 zˆ m) H 0 zˆ h , (21) dt 18 dmx dt 0 (m y (h z H 0 ) (m z M 0 ) h y ) dmy 0 ((m z M 0 ) h x m x (h z H 0 )) , (22) dt dmz dt 0 (m x h y m y h x ) assuming hz H 0 and mz M 0 , and ignoring m x h y and m y h x , the equation can be reduced to dmx dt 0 (m y H 0 M 0 h y ) dmy 0 (M 0 h x m x H 0 ) , (23) dt dmz dt 0 dmx dt 0 m y m h y dm y m h x 0 m x , (24) dt dmz dt 0 where 0 0 H 0 and m 0 M 0 . Taking the derivative over t on both sides of the first two equations in (24) gives the following equations dm y dh y d 2 mx m 2 0 dt dt dt , (25) 2 d m dh dm y x x dt 2 m dt 0 dt 19 dh y d 2 mx 2 0 (m h x 0 m x ) m dt dt , (26) 2 d my dh x ( m h ) m 0 0 y m y dt 2 dt dh y d 2 mx 2 2 0 m x 0m h x m dt dt , (27) 2 d my 2 m dh x h 0 y m 0 m y dt dt 2 Assuming h and m are e jt dependent, (27) reduces to 2 2 (0 ) m x 0m h x jm h y , (28) 2 2 ( ) m h j h y 0 m y m x 0 0m 2 2 mx 0 j0m my 2 2 m 0 z 0 xx m yx 0 xy yy 0 j0m 02 2 0m 02 2 0 0 hx 0 hy , (29) h 0 z 0 0 h , (30) 0 where xx yy 0m j and xy 2 0 m2 yx . 2 2 0 0 b and h are related by b 0 (m h) 0 (1 ) h j 0 j 0 0 0 h , (31) 0 20 where 0 (1 0m ) and 0 2 0 m 2 . 2 2 0 0 Wave propagation along the bias field direction Assume a plane wave propagates in an infinite magnetic medium along the bias direction, z axis. The plane wave has no distribution along x axis and y axis. The electromagnetic fields can be expressed as [6] ˆ x yE ˆ y ) e j z E (xE H (xˆ H x yˆ H y ) e j z . (32) Substituting (32) into Maxwell equations yields E j u H , (33) H j E xˆ x xˆ x xˆ x xˆ x ˆ x yE ˆ y ) j j yˆ zˆ (xE y z 0 yˆ j 0 0 Hx 0 H y 0 0 , (34) ˆ x yE ˆ y) zˆ (xˆ H x yˆ H y ) j (xE y z ˆ x yE ˆ y ) j (x( ˆ H x j H y ) y( ˆ j H x H y )) zˆ (xE y z (35) ˆ x yE ˆ y) yˆ zˆ (xˆ H x yˆ H y ) j (xE y z yˆ ˆ H x j H y ) y( ˆ j H x H y )) xˆ z E y yˆ z Ex j (x( , (36) xˆ H yˆ H j (xE ˆ x yE ˆ y) y x z z 21 z E y j ( H x j H y ) E j ( j H H ) x y z x , (37) H j E x z y H x j E y z j E y j ( H x j H y ) j Ex j ( j H x H y ) , (38) H E / y x H E / y x j E y j ( E y / j Ex / ) , (39) j Ex j ( j E y / E x / ) 2 2 2 Ex j ( ) E y 0 . (40) 2 2 2 ( ) E j E 0 x y For non-trivial solution, the determinant is set to zero. So ( ) , (41) which means there are two modes with different propagation constants for a plane electromagnetic wave propagating in the bias direction in an infinite magnetic material. This property is so important that it is the basis for many magnetic devices. Wave propagation transverse to bias field direction Assume the plane wave propagates along z direction, and the DC magnetic field is biased in x direction. We obtain, 22 j E y j0 H x j Ex j (j H z H y ) 0 j ( j H H ) y z , (42) H E / y x H E / y x 0 Ez 2 E y 2 0 E y . (43) 2 2 2 ( ) Ex Ex One solution is Ex=0, called ordinary wave with propagation constant same in both –z and +z direction, o 0 . (44) The other solution is Ey=0, called extraordinary wave with propagation constant as e e 2 2 . (45) 1.4 Motivation Several materials with desirable magnetic and dielectric properties have been developed for the high frequency applications. The class of materials consisting of oxides and semiconductors doped with transition metal elements or rare earth metals have been used for the design of devices in the microwave and millimeter wave frequency ranges. Oxides of iron have substantial technological value largely because they possess the combined properties of a magnetic material and an electric insulator. 23 Ferrites were initially used as magnetic cores. Over the years, ferrites have proved to be versatile magnetic materials since they are relatively inexpensive, stable and have a wide range of applications. Ferrite materials have been under intense research for several years due to their favorable electromagnetic properties [7]. They are in use in many industries such as automobile, telecommunication, data processing, electronics and instrumentation [8]. This can be attributed to suitable properties of ferrites such as high saturation magnetization and electrical resistivity, good chemical stability and low electrical losses. Ferrites have been used in information storage media such as magnetic tapes and floppy disks, in transformer cores and high frequency circuits [9]. More recently, ferrites are also used in millimeter wave ICs and power handling devices. Lower RF loss makes these materials useful in the design of microwave devices such as phase shifters. Resonant isolators can require up to 30-35 kOe magnetic fields, which require more space and increased cost. By utilizing the high internal anisotropy of hexaferrites, isolation levels of up to 20 dB can be achieved by using external field as small as 500 Oe [10]. Ferrites are also used as inductive components in low noise amplifiers, voltage-controlled oscillators and impedance matching networks [11]. The performance of these materials in their bulk form is limited up to a few megahertz due to their higher electrical conductivity and domain wall resonance [11]. However, the recent technological advances in the electronics industry demand ever more compact devices for work at higher frequencies [12, 13]. One 24 way to solve this problem is by synthesizing the ferrite particles in the nanometric scale. When the size of the magnetic particle is smaller than the critical size, the particle is in a single domain state, thus avoiding domain wall resonances. Such materials can work at higher frequencies. The recent developments in fabrication techniques have opened the possibility to manufacture ferrites in nano-scale domain. This has given way to new research areas and fields of application for the ferrites. Nanoferrites are ferrite compounds consisting of particles with the smallest dimension in the nanoscale region. These materials are of great interest since their dimensions approach that of an individual atom or molecule. As a result, the properties of nanoferrites are significantly different from those of the materials in bulk [14]. While bulk ferrites still remain important magnetic materials, the nanomaterials have emerged as strong candidates for electronics [15]. Circulators are the most widely used microwave components that rely on magnetic materials. They provide a convenient, and often essential, device for isolating different parts of an electromagnetic circuit from each other. Traditionally, circulators are passive non-reciprocal three port devices, in which microwave or radio frequency power entering any port is transmitted to the next port in rotation. Circulators can be used as a load isolator, duplexer, multiplexer, parametric amplifier and for a variety of other applications. Circulators are critical components in radar and communication systems [16], enabling the transmitter and receiver to share a common antenna, shape and steer the beam of phased 25 array radar systems. Thus, the front end can work at full duplex with a single antenna. The integrated ferrite circulator implemented in semiconductor technology can further reduce the device size, increase the power density and improve the data rate. Active quasi circulators fabricated in commercial semiconductor processes were designed for microwave and millimeter wave frequency range [17-19]. However, a ferrite based passive circulator has lower power consumption. To achieve a passive circulator in a semiconductor integrated circuit platform, microand nano-size hexaferrites are optimal. These materials exhibit uniaxial anisotropic fields with superior strength and the nanoscale size ensures that each grain forms a single magnetic domain, which may result in unidirectional ferrite layers without reduction of the anisotropic field. Most of the current ferrite devices use yttrium iron garnet (YIG) or doped YIG ferrites. These ferrites have low magnetization saturation and low effective magnetic anisotropy field, yielding a low ferromagnetic resonance frequency in the GHz range. The net effect is an upper limit on the practical operating frequency for compact structures that operate in the 10 - 18 GHz frequency range [20-22]. In principle, one can extend this frequency limit through the use of very high external fields. Such high fields would require the use of bulky, large area components with increased size and weight, which are not practical for monolithic integrated circuits. It is desired to combine monolithic microwave integrated circuits (MMIC) and digital circuitry fabricated on high frequency 26 semiconductor substrates to produce high performance, high efficiency, low weight, low cost, and small size modules. 1.5 Objective Several ferrite samples including M-type barium and strontium micro- and nano-ferrites, epsilon phase gallium substituted iron oxide are characterized in the microwave and millimeter wave frequency range. Two different measurement techniques are applied to characterize the ferrites from 8.2 GHz to 110 GHz. For the microwave measurements from 8.2 GHz to 40 GHz, an in-waveguide transmission reflection method is employed. A 2-port vector network analyzer together with waveguides was employed to determine the scattering parameters of the ferrites inside the waveguides for different frequency bands. From the Sparameters, complex permittivity and permeability are evaluated by an improved algorithm. For the millimeter wave measurement, a free space millimeter wave quasioptical spectroscopy technique has been successfully employed. This study presents dielectric and magnetic measurements in the millimeter wave range performed by the free space quasi-optical spectrometer in transmittance mode. High vacuum, high power backward wave oscillators (BWOs) have been applied as sources of coherent radiation continuously tunable in the range from 30 to 120GHz. A couple of pyramidal horn antennas and a set of polyethylene lenses along the propagation path from the source antenna to the receiver antenna have been adjusted to form a Gaussian beam as well as to focus the beam into the 27 sample. Transmittance spectra are recorded by this method. The permittivity and permeability data are derived from the transmittance spectra by modeling and curve fitting functions. Meanwhile, X-ray diffraction (XRD) and scanning electron microscopy are used to characterize the crystalline structures and the morphologies of the ferrites. Using the characterized low loss micro- and nano-size hexagonal ferrites materials [23, 24], such as barium and strontium ferrites, the upper limit operating frequency can be increased to more than tens of GHz without an increase in the external field, size and weight. The hexagonal ferrites have built-in high anisotropy fields and can remain in a stable magnetized state in the absence of an external bias field. The micro- and nano-size powders have a domain size close to a single magnetic domain. Thus, all particles remain unidirectional when a single layer may be fabricated and integrated with CMOS structures. In addition, the internal field can even be as strong as bulk materials, and therefore, can provide a self-biasing feature for millimeter wave applications in the 30 - 100 GHz range. The frequency can be further increased to over 100 GHz up to 200 GHz by employing ε-Fe2O3 materials [25]. On the basis of these micro- and nano-size hexagonal ferrites, reliable, small form factor, high performance circulators can be fabricated by employing post processing compatible with current CMOS processes. 28 1.6 Outline The first part of the thesis includes the introduction to the ferrites, crystal structures, electromagnetic properties of the ferrites, measurement techniques and the potential application as hexaferrite Y-junction circulator. The inwaveguide measurement technique for the microwave frequency range and the quasi-optical measurement technique for the millimeter wave frequency range are described in Chapter Two in detail. The measurement results from the measurement techniques on several different micro- and nano-ferrites are presented in Chapter Three. Chapter Four contains the design and possible implementation of these ferrites in novel millimeter wave devices. Chapter Five includes the design, simulation, fabrication and experimental cold test of the traveling wave tube with metamaterial structure. Finally, the summary of this work and the future scope are discussed in Chapter Six. 29 CHAPTER TWO: Characterization Method A transmission-reflection based in-waveguide technique that employs a vector network analyzer was used to determine the scattering parameters for each sample in two microwave bands (18 – 40 GHz). A free space quasi-optical spectrometer energized by backward wave oscillators was used to acquire the transmittance spectra in the millimeter wave frequency range (30- 120 GHz). 2.1 In-waveguide Method An in-waveguide transmission reflection (T/R) based waveguide technique was used to carry out the measurements. The T/R method is a category of nonresonant methods that are widely used for the measurements of electromagnetic properties of materials. In this method, the sample under test is inserted into a segment of transmission line, such as waveguide or coaxial line, which forms the two port network shown in Figure 10. The cables from the network analyzer are connected across this network. The Vector Network Analyzer records the sparameter values. Scattering equations are used to analyze the fields at the sample interfaces. These equations relate the s-parameters of the segment of transmission line filled with the sample under study to the permittivity and permeability of that sample. In T/R method, all the four s-parameters can be measured, so we have a record of more data than we have in reflection measurements. 30 Figure 10. Setup of in-waveguide measurement method. 2.1.1 Wave Propagation in Waveguide Waveguides are structures used to guide electromagnetic waves from point to point. Waveguides can be generally classified as either metal waveguides or dielectric waveguides. Metal waveguides normally take the form of an enclosed conducting metal pipe. The waves propagating inside the metal waveguide may be characterized by reflections from the conducting walls. The dielectric waveguide consists of dielectrics only and employs reflections from dielectric interfaces to propagate the electromagnetic wave along the waveguide. In the 31 measurement methods described in this section, hollow metal waveguides are employed. Given any time-harmonic source of electromagnetic radiation, the phasor electric and magnetic fields associated with the electromagnetic waves that propagate away from the source through a medium characterized by (in phasor form.) must satisfy the source-free Maxwell’s equations (in phasor form) given by E j H (46) H j E . (47) The source-free Maxwell’s equations can be manipulated into wave equations for the electric and magnetic fields. These wave equations are 2 E k 2 E 0 , (48) 2 H k 2 H 0 , k , (49) where the wavenumber k is real-valued for lossless media and complexvalued for lossy media. The electric and magnetic fields of a general wave propagating in the +z-direction through an arbitrary medium with a propagation constant of γ. are characterized by a z-dependence of e-γz. The electric and magnetic fields of the wave may be written in rectangular coordinates as E ( x, y, z ) Exy ( x, y)e z , (50) H ( x, y, z ) H xy ( x, y)e z , j , (51) where α is the wave attenuation constant and β is the wave phase constant. The propagation constant is purely imaginary (α = 0, γ = jβ) when the wave 32 travels without attenuation (no losses) or complex-valued when losses are present. By expanding the curl operator of the source free Maxwell’s equations in rectangular coordinates, we note that the derivatives of the transverse field components with respect to z are E y H y Ex H x E y , H y . H x , Ex , z z z z (52) If we equate the vector components on each side of the two Maxwell curl equations, we find j Ex H y H x H z H z H y , j E y ,(53) H x , j Ez y x x y j H x E E Ez E E y , j H y z Ex , j H z y x .(54) y x x y We may manipulate (53) and (54) to solve for the longitudinal field components in terms of the transverse field components. Ex H z H z 1 Ez 1 Ez j j , E y 2 , (55) 2 h x y h y x Hx E H z Ez H z 1 1 j z , H y 2 j . (56) 2 h y x h x y where the constant h is defined by h2 2 2 2 k 2 h2 k 2 . The equations for the transverse fields in terms of the longitudinal fields describe the different types of possible modes for guided and unguided waves. 33 Table 1. Waveguide Modes and Conditions Transverse electromagnetic Ez 0, H z 0 (TEM) Hollow waveguide does not support TEM mode Transverse electric Ez 0, H z 0 TE mode Ez 0, H z 0 TM mode Ez 0, H z 0 EH or HE mode (TE) Transverse magnetic (TM) Hybrid For simplicity, consider the case of guided or unguided waves propagating through an ideal (lossless) medium where k is real-valued. For TEM modes, the only way for the transverse fields to be non-zero with Ez 0, H z 0 is for h = 0. For the waveguide modes (TE, TM or hybrid modes), h cannot be zero since this would yield unbounded results for the transverse fields. Thus, the waveguide propagation constant can be written as h2 h h k k 1 2 jk 1 . (57) k k 2 2 2 2 The propagation constant of a wave in a waveguide (TE or TM waves) has very different characteristics than the propagation constant for a wave in TEM modes. The ratio of h/k in the waveguide mode propagation constant equation 34 can be written in terms of the cutoff frequency f c for the given waveguide mode as follows, f h h h h c , fc . k 2 f f 2 2.1.2 Determination of Scattering Parameters When a transmission line is terminated in a load, standing waves are generated inside the line. The amplitude and location of the maxima and minima in the slotted section depend on the load. The impedance is computed from the shift in null of the standing wave pattern inside the slotted section which is then used to compute the permittivity and permeability of the material. But characterization of the material becomes complicated when it shows dielectric and magnetic properties simultaneously. To characterize such materials like ferrites, one requires the measurement of four independent quantities and the complex reflection coefficient is then calculated from the scattering parameters. Consider the measurement configuration shown in Figure 2. The sample of length L is placed inside a transmission line. Port 1 and 2 represent the measurement ports for the VNA, whereas the actual measurements are desired at interfaces 1 and 2. To analyze the propagation of the incident wave, the whole setup is divided into three sections as shown in Figure 11. Thus region I consists of the wave incident at and reflected from material interface 1, region II corresponds to the wave travelling inside the material and region III consists of the transmitted wave. For simplicity, only one reflection has been shown. 35 Figure 11. Electromagnetic waves transmitting through and reflected from a sample in a transmission line Using electromagnetic theory, for a wave incident in region I we can write the expressions for the field in each section as [26]: EI C1 exp 0 x C2 exp 0 x EII C3 exp x C4 exp x (58) EIII C5 exp 0 x γ and γ0 are the propagation constants in the transmission line with and without the sample, respectively. These are evaluated as, j 2 r r c2 2 c 2 (59) 2 0 j c c 2 2 where ω is the angular frequency, c is the speed of light in vacuum and λ 0 is the cutoff wavelength of the transmission line. The constants C i mentioned in the 36 Equation (58) can be determined from the boundary conditions at the interface. The boundary condition on the electric field is the continuity of the tangential component at the interfaces: EI EII x L1 EI I x L1 EIII x L1 L (60) x L1 L where, L1 and L2 are the distances of the respective ports from the sample faces. The boundary condition on the magnetic field requires an additional assumption that no surface currents are generated so that the tangential component of magnetic field is continuous across the interface: 1 EI 0 x x L1 1 EII 0 r x x L1 . 1 EII 0 r x 1 EIII 0 x x L1 L (61) x L1 L These boundary conditions are applied to the electric field equations to find a solution for the s-parameters of the two-port network. Since the scattering matrix is symmetric, S12 = S21 and we have, S11 R 2 1 1 T 2 1 2T 2 S12 S21 R1 R2 S22 R22 1 T 2 1 2T 2 1 T 2 1 2T 2 (62) 37 where R1 and R2 are the reference plane transformations at the two ports, given by: Ri exp 0 Li . (63) The transmission (T) and reflection (R) coefficients are calculated using, T exp L , (64) 0 0 . (65) 0 0 0 Additionally, S21 for the empty sample holder is S21 R1R2 exp( 0 L) . So this approach gives us nine real equations for five unknowns in case of non-magnetic materials and seven unknowns in case of magnetic materials. Thus the system of equations is over determined and the equations can be solved in different ways. [27] 2.1.3 Determination of Complex Permittivity and Permeability Several algorithms have been developed for determining the permittivity and permeability of the sample by Nicolson, Ross [28], Weir [29] and James BakerJarvis [26]. These algorithms were further improved in the Millimeter and SubMillimeter Waves Laboratory at Tufts University to increase the accuracy of the measurements [30]. 38 Nicolson and Ross [28] combined the equations for S11 and S21 and derived explicit formulas for the calculation of permittivity and permeability. First, the reflection coefficient for the incident wave was calculated as: X X 2 1 , (66) where, X V1 S21 S11 V2 S21 S11 1 VV 1 2 V1 V2 . (67) The complex magnetic permeability and dielectric permittivity were then determined as: 1 1 c r ln 1 L T , (68) 1 c 1 r ln 1 L T where, L is the length of the sample and transmission coefficient, T V1 . 1 V1 Nicolson and Ross derived S21 and S11 for time domain measurements using a Fourier transform. This method had two major shortcomings. First, the determination of permeability and permittivity is band-limited, depending on the time response of the pulse and its repetition frequency. Secondly, in using a discrete Fourier transform, errors arise due to truncation and aliasing. Wier, [29] in 1974, presented an analogous method for determination of complex permeability and permittivity in the frequency domain for a wide range 39 from 100 MHz to 18 GHz. He formulated the formulas for complex permeability and permittivity as, 1 r 1 r 1 1 2 2 0 c 02 , (69) 1 1 2 2 c r 2 1 1 1 ln , 0 is the free space wavelength and c is the cutwith 2 2 L T off wavelength of the transmission line section. It should be noted here that Equation (24) has an infinite number of roots. This equation is ambiguous since the phase of the transmission coefficient remains unaffected if the sample length changes by a multiple of wavelength. To overcome this ambiguity, Weir introduced the use of group delay to accurately determine permeability and permittivity. Group delay through the material is strictly a function of the total length of the material. Therefore phase ambiguity can be resolved by finding a solution for permeability and permittivity from which a value of group delay is computed using, 1 g ,n d 1 2 L r 2 r 2 . (70) df 0 c n 40 The value of group delay thus computed is compared with the measured value of group delay, which is determined from the slope of the phase of the transmission coefficient ( ) versus frequency using the following equation, g 1 d . (71) 2 df The correct root should satisfy g ,n g 0 . Thus phase ambiguity at each frequency is resolved by matching the calculated and measured group delay. But this is not a very consistent method. In the measurements performed in this study, a phase unwrapping technique was used to resolve this phase ambiguity. Whenever the jump in the value of phase from one measurement frequency to the next is more than π, all the subsequent phases are shifted by 2π in the opposite direction. A drawback in the Nicolson-Ross-Weir algorithm was that in low loss materials at frequencies corresponding to integer multiples of half wavelengths, the solutions provided were observed to be divergent. At these frequencies, the scattering parameter |S11| becomes very small, making the equations algebraically unstable as S11 0. Since the solution is proportional to 1 , S11 the phase error dominates the solution at these frequencies. Many researchers use samples that have a length less than nλ/2 at the highest measurement frequency to resolve this issue. But the use of thin samples lowers the measurement sensitivity due to uncertainty in reference plane positions. James Baker-Jarvis proposed an iterative procedure for obtaining stable measurements. This 41 procedure minimizes the instability of the equations used by Nicolson-Ross-Weir and allows measurements to be taken on samples of arbitrary length. BakerJarvis used an iterative method on a set of equations to give a solution that is stable over the measurement spectrum. Sample length and air length are treated as unknowns in this system of equations. The solution is therefore independent of reference plane position, air line length and sample length. It was found that for cases where the sample length and reference plane positions are known to high accuracy, taking various linear combinations of the scattering equations and solving the equations in an iterative fashion yields a very stable solution on samples of arbitrary length. For example, one useful combination is, z 1 2 1 z 2 1 , (72) S12 S21 S11 S22 2 1 z 2 2 where, β varies as a function of sample length, uncertainty in s-parameter values and loss characteristics of material. For low loss materials, S 21 is large and β is zero whereas for high loss materials S 11 dominates, so large value of β is appropriate. In general, β is given by ratio of the uncertainty in S 21 to S11 uncertainty. The measurement was made using the Agilent 8510C vector network analyzer. The sample was placed inside the waveguide. TRL calibration was used in order to minimize the systematic errors in the measurement process. A MATLAB code was developed based on the following equations, and was used to derive complex permittivity and permeability. 42 Figure 12. The powder sample is placed in the shim with thin tape on either side Figure 13. A photograph of X-band waveguide. The powder sample was placed in the shim shown in Figure 12 and Figure 13. In order to hold the sample inside the shim, lossless thin tape was used around the shim. It has been shown that the inclusion of tape has negligible effect on the measured s-parameters. The transmission-reflection based waveguide technique has been widely used to determine the properties of solids. It can be further modified for the measurement of soft powders. The vector network analyzer measures the scattering parameters of the 2-port network formed by the waveguide shim filled 43 with the sample under study as shown in Figure 14. Figure 14. Schematic diagram of nanoferrites in waveguide. The nanopowders were filled in the sample holder that was placed between the waveguides. It is important to ensure that the sample fill the entire crosssection of the sample holder uniformly so that there are no air gaps at the corners of the shim or large air bubble between among the powders. The sample was packed tight enough such that changing the orientation of the shim does not cause any shift in the particles. The algorithm proposed by Baker-Jarvis was then used to derive the permittivity and permeability values from these data [26]. The phase unwrapping technique was employed to avoid the use of initial guess parameter [30]. Additionally, the cut-off frequency for each frequency band was calculated and set as the waveguide delay in the vector network analyzer to remove errors. In this waveguide measurement technique, the standard TRL calibration is used to position the reference planes. The reference planes were determined by the typical quarter wavelength difference ( l ) between the thru standard and the line standard (TRL standards). The recommended insertion phase ranging from 200 to 1600 is realized also through proper TRL calibration. In order for the insertion phase contributions from air to be removed from the actual transmission 44 line during the loaded material measurements, the target materials were loaded inside the waveguides adjacent to one reference plane. The modified S parameters are as follows: S11 S11e j 0 k02 kc 2 e S21 S21 j l d k02 kc 2 , (73) where l is the quarter wavelength difference between thru and line (in air), d is the thickness of the sample inside the waveguide, k0 is the wavenumber of the sample and kc is the cutoff wavenumber. These equations take into account the effect of using samples with thickness (d) values that are smaller than the waveguide shim used in the experimental setup. Return losses of less than -50 dB from the air inside the waveguide are easily achieved using these calibration techniques. This enables us to neglect any unwanted reflections from the inner walls of the waveguide when analyzing the S-parameters. The reflection and transmission by the scattering parameters inside the waveguide, in which the transmission and reflection resemble the free space formulation, can now be presented as follows: K K 2 1 ~ ~ S112 S 212 1 (74) K ~ 2 S11 ~ ~ S11 S 21 T ~ ~ 1 ( S11 S 21) 45 The transmission coefficient through the material may also be written as T e d e ( j ) d . The propagation constant through the material inside the waveguides has been derived to be: ln( TE 10 1 ) T d 2n T j d (75) Normally, a sample thickness of less than one quarter wavelength is desirable in this setup, because it will make n = 0. In order to achieve our goal and derive the complex permeability and permittivity for the loaded material inside the waveguide, we must determine the propagation constant through the material inside the waveguide. To achieve this, one must solve Maxwell’s equations with respect to Ey for the TE10 mode as shown in Figure 15. Figure 15. Propagating TE10 wave inside waveguide and the loaded material ( 2 )E y 0 , 2 2 x y where x x 1 and y y (76) 1 . Solving Maxwell’s equation yields: 46 E y C sin( x x) cos( y y) , (77) where C is a constant to be determined from the boundary conditions. The boundary condition tells us that the propagation constant components may be presented as follows: 2 0 0 x , n a , and y m b . This yields the following relationship for the propagation constant through the material inside the waveguide: 2 02 x2 y2 . The propagation constant of the TE10 is thus: 2 TE 10 1 1 0 j 2 j TE 10 0 2a 2 2 (78) 1 1 1 , 1 0 2a 2 0 TE 10 The complex permeability and permittivity associated with the propagation constant are then: 47 TE 0 j TE 10 10 Z 2 TE 1 ln( T ) j (2n T ) 1 1 , (79) j 2 2 1 2 d 1 1 0 2a 2 2 1 0 1 2 4a 2 0 . (80) In our waveguide measurement technique the propagating wave was assumed to be the TE10 mode for the measurement was done in TE10 mode. Permittivity is then calculated as follows: c j f 2 1 1 1 ln( ) j (2n T ) 1 2 d T 2 1 1 0 2a 2 . (81) The equations above are used to calculate the complex permeability and permittivity of samples inside the waveguide. It was also noticed that the permeability and permittivity of the loaded sample affect the cut-off frequency for the waveguide band. This was accounted for in the calculations by including the cut-off frequency for each band in the derivation of permeability and permittivity from the data for s-parameters. The divergence in data was eliminated by using the electrical delay function of the network analyzer. 2.2 Quasi-optical Method Free space millimeter wave quasi-optical spectroscopy technique, including technical details and measurement uncertainties analysis, has been successfully employed and presented by several researchers [31-34]. This study presents 48 complex dielectric and magnetic measurements at millimeter waves performed by the free space quasi-optical spectrometer in transmittance mode [33, 34]. Three high vacuum, high power backward wave oscillators (also called carcinotrons) (BWO) have been used as sources of coherent radiation continuously tunable in the range from 30 to 120 GHz. A couple of pyramidal horn antennas and a set of polyethylene lenses along the propagation path from the source antenna to the receiver antenna have been adjusted to form a Gaussian beam as well as to focus the beam into the sample. The diameter of the millimeter wave beam focused into the sample has been found to be around a few millimeters. The simplified schematic diagrams of the millimeter wave quasi-optical spectroscopic system are shown in Figure 16. BWO Modulator Isolator Set of lenses Horn Detector Sample Figure 16. Schematic diagram of the free-space quasi-optical millimeterwave spectrometer in the transmittance mode with BWO as radiation source. The mathematical relationships between transmittance and reflectance spectra, and refractive and absorption indexes are presented below, 49 1 R 4 R sin 2 , (81) T E 2 2 1 RE 4 RE sin 2 (n 1)2 k 2 R , (82) (n 1) 2 k 2 arctan ER sin 2 ( ) k k arctan 2 2 arctan , (83) 2 1 ER cos ( ) n k n n 1 E e4 kdf / c , (84) 2 ndf , (85) c n ik , (86) arctan 2k , (87) n k 2 1 2 where c is the speed of light, n is the refractive index of the sample material, k is the absorption index, μ is the complex magnetic permeability of the sample material, ε is the complex dielectric permittivity, T is the transmittance, R is the reflectance, φ is the phase of the transmitted wave, and ψ is the phase of reflected wave. 50 CHAPTER THREE: Characterization Results 3.1 Barium and Strontium Hexaferrites The free space magneto-optical approach has been employed successfully to study ferrites in millimeter wave frequency range [33]. This technique enables us to obtain precise transmission spectra to determine the dielectric and magnetic properties of both isotropic and anisotropic ferrites in the millimeter wave frequency range from a single set of direct measurements. The complex permittivity and permeability of the barium and strontium ferrite powders in broadband millimeter wave frequency range are shown. 3.1.1 Quasi-optical Results Several hexagonal BaM and SrM powders with different particle sizes were characterized to show the shift of ferromagnetic resonance. The characterization explores the potential relation of resonant frequencies, particle sizes and anisotropic magnetic fields inside the hexagonal ferrite powders. The particle sizes of the barium ferrite powders are located in several different size ranges. Four commercially available barium ferrite powders and two strontium ferrites were purchased from Advanced Ferrite Technology GmbH, Sigma-Aldrich Inc and BGRIMM MAGMAT with particle size 40 nanometer to 100 nanometer, 0.8 micrometer to 1 micrometer, 3 micrometer to 6 micrometer and 10 micrometer. The samples have been prepared by uniformly packing ferrite powders in specially fabricated transparent rectangular containers with thickness of 12 mm. Good surface parallelism of all ferrite samples has been achieved to ensure the 51 accuracy of the measurements. The different sized BaM powders and SrM powders were demonstrated by x-ray diffraction to have the same crystalline structure though with different particle size [35]. The transmittance spectra of BaM and SrM powder materials have been recorded in millimeter waves and are shown in Figure 17 and Figure 18. A zone of quite deep and relatively wide absorption in transmittance spectra has been observed for all the ferrite powders in this paper. This absorption is the natural ferromagnetic resonance that shifts to millimeter wave range due to the strong magnetic anisotropy of barium and strontium ferrites. For the smaller sized barium and strontium ferrite materials, relatively deep absorption in millimeter waves due to ferromagnetic resonance is also observed. But this resonance is at lower frequency comparing to larger particle size ferrite powders. Periodic structure observed in transmittance spectra in the frequencies range away from zone of deep absorption allows to calculate the complex dielectric permittivity values. The local maximum and minimum in the oscillation spectra are due to the multi reflections of the millimeter wave from the parallel surfaces of the ferrite powders in the sample holder. The two closest maxima and minima can determine the real part of complex refractive index. The decay of maximum and minimum can be curve fit to an exponential relation which indicates the imaginary part of the refractive index. The complex permittivity can be derived from the complex refractive index by assuming that the ferrite powders have permeability same as the vacuum in this frequency range. The saturation magnetization 52 (4πMs) and magnetic anisotropic field (HA) can be obtained by employing the complex dielectric permittivity and the transmittance pattern.[33] Table I shows observed peak positions of ferromagnetic resonance frequencies for BaM and SrM powders. For the calculation of complex magnetic permeability, Schlömann’s equation[36] for partially magnetized ferrites has been used: 1 3 1 2 2 ( H A 4 M s ) ( / ) , (88) 3 H A2 ( / ) 2 eff 2 2 where ω is the frequency, HA is anisotropy field, 4πMS is saturation magnetization, γ = 2.8 MHz/Oe is the gyromagnetic ratio. Demagnetizing factors are determined by the theory of Schlömann’s model for nonellipsoidal bodies. In the curve fitting process, the ferrite powders are treated by a cylinder model which shows better fitting results with demagnetizing factor equal to 2π. The complex permeability spectra are shown in Figure 19, 20, 21 and 22, respectively. Table 2. Ferromagnetic Resonant Frequency and Anisotropic Field Particle size Resonant frequency Anisotropic field HA fr(GHz) (kOe) BaM,3-6 micro 49.2 17.6 BaM,1-3 micro 49.0 17.5 BaM,0.8-1micro 46.3 16.5 BaM, 40-100 nano 42.5 15.2 SrM, 3-6 micro 53.1 19.0 SrM, 40-100 nano 48.15 17.2 53 Figure 17. The transmittance spectra of the four different size M-type barium ferrite powders. The grain sizes are 3-6 micrometer, 1-3 micrometer, 0.8-1 micrometer and 40-100 nanometer, respectively. 54 Figure 18. The transmittance spectra of the two different size M-type strontium ferrite powders. The grain sizes are 3-6 micrometer and 40-100 nanometer, respectively. 55 Figure 19. Real part of relative permeability of 4 BaM powders. 56 Figure 20. Imaginary part of relative permeability of 4 BaM powders. 57 Figure 21. Real part of relative permeability of 2 SrM powders. 58 Figure 22. Imaginary part of relative permeability of 4 SaM powders. Transmittance spectra of hexagonal barium (BaM) and strontium (SrM) nanoferrites measured by the quasi-optical technique are shown in Figure 23. A deep and sharp absorption in transmittance spectra has been observed for both barium and strontium nanoferrites in 40 – 60 GHz frequency range. This deep absorption is the natural ferromagnetic resonance that shifts to millimeter wave range due to the strong magnetic anisotropy of barium and strontium ferrites. The periodic structure observed in all transmittance spectra at the frequencies above the zone of deep absorption represents channel fringes. The analysis of channel fringes allows us to determine the complex dielectric permittivity value of 59 materials. Figure 23. Millimeter wave transmittance spectra of barium and strontium nanoferrites. Ferromagnetic resonance peaks are observed at 42.5 GHz and 48.2 GHz, respectively. Demagnetizing factors are determined by the theory of Schlömann’s model for nonellipsoidal bodies. The complex permittivity and permeability together with the center of the ferromagnetic resonance are shown in Table 3. 60 Table 3. Complex Permittivity and Resonant Frequency Chemical ε' ε'' Formula Resonant Theoretical Resonant frequency frequency BaFe12O19 1.88 0.01 42.5 GHz 48 GHz SrFe12O19 0.01 48.2 GHz 52.5 GHz 2.15 From the ferromagnetic resonance, the hexagonal barium and strontium nanoferrites show relatively strong anisotropy field of HA = 15.2 kOe and HA = 17.2 kOe and weak saturation magnetization of 4πMS = 0.07 kG and 4πMS = 0.12 kG, respectively. However, these anisotropy fields and saturation magnetization are smaller comparing to the solid barium and strontium ferrites which have anisotropy field of HA = 17.1 kOe and HA = 18.8 kOe, saturation magnetization of 4πMS = 0.37 kG and 4πMS = 0.38 kG, respectively. Comparison of anisotropy field and saturation magnetization between nano-sized and solid hexagonal ferrite is summarized in Table 4. Table 4. Anisotropy Field and Saturation Magnetization Ferrite Size Nano Solid Nano Solid SrM BaM BaM SrM HA (kOe) 15.2 17.1 17.2 18.8 4πMS (kG) 0.07 0.37 0.12 0.38 3.1.2 Other Characterization Results XRD Results To understand the weak saturation magnetization is straightforward because the nanoferrites are actually diluted by the air between each particle even though 61 the layer was compressed. The reduced anisotropy field is interesting for it is the intrinsic characteristic affected by the crystal structure. But the physical change of the powder size does affect the anisotropy field of these hexagonal ferrites. The X-ray diffraction was then performed on these nanoferrites and the diffraction pattern is compared to micro size barium and strontium ferrites in Figure 24 and Figure 25. Figure 24. XRD spectra for SrFe12O19 nanoferrite and micro-ferrite. 62 Figure 25. XRD spectra for BaFe12O19 nanoferrite and microferrite. The x-ray diffraction spectra show that both barium and strontium keep the same crystalline structure in micropowder and nanopowder particle size. This further demonstrates that the shifting of ferromagnetic resonance (towards lower frequency) and reduced anisotropy field are not caused by any crystal structure change. The micro size particle of the hexagonal ferrite has almost the same anisotropy field as the solid ferrite. This is due to the domain size of the hexagonal ferrite. The upper limit of single magnetic domain should have the size of about 100 nanometer. The nanoferrite powder with a physical dimension smaller than this single magnetic domain size will lead to a lower ferromagnetic resonance frequency. At the upper limit of single domain size, all of the particle’s internal magnetization is aligned to reduce the system energy to the lowest [37]. Therefore, at the upper 63 limit of single domain size, ferrite has the largest anisotropy field which is the sum of all magnetic moment in the particle. Below this physical upper limit of single domain size, the anisotropy field of the ferrite is determined by the volume of the particle until the dimension drops to a certain size. The spins of the magnetic moments will no longer be aligned without the application of an external magnetic field because of random thermal flips. As the powder dimension turns to even smaller size, the hexagonal ferrite is deduced to lose ferromagnetic resonance completely at room temperature. The size of barium and strontium nanoferrite powders measured in this paper is right between the upper limit of single domain size and the lower limit size of turning into superparamagnetism. SEM Results SEM images were taken on the coarse barium ferrite and fine barium ferrite from nanometer scale to micrometer scale. The results of fine barium ferrite powder at different scales are shown in Figure 26, 27 and 28. An image of coarse powder is shown in Figure 29. From the SEM images, the particle sizes follow the description from the manufacturer. 64 Figure 26. SEM image of fine barium ferrite at 200 nm scale. The particle size is from 0.8 to 1 micrometer. Figure 27. SEM image of fine barium ferrite at 1 um scale. The particle size is from 0.8 to 1 micrometer. 65 Figure 28. SEM image of fine barium ferrite with reduced magnification. The particle size is from 0.8 to 1 micrometer. Figure 29. SEM image of coarse barium ferrite. The particle size is from 3 to 6 micrometer which is much larger than fine barium ferrite. 66 3.1.3 Characterization of Ferrite/Polymer Composite A series of ferrite photoresist composites were made to achieve applications for printed circuit and integrated circuits in this work. Two barium ferrite powder material samples with different particle sizes were employed to make the composites. Different mixture ratios were chosen to allow for lithographic patterning of ferrite material in SU-8. The composites were spin cast onto silicon substrates, baked, exposed and subsequently removed to produce uniformly thick test structures. Unlike the traditional ferrite fabrication process in which mechanical polishing of macro-scaled pre-pressed and annealed ferrite blocks, this procedure utilizes low temperature processing of pre-annealed ferrite powders to generate 20-50 micrometer size ferrite composite materials for MEMS based component architectures. Thus this technique allows for a high frequency integrated circuit with magnetic components on-chip. Coarse and fine barium ferrite powders were mixed into SU-8 2000 series negative photoresist. The coarse powder has particle size from 3 to 6 micrometers and the fine powder has particle size from 0.8 to 1 micrometer. These commercially available anisotropic hard ferrite powder materials were obtained from BGRIMM MAGMAT (Beijing, China). Mixtures of SU-8 and ferrite materials were produced and photo lithographically patterned at the University of Alabama in Huntsville's Nano and Micro Devices Center. Composites of ferrite and negative photoresist were prepared from different percentages of photoresist and powder sizes. The fine barium ferrite powder was 67 mixed with SU-8 photoresist to ratio 1:1 by volume, which is equivalent at ratio 3:1 by mass. The coarse barium ferrite powder was mixed with SU-8 at ratio of 1:3 by volume, which is equivalent to 1:1 by mass. The percentage of ferrite and photoresist combinations is shown in Table 5. Table 5. Magnetic Composites Preparation Material Fine Barium Volume ferrite (BMS-3) 40 ml powder Comment Mixture stirred for 7 min. using nonmagnetic stirrer (Equivalent 3:1 mass SU-8 (Negative 2005) 40 ml ratio) Fine Ferrite (BMS-3) powder) 20 ml Mixture stirred for 7 min. using non- SU-8 (Negative 2005) 60 ml magnetic stirrer (Equivalent to 1:1 by mass) Coarse Barium Ferrite (BMS-3) 50 ml Mixture stirred for 10 min. using non- powder magnetic stirrer (Equivalent to 3:1 by SU-8 (Negative 2005) 50 ml mass) Ferrite (BMS-4 coarse powder) 20 ml Mixture stirred for 7 min. using non- SU-8 (Negative 2005) 60 ml magnetic stirrer (Equivalent to 1:1 by mass) All mixtures were stirred for 7 to 10 minutes using a non-magnetic stirrer to fully blend the components prior to spin casting and baking. It has been well established as indicated by Williams and Wang [38] that curing SU-8 has been extremely difﬁcult to strip and can therefore be used as a polymer material within the design of certain electronic and mechanical elements [39], a mega-sonic agitation process was adopted to develop [40] and remove the baked ferrite and SU-8 mixture. 68 The composites were then spin casted on the silicon wafer and followed by photolithography. Partially filled ferrite rectangles were patterned as shown in Figure 30. Figure 30. Ferrite rectangles were patterned from the ferrite photoresist composites by spin casting followed by photolithography. Transmittance spectra of the fine barium ferrite and its photoresist composite are shown in Figure 31. Transmittance for coarse barium powder and its photoresist composite is shown in Figure 32. The ferromagnetic resonant frequencies of coarse powder and its composite appear at the same range as the bulk hexagonal barium ferrite magnets. The resonant frequency of fine barium ferrite powder shows a shift to lower frequencies compared to resonance frequency for the coarse powder. This is expected due to the submicron particle size of the fine barium powder [24]. As the particle size reduces to comparable to single domain size, the thermal activation is becoming dominant and canceling out part of the magneto crystalline anisotropy [41]. The very fine ferrite particles 69 have relative large air gaps between each other which reduces the strength of interaction between separated particles. The fine powder composite behaves similar to the bulk hexagonal barium ferrite. Figure 31. Transmittance spectra of fine barium ferrite powder (0.8 to 1 micrometer) and its photoresist composite. 70 Figure 32. Transmittance spectra of coarse barium ferrite powder (3 to 6 micrometer) and its photoresist composite. The values of the strong uniaxial anisotropy (HA), saturation magnetization (4πMs) are acquired by employing the curve fitting method for ferrite with isotropic dielectric permittivity described in [33]. The ferromagnetic resonant frequencies and anisotropic magnetic fields are shown in Table 6. 71 Table 6. Ferromagnetic Resonance and Anisotropic Field Material FMR (GHz) Anisotropic field HA (kOe) Fine barium ferrite powder 46.3 16.5 Fine barium ferrite photoresist 49.2 17.6 composite Coarse barium ferrite powder Coarse barium 49.2 17.6 ferrite 49.3 17.6 photoresist composite The complex magnetic permeability can be derived from the transmittance spectra via Schlömann’s equation [36], 1 3 1 2 2 ( H A 4 M s ) ( / ) , (89) 3 H A2 ( / ) 2 eff 2 2 where ω is the angular frequency, HA is anisotropy field, 4πMS is saturation magnetization, γ is the gyromagnetic ratio. Demagnetizing factors are determined by the theory of Schlömann’s model for nonellipsoidal bodies. The real part and imaginary part of complex magnetic permeability of the powders and the magnetic photoresist composites are shown in Figure 33, 34, 35 and 36. 72 Figure 33. Real magnetic permeability of the coarse barium powder, and coarse barium photoresist composite. 73 Figure 34. Imaginary magnetic permeability of the coarse barium powder, and coarse barium photoresist composite. 74 Figure 35. Real magnetic permeability of the fine barium powder, and fine barium photoresist composite. 75 Figure 36. Imaginary magnetic permeability of the fine barium powder, and fine barium photoresist composite. The permeability spectra appear to be almost the same, although the transmittance spectra of coarse ferrite photoresist composite exhibit lower level compared to transmittance spectra for coarse barium powder. This is because the reflectance from the photoresist composite appears to be much higher than the one for the barium ferrite powder. The strength of ferromagnetic absorption of fine barium photoresist composite is higher than the fine barium powder. The ferromagnetic resonance frequency shifts back to 49.2 GHz which may be due to 76 the bonding effect from the photoresist between the fine barium powder particles. The existence of photoresist enhances the interaction between particles and prevents reduction of the crystalline anisotropy from thermal activation. Hexagonal barium ferrite magnetic composites were made with SU-8 photoresist which acts as a matrix material to be compatible with standard microelectronic fabrication processes. SEM and millimeter wave transmittance measurements were performed on the original barium powders and with their photoresist composites. The fine barium ferrite with 0.8 to 1 micrometer particles size exhibits ferromagnetic resonance at 46.3 GHz which is much lower than the resonance frequency position for the coarse barium powder with 3 to 6 micrometer particle size. The coarse powder and its photoresist composite have ferromagnetic resonance similar to bulk hexagonal barium ferrites. The composite of fine ferrite powder also shows higher ferromagnetic resonance frequency than the fine barium powder. The mixing of the photoresist with the fine powder shifts the ferromagnetic resonance from 46.3 GHz back to 49.2 GHz. Furthermore, these composites combine the high frequency anisotropic magnetic field sensitivity, with photolithographic fabrication capability. Thus Barium ferrite powders and their composites with SU-8 will be useful in a variety of high frequency applications especially in on-chip magnetic components for millimeter wave integrated circuits where classically machined and polished monolithic ferrite materials are too large to be incorporated. 77 3.2 Epsilon Iron Oxide with Metal/Non-metal Substituted 3.2.1 Synthesis and Structure The synthesis of single phase of ε- iron oxide (ε-Fe2O3) enables the development of magnetic materials which have natural ferromagnetic resonance from 50 to 200 GHz [42, 43]. Among the four polymorphs of α-, β-, γ-, ε-Fe2O3, the β- and ε- Fe2O3 are rare and must be synthesized in the laboratory [44]. Iron oxide/silica nanocomposites can be prepared by combining reverse (R)- micelle and sol-gel techniques as shown in Figure 37 [45]. Figure 37. Chemical synthesis procedure of ε-Fe2O3 using a combination of reverse-micelle and sol-gel techniques. The pure ε- Fe2O3 shows the largest coercive field value (Hc) of 20 kOe among metal oxide-based magnets at room temperature. The crystal structure is shown in Figure 38 [45]. Multiple factors contribute to the gigantic Hc in ε-Fe2O3. 78 One is that a large Hc value is expected when the particle size is sufficiently small to form a single magnetic domain [46]. A particle size of 100 nm in the material is suitable to realize a single magnetic domain. Another is the intrinsic magnetic property of the ε-Fe2O3 phase. The Hc value depends on the magnetocrystalline anisotropy constant (K) and saturated magnetization (Ms), i.e., Hc K/Ms [47]. Analysis of the initial magnetization process estimates the K value in the present material as 2–4 × 106 erg cm−3, which greatly exceeds the K values of γ-Fe2O3 (ca. 104 erg cm−3) and α-Fe2O3 (ca. 105 erg cm−3). The observed Ms value is small, 15 emu g−1 (15 A m2 kg−1) at 7.0 T. Therefore, it is concluded that the large Hc value of 20 kOe is due to (1) the suitable nanoscale size of particles that form a single magnetic domain and (2) the large K and small Ms values of ε-Fe2O3. Such high Hc is very attractive in millimeter applications. By employing a metal substitution method, the metal-substituted ε-iron oxide can exhibit an adjustable ferromagnetic resonant frequency at 35–182 GHz depending on the degree of metal substitution [48]. These nano-sized materials can be further made into composite material [49] and applied in millimeter wave devices such as phase shifter, isolator and circulator [50]. 79 Figure 38. Crystal structure of orthorhombic unit cell of ε-Fe2O3. 80 Figure 39. Schematic illustration of the distribution of metal substitutions of ε-MxFe2-xO3 (M = Ga (x = 0.61) and degree of metal substitution at each Fe site (FeA-FeD). The nano ferrite powders are pressed in a rectangular waveguide shim firmly for the in-waveguide transmission reflection measurement. An Agilent 8510C is 81 used to measure the scattering parameters in the microwave frequency range. Thru-reflect-line method is employed as the calibration process. For the quasioptical measurement, disc-shaped planar samples were made and placed between the poles of the magneto-static circuit which can provide a variable static magnetic field in excess of 7.5kOe (600,000 A/m). These specially prepared millimeter-wave nano-size absorber powders are composed of a series of ε-GaxFe2-xO3 nano ferrite. The material of this series has an orthorhombic crystal structure in the Pna2 1 space group which has our nonequivalent Fe sites (A–D), that is, the coordination geometries of the A–C sites are octahedral [FeO6] units and those of the D sites are tetrahedral [FeO4] units. Comparing with the indium–substituted ε-Fe2O3 having decreasing resonance frequency which is caused by the replacement of Fe3+ (S = 5/2) with nonmagnetic In3+ (S = 0) at B site contributing to the magnetic anisotropy [51], the gallium–substituted ε-Fe2O3 has C site and D site substituted by the Ga3+ ions where A site and B site are not affected. In the case of ε-Ga0.61Fe1.39O3, 92% of the FeD sites and 20% of the FeC sites are substituted by Ga3+ ions (Figure 39 [45]), but the FeA and FeB sites are not substituted. The field-cooled magnetization (FCM) curves in an external magnetic field of 10 Oe show that the Tc value monotonically decreases from 470 (x = 0.22) to 355K (x = 0.61) as x increases (Figure 40, left). Figure 40 (right) plots the magnetization vs. external magnetic field at 300 K. [45] The Hc value decreases from 11.6 (x = 0.22) to 4.7 kOe (x = 0.61). The saturation 82 magnetization (Ms) value at 90 kOe increases from 24.7 (x = 0.22) to 30.1 emu g1 (x = 0.40) and then decreases to 23.3 emu g-1 (x = 0.61). Figure 40. Magnetic properties of ε-GaxFe2-xO3 for (a) x =0.22, (b) x = 0.40, and (c) x = 0.61. Magnetization versus temperature curves (left) and magnetization versus external magnetic field plots at 300K (right). 83 3.2.2 In-waveguide Results 3.5 3 Re(mu) Im(mu) Re(ep) Im(ep) 2.5 Relative 2 1.5 1 0.5 0 -0.5 8.5 9 9.5 10 10.5 11 11.5 12 GHz Figure 41. Complex dielectric permittivity and magnetic permeability of εGa0.22Fe1.78O3 nano-powder. The real part of dielectric permittivity Re(ep) is about 3.4. The density of the powder is 1.30 g/cm3. The complex dielectric permittivity and magnetic permeability spectra of the nano ε-GaxFe2-xO3 powders are shown in Figure 41 and Figure 42. 84 4 3.5 Re(mu) Im(mu) Re(ep) Im(ep) 3 Relative 2.5 2 1.5 1 0.5 0 -0.5 8.5 9 9.5 10 10.5 11 11.5 12 GHz Figure 42. Complex dielectric permittivity and magnetic permeability of εGa0.29Fe1.71O3 nano-powder. The real part of dielectric permittivity Re(ep) is about 3.7. The density of the powder is 1.31 g/cm3. Table 7. Properties of the Epsilon Gallium Iron Oxide Nano Powders Ferromagnetic (GHz) resonance X-band Dielectric Permittivity ε-Ga0.29Fe1.71O3 98 3.7 ε-Ga0.22Fe1.78O3 113 3.4 3.2.3 Quasi-optical Results The EM absorption properties in W-band (75–110 GHz) of ε-GaxFe2−xO3 have been measured at room temperature using a free space EM wave 85 absorption measurement system. The powder-form samples are filled into the sample holder as described in Part III. The transmittance spectra have been obtained as shown in Figure 43. Figure 43. Transmittance spectra of 2 mm thick ε-GaxFe2-xO3 with different gallium concentration. The black curve shows the transmittance of x = 0.22 which has ferromagnetic resonance at 113 GHz. The red curve shows the transmittance of x = 0.29 which has ferromagnetic resonance at 98 GHz. The absorption spectra of ε-GaxFe2-xO3 ferrite materials with two x parameters have been recorded in millimeter waves and are shown in Figure 44. 86 The sample for x = 0.29 shows a strong absorption at 98 GHz. As x decreases, the frequency of the absorption peak shifts higher to 113 GHz (x = 0.22). As the x-value increases, the Hc of the material will decrease because the magnetic Fe3+ (S=5/2) ion is substituted by the nonmagnetic Ga3+ (3d10, S=0) ion. Figure 44. Absorption spectra of 2 mm thick ε-GaxFe2-xO3 with different gallium concentration x = 0.29 and 0.22 in the range of 70–120 GHz. As mentioned above, the fr value is proportional to Ha. When the sample consists of randomly oriented magnetic particles with a uniaxial magnetic anisotropy, the Ha value is proportional to the Hc value. 87 At the resonance frequency, the real and imaginary parts of the magnetic permeability (μ = μ' − jμ″) show a dispersive-shaped line and peak, respectively. To design millimeter wave absorbers, the magnetic permeability is important. On the basis of Landau–Lifshitz theory [52], the magnetic permeability at frequency of f is expressed as ' f M2 sin f cos f 1 40 H a M2 '' f sin 2 f 40 H a , (90) where M is the magnetization, μ0 is the vacuum magnetic permeability, ν is the gyromagnetic coefficient, Ha is the anisotropy field, and φ(f) is f tan 1 40 H a / M H a 2 f 1 . (91) μ'(f) shows dispersive-shaped lines around the fr, while μ″(f) shows absorption peaks at fr. The plot of permeability is shown in Figure 45. 88 1.8 Re(Mu),x=0.22 Im(Mu),x=0.22 Re(Mu),x=0.29 Im(Mu),x=0.29 1.6 Relative Permeability 1.4 1.2 1 0.8 0.6 0.4 0.2 0 90 95 100 105 Frequency (GHz) 110 115 120 Figure 45. Real part and imaginary part of complex magnetic permeability of ε-GaxFe2−xO3 for x = 0.29 and 0.22 by using Landau-Lifshitz theory. Figure 46 and Figure 47 show the derived complex magnetic permeability of ε-GaxFe2−xO3 by using Schlömann’s equation [36]. 89 Figure 46. Real part of complex magnetic permeability μ’ of ε-GaxFe2−xO3 for x = 0.29 (black) and 0.22 (red). The real part of the magnetic permeability displays dispersive-shaped lines at 98 GHz and 113 Hz for the ε-Ga0.29Fe1.71O3 and ε-Ga0.22Fe1.78O3, respectively. The μ″ values reach a maximum around 98 GHz and 113 GHz; μ″ max = 0.78 (98 GHz) and μ″max = 0.85 (113 GHz) which are expected as the ferromagnetic absorptions present. 90 Figure 47. Imaginary part of complex magnetic permeability μ” of εGaxFe2−xO3 for x = 0.29 (black) and 0.22 (red). 91 CHAPTER FOUR: Hexaferrites Based In-Plane Y-Junction Circulator Circulators are the most widely used microwave components that rely on magnetic materials. They provide a convenient, and often essential, device for isolating different parts of an electromagnetic circuit from each other. Traditionally, circulators are passive non-reciprocal three port devices, in which microwave or radio frequency power entering any port is transmitted to the next port in rotation. Upon this, circulators can be load isolation, duplexing, multiplexing, parametric amplifiers and other applications. Circulators are critical components in radar and communication systems. In the front end of RF circuits, the circulator is connected to the power amplifier, front-end low-noise amplifier (LNA) and antenna to enable the front-end to simultaneously transmit and receive RF signals as shown in Figure 48. Circulator Antenna Power Amplifier Low Noise Amplifier Figure 48. A circulator together with LNA and PA. The LNA and PA can transmit and receive simultaneously through the circulator which makes it very convenient when operating at millimeter wave frequency. Ferrite materials permit the control of electromagnetic propagation by a static or switchable dc magnetic field. The ferrite devices can be reciprocal or 92 nonreciprocal, linear or nonlinear, and their development requires knowledge of the ferromagnetic resonance behavior of the magnetic or ferrite materials, electromagnetic theory and related high frequency circuit theory. A ferrite is a magnetic dielectric that allows an electromagnetic wave to penetrate the ferrite, thereby permitting an interaction between wave and magnetization within the ferrite. 4.1 Design of In-plane Y-junction Circulator The underlying physical effects in current microwave magnetic devices mainly include Faraday rotation, ferromagnetic resonance (FMR), field displacement, and spin wave propagation [9, 53-56]. Whatever the basis for a given device, the operating frequency is determined essentially by the FMR frequency of the magnetic component. The FMR frequency, in turn, is determined mainly by the saturation induction (4πMs) and effective magnetic anisotropy field (Ha) of the materials, along with the external static magnetic field (H). For a magnetic film magnetized along an in-plane easy axis, for example, the FMR frequency is given by ( H H a )( H H a 4 M s ) , (92) where |γ| denotes the gyromagnetic ratio. Most of the current devices use yttrium iron garnet (YIG) or doped YIG ferrites. These ferrites are low 4πMs and low Ha materials and, therefore, generally have a low FMR frequency in the GHz range. The net effect is an upper limit on practical operating frequency for compact structures that lies in the 10-18 GHz frequency range. In principle, one 93 can extend this frequency limit through the use of very high external fields. In practice, however, the use of high fields is usually impractical because of the increased size and weight as well as incompatibility with monolithic integrated circuits technology. The appearance of low-loss hexagonal ferrites makes it perfect for usage in circulator design. The hexagonal ferrites have built-in anisotropy fields thus can provide a self-biasing for millimeter wave application in the 30-100 GHz frequency range. Recent simulations have demonstrated rather clearly the feasibility of hexagonal ferrite-based, stripline-type, mm-wave filters, phase shifters, and circulators [57] M-type BaFe12O19 (BaM) ferrite can be made into film with perpendicular anisotropy. The external bias field is substantially lower than the requisite field for a YIG-based filter. The external bias field may be further reduced if we make the BaM films with in-plane anisotropy though it has not been demonstrated in practice.[58] To design this junction circulator for compatibility with current CMOS fabrication processing, we may choose a disk or triangle geometric shape for the resonator structure. Though it is reported a triangle resonator has 17% less loss than a disc resonator operating at same frequency, considering the process of fabrication, a disk resonator is the better choice. Below is a summary of approximations and assumptions made in the preliminary design phase: [59-67] 94 1. The ferrites can be considered loss-less and magnetically saturated to avoid low field losses; 2. Fringing at the edges of striplines can be ignored; 3. The field intensities do not vary over the width of stripline conductors; 4. Striplines are purely in the TEM mode; 5. There is no z-coordinate variation of electromagnetic fields in the ferrites; 6. Coaxial center conductors are between two ferrites (the fields are the same on both sides of the conductor); 7. The electromagnetic fields fall off immediately at the ferrite and center conductor edges. We determine the characteristic impedance by using, Z0 60 eff ln 4b , (W/b<0.35 and t/b<0.25), W t 4 W t2 [1 (1 ln 0.51 2 )] 2 W t W (93) or Z 0 94.15 C 'f W /b ( ) eff 1 t / b 0.0885 eff where C 'f 0.0885 eff , (W/b>0.35), (94) 2 1 1 1 [ ln( 1) ( 1) ln( 1)] , t is 1 t / b 1 t / b 1 t / b (1 t / b) 2 the stripline thickness and b is the ground plane spacing(b = 2d for small t). 95 Now we continue the reflection coefficients and transmission coefficients in the scattering matrix describe the circulator junction. The key dimensions of the stripline center conductor, the width of the microstrip and ferrite disk are related by sin Zd W ( ) , (95) 2 R 1.84* 3Z ferrite where ψ is the angle of the edge where the stripline connected to the center conductor, W is the width of stripline and R is the radius of the ferrite disk. The propagation constant, (μ 2 μ κ 2 )sin 2 2μ [(μ 2 μ κ 2 ) 2 sin 4 4κ 2 cos 2 ]1/2 1/2 j ( 0 ) ( ) 2[(μ 1)sin 2 1] 1/2 , (96) can be reduced to j (0 )1/2 μeff 1/2 , (97) where μ eff μ2 κ 2 . μ A wave number is needed, k 2 2 0 0μeff . (98) The solutions of the electromagnetic field equations involve the Bessel function of the Nth order. For most practical circulators, N = 1 and for resonance we have J1' (kR) 0 , where J denotes the Bessel function, k is the wave number, and R is the ferrite disk radius. We can evaluate this equation and find kR = 1.84. This equation is valid when the ferrites are not magnetized, that is when the rotating modes are degenerate. Because the resonance frequency from this 96 equation is between the two resonance frequencies for the two counter-rotating modes when the disks are magnetized, it is an approximation of the operating frequency of the circulator. Then we get R 1.84 , (99) 2 μ eff where ε is the relative dielectric constant of the ferrite material. We can obtain a simpler expression for μeff to assume ω02 >> ω2, because the ferrites are biased far above resonance and ω02 >> α2 because the resonance losses need not be considered, and by manipulation of the following equations for μ and κ, M 00 (02 2 ) M 00 (02 2 ) μ 1 2 , μ 2 , (0 2 )2 402 2 2 (0 2 )2 402 2 2 2 M 00 2 M 00 (02 2 ) κ , , (02 2 )2 402 2 2 (02 2 )2 402 2 2 κ μ eff μ (100) H dc M 0 M , κ 20 . H dc H dc The imaginary components of μ and κ do not need to be considered because the ferrites are biased away from low field loss area. Substituting μ eff μ H dc M 0 we arrive at an expression for the ferrite disk radius as a H dc , function of wavelength, ferrite saturation magnetization, dielectric constant and applied magnetic field: R 1.84 2 H dc . (101) H dc 4 M s 97 We also have restrictions on stripline width to maintain the magnetic field in the ferrite as high as possible, a desired operating point for above-resonance circulators: W 30 , W 0.75R , However we should not make it too small, because losses and large stray fields will result. The circulator bandwidth is f 2 f1 κ 2.90 , (101) f0 μ where ρ is the maximum voltage reflection coefficient in the band, related to the circulator VSWR Z Z 0 jZ 0 1 . And the circulator input impedance is defined as 1 1.38 f f 0 , (102) κ f0 μ where f is the frequency where the impedance is to be evaluated and Z 0 is the stripline characteristic impedance. This impedance behaves like a parallel resonant circuit: inductive for f < f 0 and capacitive for f > f0.There are also other approximations in practical, and we can solve them by experience. 98 4.2 Simulation of In-plane Y-junction Circulator Assume we want to make a circulator working at operating frequency ω = 60 GHz. We choose micro-sized BaFe12O19 powder as the ferrite material. Magnetic parameters are list in the Table 8 below. Table 8. Magnetic Parameters of Barium Ferrite Powder Ferrite Material BaFe12O19 Ferrite ε' 4.41 4πMs 0.7 kG Ferrite ε'' 0.029 Anisotropy Ha 17.6 kOe Loss Tangent 0.0066 Ferrite Density 2.13 g/cm3 Resonant Frequency 49.2 GHz Knowing theabove parameters, we can derive the radius of the ferrite disk and the microstrip junction. Also the insertion loss and isolation can be given out. Figure 49. Top view of the circulator in the CST Microwave Studio. The ferrite disk has a radius of 0.68 mm. 99 Figure 50. Calculated S-parameter as we want the circulator operating at 60 GHz with consideration of the dielectric loss in ferrite. S31 is the insertion loss. S21 is isolation, the 15 dB isolation bandwidth is 3 GHz, meanwhile, the insertion loss is smaller than 1 dB in the 15 dB isolation frequency range. Figure 51. Simulation result from CST Microwave Studio according to above parameters. This simulation of structure follows IBM 90 nm 9RF 100 analog stack CMOS process. Dielectric loss in ferrite, conductor loss, substrate loss are all considered in this simulation. The 15 dB isolation bandwidth is 2.69 GHz and in this frequency range, the insertion loss is smaller than 1.45 dB. The calculated result shown in Figure 50 and simulated result shown in Figure 51 match each other very well which shows us the circulator can work on CMOS substrate very well. The power handling capability is pretty high for a circulator. In another word, the threshold of powder in circulator on CMOS is much higher than the need of surrounding CMOS circuits. And circulators have inherently good electromagnetic (radio frequency interference (RFI) and electromagnetic interference (EMI)) shielding. Leakage on the order of 30 dB is typical, and 80-100 dB is possible if special attention is given to the reduction of radiation. The reliability of circulators is quite high. 4.3 Fabrication The substrate and microstrip part of our design will be fabricated by commercial standard CMOS process which makes it compatible with both the practical and the most advanced process. The circulator structure will occupy top two metal layers. 101 Figure 52. Microstrip line on common CMOS structure. Yellow parts show that top layer metal form transmission line with lower layer metal as ground plane and shield from the lossy substrate. Several challenges are there when we make ferrite thin film on CMOS substrate: 1. Thickness must be fit for the fixed layer in CMOS. 2. The ferrite must be self-biased or at least have high remnant magnetization. 3. Low ferromagnetic resonance (FMR) line width should be obtained to reduce loss. 4. The high limit of temperature and pressure that a CMOS substrate can withstand. There are methods called pulsed laser deposition (PLD) and liquid phase epitaxy (LPE) being used to produce ferrite films for microwave devices over the past several years. PLD is limited for it can only make a few microns thick film with pretty low grow rate and low remnant magnetization. LPE films exhibit low microwave loss but small remnant magnetization. So they are not suitable for self-biasing ferrite applications. Considering the above challenges and situations, a new screen printing technology is employed to produce self-biased ferrite film from micro- and nanosize ferrite powders. In the modern electronics industry, this technique is usually applied in producing thick-film circuits and sensors. It is demonstrated that 102 screen printing is a technique capable of processing thick, self-biased, low-loss BaM films [68]. Remarkably, this technique has not been extended to fabricate textured ferrite films on CMOS for microwave and millimeter wave applications. In this technique, pure phase micro- or nano-size Ba-hexaferrite powders are mixed with a binder to form a suitable paste for printing. Figure 53. Transverse view of the CMOS structure. Ferrite film will be made between M1 and M2 layer. Micro- or nano-size ferrite powders are mixed with a binder and then placed in the space there. Then a blade moves across the surface to make the surface flat and remove extra mixture. This wet film will be heated to150~250 °C from 1 minute to 20 minutes to volatilize the binder with an external magnetic field ~1T perpendicular to the film plane to organize all the micro- and nano-size ferrite particles. Particles with such small size will be rearranged easily with easy axis perpendicular to the plane and have a large remnant magnetization. However, there is an optional further pressure sintering step which can increase the density of the film more. This procedure heats the film up to 900~1300 °C and presses the film with load 1 to 10 MPa for recrystallization and sintering. Figures 54 (a) and 54 (b) are SEM images of a screen-printed film surface morphology and cross section after the films were sintered, respectively. 103 Prior to sintering, micron-sized particles were loosely arranged with the film having very high porosity (~50%). After the sintering process, the film had a closely packed polycrystalline structure in which hexagonal grains range in size from ~1 to 10 μm with porosity levels of 13–15% as shown in Fig. 54(a). Shown in Figure 54(b) is the structure of the film revealed to contain elongated grains with the long axis parallel to the film plane. Some pores remain visible. XRD analysis of this sample displayed (0, 0, 2n) reflections having enhanced intensity consistent with c-axis texture perpendicular to the film plane. Shown in Figure 54(c) are hysteresis loops that display the characteristic perpendicular magnetic anisotropy. In comparison to the PLD and LPE films, these films have higher coercivity but also very high hysteresis loop squareness (~0.95), providing these thick films with self-bias properties. FMR linewidths less than 210 Oe have been measured. Although large compared with PLD and LPE films, these values are small compared with polycrystalline compacts (typically >2000 Oe) and acceptable for many MMIC applications [68]. 104 Figure 54. (a) SEM image of the surface morphology of a screen-printed BaM film after burnout and sintering procedures. (b) SEM cross section of the same film illustrating elongated grains oriented with their long axis parallel to the film plane. (c)Typical hysteresis loops for screen-printed films illustrating high loop squareness for the easy axis loop perpendicular to the film plane [68]. A spin casting method can be employed on a silicon or gallium nitride wafer to achieve the effect similar as screen printing. A diagram of the spin casting method is shown in Figure 55. The spin casting method can be modified slightly by using other film deposition methods such as pulsed laser deposition or liquid phase epitaxy. The lift off process can be substituted by polishing process. A practical recipe is shown in Table 9. 105 Figure 55. A spin casting method for fabrication of circulator on the semiconductor substrate. The process follows a) etching to get the space for ferrite in the central resonator; b) spin casting of ferrite composite to fill the dielectric layer of central resonator; c) lift off or polishing of extra ferrite composite; d) patterning the top layer of photoresist; e) top layer metal deposition; f) lift off or polishing of extra metal. Table 9. A Fabrication Recipe of The Circulator Step 1. 2. 3. 4. Cleaning Metallization Dielectric layer Photolithography-1 5. 6. 7. 8. Etch Oxide Strip Clean Photolithography-2 9. Clean 10. Electroplate Description Ultrasonic cleaner Deposit 20 nm Titanium and 480nm gold Deposit 4um SiO2 Spin cast resist, prebake, expose mask 1 (transparent at via and central pad), develop, postbake Silicon dioxide etching Strip photoresist O2 cleaning after stripping Spin cast resist, prebake, expose mask 2 (transparent at via), develop, postbake O2 cleaning after develop Carefully control thickness by periodically 106 11. Strip 12. Photolithography-3 13. Metal 14. Liftoff 15. Spin-coating 16. Liftoff 17. Metal measure it under interferometer Strip photoresist Spin cast resist, prebake, expose mask 3 (opaque central pad), develop, postbake Deposit 460nm aluminum* Liftoff resist (and aluminum upon it) Spin ferrite and photoresist, add magnets and bake (or annealing) Liftoff aluminum (and ferrite upon it) Deposit 20nm titanium and 480nm gold using shadow mask (signal pad and transmission line) 4.4 Discussion and Conclusion A hexagonal ferrite with strong magnetic anisotropic field based circulator was successfully designed. The fabrication processing shows great potential on on-chip magnetic devices. The ferrite circulator exhibits the capability of integration with a semiconductor fabrication process with simple post processing. The gallium nitride semiconductor wafer is especially suitable as the gallium nitride devices have great performance in millimeter wave frequency range, meanwhile, the gallium nitride substrate can stand high temperature up to a thousand degrees Celsius. At this temperature, the ferrite can anneal to acquire better magnetic domain alignment and small linewidth. The integrated ferrite circulator enables the front end to share an antenna with full duplex mode. Comparing with traditional YIG based circulators, the hexagonal ferrite circulator exhibits many advantages such as absence of external magnetic field, self-biasing, compact size and easy integration in the millimeter wave frequency range. 107 CHAPTER FIVE: Metamaterial Based Negative Refractive Index Traveling Wave Tube The theoretical design of a high gain Traveling Wave Tube (TWT) amplifier using a metamaterial (MTM) structure and cold-test of the MTM structure are presented in this chapter. MTM structures have unique properties such as high effective permittivity and permeability which can be harnessed in a slow-wave structure (SWS) for enabling strong interaction with an electron beam to produce signal gain. The frequency selective properties of the MTM structure provide an interesting option to suppress parasitic oscillations usually encountered in a high gain amplifier. A rectangular waveguide loaded with a uniaxial electric MTM is employed in transverse magnetic mode to provide effective negative permeability and strong axial electric field. An SWS working around 6 GHz below the X-band waveguide TE10 cutoff frequency is fabricated. The experimental results of the cold-test of the SWS and particle-in-cell simulation results of the device showing the gain and output characteristics are presented. 5.1 Background and Motivation The traveling wave tube (TWT) is an important device for high power microwave and millimeter wave amplification for applications in communications and radar. The signal gain in a TWT is obtained by synchronizing the electromagnetic wave with an electron beam. Such synchronization requires the wave to be sub-luminous in the direction of the electron beam propagation and 108 this is achieved in a slow wave structure (SWS). This leads to conversion of the kinetic energy of the beam into microwave energy leading to signal amplification. An SWS can be implemented as a folded waveguide or a coupled cavity circuit [69-71]. By employing an artificial MTM with high values of negative dielectric permittivity and negative magnetic permeability [72], the phase velocity of the electromagnetic wave can be reduced to achieve beam wave synchronization. . In an SWS for a TWT, the wave has to have a strong electric field component in the direction of the electron beam propagation for velocity modulation of the electron beam [73]. In a conventional hollow waveguide, the phase velocity is always greater than speed of light which prevents the beamwave synchronization. A possible way to reduce the wave velocity is to fill the hollow waveguide with positive permittivity dielectric material and make a hole for the beam to travel through [74]. Though such a design can be used to slow down the phase velocity of the wave, the charging of the dielectric due to the electron beam will interfere with beam propagation. An alternative approach to creating an SWS is to load the waveguide with a MTM material to achieve the necessary reduction in the wave velocity. An all metallic complementary split-ring resonator with negative refractive index has been proposed by others for application in vacuum electron devices and accelerators [75]. However, it requires very high beam velocity and the coupling to the electron beam is very weak as evidenced in the weak gain predictions in [75]. There have been other theoretical 109 investigations on using MTM type structures in TWTs [76] and other high power microwave devices [77]. A left handed metamaterial has simultaneously negative effective permittivity and negative effective permeability which creates reverse electromagnetic wave propagation [78] when compared to traditional right handed materials. By utilizing the unique properties of MTMs, a negative refractive index region can be created below the cut off frequency of the hollow waveguide. Similarly to the TE mode hollow waveguide acting as electric plasma [79], the hollow waveguide in TM mode is treated as magnetic plasma in this work. Below the TM 11 cut-off frequency, the magnetic permeability is effectively negative. Therefore, a two dimensional negative permittivity MTM [80] is designed and loaded in the waveguide. Thus, the loaded waveguide acts as double negative MTM and forms a negative refractive index pass band. This design creates the strong beam interaction mode. 5.2 Design and Simulation An X-band rectangular waveguide is selected as the essential structure for our TWT. The X-band waveguide dimensions are a = 22.43 mm and b = 10.16 mm. The cut off frequency of TMmn mode is determined by n m c c . (103) a b 2 2 The waveguide in TM mode can be treated as magnetic plasma below the cut off frequency. Thus the effective magnetic permeability μe can be written as 110 e 1 c2 / 2 . (104) Therefore, a hollow TM mode waveguide without any loading acts like a negative permeability material for frequencies below cut-off. As the frequency decreases, the effective permeability exhibits very large absolute value. This property helps reduce the phase velocity at lower frequency because of v phase c / n c / e e , n is the refractive index, c is the speed of light in free space and εe is the effective permittivity. The refractive index n must be a real number to allow the wave propagating through the waveguide. On the basis of the electric field distribution in the TM mode wave guide, a uniaxial electric resonant composite material is designed and loaded into the waveguide. This electric resonant material gives negative permittivity in a narrow frequency band below the TM11 cut off frequency. The design of the electric resonant material is shown in Fig. 56. Symmetric metallic wires are deposited on the 0.56 mm thick substrate with permittivity εr = 4.3. Figure 56. The geometry of the electric resonant material. A rectangular hole is made at the center to allow the electron beam traveling through. 111 The MTM sheets shown in Fig. 56 are repeated with a period p = 5 mm along the axis of the waveguide. With this period, the electric resonant material exhibits resonance around 6 GHz. So the loaded waveguide has simultaneously negative effective permeability and permeability around 6 GHz with a pass band of 0.3 GHz. The effective permittivity and permeability are retrieved for the interaction mode as shown in Fig. 57. The negative dispersion diagram for phase advances of 0 to 2 were calculated in CST Microwave Studio (CST-MWS) shown in Fig. 58. It indicates the structure is of the backward fundamental type [81]. 20 Effective Real Permittivity Effective Real Permeability 15 Relative Value 10 5 0 -5 -10 -15 -20 1 2 3 4 5 6 Frequency (GHz) 7 8 9 10 Figure 57. Effective permittivity and permeability of the beam interaction mode. 112 Figure 58. The dispersion diagram of the periodic SWS. The normalized phase velocity of the slow wave shown in Fig. 59 is calculated by v phase p / c , φ is the phase change of wave along one period. In the 0th harmonic (φ from 0 to ), the group velocity and phase velocity have opposite sign which demonstrates the backward wave mode. The phase velocity is reduced significantly to below 0.2c at the band edge where the phase advance is equal to . Therefore, the proposed configuration provides much lower phase velocity as the slow wave structure and strong axial electric field from the TM mode waveguide for the interaction with the electron beam. 113 Figure 59. The phase velocity in the operating harmonic. The transmission characteristics of 30 period SWS were also modeled in CST-MWS and the results are shown in Fig. 60. Figure 60. Simulation results of the S-parameters of the SWS. The peak of S21 at 5.7 GHz is the interaction mode desired. 114 The beam axial coupling impedance also called Pierce impedance [81] is a measure of the strength of interaction between the synchronous space harmonic and the electron beam. In this MTM based traveling wave tube targeted for operation at low voltages (<10 kV) the optimal synchronous mode is the -1st space harmonic within / p 1 2 / p as a forward wave. The Pierce impedance on the axis is defined as K 1 E1 2 2 21 P , (105) where, E1 is the magnitude of the -1st spatial harmonic of the axial electric field, P is the microwave power flow defined by P Wvgroup , (106) where, W is the stored electromagnetic energy per unit length. The Pierce impedance is relatively large over the negative refractive index pass band which indicates strong interaction between microwave field with electron beam. The small signal gain G can then be calculated for the synchronous case using the well known Pierce type gain equation [81] G 9.54 47.3CN , (107) Where, N is the number of wavelengths of the growing wave in the system, C is the Pierce parameter derived from the Pierce impedance as C3 I 0 K 1 , (108) 4V0 where I0 and V0 are the current and voltage of the electron beam [82]. 115 The hot simulation indicates 30 dB gain. To estimate the realistic gain of the TWT, the output power desired and thermal conditions have to be considered carefully in such compact structure. 5.3 Fabrication The SWS was fabricated using conventional printed circuit board manufacturing techniques. Forty sheets of the electric resonators are produced by depositing copper pattern on 0.56 mm FR-4 substrate with dielectric constant 4.3 and dielectric loss 0.025. The copper layer was coated with Electroless Nickel Immersion Gold (ENIG) to prevent oxidation. The thickness of the nickel coating is 3-3.8 um and the thickness of the gold is 0.05- 0.1 um. The mounting structure consists of copper blocks with precision milled slots to hold the printed circuit boards. The various sections of the assembly are shown in Fig. 61. Figure 61. The photograph of the various parts of the SWS. We designed special transition boards for the input and output coupling as shown below in Fig. 62. However, this design is very sensitive to dimensional parameters and was found to have poor coupling during experimental tests. 116 Hence, for experimental tests we excited the structure by inserting the central conductor of the coax cable by 5 mm along the axis of the circuit on the input and output sides of the structure to serve as coupling ports. The completed assembly of the MTM structure is shown in Fig. 63. Figure 62. Special input board for coupling the signal from a SMA input port. A similar board is also used to couple out the signal at the output port. Figure 63. Fully assembled SWS with input and output SMA ports. 117 5.4 Experimental Results The S-parameters are then characterized by a vector network analyzer. The measured S-parameters match with the simulation result at the interaction mode frequencies. The other two S21 passbands below and above the desired mode are TE mode which do not have interaction with the beam. The comparison between simulated and experimental results is shown in Fig. 64. The green and red traces are the theoretically predicted and experimentally measured S 11 curve. The dips in the S11 curve indicate coupling to the desired mode of the MTM structure. The variation in design and experimentally measured frequency was less than 2% which is well within the expected range due to the uncertainty in the value of the dielectric constant of the FR4 substrate at the given frequency. We used standard published values of dielectric constant of FR4 in the simulations. We observed higher transmission losses in experiment (blue) compared to theoretically predicted values (black). This can be attributed to the sub-optimal coupling provided by the transition from the SMA to the MTM boards as explained in the previous section. 118 MTM Resonance Guidance due to MTM mode TE10 Mode Figure 64. Simulated S-parameters and experimental measurement results. 5.5 Summary The MTM based TWT exhibits many advantages over existing TWT. The magnetic plasma-like TM mode waveguide loaded with the negative permittivity composite provides a double negative pass band. The negative refractive index slow wave structure significantly slows down the phase velocity of the wave. The low phase velocity also keeps the electron gun voltage quite low. The frequency selective properties of the MTM structure suppress parasitic oscillations usually encountered in a high gain amplifier because the circuit does not support other 119 interaction modes outside the design frequency. A good agreement was found between the theoretical design and experimental measurements. 120 CHAPTER SIX: Conclusion and Future Work The complex dielectric permittivity and magnetic permeability of several different sized hexagonal ferrite powders were successfully determined by using the quasi-optical technique across a wide range of millimeter wave frequencies. The shift of the ferromagnetic resonant frequencies demonstrates that the change of magnetic properties of ferrite powders depends on single particle size. The single particle size is deduced to affect the anisotropic magnetic field in the hexagonal ferrites. The properties of size dependent ferromagnetic resonance can also be used to develop electronic devices working at different frequencies. Hexagonal barium ferrite magnetic composites were made with polymer which acts as a matrix material to be compatible with standard microelectronic fabrication processes. SEM and millimeter wave transmittance measurement were performed on the original barium powders and with their photoresist composites. The coarse powder and its photoresist composite have ferromagnetic resonance similar to bulk hexagonal barium ferrites. Furthermore, these composites combine the high frequency anisotropic magnetic field sensitivity, with photolithographic fabrication capability. Thus Barium ferrite powders and their composites with polymer will be useful in variety of high frequency applications especially in on-chip magnetic components for millimeter wave integrated circuits where classically machined and polished monolithic ferrite materials are too large to be incorporated. 121 Two different ε-GaxFe2-xO3 nano-size ferrite powder samples with different xvalue were prepared. In-waveguide transmission and reflection method by vector network analyzer was used to measure the scattering parameters and thus the dielectric permittivity and magnetic permeability in the microwave frequency range. The high power backward spectrometer system was employed wave oscillator based quasi-optical to measure the millimeter wave transmittance and absorbance characteristics of theses samples. The ε-GaxFe2xO3 samples exhibit a very intense ferromagnetic resonance absorption peak at different frequencies from 90 GHz to 120 GHz. The ferromagnetic resonance peak moves to lower millimeter wave frequencies with increasing x-value of εGaxFe2-xO3 powder. Such materials are promising in integration and miniaturization of millimeter wave magnetic devices. An M-type hexagonal ferrite Y-junction circulator is designed on the commercial semiconductor substrate to achieve the on-chip self-biased magnetic devices in the millimeter wave frequency range. Since there is the strong magnetic anisotropy in the M-type hexaferrite, the weight, dimension and thus the cost can be reduced. A post processing with spin-casting of the nano ferrite composite is designed with the capability of integrating the ferrite devices on the semiconductor substrate. The successful experimental demonstration will make this hexaferrite circulator to be a great candidate for on-chip magnetic devices. The size dependence of the ferrite resonance and anisotropic field can be further investigated in the future. Such properties can be characterized and 122 verified by varying the temperature from near 0 K to higher than the coercivity temperature. The rule of the ferromagnetic resonance frequency and magnetic anisotropy field change may reveal the mechanism of FMR frequency shift. Other fabrication processes of ferrite material may apply to fabricate the passive circulator on chip. In the microfabrication process, lift off process may be substituted by polishing process to control the surface roughness. A combination of liquid phase epitaxy, spin spray or pulsed laser deposition can substitute spin casting and screen printing technique in the future. Metamaterial with pure metallic structure is ideal for traveling wave tubes. Metamaterial can be further designed with metallic structure to create desired interaction mode or suppress the undesired modes. The metamaterial provides a great potential to make the vacuum electrons devices cheaper and higher efficient. 123 APPENDIX I: List of Publications Journals [1] L. Chao and M. N. Afsar, "Size dependent ferromagnetic resonance and magnetic anisotropy of hexagonal barium and strontium ferrite powders," Journal of Applied Physics, vol. 113, p. 17E154, 2013. [2] L. Chao, M. N. Afsar, and S.-i. Ohkoshi, "Millimeter wave ferromagnetic resonance in gallium-substituted ε-iron oxide," Journal of Applied Physics, vol. 115, p. 17A510, 2014. [3] L. Chao, M. N. Afsar, and S.-i. Ohkoshi, "Microwave and millimeter wave dielectric permittivity and magnetic permeability of epsilon-gallium-ironoxide nano-powders," Journal of Applied Physics, vol. 117, p. 17B324, 2015. [4] L. Chao, E. Fu, V. J. Koomson, and M. N. Afsar, "Millimeter wave complementary metal-oxide-semiconductor on-chip hexagonal ferrite circulator," Journal of Applied Physics, vol. 115, p. 17E511, 2014. [5] L. Chao, H. Oukacha, E. Fu, V. J. Koomson, and M. N. Afsar, "Millimeter wave complementary metal–oxide–semiconductor on-chip hexagonal nano-ferrite circulator," Journal of Applied Physics, vol. 117, p. 17C123, 2015. [6] L. Chao, A. Sharma, and M. N. Afsar, "Microwave and millimeter wave ferromagnetic absorption of nanoferrites," Magnetics, IEEE Transactions on, vol. 48, pp. 2773-2776, 2012. [7] L. Chao, A. Sharma, M. N. Afsar, O. Obi, Z. Zhou, and N. Sun, "Permittivity and permeability measurement of spin-spray deposited Ni-Zn-ferrite thin film sample," Magnetics, IEEE Transactions on, vol. 48, pp. 4085-4088, 2012. [8] L. Chao, O. Sholiyi, M. N. Afsar, and J. D. Williams, "Characterization of microstructured ferrite materials: Coarse and fine barium, and photoresist composites," Magnetics, IEEE Transactions on, vol. 49, pp. 4319-4322, 2013. [9] P. K. Singh, S. Kabiri Ameri, L. Chao, M. N. Afsar, and S. Sonkusale, "Broadband millimeterwave metamaterial absorber based on embedding of dual resonators," Progress In Electromagnetics Research, vol. 142, pp. 625-638, 2013. Conferences [10] L. Chao, B. Yu, and M. Afsar, "Complex permittivity of thin films at millimeter and THz frequencies," in 2011 International Conference on Infrared, Millimeter, and Terahertz Waves, ed, 2011. [11] L. Chao, M. N. Afsar, and K. A. Korolev, "Millimeter wave dielectric spectroscopy and breast cancer imaging," in 2012 7th European Microwave Integrated Circuit Conference, ed, 2012. [12] L. Chao, A. Sharma, and M. N. Afsar, "Precise Fourier transform spectroscopy based measurement of dielectric properties of thin films at terahertz frequency range," in Instrumentation and Measurement Technology Conference (I2MTC), 2012 IEEE International, 2012, pp. 86-91. 124 [13] L. Chao and M. N. Afsar, "Complex dielectric permittivity and magnetic permeability measurement of ferrite powders at millimeter wavelength," in Instrumentation and Measurement Technology Conference (I2MTC), 2013 IEEE International, 2013, pp. 1564-1566. [14] L. Chao, M. N. Afsar, M. Zimmerman, and A. Saigal, "Non-contact dielectric characterization of lithium ionic solid electrolyte polymer," in Instrumentation and Measurement Technology Conference (I2MTC), 2013 IEEE International, 2013, pp. 925-930. [15] M. Afsar, L. Chao, and S. Ohkoshi, "Microwave and millimeter wave dielectric permittivity and magnetic permeability of Epsilon-Gallium-iron-oxide nanopowders," in Magnetics Conference (INTERMAG), 2015 IEEE, 2015, pp. 1-1. [16] L. Chao, B. Yu, A. Sharma, and M. N. Afsar, "Dielectric permittivity measurements of thin films at microwave and terahertz frequencies," in Microwave Conference (EuMC), 2011 41st European, 2011, pp. 202-205. [17] L. Chao, H. Oukacha, E. Fu, V. J. Koomson, and M. N. Afsar, "Millimeter wave hexagonal nano-ferrite circulator on silicon CMOS substrate," in Microwave Symposium (IMS), 2014 IEEE MTT-S International, 2014, pp. 1-4. [18] L. Chao and M. N. Afsar, "Precise dielectric characterization of liquid crystal polymer films at microwave frequencies by new transverse slotted cavity," in Precision Electromagnetic Measurements (CPEM 2014), 2014 Conference on, 2014, pp. 448-449. [19] L. Chao and M. N. Afsar, "A millimeter wave breast cancer imaging methodology," in Precision Electromagnetic Measurements (CPEM), 2012 Conference on, 2012, pp. 74-75. [20] L. Chao, A. Sharma, and M. N. Afsar, "Precision measurements of dielectric permittivity of common thin film materials at microwave and terahertz frequencies," in Precision Electromagnetic Measurements (CPEM), 2012 Conference on, 2012, pp. 76-77. [21] L. Chao, S. Guo, M. N. Afsar, and J. R. Sirigiri, "Metamaterial based negative refractive index traveling wave tube," in Pulsed Power Conference (PPC), 2013 19th IEEE, 2013, pp. 1-5. Patent [22] M. N. Afsar and L. Chao, "Millimeter wave 3-D breast imaging," ed: US Patent 8,948,847, 2015. 125 BIBLIOGRAPHY [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] J. Smit and H. P. J. Wijn, Ferrites: physical properties of ferrimagnetic oxides in relation to their technical applications: Wiley, 1959. Ü. Özgür, Y. Alivov, and H. Morkoç, "Microwave ferrites, part 1: fundamental properties," Journal of Materials Science: Materials in Electronics, vol. 20, pp. 789-834, 2009. A. Goldman, Modern ferrite technology: Springer Science & Business Media, 2006. A. Aharoni, "Demagnetizing factors for rectangular ferromagnetic prisms," Journal of applied physics, vol. 83, pp. 3432-3434, 1998. C. Vittoria, Magnetics, Dielectrics, and Wave Propagation with MATLAB® Codes: CRC Press, 2011. D. M. Pozar, Microwave engineering: John Wiley & Sons, 2009. M. Costa, G. P. Júnior, and A. Sombra, "Dielectric and impedance properties’ studies of the of lead doped (PbO)-Co 2 Y type hexaferrite (Ba 2 Co 2 Fe 12 O 22 (Co 2 Y))," Materials Chemistry and Physics, vol. 123, pp. 35-39, 2010. M. Sugimoto, "The past, present, and future of ferrites," Journal of the American Ceramic Society, vol. 82, pp. 269-280, 1999. J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann, and S. N. Stitzer, "Ferrite devices and materials," IEEE Transactions on Microwave Theory and Techniques, vol. 50, pp. 721-737, 2002. D. Taft, "Hexagonal ferrite isolators," Journal of Applied Physics, vol. 35, pp. 776-778, 1964. R. Valenzuela, "Novel applications of ferrites," Physics Research International, vol. 2012, 2012. J. Daniels and A. Rosencwaig, "Mössbauer study of the Ni-Zn ferrite system," Canadian Journal of Physics, vol. 48, pp. 381-396, 1970. D. Stoppels, "Developments in soft magnetic power ferrites," Journal of Magnetism and Magnetic Materials, vol. 160, pp. 323-328, 1996. A. Pradeep, P. Priyadharsini, and G. Chandrasekaran, "Sol–gel route of synthesis of nanoparticles of MgFe 2 O 4 and XRD, FTIR and VSM study," Journal of magnetism and Magnetic materials, vol. 320, pp. 2774-2779, 2008. D. Minoli, Nanotechnology applications to telecommunications and networking: John Wiley & Sons, 2005. M. I. Skolnik, "Introduction to radar," Radar Handbook, vol. 2, 1962. C.-H. Chang, Y.-T. Lo, and J.-F. Kiang, "A 30 GHz Active Quasi-Circulator With Current-Reuse Technique in CMOS Technology," Microwave and Wireless Components Letters, IEEE, vol. 20, pp. 693-695, 2010. Y. Zheng and C. E. Saavedra, "Active quasi-circulator MMIC using OTAs," Microwave and Wireless Components Letters, IEEE, vol. 19, pp. 218-220, 2009. 126 [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] D.-J. Huang, J.-L. Kuo, and H. Wang, "A 24-GHz low power and high isolation active quasi-circulator," in Microwave Symposium Digest (MTT), 2012 IEEE MTT-S International, 2012, pp. 1-3. M. Pardavi-Horvath, "Microwave applications of soft ferrites," Journal of Magnetism and Magnetic Materials, vol. 215, pp. 171-183, 2000. O. Zahwe, B. Abdel Samad, B. Sauviac, J.-P. Chatelon, M. Blanc Mignon, J. Rousseau, M. Le Berre, and D. Givord, "YIG thin film used to miniaturize a coplanar junction circulator," Journal of Electromagnetic Waves and Applications, vol. 24, pp. 25-32, 2010. S. Ghosh, S. Keyvaninia, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, "Adhesively bonded Ce: YIG/SOI integrated optical circulator," Optics letters, vol. 38, pp. 965-967, 2013. M. N. Afsar, K. A. Korolev, A. Namai, and S. Ohkoshi, "Measurements of Complex Magnetic Permeability of Nano-Size-Al Fe O Powder Materials at Microwave and Millimeter Wavelengths," Magnetics, IEEE Transactions on, vol. 48, pp. 2769-2772, 2012. L. Chao, A. Sharma, and M. N. Afsar, "Microwave and millimeter wave ferromagnetic absorption of nanoferrites," Magnetics, IEEE Transactions on, vol. 48, pp. 2773-2776, 2012. L. Chao, M. N. Afsar, and S.-i. Ohkoshi, "Millimeter wave ferromagnetic resonance in gallium-substituted ε-iron oxide," Journal of Applied Physics, vol. 115, p. 17A510, 2014. J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," Microwave Theory and Techniques, IEEE Transactions on, vol. 38, pp. 10961103, 1990. A. Sharma, "Design of Broadband Microwave Absorbers for Application in Wideband Antennas," Master of Science, Electrical and Computer Engineering, TUFTS UNIVERSITY, 2011. A. Nicolson and G. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," Instrumentation and Measurement, IEEE Transactions on, vol. 19, pp. 377-382, 1970. W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proceedings of the IEEE, vol. 62, pp. 33-36, 1974. N. N. Al-Moayed, M. N. Afsar, U. A. Khan, S. McCooey, and M. Obol, "Nano ferrites microwave complex permeability and permittivity measurements by T/R technique in waveguide," Magnetics, IEEE Transactions on, vol. 44, pp. 1768-1772, 2008. A. A. Volkov, Y. G. Goncharov, G. V. Kozlov, S. P. Lebedev, and A. M. Prokhorov, "Dielectric measurements in the submillimeter wavelength region," Infrared Physics, vol. 25, pp. 369-373, 1985. 127 [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] G. V. Kozlov, S. P. Lebedev, A. A. Mukhin, A. S. Prokhorov, I. V. Fedorov, A. M. Balbashov, and I. Y. Parsegov, "Submillimeter backward-wave oscillator spectroscopy of the rare-earth orthoferrites," Magnetics, IEEE Transactions on, vol. 29, pp. 3443-3445, 1993. K. N. Kocharyan, M. Afsar, and I. I. Tkachov, "Millimeter-wave magnetooptics: New method for characterization of ferrites in the millimeter-wave range," Microwave Theory and Techniques, IEEE Transactions on, vol. 47, pp. 26362643, 1999. K. A. Korolev, C. Shu, L. Zijing, and M. N. Afsar, "Millimeter-Wave Transmittance and Reflectance Measurement on Pure and Diluted Carbonyl Iron," Instrumentation and Measurement, IEEE Transactions on, vol. 59, pp. 2198-2203, 2010. L. Chao, A. Sharma, and M. N. Afsar, "Precision measurements of dielectric permittivity of common thin film materials at microwave and terahertz frequencies," in Precision Electromagnetic Measurements (CPEM), 2012 Conference on, 2012, pp. 76-77. E. Schlomann, "Microwave behavior of partially magnetized ferrites," Journal of Applied Physics, vol. 41, pp. 204-214, 1970. E. C. Stoner and E. P. Wohlfarth, "A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys," Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 240, pp. 599-642, 1948. J. D. Williams and W. Wang, "Study on the postbaking process and the effects on UV lithography of high aspect ratio SU-8 microstructures," Journal of Micro/Nanolithography, MEMS, and MOEMS, vol. 3, pp. 563-568, 2004. J. D. Williams and W. Wang, "Microfabrication of an electromagnetic power relay using SU-8 based UV-LIGA technology," Microsystem technologies, vol. 10, pp. 699-705, 2004. J. D. Williams and W. Wang, "Using megasonic development of SU-8 to yield ultra-high aspect ratio microstructures with UV lithography," Microsystem technologies, vol. 10, pp. 694-698, 2004. Q. Chen and Z. J. Zhang, "Size-dependent superparamagnetic properties of MgFeO spinel ferrite nanocrystallites," Applied physics letters, vol. 73, p. 3156, 1998. A. Namai, M. Yoshikiyo, K. Yamada, S. Sakurai, T. Goto, T. Yoshida, T. Miyazaki, M. Nakajima, T. Suemoto, and H. Tokoro, "Hard magnetic ferrite with a gigantic coercivity and high frequency millimetre wave rotation," Nature communications, vol. 3, p. 1035, 2012. J. Jin, S. i. Ohkoshi, and K. Hashimoto, "Giant coercive field of nanometer‐ sized iron oxide," Advanced Materials, vol. 16, pp. 48-51, 2004. S. Sakurai, A. Namai, K. Hashimoto, and S.-i. Ohkoshi, "First observation of phase transformation of all four Fe2O3 phases (γ→ ε→ β→ α-phase)," Journal of the American Chemical Society, vol. 131, pp. 18299-18303, 2009. 128 [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] S.-i. Ohkoshi and H. Tokoro, "Hard magnetic ferrite: εFe<sub>2</sub>O<sub>3</sub>," Bulletin of the Chemical Society of Japan, vol. advpub, 2013. B. D. Cullity and C. D. Graham, Introduction to magnetic materials: John Wiley & Sons, 2011. S. Chikazumi, Physics of Ferromagnetism 2e: Oxford University Press, 2009. S.-i. Ohkoshi, A. Namai, and S. Sakurai, "The Origin of Ferromagnetism in εFe2O3 and ε-GaxFe2−xO3 Nanomagnets," The Journal of Physical Chemistry C, vol. 113, pp. 11235-11238, 2009/07/02 2009. M. N. Afsar and L. Chao, "Millimeter Wave 3-D Breast Imaging," ed: Google Patents, 2013. L. Chao, E. Fu, V. J. Koomson, and M. N. Afsar, "Millimeter wave complementary metal-oxide-semiconductor on-chip hexagonal ferrite circulator," Journal of Applied Physics, vol. 115, p. 17E511, 2014. M. Yoshikiyo, A. Namai, M. Nakajima, K. Yamaguchi, T. Suemoto, and S.-i. Ohkoshi, "High-frequency millimeter wave absorption of indium-substituted ε-Fe2O3 spherical nanoparticles," Journal of Applied Physics, vol. 115, p. 172613, 2014. L. Landau and E. Lifshitz, "Phys. Z Sowjetunion 8, 153 (1935); TL Gilbert," Phys. Rev, vol. 100, p. 1243, 1955. P. Kabos and V. Stalmachov, Magnetostatic waves and their application: Chapman & Hall London, 1994. D. D. Stancil, Theory of magnetostatic waves: Springer, 1993. R. F. Soohoo, "Microwave magnetics," New York, Harper and Row Publishers, 1985, 270 p., vol. 1, 1985. C. S. Tsai and J. Su, "A wideband electronically tunable microwave notch filter in yttrium iron garnet–gallium arsenide material structure," Applied physics letters, vol. 74, pp. 2079-2080, 1999. T. Fal and R. Camley, "Hexagonal ferrites for use in microwave notch filters and phase shifters," Journal of applied physics, vol. 104, p. 023910, 2008. Y.-Y. Song, J. Das, Z. Wang, W. Tong, and C. E. Patton, "In-plane c-axis oriented barium ferrite films with self-bias and low microwave loss," Applied physics letters, vol. 93, p. 172503, 2008. H. Bosma, "On Stripline Y-Circulation at UHF," Microwave Theory and Techniques, IEEE Transactions on, vol. 12, pp. 61-72, 1964. C. Fay and R. Comstock, "Operation of the ferrite junction circulator," Microwave Theory and Techniques, IEEE Transactions on, vol. 13, pp. 15-27, 1965. J. Helszajn, "Quarter-wave coupled junction circulators using weakly magnetized disk resonators," Microwave Theory and Techniques, IEEE Transactions on, vol. 30, pp. 800-806, 1982. 129 [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] J. Helszajn and F. C. Tan, "Design data for radial-waveguide circulators using partial-height ferrite resonators," Microwave Theory and Techniques, IEEE Transactions on, vol. 23, pp. 288-298, 1975. J. Helszajn and D. S. James, "Planar triangular resonators with magnetic walls," Microwave Theory and Techniques, IEEE Transactions on, vol. 26, pp. 95-100, 1978. J. Davies, "An analysis of the m-port symmetrical H-plane waveguide junction with central ferrite post," Microwave Theory and Techniques, IRE Transactions on, vol. 10, pp. 596-604, 1962. B. Auld, "The synthesis of symmetrical waveguide circulators," Microwave Theory and Techniques, IRE Transactions on, vol. 7, pp. 238-246, 1959. J. Simon, "Broadband strip-transmission line Y-junction circulators," Microwave Theory and Techniques, IEEE Transactions on, vol. 13, pp. 335-345, 1965. J. J. Green and F. Sandy, "Microwave characterization of partially magnetized ferrites," Microwave Theory and Techniques, IEEE Transactions on, vol. 22, pp. 641-645, 1974. Y. Chen, T. Sakai, T. Chen, S. D. Yoon, A. L. Geiler, C. Vittoria, and V. G. Harris, "Oriented barium hexaferrite thick films with narrow ferromagnetic resonance linewidth," Applied physics letters, vol. 88, pp. 062516-062516-3, 2006. R. Kompfner, "The traveling-wave tube as amplifier at microwaves," Proceedings of the IRE, vol. 35, pp. 124-127, 1947. C. L. Kory and J. D. Wilson, "Novel high-gain, improved-bandwidth, finnedladder V-band traveling-wave tube slow-wave circuit design," Electron Devices, IEEE Transactions on, vol. 42, pp. 1686-1692, 1995. S. Bhattacharjee, J. H. Booske, C. L. Kory, D. W. van der Weide, S. Limbach, S. Gallagher, J. D. Welter, M. R. Lopez, R. M. Gilgenbach, and R. L. Ives, "Folded waveguide traveling-wave tube sources for terahertz radiation," Plasma Science, IEEE Transactions on, vol. 32, pp. 1002-1014, 2004. D. Smith, J. Pendry, and M. Wiltshire, "Metamaterials and negative refractive index," Science, vol. 305, pp. 788-792, 2004. A. Gilmour Jr, "Microwave tubes," Dedham, MA, Artech House, 1986, 502 p., vol. 1, 1986. A. H. W. Beck, Space-charge waves, and slow electromagnetic waves vol. 8: Pergamon Press, 1958. M. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alù, R. Temkin, and G. Shvets, "Active negative-index metamaterial powered by an electron beam," Physical Review B, vol. 86, p. 085132, 2012. Y. S. Tan and R. Seviour, "Wave energy amplification in a metamaterial-based traveling-wave structure," Europhysics Letters, vol. 87, p. 34005 (4 pp.), 2009. 130 [77] [78] [79] [80] [81] [82] D. Shiffler, J. Luginsland, D. M. French, and J. Watrous, "A Cerenkov-like Maser Based on a Metamaterial Structure," IEEE Transactions on Plasma Science, vol. 38, pp. 1462-5, 2010. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial," Applied Physics Letters, vol. 78, pp. 489-491, 2001. J. D. Baena, L. Jelinek, R. Marqués, and F. Medina, "Near-perfect tunneling and amplification of evanescent electromagnetic waves in a waveguide filled by a metamaterial: Theory and experiments," Physical Review B, vol. 72, p. 075116, 2005. M. Shapiro, G. Shvets, J. Sirigiri, and R. Temkin, "Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves," Optics letters, vol. 31, pp. 2051-2053, 2006. J. Gittins, Power traveling wave tubes: American Elsevier, 1965. J. R. Pierce, Traveling-wave tubes: Van Nostrand Princeton, New Jersey,, USA, 1950.

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