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Characterization 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
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ProQuest 10013462
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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   2232  3212 ) , (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  F2
 
, (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  0m 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 jt dependent, (27) reduces to
2
2

(0   ) m x  0m h x  jm h y
, (28)
 2
2
(



)
m



h

j

h

y
0 m
y
m x
 0
 0m
2  2
 mx   0
    j0m
 my     2   2
m   0
 z  0


  xx
m    yx
 0
 xy
 yy
0
j0m
02   2
0m
02   2
0

0
  hx 
 
0   hy  , (29)
 h 
0  z 


0
0  h , (30)
0 
where  xx   yy 
0m
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 
0m

) 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   j0 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
 2n   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 (2n  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 (2n  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  e4 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
40  H a
M2
 ''  f  
sin 2   f 
40  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 40 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 00 (02   2 )
 M 00 (02   2 )
μ  1  2
, μ   2
,
(0   2 )2  402 2 2
(0   2 )2  402 2 2
2 M 00 2
 M 00 (02   2 )

κ

,
,
(02   2 )2  402 2 2
(02   2 )2  402 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 
E1
2
2 21 P
, (105)
where, E1 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
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