ACCURATE DIAGNOSTICS OF ELECTRICAL CHARACTERISTICS OF THIN-FILM
MATERIALS IN MM-WAVE FREQUENCIES
B.Kapilevich, Siberia State University of Telecommunications & Informatics
86 Kirova str., Novosibirsk, Russia – 630102, boris@sibnet.ru
D.Muchnik, Fuel Technologies Ltd, Ariel, Israel – P.O.B. 3, 44837, mdamir@urbis.net.il
Abstract
Thin-film materials are widely used in modern technology. Their new potential applications,
for example, in electromagnetic shielding, microwave absorbers, gas sensors etc.[1] have
been reported recently. However, designing these materials with required structure and
properties as well as creating composite material configurations needs development of
measuring set-ups for diagnostics their complex dielectric permittivity. For thin-film sheets
(order of 1mm or less) high frequency electromagnetic waves can be used for this purpose.
Therefore, moving toward mm wave band (frequency 100GHz or higher) seems to be
perspective if precision determination of a conductivity and dielectric constant is required. In
order to measure thin-film materials the container consisting of the glass slabs is used. The
reflection and transmission coefficients are investigated to determine its best configuration
providing maximum sensitivity in changing real and imaginary parts of dielectric constant to
increase a resolution of diagnostics process. Examples of measurements reflectivity of thin
layer oil water-content emulsions are discussed to validate the technique considered.
Introduction
Great demands upon the advanced materials for stronger, lighter, corrosion-resistant,
economical, and easy-processing fabrication have stimulated different methods of their
diagnostics. The information concerning electrical properties of many materials is very
important in designing thin film materials with required structure and properties. They can be
in solid or liquid phases such as lightweight polymers both nonconductive and conductive [1]
or water-content emulsions of different nature. Microwave methods for diagnostics of
electrical characteristics of thin film materials are useful to observe their fine structure.
Basically, the microwave free-space technique is widely used permitting to realize noncontacting measurements. In such measurements reflection and transmission coefficients are
determined to reconstruct complex dielectric constant of the film under testing. A typical
configuration of measuring unit is shown in Fig.1 [2]. The material filling a container is
placed between the two slabs with known dielectric permittivity and illuminated by normal
incident plane wave. Since a thickness of polymer or emulsion layer is small (an order mm or
less) a short wave length radiation is preferable to obtain higher resolution with respect to
real and imaginary parts of dielectric constant. The millimeter wave band is considered in
this paper for the purpose discussed.
Both container and film parameters are responsible for measured reflection and transmission
coefficients. To reach a maximum resolution a configuration of container must be optimized
taking into account its filling by thin film material. The goal is to find a container slab
thickness providing maximum response on a change of material’s parameters. The
electromagnetic model of measured unit is used to carry out the optimization. Experiments
verifying the approach suggested as well as recommendations for accurate diagnostics of
electrical characteristics of thin film materials are discussed.
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Model description
Following [2,3] the transmission t and reflection r coefficients can be calculated from
expressions written below:
Et
(1  r12 )(1  r22 ) exp(  j 2kctc ) exp(  j 2k s t s )
t

Ei [1  r1r2 exp(  j 2kctc )]2  [r1 exp(  j 2kctc )  r2 ]2 exp(  j 2k s t s )
r
(1)
E r [1  r1 r2 exp(  j 2k c t c )][ r1  r2 exp(  j 2k c t c )]  [r2  r1 exp(  j 2k c t c )][ r1 r2  exp(  j 2k c t c )] exp(  j 2k s t s )

(2)
Ei
[1  r1 r2 exp(  j 2k c t c )] 2  [r1 exp(  j 2k c t c )  r2 ] 2 exp(  j 2k s t s )
where
kc = k0rc
ks = k0rs
r1 = (0 - rc) / (0 + rc)
r1 = (rc - rs) / (rc + rs)
rc = rc’ - jrc’’, rs = rs’ - jrs’’
(3)
(4)
(6)
(7)
(8)
0 , rc , and rs are the permittivity of the air, container and film materials and k0 is a
propagation constant in air. All dimensions correspond to Fig.1.
Fig.1 A typical configuration of measuring unit [2].
The resolution of measuring dielectric constant is determined by a sensitivity of a reflection
and transmission coefficients to changing rs’ and rs’’ that are linked functionally with a
physical and chemical structure of a material designed. So that, it is necessary to estimate the
differentials:
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t 
r 
t
'
 rs
d rs'  't' d rs''
(9)
r
'
 rs
d rs'  'r' d rs''
(10)
rs
rs
Sensitivity Analysis
Both real and imaginary parts of dielectric constant are functions of physical and chemical
structure of the material under design. Sometimes a change of composition leads to small
changing of permittivity. Therefore, the configuration of a container must be chosen to
provide maximally available response of transmission and reflection coefficients in that
sense. To reach a goal we need to investigate derivatives dt/rs’, dt/rs”, dr/rs’ and dr/rs” in a
frequency domain for fixed width of the container layer tc .Due to complexity of formulas (1)
and (2) an analytical determination of the above partial derivatives is not reasonable.
Therefore, a numerical analysis can be recommended for this purpose.
Since all derivatives are functions of real and imaginary parts of dielectric constant the two
typical situation are investigate below to simplify an analysis:
 low permittivity lossy materials (rs’= 2, rs”= 0.2, ts = 0.1mm)
corresponding to polymer films;
 high permittivity lossy materials (rs’= 20, rs”= 2, ts = 0.1mm)
corresponding to water content emulsions.
The results of derivatives calculations are shown in Fig.2 and 3 for low permittivity lossy
materials and in Fig. 4 - 5 for high permittivity lossy materials assuming that the material of
a container is a glass (rc’ 5, rc” 0) and its width is varied within 0.3mm – 0.4mm.
Comparing the behavior of transmission coefficient sensitivities we can point out that there
are maximums in dt/rs”. Their frequency positions are dependent on the width of a container
slabs. The behavior of dt/rs’ for high permittivity lossy materials demonstrates existing
maximums while they don’t take a place for low permittivity lossy materials.
Essentially different situation is observed in behavior of a sensitivity associated with
reflection coefficients. There are regions of a transition from positive to negative sensitivity
in a behavior of dt/rs’ . The locations of them along a frequency axis are dependent of the
width of the container slabs too. The function dr/rs” demonstrates sharp spikes near these
regions. Such a behavior both dr/rs’ and dr/rs” can be explained by self resonance of the
container with material under testing. Hence, if a maximum of the reflection coefficient
sensitivity is required for diagnostics of imaginary part of a dielectric constant the peaks of
spikes might be recommended to satisfy that demand. However, measurements must be done
very carefully in this case since a small declining from the frequency corresponding to the
peak may cause degrading sensitivity drastically.
Summarizing the sensitivity analysis we can state that there is no universal container’s
configuration. Depending on what is measured (reflection or transmission coefficients) the
specified width of the container’s slabs must be chosen to provide maximum sensitivity in
diagnostics of real and imaginary parts of complex permittivity of the material under test.
3 - 66
Experiments
The major purpose of the experiments is to estimate a sensitivity of reflection coefficient to
change of film’s properties. Oil emulsions with different water content filling a container are
illuminated by horn antenna connected with the output waveguide of HP-8757 scalar
network analyzer operating in 75-110 GHz band to measure a reflection coefficient. Pure
mineral oil (without a water) is used as a reference material. Then, the differences in a
reflection coefficient (measured as return loss in dB) between pure mineral oil and oil
emulsions with water are evaluated and plotted as a function of frequency. The results
corresponding to the three samples are depicted in Fig.6. All measured oil films have the
same chemical nature and water content. The only difference is the average water dropws
diameter, namely, 6.4 m – emulsions, 13.1 m –sample P44 and 21.4 m – sample P34.
The width of all tested films is equal to 0.02 mm. The width of the glass container is
0.35mm. A clear discrepancy in the frequency behavior of reflection coefficients of all
investigated films is observed. It proves that use of the technique suggested provides a good
resolution of a fine structure of tested films with different diameter of chaotic water drops
distributions. The same technique can be used in diagnostics of polymer films filled by small
metallic particles, fiber reinforced composite materials [4], etc.
Conclusion
The electromagnetic model of a three-layers container has been developed to estimate a
sensitivity of reflection and transmission coefficients to change of real and imaginary parts of
dielectric constant of tested thin film materials. The theoretical analysis has showed that
there is no universal configuration of a container providing maximum sensitivity for both
parameters simultaneously. It was found out that maximum reflection sensitivity of
imaginary part of a complex permittivity can be realized near self-resonance of a container. It
is useful for diagnostics of thin-film lossy materials. Experimental data obtained for watercontent oil emulsions have clearly indicated that the suggested technique can be successfully
applied in investigated a fine structure of thin-film materials in millimeter wave range.
References
1.Krishna Naishadham and Prasad K. Kadaba, Measurement of the Microwave Conductivity
of a Polymeric Material with Potential Applications in Absorbers and Shielding, IEEE
TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 39, NO. 7,
JULY 1991, pp1158-1164.
2. Zhihong Ma and Seichi Okamura, Permittivity Determination Using Amplitudes of Transmission and Reflection Coefficients, IEEE TRANSACTIONS ON MICROWAVE THEORY
AND TECHNIQUES, VOL. 47, NO. 5, MAY 1999, pp.546-550.
3. W.J.L. Jansen, Energy Efficient Transfer of Microwave Power to Thin Lossy Dielectrics,
J. M ICROWAVE POWER ELECTROMAGNETIC ENERGY, VOL.28, NO.4, 1993, pp.4554.
4. M.Jackson, and C.Stern. Modeling the Complex Permittivity of Thermoplastic Composite
Materials, J. MICROWAVE POWER ELECTROMAGNETIC ENERGY, VOL.27, NO.2,
1992, pp.103-111.
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Transmission Sensitivity
0.06
dt / drs’
D( f  0.3)
Low permittivity lossy sample
0.04
D( f  0.32)
D( f  0.34) 0.02
D( f  0.36)
D( f  0.38)
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4mm
0
D( f  0.4)
0.02
0.04
70
80
90
100
110
f
Frequency, GHz
Transmission Sensitivity
0.12
Low permittivity lossy sample
dt / drs”
DD( f  0.3)
0.1
DD( f  0.32)
DD( f  0.34) 0.08
DD( f  0.36)
DD( f  0.38) 0.06
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4mm
DD( f  0.4)
0.04
0.02
70
80
90
100
110
f
Freguency, GHz
Fig.2 Sensitivity of a transmission coefficient as a function of frequency for different thickness
of container layer tc ( rs = 2, rs = 0.2 )
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Reflection Sensitivity
0.15
dr / drs’
Low permittivity lossy sample
0.1
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4
D1( f  0.3)
D1( f  0.32) 0.05
D1( f  0.34)
D1( f  0.36)
0
D1( f  0.38)
D1( f  0.4) 0.05
0.1
0.15
70
80
90
100
110
f
Frequency, GHz
rr( f  Tc)  r( Tc  Es1  Es2  f )
Reflection Sensitivity
0.12
dr / drs”
Low permittivity lossy sample
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4
0.1
D2( f  0.3)
D2( f  0.32) 0.08
D2( f  0.34)
D2( f  0.36) 0.06
D2( f  0.38)
D2( f  0.4) 0.04
0.02
0
70
80
90
100
110
f
Frequency, GHz
Fig.3 Sensitivity of a reflection coefficient as a function of frequency for different thickness of
container layer tc ( rs = 2, rs = 0.2 )
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Transmission Sensitivity
0.006
dt / drs’
High permittivity lossy sample
0.004
D( f  0.3) 0.002
D( f  0.32)
0
D( f  0.34)
D( f  0.36) 0.002
D( f  0.38)
0.004
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4mm
D( f  0.4)
0.006
0.008
0.01
70
80
90
100
110
f
Frequency, GHz
Transmission Sensitivity
0.01
dt / drs”
DD( f  0.3)
High permittivity lossy sample
0.005
DD( f  0.32)
DD( f  0.34)
0
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4mm
DD( f  0.36)
DD( f  0.38) 0.005
DD( f  0.4)
0.01
0.015
70
80
90
100
110
f
Frequency, GHz
Fig.4 Sensitivity of a transmission coefficient as a function of frequency for different thickness
of container layer tc ( rs = 20, rs = 2 )
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Reflection Sensitivity
0.02
dr / drs’
0.01
D1( f  0.3)
D1( f  0.32)
D1( f  0.34)
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4mm
0
D1( f  0.36)
D1( f  0.38) 0.01
D1( f  0.4)
0.02
High permittivity lossy sample
0.03
70
80
90
100
110
f
Frequency, GHz
Reflection Sensitivity
0.025
dr /
0.3mm
0.32mm
0.34mm
0.36mm
0.38mm
0.4mm
drs”
0.02
D2( f  0.3)
D2( f  0.32)
High permittivity lossy sample
D2( f  0.34)0.015
D2( f  0.36)
D2( f  0.38)
0.01
D2( f  0.4)
0.005
0
70
80
90
100
110
f
Frequency, GHz
Fig.5 Sensitivity of a reflection coefficient as a function of frequency for different thickness of
container layer tc ( rs = 20, rs = 2 )
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Differential Return Loss, dB
Experiment Data
1,5
1
0,5
0
-0,5
95
100
105
-1
110
Emulsion
P-34
-1,5
Freuency, GHz
P-44
Fig. 6 Experimental results with different water-content oil emulsions
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