Tailored and anisotropic dielectric constants through porosity in ceramic components
ABSTRACT In this paper, different densities within a ceramic are used to provide a wide continuous range of dielectric constants for high-frequency applications. Cofiring different ceramic materials together to make a single unified structure to obtain different dielectric constant combinations is quite difficult due to phase stability issues and shrinkage mismatches. However, using various levels of porosity in order to alter the effective dielectric constant in the same material allows patterning different dielectric constants into a single unit. Since the structure is made from a single material, the varying porosity regions can be made compatible. Glassy-carbon-assisted and microcellular-structure-based porous titania allow for an extremely wide range of dielectric constants, ranging from 12 to 90, while maintaining a low loss tangent. Highly anisotropic materials are demonstrated herein to achieve a dielectric constant contrast of 90/9.6 using large-range aligned microcellular structure. Dielectric-resonator antennas are shown as an application of adjusting the bandwidth between 0.5% and 2.5% by tailoring the ceramic dielectric constant. A stratified-medium-loaded cavity resonator and a buried dielectric ring resonator internal to a microcellular substrate are used to demonstrate both the cofiring and variable dielectric constant capabilities of structured porosity.
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ABSTRACT: In porous media, the porosity introduces inhomogeneity in the bulk, which alters the mechanisms of leakage and breakdown exhibited by the dense analog. The presence of pores in solid dielectrics significantly degrades the electrical characteristics and breakdown strength of the material. Lanthanum doped BaTi0.6Zr0.4O3 composition in Ba1-xLaxTi0.6[1Â¿5x/12]Zr0.4O3 were prepared by modified chemical route. (COOH)2.2H2O, Ba(NO3)2, ZrOCl2.8H2O and La2O3 are used to precipitate barium oxalate hydrate, lanthanum oxalate hydrate and zirconium oxyhydroxide from its water solution onto the surface of suspended TiO2 particles. The lanthanum doped BaTi0.6Zr0.4O3 composition was found to be cubic by XRD analysis. A gradual shift of 2Â¿ angles to the higher angle with increasing lanthanum percentage in the BTZ reveals the contraction of perovskite lattice. The frequency dependence of dielectric permittivity and loss tan Â¿ of the ceramics has been investigated. It is found that dielectric permittivity (Â¿r) decreases and loss tan Â¿ decreases with increase in lanthanum percentage. Loss tan Â¿ increases and dielectric permittivity (Â¿r) decreases with increase in porosity. Resistivity decreases and current density increases with increase in porosity. Neither of the samples shows semiconductivity, which is believed to be because of titanium vacancy compensation.Solid Dielectrics, 2007. ICSD '07. IEEE International Conference on; 08/2007
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ABSTRACT: Dielectric materials with high dielectric constant contrast (68.7/6.37) are cofired inside low temperature cofired ceramics (LTCC) to demonstrate the capability of this processing technique for various metamaterial applications. Optical measurement shows good compatibility between the two different LTCC materials. By creating stratified-medium-loaded resonators inside electromagnetic bandgap (EBG) structures, bulk material properties of the high/low-dielectric-constant materials are characterized and verified at microwave frequencies to further prove the cofirability. This cofirability of different materials into one entity is the enabling technique for realizing artificial metamaterial substrates and vertically integrated RF front ends01/2006;
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ABSTRACT: Microwave electromagnetic bandgap (EBG) structures have potential applications in improving the radiating features of antennas and the transmission properties of waveguides. Extrusion freeforming is a rapid prototyping technique for assembling ceramic dielectric lattice structures directly from a computer design file. It is without heating, cooling or polymerization processes to contend with at the construction stage. Various limitations on overall build thickness prompted us to explore lamination by welding to produce larger three-dimensional quasi-crystals. Microwave transmission through normal and side incidence showed that the bandgap frequency was in the 90–110 GHz region in all directions, matching the design that was informed by computer modelling. In order to image the EBG internal crystal structure, micro-computed tomography was used for scanning and reconstruction. Finally, the effect of structural defects including roundness and sagging of filaments and deviation of inter-filament spacing caused by fabrication errors on bandgap frequency was investigated.Journal of Physics D Applied Physics 06/2009; 42(14):145107. · 2.53 Impact Factor
3638IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005
Tailored and Anisotropic Dielectric Constants
Through Porosity in Ceramic Components
Xun Gong, Member, IEEE, Wing Han She, Member, IEEE, Eric E. Hoppenjans, Student Member, IEEE,
Zach N. Wing, Richard G. Geyer, Senior Member, IEEE, John W. Halloran, and William J. Chappell, Member, IEEE
Abstract—In this paper, different densities within a ceramic
are used to provide a wide continuous range of dielectric con-
stants for high-frequency applications. Cofiring different ceramic
materials together to make a single unified structure to obtain
different dielectric constant combinations is quite difficult due to
phase stability issues and shrinkage mismatches. However, using
various levels of porosity in order to alter the effective dielectric
constant in the same material allows patterning different dielectric
constants into a single unit. Since the structure is made from a
single material, the varying porosity regions can be made com-
patible. Glassy-carbon-assisted and microcellular-structure-based
porous titania allow for an extremely wide range of dielectric
constants, ranging from 12 to 90, while maintaining a low loss
tangent. Highly anisotropic materials are demonstrated herein to
achieve a dielectric constant contrast of 90/9.6 using large-range
aligned microcellular structure. Dielectric-resonator antennas
are shown as an application of adjusting the bandwidth between
0.5% and 2.5% by tailoring the ceramic dielectric constant. A
stratified-medium-loaded cavity resonator and a buried dielectric
ring resonator internal to a microcellular substrate are used to
demonstrate both the cofiring and variable dielectric constant
capabilities of structured porosity.
dielectric measurements, dielectric-resonator antenna (DRA),
inhomogeneous media, resonator.
ponents such as dielectric resonators (DRs) , compact-size
filters , and antennas . Ideally, high-temperature ceramics
can be cofired to include graded dielectric constants within
a single structure. However, most of the common ceramics
do not cofire together and only discrete dielectric constants
make them suitable for various microwave passive com-
low-loss properties of ceramic materials
Manuscript received April 2, 2005; revised August 15, 2005. This work was
supported in partby the Defense AdvancedResearchProjects Agency underthe
Metamaterials Project and by the Indiana 21st Century Project.
X. Gong is with the Electrical and Computer Engineering Department,
W. H. She is with Wireless ICs, Irvine, CA 92618 USA (e-mail:
E. E. Hoppenjans and W. J. Chappell are with the Electrical and Computer
Engineering Department, Purdue University, West Lafayette, IN 47907 USA
(e-mail: email@example.com; firstname.lastname@example.org).
Z. N. Wing and J. W. Halloran are with the Department of Materials Science
and Engineering, The University of Michigan at Ann Arbor, Ann Arbor, MI
48109 USA (e-mail: email@example.com; firstname.lastname@example.org).
R. G. Geyer is with the RF Technology Division, National Institute
Digital Object Identifier 10.1109/TMTT.2005.859039
are available. To overcome these two limitations, an inhomo-
geneous medium can be created by intentionally designing
porosity within the material. By varying the level of porosity, a
wide range of dielectric constants can be created from a single
is a desirable material for microwave appli-
cations due to its high permittivity
tangent (which has been reported as low as
). It is also convenient to study this material because of its
relatively simple composition. It is well known that the relative
permittivity decreases with increasing material porosity. Thus,
controlling the porosity can yield a spectrum of dielectric con-
stants from a single material. This offers great flexibility for mi-
crowave engineers to design passive circuit components of ar-
bitrary dielectric constant combinations, shapes, and sizes.
In , a novel approach to form large-scale structured
porosity by coextruding titania shells around sacrificial carbon
cores to achieve a high porosity up to 74% was presented.
Characterization of the material properties using cavity mea-
surement was discussed. Dielectric constants as low as
were demonstrated. Two passive components were fabricated
by this new microcellular porous titania. The first example
demonstrated the cofiring capabilities of the new technique
by creating a stratified-medium-loaded cavity resonator with a
layer of lower dielectric constant microcellular porous titania
sandwiched in-between two denser titania layers. The second
dielectric ring was buried inside microcellular porous titania
to demonstrate how different porosities can be used to create
an embedded dielectric ring resonator. These examples have
demonstrated both the cofiring and variable dielectric constant
capabilities of structured porosity. The microcellular structure
was proven suitable for synthesizing relatively lower dielectric
constant materials. In this paper, in addition, glassy-carbon-as-
sisted porous titania is shown to be able to achieve relatively
higher dielectric constants (46–90) that can be controlled
as well. As an application of this effect, dielectric-resonator
antennas (DRAs) using this glassy-carbon-assisted porous
titania are shown to be able to adjust bandwidths between 0.5%
and 2.5% by tailoring the porosity of the ceramic material.
To further extend the application of microcellular structures,
high anisotropy is demonstrated herein using the large-scale
The organization of this paper is as follows. Section II intro-
duces the concept and fabrication of glassy-carbon-assisted and
microcellular porous titania. In addition, anisotropic porous ti-
tania using large-scale microcellular structure is demonstrated.
100 and low loss
0018-9480/$20.00 © 2005 IEEE
GONG et al.: TAILORED AND ANISOTROPIC DIELECTRIC CONSTANTS IN CERAMIC COMPONENTS3639
Fig. 1. Fabrication process flow of glassy-carbon-assisted porous titania.
Section III discusses the characterization of properties of the
aforementioned materials using waveguide cavity measure-
ments. Section IV presents various microwave applications
including a DRA, a stratified-medium-loaded cavity resonator,
and an embedded ring resonator.
II. POROUS CERAMICS
Nanoscale porosity ( 100 nm) may be formed with residual
sive components, because the large number of holes means a
large surface area with dangling bonds of the ceramic parti-
cles that tend to absorb species and water. These bonds absorb
electrical energy, particularly at microwave frequencies, which
microcellular porous titania structures proposed in this paper,
microscale pores (50–200
m) are formed by the addition of
carbon sacrificial spacers that are then thermally removed to
create voids within the otherwise dense ceramic. These larger
pores preserve the low loss tangent of the ceramic while cre-
ating the desired low dielectric constant.
A. Glassy-Carbon-Assisted Porous Titania
In this technique, glassy-carbon microspheres are mixed
with TiO powder to create porosity. The TiO used here is a
commercial powder consisting of 99.8% pure titanium dioxide
powder (203-4, Ferro Electronic Materials, Penn Yan, NY)
with a particle size of 1.1–1.3
as fugitive is that of the 15- m glassy-carbon microspheres
First, the carbon and raw titania powders are wet mixed for
15 min in isopropanol. Second, powder pellets are pressed in-
side a steel die to a final diameter of 12.8 mm at 150 MPa. Last,
pellets are placed in a bed of sintered powder to fire and sinter.
Carbon removal takes place in air between 450 C–600 C.
Samples are heated to 450
(1 C/min) to 600 C, and held at 600 C for 1 h to ensure
carbon burnout. Grain growth and densification increase with
firing temperature and soak time. After carbon removal, the
samples are sintered at 1350 C in air for 1 h to limit the pore
shrinkage due to the grain growth. The fabrication process flow
is illustrated in Fig. 1.
m. The form of carbon used
C/min), ramped slowly
Fig. 2. MFCX.
B. Microcellular Porous Titania Using Microfabrication of
Ceramics by Coextrusion
Microfabrication by coextrusion (MFCX) involves multiple
extrusions to achieve the desired dimensional reduction. It is a
powerful method for controlling pore morphology.
A large-scale unit cell can be reduced in size by MFCX ,
 to create structured porosity. MFCX can create very-fine-
scale structures and voids useful for decreasing the dielectric
constant of a material. When combined with the thermoplastic
(3-D) dielectric texturization from a single material can be fab-
Two stocks of materials need to be prepared for the microcel-
moplastic, which are compounded in an acrylate binder using
a high shear mixer (Brabender) to form the outer shell of a
feed rod. The second stock is created by compounding carbon
with titania at 15% volume ratio to form the partially sacri-
ficial core of the feed rod. The shells are then warm bonded
around the cores to create large-scale master feed rods with a
diameter of 15.75 mm. These master feed rods (a white shell
around a black core) are extruded through a reduction die to
achieve 3.25-mm-diameter rods. They are then arrayed together
inamicrocellularstructureand undergoa finalcoextrusion.The
15.75-mm rods are reduced to less than 1 mm in diameter. This
fabrication process flow is illustrated in Fig. 2. The porosity of
this resulting thin-veins-large-voids structure is controlled by
the size of the sacrificial carbon cores and the TiO shell thick-
ness. The two-dimensional (2-D) microcellular pattern can be
chopped into smaller sections, randomly oriented, and warm
pressed to form an isotropic medium. To fabricate macroscop-
ically isotropic media, the coextruded fibers are chopped into
1–3-mm lengths, mixed, and warm pressed to form an isotropic
resulting microcellular medium is shown in Fig. 3.
3640IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005
Fig. 3. SEM of the microcellular structure. From .
C. Microcellular Anisotropic Porous Titania Material
In order to realize anisotropic materials, long uniform
anisotropic coextruded fibers are needed. Two stock materials
are created, which are: 1) a ceramic and thermoplastic binder
stock and 2) a completely sacrificial carbon black and ther-
moplastic stock. The ceramic and sacrificial stock are warm
bonded into a core–shell structure. This 18-mm master feed
rod is extruded into 3-mm fibers. The 3-mm core–shell fibers
are bundled together and extruded to a final fiber diameter of
1 mm. Another variation is to incorporate some ceramic into
the black, making the sacrificial core partially sacrificial. This
is valuable if you have limited die fixture availability.
Alternatively, the core–shell structure can be replaced with a
pixel version. In this version, which is used for the anisotropic
media presented here, 3-mm fibers are formed from the ce-
ramic/thermoplastic stock and from the completely sacrificial
carbon stock. The level of induced macropores is controlled by
the number ratio of ceramic/sacrificial fibers. In the anisotropic
resonator, 7/19 (36.8%) of master feed rod fibers are sacrificial.
These are coextruded to form composite 3-mm fibers (5:1 re-
duction). Next, 38 composite rods are bundled together and co-
original feed rod.
The 1-mm fibers consist of sacrificial carbon channels sur-
rounded by ceramics. These fibers are loaded and aligned into a
135 C for 1 h. The fibers are then assembled and consolidated
into a solid block by applying a pressure of 20 MPa for 15 min.
A 13 mm
13 mm square is cutfrom the green block. Removal
of the sacrificial carbon and thermoplastic binder are performed
in flowingair. Binderremovaloccurs during a three-dayheating
cycle and is completed at 520 C, while carbon removal is com-
pleted at 600 C. After binder removal, one sample is fired at
1300 Candtheotherat1400 Cfor2h.Thefabricationprocess
is illustrated in Fig. 4. To verify the uniformity of the long coex-
truded fibers, microcomputed tomography (Micro CT) images
were taken. The resulting anisotropic medium is presented in
Fig. 5 and clearly shows that the fibers are aligned in only one
direction after firing.
Fig. 4. Fabrication process flow of anisotropic ceramic material.
Micro CT view of the cross sections (right) 2-D views of the cross sections.
(b) SEM close-up of the ??? 2-D view in (a). (c) Further close-up of (b).
Micro CT and SEM images of the anisotropic material. (a) (left) 3-D
III. MATERIAL CHARACTERIZATION
Ceramic samples are tested inside a metallic waveguide
cavity. This cavity is weakly coupled by two open-ended coax
connectors (measurement setup is shown in Fig. 6). In ,
cavity mode was used to characterize the complex
permittivity of the ceramic materials. However, for this
cavity mode, a significant amount of the electric field is dis-
tributed outside dielectric samples, making the extraction of
both the dielectric constant and loss tangent extremely sen-
sitive to measurement uncertainties for the low-loss ceramics
studied herein. In order to accurately characterize the dielectric
constant and loss tangent of low-loss porous ceramic materials,
DR modes are chosen due to the much higher electromagnetic
field concentration inside the ceramic samples, minimizing
GONG et al.: TAILORED AND ANISOTROPIC DIELECTRIC CONSTANTS IN CERAMIC COMPONENTS 3641
Fig. 6. Waveguide cavity measurement setup. (a) Skew view. (b) Side view.
the sensitivity to measurement uncertainties. Ansoft High Fre-
quency Structure Simulator (HFSS) simulation shows that the
resonant frequency and unloaded
gap between the ceramic samples and the bottom of the cavity
when the sample is placed directly on the bottom of the cavity.
To reduce this sensitivity, a spacer (11.18 mm in diameter and
0.78 mm in height) made of a low-
5880) is used to elevate the ceramic samples. The dimensions
of the waveguide cavity are 28.47 mm
The first resonant frequency of the empty waveguide cavity
is measured to be 5.89 GHz and its unloaded
to be 3204. Using full-wave HFSS simulations, the effective
conductivity of the cavity wall is found to be 8.98
which will be used in later simulation of the sample-loaded
cavity. Knowing the effective conductivity of the waveguide
cavity and the complex permittivity of Duroid 5880 (
9 10), HFSS parametric sweeps are con-
ducted to numerically determine the dielectric constants and
loss tangents of the ceramic samples by matching both the
resonant frequencies and unloaded
8722ES network analyzer. In order to verify the accuracy of
our measurement results, independent tests were conducted at
the National Institute of Standards and Technology (NIST),
are very sensitive to the air
material (Rogers Duroid
57.2 mm12.61 mm.
s measured by an Agilent
A. Glassy-Carbon-Assisted Porous Titania
Two glassy-carbon-assisted porous titania samples with
10.6% and 43.1% porosity are tested. Both samples are in
cylindrical form. The dimensions of the 10.6% porosity sample
are 10.56 mm in diameter and 8.81 mm in height, while the
dimensions of the 43.1% porosity sample are 10.39 mm in
diameter and 9.46 mm in height. For the 10.6% porosity
sample, the first transmission peak corresponds to the
0 1 mode  of the dielectric puck. However, due
to relatively lower dielectric constant of the 43.1% porosity
sample, the first transmission peak corresponds to the cavity
mode while the second one corresponds to the
mode. The measured transmission responses are shown in
Fig. 7. Using full-wave HFSS parametric sweeps, the dielectric
constant and loss tangent of the 10.6% porosity sample are
found to be 89.22 and 8.18
very well with the independent verification results from NIST:
89.95 and 6.67
10 , which are obtained using the more
standard Courtney method , . The dielectric constant
and loss tangent of the 43.1% porosity sample are found to be
44.79 and 1.28
10 , respectively, which are comparable
with the NIST results: 46.4 and 3.08
results for the glassy-carbon-assisted porous titania samples are
, respectively, which agree
10 . The measurement
porous titania samples.
Measured transmission coefficients for the glassy-carbon-assisted
summarized in Table I. Repeated measurements are conducted
to study the measurement uncertainties in terms of the location
of sample placement within the cavity. The results of this study
are listed in Table I from which it can be concluded that our
measurement repeatability of the dielectric constant and loss
tangent is better than 0.13% and 10.63%, respectively, due to
the uncertainty of measurement locations.
B. Porous Titania With Microcellular Structure
Two microcellular-structure-based porous titania samples
with 62.0% and 78.2% porosity are tested. The 62.0% porosity
sample is in cylindrical form with a diameter of 11.19 mm and
a height of 7.03 mm. The 78.2% porosity sample is in elliptical
shape with a semimajor axis of 11.60 mm, a semiminor axis
of 10.05 mm, and a height of 8.64 mm. In the measurement,
the semimajor axis of this sample is aligned with the shorter
side of the cavity. For both samples, the second transmission
peaks correspond to the
Fig. 8. Using HFSS simulations, the dielectric constant and loss
tangent of the 62.0% porosity sample are found to be 21.60 and
10 , respectively, which are very close to the NIST
results: 21.27 and 4.88
10 . The dielectric constant and loss
tangent of the 78.2% porosity sample are found to be 12.25 and
10 , respectively, closely matching the NIST results:
12.30 and 7.65
10 . The measurement results of the micro-
cellular porous titania samples are also summarized in Table I.
The dielectric constant deviation is less than 0.74% and the
mode and are shown in
3642IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005
SUMMARY OF MEASUREMENT RESULTS OF POROUS TITANIA SAMPLES
Measured transmission coefficients for the microcellular poroustitania
loss tangent deviation is less than 11.44% for the microcellular
Maxwell–Garnett effective medium theory (EMT) is a useful
tool for the evaluation of dielectric properties of composite
media. The effective dielectric constant of a composite medium
is given by 
medium and the inclusion medium, respectively, and
volume fraction of the inclusion medium. The calculated effec-
tive dielectric constants using Maxwell–Garnett EMT are listed
in Table I. Since Maxwell–Garnett EMT assumes that spherical
inclusions are dispersed inside a surrounding host material, for
the glassy-carbon case, the difference between the calculated
is less than 6%. For the microcellular case,
this difference is up to 38% which is due to breakdown of the
aforementioned EMT assumption.
is the effective dielectric constant of the composite
andare the dielectric constant of the host
C. Anisotropic Porous Titania With Microcellular Structure
Two microcellular-structure-based anisotropic titania sam-
ples are tested. The first sample’s dimensions are 10.03 mm
10.03 mm 3.64 mm. The coextruded fibers are aligned
along one of the 10.03-mm lateral sides. The second sample’s
dimensions are 8.20 mm
truded fibers are aligned along the 8.20-mm lateral side. The
first and second samples were fired at 1300 C and 1400 C,
respectively. SEM images of the cross section of the fibers
3.85 mm. The coex-
Fig. 9. Measurement setup for anisotropic samples inside a cavity.
(Fig. 5) show that the average diameter of the air pores inside
the fibers is approximately 50 m.
A low-frequency capacitance measurement using an Agilent
constant in different directions for the anisotropic samples. The
effective dielectric constant along the fiber is extracted to be
88.66 and the one perpendicular to the fiber is extracted to be
11.8. These low-frequency values will be shown to be close to
the high-frequency values extracted by HFSS simulations. The
difference may be due to the imperfect alignment of fibers and
variations with frequencies.
Fig. 9 shows the placement of the samples inside the wave-
guide cavity. There are two orientations used in the measure-
ment, which are: 1) 0 orientation, which is along the longer
lateral side of the cavity and 2) 90 orientation, which is along
the shorter lateral side of the cavity.
The measured transmission responses of both samples along
0 and 90 orientations are shown in Figs. 10–13. Since the
first transmission peaks, which correspond to the
mode, are only affected by the effectivedielectric constants per-
ples 1 and 2 in this direction are found to be 9.6 and 15, respec-
tively. By matching the unloaded
peaks, the effective loss tangents in this direction are quantified
to be 1
10 and 210, respectively. Using the afore-
mentioned effective dielectric constants and by matching the
resonant frequencies and unloaded
along the fibers are found to be close to 90 for both samples and
the loss tangents are 9
s of the first transmission
s of the second transmis-
and 1.6 10for samples 1
GONG et al.: TAILORED AND ANISOTROPIC DIELECTRIC CONSTANTS IN CERAMIC COMPONENTS3643
sample with dimensions of 10.03 mm ? 10.03 mm ? 3.64 mm when the
extruded fibers are aligned at 0 .
Measured and simulated transmission coefficients of the anisotropic
sample with dimensions of 10.03 mm ? 10.03 mm ? 3.64 mm when the
extruded fibers are aligned at 90 .
Measured and simulated transmission coefficients of the anisotropic
sample with dimensions of 8.20 mm ? 7.60 mm ? 3.85 mm when the extruded
fibers are aligned at 0 .
Measured and simulated transmission coefficients of the anisotropic
and 2, respectively. Simulations verified that the lower effec-
tive dielectric constant is much more sensitive than the higher
effective dielectric constant along the fibers. As a result, the ef-
fective dielectric constants along the fibers are very close ( 90)
for both samples. The discrepancy in the lower effective dielec-
tric constant is mainly due to the different firing temperature,
sample with dimensions of 8.20 mm ? 7.60 mm ? 3.85 mm when the extruded
fibers are aligned at 90 .
Measured and simulated transmission coefficients of the anisotropic
which caused a different residual porosity, affecting the effec-
tive dielectric constant. The simulated transmission responses
using these effective dielectric constants agree with measured
transmission responses within 2.4% accuracy for all resonant
frequencies below 7.3 GHz.
The measured and simulated resonant frequencies and un-
s for different modes are summarized in Table II.
One important aspect is that the effective loss tangent is much
lower perpendicular to the fibers. The lower effective dielectric
constant takes effect when the
fibers, causing a strong
-field discontinuity at the interface of
titania and air, which, in turn, forces much larger electric energy
storage inside air, greatly reducing the dielectric loss. The elec-
tric field distributions of different modes are shown in Fig. 14.
The first transmission peak for all four cases corresponds to
cavity mode, in which the
to the top surface of both samples. The second transmission
peaks for both samples in the 0 orientation correspond to the
lowest DR mode, in which the
the vertical direction. The third transmission peak for the first
sample in the 0 orientation corresponds to a higher order DR
mode. The second transmission peaks for both samples in the
90 orientation correspond to another higher order DR mode,
in which the
-field rotates orthogonal to the fibers.
-field is perpendicular to the
-field is perpendicular
-field curls along the fibers and
IV. APPLICATIONS OF POROUS CERAMICS
A. Stratified-Medium-Loaded Cavity Resonator
A major problem that may arise when cofiring two dissim-
ilar ceramics is the formation of compound due to phase sta-
bility. For example, Al TiO is formed if TiO and Al O are
cofired together above 1200 C . Furthermore, shrinkage
mismatches of different materials during densification and the
thermal expansion coefficient mismatch may cause mechanical
stresses at the boundary, leading to cracking of the final struc-
ture. To show an example of integrating two different dielec-
tric constants into a single material, a layer of microcellular
porous titania (porosity
1.4 10) is sandwiched between two layers of relatively
denser titania (
fied-medium-loaded cavity resonator shown in Fig. 15.
0.001) to form the strati-
3644IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005
SUMMARY OF MEASUREMENT RESULTS OF ANISOTROPIC CERAMIC SAMPLES
in Figs. 10–13 (both 0 and 90 ). (b) DR mode corresponding to the second
transmission peak in Figs. 10 and 12 (0 ). (c) DR mode corresponding to the
third transmission peak in Fig. 10 (0 ). (d) DR mode corresponding to the
second transmission peak in Figs. 11 and 13 (90 ).
?-field distribution for modes of the anisotropic samples. (a) Cavity
corresponding to the first transmission peak (from left to right)
(b) Microscopic view of the denser titania/microcellular porous titania
boundary. From .
15.(a) Stratified-medium-loaded resonatorbefore metallization.
The green form of a sandwich of relatively denser titania and
microcellular porous titania is warm pressed for 30 min. Binder
removal is done in air using a three-day heating schedule based
on thermogravimetric analysis. All samples are then sintered at
1300 C for 2 h. For testing, the stratified-medium-loaded res-
onator is coated with silver paste (Heraeus C8710 with a mea-
of 9.6210 S/m) to form a metallized cavity, which
is weakly excited by two open-ended coax connectors.
Quasi-static analysis  is used to determine the effective
dielectric constant and effective
ified medium. For the
cavity mode, the electric field is
perpendicular to the substrate layers. The normal electric flux
density is continuous across the dielectric boundaries
of the aforementioned strat-
. The effective dielectric constant is derived using quasi-
and the effective
is given by
Using (2) and (3), the effective dielectric constant and
stratified medium are found to be 19.92 and 3883, respectively.
of the stratified-medium-loaded cavity is given by
, 2.138 mm, and 1.405 mm.
where the dimensions of the box are
3.485 mm, and
culated to be 0.03
be 799.7 at 2.20 GHz. As a result, the total
calculated to be 663 using (5) as follows:
20.141 mm. Surface resistivity
. Thus,is found to
of the resonator is
The resonant frequencies of the stratified-medium-loaded
resonator can be calculated by treating the medium as a ho-
mogenous substrate with an effective dielectric constant of
19.92. The resonant frequency of a metallic cavity is given by
mode is 2.35 GHz and that of
The frequency response of this cavity resonator is measured
and shown in Fig. 16. The measured resonant frequency of
2.20 GHz is slightly lower than the HFSS simulated resonant
that the effective dielectric constant of the structure is around
20.36, representing a 2.2% deviation from the quasi-static
analysis result. The unloaded
the measured loaded
of 191.5 and
and are the order of the resonant mode in the-
is extracted to be 195.2 from
of 34.52 dB. The
GONG et al.: TAILORED AND ANISOTROPIC DIELECTRIC CONSTANTS IN CERAMIC COMPONENTS3645
stratified-medium-loaded cavity resonator. From .
16.Measured andsimulated transmission coefficientsofthe
circular ring is made of TiO in acrylate binder. The black matrix is made of
MFCX chopped fibers. The final sintered body is shown in (c). From .
difference between the measured and simulated unloaded
is believed to be caused by the leakage of electric field at the
connectors due to the poor soldering adhesion to the chosen
metal. In addition, discrepancies will arise due to the idealized
geometries assumed in the simulation.
B. Buried Dielectric Ring Resonator
An embedded ring resonator is designed and fabricated to
demonstrate an application of the microcellular porous titania
resonance mode is used in the embedded
ring resonator since this mode confines most of the electric field
inside the ring, leading to a high unloaded
stead of a cylinder, to avoid crowding of the
higher order modes such as the
is made from microcellular porous titania with a 62% porosity
resonator is made from denser titania (measured
1 10 ). The whole structure is coated with silver
paste (Heraeus C8710) except for a slot on the top. A microstrip
line on a Duroid 5880 substrate is placed on top of the struc-
ture with a slot in the ground plane aligned with the slot created
on the top surface of the structure, enabling magnetic field cou-
pling. The position of the slot is carefully designed to couple to
The ring resonator is green machined using a computer-aided
negative image of the resonator is milled into the microcellular
porous titania substrate block and then the ring is inserted. The
porous titania is placed on the top and the assembly is warm
pressed for 30 min, followed by binder removal and sintering
identical to the stratified-medium case.
. A ring is used, in-
mode. The substrate
1.1 10), while the ring
resonator. (a) Side view. (b) Top view. From .
MicroCTimages showingthe internalstructure ofthe embeddedring
resonator. From .
Measured and simulated frequency responses of the embedded ring
Prior to testing, the embedded resonator was imaged using
Micro CT. Fig. 18 shows the actual circular resonator sur-
rounded by the cellular matrix. Some slight internal cracking
in the matrix is apparent. However, the bulk of the substrate is
The frequency response of the embedded ring resonator
is measured with an Agilent 8722ES network analyzer. The
mode resonant frequency is 7.195 GHz,
which is only 1.8% away from the HFSS simulation result of
7.069 GHz. The measured loaded
9.48 dB, respectively. Thus, the unloaded
be 829. In Fig. 19, full-wave HFSS simulation shows that the
dense titania ring resonator has a dielectric constant of around
85, which is only 3.4% away from the expected value of 88.
The resonant frequency shown in simulation is 7.184 GHz.
The simulated loaded
respectively, implying an unloaded
and are 550.7 and
is extracted to
are 624.7 and
It is well known that DRs can be used as efficient radiators in
the microwave and millimeter-wave regions. The use of a DR
fabricated from a low-loss material can produce very high radi-
ation efficiencies due to the absence of the conductor loss. It is
for this reason that the DRA has found use in a variety of appli-
the DRA can be adjusted by manipulating the aspect ratio of the
resonator and, more importantly, the dielectric constant of the
material . Thus, by adjusting the porosity of the dielectric
3646IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005
glassy-carbon-assisted porous titania with a measured ? of 18.
Measured and simulated return losses of a DRA made of
be manipulated. Wu et al.  derived (7) using the magnetic
wall boundary derivation for the fields of the DR as follows:
is the unloaded
of the antenna,
electric constant, and the bandwidth is approximately equal to
A DRA is fabricated on a Duroid 5880 host substrate of
1.575-mm thick, 60-mm long, and 40-mm wide. The resonator
is made from a porous titania material (measured
with a diameter of 10.45 mm and a height of 6.28 mm. The
resonator is placed in the center of the substrate on the ground
plane side of the microstrip feed and is held onto the substrate
using a small amount of epoxy. The feed mechanism described
in  is used to couple energy into the resonator. In this con-
figuration, the mode excited by the coupling mechanism is the
mode. A subminiature version A (SMA) connector is
then soldered onto the microstrip line to facilitate a connection
between the antenna and measuring devices. The return loss of
the antenna is then measured with an Agilent 8720ES network
analyzer. A comparison of the simulated and measured results
is shown in Fig. 20.
As can be seen in Fig. 20, the measured resonant frequency
is 1.4% higher than the predicted value. This frequency shift
can be attributed to fabrications tolerances in the resonator di-
mensions. Moreover, as stated in , if a small air gap exists
shift in frequency. The measured
tenna is 2.2%, which agrees well with a simulated bandwidth of
As stated, the bandwidth of a DRA is proportional to the as-
pect ratio and dielectric constant of the resonator. To quantify
this dependence, a series of simulations are run using Ansoft
HFSS. The resonator used for the simulation has a diameter of
10 mm and a height of 3 mm and is placed on top of a 120
120 mm ground plane. Four DRAs are simulated, each with a
factor of the antenna,
is the free space wave number,
is the height of
is the di-
10-dB bandwidth of the an-
Fig. 21. Normalized DRA bandwidth versus dielectric constant.
different dielectric constant ranging from 18 to 90. The length
of the open microstrip line is tuned for maximum coupling for
each antenna. The simulated results are shown in Fig. 21. The
effect of the dielectric constant on the antenna bandwidth is ob-
served. As the dielectric constant increases, the bandwidth of
the antenna decreases as predicted by (7).
A new way to control the dielectric constant of titania by
varying the porosity of the material and the capability of
cofiring different dielectric constant materials are presented.
The glassy-carbon-assisted porous titania has been shown to
achieve measured dielectric constants between 46 and 90 with
very low loss tangent. The microcellular porous titania has
been shown to be able to achieve dielectric constants as low
as 12.25. Highly anisotropic materials (90/9.6 and 90/15) have
been realized using the aligned microcellular porous titania
fibers. Layers of denser titania and microcellular structures
are fired together to form a stratified-medium-loaded cavity
resonator and an embedded ring resonator. The measurement
results match Ansoft HFSS simulations to within 3.4%. This
ability to vary the porosity of the material and cofire different
porosity materials together gives component designers flexi-
bility in designing materials with varying dielectric constants.
DRAs with variable dielectric constants have been simulated to
be able to control the antenna bandwidth from 0.5% to 2.5%.
The measured antenna resonant frequency (5.07 GHz) and
bandwidth (2.2%) agree very well with the simulated results
(5.02 GHz and 2.5%). This new ceramic fabrication technique
can enable novel microwave components with more functions
and better performance.
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Xun Gong (S’02–M’05) was born in Shanghai,
China, in 1974. He received the B.S. and M.S.
degrees in electrical engineering from FuDan
University, Shanghai, China, in 1997 and 2000,
respectively, and the Ph.D. degree in electrical
engineering from The University of Michigan at
Ann Arbor, in 2004.
From January 2005 to August 2005, he was a
Post-Doctoral Research Associate with the Birck
Nanotechnology Center, Purdue University, West
Lafayette, IN. He is currently an Assistant Professor
with the Electrical and Computer Engineering Department, University of
Central Florida, Orlando. His current research is focused on integrated high-?
resonators and filters, integrated RF front-ends, metamaterials, vertical circuit
integration, and packaging.
Mr. Gong was the recipient of the Third Place Award of the Student Paper
ciety (IEEE MTT-S) International Microwave Symposium (IMS), Fort Worth,
Wing Han She (S’04–M’05) was born in Hong Kong, in 1980. She received
engineering from Purdue University, West Lafayette, IN, in 2004.
During her M.S. studies, she designed embedded DRs and filters, charac-
terized ceramic materials, and studied effective medium and electromagnetic
bandgap concepts. She is currently with Wireless ICs, Irvine, CA, where she is
responsible for system design of wireless transceivers.
Eric E. Hoppenjans (S’05) received the B.S. and
M.S. degrees in electrical engineering technology
from Purdue University, West Lafayette, IN, in 2001
and 2005, respectively, and is currently working
toward the Ph.D. degree in electrical engineering at
His current research focus is on advanced pack-
aging techniques for high-frequency circuits and
Mr. Hoppenjans is a member of the International
Microelectronics and Packaging Society (IMAPS).
Zach N. Wing received the B.S. degree in materials science engineering from
engineering from the University of Colorado, Boulder, in 2001, and is currently
working toward the Ph.D. degree in materials science engineering at The Uni-
versity of Michigan at Ann Arbor.
His current research is focused on metamaterials and fabrication of spatially
Richard G. Geyer (M’87–SM’87) was born in Lansing, MI. He received the
B.Sc. (with honors) degree from Michigan State University, East Lansing, in
1966, and the Ph.D. degree from the Colorado School of Mines, Golden, in
Since 1970, he has been involved with measurements of the electronic and
acoustic properties of materials and with numerical methods of radiated and
guided-wave electromagnetic and acoustic field theory. Since 1986, he has been
with the RF Technology Division, National Institute of Standards and Tech-
nology (NIST), Boulder, CO, where his research deals with microwave fer-
rites, ferroelectrics, nanocomposites, EMT, high-temperature superconductors,
tronic properties of materials at microwave frequencies.
Dr. Geyer is the past chair of the IEEE Antennas and Propagation Society
(AP-S)/Microwave Theory and Techniques Society (MTT-S)/Geoscience and
he was the recipient of a Best Paper Award for analytical work on transient
electromagnetic scattering in an inhomogeneous penetrable half space. In 1998,
he was the recipient (as coauthor) of a Best Poster Award from the Materials
Research Society on a paper that dealt with the dielectric characterization and
crystal structure of newly synthesized dielectric ceramics for potential use in
microwavecommunicationsystems. In1999,he wasalso therecipient (ascoau-
thor) of a Best Paper Award from Measurement Science and Technology for a
paper on complex permittivity of some ultra-low-loss dielectric crystals at cryo-
John W. Halloran received the B.S. degree from the University of Missouri,
Rolla, in 1973, and the Ph.D. degree from the Massachusetts Institute of Tech-
nology (MIT), Cambridge, in 1977.
He is currently the Department Chair of the Materials Science and Engi-
neering Department, The University of Michigan at Ann Arbor.
William J. Chappell (S’98–M’02) received the
B.S.E.E., M.S.E.E., and Ph.D. degrees from The
University of Michigan at Ann Arbor, in 1998, 2000,
and 2002, respectively.
He is currently an Assistant Professor with Purdue
University, West Lafayette, IN. He is a member of
the Birck Nanotechnology Center and the Center
for Wireless Systems and Applications. His research
focuses on silicon micromachining, polymer for-
mation, and low-loss ceramics for high-frequency
circuits and antennas. In addition, his research
interests include rapid prototyping, free-form fabrication, and small-scale
formation of electrically functioning ceramic and polymer passive components.
He also oversees projects investigating RF design for wireless sensor networks,
chemical sensors, and electrotextiles.
Dr. Chappell was the recipient of the 2004 Joel Spira Outstanding Educator
Award and has been designated as a Teacher for Tomorrow in his department.