International Materials Reviews
ISSN: 0950-6608 (Print) 1743-2804 (Online) Journal homepage: http://www.tandfonline.com/loi/yimr20
Low-loss dielectric ceramic materials and their
properties
M. T. Sebastian, R. Ubic & H. Jantunen
To cite this article: M. T. Sebastian, R. Ubic & H. Jantunen (2015) Low-loss dielectric ceramic
materials and their properties, International Materials Reviews, 60:7, 392-412
To link to this article: http://dx.doi.org/10.1179/1743280415Y.0000000007
Published online: 13 Nov 2015.
Submit your article to this journal
Article views: 4
View related articles
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=yimr20
Download by: [Penn State University]
Date: 26 November 2015, At: 11:01
FULL CRITICAL REVIEW
Low-loss dielectric ceramic materials and
their properties
M. T. Sebastian*1, R. Ubic2 and H. Jantunen1
Downloaded by [Penn State University] at 11:01 26 November 2015
In addition to the constant demand of low-loss dielectric materials for wireless telecommunication,
the recent progress in the Internet of Things (IoT), the Tactile Internet (fifth generation wireless
systems), the Industrial Internet, satellite broadcasting and intelligent transport systems (ITS) has
put more pressure on their development with modern component fabrication techniques. Oxide
ceramics are critical for these applications, and a full understanding of their crystal chemistry is
fundamental for future development. Properties of microwave ceramics depend on several
parameters including their composition, the purity of starting materials, processing conditions and
their ultimate densification/porosity. In this review the data for all reported low-loss microwave
dielectric ceramic materials are collected and tabulated. The table of these materials gives the
relative permittivity, quality factor, temperature variation of the resonant frequency, crystal
structure, sintering temperature, measurement frequency and references. In addition, the
methods commonly employed for measuring the microwave dielectric properties, important from
the applications point of view, factors affecting the dielectric loss, methods to tailor the dielectric
properties and materials for future applications, are briefly described. The data will be very useful
for scientists, industrialists, engineers and students working on current and emerging applications
of wireless communications.
Keywords: Microwave dielectrics, Dielectric resonators, LTCC, ULTCC, Microwave applications, Microwave ceramics
Introduction
Microwave dielectric materials play a key role in global
society, with a wide range of applications from terrestrial
and satellite communications, including Internet
of Things (IoT), software radio, GPS and DBS TV,
to environmental monitoring via satellite, etc. Today
low-loss dielectric materials are all-pervasive. The mobile
phone is one of the most widely spread technologies on
the planet. In many countries, the number of mobile
subscriptions exceeds the population. The IoT is posed to
make an explosive growth in the near future. In this
paradigm, many every-day objects will be networked
via radio-frequency identification (RFID), printed
electronics and sensor network technologies. According
to GSMA intelligence, the revenue from interconnected
devices for mobile network operators alone in the
segments of automotive, health, utilities and consumer
electronics will be $1.3 trillion by 2020. In order to meet
the specifications of future systems, new designs and
improved or new microwave dielectric components are
required. The recent progress in the IoT, microwave
1
Microelectronics and Materials Physics Laboratory, Department of
Electrical Engineering, University of Oulu, Oulu90014, Finland
Department of Materials Science & Engineering, Boise State University,
Boise, ID, USA
2
*Corresponding author, email mailadils@yahoo.com
392
Ñ 2015 Institute of Materials, Minerals and Mining and ASM International
Published by Maney for the Institute and ASM International
Received 26 January 2015; accepted 15 June 2015
DOI 10.1179/1743280415Y.0000000007
telecommunications, satellite broadcasting and intelligent transport systems (ITS) has resulted in an increasing
demand for low-loss dielectric materials. Indeed, low-loss
dielectric oxide ceramics have revolutionised the microwave wireless communication industry by reducing the
size and cost of filter, oscillator and antenna components
in applications ranging from cellular phones to IoT.
Wireless communication technology demands materials
with highly specialised properties. The importance of
miniaturisation cannot be overemphasised in any handheld communication application, as can be seen in the
dramatic decrease in the size and weight of devices in
recent years. This constant need for miniaturisation
provides a continuing driving force for the discovery and
development of ever smaller/lighter dielectrics which can
outperform existing materials. Recently the demand for
materials with low sintering temperature has increased
not only to lower the energy cost of devices but also to
integrate with polymers and silver-based electrodes.
Several polymer-based (polymer–ceramic) composites
have also recently been developed for wireless communication technology. In the present paper, we restrict
our discussions to ceramic materials. For polymer-based
composite dielectric materials, the reader is referred to
the recent review by Sebastian and Jantunen.1 The
number of papers published on low-loss microwave
materials and related devices has increased considerably
over the years as shown in Fig. 1.
International Materials Reviews
2015
VOL
60
NO
7
Sebastian et al.
Downloaded by [Penn State University] at 11:01 26 November 2015
1 Number of papers published on dielectric resonators
(DRs) and devices versus year
A dielectric resonator (DR) is an electromagnetic
component that exhibits resonance for a narrow range of
frequencies. The resonance is similar to that of a circular,
hollow metallic waveguide except that the boundary is
defined by a large change in permittivity rather than
conduction. Dielectric resonators generally consist of
a ceramic puck and require high values of relative
permittivity (er) and quality factor (Q) and near-zero
temperature coefficients of resonant frequency (tf). The
quality factor, which is a function of resonant frequency,
is sometimes expressed as Q f, the product of Q and the
resonant frequency (in GHz). While Q f is not technically
a dimensionless figure of merit, the units (GHz) are
almost invariably dropped. The resonant frequency is
determined by the overall physical dimensions of the puck
and the permittivity of the material and its immediate
surroundings. Optimising these three properties simultaneously is difficult.
Oxide ceramics are critical elements in these microwave devices, and a full understanding of their crystal
chemistry is fundamental to future development.
Properties of microwave ceramics depend on several
parameters including the processing conditions and the
purity of starting materials. Design of the heating/cooling schedule requires knowledge of the formation
mechanisms of various phases in multicomponent
systems, and the starting powders must sinter to high
density to obtain optimum electrical properties.
Low-permittivity ceramics are used for millimetrewave communication and also as substrates for microwave integrated circuits. Medium-1r ceramics with 1r
in the range of 25–50 are used for satellite communications and in mobile phone base stations. High-1r
materials are used in mobile phone handsets where
miniaturisation is very important. For millimetre-wave
and
substrate
applications,
temperature-stable,
low-permittivity and high-Q are required for high-speed
signal transmission with minimum attenuation.
The signal transmission speed increases as the relative
permittivity decreases. High-Q dielectrics minimise
circuit insertion losses and can be used to create highly
selective filters. In addition, a high-Q suppresses the
electrical noise in oscillator devices. Although several
manufacturers may produce similar components for the
same application, there are subtle differences in circuit
design, construction and packaging. Since frequency
Low-loss dielectric ceramic materials
drift of a device is a consequence of the overall thermal
expansion drift of its unique combination of components,
each design requires a slightly different tf for temperature
compensation. Typically, ceramics with a specific tf in the
range of 215 to þ15 ppm/uC are selected. In ceramic
production, tf and 1r specifications must be produced to
within demanding tolerances typically + 1%.2
Electronic circuits for the automotive industry, home
electronics and telecommunications have to handle a
steadily increasing amount of functionality within as
tiny a space as possible. In the development of complex
miniaturized circuits, flexible glass–ceramic composites,
the so called low-temperature cofired ceramics (LTCCs),
play a decisive role as a base material. LTCCs have
become crucial in the development of various modules
and substrates. This technology enables fabrication of
three-dimensional ceramic modules with embedded
silver or copper electrodes, and LTCCs with relative
permittivity from *4 up to w100 have been developed
showing low dielectric loss. These advantages make
LTCC technology very attractive for a variety of microand millimetre-wave applications.3 The important
characteristics required for LTCCs are (a) densification
temperature v950uC (b) 1r in the range 5–70 (c) Q f
w1000 (d) tf close to zero (e) high thermal conductivity
(f) preferably low thermal expansion and (g) chemical
compatibility with the electrode material. Low sintering
temperatures are required to avoid melting metallic
conductors like silver or gold in the fabrication of
dielectric devices.3 Most conventional electroceramics
do not meet the basic requirements with regard to sinterability for LTCC technology since they have relatively
high sintering temperatures. The different methods used
to reduce the sintering temperature of dielectrics include:
(1) addition of low melting-temperature glass phases,
(2) addition of low melting-point compounds such as
Bi2O3, B2O3, V2O5 or CuO and (3) the use of chemical
processing in order to achieve smaller particle sizes.
The first method, while commonly found effective in
decreasing the sintering temperature, usually results in a
degradation of microwave dielectric properties.
The selection of glass materials is very important for
sintering glass–ceramic composites, since the liquidation
of glass takes a dominant role in the viscous flow mechanism during sintering; hence, this method remains
the focus of intense research. The dielectric table
(supplementary file) lists the key property data of microwave dielectric materials available from published and,
to a far lesser extent, reputable unpublished sources.
These data are the relative permittivity (1r), the product
of the Q factor and the frequency (Q f ), the frequency of
measurement ( f ), the temperature coefficient of the
resonant frequency (tf), sintering temperature and crystal
structure or structural family.
Measurement of microwave dielectric
properties
The three important characteristics of an ideal low-loss
dielectric material are application optimised value of
relative permittivity (1r), low dielectric loss (loss tangent,
tand) and low temperature coefficient of resonant
frequency (tf). These three properties and different
measurement methodologies to measure them are briefly
discussed in the following sections.
International Materials Reviews
2015
VOL
60
NO
7
393
Sebastian et al.
Low-loss dielectric ceramic materials
Permittivity
When microwaves enter a dielectric medium, they are
; therefore
slowed down by a factor equal to e21/2
r
l0
c
ld ¼ pffiffiffiffi ¼ pffiffiffiffi
1r n 1r
[ n¼
c
pffiffiffiffi
ld 1r
ð1Þ
At resonant frequency, l ¼ f0 and ld , D (diameter
of resonator); therefore
c
c 2
ð2Þ
f 0 ¼ pffiffiffiffi [ 1r ¼
D 1r
Df0
Downloaded by [Penn State University] at 11:01 26 November 2015
Equation (2) is only valid in the case of resonators in free
space. It fails for resonators in more realistic situations
( e.g., on microstrips, in cavities, between shorting plates,
etc.). In order to calculate permittivity in these
geometries, several techniques have been developed and
variously discussed. Perturbation techniques rely on the
shift of f0 (and Q) of a resonant cavity caused by the
presence of a dielectric disc or sphere. Optical methods
at microwave frequencies are suited to measurements at
which l,1 cm and require a large amount of material.
Transmission-line methods have the practical difficulty
of requiring a very small waveguide for l,4 mm. All of
these methods have an accuracy of approximately ¡1%.
The exact resonance method proposed by Karpova4 and
further developed by Hakki and Coleman,5 Courtney6
and others yields errors of only ¡0.1% but is limited to
the accuracy of the measurements of resonant frequency
and sample dimensions. The reader is referred to the
recent book2 for details of these techniques. In this
paper, we restrict the discussion to the measurement of
the relative permittivity and loss tangents of low-loss
dielectric materials.
Hakki – Coleman method
Karpova4 used a re-entrant cavity for the measurement
of dielectric properties, but the physical size of the
resonant structure required could be problematic for the
low-millimetre range. In order to avoid the problem of
physical size while maintaining high accuracy, Hakki
and Coleman5 instead proposed an open-boundary
resonant structure in which a dielectric rod was positioned between much larger conducting plates (Fig. 2).
The characteristic equation which describes this
condition for an isotropic resonator in a TE0mp mode:
a
J 0 ðaÞ
K 0 ðbÞ
¼ 2b
J 1 ðaÞ
K 1 ðbÞ
K1(b) are modified Bessel functions of the second kind of
orders zero and one, respectively. The parameters a and
b are functions of geometry, resonant wavelength and
permittivity:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi
2pa
c
1r 2
ð4Þ
a¼
vp
l0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2pa
c
b¼
21
ð5Þ
l0
vp
where c is the speed of light, a is resonator radius and
vp is the phase velocity in the resonator such that:
c
pl0
ð6Þ
¼
vp
2t
where p is the number of longitudinal variations of field
along the axis and l0 ¼ c/f0. Clearly vp can be calculated
from thickness and resonant frequency alone; and b can
then be calculated from vp, frequency and radius.
The characteristic equation (3) is transcendental and
requires a graphical solution. Hakki and Coleman5 used
analogue mode charts to relate various {am} to each
corresponding value of b, resulting in somewhat limited
accuracy (Fig. 3).
Although this technique is sometimes called the
Courtney method,6 ‘Courtney, actually, only perfected
and scrutinised a parallel-plate arrangement introduced
[10 years] earlier’ by Hakki and Coleman.5 Courtney
also adapted the technique to the use of coaxial probes
(an innovation introduced 4 years earlier by Cohn and
Kelly7), allowing a greater range of sample dimensions.
An improvement in accuracy over a purely graphical
approach can be achieved by numerically solving for
each Bessel/modified Bessel function rather than trying
to read values off the mode charts of Hakki and
Coleman5 or even relying on curve fits. With modern
computers, ordinary Bessel functions and modified
Bessel functions can be numerically calculated, and these
numerical methods make it possible to solve equation (3)
for b<10. The algorithm employed in the HakCol
program8 starts by calculating b from the resonator
radius and resonant frequency. Next an approximate
corresponding value for a is calculated using a curve fit
to the m ¼ 1 (TE01p) mode chart of Hakki and
Coleman5 (Fig. 3). The polynomial which describes the
curve in Fig. 3 is:
ð3Þ
where J0(a) and J1(a) are Bessel functions of the first
kind of orders zero and one, respectively. K0(b) and
2 Schematic sketch of Courtney set-up for measuring the
dielectric constant under end shorted condition (after Ref. 6)
394
International Materials Reviews
2015
VOL
60
NO
7
3 Mode chart (after Ref. 5)
Sebastian et al.
Downloaded by [Penn State University] at 11:01 26 November 2015
a ¼ 2:3508 þ 0:34969b – 0:051220b2
þ 0:0044392b3 – 0:00020633b4 þ 3:9411
£ 1026 b5
ð7Þ
The mode TEnml, the integer n denotes the azimuthal
variation, m radial variation and l the axial variation.
The a so calculated is used as a first approximation in
order to calculate er. Next, equation (3) is evaluated
and if the two sides are unequal then er is adjusted
accordingly, a re-calculated, and the process iterates
until equation (3) is satisfied. The entire algorithm and
the HakCol program is detailed in ref.9
The TE011 mode is used for the measurements since
this mode propagates inside the sample but is evanescent
outside; therefore, a large amount of electrical energy
can be stored in high-Q DRs.10 In the end-shorted
condition, the E field becomes zero close to the metal
wall and electric energy vanishes in the air gap.7 The TE
and TM modes do not contain electric and magnetic
fields in the axial (z) direction. For the TE011 mode only
the azimuthal component of the electric field exists and
the error because of the air gap is practically eliminated.11 For cylindrical resonators, TE and TM modes
exist only if the azimuthal mode index m ¼ 0 otherwise
all other modes are hybrid, i.e., they have all six
electromagnetic components. Hybrid modes are usually
divided into two mode families: HE and TM. They are
only occasionally used in measurements of dielectrics
(e.g., for uniaxially anisotropic crystals). This method is
proposed as one of the international standard IEC
techniques12 for measurements of the complex
permittivity of low-loss solids. Hennings and Schnabel13
studied the reproducibility of the 1r measured by this
end-shorted method using 10 different samples prepared
in a batch. Their results showed a maximum variation of
0.6% in 1r. In this method, the 1r is measured only at one
resonant frequency corresponding to the TE011 mode.
If one can identify other resonant modes, then it is
possible to measure 1r at other resonant frequencies.
By using the resonant modes TE011, TE021, TE031 and
TE041, the 1r of a sample can be measured over a
range of frequencies. It may be noted that as the 1r
increases, the resonant frequency decreases and as the
dimensions of the sample decrease the resonant
frequency increases.
Shielded resonator in dielectric-rod waveguide method
For a high-Q material in a cavity, as proposed by Itoh
and Rudokas14 and modified by Kajfezz and Guillon15
(Fig. 4), most of the electrical field is contained within
the resonator itself (region 6), and very little exists in
regions 1 and 2, and even less in regions 3 and 5. To a
fair first approximation, then, the fields in regions 3 and
5 can be ignored. For the TE01d modes in this geometry,
the requirement for continuity of fields leads to two
simultaneous eigenvalue equations:
J o ðkr1 aÞ
kr2 K 0 ðkr2 aÞ
¼2
J 1 ðkr1 aÞ
kr1 K 1 ðk2 aÞ
bL ¼
w1 w2
þ þ lp l ¼ 0; 1; 2; 3. . .
2
2
Low-loss dielectric ceramic materials
ð8Þ
ð9Þ
The symbol k represents the radial propagation constants in the different regions of the model, which are
functions of both frequency and dielectric constant; and
4 Resonator in a cavity (after Ref. 9)
r is the radial distance from the geometric centre.
The arguments of the various Bessel functions are
the eigenvalues of the system, where kr1a is called the
eigenvalue of the TE0n mode, and kr2 is given by:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð10Þ
kr2 a ¼ ðk0 aÞ2 ð1r6 2 1r4 Þ 2 ðkr1 aÞ2
where k0 is called variously the propagation constant,
wavenumber or phase constant of free space, and has
units of m21:
pffiffiffiffiffiffiffiffiffi
k0 ¼ v0 10 m0
ð11Þ
In equation (9), b is the propagation constant of
the resonator. If p is the number of axial variations of
the field along the resonator’s height, then p ¼ l þ d,
where l is an integer and d is a non-integer number
smaller than unity which depends in a complicated
way on propagation constants and geometry. Whereas
for the TE011 mode discussed above, l ¼ 1 and d ¼ 0,
for the TE01d mode, l ¼ 0 and d ?.0. The symbols
(w1 and w2 are called the phase angles and are complex
hyperbolic functions of the cavity geometry and
the propagation constant of the resonator. The entire
algorithm and the ErCalc program is detailed in
reference.9
Correction for porosity
The porosity in the sintered ceramic disc influences the
measured 1r and thus the measured 1r should be
corrected to isolate the actual dielectric permittivity.
This correction can be performed in a variety of ways.
The Maxwell Garnett16 approximation treats one of
the components as a host in which inclusions of the
other component are embedded. Lichtenecker’s17
logarithmic mixing rule assumes a randomly connected
second phase and, although it is much used, is actually
one of the least accurate mixture rules available.
By contrast, the Bötcher mixture rule18 assumes a dispersion of spherical porosity (or another second phase)
in a mixture of both solid and air (or another second
phase), like that of Bruggeman,19 thereby allowing for
International Materials Reviews
2015
VOL
60
NO
7
395
Sebastian et al.
Low-loss dielectric ceramic materials
the interaction between the two phases and increasing
the accuracy even for high values of porosity:
1rm 2 1r2 d1 ð1r1 2 1r2 Þ
¼
31rm
1r1 þ 21rm
ð12Þ
where erm, er1, and er2 are the permittivities of the
mixture, phase 1 and phase 2, respectively, and d1 is the
volume fraction of phase 1. This rule is also based in
part on the work of Wiener20 and Stratton21 and
supported by Reynolds.22
The various equations typically only diverge significantly for very high or very low densities of second
phase and re-converge for densities of 0 and 100%.
Maxwell’s equation, in particular, slightly inflates the
value at intermediate densities, presumably because
it does not allow for the interaction between the two
phases.
QU ¼ ð1 þ bc1 þ bc2 ÞQL
Measurement of loss tangent/quality factor
Downloaded by [Penn State University] at 11:01 26 November 2015
The measured Q value is commonly the loaded quality
factor (QL) taking into account the external circuit
(the network analyser with coupling probes). However,
if the measurement is arranged under very weak coupling the QL is the same as unloaded one Qu and is
obtained from the following equation.
QL ¼ Qu ¼
f
Df
confinement is not complete in the z direction. As shown
in Fig. 5, the spacer isolates the sample from the effects
of losses because of the finite resistivity of the metallic
cavity.
After identifying the mode, the resonant frequency and
3dB bandwidth are determined. The network analyser is
then calibrated and S11 and S22 are measured at the
resonant frequency (Fig. 6). From these values, the coupling
coefficients bc1 and bc2 for the coupling ports are
determined using the relations bc1 ¼ (12S11)/(S11 þ S22)
and bc2 ¼ (12S22)/(S11 þ S22), where S11 and S22 are
reflection coefficients of ports 1 and 2.30 Figure 7 shows the
typical resonance spectra in reflection and transmission
configuration of a Ba(Mg1/3Ta2/3)O3 ceramic sample having
1r ¼ 38. The TE01d mode frequency is noted and the
unloaded Q factor is measured.
From the measured QL, QU can be calculated as
ð13Þ
where f is the measured resonance frequency and
Df is 3 dB band width of the peak. There are various
methods which enable measurement of the quality
factors of low-loss dielectrics.23–31 One should however
keep in mind that not all of them take into account
practical effects introduced by a real measurement
system, such as noise, cross-talk, coupling losses, transmission-line delay and impedance mismatch. Inadequate
accounting of these effects may lead to significant
uncertainty in the measured Q-factor.
For example the quality factor can be measured by
Hakki and Coleman’s end-shorted method,2,5–7,25–28 but
the quality factor measured by this method will be
somewhat low since loss occurs because of the
conducting plates and radiation effects. Fortunately,
corrections for conductor losses can be applied knowing
the surface resistance of the conducting plates.
ð14Þ
In some cases the desired mode (TE01d) may be close to
other modes but this method allows slight change of the
cavity volume by rotating the top screw, which enable
separation of the modes. This action enables the
identification of the desired resonant mode and in
addition allows the cavity to measure samples of
different dimensions. Figure 8 shows a typical test
5 The cavity set-up for the measurement of Q factor
TE01d mode DR method
To avoid the problems of the conduction and radiation
losses, the Q of a DR sample can be measured by using
the cavity method in which the DR is placed on a lowloss (e.g., single crystal quartz or Teflon) spacer inside
the cavity. This method is proposed by Krupka et al.23,29
using a transmission-mode cavity. It enables measurement of the quality factor (Q), permittivity (1r) and
temperature coefficient of resonant frequency (tf) of the
DRs, which is placed inside a cylindrical metallic cavity
usually made of copper. The inner surfaces are polished
and gold or silver coated. A loop coupling is used to feed
microwave to the DR Since the cavity has an infinite
number of modes, the diameter and height ratio of the
sample is commonly kept on the level 2–2.5 to get
maximum mode separation. Since the electric field is
symmetric in this measurement method, the sources of
loss owing to the cavity are reduced. In this method the
TE011 mode is designated as TE01d, since the field
396
International Materials Reviews
2015
VOL
60
NO
7
6 The TE011 resonance of a ceramic puck with 1r 5 38
under end shorted condition
Downloaded by [Penn State University] at 11:01 26 November 2015
Sebastian et al.
Low-loss dielectric ceramic materials
7 Microwave resonance spectra of Ba(Mg1/3Ta2/3)O3 ceramic with 1r 5 24 a reflection b transmission configuration
8 The cavity manufactured by QWED for quality factor
measurement (courtesy, J Krupka QWED, Warsaw, Poland)
fixture manufactured by QWED, Warsaw, Poland. The
evaluation of the permittivity and the dielectric loss
tangent of the sample under test require rigorous electromagnetic analysis. QWED uses the Rayleigh–Ritz
method in their software.
The TE01d mode DR method is one of the most
accurate techniques for measuring especially loss
tangent of isotropic low-loss materials.29,31 The inverse
of measured unloaded Q-factor is approximately equal
to the dielectric loss tangent if all parasitic losses can be
neglected (true in the cases when the permittivity of the
sample is large) and if the electric energy filling factor
can be assumed to be equal to unity. One must keep in
mind that these assumptions are not valid when the
sample has very low dielectric loss or permittivity value.
In the first case the conductor losses must be taken
into account. What comes to the low-permittivity
materials, the electric energy filling factor in the sample
is substantially smaller than 1. However, the advantages
of the cavity method using the TE01d mode are easy
mode identification, small parasitic losses and lack of
mode degeneracy.23 On the other hand, the evaluation of
tand requires advanced numerical computations, which
can only be done employing dedicated computer programs because of the absence of exact solutions of
Maxwell’s equation. The uncertainty in dielectric loss
tangent using TE01d mode cavity method with optimized
enclosure is of the order of 0.03 tand. The frequency
band this method is feasible depends on the size and
permittivity of the samples, and the cavity geometry.
Higher frequency measurements are performed by using
smaller cavities and samples, or by using several higher
order quasi-TE0nm modes.32
Valant et al.33 reported the effect of the test cavity
dimensions on the microwave dielectric properties of the
ceramic resonator. The electromagnetic field could penetrate
into the conducting walls of the test cavity (skin effect) lowering the Q factor. With large size of the test cavity this source
of error can be avoided. Thus in order to derive the unloaded
Q value, the test cavity should be large enough. A good
practice is to select the test cavity size in such a way that the
TE01d mode of the DR is the lowest resonance and hence it
can be easily identified. This is especially true in the case DRs
with permittivity .20 when increase of the size of the test
cavity is needed to move the resonant modes of the cavity to
lower frequencies. Figure 9 shows how the measured quality
factor decreases with the cavity diameter/disc diameter ratio.
Thus it is advisable to use 3–5 times larger cavity compared to
the size of the test sample. In addition the surface resistance of
cavity walls can be calculated from the quality factor of the
TE011 resonance of the empty cavity.15
Strip line excited by cavity method
Magnetic coupling of the DR to a 50 V microstrip line is
used in the microstrip line excited cavity method,
International Materials Reviews
2015
VOL
60
NO
7
397
Sebastian et al.
Low-loss dielectric ceramic materials
shielded resonator configuration like in shielded cavities,
the power dissipated in the resonator is given by
Pd ¼ 1 2 jS 110 j2 2 jS 210 j2
ð16Þ
The coupling factor bc is a function of the distance
between the DR and the microstrip line under fixed
shielding conditions. According to Khanna and Garault34
the unloaded voltage transmission coefficient S21u is
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
S 21u ¼ S210 ð17Þ
1 þ S2210
9 Variation of Qf with ratio of cavity diameter/sample
diameter (after Ref. 33)
Downloaded by [Penn State University] at 11:01 26 November 2015
as shown in Fig. 10 along with the equivalent circuit.34
In this method the Q factor is estimated through the so
called coupling factor, bc, which is the ratio of the
resonator-coupled resistance R at the resonant
frequency to the resistance external to the resonator.
bc ¼
R
S 110
¼
Rext S 210
ð15Þ
Here S110 and S210 are the real quantities of the reflection
and transmission coefficients, respectively, at the
resonant frequency.
When the coupling factor bc is equal to one, the power
dissipated in the external circuit is the same as the power
dissipated in the resonator (Pd), which is equally divided
into the power reflected to the generator (Pr ¼ S2110) and
the power transmitted to the load (Pt ¼ S2210). In the
10 Schematic diagram of a dielectric resonator (DR)
coupled to a microstrip line a and b equivalent circuit
(after Ref. 34)
398
International Materials Reviews
2015
VOL
60
NO
7
S21u corresponds to the voltage transmission coefficient
of the unloaded resonator. The frequencies f1 and f2
corresponding to S21u given by equation (17) are measured
(Fig. 11) and their difference Df ¼ ( f22f1) is calculated.
When the resonance frequency, f, corresponds to the peak of
the S21 curve and Df is known, the unloaded quality factor,
Qu, is calculated using equation (13).
The experimental set-up for the Q measurement by the
microstrip line excited by cavity method is shown in
Fig. 12. In this a 50 V microstrip line of width 3 mm is
etched on RT-Duroid 5880 (1r ,2.2 and thickness
1.9 mm) to the bottom wall of a rectangular cavity made
of copper. The cavity is then excited using 3.5 mm
microstrip edge connectors. The DR is placed near the
microstrip line and the TE01d mode is identified. After
system calibration, the resonant frequency is measured,
the transmission coefficient S210 corresponding to f is
recorded, and S21u is calculated using equation (17).
Finally the unloaded quality factor is calculated through
Df corresponding S21u and f.
Whispering gallery mode resonator method
TE01d, TM01d or HE11d modes of the DRs are normally
measured by the end-shorted TE011, TE01d (cavity) or
stripline methods.5,6,25,31 However, the measured Q of
these modes depends not only on the material’s tand but
also on the radiation and conduction losses of the cavity
as stated earlier. Thus simple measurement by the above
methods for very low-loss dielectrics are not accurate
enough. The Whispering Gallery modes (WGMs)35–39
11 Typical resonant curve of a dielectric resonator (DR)
coupled to a microstrip line used in determining the
quality factor by the stripline method
Sebastian et al.
Low-loss dielectric ceramic materials
the diameter of the DR the number of modes in a
bandwidth increases. This means that samples with
small resonator diameter, the frequency interval between
two successive modes will be large. Dielectric resonators
acting in WGMs can be excited in different ways. In the
low-frequency range, an electric or magnetic dipole is
used. However, this type of excitation is stationary, and
travelling WGMs cannot be excited. In the millimetrewavelength frequency region dielectric image waveguides or microstrip transmission lines are used to excite
travelling WGMs.
Split-postdielectric resonator method
Downloaded by [Penn State University] at 11:01 26 November 2015
12 The experimental set-up for measuring quality factor by
the stripline method. The dielectric resonator (DR) is
coupled to the stripline
has been reported to be able to confine the entire field
within the resonator which yields negligible radiation
and conductor losses at microwave frequencies. The
Q factor of WGM dielectric resonators is limited only by
the intrinsic losses in the dielectric material leading to
the situation where the measured WGM Q factor is
approximately equal to 1/tand. In this method, most of
the electromagnetic energy is confined to the dielectric
near the perimeter of the air-dielectric.37,38 One
additional advantage of using the WGMs technique is
that it allows measurements of two permittivity components of uniaxially anisotropic materials and is very
useful, for example, in the case of several single-crystals.
In this technique measurements of resonant frequencies
and Q factors of two modes belonging to different
mode families employing rigorous numerical analysis,
e.g. mode-matching, are needed. The electrical energy
filling factors for E (quasi-TM mode) and H (quasi-TE
mode) modes are then calculated.37,39
P1’ ¼ 2
Lf 1’
L1’ f
ð18Þ
P1ll ¼ 2
Lf 1ll
L1ll f
ð19Þ
The dielectric tand can be solved38 using the equation
Q21
ðEÞ ¼ tan dðP1’ þ P1II Þ þ Rs =G ðEÞ
ð20Þ
Q21
ðHÞ ¼ tan dðP1’ þ P1II Þ þ Rs =G ðHÞ
ð21Þ
where Rs is the surface resistance of the cavity, 1ll is the
permittivity parallel to the anisotropic axis and 1His the
one perpendicular to it. In general the conductor losses
decrease as the surface resistance becomes smaller and as
the geometric factor (G) increases.39 However for the
WGM the geometric factor, G, is sufficiently large and
thus the effect of the cavity can be ignored. In addition
the radiation losses are negligible for these modes.
The spurious modes in WGM method dominate since
the propagation constant along the z axis is very small
and unwanted modes leak out axially. The WGM
dielectric resonators are classified as WGEn,m,l or
WGHn,m,l.These correspond to the case where the electric field is essentially transverse, or axial. WGMs are
periodic according to the azimuthal number, and with
The split-post-dielectric resonator (SPDR), shown in
Fig. 13, is an accurate method for measuring the complex permittivity and loss tangent of substrates and thin
films at a single frequency in the range of 1–20 GHz.40–43
This arrangement allows the formation of an evanescent
electromagnetic field, not only in the air gap, but also in
the cavity region for radii greater than the radius of the
dielectric resonators which simplifies the numerical
analysis and reduces possible radiation effects. In the
SPDR method, a flat sample of the test material is
inserted through one of the open sides of the fixture and
positioned between two low-loss dielectric rods or
resonators kept in a metallic enclosure.
The sample is in contact with one of the resonators and
separated from the other by a small air gap. The electric
field in resonators is parallel to the surface. This means that
the test sample should have strictly parallel faces, the
thickness of the sample should be less than that of the fixture air gap, and the sample should have enough area to
cover the inside of the fixture. In these conditions, the accuracy of the measurement is not affected by the air gap
between the sample and the resonator. The required
thickness of the sample also depends on the 1r of the material and materials with high 1r must be thinner. Several
modes are commonly excited, but the TE01d mode is preferred since it is insensitive to the presence of air gaps
perpendicular to z-axis of the fixture.
The complex permittivity is calculated based on electromagnetic modelling of the split-post-resonant structure using the Rayleigh–Ritz technique.40 The real part
of the complex permittivity can be iterated from the
measured resonant frequencies and thickness of the test
sample, h, using the following equation 41
19r ¼ 1 þ
f0 2fs
hf0 K 1 ð19r ; hÞ
ð22Þ
where f0 is the resonant frequency of the empty SPDR,
fs is the resonant frequency of the SPDR with the
dielectric sample. K1 is a function of 1’r and h and is
evaluated for a number of 1r using the Rayleigh–Ritz
technique.40 The tand of the sample is calculated from
the measured unloaded Q factors of the SPDR with and
without the dielectric sample from
1
1
1
2
2
ð23Þ
Pe
tan d ¼
Qu Qd Qc
21
denote losses of the dielectric and
where Q21
d and Qc
metallic parts of the resonator, respectively. Pe is the
electric energy filling factor of the sample given by the
following equation
International Materials Reviews
2015
VOL
60
NO
7
399
Sebastian et al.
Low-loss dielectric ceramic materials
13 Schematic sketch of split-postdielectric resonator (SPDR)
Downloaded by [Penn State University] at 11:01 26 November 2015
N
X
1
¼
Pei tan di
Qd
i¼1
ÐÐÐ
Pei ¼ ÐÐÐ
vd
1i jEj2 dv
2
vt 1ðvÞjEj dv
ð24Þ
accuracy and is convenient and fast for low-loss laminar
dielectrics such as substrates or LTCCs, printed circuit
boards and even for thin films.
ð25Þ
Measurement of dielectric properties of powder
samples
where Pei and tandi are the electric energy filling factor
and the dielectric loss tangent for the ith dielectric
region, respectively.
Uncertainty of the permittivity depends on the sample
thickness h as follows: Der/er ¼ ¡(0.0015þDh h21) and
the accuracy of the loss tangent is , ¡0.03 tand. For the
complex permittivity of a sample, the resonant
frequencies and Q factors of the empty SPDR and the
SPDR containing the test sample must be measured. The
SPDR is operated in a particular mode with a particular
resonant frequency which depends on resonator
dimensions and to a limited extent the electrical
properties of the test sample; thus each SPDR is
designed for a particular nominal frequency and
the actual measurement is taken close to this frequency.
The size of the sample is determined by the nominal
frequency. This means that, for example, a nominal
frequency of 5–6 GHz requires a minimum sample size
of 3063062.1 mm. QWED provides SPDRs (Fig. 14)
with dedicated software for the evaluation of
permittivity and loss tangents. Compared to the reflection-transmission methods, the SPDR provides superior
Low-loss dielectric ceramic powders are also more and
more used to enhance dielectric properties of polymers.
In the last 10 years interesting polymer ceramic composites have been introduced enabling free adjustment of
permittivity of devices being important in several
applications areas where design of telecommunication
devices has limited space. Additionally one overwhelming example is advanced printed electronics,
where inks are based on low temperature curing polymers with embedded dielectric ceramic particles. In these
cases it is crucial to know the dielectric properties of
powder particles, which can differ significantly if compared to the bulk properties. However, very few papers
are published44–50 on the measurement of powder
samples. More recently Tuhkala et al.48–50 reported an
indirectly coupled open-ended coaxial cavity resonator
method operating in TEM mode at 4 GHz to estimate
the relative permittivity and loss tangents of powder
samples. In this method the open-ended coaxial cavity
with optimised dimensions and conductivity is filled with
dielectric materials in powder form and the effective
dielectric properties are determined by the shift of
resonant frequency and change in Q factor between an
empty resonator and a filled resonator. A schematic
set-up for the measurement is shown in Fig. 15.
For a completely filled cavity, the effective dielectric
constant is given by
1r ¼ ðc=4Lfr Þ2
14 Photographs of split-postdielectric resonators (SPDRs)
produced by QWED, Poland. (Courtesy, QWED Poland)
400
International Materials Reviews
2015
VOL
60
NO
7
ð26Þ
where c is the speed of the light in vacuum, L is the
resonator length and fr is the resonant frequency. The
dielectric constant of powder samples can be obtained
from measured resonator response, volume fractions of
each phase (powder, air and different phases) and
calculating the effective dielectric constant using Bruggeman
symmetric19 and the Looyenga51 mixing rules.
In the same manner the effective loss tangent of the
powder sample (with different phases) is estimated from
the difference in Q factor between an empty resonator
and a filled resonator using the equation
Sebastian et al.
Low-loss dielectric ceramic materials
The tf value is measured by following the drift in the
resonant peak frequency ( fo) as a function of temperature. Choosing an arbitrary temperature to use as standard, say 258C, the ratio fo(T )/fo(258C) can be defined at
each temperature. Then, tf is obtained from the slope of
a graph of fo(T )/fo(258C) versus the reduced temperature
T9 ¼ T2258C:
Downloaded by [Penn State University] at 11:01 26 November 2015
tf ¼
15 Schematic set-up for microwave measurements of
powder samples (after Ref. 53)
tandeff ¼ 1=Qfilled 2 1=Qempty
ð27Þ
and utilising general mixing rules.
The method expects careful estimation of the volume
fraction of the powder, homogeneous distribution of
the powder throughout the cavity, management of
measurement environment (mainly humidity) and probe
coupling, which should be loose enough not disturbing
the measurement itself and producing symmetric
resonance peak.
Tuhkala et al.52,53 estimated the microwave dielectric
properties of several materials with reasonable accuracy
by this technique. The method is shown to be useful for
studying the properties of powders in several ways. They
also reported estimation of humidity level of the powders,53 effect of surfactant treatment,54 evaluation of the
amount of two powder phases52 using the above
method.48
Measurement of temperature coefficient of
resonant frequency (tf)
The temperature coefficient of resonant frequency, tf,
is the parameter which indicates how much the resonant
frequency drifts with temperature. In many cases
microwave devices in order to operate correctly require
tf value close to zero. The tf relates to the linear
expansion coefficient of the sample itself, aL, and
dependence of the material’s dielectric permittivity with
temperature.2 Mathematically tf relates to the temperature coefficient of the permittivity, t1, as follows
tf ¼ 2aL 2
t1
2
ð28Þ
It may be noted that equation (31) is valid for 100%
electric energy storage in the sample and thermal
expansion of the metal cavity enclosing the DR is negligible. In general the electronic ceramic materials has aL
close to þ10 ppm/8C meaning a significant influence
of t1 on tf.
dð f o =f o ð25o ÞÞ
1 dfo
¼
dT9
f o ð25Þ dT9
ð29Þ
The actual curve of the graph is never linear but very
nearly parabolic and is easily fitted with a quadratic
equation in terms of fo(T)/fo(258) and T2258. In this
equation, the first-order coefficient is tf, which is the
slope of the curve at 258C. The second-order coefficient
is the so-called non-linearity or double-derivative factor
(tf’). Its sign shows whether the parabola is concave up
(þ) or down (2), and its magnitude indicates the
severity of curvature. Both numbers are usually scaled
up by 106 and reported in parts per million per degree
(ppm/8C) or MK21.
If tf is measured by the cavity method, then the
thermal expansion of the cavity during heating
(or contraction during cooling – measurements are best
done upon cooling) limits the accuracy of the method, in
which case very low-aL materials (e.g., invar,
aL ¼ 1.2 ppm/8C) can be used for the cavity. The
WGMs and also for TE01d mode resonant structures are
reliable methods for tf measurements since the thermal
expansion of the cavity is negligibly small especially if
the relative permittivity of the sample is large and the
sample is situated away from cavity walls.
The temperature coefficient of dielectric permittivity
t1 can be obtained by the parallel-plate capacitor
method using an LCR meter at low frequency.
Factors affecting dielectric losses
The tand is known to be very sensitive to humidity6,55
meaning that the microwave measurements should be
done in a humidity-controlled room. Before the
experiments the samples should be heated in an oven to
remove adsorbed moisture. However, the content of the
dielectric has the main effect on the loss values. When
especially low-loss materials are desired, the starting
materials should be selected the way they have the lowest
possible concentration of dipoles and charge carriers
with the lowest possible mobility.56 Dielectric loss is also
affected by disordered charge distributions in the crystal
lattice56,57 which occur if the charge distribution in a
crystal deviates from perfect periodicity. In 1964
Schlömann56 reported that the loss tangent increases in
ionic non-conducting crystals when ions are disordered
in such a way that they violate periodicity. The loss
tangent thus depends strongly on the spatial correlation
between charge deviations and is negligible if the disordered charge distribution in the crystal maintains
charge neutrality within a short range of the order of the
lattice constant.
The intrinsic quality factor (QU ¼ 1/tand) of any given
material is frequency dependent. For many materials
tand almost linearly increases as the frequency increases
and thus often the intrinsic quality factor is reported as
(QU f ¼ f/tand) (in GHz) as a first approximation. This
is most valid for well-densified ceramics within a limited
International Materials Reviews
2015
VOL
60
NO
7
401
Sebastian et al.
Low-loss dielectric ceramic materials
Downloaded by [Penn State University] at 11:01 26 November 2015
frequency range. In practice, higher QUf values for
samples measured at higher frequencies (5–12 GHz)
than at lower frequencies. More recently Li and Chen
reported58 that the product Q f is frequency dependent
and increases with frequency. The frequency dependence
of Q f value is attributed to the presence of defectsinduced extrinsic dielectric loss. It may be noted that
larger samples resonating at lower frequencies statistically contain more imperfections than smaller ceramic
discs resonating at higher frequencies.
The presence of porosity decreases the Q factor further
because of presence of moisture in the pores.
A fundamental theory of intrinsic losses set the lower limit
of losses found in pure defect-free single crystals.59 In a
dielectric several phonon processes contribute to intrinsic
losses and their importance depends on the ac field
frequency, temperature range and symmetry of the crystal
under consideration. The loss mechanisms are different
for a crystal with and without a centre of symmetry.
Gurevich & Tagantsev59 obtained numerical estimates
of tand of ideal crystals.
For an ideal crystal with a hexagonal symmetry when
T%TD.
tan d ¼
gvðkTÞ5
1r rv 5s h 2 ðkT D Þ2
ð30Þ
and for rhombohedral or cubic symmetry
gv 2 ðkTÞ4
tan d ¼
1r rv 5s hðkT D Þ2
ð31Þ
where g is a dimensionless anharmonicity parameter
ranging between 1 and 100, v is the angular frequency,
k ¼ Boltzmann constant, T ¼ absolute temperature,
vs ¼ sound velocity, TD ¼ Debye temperature and
r is the mass density.
Owing to the complicating factors introduced by a
variety of extrinsic mechanisms, there is no predictive
theory to account for the microwave loss in dielectric
ceramics meaning that finding new dielectric resonator
materials is largely done by trial and error and involves
the preparation and testing a large number of samples.
This is a laborious and time-consuming job. The Q
factor is highly dependent on not only the extrinsic and
intrinsic quality of the ceramic sample but also the
method of measurement, the measurement environment
and the frequency at which the sample is measured.
A given material sample may exhibit greatly differing Q
values when tested in different test fixtures and
environments which may vary in size, shape, conductor
quality, coupling, type of sample support, ambient
temperature and relative humidity.
data on materials of identical composition and manufactured in different laboratories using different processing conditions would be expected to lead to small
variations in properties. The dielectric data measured by
impedance methods at low frequencies are not included
in the Table since it is unreliable when the loss tangent is
less than 1023. The Table shows nearly 4000 low-loss
dielectric ceramic compositions reported in the literature. About 35% of them belong to the interesting,
widely applicable perovskite family. The analysis of
crystal systems shows that many of them enable interesting low-loss dielectric properties. The most common
one is orthorhombic (35%), followed by hexagonal
(18%), monoclinic (12%), cubic (12%) and tetragonal
(10%) crystal systems. About 60% of the reported lowloss dielectric ceramics are based on alkaline earth
metals like Ba, Sr, Ca or Mg. Additionally, titanates
(46%) and compositions containing rare earths (40%) or
tantalates/niobates (39%) are widely reported. Silicates
and tungstates are also well represented. Understanding
the relation between bonding mechanisms and the
microwave dielectric properties is essential. The silicates,
to mention one example, have in general predominantly
covalent bonding which geometrically restricts the
movement of atoms and leads to low dielectric loss. On
the other hand, the low dielectric polarisability of silicon
and the strong covalent bonds in silicates yield low 1r.
Thus, in general, the silicates and tungstates have low 1r,
niobates and tantalates have medium 1r, and titanates
have relatively larger 1r. Another example is formed by
an octahedral arrangement of anions within a perovskite
family of materials where octahedral tilting, brought on
by a geometrical instability related to the relative sizes of
A and B cations, is accompanied by symmetry lowering
and affects the dielectric loss. As expected the reported
quality factors of the microwave dielectric ceramics
decrease significantly with increasing relative permittivity as shown in Fig. 16. The inset in Fig. 16 shows the
variation of quality factor frequency product with relative permittivity in the logarithmic scale.
The 0.993MgO–0.007B2O3 material has the highest
quality factor (Qf ¼ 773 700 GHz, with er ¼ 9.3 and tf
of 255 ppm/uC). On the other hand, the composition
0.8SiO2–0.2B2O3 has the lowest relative permittivity
(er ¼ 3.6, Qf ¼ 70 600 GHz and tf of 211 ppm/uC).
Its relatively low Qf value can be explained by the glassy
nature of this material. AlPO4 is difficult to densify and
Low-loss dielectric ceramics
A list of low-loss ceramic dielectric materials with
sintering temperature, crystal structure, relative permittivity, quality factor-frequency product, measurement
frequency, temperature variation of resonant frequency
and references are given in the supplementary file. In
tabulating these data, we make no judgement on the
measurement method and the reliability of the result.
The ceramic properties such as porosity, grain size, raw
materials used, measurement methods and equipment
used for measurements affect the dielectric properties
and readers should be aware that exact comparison of
402
International Materials Reviews
2015
VOL
60
NO
7
16 Variation of Qf as a function of relative permittivity
Downloaded by [Penn State University] at 11:01 26 November 2015
Sebastian et al.
it has a very low permittivity of 3.0. These low-er
materials are important for increasing the signal speed in
communication systems. At the other end of the scale
Ba0.6Sr0.4TiO3 þ 0.5 wt-% MgCo2(VO4)2 composite
represents
the
highest
relative
permittivity
(Qf ¼ 300 GHz, with er ¼ 2763). Figure 17 shows the
variation of tf with relative permittivity.
In general the materials with lower relative permittivity show negative tf and high permittivity materials
have a positive tf. The Bi6Ti5TeO22 has the highest
temperature
variation
of
resonant
frequency
(Qf ¼ 220 GHz, with er ¼ 350 and tf of þ2600 ppm/uC)
and BaNb2O6 (hexagonal) has the highest negative tf
(Qf ¼ 4000 GHz, with er ¼ 42 and tf of 2800 ppm/uC);
however, this is a question of optimisation since there
are several ways to tune the tf value such as by forming
composites with positive and negative tf materials. The
table (supplementary file) shows the availability of
materials with almost any desired relative permittivity
especially in the range of 5–100; however, simultaneously satisfying a desired relative permittivity with
excellent Qf and tf values is difficult.
Tailoring microwave dielectric properties
Microwave dielectric properties can be tailored by
chemical methods like doping, slight deviations from
stoichiometry, or the formation of composites of
dielectrics with oppositely signed tf values.60–66 Luiten
et al.64,67 used paramagnetic effects of impurity ions to
compensate for the permittivity–temperature dependence (t1), which is related to tf by equation (28); but
this technique is not applicable at cryogenic temperatures or even room temperature because of the finite
energy gap of paramagnetic resonance. Hartnett
et al.68,69 proposed a method of compensating for the
frequency–temperature dependence (tf) of high-Q
monolithic sapphire resonators near liquid-nitrogen
temperatures by doping single-crystal sapphire with Ti3þ
ions. Breeze et al.70 reported a new method of achieving
temperature compensation by coating a film of TiO2 on
the surface of an alumina disc. The composite resonators
obtained by firing at 1400uC showed a temperature
compensation depending on the volume fraction
of TiO2. Materials having negative tf are usually tailored
17 Variation of the coefficient of temperature variation of
the resonant frequency as a function of relative
permittivity
Low-loss dielectric ceramic materials
by adding TiO2, CaTiO3 or SrTiO3, all of which
have high positive tf values.66,71–79 Similarly, positive tf
materials can be tailored by adding negative tf
materials.80,81 For example, the addition of about
17 mol% TiO2 in ZnAl2O4 results in a nearly zero tf as
shown in Fig. 18. The quality factor and the relative
permittivity also vary with TiO2 content.
Of course, this technique can only be used when the
additive material does not react with the parent material.
It is also possible to tailor tf by stacking positive and
negative tf resonators. The resultant properties depend
on the volume fraction or thickness of the two different
resonator materials.82–85 Fig. 19 shows a sketch of the
stacking and the variation of tf as a function of
the volume fraction of the negative tf (266 ppm/uC)
resonator Sr(Y1/2Nb1/2)O3 in a composite with the
positive tf (þ 78 ppm/uC) resonator Ba5Nb4O15. It was
reported83 that the properties slightly change on
reversing the bottom and top resonator samples. The
samples can be joined using low-loss adhesives, but the
use of adhesives lowers the quality factor.84
It is also possible to tailor properties by solid-solution
formation between positive and negative tf materials
provided they have similar crystallographic structures.86–91 If the end members have different crystal
structures, then a phase transition at some intermediate
composition may result in sudden change in the
18 Variation of dielectric properties of (12x)ZnAl2O4–xTiO2 as
a function of x a tf b quality factor. Inset of figure b shows
variation of resonant frequency with TiO2 content (after
Ref. 66)
International Materials Reviews
2015
VOL
60
NO
7
403
Sebastian et al.
Low-loss dielectric ceramic materials
Downloaded by [Penn State University] at 11:01 26 November 2015
dielectric properties.87 Fig. 20 shows the variation of the
dielectric properties of (12x)CaTiO3–xNdAlO3 solid
solution. A zero tf is observed for x ¼ 0.3. The solid
solution can be represented by Ca12xNdxTi12xAlxO3.
A slight non-stoichiometry is also sometimes found to
improve the densification and microwave dielectric
properties.92–96 The presence of vacancies can facilitate
atomic diffusion and thereby increase densification.
For example, slight Ba or Mg deficiencies in
Ba(Mg1/3Ta2/3)O3 is found to improve densification,
order parameter and quality factor, as shown in Fig. 21.
The addition of suitable dopants can improve the
microwave dielectric properties, and a study of the
dielectric table reveals that the microwave dielectric
19 a Schematic sketch of stacking of positive and negative
tf resonators having varying thickness b Variation of tf
of Ba5Nb4O15 ceramic as a function volume fraction of
stacked Sr(Y1/2Nb1/2)O3ceramic (after Ref. 83)
20 Variation of dielectric properties a tf b relative permittivity and c Qf as a function x in (12x)CaTiO3–xNdAlO3
solid solution (after Ref. 92)
404
International Materials Reviews
2015
VOL
60
NO
7
21 a Variation of bulk density and order parameter as a
function of x in Ba(Mg0.33xTa0.67)O3 ceramics b Variation
of the relative permittivity and tf as a function of x in
Ba(Mg0.33x Ta0.0.67)O3 ceramics (after Ref 95)
Downloaded by [Penn State University] at 11:01 26 November 2015
Sebastian et al.
properties can also be tailored to some extent by suitable
chemical substitution.97–102 Usually, the dopant partially
substitutes at appropriate sites in the parent material.
For example, it is reported that the quality factor
reaches a maximum when the ionic radius of the dopant
is close to the average ionic radius of the B-site ion in
Ba(Mg1/3Ta2/3)O3 (BMT) and Ba(Zn1/3Nb2/3)O3 (BZN)
ceramics.103,104 In BMT the Qf reaches a maximum
when the ionic radius of the dopant is between 0.6 and
0.7 Å, and the weighted average ionic radius of Mg and
Ta is 0.653 Å. Figure 22a shows the variation of Qf in
BMT ceramics as a function of the concentration of
various dopants. A very small amount of dopant is
found to improve the quality factor, with slight changes
in relative permittivity and tf. Figure 22b shows the
variation of Qf in BMT as a function of the ionic radius
of the dopant.
Many of the materials are difficult to densify even
sintering at high temperatures, and such materials are
usually densified by adding a small amount of lowmelting-temperature compounds or glasses. The high
sintering temperatures can also be lowered and the
densification improved by liquid-phase sintering via the
addition of low-melting-temperature compounds such as
V2O5, Bi2O3, CuO, LiF, MgF2, CuO, B2O3, Nb2O5,
Li2CO3, BaCuB2O5, MoO3, Li2WO4, CuV2O6, PbO, etc.
Low-loss dielectric ceramic materials
and glasses such as Li2O–B2O3–SiO2, Li2O–MgO–ZnO–
B2O3–SiO2, MgO–B2O3–SiO2, ZnO–B2O3, CaO–B2O3–
SiO2, B2O3–P2O5, MgO–CaO–Al2O3–SiO2, ZnB2O4,
Bi2O3–B2O3,
Al2O3–B2O3–SiO2,
ZnO–B2O3–SiO2,
BaO–B2O3–SiO2, Bi2O3–B2O3–ZnO–SiO2, PbO–B2O3,
PbO–B2O3–SiO2, Li2O–Zn–B2O3, Li2O–B2O3–SiO2,
Bi2O3–B2O3–ZnO–SiO2,
BaO–
Li2O–MgO–B2O3,
B2O3–SiO2–CaO–Al2O3, BaO–B2O3–Li2O–CuO–, PbO–
Al2O3–SiO2, La2O3–ZnO–B2O3, PbO–Bi2O3–B2O3–
ZnO–TiO2. The addition of a small amount of several
glasses is found to be effective in lowering the sintering
temperature and improving microwave dielectric properties of BMT ceramics. Figure 23 shows the effect of
some selected glasses on the Qf and tf of BMT ceramics.
Although the addition of larger amounts of glass considerably lowers the sintering temperature, it also
degrades the microwave dielectric properties. In general
glasses have negative tf values, and glass addition
improves the tf of materials with positive values of tf.
Compounds like CeO2, MnCO3, SnO2, NiO, ZnO,
WO3, TiO2, Yb2O3, ZrO2 etc. have also been used to aid
solid-state sintering and improving the dielectric
properties.103,106–112 Partial substitution by elements
with higher dielectric polarisability can increase the
relative permittivity.113 For example, as shown in
Fig. 24, substituting 44% of the Sr2þ(ai ¼ 4.24 Å3)114 in
Sr9Ce2Ti12O36 with Pb2þ(ai ¼ 6.58 Å3)114 increases the
relative permittivity from 183 to about 800.113
In several complex perovskites an order–disorder
transition is found to affect the microwave dielectric
properties. Improvement in ordering by annealing or
doping is found to improve the quality factor
considerably.103–105 The purity and origin of the initial
raw materials can also influence the phase formation,
densification and microwave dielectric properties. The
presence of porosity decreases the relative permittivity
and a correction for porosity can be performed using
mixture rules, as discussed in section Correction for
Porosity. The presence of porosity considerably
increases the loss tangent for otherwise dense ceramics,
as shown in Fig. 25 for alumina.115
A dense ceramic usually optimises the microwave
dielectric properties. Figure 26 shows a typical microstructure of thermally etched dense ceria ceramic
sintered at 1675uC. Ceria has a relative permittivity of
24 and Qf of 65 000 GHz.116 All types of defects
contribute to extrinsic dielectric losses. For an ideal
material, loss is mainly a manifestation of the interaction
of the phonons with microwaves, hence it is possible to
improve the quality factor by suppressing the phonons
by cooling the ceramics. Figure 27 shows the variation of
the quality factor of ceria ceramic as a function of
cooling. The quality factor reaches a maximum of about
10 000 at 6 GHz at 50 K.
Applications of low-loss dielectric
ceramics
Materials for LTCC applications
22 a Variation of the quality factor of Ba(Mg1/3Ta2/3)O3
ceramics as a function of the dopant concentration
b Variation of the quality factor of Ba(Mg1/3Ta2/3)O3
ceramics as a function of the dopant ionic radii (after Ref. 98)
High and low temperature co-fired ceramics, HTCC and
LTCC respectively, have created a new generation of
small and lightweight electronic multilayer components
with application area such as capacitors and microwave
products. The LTCC tapes are fabricated from suitable
choice of low-temperature sinterable dielectric materials.
International Materials Reviews
2015
VOL
60
NO
7
405
Sebastian et al.
Low-loss dielectric ceramic materials
Downloaded by [Penn State University] at 11:01 26 November 2015
24 Variation of the relative permittivity as a function of Pb
substitution for Sr in Sr9Ce2Ti12O36 ceramics (after Ref. 107)
25 Variation of loss tangent as a function of porosity in
alumina (after Ref. 108)
23 Variation of a quality factor b tf of BMT as a function of
glass content (after Ref. 100)
Currently these LTCC substrates are being developed by
industrial organisations like DuPont, Ferro and
Motorola. The developmental activities (basic, applied
and product development) of dielectric materials have
shown substantial increase in the last decade resulting in
a variety of dielectric materials for choosing the required
compositions with respective properties.
406
International Materials Reviews
2015
VOL
60
NO
7
Ceramic composition that has a sintering temperature
from 700 to 950uC can be categorised to belong to
LTCCs. The upper limit comes from the requirement
that the tapes made of it should densify in co-firing with
high conductive electrode material like Ag or Cu. At
lower sintering temperatures than 700uC, other electrode
material like Al, Pd or different mixtures should be
selected and the resistance of the electrodes increases
highly. One must note in order to enable multilayer
co-fired structures, the tapes made of the LTCC have to be
co-fired with Ag or Cu pastes without excess reactions.
Low-melting and low-loss glasses are usually added to
low-loss dielectric ceramics in order to decrease the
sintering temperature below the melting point of
the silver electrode. The addition of glasses degrades the
dielectric and mechanical properties. Another option is
to add sintering aids which is the most common way
with LTCCs having high relative permittivity. The Table
includes several compositions such as vanadates, telleurates, tungstates, molybdnates and phosphates based
on Li, Mg, suitable for glass free LTCC applications and
several ceramic glass composites. The reader is referred
to the review on LTCC for more details in reference.3
Sebastian et al.
Downloaded by [Penn State University] at 11:01 26 November 2015
26 SEM microstructure of thermally etched ceria sintered at
16758C (courtesy P S Anjana)
27 Variation of quality factor of ceria on cooling (after Ref.
109)
It may be noted that many of these reported LTCC
materials are not prepared in tape form and the
reactivity with electrode, thermal expansion, thermal
conductivity, etc. are not reported in the literature.
Although several glass free LTCC materials are available, tapes of very few glass free materials are reported
in the literature.117,118 The important characteristics
required for LTCC applications are as follows:
(a) relative permittivity erw4
(b) tand v1022 at 5 GHz
(c) tf in the range of 210 to þ10 ppm/uC
(d) no reactivity with the electrode materials
(e) coefficient of linear thermal expansion less than
20 ppm/uC or matching with that of silicon
(f) high thermal conductivity.
Materials for ULTCC applications
There is a clear need for electroceramic compositions
feasible for co-firing with organic or semiconductive
structures expecting sintering temperatures less than
650uC using aluminium or less than 400uC using nano
silver ink electrodes. In semiconductors, metal electrode
should be deposited on top of the dielectric layers with
Low-loss dielectric ceramic materials
low temperature process. Additionally, multilayer
packages similar nowadays to those made by LTCC
technology but with much lower sintering temperature
would enable co-firing of semiconductor devices into the
package. In the recent decade several electroceramic
compositions with sintering temperature below 700uC
have been reported as shown in the Table. These
materials fall in two categories. The first one
(category II) covers compositions having sintering temperature over 400 up to 700uC. This category is justified
since in these temperatures only Al, Pd or different metal
mixture electrodes with relative low conductivity can be
used. These ULTCC II category materials can be used
on some metal, glass or ceramics substrates, but their
feasibility for real multilayer applications is somewhat
limited although there are many interesting compositions like Li2Mo4O12 sintered at 630uC has the highest
Qf of 108 000 GHz with er ¼ 8.8 and tf ¼ 289,119
Zn2Te3O8 þ 30 wt-% TiTe3O8 sintered at 610uC has the
lowest tf of 3 ppm/uC with er ¼ 19.8 and
Qf ¼ 50 000 GHz.120 The [(Li0.5Bi0.5)x Bix][MoxV12x]O4
with x ¼ 0.098 when sintered at 650uC has the highest er
of 81 with Qf of 8000 GHz, tf of 10 ppm/uC.121
The main application areas can be found at moderately
low frequency areas. Important application fields could
be multilayer capacitors and packages.
The category I, with sintering temperature at 400uC or
below, should be feasible with commercially available
highly conductive nano silver inks in co-firing. These
compositions have commonly ultra-low sintering
temperature inherently. Although only very few compositions so far belonging to this category are reported,
they will in the future provide great opportunities with
integrated applications with semiconductor devices or
on organic substrates. The NaAgMoO4 has the lowest
sintering temperature of 400uC among the reported
materials. It has a relative permittivity of 7.9 with Qf of
33 000 GHz and tf of 2120 ppm/uC.122 On the other
hand, most of these ULTCC I materials are based on
vanadates and molybdates which are soluble in water.
This means the ultimate device needs suitable encapsulation. The research and development of ULTCC
materials are still in their initial stage. There is an urgent
need for developing materials with sintering temperature
less than 400uC for future applications.
Materials for dielectric resonators
Ceramic dielectric resonators are widely used for
commercial and military purposes from MHz frequencies
up to 50 GHz. Their main advantages are compact size,
temperature stability and high unloaded Q factor.
Commonly used products are dielectric resonator
oscillators (DROs), low-loss filters and combiners, and in
unmetallized form are intended to operate in the TE01d
mode. With different kind of cavity shielding or metallic
coating, the performance of the DR is adjusted for the
product demands. In the case of DROs a low phase noise is
needed and thus materials with high-Q factor are used. In
commercial DROs, the ceramic resonators have relative
permittivity from 20 up to 50 with Q f values as high as
100 000 GHz. The dielectric properties are commonly
measured in the frequency range from 2 GHz up to
10 GHz. Regardless of the application, thermal stability
of the resonant frequency (210vTf v10 ppm/uC) is
desirable.
International Materials Reviews
2015
VOL
60
NO
7
407
Sebastian et al.
Low-loss dielectric ceramic materials
Materials for dielectric ceramic antennas
Downloaded by [Penn State University] at 11:01 26 November 2015
The ceramic dielectric resonators are often enclosed
inside metal cavities to confine radiation and to maintain
a high-quality factor which is important for filter and
oscillator applications. When the metallic shield is
removed and with suitable feeding to excite appropriate
mode, the resonators could become efficient radiators.
McAllister and Long123 proposed the use of resonators
for antenna applications. For details of dielectric
resonator antennas (DRA), the reader is referred to the
recent reviews.124–126 There is no inherent conductor loss
in dielectric resonators which leads to high radiation
efficiency. Simple coupling schemes can be used for
DRA to most of the transmission lines used in microwave and millimetre-wave frequencies. Experimental
and theoretical studies are extensively done on DRA
with different shapes or geometries such as cylindrical,
rectangular, circular, ring, conical, hemispherical and
square-shaped structures. The dimension of the resonator is related to free space wavelength and er by
equation (2) and by choosing a high er, the size of the
DRA can be significantly reduced at the expense of
bandwidth. The operating band width can be varied for
a wide frequency range by suitably selecting the resonator parameters and a band width of 117% have been
reported.127 The lowest frequency of DRA reported is
55 MHz128 and the highest 94 GHz.129 DRA’s with
dimensions ranging from a few millimetre with er in the
range of 6–100 have been reported.124–126 Very thin
(v4 mm) structures are needed especially when
integrated to portable terminals. Ceramic dielectric
materials are widely used for GPS patch antennas
leading to high performance and miniaturisation.
Ceramic antennas have also been proposed for
multi-purpose
targets
like
machine-to-machine
communication.130 They are supposed to operate in
the Zigbee, ISM and cellular bands including LTE in the
frequency band between 700 and 2500 MHz. Ceramic
chip antenna is calculated to provide 80% reduction in
PCB space for 2.45 GHz applications.
Materials for millimetre-wave applications
The millimetre-wave radio spectrum is expected to be
used in the future (e.g. 5G networks) since higher carrier
frequencies are possible as compared to the current
systems, such as 4G and Wi-Fi. For millimetre-wave
applications the relative permittivity should be
approximately in the range of 6–20 having very highquality factors greater than 75 000 GHz with temperature stable dielectric properties. High permittivity
materials in general have lower quality factors and also
have the problem of fabricating extremely small sized
resonators. ZnAl2O4–TiO2-, Mg2SiO4-, Mg4Ta2O9- and
Al2O3-based materials are some of the examples for
possible millimetre-wave communication in radars,
space, 5G and military applications.
Materials for future applications and
conclusions
The DR table indicates a large number of materials with
very useful microwave dielectric properties. However,
important emerging technologies will require seamless
co-firing with plastics or paper substrates (printed
electronics) or semiconductor devices. The DR table
408
International Materials Reviews
2015
VOL
60
NO
7
exhibits about 120 materials with Ultra Low Sintering
Temperature (ULTCC – sintering temperature less than
700uC) and with materials like NaAgMoO4 sintering
temperature even lower than 400uC. However, further
research is required to enable low-loss dielectric microwave ceramics to integrate with plastics and feasible with
nano silver and other electrode materials. Recently room
temperature curable silica ink has been screen printed on
flexible mylar substrate for printed applications.131 The
screen printed silica has a relative permittivity of 2.4 and
tand of 0.003 at 15 GHz. Another field of application,
the health care systems or monitoring, requires suitable
antenna materials for bio-implantable communication
devices.132 Apatite-type materials with reasonably
good microwave dielectric properties are reported133
(see the Table). However, their biocompatibility needs to
be investigated for practical applications.
One interesting field for microwave ceramics is lowloss polymer–ceramic dielectric composites reported for
antenna and printed circuit board applications.1 However, they are rigid and not bendable or stretchable
especially if the loading level of ceramic is high. Flexible,
bendable and stretchable dielectrics which can cover
even curved surfaces are important for applications in
electronic control systems, consumer electronics, heart
pacemakers, body worn antenna, etc. The requirements
for a material to be used as a flexible dielectric waveguide are mechanical flexibility, high relative permittivity, low dielectric loss, high thermal conductivity, low
coefficient of thermal expansion (CTE), etc. Recently
low-loss ceramic-filled butyl rubber and silicon rubberbased composites have been reported,134–136 but further
work is needed for device optimisation.
Several applications areas like the semiconductor
industry are in constant need for low-loss materials with
ultra-low relative permittivity (low k materials) to
reduce RC signal delay. Lowering the relative permittivity decreases power consumption and reduces crosstalk between nearby interconnects. Silica, which has the
lowest permittivity of about 4.0, is commonly used as
the low k material. Further decrease of the permittivity
can be achieved by introducing porosity. However, the
presence of porosity degrades the mechanical properties.
Fluorination of silica (SiOF) lowered the permittivity to
about 3.6.138 SiCOH with k of about 2.4 have also been
reported.137 Recently several organic or hybrid dielectric
materials have been developed137 with even lower permittivities, but they are not suitable for very large-scale
integration (VLSI) chips because of their poor chemical,
mechanical and thermal properties. There remains a
need to develop materials with lower relative permittivities and good mechanical, chemical and thermal
properties in order to increase the signal speed.
As a conclusion, the study of the DR table reveals that
many tantalates, niobates, titanates, silicates, tungstates,
molybdanates, vanadates or tellurates based on alkali
earth metal and rare earths show low dielectric loss.
It seems that most of the low-loss dielectric microwave
ceramic materials have an octahedral or tetrahedral
arrangement of atoms. However, further investigation,
including especially spectroscopic and XRD studies, is
needed to understand the relationship between chemical
bonding, lattice vibrations, atomic coordination,
secondary phases, impurities and microwave dielectric
properties. Such studies would be useful for finding new
Sebastian et al.
low-loss dielectric ceramic compositions for present and
future applications. Attempts should be also done to
lower the cost of production of microwave materials
with emphasis on use of environment friendly materials
with the possibility of recycling.138 In the near future, the
new emerging communication applications like 5G
network machine-to-machine connection and IoT will
need novel dielectric ceramics with feasible component
fabrication technologies. This means that the low-loss
microwave ceramics will continue to be an active area of
research in years to come. The future will show their
importance for improved performance with cost-efficient
and miniaturised devices. The operational details of 5G
networks and the IoT are still not available and hence
the material requirements are yet to be determined.
Acknowledgement
Downloaded by [Penn State University] at 11:01 26 November 2015
The authors are grateful to European Research Council
(ERC project) and the US National Science Foundation
(DMR 1052788) for financial support.
References
1. M. T. Sebastian and H. Jantunen: ‘Polymer-ceramic composites
of 0-3 connectivity for circuits in electronics: a review’,
International J. Appl. Cer. Techn., 2010, 7, 415–434.
2. M. T. Sebastian: ‘Dielectric materials for wireless
communication’, 2008, Oxford, UK, Elsevier.
3. M. T. Sebastian and H. Jantunen: ‘Low loss dielectric materials for
LTCC applications. A review’, Int. Mater. Rev, 2008, 53, 57–90.
4. O. V. Karpova:""' ‘On an absolute method of measurement of dielectric properties of a solid using a Л – shaped resonator’, Sovt.
Phys., 1959, 1, 220–228.
5. B. W. Hakki and P. D. Coleman: ‘A dielectric resonator method
of measuring inductive capacities in the millimeter range’, IRE
Trans. Microwave Theory Tech, 1960, 8, 402–410.
6. W. Courtney: ‘Analysis and evaluation of a method of measuring
complex permittivity and permeability of microwave materials’,
IEEE Trans. Microwave Theory & Tech., MTT-, 1970, 476, 485.
7. S. B. Cohn and K. C. Kelly: ‘Microwave measurements of high
dielectric constant materials’, IEEE Trans. Microwave Theory
Tech., 1966, 14, 406–410.
8. Available at: http://coen.boisestate.edu/rickubic/files/2012/05/
HakCol.exe, 2013.
9. R. Ubic: ‘Software for calculating permittivity of resonator’,
in HakCol & ErCalc’, Ceramic Transactions, (Ed. J. Akedo,
T.-Y.Tseng, X.M. Chen and H.-T. Lin), 2014, 65–75.
10. Y. Kobayashi and S. Tanaka: ‘Resonant modes of dielectric rod
resonator short circuited at both ends by parallel plate conducting
plates’, IEEE Microwave Theory Tech., 1980, 28, 1077–1085.
11. D. L. Rebsh, D. C. Webb, R. A. Moore and J. D. Cawlishaw:
‘Mode chart for accurate design of cylindrical dielectric
resonators’, IEEE Microwave Theory and Tech., 1965, 468–469.
12. IEC 61338, section1-1,1-2 and 1-3 (1996-2003): ‘Wave guide type
dielectric resonators. Part 1. General information and test conditionssection 3. Measurement method of complex permittivity for dielectric
resonator materials at microwave frequency’, International
Electrotechnical Commission (IEC), 2005, Geneva, Switzerland, .
13. D. Hennings and P. Schnabel: ‘Dielectric characterization of
Ba2Ti9O20 type ceramics at microwave frequencies’, Philips Res.
Rept., 1983, 38, 295–311.
14. T. Itoh and R. S. Rudokos: ‘New method for computing the
resonant frequencies of dielectric resonators’, IEEE trans.
Microwave Theory Tech., 1977, 25, 52–54.
15. D. Kajfezz and P. Guillon: ‘Dielectric Resonators’, 1986,
Dedham, MA, Artech House Inc.
16. C. M. Garnet: ‘Colours in metal glasses and metal films’, Phil.
Trans. Royal Society of London. Series A: Mathematical,,
Physical, and Engineering Sciences, 1904, 3, 385–420.
17. K. Lichtenecker: ‘Die Dielektrizittskonstante natrlicher und
knstlicher Mischkrper’, Physikalische Zeitschrift, 1926, XXVII
115–158.
18. C. J. F. Bötcher: ‘The Dielectric Constant of Crystalline Powders,
Recueil des Travaux Chimiques des Pays-Bas’, Journal of the
Royal Netherlands Chemical Society, 1945, 64, 47–51.
Low-loss dielectric ceramic materials
19. D. A. G. Bruggeman: ‘Calculation of various physics constants in
heterogenous substances I Dielectricity constants and
conductivity of mixed bodies from isotropic substances’,
Annalen der Physik., 1935, 24, 636–664.
20. O. Wiener: ‘Theorie d. Mischkörpers F.D Feld d. Station.
Strömung. I. Herkunft und Stellung der Aufgabe’, Abhandlungen
Math. Phys. Klasse Sächs. Akademie der Wissenschaften
(Leipzig), 1912, 32, 509–523.
21. J. A. Stratton: ‘Electromagnetic Theory’, 1941, New York,
McGraw-Hill.
22. J. A. Reynolds and J. M. Hough: ‘Formulae for Dielectric
Constant of Mixtures’, Proceedings of the Physical Society,
1957, 70, 769–775.
23. J. Krupka: ‘Frequency domain complex permittivity
measurements at microwave frequencies’, Meas. Sc. & Tech.,
2005, 16, R1–R16.
24. P. Whelss and D. Kajfezz: ‘The use of higher order resonant modes in
measuring the dielectric constant of dielectric resonators’, IEEE.
Symp. Digest. St. Louis, 1985, MTT-S, 473–476.
25. Y. Kobayashi and M. Katoh: ‘Microwave measurement of
dielectric properties of low loss materials by the dielectric rod
resonator method’, IEEE Microwave Theory and Tech., 1985,
33, 586–592.
26. M. W. Pospieszalski: ‘On the theory and applications of the
dielectric post resonator’, IEEE Microwave Theory and Tech.,
1977, 25, 697–7000.
27. H. Takagi, N. Funnami, H. Tamura and K. Akino: ‘Measurement
accuracy of complex permittivity in the dielectric rod resonator
method’, Jpn. J. Appl. Phys., 1992, 31, 3269–3271.
28. Y. Kobayashi and H. Tamura: ‘Round robin test on a dielectric
resonator method for measuring complex permittivity at
microwave frequency’, ICIE Trans. on Electronics, 1994, E77-C,
882–887.
29. J. Krupka, K. Derzakowski, B. Riddle and J. B. Jarvis:
‘A dielectric resonator for measurements of complex permittivity
of low loss materials as a function of temperature’, Meas. Sci.
Techn., 1998, 9, 1751–1756.
30. K. Leong, J. Mazierska and J. Krupka: ‘Measurement of
unloaded Q factor of transmission mode dielectric resonators’,
IEEE Symposium Digest, 1997, 97, 1639–1642.
31. H. Takamura, H. Matsumoto and K. Wakino: ‘Low temperature
properties of microwave dielectrics’, Proc. 7 th Meeting on
Ferroelectric Materials and their Applications. Jpn. J. Appl.
Phys., 1989, (Supl. S-28-2), 21–23.
32. J. Krupka, W-T. Huang and M-J. Tung: ‘Complex permittivity
measurements of low loss microwave ceramics employing higher
order quasi TEonp modes excited in a cylindrical dielectric
sample’, Measurement Science & Technology, 2005, 16, 1014–1020.
33. M. Valant, D. Suvorov and S. Macek: ‘Measurement error
analysis in the determination of microwave dielectric properties
using cavity reflection method’, Ferroelectr., 1996, 176, 167–177.
34. A. P. S. Khanna and G. Garault: ‘Determination og loaded,
unloaded and external quality factors of a dielectric resonator
coupled to a microstrupline’, IEEE Trans. Microwave Theory
and Tech., 1983, 31, 261–264.
35. J. R. Wait: ‘Electromagnetic Whispering Gallery Modes in a
dielectric rod’, Radio Sci., 1967, 2, 1005–1017.
36. D. Cros and P. Guillon: ‘Whispering Gallery dielectric resonator
modes for w-band devices’, IEEE Microwave Theory and Tech.,
1990, 38, 1667–1674.
37. J. Krupka, D. Cros, M. Aubourg and P. Guillon: ‘Study of Whispering
Gallery Modes in anisotropi single crystal dielectric resonators’, IEEE
Trans. Microwave Theory and Tech., 1994, 42, 56–61.
38. E. N. Ivanov, D. G. Blair and V. I. Kalinichev: ‘Approximate
approach to the design of shielded dielectric disk resonators
with whispering Gallery Modes’, IEEE Trans. Microwave
Theory and Tech., 1993, 41, 632–637.
39. J. Krupka, K. Derzakowski, A. Abramowicz, M. E. Tobar and
R. G. Geyer: ‘Whispering gallery modes for complex
permittivity measurements of ultra low loss dielectric materials’,
IEEE Microw. Theory Tech., 1999, 47, 752–759.
40. J. Krupka, A. P. Gregonry, O. C. Kochard, R. N. Clarke,
B. Riddle and J. Baker-Jarvis: ‘Uncertainity of complex
permittivity measurement by split post dielectric resonator
techniques’, J. Eur. Ceram. Soc., 2001, 21, 2673–2676.
41. J. Krupka, S. Gabelich, K. Derzakowski and B. M. Pierce:
‘Comparison of split post dielectric resonator and ferrite disc
resonator techniques for microwave permittivity measurements
of polycrystalline ytterium iron garnet’, Measur. Sci. Tech.,
1999, 10, 1004–1008.
International Materials Reviews
2015
VOL
60
NO
7
409
Sebastian et al.
Low-loss dielectric ceramic materials
Downloaded by [Penn State University] at 11:01 26 November 2015
42. G. Kent: ‘An evanescent mode tester for ceramic dielectric
substrates’, IEEE Microwave Theory and Tech., 1988, 36
1451–1454.
43. J. Krupka: ‘Precise measurement of complex permittivity of
dielectric materials at microwave frequencies’, Mater. Chem.
Phys., 2003, 79, 195–198.
44. N. L. Conger and S. E. Tung: ‘Measurement of dielectric constant
and loss factor of powder materials in the microwave region’, Rev.
Sci. Instr., 1967, 38, 384–386.
45. S. O. Nelson and A. W. Kraszewski: ‘Sensing pulverized material
mixture proportions by resonant cavity measurements’, IEEE
Trans. Instr. Meas., 1998, 47, 1201–1204.
46. S. O. Nelson and P. G. Bartley: ‘Open ended coaxial line
permittivity measurements on pulverised sample’, IEEE Trans.
Meas., 1998, 47, 133–137.
47. H. Ebara, T. Inoue and O. Hashimoto: ‘Measurement method of
complex permittivity and permeability of a powdered material
using waveguide in microwave band’, Sci. Tech. Adv. Mater.,
2006, 7, 77–83.
48. M. Tuhkala, J. Juuti and H. Jantunen: ‘Method to characterize
dielectric properties of powdery substances’, J. Appl. Phys.,
2013, 114, 014108.
49. D. L. Gershon, J. P. Carmel, T. M. Antonsen and R. M.
Hutcheon: ‘Open ended coaxial probable for high temperature
and broad band dielectric measurements’, IEEE Trans. Micro.
Theo. Tech., 1999, 47, 1640–1648.
50. K. Murata, A. Hanawa and R. Nozaki: ‘Broad band complex
permittivity measurement technique of material with thin
configuration at microwave frequencies’, J. Appl. Phys., 2005,
98, 084107.
51. H. Looyenga: ‘Dielectric constants of mixtures’, Physica, 1965, 31,
401–406.
52. M. Tuhkala, J. Juuuti and H. Jantunen: ‘An indirectly coupled
open ended resonator applied to characterize dielectric
properties of MgTiO3-CaTiO3 powders’, J. Appl. Phys., 2014,
115, 184101.
53. M. Tuhkala, J. Juuti and H. Jantunen: ‘Use of an open ended
coaxial cavity method to characterize powders substances
exposed to humidity’, Appl. Phys. Lett., 2013, 103, 142907.
54. M. Tuhkala, J. Juuti and H. Jantunen: ‘Determination of complex
permittivity of surfactant treated powders using an open ended
coaxial cavity resonator’, Powder Technology, 2014, 256, 140–145.
55. J. Molla, M. Gonzalez, R. Villa and A. Ibara: ‘Effect of humidity
on microwave dielectric losses of porous alumina’, J. Appl. Phys.,
1999, 85, 1727–1730.
58. E. Schloman: ‘Dielectric losses in ionic crystals with disordered
charge distributions’, Phys. Rev., 1964, 135, A413–A419.
57. V. S. Vinogradov: ‘Fiz. Tverd. Tela. 2(1960)2622. (English
Translation)’, Sovt. Phys. Sol. St., 1961, 2, 2338.
58. L. Li and X. M. Chen: ‘Frequency dependent QF value of
microwave dielectric ceramics’, J. Amer. Ceram. Soc., 2014.
59. G. L. Gurevich and A. K. Tagantsev: ‘Intrinsic dielectric los in
crystals’, Adv. Physics, 1991, 40, 719–767.
60. K. S. Hong, I. T. Kim and S. J. Yoon: ‘Effect of nonstoichiometry and chemical inhomogeneity on the order-disorder
phase transformation in the complex perovskite compound
Ba(Ni1/3Nb2/3)O3 and Ba(Zn1/3Nb2/3)O3’, J. Mater. Sci., 1995,
30, 514–521.
61. L. A. Khalam and M. T. Sebastian: ‘Effect of cation substitution
and non-stoichiometry on the microwave dielectric properties of
Sr(B1/2B’’1/2)O3 [B0¼lanthanides] ’, J. Am. Ceram. Soc., 2007,
89, 3689–3695.
62. S. G. Santiago, R. T. Wang and G. J. Dick: ‘Improved
performance of a temperature compensated LN2 cooled
sapphire oscillator’ ‘IEEE 1995, San Fransisco, Ca, USA. Proc.
IEEE Int. Freq. Control Symp.1995’, 397–400.
63. J. G. Hartnett, M. E. Tobar, E. N. Ivanov and D. Cross: ‘High
frequency compensated sapphire/rutile resonator’, Electron.
Lett., 2000, 36, 726–727.
64. A. N. Luitenen, A. G. Mann and D. G. Blair: ‘Paramagnetic
susceptibility and permittivity measurements at microwave
frequencies in cryogenic sapphire resonators’, J. Phys. D. Appl.
Phys., 1996, 29, 2082–2090.
65. J. Krupka, D. Cross, A. N. Luitenen and M. E. Tobar: ‘Design of
very high Q sapphire resonators’, Electron. Lett., 1996, 32,
670–671.
66. K. P. Surendran, N. Santha, P. Mohanan and M. T. Sebastian:
‘Temperature stable low permittivity ceramic dielectrics in
(1-x)ZnAl2O4-xTiO2 system for microwave substrate applications’,
Eur. Phys. J.B., 2004, 41, 301–306.
410
International Materials Reviews
2015
VOL
60
NO
7
67. A. N. Luiten, A G Mann, N. J. Mc Donald and D. G. Blair:
‘Latest results of the UWA cryogenic sapphire oscillator’ ‘IEEE
1995, San Fransisco, Ca, USA. Proc. Freq. Control
Symp.’,1995, 433–437.
68. J. G. Hartnett, M. E. Tobar, A. G. Mann, J. Krupka and E. N.
Ivanov: ‘Temperature dependence of Ti3þ doped sapphire
whispering gallery mode resonator’, Electron. Lett., 1998, 34,
195–196.
69. J. G. Hartnett, M. E. Tobar, A. G. Mann, E. N. Ivanov, J. Krupka
and R. Geyer: ‘Frequency-temperature compensation in Ti4±
doped sapphire whispering gallery mode resonators’, IEEE Trans.
Ultrason. Ferroelectr. Freq. Control, 1999, 46, 993–999.
70. J. Breeze, S. J. Penn, M. Poole, N. Mc and N. Alford: ‘Layered
Al2O3–TiO2 composite dielectric resonators’, Electron. Lett.,
2000, 36, 883–884.
71. D. Thomas and M. T. Sebastian: ‘Temperature compensated
LiMgPO4: A new glass free low temperature cofired ceramic’,
J. Amer. Ceram. Soc., 2010, 93, 3828–3831.
72. Y. Guo, H. Ohsato and K. Kakimoto: ‘Characterization and
dielectric behaviour of willemite and TiO2 doped willemite at
millimeterwave frequency’, J. Eur. Ceram. Soc., 2006, 26,
1827–1830.
73. K. P. Surendran, P. V. Bijumon, P. Mohanan and M. T.
Sebastian: ‘(1-x) MgAl2O4-xTiO2 dielectrics for microwave and
millimeter wave applications’, Appl. Phys., 2005, A81, 823–826.
74. S-F. Wang, C-Y. Huang and Y-L. Liu: ‘Effects of CaTiO3 and
SrTiO3 additions on the microstructure and microwave dielectric
properties of ultra-low fire TeO2 ceramics’, J. Amer. Ceram.
Soc., 2010, 93, 3272–3277.
75. C-L. Huang and J-Y. Chen: ‘Low loss microwave dielectrics using
SrTiO3 modified (Mg0.95Co0.05)2TiO4-ceramics’, J. Alloys &
Compounds, 2009, 485, 706–710.
76. J. Guo, D. Zhou, L. Wang, H. Wang, T. Shao, Z. M. Qi and Xi
Yao: ‘Infra red spectra, raman spectra, microwave dielectric
properties and simulation for effective permittivity of
temperature stable ceramics AMO4-TiO2 (A¼Ca, Sr)’, Dalton
Transactions, 2013, 42, 1483–1491.
77. C-L. Huang, J-Y. Chen and C-C. Liang: ‘Dielectric properties and
mixture behaviour of Mg4Nb2O9-SrTiO3 ceramic system at
microwave frequeny’, J. Alloys & Compounds, 2009, 478, 554–558.
78. J-W. Choi, J-Y. Ha, S-J. Yoon, H-J. Kim and K. H. Yoon:
‘Microwave dielectric characteristics of 0.75(Al1/2Ta1/2)O20.25(Ti1-xSnx)O2 ceramics’, J. Eur. Ceram. Soc., 2003, 23,
2507–2510.
79. M. Hu, Y. Fu, C. Luo, H. Gu, W. Lei and Q. Shen:
‘Microstructure and microwave dielectric properties of
xCa(Al0.5Nb0.5)O3 þ (1-x)SrTiO3 solid solution’, J. Amer.
Ceram. Soc., 2010, 93, 3354–3359.
80. N. Ichinose and K. Mutoh: ‘Microwave dielectric properties in the
(1-x) (Na1/2La1/2)TiO3-x(Li1/2Sm1/2)TiO3 ceramic system’, J. Eur.
Ceram. Soc., 2003, 23, 2455–2459.
81. J-S. Kim, C. I. Cheon, H-J. Kang, C-H. Lee, K-Y. Kim, S. Nahm
and J-D. Byun: ‘Crystal structure and microwave dielectric
properties
of
CaTiO3-(Li1/2Nd1/2)TiO3-(Ln1/3Nd1/3)
TiO3(Ln¼La, Dy) ceramics’, Jpn. J. Appl. Phys., 1999, 38,
5633–5637.
82. Y. Zhang, B. Fu, M. Hong, M. Xiang, L. Liu and T. Lang:
‘Microstructure and microwave dielectric properties of
MgNb2O6- ZnTa2O6 composite ceramics prepared by layered
stacking method’, J. Mater. Sc. Mater. Electr., 2014, 25,
5475–5480.
83. I. N. Jawahan, P. Mohanan and M. T. Sebastian: ‘A novel
method of achieving temperature compensation by stacking
positive and negative (f resonators’, Materials Science and
Engineering, 2003, B97, 258–264.
84. L. Li and X. M. Chen: ‘Adhesive bonded Ca(Mg1/3Nb2/3)O3/
Ba(Zn1/3Nb2/3)O3 layered dielectric resonators with tunable
temperature coefficient resonant frequency’, J. Amer. Ceram.
Soc., 2006, 89, 544–549.
85. L. Li, X. M. Chen and X. Cheng: ‘Characterization of MgTiO3CaTiO3 layered microwave dielectric resonators with TE01d
mode’, J. Amer. Ceram. Soc., 2006, 89, 557–561.
86. M. W. Lufasso, E. Hopkins, S. M. Bell and A. Llobet:
‘Crystal chemistry and microwave dielectric properties of
Ba3MNb2-xSbxO9 (M¼Mg, Ni, Zn)’, Chem. Mater., 2005, 17,
4250–4255.
87. K. P. Surendran, M. R. Varma and M. T. Sebastian: ‘Microwave
dielectric properties of RE1-xRE’xTiNbO6 [RE¼Pr, Nd, Sm;
RE’¼Gd, Dy, Y] ceramics’, J. Am. Ceram. Soc., 2003, 86,
1695–1699.
Downloaded by [Penn State University] at 11:01 26 November 2015
Sebastian et al.
88. J. Kato, H. Kagata and K. Nishimoto: ‘Dielectric properties of
(Pb,Ca)(Me,Nb)O3 at microwave frequencies’, Jpn. J Appl.
Phys., 1992, 31, 3144–3147.
89. K. Wakino, M. Murata and H. Tamura: ‘Far infrared reflection
spectra of Ba(Zn,Ta)O3-BaZrO3 dielectric resonator material’,
J. Amer. Ceram. Soc., 1986, 69, 34–37.
90. P. P. Ma, L. Yi, X. Q. Liu, L. Li and X. M. Chen: ‘Effects of post
densification annealing upon microstructures and microwave
dielectric characteristics in Ba((Co.06-x/2Zn0.4-x/2 Mgx)1/3Nb2/3)O3
ceramics’, J Amer. Cer. Soc., 2013, 96, 3417–3424.
91. B. Jancar, D. Suvorov, M. Valant and G. Drazic:
‘Characterization of CaTiO3-NdAlO3 dielectric ceramics’,
J. Eur. Ceram. Soc., 2003, 3, 1391–1400.
92. C-S. Chen, C-C. Chou, W-J. Shih, K-S. Liu, C-S. Chen and
I-N. Lin: ‘Microwave dielectric properties of glass ceramic
composites for low temperature cofireable ceramics’, Mater.
Chem. Phys., 2003, 79, 129–134.
93. D. A. Durilin, O. V. Ovchar and A. G. Belous: ‘Effect of
nonstoichiometry on the structure and microwave dielectric
properties of Ba1-x(Zn1/2W1/2)O3-x and Ba(Zn1/2-yW1/2)O3-y/2’,
Inorganic Mater., 2011, 47, 313–316.
94. K. P. Surendran, M. T. Sebastian, P. Mohanan, R. L. Moreira
and A. Dias: ‘Effect of stoichiometry on the microwave
dielectric properties of Ba(Mg1/3Ta2/3)O3 dielectric ceramics’,
Chem. Mater., 2005, 17, 142–151.
95. A. G. Belous, O. V. Ovchar, A. V. Krameeranko, B. Jancar,
J. Bezjak and D. Suvorov: ‘Effect of nonstoichiometry on the
structure and microwave dielectric properties of Ba(Co1/3Nb2/
3)O3’, Inorganic Mater., 2010, 46, 529–533.
96. H. Wu and P. K. Davies: ‘Influence of non-stoichiometry on the
structure and properties of Ba(Zn1/3Nb2/3)O3 microwave
dielectrics. I. Substitution of Ba3W2O9’, J. Am. Ceram. Soc.,
2006, 89, 2239–2249.
97. M. Terada, K. Kuwamura, I. Kagomiya, K. Kakimoto and
H. Ohsato: ‘Effect of Ni substitution on the microwave dielectric
properties of cordierite’, J. Eur. Ceram. Soc., 2007, 27, 3045–3048.
98. H-J. Lee, I-T. Kim and K. S. Hong: ‘Dielectric properties of
AB2O6 comopunds at microwave frequencies (A¼Ca, Mg, Mn,
Co, Ni, Zn and B¼Nb,Ta)’, Jpn. J. Appl. Phys., 1997, 36,
L1318–L1320.
99. G. Sumesh and M. T. Sebastian: ‘Microwave dielectric properties
of Ca[Li1/3A2/3)1-xMx]O3-d [A¼Nb,Ta and M¼Ti,Zr,Sn] complex
perovskite’, in ‘Perovskite:Structure properties and Uses’, (ed.
M. Borowski), 283–317; 2010, Huntington, NY, USA, Nova
science Publishers Inc.
100. L. A. Khalam and M. T. Sebastian: ‘Low loss dielectrics in the
Ca(B’1/2Nb1/2)O3 [B’¼lanthanides, Y] system’, J. Am. Ceram.
Soc., 2007, 90, 1467–1474.
101. L. Fang, Q. Liu, Y. Tang and H. Zhang: ‘Adjustable dielectric
properties of Li2CuxZn1-xTi3O8 (x¼0 to 1) ceramics with low
sintering temperature’, Ceram. Intl., 2013, 38, 6431–6434.
102. X. Kuang, M. M. B. Allix, J. B. Claridge, H. J. Niu, M. J.
Rossiensky, R. M. Ibberson and D. Iddles: ‘Crystal structure,
microwave dielectric properties and AC conductivity of B-cation
deficient hexagonal perovskites La5MxTi4-xO15 (x¼0.5, 1,:
M¼Zn, Mg, Ga, Al)’, J. Mater. Chem, 2006, 16, 1038–1045.
103. K. P. Surendran, M. T. Sebastian, P. Mohanan and M. V. Jacob:
‘The effects of dopants on the microwave dielectric properties of
Ba(Mg1/3Ta2/3)O3 ceramics’, J. Appl. Phys., 2005, 98, 094114.
104. M. R. Varma and M. T. Sebastian: ‘The effects of dopant additives
on the microwave dielectric properties of Ba(zn1/3Nb2/3)O3
ceramics’, J. Eur. Ceram. Soc., 2007, 27, 2827–2833.
105. K. P. Surendran, P. Mohanan and M. T. Sebastian: ‘The effects
of glass additives on the microwave dielectric properties of
Ba(Mg1/3Ta2/3)O3 ceramics’, Solid St. Chem., 2004, 177,
4031–4046.
106. A. Ioachin, M. G. Banau, M. I. Toacsan, L. Nedelcu, D. Ghetu,
H. V. Alexander, G. Toica, G. Annino, M. Cassettari and M.
Martnelli: ‘Nickel doped (Zr0.8Sn0.2)TiO4 for microwave and
millimeter wave applications’, Mater. Sci. Eng. B, 2014, 118,
205–209.
107. C. -L. Huang, C. -S. Hsu and R. -J. Lin: ‘Improved high-Q
microwave dielectric resonator using ZnO andWO3-doped Zr0.
8Sn0.2TiO4 ceramics’, Mater. Res. Bull., 2001, 36, 1985–1993.
108. K. H. Yoon, Y. S. Kim and E. S. Kim: ‘Microwave dielectric
properties of (Zr0.8Sn0.2)TiO4 ceramics with pentavalent
additives’, J. Mater. Res., 1995, 10, 2085–2090.
109. W. -Y. Lin, R. F. Speyer, W. S. Hackenberger and T. R. Shrout:
‘Microwave properties of Ba2Ti9O20 doped with zirconium and tin
oxide’, J. Am. Ceram. Soc., 1999, 82, 1207–1211.
Low-loss dielectric ceramic materials
110. S. F. Wang, Y. F. Hsu, T. -H. Weng, C. -C. Chiang, J. P. Chu and
C. -Y. Huang: ‘Effects of additives on the microstructure and
dielectric properties of Ba2Ti9O20 microwave ceramics’,
J. Mater. Res., 2003, 18, 1179–1187.
111. L. A. Khalam and M. T. Sebastian: ‘Microwave dielectric
properties of Sr(B1/2Nb1/2)O3 [B¼La, Pr, Nd, Sm, Eu, Gd, Tb,
Dy, Ho, Y, Er, Yb and In] ceramics’, Int. J. Appl. Ceram.
Tech., 2006, 3, 364–374.
112. J.-I. Yang, S. Nahm, C.-H. Choi, H.-J. Lee and H.-M.
Park: ‘Microstructure and microwave dielectric properties of
Ba(Zn1/3Ta2/3)O3 with ZrO2 addition’, J. Am. Ceram. Soc.,
85, 165–168.
113. S. Kamba, M. Savinov, F. Luafek, O. Tkac, C. Kadlec, E. J. John,
G. Subodh, M. T. Sebastian, M. Klementova, V. Bovtun, J.
Pokorny, V. Goian and J. Petzelt: ‘Ferroelectric and incipent
ferroelectric properties of a novel Sr9-xPbxCe2Ti2O36 (x¼0-9)
ceramic system’, Chem. Mater., 2009, 21, 811–819.
114. N. W. Grimes and R. W. Grimes: ‘Dielectric polarizability of ions
and the corresponding effective number of electrons’, J.Phys.:
Condens. Matter, 1998, 10, 3029–3034.
115. N. McN Alford, J. Breeze, X. Wang, S. J. Penn, S. Dalla, S. J.
Webb, N. Ljepojevic and X. Aupi: ‘Dielectric loss of oxide
single crystals and polycrystalline analogues from 10 to 320 K’,
J. Eur. Ceram. Soc., 2001, 21, 2605–2611.
116. N. Santha, M. T. Sebastian, P. Mohanan, N. Mc, N. Alford, K.
Sarma, R. C. Pullar, S. Kamba, A. Pashkin, P. Samukhina and
J. Petzelt: ‘Effect of doping on the dielectric properties of CeO2
in the microwave and sub-millimeter frequency range’, J. Amer.
Ceram. Soc., 2004, 87, 1233–1237.
117. D. Thomas, P. Abhilash and M. T. Sebastian: ‘Casting and
characterization of LiMgPO4 glass free LTCC tape for
microwave applications’, J. Eur. Ceram. Soc., 2013, 33, 87–93.
118. P. Abhilash, M. T. Sebastian and K. P. Surendran: ‘Glass free,
non-aqueous LTCC tapes of Bi4(SiO4)3’, J. Eur. Cer.
Soc.(submitted).
119. D. Zhou, C. A. Rindall, H. Wang, L-X. Pang and Xi Yao:
‘Microwave dielectric ceramics in Li2O-Bi2O3-MoO3 system with
ultra low sintering temperatures’, J. Amer. Cer. Soc., 2010, 93,
1096–1100.
120. S. F. Wang, Y-F. Hsu, Y-R. Wang and C-C. Sung: ‘Ultra low fire
Zn2Te3O8-TiTe3O8 ceramic Composites’, J. Amer. Ceram. Soc.,
2010, 94, 812–816.
121. D. Zhou, C. A. Rindall, H. Wang, L-X. Pang and X. Yao:
‘Ultra low firing high-k scheelite structures based on
[(Li0.5Bi0.5)xBi1-x][MoxV1-x]O4 microwave ceramics’, J. Amer.
Cer. Soc., 2010, 93, 2147–2150.
122. D. Zhou, L-X. Pang, Z-M. Qi, B-B. jin and Xi Yao: ‘Novel
ultralow temperature cofired microwave dielectric ceramic at 400
degree and its chemical compatibility with base metal’, Scientific
Reports, 2014, 4, 05980.
123. M. W. Mcallister and S. A. Long: ‘Rectangular
dielectric resonator antenna’, IEEE Electronic Letters, 1983, 19,
218–219.
124. A. Petoso and A. Ittipiboon: ‘Dielectric resonator antennas. a
historical review and the current state of the art’, IEEE antennas
and Propagation Magazine, 2010, 52, 91–116.
125. A. Petosa: ‘Dielectric Resonator Antenna Handbook’, 2007,
Norwood, Ma, Artech House.
126. D. Soren, R. Ghatak, R. K. Mishra and D. Poddar: ‘Dielectric
resonator antennas: designs and advances’, Progr. Electromag.
Res. B., 2014, 60, 195–213.
127. M. N. Jazi and T. A. Denidni: ‘Design and implemenatation of
an
ultrawideband
hybrid
skirt
monople
dielectric
resonator antenna’, IEEE and Wireless Propagation Lett, 2008,
7, 493–496.
128. S. P. Kingley and S. G. OKeefe: ‘beam steering and monopulse
processing of probe fed dielectric resonator antenna’, Proc.
Rada Sonar Navigation, 1999, 3, 121–125.
129. J. Svedin, L. G. huss, d. karlen, P. enoksson and C. Rusu:
‘A micromachined 94 GHz dielectric resonator antenna for focal
plane array applications’ ‘IEEE intl. Microwave symposium,
Honolulu, IEEE MTT-S’, 1375–1378; 2007.
130. J. liflander: ‘Ceramic chip antennas vs. PCB trace antennas: a
comparison’, ‘MPDIGEST. Feature article’; 2010, White paperwww.pulseelectronics.com/download/3721/g041/pdf.
131. J. Varghese, K. P. Surendran and M. T. Sebastian: ‘Room
temperature curable silica ink’, Royal Soc. Chem. Adv., 2014, 4,
47701–4707.
132. A. K. Skirvervik: ‘Implantable antennas:The challenge of
efficiency’, ‘IEEE Proc.7 th European conference on Antennas
International Materials Reviews
2015
VOL
60
NO
7
411
Sebastian et al.
Low-loss dielectric ceramic materials
Downloaded by [Penn State University] at 11:01 26 November 2015
and Propagation (EUCAP 2013), Gothenberg, Published by
IEEE’, 3617–3631.
133. D. Thomas, P. Abhilash and M. T. Sebastian: ‘Effect of isovalent
substitutions on the microwave dielectric properties of
Ca4La6(SiO4)4(PO4)2O2 apatite’, J Alloys & Compounds, 2013,
546, 72–76.
134. L. K. Namitha and M. T. Sebastian: ‘Microwave dielectric
properties of flexible silicone rubber- Ba(Zn1/3Ta2/3)O3
composite substrates’, Mater. Res. Bull., 2013, 48, 4911–4916.
135. J. Chameswary and M. T. Sebastian: ‘Development of butyl
rubber-rutile composites for flexible microwave substrate
applications’, Ceram. Intl., 2014, 40, 7439–7448.
412
International Materials Reviews
2015
VOL
60
NO
7
136. J. Chameswary, L. k. Namitha, m. Brahmakumar and M. T.
Sebastian: ‘Material characterization and microwave Substrat
applications of alumina-filled butyl rubber composites’, Int.
J. Appl. Ceram. Technol., 2014, 11, 916–926.
137. A. Grill, S. M. Gates, T. E. Ryan, S. V. Nguyen and
D. Priyadarshini: ‘Progress in the development and
understanding of advanced low k and ultralow k dielectrics for
very large scale interconnects-state of the art’, Appl. Phys.
Reviews, 2014, 1, 011306.
138. I. Reaney and D. Iddles: ‘Microwave ceramics for resonators and
filters in mobile phone networks’, J. Amer. Ceram. Soc., 2006, 89,
2063–2072.