Growth and Characterization of Zinc Ferrite Thin Films for High Frequency
Applications
by
Jiqing Hu
A DISSERTATION
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented September 5, 2005
Commencement June 2006
AN ABSTRACT OF THE DISSERTATION OF
Jiqing Hu for the degree of Doctor of Philosophy in Electrical and Computer
Engineering presented on September 5, 2005
Title: Growth and Characterization of Zinc Ferrite Thin Films for High Frequency
Applications
Abstract approved:
Chih-Hung (Alex) Chang
Shih-Lien L. Lu
Raghu K. Settaluri
Ferrites have been used for various high frequency applications as bulk
materials. These applications, however, are limited to large dimension devices. In
this thesis, thin film ferrites were deposited from a low temperature solution-based
deposition process that is suitable for micro-scale high frequency applications. The
low temperature nature of this deposition technique makes it an excellent back end
process. In this work, a high rate deposition process for zinc ferrite thin films was
established. A deposition rate of 0.2 µm/min was determined by the surface
profiler. The deposited films have a plate-like morphology with fibrous texture.
Zinc was uniformly incorporated into the ferrite film confirmed by the local
chemical analysis by Energy Dispersive X-ray spectroscopy. The deposited films
are polycrystalline with a typical cubic ferrite structure. The overall composition
of the films was determined by Auger electron spectroscopy as ZnxFeyO4, x ranges
from 0.25 to 0.55, and y ranges from 2.2 to 2.7.
A model consisting of resistors, capacitors and inductors was constructed
and used for the analysis of impedance spectroscopy. The dielectric properties of
zinc ferrite thin films were obtained by fitting the data to the model. The results
show that the dielectric constants are around 15 regardless of Zn/Fe ratio. This
value is consistent with most of the reported values for bulk ferrite materials. The
resistivity changes from 0.6x106 ohm.meter to 1.3 x106 ohm.meter when Zn/Fe
ratio varies from 0.06 to 0.14.
A grounded coplanar waveguide structure was developed for microwave
characterization of the thin film material to obtain the complex relative
permittivity and the complex relative permeability. The method is based on
conformal mapping and determination of filling factors for the coplanar waveguide
configuration and is applicable to a wide range of dielectric as well as magnetic
materials. The proposed approach was validated by determining the scattering
parameters of a number of test structures using the 3D full-wave electromagnetic
simulation. In all examples, the extracted parameters from the proposed technique
resulted in values that are within 2% error.
© Copyright by Jiqing Hu
September 5, 2005
All Rights Reserved
Growth and Characterization of Zinc Ferrite Thin Films for High Frequency
Applications
by
Jiqing Hu
A DISSERTATION
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented September 5, 2005
Commencement June 2006
Doctor of Philosophy dissertation of Jiqing Hu presented on September 5, 2005.
APPROVED:
Major Professor, representing Electrical and Computer Engineering
Major Professor, representing Electrical and Computer Engineering
Major Professor, representing Electrical and Computer Engineering
Director of the School of Electrical Engineering and Computer Science
Dean of the Graduate School
I understand that my dissertation will become part of the permanent collection of
Oregon State University libraries. My signature below authorizes release of my
dissertation to any reader upon request.
Jiqing Hu, Author
ACKNOWLEDGEMENTS
I would like to thank Dr. Chih-Hung Chang for enormous support and
invaluable guidance during the last two years. I would like thank Dr. Shih-lien Lu,
without him, I would not start and continue my PhD study. Thanks to Dr. Raghu
K. Settaluri for advising me in the high frequency area, and creating this exciting
project.
I deeply thank that Dr. Chih-Hung Chang, Dr. Shih-lien Lu, and Dr.
Raghu K. Settaluri cooperate and advise me as my major professors and lead me in
this researches with their time and energy.
I would like to thank Dr Huaping Liu for showing interest in my academic
progress all through these years and also for serving in my graduate committee.
His timely advice and guidance will always be appreciated. Thanks to Dr. Keith L.
Levien, who kindly act as Graduate Council Representative.
I would like to express my gratitude to all those who gave me the
possibility to complete this thesis. Special thanks are due to: Dr. Tianbao Xie
from Linfield College for his timely assistance with AUGER measurements; Dr.
Chunfei Li from Portland State University for his valuable assistance in SEM
measurements; Dr. Michael Nesson from Oregon State University for his
assistance in TEM measurements; for Mr. Arien Sligar for his help and discussion
in HFSS simulations.
Thanks to all the people in our lab at Chemical engineering department,
Yu-jen Chang, Shuhong Liu, Prakash Mugdur, Doohyoung Lee, and Yuwei Su for
their helps and supports. I will remember the wonderful time and fun in this lab.
I will remember Oregon State University as well as the beautifully town
Corvallis in my life. I had wonderful time with my friends here.
I would like to thank my parents who support me with their love, so I can
went from primary school to university, and finally to complete my PhD.
Most importantly, I would like to thank my wife, Xiaoming Wen, who uses
her life time to support me as cooking delicious food and taking care of my
daughter Sunnya Kailang Hu. I will remember the words my daughter always asks
me when I leave for school at night. I owe them too much. Without their support, I
can not go through the difficulties I encountered.
Thanks to all people who help me in completing my PhD study I did not
mention above.
Finally I would like to thank GOD for guiding to a wonderful and abundant
life.
This work was supported by the US national Science Foundation under
grant #ECS-0401357.
CONTRIBUTION OF AUTHORS
Mr. DooHyoung Lee assisted with TEM electron diffraction pattern and data
analysis for the papers of first one: “High-rate Deposition of Zinc Ferrite Thin
Films from a Soft Solution Process”, and the second one: “Impedance
Spectroscopy Characterization of Zinc Ferrite Thin Film from a Soft Solution
Process”.
TABLE OF CONTENTS
Page
CHAPTER 1. Introduction ……………………………………………..
1
CHAPTER 2. Background for High-rate Deposition of Zinc Ferrite Thin
Films from a Soft Solution Process………………………………………
4
CHAPTER 3. High-rate Deposition of Zinc Ferrite Thin Films from a
Soft Solution Process ……………………………………………………
14
CHAPTER 4. Background for Impedance Spectroscopy Characterization
of Zinc Ferrite Thin Film from a Soft Solution Process…………………
32
CHAPTER 5. Impedance Spectroscopy Characterization of Zinc Ferrite
Thin Film from a Soft Solution Process………………………………...
39
CHAPTER 6. A grounded coplanar waveguide based technique for
nondestructive measurement of high frequency complex permittivity and
permeability of thin films …………………………………………….
63
CHAPTER 7. Conclusions ………………………….….………………
99
Bibliograpgy ……………………………………………………….…
101
LIST OF FIGURES
Figure
Page
2. 1. The ferrite plating kinetic mechanism proposed by M. Abe ……….
5
2. 2. The Schematic of the Auger Electron Spectroscopy ………………..
7
2. 3. The schema of TEM …………………………………………………
11
2. 4. The schema of SEM ………………………………………………….
12
3. 1. A schematic diagram of the spin and spray ferrite deposition system..
25
3. 2. (a) Ferrite film thickness plotted as a function of deposition time (b)
SEM images of cross-sectional structure of zinc ferrite thin films with
deposition time of 45minutes.......................................................................
26
3. 3. SEM images of plane-view structure of zinc ferrite thin films with
different deposition time (a) 15 min. (b) 45 min. (c) 75 min. and (d) higher
magnification image for (b)……….............................................................
28
3. 4. (a) Bright field TEM image of zinc ferrite thin film (b) EDX spectra
from selected area (c) Selected area electron diffraction pattern................
29
3. 5. (a) Auger spectra of a zinc ferrite thin film deposited from 0.2 g/L
ZnCl2 in the precursor solution (b) Atomic ratio of Zn/Fe in film plotted as
a function ZnCl2 concentration in solution. ..............................................
30
4.1. Schematic diagrams of two parallel-plate capacitor. …………………
35
5. 1. The schematic of the spin spraying ferrite deposition set up………….
53
5. 2. A schematic diagram of impedance spectroscopy measurements ……
54
5. 3 a) SEM imagne, b) The EDX results, c). TEM diffraction pattern …..
55
5. 4. A model of resistor Rs follows parallel Resistor Rp and capacitor Cp
56
LIST OF FIGURES (Continued)
Figure
Page
5. 5. The impedance spectroscopy of the setup without samples …………..
57
5. 6. The impedance spectroscopy of the 10Mohm Resistor after trunk and
the fitted line ………………………………………………………………..
58
5.7. The impedance spectroscopy of the 10Mohm Resistor parallel to the
sample after deleting the high frequency data and fitted ………………..….
59
5. 8. The impedance spectroscopy of the sample …………………………...
60
5. 9. The dielectric constants vary with the ZnCl2 in the solution …………
61
5. 10. The resistivity vary with the ZnCl2 in the solution ………………..
62
6. 1. The grounded coplanar waveguide structure …………………………
92
6. 2. The conformal mapping technique ……………………………………
92
6. 3. Conformal mapping for the proposed structure ……………………….
93
6. 4. A model of resistor Rs follows parallel Resistor Rp and capacitor Cp
93
6. 5 The impedance spectroscopy of the setup without samples ………..….
94
6. 6. The impedance spectroscopy of the 10Mohm Resistor after trunk and
the fitted line ……………………………………………………………....
95
6. 7. The impedance spectroscopy of the 10Mohm Resistor parallel to the
sample after deleting the high frequency data and fitted ……………….…..
96
6. 8. The extracted results. a). The real dielectric constant, b). The
imaginary dielectric constant, c). The real relative Mu, and d). The
imaginary relative Mu. ……………………………………………….……
97
LIST OF TABLES
Table
Page
3. 1. Composition of Zn ferrite thin films determined by AES
31
6. 1 Summary of results
98
Growth and Characterization of Zinc Ferrite Thin Films for High Frequency
Applications
CHAPTER 1
Introduction
The continued down scaling of device dimensions and the rapid growth in
the demand for system-on-chip (SOC) are driving significant improvement in their
performance with lower fabrication costs. However, there is much room to
improve the performance of high frequency circuits from the passive circuits, such
as transmission lines, planar inductors and capacitors through reducing losses and
parasite effects at high frequency. in which the building block in an RF system
requires the use of passive components. Ferrites with their high permeability and
high permittivity are major candidates for these improvements to relieve typical
problems encountered in high frequency applications like as eddy current,
radiation, and coupling.
In recent years, ferrite materials have received much attention in high
frequency applications such as inductors, waveguides, isolators, circulators, and
phase shifters. In the past, the development of polycrystalline ferrite thin films is
mainly motivated by magnetic recording applications. These films, however, are
normally too thin (less than 1 um) and the growth rate is normally too slow for
microwave device. Moreover, their microwave properties, which changes greatly
at high frequency because of eddy current and dynamical magnetization, were not
investigated. Most importantly, the annealing temperature (more than 600oC) is
not acceptable for backend processes. Ferrite plating, put forward by M. Abe, has
the capability to deposit ferrite thin films with a growth rate as high as 100 nm/min
at a temperature less than 200oC. This is suitable for monolithic integration within
a system on a chip. In addition, it is applicable to many different types of
substrates.
Ferrites, as spinel ferrite structure, contain all the material as MFe2O4
(M[Fe2]O4, where M as Zn, Cd,, and inverse spinel Fe[MFe]O4 where M as Ni,
Co, Fe, Mn, Cu). Spinel ferrites have a crystal structure that has the space group,
fd3m, consists of 56 atoms; 32 are oxygen anions assuming a close packed cubic
structure, and the remainder are metal cations residing on 8 of the 64 available
tetrahedral (A) sites and 16 of the 32 available octahedral (B) sites. The A-site
cations reside on the interstices of 2 interpenetrating fcc lattices, whereas the Bsite cations reside on the interstices of 4 interpenetrating fcc lattices. The size and
valence of the cations species determines the filling of these sites which in turn
strongly influences the materials’ magnetic and electronic properties. Zinc ferrite
is suitable candidate among several ferrite materials with good potentials for high
frequency applications.
The objectives of this research are, first, to establish a low-temperature and
high-rate deposition process for zinc ferrite thin films and to investigate the
relation between the processing parameters and thin film properties including
chemical, structural, and electrical properties; second, to study the low frequency
dielectric properties of zinc ferrite thin films using impedance spectroscopy; and
third, to develop a method to measure the complex relative permittivity and
complex relative permeability at high frequency.
CHAPTER 2
Background for High-rate Deposition of Zinc Ferrite Thin Films from a Soft
Solution Process
Chemical solution deposition (CSD) of thin films originated more than a
century ago (in 1835) as Liebig reported the deposition of silver (the silver mirror
deposition) using a chemical solution technique [37]. The first reported deposition
of a compound semiconductor film was the formation of “lusterfarben” (meaning
lustrous colors) on metals from thiosulphate solutions of copper sulfate, lead
acetate and antimony tartrate which resulted in “splendid” colored films of CuS,
PbS and SbS respectively [38]. In 1983, the soft solution deposition (SSD) of
ferrite thin film was put forward by M. Abe and his colleagues in Japan, who also
named the soft solution deposition of ferrite as ferrite plating. Before that, the
ferrite thin film was conventionally prepared at higher temperature (normally
higher than 600oC) by sputtering, vacuum evaporation, molecular beam epitaxy,
liquid-phase epitaxy. Ferrite plating mimicked a bio-mineralization process of
synthesis of magnetosomes by magmetotactic bacteria. The mechanism of ferrite
plating proposed by M. Abe is shown in Figure 1. The initial condition for ferrite
plating is the adsorption OH groups on the substrate that could react with the Fe2+
ions and replaced the H+ ions with Fe2+ ions. Without the OH- group, the Fe2+ ions
can not stick on the substrate surface to form a ferrite thin film. The Fe2+ ions then
are oxidized to Fe3+ by an oxidation solution such as sodium nitrate NaNO2
solution. The Fe2+ and Fe3+ then absorb H2O to form OH group. The OH group
will then adsorb the Fe2+ to repeat above sequence to continue the ferrite thin film
growth.
This mechanism only discussed the heterogeneous film formation
process, however, in the solution, a homogeneous reaction is likely to occur as
well. A good example regarding to reaction mechanism of soft solution deposition
may be found from the kinetic mechanism of CdS deposition by chemical bath
deposition, put forward by D. Lincot (1992), and further studied by C. Voss, Y.J.
Chang,
S.
Subramanian,
S.O.
Ryu,
T.-J.
Lee,
and
C.-H.
Chang.
Fe2+, Mn+
Substrate
[I] Adsorption
[II] Oxidation
Spinel ferrite
NaNO2
O2-H+
O2-H+
O2-H+
O2-H+
O2-H+
O2-H+
O2-H+
[III]
Adsorption
[III]’ Spinel formation
O2O2O2O2O2O2O2-
Fe2Fe2Fe2Fe2Fe2M2-
H 2O
O2Fe3O2Fe2O2Fe3O2Fe2O2Fe3O2M2O2-
O2O2O2- H+
Fe3Fe2O2O2O2- H+
Fe2Fe322O
O
O2- H+
Fe3M22O2O
O2- H+
Fe2Fe3O2O2O2- H+
Fe3- 2- Fe22O
O
O2- H+
M2Fe322O
O
O2-H+
Repeat
Figure 1. The ferrite plating kinetic mechanism proposed by M. Abe.
In Principle, the SSD involves a sequence of nucleation, crystal growth ,
Ostwald ripening, re-crystallization, coagulation and can be used to deposit any
compound that satisfies four basic requirements:
First, the compound can be made by simple precipitation. This generally,
although not exclusively, refers to the formation of a stoichiometric compound
formed by ionic reaction.
Second, the compound should be relatively (and preferably highly)
insoluble in the solution used (except in a very few cases, this has been water).
Third, the compound should be chemically stable in the solution.
Fourth, if the reaction proceeds via the free anion, then this anion should be
relatively slowly generated (to prevent sudden precipitation). If the reaction is of
the complex-decomposition type, then decomposition of the metal complex should
similarly occur relatively slow.
Of course there are other specific factors that need to be taken into account,
particularly whether the compound will form an adherent film on the substrate or
not. However, these four factors are major requirements.
Ferrite plating satisfy these four general requirements. The main objective
of this research on ferrite plating focus on how to improve the deposition speed
and what properties the deposited films possess.
M. Abe has developed several methods to increase the deposition rate, such
as ultrasound horn acceleration, laser beam acceleration and spin ferrite plating,
each method can improve the deposition rate to some extent. The most promising
one is to use Ar laser beam to enhance the deposition rate as high as 300nm per
minute.
X-Y Oscilloscope
Sweep
Supply
Lock-In Amplifier
Sample
Carrousel
Specimen
Mount
Electron Gun
Electron
Multiplier
Magnetic Shield
Figure 2. The Schematic of the Auger Electron Spectroscopy
Inspired by the spin spray ferrite plating which is not limited by the
solution volume and Ar laser beam accelerated ferrite deposition, a deposition
setup similar to the spin and spray ferrite plating with light enhancement from a
Halogen light was developed. The film thickness, roughness, and morphology
were measured by a surface profiler and SEM. The film thickness and surface
roughness were characterized by a stylus surface profilometer. The morphology
and crystal structure were examined by transmission electron microscopy and
selected area electron diffraction (SAED). The overall chemical composition of the
films was characterized by Auger spectroscopy.
Auger Electron Spectroscopy (Auger spectroscopy or AES) developed in
the late 1960's was derived from the effect first observed by a French Physicist,
Pierre Auger in the mid-1920's. AES can be used to study the constituents and the
concentrations of surface material, such as Zinc ferrite thin films. The schema of
AES as described in Figure 2, mainly contains the electron gun, electron collector
and electron multiplier. The AES involves three basic steps: (1)
ionization (by removal of a core electron), (2)
Atomic
Electron emission (the Auger
process), and (3) Analysis of the emitted Auger electrons. The last stage is simply
a technical problem of detecting charged particles with high sensitivity, with the
additional requirement that the kinetic energies of the emitted electrons must be
determined.
In the Atomic ionization, the accelerated high energy (2~10KeV) electron
beam from the electron gun hits the surface of the sample. Such electrons have
sufficient energy to hit out electrons at all levels of the lighter elements, and higher
core levels of the heavier elements, and then to ionize the elements. With this
process, the inner electron is removed, and the atom is ionized with holes in a
variety of inner shell levels.
The ionized atom that has its inner core electron removed is a highly
excited state and not stable. It will rapidly relax back to a lower energy state by
one of two routes : X-ray fluorescence , or Auger emission. In the auger process,
one electron falls from a higher level to fill an initial core hole in the inner-shell
and the energy liberated in this process is simultaneously transferred to a second
electron; a fraction of this energy is required to overcome the binding energy of
this second electron, the remainder is retained by this emitted the electron, called
Auger electron, as kinetic energy. In the Auger process, the final state is a doublyionized atom with outer core holes. This can be expressed as
KE = Ei - ( Ej1 + Ej2 ) (i<j)
Where KE is kinetic energy of the Auger electrons, and Ei is the inner core
i-shell energy level, and Ej1 and Ej2 are the outer core j-shell energy levels of the
auger electrons. If I is K-shell and j is L-shell, we call KLL auger transition. The
kinetic energy KE can be analyzed to identify the material the high energy electron
hit qualitatively. The amount of the auger electrons from the auger transition is
used to analyze the concentration of the constituents quantitatively.
The Transmission Electron Microscope, also called TEM,
and the
scanning electron microscope, also called SEM was used in this research to study
the structure. The TEM, or the Transmission Electron Microscope, was the first
type of Electron Microscope to be developed to overcome the limitation of light
microscope with less than 1000 magnification and a resolution of 0.2 microns, and
achieved the more than 10,000 magnifications so as to be able to observe small
feature which can not be observed with light microscopes.
The figure 3 is the schema of A TEM, which consists of the electron gun
generating desired energy electron beams, several magnetic lenses functioning as
lens to light, and several apertures. It works much like a light microscope, or a
slide projector. The electron beams transmit the sample and form the image of the
sample on the screen. The TEM uses magnetic lens, but light microscope use light
lenses which are made from transparent materials such as glasses.
The TEM can achieve very high magnifications, but it needs high energy
electron beams so as to transmit through the samples, and the sample has to be
very thin to get good images. The other drawbacks are that high energy of
electrons increases the possibility to damage the samples, and the image is not the
surface image. These limitations are overcome by the scanning electron
microscope (SEM).
Electron
Source
First Condenser
Lens
Second Condenser
Lens
Condenser
Aperture
Sample
Objective Lens
Objective
Aperture
Selected Area
Aperture
First Intermediate Lens
Second Intermediate Lens
Figure 3. The schema of TEM
Electron
Source
First Condenser
Lens
Condenser
Aperture
Second Condenser
Lens
Objective
Aperture
Scan
Coils
Objective
Lens
Sample
Figure 4. The schema of SEM
The scanning electron microscope (SEM) was developed more than 30
year later after
TEM was developed. In SEM, as the name means, the electron
beams are moved by electric fields to scan the sample. The figure is the schema of
the SEM, which consists of electron gun for generating electron beans, magnetic
lenses for focusing electrons, apertures for controlling the energy ranges, and the
electric field plates to sweep the electron beams to control the times electron
beams stay on the spot. This sweeping function is the same as the in electron
scope, or in TV. The Transmission Electron Microscope, also called TEM, was
the first type of Electron Microscope to be developed to overcome the limitation of
light microscope with less than 1000 magnification and a resolution of 0.2
microns, and achieved the more than 10,000 magnifications so as to be able to
observe small feature which can not be observed with light microscopes.
CHAPTER 3
High-rate Deposition of Zinc Ferrite Thin Films from a Soft Solution Process
High-rate Deposition of Zinc Ferrite Thin Films from a Soft
Solution Process
Jiqing Hu1, 2, DooHyoung Lee1, Raghu K. Settaluri2, Chih-Hung Chang1,*
1
2
Department of Chemical Engineering, Oregon State University
School of Electrical Engineering and Computer Science, Oregon State University
Corvallis, OR 97331 USA
* Author to whom all correspondence should be addressed
Department of Chemical Engineering, 103 Gleeson Hall, Corvallis OR 97331,
USA
Phone: 541.737.8548, Fax: 541.737.4600, E-mail: changch@engr.orst.edu
The continued down scaling of device dimensions, and the rapid growth in
the demand for advanced portable wireless communication systems, system-onchip (SOC), are driving significant improvement for better performance with lower
cost. Many of these improvements come from the use of smaller active devices. It
is expected that ultra-high speed RF devices (fmax~230 GHz) with a minimum
dimension of 45nm will be in production by 2010. The fabrication of a RF system
requires the use of passive components such as transmission lines, planar inductors
and capacitors. Thus, there is much room for improvement from the passive
components through reducing losses and parasite effects at high frequency [1].
The spinel ferrite (MFe2O4, M=Zn, Mn, and Ni) is an ideal material system
for high frequency passive components because of its high permeability, resistivity
and permittivity. Ferrites with the spinel structure include normal spinel M[Fe2]O4,
where M as Zn, Cd, and Ca and inverse spinel Fe[MFe]O4 where M as Ni, Co,
Mn, Cu. Spinel ferrite crystal structure possesses the space group fd3m and
consists of 56 atoms; 32 are oxygen anions assuming a close packed cubic
structure, and the remainders are metal cations residing on 8 of the 64 available
tetrahedral (A) sites and 16 of the 32 available octahedral (B) sites [2]. The size
and valence of the cation species determine the filling of these sites and strongly
influence the material’s magnetic and electronic properties.
There are a variety of deposition techniques available for the preparation of
thin film ferrites. Sputtering, thermal evaporation, liquid phase epitaxy, chemical
vapor deposition, spin coating, and sol gel [3-5]. These techniques typically
require high temperatures (> ~ 600oC) for the crystallization of ferrites. Ferrite
plating is a soft-solution processing technique developed by Abe and Tamaura for
the deposition of crystalline spinel thin film ferrites [6]. It has the advantage of
low cost, low temperature, and good conformal coverage. In ferrite plating the
metal ions are supplied by a metal chloride salt (e.g FeCl2, NiCl2, CoCl2, etc)
solution. The oxygen source is provided through hydroxide ions in the solution.
The oxidizing agent such as NaNO2 oxidizes the Fe2+ to Fe3+. The growth
mechanism [7] is a three-step process; first OH-1 is adsorbed on the substrate
surface followed by the adsorption of metal ions replacing the H+ ions. The Fe2+
ions were then oxidized to Fe3+ by the oxidizing agent, NaNO2. Repeating of this
three-step process formed the spinel ferrite thin film. This process was selfregulated at the molecular level. The typical deposition rate for ferrite plating is
around 30nm/min, which might be too slow to deposit films at tens of µm for
microwave applications. Fortunately, it has been demonstrated [8] that by
irradiating the substrate with intensive light the deposition rate can be increased by
a factor of 5 to 10. In this paper, we described a spin-and-spray deposition system
that utilized light-enhanced ferrite plating to achieve relatively high growth rate
(about 0.2 µm per minutes).
The zinc ferrite thin films were deposited using a spin and spray system. A
schematic diagram of this system is shown in Fig. 1. In this system, two reactive
solutions including the metal ion source that contains FeCl2 (Aldrich) and ZnCl2
(Fisher) aqueous solution, and the oxidation source that contains an aqueous
solution of NaNO2 (Mallinckrodt) and CH2COONH4 (Alfa Aesar 97%) were
sprayed through two nozzles continuously on the substrates at a rate of
(50ml/min). The reactant concentrations were given in Table I. The substrates
were rotating between the two nozzles around 1000 rpm. The substrates were
heated (T=80-90oC) and activated through a halogen-lamp that is controlled by a
transformer. The film thickness, roughness, and morphology were measured by a
surface profiler and SEM (FEI Siron with a Schottky type field emission electron
source). The film thickness and surface roughness were characterized by a Vecco
Dektak8 stylus surface profilometer. The morphology and crystal structure were
examined by transmission electron microscopy using bright field imaging (FEI
Tecnai F20) and selected area electron diffraction (SAED) (Philips CM12). The
overall chemical composition of the films was characterized by Auger
spectroscopy using a Physical Electronics SAM 590. The AES was working at
ultra high vacuum (2.9x10-9 torr), the primary exciting electron current and energy
were 100 nA and 5 keV, respectively. The energy resolution was better than 2 eV.
The local chemical composition was characterized by Energy Dispersive X-ray
spectroscopy in SEM and TEM.
The deposited film has a golden brown color. The deposited ferrite film
thickness vs. deposition time was given in Fig. 2(a). The film thickness was
determined by the surface profiler. The deposition rate could be estimated from the
plot to be 0.2 µm/min. This high deposition rate is attractive for most microwave
device applications. Fig. 2b. Shows the SEM image of cross-sectional structure of
a zinc ferrite thin film with a deposition time of 45 minutes. The thickness from
the SEM image agreed well with the measurements from the surface profiler. Fig.
3 (a), (b), and (c) show the SEM images of plane-view structure of zinc ferrite thin
films with different deposition time at 15 minutes, 45 minutes and 75 minutes
respectively. The films were composed of round aggregates of small grains. The
aggregate grew bigger and developed a cauliflower-like appearance with longer
deposition time. The higher magnification image shown in Fig. 3 (d) indicated the
grains have a plate-like morphology with fibrous texture.
The film structures were further characterized by analytical TEM. TEM
samples were prepared by scraping off the thin films from the substrate and place
them on lacey carbon coated copper grids. Fig. 4.(a) shows a bright-field image of
a ferrite thin film. It has a plate-like fibrous morphology, consistent with the SEM
results. Chemical analysis was performed using EDX on various locations of the
films using electron probe with nanometer size. The results shown in Fig.4.(b)
from one of the samples indicated the films contained Fe, Zn, O, C, and Cu.
Carbon and Copper X-ray signals could be attributed to the TEM grid. This EDX
analysis confirmed that we have uniformly incorporated zinc into the ferrite thin
films. Fig. 4(c) shows the selected area electron diffraction (SAED) patterns of the
film. The ring pattern indicated the films were polycrystalline. The electron
diffraction pattern can be indexed according to cubic zinc ferrite structures [9].
Through Auger electron spectroscopy, the constituents of the deposited
film and the concentration of each constituent were analyzed. Fig. 5 (a) shows an
AES spectrum for a zinc ferrite thin film deposited from 0.2 g/L ZnCl2 in the
precursor solution. In the spectra of all thin films, there are three peaks from 450
eV to 550 eV, with the highest peak around 500 eV. These three peaks are the
KLL peaks of oxygen [10]. The positions of the KLL peaks are very close to those
of the standard peaks of oxygen and correspond to 503 eV as the highest peak, 483
eV the second highest peak, and 468 eV the third highest peak. In the spectra of
all thin films, there is a second group of peaks from 570 eV to 750 eV. These
three peaks are the LMM peaks of iron [10]. The positions of the LMM peaks in
the second group are very close to those of the standard peaks of iron and
correspond to 703eV as the stand peak of iron, and some of the peaks represent the
peaks of 550eV, 562eV, 591eV, 610eV, and 651eV. Around 1000eV, there is a
peak which may represent the LMM peak of zinc or the KLL peak of sodium [10].
There is a peak around 220eV for sodium that did not appear in all spectra. Thus
the peak around 1000eV represents zinc. There is a peak around 300eV which
comes from carbon that may result from adsorption of gaseous carbon species. The
AES analysis indicated that our samples contain oxygen, iron. zinc and some
carbon. The atomic concentration can be determined by the auger electron signal.
The atomic concentration of each constituent in the sample is expressed as
Ix
Sx
Cα =
Iα
α Sα
Where, I x is the peak-to-peak Auger amplitude of the constituent component from
the sample, and S x is the respective sensitivity. According to the table of the
relative sensitivities at 5kV, the sensitivity of oxygen at KLL peak 503eV is 0.4,
the sensitivity of iron at LMM peak 703eV is 0.21, the sensitivity of Zinc at LMM
peak 994eV is 0.19, and the sensitivity of carbon at the KLL peak 272eV is 0.14.
The obtained film compositions and their corresponding solution concentration
were given in Table I. Fig. 5(b) shows the Zn/Fe ratio in the solution vs. the Zn/Fe
ratio in the deposited film. The plot indicates that zinc concentration in the film
increased with zinc concentration in the precursor solution initially then reached a
saturation level at higher concentration.
In conclusion, the Zinc ferrite thin films have been successfully deposited
at a relatively high rate (~ 0.2 µm/min). SEM and TEM measurements indicated
the films have a plate-like morphology with fibrous texture. Zinc was uniformly
incorporated into the ferrite thin films confirmed by the local chemical analysis by
EDX. The deposited films are polycrystalline with a typical cubic ferrite structure.
The overall composition of the films were determined by Auger electron
spectroscopy as ZnxFeyO4, x ranges from 0.25 to 0.55, and y ranges from 2.2 to
2.7.
Acknowledgements
The authors would like to acknowledge Dr. Chunfei Li at Portland State University
for his assistance of SEM and TEM measurements. Dr. Tianbao Xie at Linfield
College for his assistance of AES measurement. This work was supported by the
US National Science Foundation under grant # ECS-0401357.
References
[1] A. Sligar, R.K. Settaluri, C.-H. Chang, Novel Crosstalk Suppression Schemes
Employing Magnetic Thin Films, Adv. Micro., March/April 2005, VOL. 32 (2).
[2] V.G. Harris, N.C. Koon, C.M. Williams, Q. Zhang, M. Abe, J.P. Kirkland,
Appl. Phys. Lett. 68 (1996) 2082.
[3] J.M. Robertson, M. Jansen, B. Hoekstra, and P.F. Bongers, J. Cryst. Growth,
41, (1977) 29.
[4] M.F. Gillies, R. Coehoorn, J.B.A. van Zon, D. Alders, J. Appl. Phys. 83 (1998)
6855.
[5] J-G. Lee, J-Y. Park, Y-J. Oh, C. S. Kim, J. Appl. Phys. 84 (1998) 2801.
[6] M. Abe, T. Itoh, Y. Tamaura, Thin Solid Films 216 (1992) 155.
[7]M. Abe, MRS Bulletin September (2000) 51.
[8] T. Itoh, S, Hori, M. Abe, Y. Tamaura, J. Appl. Phys. 69 (1991) 5911.
[9] M.E. Fleet, Acta Crystallogr., Sec. B. 38 (1982) 1718.
[10] Lawrence E. Davis, Noel C. MacDonald, Paul W. Palmberg, Gerald E. Riach
and Roland E. Weber, handbook of Auger Electron Spectroscopy, 2nd ed. Physical
Electron Division Perkin-Elmer Co. Eden Prairie, Minnesota 1976.
Fig. 1. A schematic diagram of the spin and spray ferrite deposition system.
Fig. 2. (a) Ferrite film thickness plotted as a function of deposition time (b) SEM
images of cross-sectional structure of zinc ferrite thin films with deposition time of
45 minutes.
Fig. 3. SEM images of plane-view structure of zinc ferrite thin films with different
deposition time (a) 15 min. (b) 45 min. (c) 75 min. and (d) higher magnification
image for (b).
Fig. 4. (a) Bright field TEM image of zinc ferrite thin film (b) EDX spectra from
selected area (c) Selected area electron diffraction pattern.
Fig. 5. (a) Auger spectra of a zinc ferrite thin film deposited from 0.2 g/L ZnCl2 in
the precursor solution (b) Atomic ratio of Zn/Fe in film plotted as a function ZnCl2
concentration in solution.
Tubes
Halogen Lamp
Peristaltic
Pump
Spray Nozzles
Substrates
Spinning Stage
NaNO2 & ACE
FeCl2 & ZnCl2
Transformer
Fig. 1.
12
THickness (um)
(a) 10
8
6
4
2
0
0
20
40
60
-2
Deposition time (minutes)
(b)
Fig. 2.
80
(a)
(b)
(c)
(d)
Fig. 3.
Bright Field
(a)
2
1
100 nm
150 Fe
Fe
Fe
O
Cu
50
EDX Bright Field Area 2
Fe
Counts
O
C
Counts
(b)100
60
EDX Bright Field Area 1
Fe
Fe
40 C
20
Cu
Zn
Cu
Zn
Cu
Zn
Zn
0
0
0
5
10
15
Energy (keV)
20
0
5
10
15
Energy (keV)
20
(c)
JCPDS
(85-1436)
Fe3O4
JCPDS
(82-1049)
ZnFe2 O4
Obtained
Ferrite
thin film
4.8457
4.8733
-
2.9673
2.9843
-
2.5305 (311)
2.5450
2.527
2.4228
2.4366
-
2.0982 (400)
2.1102
2.075
1.9254
1.9364
-
1.7132
1.7299
-
1.6152
1.6244
-
1.4836 (440)
1.4921
1.482
311
Fig.4.
400
440
(a)
Auger Electron Spetroscopy
40000
O
35000
Fe
30000
20000
Zn
15000
Fe
10000
5000
O
0
200
400
600
800
1000
1200
Ele ctron Energy (eV)
(b)
Zinc Iron Atomic Ratio
0.16
0.14
Zinc Iron Ratio
dN(E)/dE
25000
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.2
0.4
0.6
0.8
Zinc Cloride Concentration in Solution (g/l)
Fig.5.
1
Table I. Composition of Zn ferrite thin films determined by AES
ZnCl2
(g/L)
IO
Auger peak-topeak amplitude
IFe
IZn
Auger peak-topeak amplitude
Auger peak-topeak amplitude
Composition
0.000
16.20
5.30
0.000
Fe2.490O4
0.020
16.20
5.20
0.332
Zn0.28Fe2.445O4
0.050
16.15
5.10
0.278
Zn0.24Fe2.410O4
0.100
16.20
8.10
0.681
Zn0.372Fe3.810O4
0.200
16.30
4.70
0.400
Zn0.38Fe2.200O4
0.400
16.22
5.08
0.635
Zn0.55Fe2.400O4
0.600
16.13
5.81
0.665
Zn0.51Fe2.70O4
0.801
16.15
5.20
0.550
Zn0.47Fe2.450O4
All precursor solution contains FeCl2 3g/L, NaNO2 0.5g/L, CH3COONH4 5g/L
with varied ZnCl2 concentration in De-ionized water.
CHAPTER 4
Background for Impedance Spectroscopy Characterization of Zinc Ferrite Thin
Film from a Soft Solution Process
Ferrites, as solid state materials, have the following properties: mechanical,
thermal, electrical, magnetic, dielectric, and optical properties that need to be
considered. The dielectric properties of ferrites are equally important as the
magnetic properties because the duality of the complex permeability and the
complex permittivity. There are many studies regarding to the magnetic properties
of ferrites through measuring the permeability and B-H loops. The study of their
dielectric properties, however, is relatively rare.
Ferrite are soft magnetic materials, they could also be used for dielectrics.
Dielectric materials usually have very high resistance. Because the electrical
current can not flow through it easily, dielectric materials can prevent the leakage
of an electrical current or electrical free charges moving inside its body. Dielectric
material is distinctly different from the electrical conductor which provides the
path for free charges moving inside its body when applied electric voltage or
electric field. Even the dielectric materials do not provide the path for electrical
charges to pass through its body, when an electric field was applied on its body, a
phenomenon called Polarization will occur inside the body, in which the bonded
charge particles align with the applied electric field. This alignment of the bonded
charge particles will produce additional electric field to compensate the applied
electric field. The fundamental basis of the phenomena is the interaction of the
dielectric material with the applied electric field, and this interaction could be
characterized by the dielectric constant.
Ferrites with the spinel ferrite structure contain all the material as MFe2O4 (
M[Fe2]O4, where M as Zn, Cd,, and inverse spinel Fe[MFe]O4 where M as Ni,
Co, Fe, Mn, Cu). Spinal ferrite crystal structure possesses the space group, fd3m,
structure and consists of 56 atoms; 32 are oxygen anions assuming a close packed
cubic structure of lattice parameter a0/2, where a0 is the length of a ferrite unit
structure, and the remainders are metal cations residing on 8 of the 64 available
tetrahedral (A) sites and 16 of the 32 available octahedral (B) sites. The size and
valence of the cation species determines the filling of these sites and in turn
strongly influences the materials’ magnetic and electronic properties: high
permeability and high permittivity. These properties are benefit to high frequency
applications.
The crystal ferrite is an ionic material, the outer shell of the oxygen anion
has 8 electrons which is complete filled and stable, and the outer shell of the metal
cations is empty and stable as well. When the ferrite is subjected to an applied
electric field, there are not many free carriers, and the ferrite behaves as an
insulator with high resistance. The Fe2+ has 6 orbit 3d electrons, and one of the 6
electrons may transfer to the s orbit of the next shell and become the free electron
that would contribute some conductivities. There is a hop effect that the electrons
may hop from one iron atom to anther iron atom if the hop requirement is satisfied.
This hop effect will contributes to the conductivities.
As stated earlier, permittivity (also called dielectric constant when
comparing to free space), loss tangent, and conductivity are three important
properties for dielectric materials. First, the permittivity will be discussed. The
force of two point charges inside a dielectric material which fills all the space is
given by the well-known Coulomb's law as:
F=
q1q2 rˆ
4πε r 2
(1)
where F is the coulomb force of interaction between two charges q1 and
q2 (each expressed in unit of coulombs) separated by a distance of r in a dielectric
medium; and r is the unit vector along the direction of r,
is the dielectric
permittivity of the filled dielectric material. If the filled material is free space, or
empty space, or vacuum space,
expressed as
o,
and
o
is the dielectric permittivity of the free space
has a value of (1/36 )x10-9 farad/meter or 8.85x10-12
farad/meter in SI units. And the permittivity of a dielectric material
expressed as o r related to the free space.
r
can be
is the dielectric constant of the
dielectric material or the relative permittivity, and is dimensionless. So the
dielectric constant of free space is 1. Using the Coulomb's law to describe the
dielectric constant and permittivity is under an ideal assumption that the dielectric
material fills all the space and there are no boundary effects.
The two-parallel-plate capacitor structure is a practical and popular
structure to characterize the dielectric materials. The two plates are separated by a
distance h under an applied voltage V. Because of the applied voltage, charges will
accumulate at the external surface of the two plates which have an area of A
square meters.
(a)
(b)
Figure 1. Schematic diagrams of two parallel-plate capacitor.
As shown in Figure 1(a), the space between the two plates are free space,
the electric field is expressed as
E=V/d,
the free charge accumulated at one of the internal surfaces of the two plates
equals to Q0
where Q0=C0V,
where the capacitance of the two parallel-plate capacitor is
C0 =
ε0 A
d .
As shown in Figure 1(b), the space between the two plates is filled with
dielectric materials with a dielectric constant of ε r , and the capacitance of the two
parallel-plate capacitor becomes
C=
ε 0ε r A
d
,
the free charge that is accumulated at one of the external surfaces of the
two plates equal to Q
where Q=CV ,
The electric field is normal to the inner surface of the parallel plates,
especially at the center of the plates. As the location approaches to the edge of the
plates, the electric field may not be normal to the surface of the plates. Fortunately,
dimension of the plates becomes much larger than the distance, d, this fringe effect
can be ignored.
The terms discussed above are the dielectric constant and permittivity
under applied static electric field. Even though the dielectric materials has large
resistance, there are still some free carriers inside. The moving free carriers will
contribute to the leakage current and consume the electric energy, which can be
termed as the loss tangent of power consumption. For ideal capacitors, when an
alternative electric field is applied, the electrical energy is stored as potential
energy through charge accumulation at the surface in positive half circle, and then
the charge cumulated are discharge to give off energy in the negative half circle,
and there is no energy dissipated within the dielectric materials. In reality, when an
alternative electric field is applied, there will be free charges escaped which will
be able to move around and consume the electric energy. For the parallel-plate
capacitor, the ratio of the energy consumed to the energy stored in the capacitor is
the loss tangent of the power consumption.
When an electric field is applied to the zinc ferrite thin films, there are a
few phenomena occurred from atomic to the macroscopic level. At the atomic
level, through atomic polarization, the center of positive nuclei and negative
electron clouds are away from the original position with a small displacement. In
ferrite, as an ionic material, the ionic polarization occurs at the molecular level that
will displace the cation and anion sublattices. The ferrite crystal may polarize and
become bipolar, or dipolar under an electric field. The zinc ferrite thin films
deposited by spin-and-spray solution-based technique are polycrystalline with
grain boundaries. The polarized charges or some free charges accumulated at the
boundary, and limit or restrict the movement of the charges moving inside the zinc
ferrite thin films. All these phenomena will contribute to the dielectric properties
of the zinc ferrite thin films.
When the zinc ferrite is under an alternative electric field, the polarization
of the material is related to the dielectric constant or relative permittivity, and the
energy dissipated as the leakage, heat energy through friction and other ways was
termed as the loss tangent of power dissipation. At different levels, the dielectric
constant and loss tangent may have different characteristics at different frequency,
which could be characterized by the impedance spectroscopy. The impedance
spectroscopy is a classical method for studying the frequency response of
dielectric materials. This method was put forward 60 years by K. S. Cole and R. H.
Cole through the famous Cole-Cole diagram. A plethora of of models describe the
dielectric material were developed since then, such as the Debye relation model.
As discussed earlier, the origin of the dielectric properties ranges from the atomic
level to the macroscopic level, and it is difficult to construct a model to describe
the dielectric properties at all levels.
Impedance Spectroscopy is ideal for investigating the electrical response of
dielectric materials as a function of frequency.
It can be used to study the
impedance behavior of a material and be analyzed based on an idealized circuit
model with discrete electrical components. The analysis is mainly accomplished
by fitting the impedance data to an equivalent circuit, which is representative of
the material under investigation. For studying the zinc ferrite thin films using the
impedance spectroscopy, a model consisting of resistors, capacitors and inductors
was constructed and compares with the data from the impedance spectroscopy
measurements. The dielectric properties of zinc ferrite thin film were obtained by
fitting the data to the model.
CHAPTER 5
Impedance Spectroscopy Characterization of Zinc Ferrite Thin Film from a Soft
Solution Process
Impedance Spectroscopy Characterization of Zinc Ferrite Thin Film from a
Soft Solution Process
Jiqing Hu1, 2, DooHyoung Lee1, Raghu K. Settaluri2, Chih-Hung Chang1,*
1
2
Department of Chemical Engineering, Oregon State University
School of Electrical Engineering and Computer Science, Oregon State University
Corvallis, OR 97331 USA
* Author to whom all correspondence should be addressed
Department of Chemical Engineering, 103 Gleeson Hall, Corvallis OR 97331,
USA
Phone: 541.737.8548, Fax: 541.737.4600, E-mail: changch@engr.orst.edu
Abstract:
The spinel ferrite (MFe2O4, M=Zn, Mn, and Ni) is an ideal material system
for high frequency passive components because of its high permeability, resistivity
and permittivity. A model consisting of resistors, capacitors and inductors was
constructed and used for the analysis of impedance spectroscopy. The dielectric
properties of zinc ferrite thin films were obtained by fitting the data to the model.
The results show that the dielectric constants are around 15 regardless of Zn/Fe
ratio. This value is consistent with most of the reported values for bulk ferrite
materials. The resistivity changes from 0.6x106 ohm.meter to 1.3 x106 ohm.meter
when Zn/Fe ratio varies from 0.6x106 ohm.meter to 1.3 x106 ohm.meter.
Introduction
The continued down scaling of device dimensions, and the rapid growth in
the demand for advanced portable wireless communication systems, system-onchip (SOC), are driving significant improvement for better performance with lower
cost. Many of these improvements come from the use of smaller active devices. It
is expected that ultra-high speed RF devices (fmax~230 GHz) with a minimum
dimension of 45nm will be in production by 2010. The fabrication of a RF system
requires the use of passive components such as transmission lines, planar inductors
and capacitors. Thus, there is much room for improvement from the passive
components through reducing losses and parasite effects at high frequency [1].
Ferrites with the spinel structure include normal spinel M[Fe2]O4, where
M as Zn, Cd, and Ca and inverse spinel Fe[MFe]O4 where M as Ni, Co, Mn, Cu.
Spinel ferrite crystal structure possesses the space group fd3m and consists of 56
atoms; 32 are oxygen anions assuming a close packed cubic structure, and the
remainders are metal cations residing on 8 of the 64 available tetrahedral (A) sites
and 16 of the 32 available octahedral (B) sites [2]. The size and valence of the
cation species determine the filling of these sites and strongly influence the
material’s magnetic and electronic properties. The spinel ferrite (MFe2O4, M=Zn,
Mn, and Ni) is an ideal material system for high frequency passive components
because of its high permeability, resistivity and permittivity. There are a variety of
deposition techniques available for the preparation of thin film ferrites. Sputtering,
thermal evaporation, liquid phase epitaxy, chemical vapor deposition, spin coating,
and sol gel [3-5]. These techniques typically require high temperatures (> ~ 600oC)
for the crystallization of ferrites. Ferrite plating is a soft-solution processing
technique developed by Abe and Tamaura for the deposition of crystalline spinel
thin film ferrites [6]. It has the advantage of low cost, low temperature, and good
conformal coverage. In ferrite plating the metal ions are supplied by the metal
chloride salt (e.g FeCl2, NiCl2, CoCl2, etc) solution.
In this paper, the dielectric properties of zinc ferrite thin films deposited
from a light-enhanced spin and spray system were studied using impedance
spectroscopy. Impedance spectroscopy is a powerful tool for investigating the
electrical properties of materials. This was achieved by studying the impedance
behavior of the material and analyzed through an equivalent circuit. A model
consisting of resistors, capacitors and inductors was built to describe the zinc
ferrite thin films. The electrical properties including dielectric constant or
permittivity, and conductivity were obtained through fitting the impedance data
using this model.
Experimental
The zinc ferrite thin films were deposited on the Ta/Si/Au substrates, using
a spin and spray system. A schematic diagram of this system is shown in Fig. 1. In
this system, two reactive solutions including the metal ion source that contains
FeCl2 (3g/L) and ZnCl2 (0.02g/L to 0.8g/L) aqueous solution, and the oxidation
source that contains an aqueous solution of NaNO2 (0.5g/L) and CH2COONH4
(5g/L) were sprayed through two nozzles continuously on the substrates. The
substrates were rotating between the two nozzles. The substrates were heated and
activated through a halogen-lamp that is controlled by a transformer. The film
thickness, roughness, and morphology were measured by a surface profiler and
SEM (FEI Siron with a Schottky type field emission electron source). The film
thickness was measured by a Vecco Dektak8 stylus surface profilometer. The
morphology and crystal structure were examined by transmission electron
microscopy using bright field imaging (FEI Tecnai F20) and selected area electron
diffraction (SAED). The overall chemical composition of the films was
characterized by Auger spectroscopy using a Physical Electronics SAM 590. The
AES was working at ultra high vacuum (2.9x10-9 torr), the primary exciting
electron current and energy were 100 nA and 5 keV, respectively. The energy
resolution was better than 2 eV. The local chemical composition was characterized
by Energy Dispersive X-ray spectroscopy in SEM and TEM.
The impedance spectroscopy was performed using a Solartron SI 1287
electrochemical interface along with a SI 1260 frequency response analyzer. The
sample was tested using a probe station (J-micro 327 model). A tungsten probe
with a 1mm diameter bar was in contact with the tantalum substrate and another
1mm diameter tungsten probe was in contact with the ferrite thin film.
A
schematic diagram is as Figure 2. As the impedance analyzer sweeps the
frequency, the frequency response was collected by the Zplot software.
Results and discussion
The film structures were characterized by analytical TEM. TEM samples
were prepared by scraping off the thin films from the substrate and place them on
lacey carbon coated copper grids. Fig. 3.(a) shows a bright-field image of a ferrite
thin film. It has a plate-like fibrous morphology. Chemical analysis was performed
using EDX on various locations of the films using electron probe with nanometer
size. The results shown in Fig.3.(b) from one of the samples indicated the films
contained Fe, Zn, O, C, and Cu. Carbon and Copper X-ray signals could be
attributed to the TEM grid. This EDX analysis confirms that we have uniformly
incorporated zinc into the ferrite thin films. Fig. 3(c) shows the selected area
electron diffraction (SAED) patterns of the film. The ring pattern indicated the
films were polycrystalline. The electron diffraction pattern can be indexed
according to cubic zinc ferrite structures [4].
Through Auger electron spectroscopy, the constituents of the deposited
film and the concentration of each constituent were analyzed. The overall
composition of the films was determined by Auger electron spectroscopy as
ZnxFeyO4, x ranges from 0.25 to 0.55, and y ranges from 2.2 to 2.7.
The simplest model to describe a dielectric material filled inside two
parallel plates is shown in Fig.4, a resistor Rs follows with the parallel of a resistor
Rp and capacitor Cp.
Rs is the contacting resistance between the dielectric
material and the electrode, Rp is related to the power dissipation inside the
dielectric material, and Cp is the capacitance between the two plates. The
impedance analysis of the model is as follows.
Z = Rs +
Rp
1 + jωCpRp
(1)
Where Z is the impedance between 1 and 2 nodes in figure 4, and
is the angular
frequency.
Z = Zr + jZi = Rs +
Rp
1 + jωCpRp
(2)
Where Zr is the real part, and Zi is imaginary part of the impedance Z.
Rp
ωCpRp 2
Z = Rs +
−j
1 + ω 2 Cp 2 Rp 2
1 + ω 2 Cp 2 Rp 2
(3)
As ω → ∞ , Z = Z = Rs
As ω → 0 , Z = Z = Rs + Rp
Zr = Rs +
Zi = −
Rp
1 + ω Cp 2 Rp 2
2
ωCpRp 2
1 + ω 2 Cp 2 Rp 2
As ωCpRp → 1 , Zi = −
(4)
(5)
Rp
which arrives at the minimum position of Zi
2
From the minimum Zi position, we can obtain the Cp value and the Rp value.
Rp
Rp 2
ωCpRp 2
( Zr − Rs − Rp / 2) 2 + Zi 2 = (
)
(
)2
−
+
2
2
2
2
2
2
2
1 + ω Cp Rp
1 + ω Cp Rp
Rp
) 2 ((1 − ω 2 Cp 2 Rp 2 ) 2 + ( 2ωCpRp ) 2 )
=(
2
2
2
(1 + ω Cp Rp ) ⋅ 2
Rp
=(
) 2 (1 + ω 2 Cp 2 Rp 2 ) 2
2
2
2
(1 + ω Cp Rp ) ⋅ 2
Rp
= ( )2
2
(6)
Equation (6) describes a circle with the center at (Rs+Rp/2, 0) and the
diameter of Rp. The imaginary part Zi is always less than 0, so it is a semicircle in
the negative imaginary plane.
When ωCpRp = 1 , -Zi achieves its maximum value, and the angular frequency is
denoted as
max,
Cp = 1 /(ω max Rp)
(7).
From the semicircle in the complex plane, we can locate Rs and Rp, and f
at the maximum Zi, in order to calculate Cp. However, this method has a major
disadvantage that the frequency at maximum can not always be determined easily.
The bode plots (which plots the logZ and phase angle vs logf) has an important
advantage that the region which are dominated by the resistive elements such as Rs
and Rp has the slop of zero and the region dominated by capacitive elements has a
slope of -1 for the ideal case. The elements of the Rs and Rp can be determined
from the high frequency regions of the bode plots according to the condition of
frequency approaches to 0, Z approaches to Rs, and frequency approaches to
infinity, Z approaches to Rs+Rp.
From region dominated by capacitors for which has a slop of -1,
logZ’=-(log +logCp)=-log2
-logf-logCp,
(7)
Where Z’ is the fitted line.
As logf=-log2 , or f=1/2 , logZ’=LogCp,
Cp=Z’(1/2 ) .
(8)
The Cp value is calculated from the Bode plots.
These are the two ways to calculate Cp, Rs and Rp of the thin film under
the two probes. The theoretical foundation for calculating the capacitance and Rs
and Rp was discussed above. In the following section, an example of obtaining the
capacitance from the zinc ferrite thin film deposited using a solution containing
0.2g/L of ZnCl2 was presented here.
Before measuring the capacitance and resistance of the zinc ferrite thin
films, the capacitance and resistance from the system, including the substrate, the
probe, the interface between the probe to the contacting area, and even the
measuring equipment must be considered. Figure 5 show the impedance spectra of
the measurement as the probes contact on the substrate surfaces and the zinc ferrite
thin film in the sample are not within the electric flowing path. There is no
semicircle in the frequency range up to a 30MHz. The behavior is dominated as a
small resistance resistor. This means that there is no contacting capacitance effect
when measurement was done in this frequency range. We can conclude that the
setup is in a resistance dominated range with a zero slope, and the impedance is
40.99 ohm. There are some strange signal after 1MHz, this is from the SI1287
electrical interface and SI1260 frequency response analyzer.
The SI 1287 and SI 1260 have a measurement limitation below an
impedance around 50pF. There is an internal capacitance around 50pF. To remove
the effect of this internal capacitance, a 10M ohm resistor was used to show the
internal capacitance.
Figure 6 shows the impedance spectra of a 10M ohm
resistor. From figure 6(a), at a frequency less than 10 Hz, the impedance is
dominated by the resistance, and at frequency from 2x103 to 2x104 Hz, the
impedance is dominated by the capacitance. Figure 6 shows the impedance spectra
with the data points of frequency up to 40kHz after removing a spike point. The
spectra can be fitted with the model shown in figure 4 as Rs=4572 ohm,
Rp=10.194Mohm, and Cp=63.1pF with less than 1% error in fitting.
A capacitance value of Cp=63.1pF was obtained from the measurement
system using a 10M ohm resistor. This capacitance must be considered for the
future measurements. The following section discuss measurements of zinc ferrite
thin films with and without the 10M ohm resistor.
Figure 7 shows the impedance spectra of the 10Mohm resistor parallel with
the zinc ferrite sample. At frequency less than 30 Hz, the resistance is dominated
by the value of 5.18M ohm and the bode plot has a zero slope. At frequency from
5 kHz to 70 kHz, the slope is -1 as the capacitance dominates. After 100kHz, there
are some strange signals because of the measurement accuracy range. So the data
points are ranged up to the frequency at 50kHz. The spectra can be fitted using the
model Rs=1717 ohm, Rp=5.37Mohm, and Cp=132.4pF with less than 1% error in
fitting. The capacitance of the thin film under the probe would be calculated as
132.4pF-63.1pF=69.3pF, and R=5.37x10.194/(10.194-5.31)=11.35Mohm.
Figure 8 shows the impedance spectra of the sample without the 10M ohm
resistor. At frequency less than 3 Hz, the resistance is dominated by a value of
19.5Mohm. At a frequency range from 1 kHz to 70 kHz, the slope is -1 as the
capacitance dominates. The data can be fitted using the model with parameters
Rs=2295 ohm, Rp=15.53Mohm, and Cp=119pF with an error less than 2%. The
capacitance of the thin film under the probe is 119pF-63.1pF=55.7pF, and
R=15.53Mohm, little larger than =11.35Mohm.
From these two methods, an average capacitance of 62.5pF is obtained.
The thickness of film is about 1.5um and the diameter of the probe bar is 1mm, so
the dielectric constant can be calculated from
C=
ε 0ε r A
d
(9)
and obtain that r=13.5, and the resistance is about 15Mohm.
Following the same procedures, the capacitance and resistance for a set of
samples with different Zn/Fe ratio were measured and the results were given in
figure 9 and figure 10. Figure 9 shows that the dielectric constants are around 15
for several zinc ferrite thin films with different Zn/Fe ratio. This value is consistent
with most of the reported values for bulk ferrite materials. All zinc ferrite thin
films have high resistivity ranging from 0.6x106 ohm.meter to 1.3 x106 ohm.meter.
In general, the resistivity increase as the Zn/Fe increase.
Conclusions
We used impedance spectroscopy to study the electrical properties of zinc ferrite
thin films deposited by a spin and spray soft solution process. A model consisting
of resistors, capacitors and inductors was constructed and used for the analysis of
impedance spectroscopy. The dielectric properties of zinc ferrite thin films were
obtained by fitting the data to the model. The results show that the dielectric
constants are around 15 regardless of Zn/Fe ratio. This value is consistent with
most of the reported values for bulk ferrite materials. The resistivity changes from
0.6x106 ohm.meter to 1.3 x106 ohm.meter when Zn/Fe ratio varies from 0.6x106
ohm.meter to 1.3 x106 ohm.meter.
Acknowledgements
The authors would like to acknowledge Dr. Chunfei Li at Portland State University
for his assistance of SEM and TEM measurements. Dr. Tianbao Xie at Linfield
College for his assistance of AES measurement. This work was supported by the
US National Science Foundation under grant # ECS-0401357.
References
[1] Claude Gabrielli, Identification of electrochemical processes by frequency
response analysis. Solartron Techinical report number 004,
[2] Claude gabrielli,Use and application of electrochemical impedance techniques.
Solartron Technical report 24, 1997.
[3] V.G. Harris, N.C. Koon, C.M. Williams, Q. Zhang, M. Abe, J.P. Kirkland,
Appl. Phys. Lett. 68 (1996) 2082
[4] M.E. Fleet, Acta Crystallogr., Sec. B. 38 (1982) 1718.
[5] J-G. Lee, J-Y. Park, Y-J. Oh, C. S. Kim, J. Appl. Phys. 84 (1998) 2801.
[6] M. Abe, T. Itoh, Y. Tamaura, Thin Solid Films 216 (1992) 155.
[7]M. Abe, MRS Bulletin September (2000) 51.
[8] T. Itoh, S, Hori, M. Abe, Y. Tamaura, J. Appl. Phys. 69 (1991) 5911.
[9] M.E. Fleet, Acta Crystallogr., Sec. B. 38 (1982) 1718.
[10] Lawrence E. Davis, Noel C. MacDonald, Paul W. Palmberg, Gerald E. Riach
and Roland E. Weber, handbook of Auger Electron Spectroscopy, 2nd ed. Physical
Electron Division Perkin-Elmer Co. Eden Prairie, Minnesota 1976.
Tubes
Halogen Lamp
Peristaltic
Pump
Spray Nozzles
Substrates
Spinning Stage
NaNO2 & ACE
Transformer
FeCl2 & ZnCl2
Fig. 1 A schematic diagram of the spin and spray ferrite deposition system.
SI 1287
Compute
d
SI 1260
Figure 2. A schematic diagram of impedance spectroscopy measurements
Bright Field
2
1
100 nm
250
100
Fe
Fe
200 O
C
80
150
Counts
Counts
Fe
EDX Bright Field Area 1
Fe
100
O
C
Fe
Fe
60
40
Cu
Zn
Cu
Zn
50
EDX Bright Field Area 2
Cu
Zn
Cu
Zn
20
S
0
0
0
5
10
15
Energy (keV)
20
0
5
10
15
Energy (keV)
Fig. 3 a) SEM image, b) The EDX results, c). TEM diffraction pattern
20
Rp
1
Rs
2
Cp
Fig.4. A model of resistor Rs follows parallel Resistor Rp and capacitor Cp
-50
102
|Z|
101
-25
10-1
10-2
10-1
100
101
102
103
104
105
106
107
Z''
100
108
0
Frequency (Hz)
25
-200
theta
-100
50
-50
0
200
10-2
-25
0
Z'
100
10-1
100
101
102
103
104
Frequency (Hz)
105
106
107
108
(b)
(a)
Figure 5 The impedance spectra of the setup without samples
25
50
108
-1e7
FitResult
FitResult
|Z|
107
106
105
104
10-2
-5e6
10-1
100
101
102
103
104
105
Z''
Frequency (Hz)
-100
0
theta
-75
-50
-25
0
25
10-2
10-1
100
101
102
103
104
5e6
105
0
Frequency (Hz)
(a)
5.0e6
1.0e7
Z'
(b)
Figure 6. The impedance spectra of a 10Mohm Resistor with model fitting.
1.5e7
10 7
-5.0e6
FitResult
FitResult
|Z|
10
6
10 5
10 4
10 -2
-2.5e6
10-1
100
101
102
103
10 4
10 5
Z''
Frequency (Hz)
-100
0
theta
-75
-50
-25
0
25
10 -2
2.5e6
10-1
100
101
102
103
10 4
0
10 5
(a)
2.5e6
5.0e6
Z'
Frequency (Hz)
(b)
Figure 7. The impedance spectra of the thin ferrite thin film and a parallel
10Mohm Resistor along with model fitting.
7.5e6
-7.5e6
107
FitResult
FitResult
|Z|
106
105
-5.0e6
104
102
103
104
105
Z''
Frequency (Hz)
-2.5e6
-90
theta
-80
-70
-60
0
-50
102
0
103
104
2.5e6
105
Frequency (Hz)
(a)
5.0e6
Z'
(b)
Figure 8. The impedance spectra of the thin ferrite thin film.
7.5e6
Dielectric constants of zinc ferrite thin films
20
18
16
14
12
10
8
6
4
2
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Zn/Fe ratio
Figure 9. Dielectric constants of zinc ferrite thin films vary with Zn/Fe ratio.
1.6
Resistivity (mOhm.Meter)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Zn/Fe ratio
Figure 10. Resistivity of thin ferrite thin films vary with Zn/Fe ratio.
0.14
CHAPTER 6
A grounded coplanar waveguide based technique for nondestructive measurement
of high frequency complex permittivity and permeability of thin films
Abstract:
Characterization of thin film materials for determining the complex permittivity
and permeabilities is very important for a wide range of RF/microwave
applications.
This chapter presents a simple extraction procedure for the
extraction of these parameters using grounded coplanar waveguide configuration.
Conformal mapping is used for obtaining the filling factors for the grounded
coplanar waveguide structure. Software programs have been developed in Matlab
platform to extract the complex permeability and permittivity parameters from the
full-wave 3D electromagnetic simulations carried out using Ansoft’s HFSS
software. This grounded coplanar waveguide based technique can achieve less
than 2% error for extracting these parameters from the full-wave simulation
results. The chapter describes a systematic methodology to extract the parameters.
This method is also applicable for measurement based extraction procedure to
determine the material parameters for material of unknown characteristics.
Introduction
Continued down scaling of device dimensions and the rapid growth in the
novel fabrication technologies are enabling factors for the realization of high
performance wireless communication systems. With the implementation of new
thin film dielectric materials in the recent fabrication schemes, measurement of
key material parameters such as of complex permittivity and permeability have
gained prominent importance. High Dielectric Constant in oxides with the
perovskite structure such as ACu3Ti4O12 and ACu3Ti3FeO12 has been a hot
topic in recent years. This material has colossal permittivity of four to five fold at
the low frequency of the order of tens of Mega hertz. A common technique for
measurement of relative permittivity is by measuring the parallel plate capacitance
of a test structure filled with the material under test. However, this technique has
limited application for RF and microwave frequencies. Recently, authors have
been studying the ferrite properties and thin film deposition techniques low
temperatures, which is very useful for high frequency application at backend
processing. In this chapter, we propose a procedure using grounded coplanar
waveguide structure as the test structure to characterize the complex permittivity
and permeability of the thin films. We will demonstrate the validity of technique
with the help of full-wave 3D electromagnetic simulations, which can be easily
extended to extract the material properties from the measurement.
In recent years, several researchers have reported use of network analysis
techniques for characterizing the high frequency properties of thin films. M. Wu
and his colleagues prepared the sample with sol-gel techniques and measured the
transmission and reflection coefficient of the prepared sample to calculate complex
permeability and complex permittivity. The technique using the network analyzer
to measure the permittivity and/ or permeability was first reported by A. M.
Nicolson and G. F. Ross [46] in time domain, and then followed by William B.
Weir in the frequency domain. Weir’s technique measures the transmission and
reflection coefficient of waveguide or TEM transmission line inserted with sample
materials. His model has three regions, in which the two end side regions have the
same characterization. This technique uses two close frequencies or the average
group delay to resolve the phase ambiguity when the sample length of the material
is longer than the wavelength in the dielectric material. Trevor William and his
colleagues extended the Weir’s model by adding another layer for the deposition
of the material under test and measured its complex permittivity. Sebastien,
Lefrancois and his co-workers studied the resonant structures using Weir’s
configuration to characterize the material. Other researchers [33] used the openend coaxial probe to characterize the materials where, one end of the weir structure
is open or closed to result in a one port network. In all these models, the wave
propagates in a direction from the one end of the test sample to another end with a
uniform cross section. However, in the case of coplanar waveguide geometry, the
central conductor is buried between two dielectric layers which are fabricated in
sequence and their dielectric and magnetic properties may be different. For this
configuration, several analytical procedures have been reported. The coplanar
waveguide and stripline configuration are known to be popular for the
characterization of high frequency dielectric and magnetic properties.
The extraction procedure for the high frequency characterization generally
involves measurement of scattering parameters of the sample using microwave
network analyzer. The effective permittivity and permeability calculation are the
approximated with formulae derived from the conformal mapping techniques. In
1970s, the large computation seemed not practical and this technique was not
popular. In recent years, due to the increased computational resources, this
technique regained a lot of attention.
Several new configurations have been
reported to characterize the permittivity and permeability of materials based on
measured s-parameters. The two important concepts, which are: a) the duality
relationship of permittivity and permeability and b) filling factors or the filling
fractions proved to be the key aspects in these techniques, particularly with
reference to the coplanar waveguide configuration. However, due to certain
approximations, the results have not been quite promising. Walter Barry’s research
[2] showed that the mismatch at the strip-line-to-coax joint and any impedance
difference between the stripline and the network analyzer port may result in larger
values of measured ’’ and ’’ for lower loss materials. Robert A Pucel and
Daniel J. masse [23, 33] pointed out that dielectric losses and ohmic conducting
losses also affect the results. Since calculation of complex permittivity and
complex permeability is a reversing problem, A Raj stated four challenges in terms
of isolating the conductor, dielectric and radiation losses, as well as dispersion. On
the configurations or testing structures, Giovanni Ghione [8] studied four
configurations: CPW1, CPW2, CPW3 and CPW4; and Said S. Bedair Ingo Wolf,
studied three structures: SCPW1. SCPW2 and SCPW3 by referring to the
conformal mapping results by C. Veyres and Fouad Hanna[4]. The configurations
stated have not been quite successsful to characterize the deposited thin films on
conduction or glass substrates.
In this chapter, the author proposes a grounded coplanar waveguide
configuration to obtain the complex permittivity and permeability by using the
measured S-parameters of thin film deposited on a dielectric substrate with or
without a conduction layer. For validation, full-wave EM simulations using
Ansoft’s HFSS software will be used to substitute the measurement results.
Software has been developed on Matlab platform to extract the complex
permittivity and complex permeability of the test material from the s-parameters.
Basic Structure
The proposed configuration for the material parameter extraction is shown
in Fig. 1. The structure is a grounded coplanar waveguide, the bottom part (part 2)
is filled with silicon dioxide on the conductive material as the support frame; and
top part (part 1) is the dielectric material under test and has been deposited on the
surface of the supporting conductive material. The dielectric constant of the
dielectric material within the supporting frame is considered to be 4 with no
dielectric losses. The dielectric thicknesses h1 and h2 are chosen to be 30 um. The
conductor thickness is considered to be 0.1 um, and the separation between
conductors to be 5um. The center wire has a width of 100 um. The HFSS was
used to simulate the structure with different test dielectric materials, and the S
parameters, Z parameters, and other parameters from the simulation are used for
the purpose of material parameter extraction.
A Matlab code was developed to extract the complex relative permittivity
(dielectric constant) and the complex relative permeability from the simulated S or
Z parameters by using the conformal mapping techniques. The extracted complex
relative permittivity and the complex relative permeability are compared with the
input values provided in the HFSS simulation. The theory and results are discussed
in the following.
Theoretical approach
The theoretical approach in this study has three sections. The first section is
to study the relationship of the S parameters or Z parameters, which can be
measured from the network analyzer. The second section is using the duality
properties and the filling factors to construct a relationship between the effective
permittivity and the effective permeability to the relative permittivity and relative
permeability of the materials filling in the structure of the transmission line. The
last section is to derive the filling factors, which are critical for constructing the
relationship proved in the second section. Using these three sections, a series of
equations are constructed solving which, unknown complex permittivity and
complex permeability of the test material can be obtained.
The effective permittivity and permeability of transmission lines
A transmission line is an electromagnetic guiding system for efficient
point-to-point transmission of electric signals (information) and power. The
ABCD matrix of a transmission line, which expresses voltages and current
transportation between the input and output can be expressed as:
A = cosh γ l
(1)
B = Z c sinh γ l
(2)
sinh γ l
Zc
(3)
D = cosh γ l
(4)
C =
Z
where l , c , and γ = α + j β
are the length,
the characteristic
impedance, and the complex propagation constant of the transmission line,
respectively.
When a transmission line is measured with an input impedance or source
impedance Z 01 and output impedance or load impedance Z 02 , S-parameters,
impedance Z and ABCD matrices can be obtained directly or indirectly. The
conversion between the S-parameters, impedance Z and ABCD matrix are as
follows [7]:
1) Calculating S-parameters from impedance Z:
S 11 =
S 12 =
S 21 =
S 22 =
*
( Z 11 − Z 01
)( Z 22 + Z 02 ) − Z 12 Z 21
( Z 11 + Z 01 )( Z 22 + Z 02 ) − Z 12 Z 21
( Z 11
2 Z 12 ( R 01 R 02 ) 0 . 5
+ Z 01 )( Z 22 + Z 02 ) − Z 12 Z 21
( Z 11
2 Z 21 ( R 01 R 02 ) 0 . 5
+ Z 01 )( Z 22 + Z 02 ) − Z 12 Z 21
*
( Z 11 + Z 01 )( Z 22 + Z 02
) − Z 12 Z 21
( Z 11 + Z 01 )( Z 22 + Z 02 ) − Z 12 Z 21
(5)
(6)
(7)
(8)
2) Calculating impedance parameters Z from S parameters:
Z 11 =
Z 12
*
+ S 11 Z 01 )( 1 − S 22 ) + S 12 S 21 Z 01
( Z 01
(1 − S 11 )( 1 − S 22 ) − S 12 S 21
(9)
2 S 12 ( R 01 R 02 ) 0 .5
=
(1 − S 11 )( 1 − S 22 ) − S 12 S 21
(10)
2 S 21 ( R 01 R 02 ) 0 . 5
(1 − S 11 )( 1 − S 22 ) − S 12 S 21
(11)
Z 21 =
Z 22
*
(1 − S 11 )( Z 02
− S 22 Z 02 ) + S 12 S 21 Z 01
=
(1 − S 11 )( 1 − S 22 ) − S 12 S 21
(12)
3). Calculating the Sparameters from ABCD matrix:
S 11 =
S 12 =
S 21 =
S 22 =
AZ
AZ
02
02
+ B − CZ
+ B + CZ
Z 02 − DZ
01 Z 02 + DZ
*
01
*
01
2 ( AD − BC )( R 01 R 02 ) 0 . 5
AZ 02 + B + CZ 01 Z 02 + DZ
AZ
02
− AZ
AZ
02
2 ( R 01 R 02 ) 0 . 5
+ B + CZ 01 Z 02 + DZ
*
02
+ B − CZ
+ B + CZ
01
01
Z
*
02
(13)
01
01
(15)
01
+ DZ
Z 02 + DZ
(14)
*
01
01
(16)
4). Calculating ABCD matrix from S parameters:
A =
*
( Z 01
+ S 11 Z 01 )( 1 − S 22 ) + S 12 S 21 Z 01
2 S 12 ( R 01 R 02 ) 0 . 5
(17)
*
*
+ S 11 Z 01 )( Z 02
+ S 22 Z 02 ) − S 12 S 21 Z 01 Z 02
( Z 01
B =
2 S 12 ( R 01 R 02 ) 0 .5
C =
(1 − S 11 )( 1 − S 22 ) − S 12 S 21
2 S 12 ( R 01 R 02 ) 0 .5
*
+ S 22 Z 02 ) + S 12 S 21 Z 02
(1 − S 11 )( Z 02
D =
2 S 12 ( R 01 R 02 ) 0 . 5
(19)
(20)
(18)
5). Calculating impedance Z from ABCD matrix:
Z 11 =
A
C
(21)
Z 12 =
AD − BC
C
(22)
Z 21 =
1
C
Z 22 =
D
C
(23)
(24)
6). Calculating the ABCD matrix from the impedance
A =
B =
C =
D =
Z 11
Z 21
(25)
Z 11 Z 22 − Z 12 Z 21
Z 21
(26)
1
Z 21
(27)
Z 22
Z 21
(28)
Where R 01 and R 02 are real part of Z 01 and Z 02 respectively, and
*
*
Z 01
and Z 02
are the conjugate of Z 01 and Z 02 respectively.
From the ABCD matrix given in equations (1) to (4), the relationship of
l , length of the transmission line, Z c , the characteristic impedance of
transmission line, and γ = α + j β
,
the propagation constant
with S-
parameters and source impedance Z 01 and load impedance Z 02 are as follows:
cosh γ l =
*
+ S 11 Z 01 )( 1 − S 22 ) + S 12 S 21 Z 01
( Z 01
2 S 12 ( R 01 R 02 ) 0 . 5
(29)
*
*
( Z 01
+ S 11 Z 01 )( Z 02
+ S 22 Z 02 ) − S 12 S 21 Z 01 Z 02
Z c sinh γ l =
2 S 12 ( R 01 R 02 ) 0 . 5
(30)
(1 − S 11 )( 1 − S 22 ) − S 12 S 21
sinh γ l
=
Zc
2 S 12 ( R 01 R 02 ) 0 .5
cosh γ l =
*
(1 − S 11 )( Z 02
+ S 22 Z 02 ) + S 12 S 21 Z 02
2 S 12 ( R 01 R 02 ) 0 . 5
(31)
(32)
From using equation (2) dividing equation (3), the characteristic impedance
is expressed as follows:
Zc =
B
C
(33)
From (1) - (4), the propagation constant can be expressed as
γ =
atanh (
B ⋅C
)
A⋅D
l
(34)
or
γ = acosh ( A ) l
or
(35)
γ = acosh ( D ) l
(36)
From the above equations, the characteristic impedance Z c and the
propagation constant γ
= α
+
jβ
can be derived.
However,
to
obtain accurate results, an ambiguity for the solution of the propagation
constant γ = α + j β needs to be resolved. When the wavelength is twice the
length of the structure, the ambiguity is resolved. This strategy is used in this
chapter.
The
characteristic
impedance
Zc
and
the
propagation
constant γ = α + j β can also be expressed as:
Zc = Zv_c
γ =ω
µ reff
ε reff
ε 0µ0
ε reff µ reff
(37)
(38)
Where Z v _ c is the characteristic impedance, when the filled dielectric
materials are replaced with vacuum, ω is the angular frequency of the signal, and
ε reff
and µ reff
are effective relative permittivity and effective relative
permeability of structure filled with dielectric materials (Juan Hinojosa, and R.A
Pucel).
From (37) and (38), the effective relative permittivity and effective relative
permeability can be derived as
ε reff =
µ reff =
Z v _ cγ
ωZ c ε 0µ0
(39)
Z cγ
ωZ v _ c ε0µ0
(40)
From above deduction, the effective relative permittivity or complex
dielectric constant and the effective permeability can be derived from the Sparameters, or impedance, or the ABCD matrix.
The filling factors of transmission lines
The S-parameters of a transmission line are the collective effects of the
complex permeability and the complex permittivity of the materials. If the
transmission line contains two or more different materials with different dielectric
and magnetic properties, the measured impedance Z or S-parameters will be
dependent on the effective parameters.
The effective permittivity is defined as the ratio of total capacitance to the
capacitance of the respective configuration in which all dielectric materials are
replaced with free space or vacuum as:
ε
reff
=
C
C
total
f
(41)
Where Ctotal is the total capacitance, and C f is capacitance with free
space.
The Ctotal can be expressed as the sum of the capacitance contributed by
each of the filling materials as:
Ctotal =
Ci
(42)
i
where, Ci is the capacitance contributed by the filling material i , or the
capacitance only with the i _ th filling material, which has a linear relationship to
the dielectric constant of the responsive filling material. Therefore, the effective
complex permittivity can be represented as:
ε
reff
=
i
qε
i
ri
(43)
Where ε ri and qi are the complex permittivity and the filling factor of the
i _ th filling material respectively. The filling factor qi is defined as the ratio of
energy stored in the i _ th filling materials to the total energy stored in all the
filling materials, or from the ratio of capacitance when only the i _ th filling is
filled to that without any filling materials.
By using the duality, the effective complex permeability can be represented
as
1
µ
q
=
i
reff
µ
i
ri
(44)
where µri is the complex permeability of the i _ th filling material.
In this study, the structure used only has two filling materials, and the
equations (43) and (44) can be expressed as
ε
reff
1
µ
reff
= q1ε r1 + q2ε r 2
=
q1
µr1
+
(45)
q2
µr 2
(46)
The above equations provide a relationship between the effective
permittivity and effective permeability with the filling factors and with that of the
permittivity and the permeability of each filling material. The following section
will discuss the calculation of the filling factors.
Calculation of filling factors using conformal mapping
Once all the filling factors are derived and the all complex relative
permittivity and the complex relative permeability are known for all materials
except for the material under test, the unknown complex relative permittivity and
complex relative permeability can be derived.
The conformal mapping can provide a means to analyze the contribution of
each material in the transmission line configurations, especially in coplanar
waveguide. The presented analysis is quasi-static with capacitance calculation, as
the dispersion effects are ignored.
The fundamental of conformal mapping is based on the SchwarzChristoffel transformation, and figure 2 shows a special case of transferring a
rectangle into segments in a line:
In figure 2, points A, B, C, and D are conformally mapped with a, b, c, and
d respectively with:
w = A⋅
dt
Z
(1 − t )(1 − k 2 ⋅ t 2 )
2
0
AB = A ⋅ 2
dt
1
0
BC = A ⋅
= A⋅
(1 − t )(1 − k 2 ⋅ t 2 )
2
1/ k
1
1
0
= A ⋅ 2 K (k )
(48)
dt
(t − 1)(1 − k ⋅ t )
2
2
2
dt
(1 − t )(1 − k ' ⋅t )
= A ⋅ K (k ' )
2
Where k ' = 1 − k
(47)
2
2
2
(49)
1/ k
1
dx
=
( x − 1)(1 − k ⋅ x )
2
2
2
1
0
dt
(1 − t )(1 − k ' ⋅t )
2
2
2
(50)
with the transformation:
k ⋅ x + (k
2
2
'
)
2
⋅t =1
2
(51)
The capacitance between segment DC and AB is
C=
ε 0ε r DC ⋅ 1 ε 0ε r AB ⋅ 1
BC
=
BC
=
2ε 0ε r K (k )
K (k ' )
(52)
The parallel plate capacitance equation is valid only when the length of AB
is much larger than the length of BC.
The capacitance of the conductor ab to the ground conductors c and d in
the top or bottom half plane can be described with equation (52). Therefore, the
total capacitance is twice the value in the equation (52) and can be shown as:
C=
2ε 0ε r DC ⋅ 1 2ε 0ε r AB ⋅ 1 4ε 0ε r K ( k )
=
=
BC
BC
K (k ' )
(53)
In this study, since the ground coplanar waveguide configuration was used,
the top or bottom part can described by using the structure as shown in figure 3.
In figure 3, the points A, B, C, and D are conformally mapped with a, b, c,
and d through a series of conformal mappings, and the light black axis is the
boundary plan interfacing with free space or air.
The Z-plane was transformed with the following mapping function (54)
t = cosh 2 (
π ⋅z
)
2⋅h
(54)
and the result plane t is as follows:
w=
t
t0
dt
t (t − 1)(t − t1 )(t − t2 )
(55)
CD = AB = K (k1 )
(56)
BC = AD = K (k1' )
Where k1 = tanh(
(57)
π ⋅ a1
π ⋅ a2
) / tanh(
) and k1' = 1 − k12
2⋅h
2⋅h
The capacitance of the conductor AB and ground conductor CD is as
follows:
C=
ε 0ε r DC ⋅ 1 ε 0ε r AB ⋅ 1 ε 0ε r K ( k1 )
BC
=
BC
=
K ( k1' )
(58)
Here again, the total capacitance of the center conductive wire to the
ground wire is twice the value derived from figure 3. The capacitance of the top or
bottom half plane in a ground coplanar waveguide can be shown as:
C=
2ε 0ε r DC ⋅ 1 2ε 0ε r AB ⋅ 1 2ε 0ε r K ( k1 )
=
=
BC
BC
K (k1' )
(59)
From the above equations, the filling factors of ground coplanar waveguide
in figure 1 can be calculated as follows:
The capacitance in the top section 1:
Filling with the dielectric material which has the dielectric constant ε r1
C1 =
2ε 0ε r1 DC ⋅ 1 2ε 0ε r1 AB ⋅ 1 2ε 0ε r1 K ( k1 )
=
=
BC
BC
K ( k1' )
Where k1 = tanh(
π ⋅ a1
2 ⋅ h1
) / tanh(
π ⋅ a2
2 ⋅ h1
(60)
) and k1' = 1 − k12
As area filled with the dielectric material is free space, the capacitance is:
C1 _ f =
2ε 0 DC ⋅ 1 2ε 0 AB ⋅ 1 2ε 0 K ( k1 )
=
=
BC
BC
K (k1' )
Where k1 = tanh(
π ⋅ a1
2 ⋅ h1
) / tanh(
π ⋅ a2
2 ⋅ h1
(61)
) and k1' = 1 − k12 , the same as in
equation (60).
In the same way, the bottom half plane can be derived as follows.
The capacitance in the top section 2:
Filling with the dielectric material which has the dielectric constant ε r 2
C2 =
2ε 0ε r 2 DC ⋅ 1 2ε 0ε r 2 AB ⋅ 1 2ε 0ε r 2 K (k1 )
=
=
BC
BC
K (k1' )
Where k 2 = tanh(
π ⋅ a1
2 ⋅ h2
) / tanh(
π ⋅ a2
2 ⋅ h2
(62)
) and k2' = 1 − k 22
As area filled with the dielectric material is free space, the capacitance is:
C2 _ f =
2ε 0 DC ⋅ 1 2ε 0 AB ⋅ 1 2ε 0 K (k 2 )
=
=
BC
BC
K (k 2' )
(63)
Where k1 = tanh(
π ⋅ a1
2 ⋅ h1
) / tanh(
π ⋅ a2
2 ⋅ h1
) and k2' = 1 − k 22 , the same as in
equation (62).
The total capacitance as filled with dielectrics,
Ctotal = C2 + C2 =
2ε 0ε r1K (k1 ) 2ε 0ε r 2 K ( k2 )
+
K ( k1' )
K ( k2' )
(64)
The total capacitance without dielectrics,
Ctotal _ f = C1 _ f + C2 _ f =
2ε 0 K (k1 ) 2ε 0 K ( k 2 )
+
K (k1' )
K (k2' )
By using equation (41) ε
ε
reff
=
reff
=
(65)
Ctotal
,
Cf
Ctotal
Cf
2ε 0ε r1K (k1 ) 2ε 0ε r 2 K (k2 )
+
K ( k1' )
K (k2' )
=
2ε 0 K ( k1 ) 2ε 0 K (k 2 )
+
K (k1' )
K (k2' )
ε r1 K (k1 )
+
ε r 2 K ( k2 )
K (k )
K (k2' )
K (k1 ) K (k2 )
(66)
+
K (k1' ) K (k2' )
K ( k1 )
K ( k2 )
'
K ( k1 )
K (k2' )
=
ε +
ε
K (k1 ) K ( k2 ) r1 K (k1 ) K ( k2 ) r 2
+
+
K (k1' ) K ( k2' )
K (k1' ) K ( k2' )
= q1ε r1 + q2ε r 2
=
which is:
'
1
ε
reff
= q1ε r1 + q2ε r 2
(67)
K (k1 )
K ( k2 )
'
K (k1 )
K ( k2' )
where q1 =
and q2 =
K (k1 ) K (k 2 )
K (k1 ) K (k2 )
+
+
'
'
K (k1 ) K (k 2 ) r1
K (k1' ) K (k2' )
Based on the above derivation, a Matlab code was developed to extract the
complex relative permittivity and complex relative permeability from the Ansoft
HFSS simulated S-parameters and the impedance Z parameters with the structure
shown in figure 1.
This thesis work mainly focuses on the extraction of the material
parameters from HFSS simulated S-parameters. This is the method about how to
extract the complex permeability and the complex permeability from the Sparameters of a coplanar waveguide. This method can also be used to derive the
electrical parameters of the coplanar waveguide for a known physical
configuration and material properties.
Results and discussion
The grounded coplanar waveguide structure shown in figure 1 was
simulated using HFSS to determine the scattering parameters. The bottom filling
material was considered to be silicon dioxide with a dielectric constant of 4.0 and
with no dielectric loss. The material under test is placed in the top layer. Initially,
this was considered to be Gallium Arsenide with no dielectric loss and with a
dielectric constant of 12.9 and with a relative permeability of 1. The primary
objective is to extract the complex permittivity and permeability using the
procedure explained in the previous section and to compare these values with the
input material parameters of GaAs. The configuration of the grounded coplanar
waveguide is: the width of the center conductor is 100um, the distance between the
center conductor to anyone of the side ground conductors is 5um, thickness of the
bottom or the top area is 30um, and the dimension of the ground coplanar wave
guide is 500um x 500um x 60.2um. Ansoft HFSS was used to simulate and the Sparameters. The extracted results are shown in figure 5.
From figure 5, it may be seen that the real dielectric constant varies from
12.92 to 13.04 within the frequency range of 5GHz to 15GHz. The dielectric
constant used in the simulation is 12.9, indicating a maximum error of 1%. The
real relative permeability varies from 1.017 to 1.006 resulting a maximum error of
2%. It may be noted that these results could arise from the finite nature of the mesh
size used during the full-wave simulation on HFSS. Since the material used is
lossless in nature, the imaginary parts are zero for the permittivity and
permeability. The extracted imaginary parts are in the range of 10-9, which can be
considered to be small enough for the purpose of validation.
Next the material under test was chosen to be diamond_pl_cvd, which has
a dielectric constant of 3.5. From figure 6, the results show that the real dielectric
constant ranges from 3.5228 to 3.5242 within the frequency range of 5GHz to
15GHz resulting in a maximum percentage error of 1%.
The real relative
permeability ranges from 1.017 to 1.006 and the percentage error is within 2%.
The imaginary parts of the permittivity and permeability were again found to be of
the order of 10-9.
Figure 7 shows the extracted parameters for Arlon AR 1000 with a
dielectric constant of 10 and a loss tangent of 0.0035. The results show that the
real dielectric constant ranges from 10.12 to 10.17 within the frequency from
5GHz to 15GHz. The dielectric constant used in the simulation is 10, which has
error of 2%. The real relative permeability ranges from 1.008 to 1.002 within the
frequency from 5GHz to 15GHz, and the value used in the simulation is 1, so the
error is with 2%. The error in loss tangent was found to be within 2%.
A user defined material was used in the simulation. The dielectric constant
and relative permeability used in the simulation are 2 and 5, with loss tangent of
0.004 and 0.006, respectively.
From figure 8, the results show that the real
dielectric constant and relative permeability range from 2.028 to 2.043, and 5.30 to
5.36, with imaginary parts of -0.0081 to -0.0086, -0.0332 to – 0.0348, respectively,
within the frequency from 5GHz to 15GHz. The dielectric loss tangent is found to
be within 1% error.
Several dielectric materials (include lossless and lossy dielectric materials)
are used in the simulation with the configuration as above, and the summary of
material properties is listed in table 1. In general, the extracting results are all
within 2% error.
Conclusions
A grounded coplanar waveguide structure was proposed to obtain the
complex relative permittivity and the complex relative permeability of any thin
film material. Ahe method of extracting the complex relative permittivity and the
complex relative permeability from the concept of filling factors and duality of
permittivity and permeability is presented. The filling factors are calculated by
using conformal mapping. The theory is validated with Ansoft HFSS simulation
by considering a dielectric material of known characteristics. The Matlab code
based on the theoretical approach was developed to successfully extract the
complex relative permittivity and the complex relative permeability. The proposed
technique was tested for various cases of dielectric materials with different relative
permittivities and permeabilities and in all cases the maximum percentage error for
real and imaginary parts was found to be within 2%.
References
1. Rajeev Bansal, Handbook of enginnering electromagnetics
2. Walter Barry, IEEE transaction on microwave theory and techniques, vol.
MTT-34, No.1, Jan 1986
3. Said S. Bedair, IEEE transaction on microwave theory and techniques, vol.
40, No.1, Jan 1992
4. C. Veyres, Fouad Hanna, Int. J. electronics, 1980, vol. 48, No.1, pp47-56
5. Michele Goano, Francesco Bertazzi, Paolo Caravelli, IEEE transaction on
microwave theory and techniques, vol. 49, No.9, Sep 1992
6. Adnan Gorur, Ceyhun Karpuz. Microwave and optical technology letters,
vol. 20, No. 5, Mar. 1999
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vol. 42, No.2, Feb 1994
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and techniques, vol. MTT-35, No.3, Mar 1987
9. G. Chiodelli, V. Massarotti, D. Capsoni, M. Bini, C.B. Azzoni, M.C.
Mozzati, P. Lupotto, Solid State Communication 132(2004) 241-246
10. C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, A. P. Ramirez,
Science, vol 293, Jul 2001
11. Lixin He, J. B. Neaton, David Vanderbilt, Morrel H. Cohen, Physical
Review B, vol 67, 012103(2003)
12. Lei Zhang, Zhong-Jia Tang, Physical Review B, vol 70, 174306(2004)
13. P. Lunkenheimer, R. Fichtl, S. G. Ebbinghaus, A. Loidl, Physical Review
B, vol 70, 172102(2004)
14. B. Renner, P. Lunkenheimer, Journal of applied physics, vol 96 No. 8
15. Morrel H. Cohen, J. B. Neaton, Lixin He, David Vanderbilt, Journal of
applied physics, vol 94 No. 5
16. C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, A. P. Ramirez, A. P.
Ramirez, Physical Review B, vol 67, 092106(2003)
17. Wolfgang Hilberg, IEEE transaction on microwave theory and techniques,
vol. MTT-17, No.5, May 1969
18. D. Jessie, L. Larson, electronics letters, 6th Dec 2001, vol.37, No.25
19. William B. Weir, proceedings of the IEEE, vol.62, No.1, Jan 1974
20. Hyunkieu Yang, Sangseol Lee, Microwave and optical technology letters,
vol. 32, No. 2, Jan. 2002
21. Harold A. Wheeler, IEEE transaction on microwave theory and techniques,
Mar 1965
22. Anthony Lai, Tatsuo Itoh, IEEE microwave magazine, Sep 2004
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and techniques, vol. MTT-20, No.5, May 1972
24. G. Hasnain, A. Dienes, J. R. Whinnery, IEEE transaction on microwave
theory and techniques, vol. MTT-34, No.6, Jun 1986
25. Mingzhong Wu, Haijun Zhang, Xi Yao, Liangying Zhang, J. Phys. D:
Applied Physics 34(2001) 889-895
26. Hoton How, Carmine Vittoria, IEEE transaction on magnetics, vol.41,
No.3, Mar 2005
27. Richard Langman, Alan Belle, Daniel Bulte, Tony Christopoulos, IEEE
transaction on magnetics, vol.39, No.5, Sep 2003
28. Ki Hyeon Kim, Shigehiro Ohnuma, Masahiro Yamaguchi, IEEE
transaction on magnetics, vol.40, No.4, Jul 2004
29. Ki Hyeon Kim, Masahiro Yamaguchi, Shinji Ikeda, Ken-Ichi Arai, IEEE
transaction on magnetics, vol.39, No.5, Sep 2003
30. Robert A. Pucel, Daniel J. Masse, Curtis P. Hartwig, IEEE transaction on
microwave theory and techniques, vol. MTT-16, No.6, Jun 1968
31. N. X. Sun, S. X. Wang, T. J. Silva, A. B. Kos, IEEE transaction on
magnetics, vol.38, No.1, Jan 2002
32. Jame Baker-Jarvis, Michael D. Janezic, Paul D. Domich, Richard G.
Geyer, IEEE transactions on instrumentation and measurement, vol.43,
No.5, Oct 1994
33. Ching-Lieh Li, Kun-Mu Chen, IEEE transactions on instrumentation and
measurement, vol.44, No.1, Feb 1995
34. Matthew Gillick, Ian D. Robertson, Jai S. Joshi, IEEE transaction on
microwave theory and techniques, vol.41, No.9, Sept 1993
35. Stuart M. Wentworth, Dean P. Neikirk, Carl R. Brahce, IEEE transaction
on components, hybrid, and manufacturing technology, vol.12, No.3, Sep
1989
36. Kamal Sarabandi, Fawwaz T. Ulaby, IEEE transactions on instrumentation
and measurement, vol.37, No.4, Dec 1988
37. Victor Fouad Hanna, Dominique Thebault, IEEE transaction on microwave
theory and techniques, vol. MTT-32, No.12, Dec 1984
38. Harold A. Wheeler, IEEE transaction on microwave theory and techniques,
May 1964
39. Juan Hinojosa, IEEE microwave and wireless components letters, vol.
11,No. 2, Feb 2001
40. Ahmet Soydan Akyol, Lionel Edward Davis, IEEE transaction on
microwave theory and techniques, vol.51, No.5, May 2003
41. Sebastien Lefrancois, Daniel Pasquet, Genevieve Maze-Merceur, IEEE
transaction on microwave theory and techniques, vol.44, No.9, Sep 1996
42. Chinmoy Das Gupta, IEEE transaction on microwave theory and
techniques, vol. MTT-22, No.4, April 1974
43. Michael D. Janezic, Jeffrey A. Jargon, IEEE microwave and guided wave
letters, vol. 9, No. 2, Feb 1999
44. Byoungjoong Kang, Jeiwon Cho, Changyul Cheon, Youngwoo Kwon,
IEEE microwave and wireless components letters, vol. 15, No. 5, May
2005
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pp. 377–382, Nov. 1970.
Conductors
Ground Plane
1
h1
h2
Ground Plane
2
Figure 1. The grounded coplanar waveguide structure.
Z
w
D
C
-1/k
A
B
Figure 2. The conformal mapping technique
d
-1
1
a
b
1/k
c
D
C
b
a
a1
A
B
d
w
z
Figure 3. Conformal mapping for the proposed structure
1
D1
A1
t1
B1
t2
C1
t
Figure 4. The t-plane transformation after mapping.
c
a2
h
a)
b)
d)
Figure 5. The extracted results. a). The real part of dielectric constant, b).
The imaginary part of dielectric constant, c). The real relative Mu, and d). The
imaginary relative Mu.
a)
b)
c)
d)
Figure 6. The extracted results. a). The real part of dielectric constant, b).
The imaginary part of dielectric constant, c). The real relative Mu, and d). The
imaginary relative Mu.
b)
d)
Figure 7. The extracted results. a). The real dielectric constant, b). The
imaginary dielectric constant, c). The real relative Mu, and d). The imaginary
relative Mu.
a)
c)
b)
d)
Figure 8. The extracted results. a). The real dielectric constant, b). The
imaginary dielectric constant, c). The real relative Mu, and d). The imaginary
relative Mu.
Table 1. Summary of results
Testing Material
Relative
Relative permeability
permittivity
dielectric
Magnetic
loss
loss
tangent
tangent
Silicon nitride
7
1
0
0
diamond
16.5
1
0
0
Gallium Arsenide
12.9
1
0
0
sapphire
10
1
0
0
Arlon AR 1000™
10
1
0.0035
0
AL-N
8.8
1
0
0
Roggers TMM
6
1
0.023
0
Diamond-hi-pres
5.7
1
0
0
Diamond_pl_cvd
3.5
1
0
0
Silicon dioxide
4
1
0
0
Neltec
2.08
1
0.0006
0
2.5
1
0.0022
0
2.6
1
0.0033
0
3.5
0
0.026
0
Cyanate_ester
3.8
1
0
0
UserDefined
2
5
0.004
0.006
6™
NY9208(tm)
Arlon CuClad
250GX(tm)
Sheldahl ComClad
HF(tm)
Arlon AR 350
(tm)
CHAPTER 7
Conclusions
In this work, a spin spraying ferrite deposition set-up was initially
constructed inspired by combining advantages of the spin spraying ferrite plating
and laser beam accelerating deposition. Zinc ferrite thin films were successfully
deposited on different substrates, such as on the titanium surface of
Golden/titanium substrates and on the silicon dioxide surface of the silicon
dioxide/silicon/golden substrates. The Zinc ferrite thin films have been
successfully deposited at a relatively high rate (~ 0.2 µm/min). SEM and TEM
measurements indicated the films have a plate-like morphology with fibrous
texture. Zinc was uniformly incorporated into the ferrite thin films confirmed by
the local chemical analysis by EDX. The deposited films are polycrystalline with a
typical cubic ferrite structure. The overall composition of the films was determined
by Auger electron spectroscopy as ZnxFeyO4, x ranges from 0.25 to 0.55, and y
ranges from 2.2 to 2.7.
The dielectric properties of the deposited zinc ferrite thin films were
measured by the impedance analyzer at low frequency. The impedance
spectroscopy measurements show the dielectric constant of the ferrite material is
around 15, which is in the range of dielectric constant of bulk ferrite materials in
the history, even though there are large value for the ferrite material. The
resistivity of the deposited zinc ferrite is larger than 0.6x106 ohm*m.
In order to measure the dielectric properties of the ferrite, a novel grounded
coplanar waveguide structure was put forward and a method to extract the
dielectric properties of thin films were analyzed and put forward. To verify this
methods, the results from Ansoft HFSS, such as S parameters and impedance Z,
were used to replace the network analyzer output, and matlab codes were
developed to extract the complex relative permittivity and the complex relative
permeability. The extracting results were within the range of 2% errors. This
shows the extracting method is validate.
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